diff --git a/doc/_static/css/theme.css b/doc/_static/css/theme.css
index 909adec4e..691982f99 100644
--- a/doc/_static/css/theme.css
+++ b/doc/_static/css/theme.css
@@ -1,5096 +1,5096 @@
 @charset "UTF-8";
 * {
   -webkit-box-sizing: border-box;
   -moz-box-sizing: border-box;
   box-sizing: border-box;
 }
 
 article, aside, details, figcaption, figure, footer, header, hgroup, nav, section {
   display: block;
 }
 
 audio, canvas, video {
   display: inline-block;
   *display: inline;
   *zoom: 1;
 }
 
 audio:not([controls]) {
   display: none;
 }
 
 [hidden] {
   display: none;
 }
 
 * {
   -webkit-box-sizing: border-box;
   -moz-box-sizing: border-box;
   box-sizing: border-box;
 }
 
 html {
   font-size: 100%;
   -webkit-text-size-adjust: 100%;
   -ms-text-size-adjust: 100%;
 }
 
 body {
   margin: 0;
 }
 
 a:hover, a:active {
   outline: 0;
 }
 
 abbr[title] {
   border-bottom: 1px dotted;
 }
 
 b, strong {
   font-weight: bold;
 }
 
 blockquote {
   margin: 0;
 }
 
 dfn {
   font-style: italic;
 }
 
 ins {
   background: #ff9;
   color: #000;
   text-decoration: none;
 }
 
 mark {
   background: #ff0;
   color: #000;
   font-style: italic;
   font-weight: bold;
 }
 
 pre, code, .rst-content tt, .rst-content code, kbd, samp {
   font-family: monospace, serif;
   _font-family: "courier new", monospace;
   font-size: 1em;
 }
 
 pre {
   white-space: pre;
 }
 
 q {
   quotes: none;
 }
 
 q:before, q:after {
   content: "";
   content: none;
 }
 
 small {
   font-size: 85%;
 }
 
 sub, sup {
   font-size: 75%;
   line-height: 0;
   position: relative;
   vertical-align: baseline;
 }
 
 sup {
   top: -0.5em;
 }
 
 sub {
   bottom: -0.25em;
 }
 
 ul, ol, dl {
   margin: 0;
   padding: 0;
   list-style: none;
   list-style-image: none;
 }
 
 li {
   list-style: none;
 }
 
 dd {
   margin: 0;
 }
 
 img {
   border: 0;
   -ms-interpolation-mode: bicubic;
   vertical-align: middle;
   max-width: 100%;
 }
 
 svg:not(:root) {
   overflow: hidden;
 }
 
 figure {
   margin: 0;
 }
 
 form {
   margin: 0;
 }
 
 fieldset {
   border: 0;
   margin: 0;
   padding: 0;
 }
 
 label {
   cursor: pointer;
 }
 
 legend {
   border: 0;
   *margin-left: -7px;
   padding: 0;
   white-space: normal;
 }
 
 button, input, select, textarea {
   font-size: 100%;
   margin: 0;
   vertical-align: baseline;
   *vertical-align: middle;
 }
 
 button, input {
   line-height: normal;
 }
 
 button, input[type="button"], input[type="reset"], input[type="submit"] {
   cursor: pointer;
   -webkit-appearance: button;
   *overflow: visible;
 }
 
 button[disabled], input[disabled] {
   cursor: default;
 }
 
 input[type="checkbox"], input[type="radio"] {
   box-sizing: border-box;
   padding: 0;
   *width: 13px;
   *height: 13px;
 }
 
 input[type="search"] {
   -webkit-appearance: textfield;
   -moz-box-sizing: content-box;
   -webkit-box-sizing: content-box;
   box-sizing: content-box;
 }
 
 input[type="search"]::-webkit-search-decoration, input[type="search"]::-webkit-search-cancel-button {
   -webkit-appearance: none;
 }
 
 button::-moz-focus-inner, input::-moz-focus-inner {
   border: 0;
   padding: 0;
 }
 
 textarea {
   overflow: auto;
   vertical-align: top;
   resize: vertical;
 }
 
 table {
   border-collapse: collapse;
   border-spacing: 0;
 }
 
 td {
   vertical-align: top;
 }
 
 .chromeframe {
   margin: 0.2em 0;
   background: #ccc;
   color: black;
   padding: 0.2em 0;
 }
 
 .ir {
   display: block;
   border: 0;
   text-indent: -999em;
   overflow: hidden;
   background-color: transparent;
   background-repeat: no-repeat;
   text-align: left;
   direction: ltr;
   *line-height: 0;
 }
 
 .ir br {
   display: none;
 }
 
 .hidden {
   display: none !important;
   visibility: hidden;
 }
 
 .visuallyhidden {
   border: 0;
   clip: rect(0 0 0 0);
   height: 1px;
   margin: -1px;
   overflow: hidden;
   padding: 0;
   position: absolute;
   width: 1px;
 }
 
 .visuallyhidden.focusable:active, .visuallyhidden.focusable:focus {
   clip: auto;
   height: auto;
   margin: 0;
   overflow: visible;
   position: static;
   width: auto;
 }
 
 .invisible {
   visibility: hidden;
 }
 
 .relative {
   position: relative;
 }
 
 big, small {
   font-size: 100%;
 }
 
 @media print {
   html, body, section {
     background: none !important;
   }
 
   * {
     box-shadow: none !important;
     text-shadow: none !important;
     filter: none !important;
     -ms-filter: none !important;
   }
 
   a, a:visited {
     text-decoration: underline;
   }
 
   .ir a:after, a[href^="javascript:"]:after, a[href^="#"]:after {
     content: "";
   }
 
   pre, blockquote {
     page-break-inside: avoid;
   }
 
   thead {
     display: table-header-group;
   }
 
   tr, img {
     page-break-inside: avoid;
   }
 
   img {
     max-width: 100% !important;
   }
 
   @page {
     margin: 0.5cm;
   }
   p, h2, .rst-content .toctree-wrapper p.caption, h3 {
     orphans: 3;
     widows: 3;
   }
 
   h2, .rst-content .toctree-wrapper p.caption, h3 {
     page-break-after: avoid;
   }
 }
 .fa:before, .wy-menu-vertical li span.toctree-expand:before, .wy-menu-vertical li.on a span.toctree-expand:before, .wy-menu-vertical li.current > a span.toctree-expand:before, .rst-content .admonition-title:before, .rst-content h1 .headerlink:before, .rst-content h2 .headerlink:before, .rst-content h3 .headerlink:before, .rst-content h4 .headerlink:before, .rst-content h5 .headerlink:before, .rst-content h6 .headerlink:before, .rst-content dl dt .headerlink:before, .rst-content p.caption .headerlink:before, .rst-content tt.download span:first-child:before, .rst-content code.download span:first-child:before, .icon:before, .wy-dropdown .caret:before, .wy-inline-validate.wy-inline-validate-success .wy-input-context:before, .wy-inline-validate.wy-inline-validate-danger .wy-input-context:before, .wy-inline-validate.wy-inline-validate-warning .wy-input-context:before, .wy-inline-validate.wy-inline-validate-info .wy-input-context:before, .wy-alert, .rst-content .note, .rst-content .attention, .rst-content .caution, .rst-content .danger, .rst-content .error, .rst-content .hint, .rst-content .important, .rst-content .tip, .rst-content .warning, .rst-content .seealso, .rst-content .admonition-todo, .btn, input[type="text"], input[type="password"], input[type="email"], input[type="url"], input[type="date"], input[type="month"], input[type="time"], input[type="datetime"], input[type="datetime-local"], input[type="week"], input[type="number"], input[type="search"], input[type="tel"], input[type="color"], select, textarea, .wy-menu-vertical li.on a, .wy-menu-vertical li.current > a, .wy-side-nav-search > a, .wy-side-nav-search .wy-dropdown > a, .wy-nav-top a {
   -webkit-font-smoothing: antialiased;
 }
 
 .clearfix {
   *zoom: 1;
 }
 .clearfix:before, .clearfix:after {
   display: table;
   content: "";
 }
 .clearfix:after {
   clear: both;
 }
 
 /*!
  *  Font Awesome 4.2.0 by @davegandy - http://fontawesome.io - @fontawesome
  *  License - http://fontawesome.io/license (Font: SIL OFL 1.1, CSS: MIT License)
  */
 /* FONT PATH
  * -------------------------- */
 @font-face {
   font-family: 'FontAwesome';
   src: url("../fonts/fontawesome-webfont.eot?v=4.2.0");
   src: url("../fonts/fontawesome-webfont.eot?#iefix&v=4.2.0") format("embedded-opentype"), url("../fonts/fontawesome-webfont.woff?v=4.2.0") format("woff"), url("../fonts/fontawesome-webfont.ttf?v=4.2.0") format("truetype"), url("../fonts/fontawesome-webfont.svg?v=4.2.0#fontawesomeregular") format("svg");
   font-weight: normal;
   font-style: normal;
 }
 .fa, .wy-menu-vertical li span.toctree-expand, .wy-menu-vertical li.on a span.toctree-expand, .wy-menu-vertical li.current > a span.toctree-expand, .rst-content .admonition-title, .rst-content h1 .headerlink, .rst-content h2 .headerlink, .rst-content h3 .headerlink, .rst-content h4 .headerlink, .rst-content h5 .headerlink, .rst-content h6 .headerlink, .rst-content dl dt .headerlink, .rst-content p.caption .headerlink, .rst-content tt.download span:first-child, .rst-content code.download span:first-child, .icon {
   display: inline-block;
   font: normal normal normal 14px/1 FontAwesome;
   font-size: inherit;
   text-rendering: auto;
   -webkit-font-smoothing: antialiased;
   -moz-osx-font-smoothing: grayscale;
 }
 
 /* makes the font 33% larger relative to the icon container */
 .fa-lg {
   font-size: 1.33333em;
   line-height: 0.75em;
   vertical-align: -15%;
 }
 
 .fa-2x {
   font-size: 2em;
 }
 
 .fa-3x {
   font-size: 3em;
 }
 
 .fa-4x {
   font-size: 4em;
 }
 
 .fa-5x {
   font-size: 5em;
 }
 
 .fa-fw {
   width: 1.28571em;
   text-align: center;
 }
 
 .fa-ul {
   padding-left: 0;
   margin-left: 2.14286em;
   list-style-type: none;
 }
 .fa-ul > li {
   position: relative;
 }
 
 .fa-li {
   position: absolute;
   left: -2.14286em;
   width: 2.14286em;
   top: 0.14286em;
   text-align: center;
 }
 .fa-li.fa-lg {
   left: -1.85714em;
 }
 
 .fa-border {
   padding: .2em .25em .15em;
   border: solid 0.08em #eee;
   border-radius: .1em;
 }
 
 .pull-right {
   float: right;
 }
 
 .pull-left {
   float: left;
 }
 
 .fa.pull-left, .wy-menu-vertical li span.pull-left.toctree-expand, .wy-menu-vertical li.on a span.pull-left.toctree-expand, .wy-menu-vertical li.current > a span.pull-left.toctree-expand, .rst-content .pull-left.admonition-title, .rst-content h1 .pull-left.headerlink, .rst-content h2 .pull-left.headerlink, .rst-content h3 .pull-left.headerlink, .rst-content h4 .pull-left.headerlink, .rst-content h5 .pull-left.headerlink, .rst-content h6 .pull-left.headerlink, .rst-content dl dt .pull-left.headerlink, .rst-content p.caption .pull-left.headerlink, .rst-content tt.download span.pull-left:first-child, .rst-content code.download span.pull-left:first-child, .pull-left.icon {
   margin-right: .3em;
 }
 .fa.pull-right, .wy-menu-vertical li span.pull-right.toctree-expand, .wy-menu-vertical li.on a span.pull-right.toctree-expand, .wy-menu-vertical li.current > a span.pull-right.toctree-expand, .rst-content .pull-right.admonition-title, .rst-content h1 .pull-right.headerlink, .rst-content h2 .pull-right.headerlink, .rst-content h3 .pull-right.headerlink, .rst-content h4 .pull-right.headerlink, .rst-content h5 .pull-right.headerlink, .rst-content h6 .pull-right.headerlink, .rst-content dl dt .pull-right.headerlink, .rst-content p.caption .pull-right.headerlink, .rst-content tt.download span.pull-right:first-child, .rst-content code.download span.pull-right:first-child, .pull-right.icon {
   margin-left: .3em;
 }
 
 .fa-spin {
   -webkit-animation: fa-spin 2s infinite linear;
   animation: fa-spin 2s infinite linear;
 }
 
 @-webkit-keyframes fa-spin {
   0% {
     -webkit-transform: rotate(0deg);
     transform: rotate(0deg);
   }
   100% {
     -webkit-transform: rotate(359deg);
     transform: rotate(359deg);
   }
 }
 @keyframes fa-spin {
   0% {
     -webkit-transform: rotate(0deg);
     transform: rotate(0deg);
   }
   100% {
     -webkit-transform: rotate(359deg);
     transform: rotate(359deg);
   }
 }
 .fa-rotate-90 {
   filter: progid:DXImageTransform.Microsoft.BasicImage(rotation=1);
   -webkit-transform: rotate(90deg);
   -ms-transform: rotate(90deg);
   transform: rotate(90deg);
 }
 
 .fa-rotate-180 {
   filter: progid:DXImageTransform.Microsoft.BasicImage(rotation=2);
   -webkit-transform: rotate(180deg);
   -ms-transform: rotate(180deg);
   transform: rotate(180deg);
 }
 
 .fa-rotate-270 {
   filter: progid:DXImageTransform.Microsoft.BasicImage(rotation=3);
   -webkit-transform: rotate(270deg);
   -ms-transform: rotate(270deg);
   transform: rotate(270deg);
 }
 
 .fa-flip-horizontal {
   filter: progid:DXImageTransform.Microsoft.BasicImage(rotation=0);
   -webkit-transform: scale(-1, 1);
   -ms-transform: scale(-1, 1);
   transform: scale(-1, 1);
 }
 
 .fa-flip-vertical {
   filter: progid:DXImageTransform.Microsoft.BasicImage(rotation=2);
   -webkit-transform: scale(1, -1);
   -ms-transform: scale(1, -1);
   transform: scale(1, -1);
 }
 
 :root .fa-rotate-90,
 :root .fa-rotate-180,
 :root .fa-rotate-270,
 :root .fa-flip-horizontal,
 :root .fa-flip-vertical {
   filter: none;
 }
 
 .fa-stack {
   position: relative;
   display: inline-block;
   width: 2em;
   height: 2em;
   line-height: 2em;
   vertical-align: middle;
 }
 
 .fa-stack-1x, .fa-stack-2x {
   position: absolute;
   left: 0;
   width: 100%;
   text-align: center;
 }
 
 .fa-stack-1x {
   line-height: inherit;
 }
 
 .fa-stack-2x {
   font-size: 2em;
 }
 
 .fa-inverse {
   color: #fff;
 }
 
 /* Font Awesome uses the Unicode Private Use Area (PUA) to ensure screen
    readers do not read off random characters that represent icons */
 .fa-glass:before {
   content: "";
 }
 
 .fa-music:before {
   content: "";
 }
 
 .fa-search:before, .icon-search:before {
   content: "";
 }
 
 .fa-envelope-o:before {
   content: "";
 }
 
 .fa-heart:before {
   content: "";
 }
 
 .fa-star:before {
   content: "";
 }
 
 .fa-star-o:before {
   content: "";
 }
 
 .fa-user:before {
   content: "";
 }
 
 .fa-film:before {
   content: "";
 }
 
 .fa-th-large:before {
   content: "";
 }
 
 .fa-th:before {
   content: "";
 }
 
 .fa-th-list:before {
   content: "";
 }
 
 .fa-check:before {
   content: "";
 }
 
 .fa-remove:before,
 .fa-close:before,
 .fa-times:before {
   content: "";
 }
 
 .fa-search-plus:before {
   content: "";
 }
 
 .fa-search-minus:before {
   content: "";
 }
 
 .fa-power-off:before {
   content: "";
 }
 
 .fa-signal:before {
   content: "";
 }
 
 .fa-gear:before,
 .fa-cog:before {
   content: "";
 }
 
 .fa-trash-o:before {
   content: "";
 }
 
 .fa-home:before, .icon-home:before {
   content: "";
 }
 
 .fa-file-o:before {
   content: "";
 }
 
 .fa-clock-o:before {
   content: "";
 }
 
 .fa-road:before {
   content: "";
 }
 
 .fa-download:before, .rst-content tt.download span:first-child:before, .rst-content code.download span:first-child:before {
   content: "";
 }
 
 .fa-arrow-circle-o-down:before {
   content: "";
 }
 
 .fa-arrow-circle-o-up:before {
   content: "";
 }
 
 .fa-inbox:before {
   content: "";
 }
 
 .fa-play-circle-o:before {
   content: "";
 }
 
 .fa-rotate-right:before,
 .fa-repeat:before {
   content: "";
 }
 
 .fa-refresh:before {
   content: "";
 }
 
 .fa-list-alt:before {
   content: "";
 }
 
 .fa-lock:before {
   content: "";
 }
 
 .fa-flag:before {
   content: "";
 }
 
 .fa-headphones:before {
   content: "";
 }
 
 .fa-volume-off:before {
   content: "";
 }
 
 .fa-volume-down:before {
   content: "";
 }
 
 .fa-volume-up:before {
   content: "";
 }
 
 .fa-qrcode:before {
   content: "";
 }
 
 .fa-barcode:before {
   content: "";
 }
 
 .fa-tag:before {
   content: "";
 }
 
 .fa-tags:before {
   content: "";
 }
 
 .fa-book:before, .icon-book:before {
   content: "";
 }
 
 .fa-bookmark:before {
   content: "";
 }
 
 .fa-print:before {
   content: "";
 }
 
 .fa-camera:before {
   content: "";
 }
 
 .fa-font:before {
   content: "";
 }
 
 .fa-bold:before {
   content: "";
 }
 
 .fa-italic:before {
   content: "";
 }
 
 .fa-text-height:before {
   content: "";
 }
 
 .fa-text-width:before {
   content: "";
 }
 
 .fa-align-left:before {
   content: "";
 }
 
 .fa-align-center:before {
   content: "";
 }
 
 .fa-align-right:before {
   content: "";
 }
 
 .fa-align-justify:before {
   content: "";
 }
 
 .fa-list:before {
   content: "";
 }
 
 .fa-dedent:before,
 .fa-outdent:before {
   content: "";
 }
 
 .fa-indent:before {
   content: "";
 }
 
 .fa-video-camera:before {
   content: "";
 }
 
 .fa-photo:before,
 .fa-image:before,
 .fa-picture-o:before {
   content: "";
 }
 
 .fa-pencil:before {
   content: "";
 }
 
 .fa-map-marker:before {
   content: "";
 }
 
 .fa-adjust:before {
   content: "";
 }
 
 .fa-tint:before {
   content: "";
 }
 
 .fa-edit:before,
 .fa-pencil-square-o:before {
   content: "";
 }
 
 .fa-share-square-o:before {
   content: "";
 }
 
 .fa-check-square-o:before {
   content: "";
 }
 
 .fa-arrows:before {
   content: "";
 }
 
 .fa-step-backward:before {
   content: "";
 }
 
 .fa-fast-backward:before {
   content: "";
 }
 
 .fa-backward:before {
   content: "";
 }
 
 .fa-play:before {
   content: "";
 }
 
 .fa-pause:before {
   content: "";
 }
 
 .fa-stop:before {
   content: "";
 }
 
 .fa-forward:before {
   content: "";
 }
 
 .fa-fast-forward:before {
   content: "";
 }
 
 .fa-step-forward:before {
   content: "";
 }
 
 .fa-eject:before {
   content: "";
 }
 
 .fa-chevron-left:before {
   content: "";
 }
 
 .fa-chevron-right:before {
   content: "";
 }
 
 .fa-plus-circle:before {
   content: "";
 }
 
 .fa-minus-circle:before {
   content: "";
 }
 
 .fa-times-circle:before, .wy-inline-validate.wy-inline-validate-danger .wy-input-context:before {
   content: "";
 }
 
 .fa-check-circle:before, .wy-inline-validate.wy-inline-validate-success .wy-input-context:before {
   content: "";
 }
 
 .fa-question-circle:before {
   content: "";
 }
 
 .fa-info-circle:before {
   content: "";
 }
 
 .fa-crosshairs:before {
   content: "";
 }
 
 .fa-times-circle-o:before {
   content: "";
 }
 
 .fa-check-circle-o:before {
   content: "";
 }
 
 .fa-ban:before {
   content: "";
 }
 
 .fa-arrow-left:before {
   content: "";
 }
 
 .fa-arrow-right:before {
   content: "";
 }
 
 .fa-arrow-up:before {
   content: "";
 }
 
 .fa-arrow-down:before {
   content: "";
 }
 
 .fa-mail-forward:before,
 .fa-share:before {
   content: "";
 }
 
 .fa-expand:before {
   content: "";
 }
 
 .fa-compress:before {
   content: "";
 }
 
 .fa-plus:before {
   content: "";
 }
 
 .fa-minus:before {
   content: "";
 }
 
 .fa-asterisk:before {
   content: "";
 }
 
 .fa-exclamation-circle:before, .wy-inline-validate.wy-inline-validate-warning .wy-input-context:before, .wy-inline-validate.wy-inline-validate-info .wy-input-context:before, .rst-content .admonition-title:before {
   content: "";
 }
 
 .fa-gift:before {
   content: "";
 }
 
 .fa-leaf:before {
   content: "";
 }
 
 .fa-fire:before, .icon-fire:before {
   content: "";
 }
 
 .fa-eye:before {
   content: "";
 }
 
 .fa-eye-slash:before {
   content: "";
 }
 
 .fa-warning:before,
 .fa-exclamation-triangle:before {
   content: "";
 }
 
 .fa-plane:before {
   content: "";
 }
 
 .fa-calendar:before {
   content: "";
 }
 
 .fa-random:before {
   content: "";
 }
 
 .fa-comment:before {
   content: "";
 }
 
 .fa-magnet:before {
   content: "";
 }
 
 .fa-chevron-up:before {
   content: "";
 }
 
 .fa-chevron-down:before {
   content: "";
 }
 
 .fa-retweet:before {
   content: "";
 }
 
 .fa-shopping-cart:before {
   content: "";
 }
 
 .fa-folder:before {
   content: "";
 }
 
 .fa-folder-open:before {
   content: "";
 }
 
 .fa-arrows-v:before {
   content: "";
 }
 
 .fa-arrows-h:before {
   content: "";
 }
 
 .fa-bar-chart-o:before,
 .fa-bar-chart:before {
   content: "";
 }
 
 .fa-twitter-square:before {
   content: "";
 }
 
 .fa-facebook-square:before {
   content: "";
 }
 
 .fa-camera-retro:before {
   content: "";
 }
 
 .fa-key:before {
   content: "";
 }
 
 .fa-gears:before,
 .fa-cogs:before {
   content: "";
 }
 
 .fa-comments:before {
   content: "";
 }
 
 .fa-thumbs-o-up:before {
   content: "";
 }
 
 .fa-thumbs-o-down:before {
   content: "";
 }
 
 .fa-star-half:before {
   content: "";
 }
 
 .fa-heart-o:before {
   content: "";
 }
 
 .fa-sign-out:before {
   content: "";
 }
 
 .fa-linkedin-square:before {
   content: "";
 }
 
 .fa-thumb-tack:before {
   content: "";
 }
 
 .fa-external-link:before {
   content: "";
 }
 
 .fa-sign-in:before {
   content: "";
 }
 
 .fa-trophy:before {
   content: "";
 }
 
 .fa-github-square:before {
   content: "";
 }
 
 .fa-upload:before {
   content: "";
 }
 
 .fa-lemon-o:before {
   content: "";
 }
 
 .fa-phone:before {
   content: "";
 }
 
 .fa-square-o:before {
   content: "";
 }
 
 .fa-bookmark-o:before {
   content: "";
 }
 
 .fa-phone-square:before {
   content: "";
 }
 
 .fa-twitter:before {
   content: "";
 }
 
 .fa-facebook:before {
   content: "";
 }
 
 .fa-github:before, .icon-github:before {
   content: "";
 }
 
 .fa-unlock:before {
   content: "";
 }
 
 .fa-credit-card:before {
   content: "";
 }
 
 .fa-rss:before {
   content: "";
 }
 
 .fa-hdd-o:before {
   content: "";
 }
 
 .fa-bullhorn:before {
   content: "";
 }
 
 .fa-bell:before {
   content: "";
 }
 
 .fa-certificate:before {
   content: "";
 }
 
 .fa-hand-o-right:before {
   content: "";
 }
 
 .fa-hand-o-left:before {
   content: "";
 }
 
 .fa-hand-o-up:before {
   content: "";
 }
 
 .fa-hand-o-down:before {
   content: "";
 }
 
 .fa-arrow-circle-left:before, .icon-circle-arrow-left:before {
   content: "";
 }
 
 .fa-arrow-circle-right:before, .icon-circle-arrow-right:before {
   content: "";
 }
 
 .fa-arrow-circle-up:before {
   content: "";
 }
 
 .fa-arrow-circle-down:before {
   content: "";
 }
 
 .fa-globe:before {
   content: "";
 }
 
 .fa-wrench:before {
   content: "";
 }
 
 .fa-tasks:before {
   content: "";
 }
 
 .fa-filter:before {
   content: "";
 }
 
 .fa-briefcase:before {
   content: "";
 }
 
 .fa-arrows-alt:before {
   content: "";
 }
 
 .fa-group:before,
 .fa-users:before {
   content: "";
 }
 
 .fa-chain:before,
 .fa-link:before,
 .icon-link:before {
   content: "";
 }
 
 .fa-cloud:before {
   content: "";
 }
 
 .fa-flask:before {
   content: "";
 }
 
 .fa-cut:before,
 .fa-scissors:before {
   content: "";
 }
 
 .fa-copy:before,
 .fa-files-o:before {
   content: "";
 }
 
 .fa-paperclip:before {
   content: "";
 }
 
 .fa-save:before,
 .fa-floppy-o:before {
   content: "";
 }
 
 .fa-square:before {
   content: "";
 }
 
 .fa-navicon:before,
 .fa-reorder:before,
 .fa-bars:before {
   content: "";
 }
 
 .fa-list-ul:before {
   content: "";
 }
 
 .fa-list-ol:before {
   content: "";
 }
 
 .fa-strikethrough:before {
   content: "";
 }
 
 .fa-underline:before {
   content: "";
 }
 
 .fa-table:before {
   content: "";
 }
 
 .fa-magic:before {
   content: "";
 }
 
 .fa-truck:before {
   content: "";
 }
 
 .fa-pinterest:before {
   content: "";
 }
 
 .fa-pinterest-square:before {
   content: "";
 }
 
 .fa-google-plus-square:before {
   content: "";
 }
 
 .fa-google-plus:before {
   content: "";
 }
 
 .fa-money:before {
   content: "";
 }
 
 .fa-caret-down:before, .wy-dropdown .caret:before, .icon-caret-down:before {
   content: "";
 }
 
 .fa-caret-up:before {
   content: "";
 }
 
 .fa-caret-left:before {
   content: "";
 }
 
 .fa-caret-right:before {
   content: "";
 }
 
 .fa-columns:before {
   content: "";
 }
 
 .fa-unsorted:before,
 .fa-sort:before {
   content: "";
 }
 
 .fa-sort-down:before,
 .fa-sort-desc:before {
   content: "";
 }
 
 .fa-sort-up:before,
 .fa-sort-asc:before {
   content: "";
 }
 
 .fa-envelope:before {
   content: "";
 }
 
 .fa-linkedin:before {
   content: "";
 }
 
 .fa-rotate-left:before,
 .fa-undo:before {
   content: "";
 }
 
 .fa-legal:before,
 .fa-gavel:before {
   content: "";
 }
 
 .fa-dashboard:before,
 .fa-tachometer:before {
   content: "";
 }
 
 .fa-comment-o:before {
   content: "";
 }
 
 .fa-comments-o:before {
   content: "";
 }
 
 .fa-flash:before,
 .fa-bolt:before {
   content: "";
 }
 
 .fa-sitemap:before {
   content: "";
 }
 
 .fa-umbrella:before {
   content: "";
 }
 
 .fa-paste:before,
 .fa-clipboard:before {
   content: "";
 }
 
 .fa-lightbulb-o:before {
   content: "";
 }
 
 .fa-exchange:before {
   content: "";
 }
 
 .fa-cloud-download:before {
   content: "";
 }
 
 .fa-cloud-upload:before {
   content: "";
 }
 
 .fa-user-md:before {
   content: "";
 }
 
 .fa-stethoscope:before {
   content: "";
 }
 
 .fa-suitcase:before {
   content: "";
 }
 
 .fa-bell-o:before {
   content: "";
 }
 
 .fa-coffee:before {
   content: "";
 }
 
 .fa-cutlery:before {
   content: "";
 }
 
 .fa-file-text-o:before {
   content: "";
 }
 
 .fa-building-o:before {
   content: "";
 }
 
 .fa-hospital-o:before {
   content: "";
 }
 
 .fa-ambulance:before {
   content: "";
 }
 
 .fa-medkit:before {
   content: "";
 }
 
 .fa-fighter-jet:before {
   content: "";
 }
 
 .fa-beer:before {
   content: "";
 }
 
 .fa-h-square:before {
   content: "";
 }
 
 .fa-plus-square:before {
   content: "";
 }
 
 .fa-angle-double-left:before {
   content: "";
 }
 
 .fa-angle-double-right:before {
   content: "";
 }
 
 .fa-angle-double-up:before {
   content: "";
 }
 
 .fa-angle-double-down:before {
   content: "";
 }
 
 .fa-angle-left:before {
   content: "";
 }
 
 .fa-angle-right:before {
   content: "";
 }
 
 .fa-angle-up:before {
   content: "";
 }
 
 .fa-angle-down:before {
   content: "";
 }
 
 .fa-desktop:before {
   content: "";
 }
 
 .fa-laptop:before {
   content: "";
 }
 
 .fa-tablet:before {
   content: "";
 }
 
 .fa-mobile-phone:before,
 .fa-mobile:before {
   content: "";
 }
 
 .fa-circle-o:before {
   content: "";
 }
 
 .fa-quote-left:before {
   content: "";
 }
 
 .fa-quote-right:before {
   content: "";
 }
 
 .fa-spinner:before {
   content: "";
 }
 
 .fa-circle:before {
   content: "";
 }
 
 .fa-mail-reply:before,
 .fa-reply:before {
   content: "";
 }
 
 .fa-github-alt:before {
   content: "";
 }
 
 .fa-folder-o:before {
   content: "";
 }
 
 .fa-folder-open-o:before {
   content: "";
 }
 
 .fa-smile-o:before {
   content: "";
 }
 
 .fa-frown-o:before {
   content: "";
 }
 
 .fa-meh-o:before {
   content: "";
 }
 
 .fa-gamepad:before {
   content: "";
 }
 
 .fa-keyboard-o:before {
   content: "";
 }
 
 .fa-flag-o:before {
   content: "";
 }
 
 .fa-flag-checkered:before {
   content: "";
 }
 
 .fa-terminal:before {
   content: "";
 }
 
 .fa-code:before {
   content: "";
 }
 
 .fa-mail-reply-all:before,
 .fa-reply-all:before {
   content: "";
 }
 
 .fa-star-half-empty:before,
 .fa-star-half-full:before,
 .fa-star-half-o:before {
   content: "";
 }
 
 .fa-location-arrow:before {
   content: "";
 }
 
 .fa-crop:before {
   content: "";
 }
 
 .fa-code-fork:before {
   content: "";
 }
 
 .fa-unlink:before,
 .fa-chain-broken:before {
   content: "";
 }
 
 .fa-question:before {
   content: "";
 }
 
 .fa-info:before {
   content: "";
 }
 
 .fa-exclamation:before {
   content: "";
 }
 
 .fa-superscript:before {
   content: "";
 }
 
 .fa-subscript:before {
   content: "";
 }
 
 .fa-eraser:before {
   content: "";
 }
 
 .fa-puzzle-piece:before {
   content: "";
 }
 
 .fa-microphone:before {
   content: "";
 }
 
 .fa-microphone-slash:before {
   content: "";
 }
 
 .fa-shield:before {
   content: "";
 }
 
 .fa-calendar-o:before {
   content: "";
 }
 
 .fa-fire-extinguisher:before {
   content: "";
 }
 
 .fa-rocket:before {
   content: "";
 }
 
 .fa-maxcdn:before {
   content: "";
 }
 
 .fa-chevron-circle-left:before {
   content: "";
 }
 
 .fa-chevron-circle-right:before {
   content: "";
 }
 
 .fa-chevron-circle-up:before {
   content: "";
 }
 
 .fa-chevron-circle-down:before {
   content: "";
 }
 
 .fa-html5:before {
   content: "";
 }
 
 .fa-css3:before {
   content: "";
 }
 
 .fa-anchor:before {
   content: "";
 }
 
 .fa-unlock-alt:before {
   content: "";
 }
 
 .fa-bullseye:before {
   content: "";
 }
 
 .fa-ellipsis-h:before {
   content: "";
 }
 
 .fa-ellipsis-v:before {
   content: "";
 }
 
 .fa-rss-square:before {
   content: "";
 }
 
 .fa-play-circle:before {
   content: "";
 }
 
 .fa-ticket:before {
   content: "";
 }
 
 .fa-minus-square:before {
   content: "";
 }
 
 .fa-minus-square-o:before, .wy-menu-vertical li.on a span.toctree-expand:before, .wy-menu-vertical li.current > a span.toctree-expand:before {
   content: "";
 }
 
 .fa-level-up:before {
   content: "";
 }
 
 .fa-level-down:before {
   content: "";
 }
 
 .fa-check-square:before {
   content: "";
 }
 
 .fa-pencil-square:before {
   content: "";
 }
 
 .fa-external-link-square:before {
   content: "";
 }
 
 .fa-share-square:before {
   content: "";
 }
 
 .fa-compass:before {
   content: "";
 }
 
 .fa-toggle-down:before,
 .fa-caret-square-o-down:before {
   content: "";
 }
 
 .fa-toggle-up:before,
 .fa-caret-square-o-up:before {
   content: "";
 }
 
 .fa-toggle-right:before,
 .fa-caret-square-o-right:before {
   content: "";
 }
 
 .fa-euro:before,
 .fa-eur:before {
   content: "";
 }
 
 .fa-gbp:before {
   content: "";
 }
 
 .fa-dollar:before,
 .fa-usd:before {
   content: "";
 }
 
 .fa-rupee:before,
 .fa-inr:before {
   content: "";
 }
 
 .fa-cny:before,
 .fa-rmb:before,
 .fa-yen:before,
 .fa-jpy:before {
   content: "";
 }
 
 .fa-ruble:before,
 .fa-rouble:before,
 .fa-rub:before {
   content: "";
 }
 
 .fa-won:before,
 .fa-krw:before {
   content: "";
 }
 
 .fa-bitcoin:before,
 .fa-btc:before {
   content: "";
 }
 
 .fa-file:before {
   content: "";
 }
 
 .fa-file-text:before {
   content: "";
 }
 
 .fa-sort-alpha-asc:before {
   content: "";
 }
 
 .fa-sort-alpha-desc:before {
   content: "";
 }
 
 .fa-sort-amount-asc:before {
   content: "";
 }
 
 .fa-sort-amount-desc:before {
   content: "";
 }
 
 .fa-sort-numeric-asc:before {
   content: "";
 }
 
 .fa-sort-numeric-desc:before {
   content: "";
 }
 
 .fa-thumbs-up:before {
   content: "";
 }
 
 .fa-thumbs-down:before {
   content: "";
 }
 
 .fa-youtube-square:before {
   content: "";
 }
 
 .fa-youtube:before {
   content: "";
 }
 
 .fa-xing:before {
   content: "";
 }
 
 .fa-xing-square:before {
   content: "";
 }
 
 .fa-youtube-play:before {
   content: "";
 }
 
 .fa-dropbox:before {
   content: "";
 }
 
 .fa-stack-overflow:before {
   content: "";
 }
 
 .fa-instagram:before {
   content: "";
 }
 
 .fa-flickr:before {
   content: "";
 }
 
 .fa-adn:before {
   content: "";
 }
 
 .fa-bitbucket:before, .icon-bitbucket:before {
   content: "";
 }
 
 .fa-bitbucket-square:before {
   content: "";
 }
 
 .fa-tumblr:before {
   content: "";
 }
 
 .fa-tumblr-square:before {
   content: "";
 }
 
 .fa-long-arrow-down:before {
   content: "";
 }
 
 .fa-long-arrow-up:before {
   content: "";
 }
 
 .fa-long-arrow-left:before {
   content: "";
 }
 
 .fa-long-arrow-right:before {
   content: "";
 }
 
 .fa-apple:before {
   content: "";
 }
 
 .fa-windows:before {
   content: "";
 }
 
 .fa-android:before {
   content: "";
 }
 
 .fa-linux:before {
   content: "";
 }
 
 .fa-dribbble:before {
   content: "";
 }
 
 .fa-skype:before {
   content: "";
 }
 
 .fa-foursquare:before {
   content: "";
 }
 
 .fa-trello:before {
   content: "";
 }
 
 .fa-female:before {
   content: "";
 }
 
 .fa-male:before {
   content: "";
 }
 
 .fa-gittip:before {
   content: "";
 }
 
 .fa-sun-o:before {
   content: "";
 }
 
 .fa-moon-o:before {
   content: "";
 }
 
 .fa-archive:before {
   content: "";
 }
 
 .fa-bug:before {
   content: "";
 }
 
 .fa-vk:before {
   content: "";
 }
 
 .fa-weibo:before {
   content: "";
 }
 
 .fa-renren:before {
   content: "";
 }
 
 .fa-pagelines:before {
   content: "";
 }
 
 .fa-stack-exchange:before {
   content: "";
 }
 
 .fa-arrow-circle-o-right:before {
   content: "";
 }
 
 .fa-arrow-circle-o-left:before {
   content: "";
 }
 
 .fa-toggle-left:before,
 .fa-caret-square-o-left:before {
   content: "";
 }
 
 .fa-dot-circle-o:before {
   content: "";
 }
 
 .fa-wheelchair:before {
   content: "";
 }
 
 .fa-vimeo-square:before {
   content: "";
 }
 
 .fa-turkish-lira:before,
 .fa-try:before {
   content: "";
 }
 
 .fa-plus-square-o:before, .wy-menu-vertical li span.toctree-expand:before {
   content: "";
 }
 
 .fa-space-shuttle:before {
   content: "";
 }
 
 .fa-slack:before {
   content: "";
 }
 
 .fa-envelope-square:before {
   content: "";
 }
 
 .fa-wordpress:before {
   content: "";
 }
 
 .fa-openid:before {
   content: "";
 }
 
 .fa-institution:before,
 .fa-bank:before,
 .fa-university:before {
   content: "";
 }
 
 .fa-mortar-board:before,
 .fa-graduation-cap:before {
   content: "";
 }
 
 .fa-yahoo:before {
   content: "";
 }
 
 .fa-google:before {
   content: "";
 }
 
 .fa-reddit:before {
   content: "";
 }
 
 .fa-reddit-square:before {
   content: "";
 }
 
 .fa-stumbleupon-circle:before {
   content: "";
 }
 
 .fa-stumbleupon:before {
   content: "";
 }
 
 .fa-delicious:before {
   content: "";
 }
 
 .fa-digg:before {
   content: "";
 }
 
 .fa-pied-piper:before {
   content: "";
 }
 
 .fa-pied-piper-alt:before {
   content: "";
 }
 
 .fa-drupal:before {
   content: "";
 }
 
 .fa-joomla:before {
   content: "";
 }
 
 .fa-language:before {
   content: "";
 }
 
 .fa-fax:before {
   content: "";
 }
 
 .fa-building:before {
   content: "";
 }
 
 .fa-child:before {
   content: "";
 }
 
 .fa-paw:before {
   content: "";
 }
 
 .fa-spoon:before {
   content: "";
 }
 
 .fa-cube:before {
   content: "";
 }
 
 .fa-cubes:before {
   content: "";
 }
 
 .fa-behance:before {
   content: "";
 }
 
 .fa-behance-square:before {
   content: "";
 }
 
 .fa-steam:before {
   content: "";
 }
 
 .fa-steam-square:before {
   content: "";
 }
 
 .fa-recycle:before {
   content: "";
 }
 
 .fa-automobile:before,
 .fa-car:before {
   content: "";
 }
 
 .fa-cab:before,
 .fa-taxi:before {
   content: "";
 }
 
 .fa-tree:before {
   content: "";
 }
 
 .fa-spotify:before {
   content: "";
 }
 
 .fa-deviantart:before {
   content: "";
 }
 
 .fa-soundcloud:before {
   content: "";
 }
 
 .fa-database:before {
   content: "";
 }
 
 .fa-file-pdf-o:before {
   content: "";
 }
 
 .fa-file-word-o:before {
   content: "";
 }
 
 .fa-file-excel-o:before {
   content: "";
 }
 
 .fa-file-powerpoint-o:before {
   content: "";
 }
 
 .fa-file-photo-o:before,
 .fa-file-picture-o:before,
 .fa-file-image-o:before {
   content: "";
 }
 
 .fa-file-zip-o:before,
 .fa-file-archive-o:before {
   content: "";
 }
 
 .fa-file-sound-o:before,
 .fa-file-audio-o:before {
   content: "";
 }
 
 .fa-file-movie-o:before,
 .fa-file-video-o:before {
   content: "";
 }
 
 .fa-file-code-o:before {
   content: "";
 }
 
 .fa-vine:before {
   content: "";
 }
 
 .fa-codepen:before {
   content: "";
 }
 
 .fa-jsfiddle:before {
   content: "";
 }
 
 .fa-life-bouy:before,
 .fa-life-buoy:before,
 .fa-life-saver:before,
 .fa-support:before,
 .fa-life-ring:before {
   content: "";
 }
 
 .fa-circle-o-notch:before {
   content: "";
 }
 
 .fa-ra:before,
 .fa-rebel:before {
   content: "";
 }
 
 .fa-ge:before,
 .fa-empire:before {
   content: "";
 }
 
 .fa-git-square:before {
   content: "";
 }
 
 .fa-git:before {
   content: "";
 }
 
 .fa-hacker-news:before {
   content: "";
 }
 
 .fa-tencent-weibo:before {
   content: "";
 }
 
 .fa-qq:before {
   content: "";
 }
 
 .fa-wechat:before,
 .fa-weixin:before {
   content: "";
 }
 
 .fa-send:before,
 .fa-paper-plane:before {
   content: "";
 }
 
 .fa-send-o:before,
 .fa-paper-plane-o:before {
   content: "";
 }
 
 .fa-history:before {
   content: "";
 }
 
 .fa-circle-thin:before {
   content: "";
 }
 
 .fa-header:before {
   content: "";
 }
 
 .fa-paragraph:before {
   content: "";
 }
 
 .fa-sliders:before {
   content: "";
 }
 
 .fa-share-alt:before {
   content: "";
 }
 
 .fa-share-alt-square:before {
   content: "";
 }
 
 .fa-bomb:before {
   content: "";
 }
 
 .fa-soccer-ball-o:before,
 .fa-futbol-o:before {
   content: "";
 }
 
 .fa-tty:before {
   content: "";
 }
 
 .fa-binoculars:before {
   content: "";
 }
 
 .fa-plug:before {
   content: "";
 }
 
 .fa-slideshare:before {
   content: "";
 }
 
 .fa-twitch:before {
   content: "";
 }
 
 .fa-yelp:before {
   content: "";
 }
 
 .fa-newspaper-o:before {
   content: "";
 }
 
 .fa-wifi:before {
   content: "";
 }
 
 .fa-calculator:before {
   content: "";
 }
 
 .fa-paypal:before {
   content: "";
 }
 
 .fa-google-wallet:before {
   content: "";
 }
 
 .fa-cc-visa:before {
   content: "";
 }
 
 .fa-cc-mastercard:before {
   content: "";
 }
 
 .fa-cc-discover:before {
   content: "";
 }
 
 .fa-cc-amex:before {
   content: "";
 }
 
 .fa-cc-paypal:before {
   content: "";
 }
 
 .fa-cc-stripe:before {
   content: "";
 }
 
 .fa-bell-slash:before {
   content: "";
 }
 
 .fa-bell-slash-o:before {
   content: "";
 }
 
 .fa-trash:before {
   content: "";
 }
 
 .fa-copyright:before {
   content: "";
 }
 
 .fa-at:before {
   content: "";
 }
 
 .fa-eyedropper:before {
   content: "";
 }
 
 .fa-paint-brush:before {
   content: "";
 }
 
 .fa-birthday-cake:before {
   content: "";
 }
 
 .fa-area-chart:before {
   content: "";
 }
 
 .fa-pie-chart:before {
   content: "";
 }
 
 .fa-line-chart:before {
   content: "";
 }
 
 .fa-lastfm:before {
   content: "";
 }
 
 .fa-lastfm-square:before {
   content: "";
 }
 
 .fa-toggle-off:before {
   content: "";
 }
 
 .fa-toggle-on:before {
   content: "";
 }
 
 .fa-bicycle:before {
   content: "";
 }
 
 .fa-bus:before {
   content: "";
 }
 
 .fa-ioxhost:before {
   content: "";
 }
 
 .fa-angellist:before {
   content: "";
 }
 
 .fa-cc:before {
   content: "";
 }
 
 .fa-shekel:before,
 .fa-sheqel:before,
 .fa-ils:before {
   content: "";
 }
 
 .fa-meanpath:before {
   content: "";
 }
 
 .fa, .wy-menu-vertical li span.toctree-expand, .wy-menu-vertical li.on a span.toctree-expand, .wy-menu-vertical li.current > a span.toctree-expand, .rst-content .admonition-title, .rst-content h1 .headerlink, .rst-content h2 .headerlink, .rst-content h3 .headerlink, .rst-content h4 .headerlink, .rst-content h5 .headerlink, .rst-content h6 .headerlink, .rst-content dl dt .headerlink, .rst-content p.caption .headerlink, .rst-content tt.download span:first-child, .rst-content code.download span:first-child, .icon, .wy-dropdown .caret, .wy-inline-validate.wy-inline-validate-success .wy-input-context, .wy-inline-validate.wy-inline-validate-danger .wy-input-context, .wy-inline-validate.wy-inline-validate-warning .wy-input-context, .wy-inline-validate.wy-inline-validate-info .wy-input-context {
   font-family: inherit;
 }
 .fa:before, .wy-menu-vertical li span.toctree-expand:before, .wy-menu-vertical li.on a span.toctree-expand:before, .wy-menu-vertical li.current > a span.toctree-expand:before, .rst-content .admonition-title:before, .rst-content h1 .headerlink:before, .rst-content h2 .headerlink:before, .rst-content h3 .headerlink:before, .rst-content h4 .headerlink:before, .rst-content h5 .headerlink:before, .rst-content h6 .headerlink:before, .rst-content dl dt .headerlink:before, .rst-content p.caption .headerlink:before, .rst-content tt.download span:first-child:before, .rst-content code.download span:first-child:before, .icon:before, .wy-dropdown .caret:before, .wy-inline-validate.wy-inline-validate-success .wy-input-context:before, .wy-inline-validate.wy-inline-validate-danger .wy-input-context:before, .wy-inline-validate.wy-inline-validate-warning .wy-input-context:before, .wy-inline-validate.wy-inline-validate-info .wy-input-context:before {
   font-family: "FontAwesome";
   display: inline-block;
   font-style: normal;
   font-weight: normal;
   line-height: 1;
   text-decoration: inherit;
 }
 
 a .fa, a .wy-menu-vertical li span.toctree-expand, .wy-menu-vertical li a span.toctree-expand, .wy-menu-vertical li.on a span.toctree-expand, .wy-menu-vertical li.current > a span.toctree-expand, a .rst-content .admonition-title, .rst-content a .admonition-title, a .rst-content h1 .headerlink, .rst-content h1 a .headerlink, a .rst-content h2 .headerlink, .rst-content h2 a .headerlink, a .rst-content h3 .headerlink, .rst-content h3 a .headerlink, a .rst-content h4 .headerlink, .rst-content h4 a .headerlink, a .rst-content h5 .headerlink, .rst-content h5 a .headerlink, a .rst-content h6 .headerlink, .rst-content h6 a .headerlink, a .rst-content dl dt .headerlink, .rst-content dl dt a .headerlink, a .rst-content p.caption .headerlink, .rst-content p.caption a .headerlink, a .rst-content tt.download span:first-child, .rst-content tt.download a span:first-child, a .rst-content code.download span:first-child, .rst-content code.download a span:first-child, a .icon {
   display: inline-block;
   text-decoration: inherit;
 }
 
 .btn .fa, .btn .wy-menu-vertical li span.toctree-expand, .wy-menu-vertical li .btn span.toctree-expand, .btn .wy-menu-vertical li.on a span.toctree-expand, .wy-menu-vertical li.on a .btn span.toctree-expand, .btn .wy-menu-vertical li.current > a span.toctree-expand, .wy-menu-vertical li.current > a .btn span.toctree-expand, .btn .rst-content .admonition-title, .rst-content .btn .admonition-title, .btn .rst-content h1 .headerlink, .rst-content h1 .btn .headerlink, .btn .rst-content h2 .headerlink, .rst-content h2 .btn .headerlink, .btn .rst-content h3 .headerlink, .rst-content h3 .btn .headerlink, .btn .rst-content h4 .headerlink, .rst-content h4 .btn .headerlink, .btn .rst-content h5 .headerlink, .rst-content h5 .btn .headerlink, .btn .rst-content h6 .headerlink, .rst-content h6 .btn .headerlink, .btn .rst-content dl dt .headerlink, .rst-content dl dt .btn .headerlink, .btn .rst-content p.caption .headerlink, .rst-content p.caption .btn .headerlink, .btn .rst-content tt.download span:first-child, .rst-content tt.download .btn span:first-child, .btn .rst-content code.download span:first-child, .rst-content code.download .btn span:first-child, .btn .icon, .nav .fa, .nav .wy-menu-vertical li span.toctree-expand, .wy-menu-vertical li .nav span.toctree-expand, .nav .wy-menu-vertical li.on a span.toctree-expand, .wy-menu-vertical li.on a .nav span.toctree-expand, .nav .wy-menu-vertical li.current > a span.toctree-expand, .wy-menu-vertical li.current > a .nav span.toctree-expand, .nav .rst-content .admonition-title, .rst-content .nav .admonition-title, .nav .rst-content h1 .headerlink, .rst-content h1 .nav .headerlink, .nav .rst-content h2 .headerlink, .rst-content h2 .nav .headerlink, .nav .rst-content h3 .headerlink, .rst-content h3 .nav .headerlink, .nav .rst-content h4 .headerlink, .rst-content h4 .nav .headerlink, .nav .rst-content h5 .headerlink, .rst-content h5 .nav .headerlink, .nav .rst-content h6 .headerlink, .rst-content h6 .nav .headerlink, .nav .rst-content dl dt .headerlink, .rst-content dl dt .nav .headerlink, .nav .rst-content p.caption .headerlink, .rst-content p.caption .nav .headerlink, .nav .rst-content tt.download span:first-child, .rst-content tt.download .nav span:first-child, .nav .rst-content code.download span:first-child, .rst-content code.download .nav span:first-child, .nav .icon {
   display: inline;
 }
 .btn .fa.fa-large, .btn .wy-menu-vertical li span.fa-large.toctree-expand, .wy-menu-vertical li .btn span.fa-large.toctree-expand, .btn .rst-content .fa-large.admonition-title, .rst-content .btn .fa-large.admonition-title, .btn .rst-content h1 .fa-large.headerlink, .rst-content h1 .btn .fa-large.headerlink, .btn .rst-content h2 .fa-large.headerlink, .rst-content h2 .btn .fa-large.headerlink, .btn .rst-content h3 .fa-large.headerlink, .rst-content h3 .btn .fa-large.headerlink, .btn .rst-content h4 .fa-large.headerlink, .rst-content h4 .btn .fa-large.headerlink, .btn .rst-content h5 .fa-large.headerlink, .rst-content h5 .btn .fa-large.headerlink, .btn .rst-content h6 .fa-large.headerlink, .rst-content h6 .btn .fa-large.headerlink, .btn .rst-content dl dt .fa-large.headerlink, .rst-content dl dt .btn .fa-large.headerlink, .btn .rst-content p.caption .fa-large.headerlink, .rst-content p.caption .btn .fa-large.headerlink, .btn .rst-content tt.download span.fa-large:first-child, .rst-content tt.download .btn span.fa-large:first-child, .btn .rst-content code.download span.fa-large:first-child, .rst-content code.download .btn span.fa-large:first-child, .btn .fa-large.icon, .nav .fa.fa-large, .nav .wy-menu-vertical li span.fa-large.toctree-expand, .wy-menu-vertical li .nav span.fa-large.toctree-expand, .nav .rst-content .fa-large.admonition-title, .rst-content .nav .fa-large.admonition-title, .nav .rst-content h1 .fa-large.headerlink, .rst-content h1 .nav .fa-large.headerlink, .nav .rst-content h2 .fa-large.headerlink, .rst-content h2 .nav .fa-large.headerlink, .nav .rst-content h3 .fa-large.headerlink, .rst-content h3 .nav .fa-large.headerlink, .nav .rst-content h4 .fa-large.headerlink, .rst-content h4 .nav .fa-large.headerlink, .nav .rst-content h5 .fa-large.headerlink, .rst-content h5 .nav .fa-large.headerlink, .nav .rst-content h6 .fa-large.headerlink, .rst-content h6 .nav .fa-large.headerlink, .nav .rst-content dl dt .fa-large.headerlink, .rst-content dl dt .nav .fa-large.headerlink, .nav .rst-content p.caption .fa-large.headerlink, .rst-content p.caption .nav .fa-large.headerlink, .nav .rst-content tt.download span.fa-large:first-child, .rst-content tt.download .nav span.fa-large:first-child, .nav .rst-content code.download span.fa-large:first-child, .rst-content code.download .nav span.fa-large:first-child, .nav .fa-large.icon {
   line-height: 0.9em;
 }
 .btn .fa.fa-spin, .btn .wy-menu-vertical li span.fa-spin.toctree-expand, .wy-menu-vertical li .btn span.fa-spin.toctree-expand, .btn .rst-content .fa-spin.admonition-title, .rst-content .btn .fa-spin.admonition-title, .btn .rst-content h1 .fa-spin.headerlink, .rst-content h1 .btn .fa-spin.headerlink, .btn .rst-content h2 .fa-spin.headerlink, .rst-content h2 .btn .fa-spin.headerlink, .btn .rst-content h3 .fa-spin.headerlink, .rst-content h3 .btn .fa-spin.headerlink, .btn .rst-content h4 .fa-spin.headerlink, .rst-content h4 .btn .fa-spin.headerlink, .btn .rst-content h5 .fa-spin.headerlink, .rst-content h5 .btn .fa-spin.headerlink, .btn .rst-content h6 .fa-spin.headerlink, .rst-content h6 .btn .fa-spin.headerlink, .btn .rst-content dl dt .fa-spin.headerlink, .rst-content dl dt .btn .fa-spin.headerlink, .btn .rst-content p.caption .fa-spin.headerlink, .rst-content p.caption .btn .fa-spin.headerlink, .btn .rst-content tt.download span.fa-spin:first-child, .rst-content tt.download .btn span.fa-spin:first-child, .btn .rst-content code.download span.fa-spin:first-child, .rst-content code.download .btn span.fa-spin:first-child, .btn .fa-spin.icon, .nav .fa.fa-spin, .nav .wy-menu-vertical li span.fa-spin.toctree-expand, .wy-menu-vertical li .nav span.fa-spin.toctree-expand, .nav .rst-content .fa-spin.admonition-title, .rst-content .nav .fa-spin.admonition-title, .nav .rst-content h1 .fa-spin.headerlink, .rst-content h1 .nav .fa-spin.headerlink, .nav .rst-content h2 .fa-spin.headerlink, .rst-content h2 .nav .fa-spin.headerlink, .nav .rst-content h3 .fa-spin.headerlink, .rst-content h3 .nav .fa-spin.headerlink, .nav .rst-content h4 .fa-spin.headerlink, .rst-content h4 .nav .fa-spin.headerlink, .nav .rst-content h5 .fa-spin.headerlink, .rst-content h5 .nav .fa-spin.headerlink, .nav .rst-content h6 .fa-spin.headerlink, .rst-content h6 .nav .fa-spin.headerlink, .nav .rst-content dl dt .fa-spin.headerlink, .rst-content dl dt .nav .fa-spin.headerlink, .nav .rst-content p.caption .fa-spin.headerlink, .rst-content p.caption .nav .fa-spin.headerlink, .nav .rst-content tt.download span.fa-spin:first-child, .rst-content tt.download .nav span.fa-spin:first-child, .nav .rst-content code.download span.fa-spin:first-child, .rst-content code.download .nav span.fa-spin:first-child, .nav .fa-spin.icon {
   display: inline-block;
 }
 
 .btn.fa:before, .wy-menu-vertical li span.btn.toctree-expand:before, .rst-content .btn.admonition-title:before, .rst-content h1 .btn.headerlink:before, .rst-content h2 .btn.headerlink:before, .rst-content h3 .btn.headerlink:before, .rst-content h4 .btn.headerlink:before, .rst-content h5 .btn.headerlink:before, .rst-content h6 .btn.headerlink:before, .rst-content dl dt .btn.headerlink:before, .rst-content p.caption .btn.headerlink:before, .rst-content tt.download span.btn:first-child:before, .rst-content code.download span.btn:first-child:before, .btn.icon:before {
   opacity: 0.5;
   -webkit-transition: opacity 0.05s ease-in;
   -moz-transition: opacity 0.05s ease-in;
   transition: opacity 0.05s ease-in;
 }
 
 .btn.fa:hover:before, .wy-menu-vertical li span.btn.toctree-expand:hover:before, .rst-content .btn.admonition-title:hover:before, .rst-content h1 .btn.headerlink:hover:before, .rst-content h2 .btn.headerlink:hover:before, .rst-content h3 .btn.headerlink:hover:before, .rst-content h4 .btn.headerlink:hover:before, .rst-content h5 .btn.headerlink:hover:before, .rst-content h6 .btn.headerlink:hover:before, .rst-content dl dt .btn.headerlink:hover:before, .rst-content p.caption .btn.headerlink:hover:before, .rst-content tt.download span.btn:first-child:hover:before, .rst-content code.download span.btn:first-child:hover:before, .btn.icon:hover:before {
   opacity: 1;
 }
 
 .btn-mini .fa:before, .btn-mini .wy-menu-vertical li span.toctree-expand:before, .wy-menu-vertical li .btn-mini span.toctree-expand:before, .btn-mini .rst-content .admonition-title:before, .rst-content .btn-mini .admonition-title:before, .btn-mini .rst-content h1 .headerlink:before, .rst-content h1 .btn-mini .headerlink:before, .btn-mini .rst-content h2 .headerlink:before, .rst-content h2 .btn-mini .headerlink:before, .btn-mini .rst-content h3 .headerlink:before, .rst-content h3 .btn-mini .headerlink:before, .btn-mini .rst-content h4 .headerlink:before, .rst-content h4 .btn-mini .headerlink:before, .btn-mini .rst-content h5 .headerlink:before, .rst-content h5 .btn-mini .headerlink:before, .btn-mini .rst-content h6 .headerlink:before, .rst-content h6 .btn-mini .headerlink:before, .btn-mini .rst-content dl dt .headerlink:before, .rst-content dl dt .btn-mini .headerlink:before, .btn-mini .rst-content p.caption .headerlink:before, .rst-content p.caption .btn-mini .headerlink:before, .btn-mini .rst-content tt.download span:first-child:before, .rst-content tt.download .btn-mini span:first-child:before, .btn-mini .rst-content code.download span:first-child:before, .rst-content code.download .btn-mini span:first-child:before, .btn-mini .icon:before {
   font-size: 14px;
   vertical-align: -15%;
 }
 
 .wy-alert, .rst-content .note, .rst-content .attention, .rst-content .caution, .rst-content .danger, .rst-content .error, .rst-content .hint, .rst-content .important, .rst-content .tip, .rst-content .warning, .rst-content .seealso, .rst-content .admonition-todo {
   padding: 12px;
   line-height: 24px;
   margin-bottom: 24px;
   background: #e7f2fa;
 }
 
 .wy-alert-title, .rst-content .admonition-title {
   color: #fff;
   font-weight: bold;
   display: block;
   color: #fff;
   background: #6ab0de;
   margin: -12px;
   padding: 6px 12px;
   margin-bottom: 12px;
 }
 
 .wy-alert.wy-alert-danger, .rst-content .wy-alert-danger.note, .rst-content .wy-alert-danger.attention, .rst-content .wy-alert-danger.caution, .rst-content .danger, .rst-content .error, .rst-content .wy-alert-danger.hint, .rst-content .wy-alert-danger.important, .rst-content .wy-alert-danger.tip, .rst-content .wy-alert-danger.warning, .rst-content .wy-alert-danger.seealso, .rst-content .wy-alert-danger.admonition-todo {
   background: #fdf3f2;
 }
 .wy-alert.wy-alert-danger .wy-alert-title, .rst-content .wy-alert-danger.note .wy-alert-title, .rst-content .wy-alert-danger.attention .wy-alert-title, .rst-content .wy-alert-danger.caution .wy-alert-title, .rst-content .danger .wy-alert-title, .rst-content .error .wy-alert-title, .rst-content .wy-alert-danger.hint .wy-alert-title, .rst-content .wy-alert-danger.important .wy-alert-title, .rst-content .wy-alert-danger.tip .wy-alert-title, .rst-content .wy-alert-danger.warning .wy-alert-title, .rst-content .wy-alert-danger.seealso .wy-alert-title, .rst-content .wy-alert-danger.admonition-todo .wy-alert-title, .wy-alert.wy-alert-danger .rst-content .admonition-title, .rst-content .wy-alert.wy-alert-danger .admonition-title, .rst-content .wy-alert-danger.note .admonition-title, .rst-content .wy-alert-danger.attention .admonition-title, .rst-content .wy-alert-danger.caution .admonition-title, .rst-content .danger .admonition-title, .rst-content .error .admonition-title, .rst-content .wy-alert-danger.hint .admonition-title, .rst-content .wy-alert-danger.important .admonition-title, .rst-content .wy-alert-danger.tip .admonition-title, .rst-content .wy-alert-danger.warning .admonition-title, .rst-content .wy-alert-danger.seealso .admonition-title, .rst-content .wy-alert-danger.admonition-todo .admonition-title {
   background: #f29f97;
 }
 
 .wy-alert.wy-alert-warning, .rst-content .wy-alert-warning.note, .rst-content .attention, .rst-content .caution, .rst-content .wy-alert-warning.danger, .rst-content .wy-alert-warning.error, .rst-content .wy-alert-warning.hint, .rst-content .wy-alert-warning.important, .rst-content .wy-alert-warning.tip, .rst-content .warning, .rst-content .wy-alert-warning.seealso, .rst-content .admonition-todo {
   background: #ffedcc;
 }
 .wy-alert.wy-alert-warning .wy-alert-title, .rst-content .wy-alert-warning.note .wy-alert-title, .rst-content .attention .wy-alert-title, .rst-content .caution .wy-alert-title, .rst-content .wy-alert-warning.danger .wy-alert-title, .rst-content .wy-alert-warning.error .wy-alert-title, .rst-content .wy-alert-warning.hint .wy-alert-title, .rst-content .wy-alert-warning.important .wy-alert-title, .rst-content .wy-alert-warning.tip .wy-alert-title, .rst-content .warning .wy-alert-title, .rst-content .wy-alert-warning.seealso .wy-alert-title, .rst-content .admonition-todo .wy-alert-title, .wy-alert.wy-alert-warning .rst-content .admonition-title, .rst-content .wy-alert.wy-alert-warning .admonition-title, .rst-content .wy-alert-warning.note .admonition-title, .rst-content .attention .admonition-title, .rst-content .caution .admonition-title, .rst-content .wy-alert-warning.danger .admonition-title, .rst-content .wy-alert-warning.error .admonition-title, .rst-content .wy-alert-warning.hint .admonition-title, .rst-content .wy-alert-warning.important .admonition-title, .rst-content .wy-alert-warning.tip .admonition-title, .rst-content .warning .admonition-title, .rst-content .wy-alert-warning.seealso .admonition-title, .rst-content .admonition-todo .admonition-title {
   background: #f0b37e;
 }
 
 .wy-alert.wy-alert-info, .rst-content .note, .rst-content .wy-alert-info.attention, .rst-content .wy-alert-info.caution, .rst-content .wy-alert-info.danger, .rst-content .wy-alert-info.error, .rst-content .wy-alert-info.hint, .rst-content .wy-alert-info.important, .rst-content .wy-alert-info.tip, .rst-content .wy-alert-info.warning, .rst-content .seealso, .rst-content .wy-alert-info.admonition-todo {
   background: #e7f2fa;
 }
 .wy-alert.wy-alert-info .wy-alert-title, .rst-content .note .wy-alert-title, .rst-content .wy-alert-info.attention .wy-alert-title, .rst-content .wy-alert-info.caution .wy-alert-title, .rst-content .wy-alert-info.danger .wy-alert-title, .rst-content .wy-alert-info.error .wy-alert-title, .rst-content .wy-alert-info.hint .wy-alert-title, .rst-content .wy-alert-info.important .wy-alert-title, .rst-content .wy-alert-info.tip .wy-alert-title, .rst-content .wy-alert-info.warning .wy-alert-title, .rst-content .seealso .wy-alert-title, .rst-content .wy-alert-info.admonition-todo .wy-alert-title, .wy-alert.wy-alert-info .rst-content .admonition-title, .rst-content .wy-alert.wy-alert-info .admonition-title, .rst-content .note .admonition-title, .rst-content .wy-alert-info.attention .admonition-title, .rst-content .wy-alert-info.caution .admonition-title, .rst-content .wy-alert-info.danger .admonition-title, .rst-content .wy-alert-info.error .admonition-title, .rst-content .wy-alert-info.hint .admonition-title, .rst-content .wy-alert-info.important .admonition-title, .rst-content .wy-alert-info.tip .admonition-title, .rst-content .wy-alert-info.warning .admonition-title, .rst-content .seealso .admonition-title, .rst-content .wy-alert-info.admonition-todo .admonition-title {
   background: #6ab0de;
 }
 
 .wy-alert.wy-alert-success, .rst-content .wy-alert-success.note, .rst-content .wy-alert-success.attention, .rst-content .wy-alert-success.caution, .rst-content .wy-alert-success.danger, .rst-content .wy-alert-success.error, .rst-content .hint, .rst-content .important, .rst-content .tip, .rst-content .wy-alert-success.warning, .rst-content .wy-alert-success.seealso, .rst-content .wy-alert-success.admonition-todo {
   background: #dbfaf4;
 }
 .wy-alert.wy-alert-success .wy-alert-title, .rst-content .wy-alert-success.note .wy-alert-title, .rst-content .wy-alert-success.attention .wy-alert-title, .rst-content .wy-alert-success.caution .wy-alert-title, .rst-content .wy-alert-success.danger .wy-alert-title, .rst-content .wy-alert-success.error .wy-alert-title, .rst-content .hint .wy-alert-title, .rst-content .important .wy-alert-title, .rst-content .tip .wy-alert-title, .rst-content .wy-alert-success.warning .wy-alert-title, .rst-content .wy-alert-success.seealso .wy-alert-title, .rst-content .wy-alert-success.admonition-todo .wy-alert-title, .wy-alert.wy-alert-success .rst-content .admonition-title, .rst-content .wy-alert.wy-alert-success .admonition-title, .rst-content .wy-alert-success.note .admonition-title, .rst-content .wy-alert-success.attention .admonition-title, .rst-content .wy-alert-success.caution .admonition-title, .rst-content .wy-alert-success.danger .admonition-title, .rst-content .wy-alert-success.error .admonition-title, .rst-content .hint .admonition-title, .rst-content .important .admonition-title, .rst-content .tip .admonition-title, .rst-content .wy-alert-success.warning .admonition-title, .rst-content .wy-alert-success.seealso .admonition-title, .rst-content .wy-alert-success.admonition-todo .admonition-title {
   background: #1abc9c;
 }
 
 .wy-alert.wy-alert-neutral, .rst-content .wy-alert-neutral.note, .rst-content .wy-alert-neutral.attention, .rst-content .wy-alert-neutral.caution, .rst-content .wy-alert-neutral.danger, .rst-content .wy-alert-neutral.error, .rst-content .wy-alert-neutral.hint, .rst-content .wy-alert-neutral.important, .rst-content .wy-alert-neutral.tip, .rst-content .wy-alert-neutral.warning, .rst-content .wy-alert-neutral.seealso, .rst-content .wy-alert-neutral.admonition-todo {
   background: #f3f6f6;
 }
 .wy-alert.wy-alert-neutral .wy-alert-title, .rst-content .wy-alert-neutral.note .wy-alert-title, .rst-content .wy-alert-neutral.attention .wy-alert-title, .rst-content .wy-alert-neutral.caution .wy-alert-title, .rst-content .wy-alert-neutral.danger .wy-alert-title, .rst-content .wy-alert-neutral.error .wy-alert-title, .rst-content .wy-alert-neutral.hint .wy-alert-title, .rst-content .wy-alert-neutral.important .wy-alert-title, .rst-content .wy-alert-neutral.tip .wy-alert-title, .rst-content .wy-alert-neutral.warning .wy-alert-title, .rst-content .wy-alert-neutral.seealso .wy-alert-title, .rst-content .wy-alert-neutral.admonition-todo .wy-alert-title, .wy-alert.wy-alert-neutral .rst-content .admonition-title, .rst-content .wy-alert.wy-alert-neutral .admonition-title, .rst-content .wy-alert-neutral.note .admonition-title, .rst-content .wy-alert-neutral.attention .admonition-title, .rst-content .wy-alert-neutral.caution .admonition-title, .rst-content .wy-alert-neutral.danger .admonition-title, .rst-content .wy-alert-neutral.error .admonition-title, .rst-content .wy-alert-neutral.hint .admonition-title, .rst-content .wy-alert-neutral.important .admonition-title, .rst-content .wy-alert-neutral.tip .admonition-title, .rst-content .wy-alert-neutral.warning .admonition-title, .rst-content .wy-alert-neutral.seealso .admonition-title, .rst-content .wy-alert-neutral.admonition-todo .admonition-title {
   color: #404040;
   background: #e1e4e5;
 }
 .wy-alert.wy-alert-neutral a, .rst-content .wy-alert-neutral.note a, .rst-content .wy-alert-neutral.attention a, .rst-content .wy-alert-neutral.caution a, .rst-content .wy-alert-neutral.danger a, .rst-content .wy-alert-neutral.error a, .rst-content .wy-alert-neutral.hint a, .rst-content .wy-alert-neutral.important a, .rst-content .wy-alert-neutral.tip a, .rst-content .wy-alert-neutral.warning a, .rst-content .wy-alert-neutral.seealso a, .rst-content .wy-alert-neutral.admonition-todo a {
   color: #2980B9;
 }
 
 .wy-alert p:last-child, .rst-content .note p:last-child, .rst-content .attention p:last-child, .rst-content .caution p:last-child, .rst-content .danger p:last-child, .rst-content .error p:last-child, .rst-content .hint p:last-child, .rst-content .important p:last-child, .rst-content .tip p:last-child, .rst-content .warning p:last-child, .rst-content .seealso p:last-child, .rst-content .admonition-todo p:last-child {
   margin-bottom: 0;
 }
 
 .wy-tray-container {
   position: fixed;
   bottom: 0px;
   left: 0;
   z-index: 600;
 }
 .wy-tray-container li {
   display: block;
   width: 300px;
   background: transparent;
   color: #fff;
   text-align: center;
   box-shadow: 0 5px 5px 0 rgba(0, 0, 0, 0.1);
   padding: 0 24px;
   min-width: 20%;
   opacity: 0;
   height: 0;
   line-height: 56px;
   overflow: hidden;
   -webkit-transition: all 0.3s ease-in;
   -moz-transition: all 0.3s ease-in;
   transition: all 0.3s ease-in;
 }
 .wy-tray-container li.wy-tray-item-success {
   background: #27AE60;
 }
 .wy-tray-container li.wy-tray-item-info {
   background: #2980B9;
 }
 .wy-tray-container li.wy-tray-item-warning {
   background: #E67E22;
 }
 .wy-tray-container li.wy-tray-item-danger {
   background: #E74C3C;
 }
 .wy-tray-container li.on {
   opacity: 1;
   height: 56px;
 }
 
 @media screen and (max-width: 768px) {
   .wy-tray-container {
     bottom: auto;
     top: 0;
     width: 100%;
   }
   .wy-tray-container li {
     width: 100%;
   }
 }
 button {
   font-size: 100%;
   margin: 0;
   vertical-align: baseline;
   *vertical-align: middle;
   cursor: pointer;
   line-height: normal;
   -webkit-appearance: button;
   *overflow: visible;
 }
 
 button::-moz-focus-inner, input::-moz-focus-inner {
   border: 0;
   padding: 0;
 }
 
 button[disabled] {
   cursor: default;
 }
 
 .btn {
   /* Structure */
   display: inline-block;
   border-radius: 2px;
   line-height: normal;
   white-space: nowrap;
   text-align: center;
   cursor: pointer;
   font-size: 100%;
   padding: 6px 12px 8px 12px;
   color: #fff;
   border: 1px solid rgba(0, 0, 0, 0.1);
   background-color: #27AE60;
   text-decoration: none;
   font-weight: normal;
   font-family: "Lato", "proxima-nova", "Helvetica Neue", Arial, sans-serif;
   box-shadow: 0px 1px 2px -1px rgba(255, 255, 255, 0.5) inset, 0px -2px 0px 0px rgba(0, 0, 0, 0.1) inset;
   outline-none: false;
   vertical-align: middle;
   *display: inline;
   zoom: 1;
   -webkit-user-drag: none;
   -webkit-user-select: none;
   -moz-user-select: none;
   -ms-user-select: none;
   user-select: none;
   -webkit-transition: all 0.1s linear;
   -moz-transition: all 0.1s linear;
   transition: all 0.1s linear;
 }
 
 .btn-hover {
   background: #2e8ece;
   color: #fff;
 }
 
 .btn:hover {
   background: #2cc36b;
   color: #fff;
 }
 .btn:focus {
   background: #2cc36b;
   outline: 0;
 }
 .btn:active {
   box-shadow: 0px -1px 0px 0px rgba(0, 0, 0, 0.05) inset, 0px 2px 0px 0px rgba(0, 0, 0, 0.1) inset;
   padding: 8px 12px 6px 12px;
 }
 .btn:visited {
   color: #fff;
 }
 .btn:disabled {
   background-image: none;
   filter: progid:DXImageTransform.Microsoft.gradient(enabled = false);
   filter: alpha(opacity=40);
   opacity: 0.4;
   cursor: not-allowed;
   box-shadow: none;
 }
 
 .btn-disabled {
   background-image: none;
   filter: progid:DXImageTransform.Microsoft.gradient(enabled = false);
   filter: alpha(opacity=40);
   opacity: 0.4;
   cursor: not-allowed;
   box-shadow: none;
 }
 .btn-disabled:hover, .btn-disabled:focus, .btn-disabled:active {
   background-image: none;
   filter: progid:DXImageTransform.Microsoft.gradient(enabled = false);
   filter: alpha(opacity=40);
   opacity: 0.4;
   cursor: not-allowed;
   box-shadow: none;
 }
 
 .btn::-moz-focus-inner {
   padding: 0;
   border: 0;
 }
 
 .btn-small {
   font-size: 80%;
 }
 
 .btn-info {
   background-color: #2980B9 !important;
 }
 .btn-info:hover {
   background-color: #2e8ece !important;
 }
 
 .btn-neutral {
   background-color: #f3f6f6 !important;
   color: #404040 !important;
 }
 .btn-neutral:hover {
   background-color: #e5ebeb !important;
   color: #404040;
 }
 .btn-neutral:visited {
   color: #404040 !important;
 }
 
 .btn-success {
   background-color: #27AE60 !important;
 }
 .btn-success:hover {
   background-color: #229955 !important;
 }
 
 .btn-danger {
   background-color: #E74C3C !important;
 }
 .btn-danger:hover {
   background-color: #ea6153 !important;
 }
 
 .btn-warning {
   background-color: #E67E22 !important;
 }
 .btn-warning:hover {
   background-color: #e98b39 !important;
 }
 
 .btn-invert {
   background-color: #222;
 }
 .btn-invert:hover {
   background-color: #2f2f2f !important;
 }
 
 .btn-link {
   background-color: transparent !important;
   color: #2980B9;
   box-shadow: none;
   border-color: transparent !important;
 }
 .btn-link:hover {
   background-color: transparent !important;
   color: #409ad5 !important;
   box-shadow: none;
 }
 .btn-link:active {
   background-color: transparent !important;
   color: #409ad5 !important;
   box-shadow: none;
 }
 .btn-link:visited {
   color: #9B59B6;
 }
 
 .wy-btn-group .btn, .wy-control .btn {
   vertical-align: middle;
 }
 
 .wy-btn-group {
   margin-bottom: 24px;
   *zoom: 1;
 }
 .wy-btn-group:before, .wy-btn-group:after {
   display: table;
   content: "";
 }
 .wy-btn-group:after {
   clear: both;
 }
 
 .wy-dropdown {
   position: relative;
   display: inline-block;
 }
 
 .wy-dropdown-active .wy-dropdown-menu {
   display: block;
 }
 
 .wy-dropdown-menu {
   position: absolute;
   left: 0;
   display: none;
   float: left;
   top: 100%;
   min-width: 100%;
   background: #fcfcfc;
   z-index: 100;
   border: solid 1px #cfd7dd;
   box-shadow: 0 2px 2px 0 rgba(0, 0, 0, 0.1);
   padding: 12px;
 }
 .wy-dropdown-menu > dd > a {
   display: block;
   clear: both;
   color: #404040;
   white-space: nowrap;
   font-size: 90%;
   padding: 0 12px;
   cursor: pointer;
 }
 .wy-dropdown-menu > dd > a:hover {
   background: #2980B9;
   color: #fff;
 }
 .wy-dropdown-menu > dd.divider {
   border-top: solid 1px #cfd7dd;
   margin: 6px 0;
 }
 .wy-dropdown-menu > dd.search {
   padding-bottom: 12px;
 }
 .wy-dropdown-menu > dd.search input[type="search"] {
   width: 100%;
 }
 .wy-dropdown-menu > dd.call-to-action {
   background: #e3e3e3;
   text-transform: uppercase;
   font-weight: 500;
   font-size: 80%;
 }
 .wy-dropdown-menu > dd.call-to-action:hover {
   background: #e3e3e3;
 }
 .wy-dropdown-menu > dd.call-to-action .btn {
   color: #fff;
 }
 
 .wy-dropdown.wy-dropdown-up .wy-dropdown-menu {
   bottom: 100%;
   top: auto;
   left: auto;
   right: 0;
 }
 
 .wy-dropdown.wy-dropdown-bubble .wy-dropdown-menu {
   background: #fcfcfc;
   margin-top: 2px;
 }
 .wy-dropdown.wy-dropdown-bubble .wy-dropdown-menu a {
   padding: 6px 12px;
 }
 .wy-dropdown.wy-dropdown-bubble .wy-dropdown-menu a:hover {
   background: #2980B9;
   color: #fff;
 }
 
 .wy-dropdown.wy-dropdown-left .wy-dropdown-menu {
   right: 0;
   left: auto;
   text-align: right;
 }
 
 .wy-dropdown-arrow:before {
   content: " ";
   border-bottom: 5px solid whitesmoke;
   border-left: 5px solid transparent;
   border-right: 5px solid transparent;
   position: absolute;
   display: block;
   top: -4px;
   left: 50%;
   margin-left: -3px;
 }
 .wy-dropdown-arrow.wy-dropdown-arrow-left:before {
   left: 11px;
 }
 
 .wy-form-stacked select {
   display: block;
 }
 
 .wy-form-aligned input, .wy-form-aligned textarea, .wy-form-aligned select, .wy-form-aligned .wy-help-inline, .wy-form-aligned label {
   display: inline-block;
   *display: inline;
   *zoom: 1;
   vertical-align: middle;
 }
 
 .wy-form-aligned .wy-control-group > label {
   display: inline-block;
   vertical-align: middle;
   width: 10em;
   margin: 6px 12px 0 0;
   float: left;
 }
 .wy-form-aligned .wy-control {
   float: left;
 }
 .wy-form-aligned .wy-control label {
   display: block;
 }
 .wy-form-aligned .wy-control select {
   margin-top: 6px;
 }
 
 fieldset {
   border: 0;
   margin: 0;
   padding: 0;
 }
 
 legend {
   display: block;
   width: 100%;
   border: 0;
   padding: 0;
   white-space: normal;
   margin-bottom: 24px;
   font-size: 150%;
   *margin-left: -7px;
 }
 
 label {
   display: block;
   margin: 0 0 0.3125em 0;
   color: #333;
   font-size: 90%;
 }
 
 input, select, textarea {
   font-size: 100%;
   margin: 0;
   vertical-align: baseline;
   *vertical-align: middle;
 }
 
 .wy-control-group {
   margin-bottom: 24px;
   *zoom: 1;
   max-width: 68em;
   margin-left: auto;
   margin-right: auto;
   *zoom: 1;
 }
 .wy-control-group:before, .wy-control-group:after {
   display: table;
   content: "";
 }
 .wy-control-group:after {
   clear: both;
 }
 .wy-control-group:before, .wy-control-group:after {
   display: table;
   content: "";
 }
 .wy-control-group:after {
   clear: both;
 }
 
 .wy-control-group.wy-control-group-required > label:after {
   content: " *";
   color: #E74C3C;
 }
 
 .wy-control-group .wy-form-full, .wy-control-group .wy-form-halves, .wy-control-group .wy-form-thirds {
   padding-bottom: 12px;
 }
 .wy-control-group .wy-form-full select, .wy-control-group .wy-form-halves select, .wy-control-group .wy-form-thirds select {
   width: 100%;
 }
 .wy-control-group .wy-form-full input[type="text"], .wy-control-group .wy-form-full input[type="password"], .wy-control-group .wy-form-full input[type="email"], .wy-control-group .wy-form-full input[type="url"], .wy-control-group .wy-form-full input[type="date"], .wy-control-group .wy-form-full input[type="month"], .wy-control-group .wy-form-full input[type="time"], .wy-control-group .wy-form-full input[type="datetime"], .wy-control-group .wy-form-full input[type="datetime-local"], .wy-control-group .wy-form-full input[type="week"], .wy-control-group .wy-form-full input[type="number"], .wy-control-group .wy-form-full input[type="search"], .wy-control-group .wy-form-full input[type="tel"], .wy-control-group .wy-form-full input[type="color"], .wy-control-group .wy-form-halves input[type="text"], .wy-control-group .wy-form-halves input[type="password"], .wy-control-group .wy-form-halves input[type="email"], .wy-control-group .wy-form-halves input[type="url"], .wy-control-group .wy-form-halves input[type="date"], .wy-control-group .wy-form-halves input[type="month"], .wy-control-group .wy-form-halves input[type="time"], .wy-control-group .wy-form-halves input[type="datetime"], .wy-control-group .wy-form-halves input[type="datetime-local"], .wy-control-group .wy-form-halves input[type="week"], .wy-control-group .wy-form-halves input[type="number"], .wy-control-group .wy-form-halves input[type="search"], .wy-control-group .wy-form-halves input[type="tel"], .wy-control-group .wy-form-halves input[type="color"], .wy-control-group .wy-form-thirds input[type="text"], .wy-control-group .wy-form-thirds input[type="password"], .wy-control-group .wy-form-thirds input[type="email"], .wy-control-group .wy-form-thirds input[type="url"], .wy-control-group .wy-form-thirds input[type="date"], .wy-control-group .wy-form-thirds input[type="month"], .wy-control-group .wy-form-thirds input[type="time"], .wy-control-group .wy-form-thirds input[type="datetime"], .wy-control-group .wy-form-thirds input[type="datetime-local"], .wy-control-group .wy-form-thirds input[type="week"], .wy-control-group .wy-form-thirds input[type="number"], .wy-control-group .wy-form-thirds input[type="search"], .wy-control-group .wy-form-thirds input[type="tel"], .wy-control-group .wy-form-thirds input[type="color"] {
   width: 100%;
 }
 
 .wy-control-group .wy-form-full {
   float: left;
   display: block;
   margin-right: 2.35765%;
   width: 100%;
   margin-right: 0;
 }
 .wy-control-group .wy-form-full:last-child {
   margin-right: 0;
 }
 
 .wy-control-group .wy-form-halves {
   float: left;
   display: block;
   margin-right: 2.35765%;
   width: 48.82117%;
 }
 .wy-control-group .wy-form-halves:last-child {
   margin-right: 0;
 }
 .wy-control-group .wy-form-halves:nth-of-type(2n) {
   margin-right: 0;
 }
 .wy-control-group .wy-form-halves:nth-of-type(2n+1) {
   clear: left;
 }
 
 .wy-control-group .wy-form-thirds {
   float: left;
   display: block;
   margin-right: 2.35765%;
   width: 31.76157%;
 }
 .wy-control-group .wy-form-thirds:last-child {
   margin-right: 0;
 }
 .wy-control-group .wy-form-thirds:nth-of-type(3n) {
   margin-right: 0;
 }
 .wy-control-group .wy-form-thirds:nth-of-type(3n+1) {
   clear: left;
 }
 
 .wy-control-group.wy-control-group-no-input .wy-control {
   margin: 6px 0 0 0;
   font-size: 90%;
 }
 
 .wy-control-no-input {
   display: inline-block;
   margin: 6px 0 0 0;
   font-size: 90%;
 }
 
 .wy-control-group.fluid-input input[type="text"], .wy-control-group.fluid-input input[type="password"], .wy-control-group.fluid-input input[type="email"], .wy-control-group.fluid-input input[type="url"], .wy-control-group.fluid-input input[type="date"], .wy-control-group.fluid-input input[type="month"], .wy-control-group.fluid-input input[type="time"], .wy-control-group.fluid-input input[type="datetime"], .wy-control-group.fluid-input input[type="datetime-local"], .wy-control-group.fluid-input input[type="week"], .wy-control-group.fluid-input input[type="number"], .wy-control-group.fluid-input input[type="search"], .wy-control-group.fluid-input input[type="tel"], .wy-control-group.fluid-input input[type="color"] {
   width: 100%;
 }
 
 .wy-form-message-inline {
   display: inline-block;
   padding-left: 0.3em;
   color: #666;
   vertical-align: middle;
   font-size: 90%;
 }
 
 .wy-form-message {
   display: block;
   color: #999;
   font-size: 70%;
   margin-top: 0.3125em;
   font-style: italic;
 }
 .wy-form-message p {
   font-size: inherit;
   font-style: italic;
   margin-bottom: 6px;
 }
 .wy-form-message p:last-child {
   margin-bottom: 0;
 }
 
 input {
   line-height: normal;
 }
 
 input[type="button"], input[type="reset"], input[type="submit"] {
   -webkit-appearance: button;
   cursor: pointer;
   font-family: "Lato", "proxima-nova", "Helvetica Neue", Arial, sans-serif;
   *overflow: visible;
 }
 input[type="text"], input[type="password"], input[type="email"], input[type="url"], input[type="date"], input[type="month"], input[type="time"], input[type="datetime"], input[type="datetime-local"], input[type="week"], input[type="number"], input[type="search"], input[type="tel"], input[type="color"] {
   -webkit-appearance: none;
   padding: 6px;
   display: inline-block;
   border: 1px solid #ccc;
   font-size: 80%;
   font-family: "Lato", "proxima-nova", "Helvetica Neue", Arial, sans-serif;
   box-shadow: inset 0 1px 3px #ddd;
   border-radius: 0;
   -webkit-transition: border 0.3s linear;
   -moz-transition: border 0.3s linear;
   transition: border 0.3s linear;
 }
 input[type="datetime-local"] {
   padding: 0.34375em 0.625em;
 }
 input[disabled] {
   cursor: default;
 }
 input[type="checkbox"], input[type="radio"] {
   -webkit-box-sizing: border-box;
   -moz-box-sizing: border-box;
   box-sizing: border-box;
   padding: 0;
   margin-right: 0.3125em;
   *height: 13px;
   *width: 13px;
 }
 input[type="search"] {
   -webkit-box-sizing: border-box;
   -moz-box-sizing: border-box;
   box-sizing: border-box;
 }
 input[type="search"]::-webkit-search-cancel-button, input[type="search"]::-webkit-search-decoration {
   -webkit-appearance: none;
 }
 input[type="text"]:focus, input[type="password"]:focus, input[type="email"]:focus, input[type="url"]:focus, input[type="date"]:focus, input[type="month"]:focus, input[type="time"]:focus, input[type="datetime"]:focus, input[type="datetime-local"]:focus, input[type="week"]:focus, input[type="number"]:focus, input[type="search"]:focus, input[type="tel"]:focus, input[type="color"]:focus {
   outline: 0;
   outline: thin dotted \9;
   border-color: #333;
 }
 input.no-focus:focus {
   border-color: #ccc !important;
 }
 input[type="file"]:focus, input[type="radio"]:focus, input[type="checkbox"]:focus {
   outline: thin dotted #333;
   outline: 1px auto #129FEA;
 }
 input[type="text"][disabled], input[type="password"][disabled], input[type="email"][disabled], input[type="url"][disabled], input[type="date"][disabled], input[type="month"][disabled], input[type="time"][disabled], input[type="datetime"][disabled], input[type="datetime-local"][disabled], input[type="week"][disabled], input[type="number"][disabled], input[type="search"][disabled], input[type="tel"][disabled], input[type="color"][disabled] {
   cursor: not-allowed;
   background-color: #fafafa;
 }
 
 input:focus:invalid, textarea:focus:invalid, select:focus:invalid {
   color: #E74C3C;
   border: 1px solid #E74C3C;
 }
 
 input:focus:invalid:focus, textarea:focus:invalid:focus, select:focus:invalid:focus {
   border-color: #E74C3C;
 }
 
 input[type="file"]:focus:invalid:focus, input[type="radio"]:focus:invalid:focus, input[type="checkbox"]:focus:invalid:focus {
   outline-color: #E74C3C;
 }
 
 input.wy-input-large {
   padding: 12px;
   font-size: 100%;
 }
 
 textarea {
   overflow: auto;
   vertical-align: top;
   width: 100%;
   font-family: "Lato", "proxima-nova", "Helvetica Neue", Arial, sans-serif;
 }
 
 select, textarea {
   padding: 0.5em 0.625em;
   display: inline-block;
   border: 1px solid #ccc;
   font-size: 80%;
   box-shadow: inset 0 1px 3px #ddd;
   -webkit-transition: border 0.3s linear;
   -moz-transition: border 0.3s linear;
   transition: border 0.3s linear;
 }
 
 select {
   border: 1px solid #ccc;
   background-color: #fff;
 }
 select[multiple] {
   height: auto;
 }
 
 select:focus, textarea:focus {
   outline: 0;
 }
 
 select[disabled], textarea[disabled], input[readonly], select[readonly], textarea[readonly] {
   cursor: not-allowed;
   background-color: #fafafa;
 }
 
 input[type="radio"][disabled], input[type="checkbox"][disabled] {
   cursor: not-allowed;
 }
 
 .wy-checkbox, .wy-radio {
   margin: 6px 0;
   color: #404040;
   display: block;
 }
 .wy-checkbox input, .wy-radio input {
   vertical-align: baseline;
 }
 
 .wy-form-message-inline {
   display: inline-block;
   *display: inline;
   *zoom: 1;
   vertical-align: middle;
 }
 
 .wy-input-prefix, .wy-input-suffix {
   white-space: nowrap;
   padding: 6px;
 }
 .wy-input-prefix .wy-input-context, .wy-input-suffix .wy-input-context {
   line-height: 27px;
   padding: 0 8px;
   display: inline-block;
   font-size: 80%;
   background-color: #f3f6f6;
   border: solid 1px #ccc;
   color: #999;
 }
 
 .wy-input-suffix .wy-input-context {
   border-left: 0;
 }
 
 .wy-input-prefix .wy-input-context {
   border-right: 0;
 }
 
 .wy-switch {
   width: 36px;
   height: 12px;
   margin: 12px 0;
   position: relative;
   border-radius: 4px;
   background: #ccc;
   cursor: pointer;
   -webkit-transition: all 0.2s ease-in-out;
   -moz-transition: all 0.2s ease-in-out;
   transition: all 0.2s ease-in-out;
 }
 .wy-switch:before {
   position: absolute;
   content: "";
   display: block;
   width: 18px;
   height: 18px;
   border-radius: 4px;
   background: #999;
   left: -3px;
   top: -3px;
   -webkit-transition: all 0.2s ease-in-out;
   -moz-transition: all 0.2s ease-in-out;
   transition: all 0.2s ease-in-out;
 }
 .wy-switch:after {
   content: "false";
   position: absolute;
   left: 48px;
   display: block;
   font-size: 12px;
   color: #ccc;
 }
 
 .wy-switch.active {
   background: #1e8449;
 }
 .wy-switch.active:before {
   left: 24px;
   background: #27AE60;
 }
 .wy-switch.active:after {
   content: "true";
 }
 
 .wy-switch.disabled, .wy-switch.active.disabled {
   cursor: not-allowed;
 }
 
 .wy-control-group.wy-control-group-error .wy-form-message, .wy-control-group.wy-control-group-error > label {
   color: #E74C3C;
 }
 .wy-control-group.wy-control-group-error input[type="text"], .wy-control-group.wy-control-group-error input[type="password"], .wy-control-group.wy-control-group-error input[type="email"], .wy-control-group.wy-control-group-error input[type="url"], .wy-control-group.wy-control-group-error input[type="date"], .wy-control-group.wy-control-group-error input[type="month"], .wy-control-group.wy-control-group-error input[type="time"], .wy-control-group.wy-control-group-error input[type="datetime"], .wy-control-group.wy-control-group-error input[type="datetime-local"], .wy-control-group.wy-control-group-error input[type="week"], .wy-control-group.wy-control-group-error input[type="number"], .wy-control-group.wy-control-group-error input[type="search"], .wy-control-group.wy-control-group-error input[type="tel"], .wy-control-group.wy-control-group-error input[type="color"] {
   border: solid 1px #E74C3C;
 }
 .wy-control-group.wy-control-group-error textarea {
   border: solid 1px #E74C3C;
 }
 
 .wy-inline-validate {
   white-space: nowrap;
 }
 .wy-inline-validate .wy-input-context {
   padding: 0.5em 0.625em;
   display: inline-block;
   font-size: 80%;
 }
 
 .wy-inline-validate.wy-inline-validate-success .wy-input-context {
   color: #27AE60;
 }
 
 .wy-inline-validate.wy-inline-validate-danger .wy-input-context {
   color: #E74C3C;
 }
 
 .wy-inline-validate.wy-inline-validate-warning .wy-input-context {
   color: #E67E22;
 }
 
 .wy-inline-validate.wy-inline-validate-info .wy-input-context {
   color: #2980B9;
 }
 
 .rotate-90 {
   -webkit-transform: rotate(90deg);
   -moz-transform: rotate(90deg);
   -ms-transform: rotate(90deg);
   -o-transform: rotate(90deg);
   transform: rotate(90deg);
 }
 
 .rotate-180 {
   -webkit-transform: rotate(180deg);
   -moz-transform: rotate(180deg);
   -ms-transform: rotate(180deg);
   -o-transform: rotate(180deg);
   transform: rotate(180deg);
 }
 
 .rotate-270 {
   -webkit-transform: rotate(270deg);
   -moz-transform: rotate(270deg);
   -ms-transform: rotate(270deg);
   -o-transform: rotate(270deg);
   transform: rotate(270deg);
 }
 
 .mirror {
   -webkit-transform: scaleX(-1);
   -moz-transform: scaleX(-1);
   -ms-transform: scaleX(-1);
   -o-transform: scaleX(-1);
   transform: scaleX(-1);
 }
 .mirror.rotate-90 {
   -webkit-transform: scaleX(-1) rotate(90deg);
   -moz-transform: scaleX(-1) rotate(90deg);
   -ms-transform: scaleX(-1) rotate(90deg);
   -o-transform: scaleX(-1) rotate(90deg);
   transform: scaleX(-1) rotate(90deg);
 }
 .mirror.rotate-180 {
   -webkit-transform: scaleX(-1) rotate(180deg);
   -moz-transform: scaleX(-1) rotate(180deg);
   -ms-transform: scaleX(-1) rotate(180deg);
   -o-transform: scaleX(-1) rotate(180deg);
   transform: scaleX(-1) rotate(180deg);
 }
 .mirror.rotate-270 {
   -webkit-transform: scaleX(-1) rotate(270deg);
   -moz-transform: scaleX(-1) rotate(270deg);
   -ms-transform: scaleX(-1) rotate(270deg);
   -o-transform: scaleX(-1) rotate(270deg);
   transform: scaleX(-1) rotate(270deg);
 }
 
 @media only screen and (max-width: 480px) {
   .wy-form button[type="submit"] {
     margin: 0.7em 0 0;
   }
   .wy-form input[type="text"], .wy-form input[type="password"], .wy-form input[type="email"], .wy-form input[type="url"], .wy-form input[type="date"], .wy-form input[type="month"], .wy-form input[type="time"], .wy-form input[type="datetime"], .wy-form input[type="datetime-local"], .wy-form input[type="week"], .wy-form input[type="number"], .wy-form input[type="search"], .wy-form input[type="tel"], .wy-form input[type="color"] {
     margin-bottom: 0.3em;
     display: block;
   }
   .wy-form label {
     margin-bottom: 0.3em;
     display: block;
   }
 
   .wy-form input[type="password"], .wy-form input[type="email"], .wy-form input[type="url"], .wy-form input[type="date"], .wy-form input[type="month"], .wy-form input[type="time"], .wy-form input[type="datetime"], .wy-form input[type="datetime-local"], .wy-form input[type="week"], .wy-form input[type="number"], .wy-form input[type="search"], .wy-form input[type="tel"], .wy-form input[type="color"] {
     margin-bottom: 0;
   }
 
   .wy-form-aligned .wy-control-group label {
     margin-bottom: 0.3em;
     text-align: left;
     display: block;
     width: 100%;
   }
   .wy-form-aligned .wy-control {
     margin: 1.5em 0 0 0;
   }
 
   .wy-form .wy-help-inline, .wy-form-message-inline, .wy-form-message {
     display: block;
     font-size: 80%;
     padding: 6px 0;
   }
 }
 @media screen and (max-width: 768px) {
   .tablet-hide {
     display: none;
   }
 }
 
 @media screen and (max-width: 480px) {
   .mobile-hide {
     display: none;
   }
 }
 
 .float-left {
   float: left;
 }
 
 .float-right {
   float: right;
 }
 
 .full-width {
   width: 100%;
 }
 
 .wy-table, .rst-content table.docutils, .rst-content table.field-list {
   border-collapse: collapse;
   border-spacing: 0;
   empty-cells: show;
   margin-bottom: 24px;
 }
 .wy-table caption, .rst-content table.docutils caption, .rst-content table.field-list caption {
   color: #000;
   font: italic 85%/1 arial, sans-serif;
   padding: 1em 0;
   text-align: center;
 }
 .wy-table td, .rst-content table.docutils td, .rst-content table.field-list td, .wy-table th, .rst-content table.docutils th, .rst-content table.field-list th {
   font-size: 90%;
   margin: 0;
   overflow: visible;
   padding: 8px 16px;
 }
 .wy-table td:first-child, .rst-content table.docutils td:first-child, .rst-content table.field-list td:first-child, .wy-table th:first-child, .rst-content table.docutils th:first-child, .rst-content table.field-list th:first-child {
   border-left-width: 0;
 }
 .wy-table thead, .rst-content table.docutils thead, .rst-content table.field-list thead {
   color: #000;
   text-align: left;
   vertical-align: bottom;
   white-space: nowrap;
 }
 .wy-table thead th, .rst-content table.docutils thead th, .rst-content table.field-list thead th {
   font-weight: bold;
   border-bottom: solid 2px #e1e4e5;
 }
 .wy-table td, .rst-content table.docutils td, .rst-content table.field-list td {
   background-color: transparent;
   vertical-align: middle;
 }
 
 .wy-table td p, .rst-content table.docutils td p, .rst-content table.field-list td p {
   line-height: 18px;
 }
 .wy-table td p:last-child, .rst-content table.docutils td p:last-child, .rst-content table.field-list td p:last-child {
   margin-bottom: 0;
 }
 
 .wy-table .wy-table-cell-min, .rst-content table.docutils .wy-table-cell-min, .rst-content table.field-list .wy-table-cell-min {
   width: 1%;
   padding-right: 0;
 }
 .wy-table .wy-table-cell-min input[type=checkbox], .rst-content table.docutils .wy-table-cell-min input[type=checkbox], .rst-content table.field-list .wy-table-cell-min input[type=checkbox], .wy-table .wy-table-cell-min input[type=checkbox], .rst-content table.docutils .wy-table-cell-min input[type=checkbox], .rst-content table.field-list .wy-table-cell-min input[type=checkbox] {
   margin: 0;
 }
 
 .wy-table-secondary {
   color: gray;
   font-size: 90%;
 }
 
 .wy-table-tertiary {
   color: gray;
   font-size: 80%;
 }
 
 .wy-table-odd td, .wy-table-striped tr:nth-child(2n-1) td, .rst-content table.docutils:not(.field-list) tr:nth-child(2n-1) td {
   background-color: #f3f6f6;
 }
 
 .wy-table-backed {
   background-color: #f3f6f6;
 }
 
 /* BORDERED TABLES */
 .wy-table-bordered-all, .rst-content table.docutils {
   border: 1px solid #e1e4e5;
 }
 .wy-table-bordered-all td, .rst-content table.docutils td {
   border-bottom: 1px solid #e1e4e5;
   border-left: 1px solid #e1e4e5;
 }
 .wy-table-bordered-all tbody > tr:last-child td, .rst-content table.docutils tbody > tr:last-child td {
   border-bottom-width: 0;
 }
 
 .wy-table-bordered {
   border: 1px solid #e1e4e5;
 }
 
 .wy-table-bordered-rows td {
   border-bottom: 1px solid #e1e4e5;
 }
 .wy-table-bordered-rows tbody > tr:last-child td {
   border-bottom-width: 0;
 }
 
 .wy-table-horizontal tbody > tr:last-child td {
   border-bottom-width: 0;
 }
 .wy-table-horizontal td, .wy-table-horizontal th {
   border-width: 0 0 1px 0;
   border-bottom: 1px solid #e1e4e5;
 }
 .wy-table-horizontal tbody > tr:last-child td {
   border-bottom-width: 0;
 }
 
 /* RESPONSIVE TABLES */
 .wy-table-responsive {
   margin-bottom: 24px;
   max-width: 100%;
   overflow: auto;
 }
 .wy-table-responsive table {
   margin-bottom: 0 !important;
 }
 .wy-table-responsive table td, .wy-table-responsive table th {
   white-space: nowrap;
 }
 
 a {
   color: #2980B9;
   text-decoration: none;
   cursor: pointer;
 }
 a:hover {
   color: #3091d1;
 }
 a:visited {
   color: #9B59B6;
 }
 
 html {
   height: 100%;
   overflow-x: hidden;
 }
 
 body {
   font-family: "Lato", "proxima-nova", "Helvetica Neue", Arial, sans-serif;
   font-weight: normal;
   color: #404040;
   min-height: 100%;
   overflow-x: hidden;
   background: #edf0f2;
 }
 
 .wy-text-left {
   text-align: left;
 }
 
 .wy-text-center {
   text-align: center;
 }
 
 .wy-text-right {
   text-align: right;
 }
 
 .wy-text-large {
   font-size: 120%;
 }
 
 .wy-text-normal {
   font-size: 100%;
 }
 
 .wy-text-small, small {
   font-size: 80%;
 }
 
 .wy-text-strike {
   text-decoration: line-through;
 }
 
 .wy-text-warning {
   color: #E67E22 !important;
 }
 
 a.wy-text-warning:hover {
   color: #eb9950 !important;
 }
 
 .wy-text-info {
   color: #2980B9 !important;
 }
 
 a.wy-text-info:hover {
   color: #409ad5 !important;
 }
 
 .wy-text-success {
   color: #27AE60 !important;
 }
 
 a.wy-text-success:hover {
   color: #36d278 !important;
 }
 
 .wy-text-danger {
   color: #E74C3C !important;
 }
 
 a.wy-text-danger:hover {
   color: #ed7669 !important;
 }
 
 .wy-text-neutral {
   color: #404040 !important;
 }
 
 a.wy-text-neutral:hover {
   color: #595959 !important;
 }
 
 h1, h2, .rst-content .toctree-wrapper p.caption, h3, h4, h5, h6, legend {
   margin-top: 0;
   font-weight: 700;
   font-family: "Roboto Slab", "ff-tisa-web-pro", "Georgia", Arial, sans-serif;
 }
 
 p {
   line-height: 24px;
   margin: 0;
   font-size: 16px;
   margin-bottom: 24px;
 }
 
 h1 {
   font-size: 175%;
 }
 
 h2, .rst-content .toctree-wrapper p.caption {
   font-size: 150%;
 }
 
 h3 {
   font-size: 125%;
 }
 
 h4 {
   font-size: 115%;
 }
 
 h5 {
   font-size: 110%;
 }
 
 h6 {
   font-size: 100%;
 }
 
 hr {
   display: block;
   height: 1px;
   border: 0;
-  border-top: 1px solid #e1e4e5;
+  border-top: 2px solid #e1e4e5;
   margin: 24px 0;
   padding: 0;
 }
 
 code, .rst-content tt, .rst-content code {
   white-space: nowrap;
   max-width: 100%;
   background: #fff;
   border: solid 1px #e1e4e5;
   font-size: 75%;
   padding: 0 5px;
   font-family: Consolas, "Andale Mono WT", "Andale Mono", "Lucida Console", "Lucida Sans Typewriter", "DejaVu Sans Mono", "Bitstream Vera Sans Mono", "Liberation Mono", "Nimbus Mono L", Monaco, "Courier New", Courier, monospace;
   color: #E74C3C;
   overflow-x: auto;
 }
 code.code-large, .rst-content tt.code-large {
   font-size: 90%;
 }
 
 .wy-plain-list-disc, .rst-content .section ul, .rst-content .toctree-wrapper ul, article ul {
   list-style: disc;
   line-height: 24px;
   margin-bottom: 24px;
 }
 .wy-plain-list-disc li, .rst-content .section ul li, .rst-content .toctree-wrapper ul li, article ul li {
   list-style: disc;
   margin-left: 24px;
 }
 .wy-plain-list-disc li p:last-child, .rst-content .section ul li p:last-child, .rst-content .toctree-wrapper ul li p:last-child, article ul li p:last-child {
   margin-bottom: 0;
 }
 .wy-plain-list-disc li ul, .rst-content .section ul li ul, .rst-content .toctree-wrapper ul li ul, article ul li ul {
   margin-bottom: 0;
 }
 .wy-plain-list-disc li li, .rst-content .section ul li li, .rst-content .toctree-wrapper ul li li, article ul li li {
   list-style: circle;
 }
 .wy-plain-list-disc li li li, .rst-content .section ul li li li, .rst-content .toctree-wrapper ul li li li, article ul li li li {
   list-style: square;
 }
 .wy-plain-list-disc li ol li, .rst-content .section ul li ol li, .rst-content .toctree-wrapper ul li ol li, article ul li ol li {
   list-style: decimal;
 }
 
 .wy-plain-list-decimal, .rst-content .section ol, .rst-content ol.arabic, article ol {
   list-style: decimal;
   line-height: 24px;
   margin-bottom: 24px;
 }
 .wy-plain-list-decimal li, .rst-content .section ol li, .rst-content ol.arabic li, article ol li {
   list-style: decimal;
   margin-left: 24px;
 }
 .wy-plain-list-decimal li p:last-child, .rst-content .section ol li p:last-child, .rst-content ol.arabic li p:last-child, article ol li p:last-child {
   margin-bottom: 0;
 }
 .wy-plain-list-decimal li ul, .rst-content .section ol li ul, .rst-content ol.arabic li ul, article ol li ul {
   margin-bottom: 0;
 }
 .wy-plain-list-decimal li ul li, .rst-content .section ol li ul li, .rst-content ol.arabic li ul li, article ol li ul li {
   list-style: disc;
 }
 
 .codeblock-example {
   border: 1px solid #e1e4e5;
   border-bottom: none;
   padding: 24px;
   padding-top: 48px;
   font-weight: 500;
   background: #fff;
   position: relative;
 }
 .codeblock-example:after {
   content: "Example";
   position: absolute;
   top: 0px;
   left: 0px;
   background: #9B59B6;
   color: white;
   padding: 6px 12px;
 }
 .codeblock-example.prettyprint-example-only {
   border: 1px solid #e1e4e5;
   margin-bottom: 24px;
 }
 
 .codeblock, pre.literal-block, .rst-content .literal-block, .rst-content pre.literal-block, div[class^='highlight'] {
   border: 1px solid #e1e4e5;
   padding: 0px;
   overflow-x: auto;
   background: #fff;
   margin: 1px 0 24px 0;
 }
 .codeblock div[class^='highlight'], pre.literal-block div[class^='highlight'], .rst-content .literal-block div[class^='highlight'], div[class^='highlight'] div[class^='highlight'] {
   border: none;
   background: none;
   margin: 0;
 }
 
 div[class^='highlight'] td.code {
   width: 100%;
 }
 
 .linenodiv pre {
   border-right: solid 1px #e6e9ea;
   margin: 0;
   padding: 12px 12px;
   font-family: Consolas, "Andale Mono WT", "Andale Mono", "Lucida Console", "Lucida Sans Typewriter", "DejaVu Sans Mono", "Bitstream Vera Sans Mono", "Liberation Mono", "Nimbus Mono L", Monaco, "Courier New", Courier, monospace;
   font-size: 12px;
   line-height: 1.5;
   color: #d9d9d9;
 }
 
 div[class^='highlight'] pre {
   white-space: pre;
   margin: 0;
   padding: 12px 12px;
   font-family: Consolas, "Andale Mono WT", "Andale Mono", "Lucida Console", "Lucida Sans Typewriter", "DejaVu Sans Mono", "Bitstream Vera Sans Mono", "Liberation Mono", "Nimbus Mono L", Monaco, "Courier New", Courier, monospace;
   font-size: 12px;
   line-height: 1.5;
   display: block;
   overflow: auto;
   color: #404040;
 }
 
 @media print {
   .codeblock, pre.literal-block, .rst-content .literal-block, .rst-content pre.literal-block, div[class^='highlight'], div[class^='highlight'] pre {
     white-space: pre-wrap;
   }
 }
 .hll {
   background-color: #ffffcc;
   margin: 0 -12px;
   padding: 0 12px;
   display: block;
 }
 
 .c {
   color: #999988;
   font-style: italic;
 }
 
 .err {
   color: #a61717;
   background-color: #e3d2d2;
 }
 
 .k {
   font-weight: bold;
 }
 
 .o {
   font-weight: bold;
 }
 
 .cm {
   color: #999988;
   font-style: italic;
 }
 
 .cp {
   color: #999999;
   font-weight: bold;
 }
 
 .c1 {
   color: #999988;
   font-style: italic;
 }
 
 .cs {
   color: #999999;
   font-weight: bold;
   font-style: italic;
 }
 
 .gd {
   color: #000000;
   background-color: #ffdddd;
 }
 
 .gd .x {
   color: #000000;
   background-color: #ffaaaa;
 }
 
 .ge {
   font-style: italic;
 }
 
 .gr {
   color: #aa0000;
 }
 
 .gh {
   color: #999999;
 }
 
 .gi {
   color: #000000;
   background-color: #ddffdd;
 }
 
 .gi .x {
   color: #000000;
   background-color: #aaffaa;
 }
 
 .go {
   color: #888888;
 }
 
 .gp {
   color: #555555;
 }
 
 .gs {
   font-weight: bold;
 }
 
 .gu {
   color: #800080;
   font-weight: bold;
 }
 
 .gt {
   color: #aa0000;
 }
 
 .kc {
   font-weight: bold;
 }
 
 .kd {
   font-weight: bold;
 }
 
 .kn {
   font-weight: bold;
 }
 
 .kp {
   font-weight: bold;
 }
 
 .kr {
   font-weight: bold;
 }
 
 .kt {
   color: #445588;
   font-weight: bold;
 }
 
 .m {
   color: #009999;
 }
 
 .s {
   color: #dd1144;
 }
 
 .n {
   color: #333333;
 }
 
 .na {
   color: teal;
 }
 
 .nb {
   color: #0086b3;
 }
 
 .nc {
   color: #445588;
   font-weight: bold;
 }
 
 .no {
   color: teal;
 }
 
 .ni {
   color: purple;
 }
 
 .ne {
   color: #990000;
   font-weight: bold;
 }
 
 .nf {
   color: #990000;
   font-weight: bold;
 }
 
 .nn {
   color: #555555;
 }
 
 .nt {
   color: navy;
 }
 
 .nv {
   color: teal;
 }
 
 .ow {
   font-weight: bold;
 }
 
 .w {
   color: #bbbbbb;
 }
 
 .mf {
   color: #009999;
 }
 
 .mh {
   color: #009999;
 }
 
 .mi {
   color: #009999;
 }
 
 .mo {
   color: #009999;
 }
 
 .sb {
   color: #dd1144;
 }
 
 .sc {
   color: #dd1144;
 }
 
 .sd {
   color: #dd1144;
 }
 
 .s2 {
   color: #dd1144;
 }
 
 .se {
   color: #dd1144;
 }
 
 .sh {
   color: #dd1144;
 }
 
 .si {
   color: #dd1144;
 }
 
 .sx {
   color: #dd1144;
 }
 
 .sr {
   color: #009926;
 }
 
 .s1 {
   color: #dd1144;
 }
 
 .ss {
   color: #990073;
 }
 
 .bp {
   color: #999999;
 }
 
 .vc {
   color: teal;
 }
 
 .vg {
   color: teal;
 }
 
 .vi {
   color: teal;
 }
 
 .il {
   color: #009999;
 }
 
 .gc {
   color: #999;
   background-color: #EAF2F5;
 }
 
 .wy-breadcrumbs li {
   display: inline-block;
 }
 .wy-breadcrumbs li.wy-breadcrumbs-aside {
   float: right;
 }
 .wy-breadcrumbs li a {
   display: inline-block;
   padding: 5px;
 }
 .wy-breadcrumbs li a:first-child {
   padding-left: 0;
 }
 .wy-breadcrumbs li code, .wy-breadcrumbs li .rst-content tt, .rst-content .wy-breadcrumbs li tt {
   padding: 5px;
   border: none;
   background: none;
 }
 .wy-breadcrumbs li code.literal, .wy-breadcrumbs li .rst-content tt.literal, .rst-content .wy-breadcrumbs li tt.literal {
   color: #404040;
 }
 
 .wy-breadcrumbs-extra {
   margin-bottom: 0;
   color: #b3b3b3;
   font-size: 80%;
   display: inline-block;
 }
 
 @media screen and (max-width: 480px) {
   .wy-breadcrumbs-extra {
     display: none;
   }
 
   .wy-breadcrumbs li.wy-breadcrumbs-aside {
     display: none;
   }
 }
 @media print {
   .wy-breadcrumbs li.wy-breadcrumbs-aside {
     display: none;
   }
 }
 .wy-affix {
   position: fixed;
   top: 1.618em;
 }
 
 .wy-menu a:hover {
   text-decoration: none;
 }
 
 .wy-menu-horiz {
   *zoom: 1;
 }
 .wy-menu-horiz:before, .wy-menu-horiz:after {
   display: table;
   content: "";
 }
 .wy-menu-horiz:after {
   clear: both;
 }
 .wy-menu-horiz ul, .wy-menu-horiz li {
   display: inline-block;
 }
 .wy-menu-horiz li:hover {
   background: rgba(255, 255, 255, 0.1);
 }
 .wy-menu-horiz li.divide-left {
   border-left: solid 1px #404040;
 }
 .wy-menu-horiz li.divide-right {
   border-right: solid 1px #404040;
 }
 .wy-menu-horiz a {
   height: 32px;
   display: inline-block;
   line-height: 32px;
   padding: 0 16px;
 }
 
 .wy-menu-vertical header, .wy-menu-vertical p.caption {
   height: 32px;
   display: inline-block;
   line-height: 32px;
   padding: 0 1.618em;
   margin-bottom: 0;
   display: block;
   font-weight: bold;
   text-transform: uppercase;
   font-size: 80%;
   color: #555;
   white-space: nowrap;
 }
 .wy-menu-vertical ul {
   margin-bottom: 0;
 }
 .wy-menu-vertical li.divide-top {
   border-top: solid 1px #404040;
 }
 .wy-menu-vertical li.divide-bottom {
   border-bottom: solid 1px #404040;
 }
 .wy-menu-vertical li.current {
   background: #e3e3e3;
 }
 .wy-menu-vertical li.current a {
   color: gray;
   border-right: solid 1px #c9c9c9;
   padding: 0.4045em 2.427em;
 }
 .wy-menu-vertical li.current a:hover {
   background: #d6d6d6;
 }
 .wy-menu-vertical li code, .wy-menu-vertical li .rst-content tt, .rst-content .wy-menu-vertical li tt {
   border: none;
   background: inherit;
   color: inherit;
   padding-left: 0;
   padding-right: 0;
 }
 .wy-menu-vertical li span.toctree-expand {
   display: block;
   float: left;
   margin-left: -1.2em;
   font-size: 0.8em;
   line-height: 1.6em;
   color: #4d4d4d;
 }
 .wy-menu-vertical li.on a, .wy-menu-vertical li.current > a {
   color: #404040;
   padding: 0.4045em 1.618em;
   font-weight: bold;
   position: relative;
   background: #fcfcfc;
   border: none;
   border-bottom: solid 1px #c9c9c9;
   border-top: solid 1px #c9c9c9;
   padding-left: 1.618em -4px;
 }
 .wy-menu-vertical li.on a:hover, .wy-menu-vertical li.current > a:hover {
   background: #fcfcfc;
 }
 .wy-menu-vertical li.on a:hover span.toctree-expand, .wy-menu-vertical li.current > a:hover span.toctree-expand {
   color: gray;
 }
 .wy-menu-vertical li.on a span.toctree-expand, .wy-menu-vertical li.current > a span.toctree-expand {
   display: block;
   font-size: 0.8em;
   line-height: 1.6em;
   color: #333333;
 }
 .wy-menu-vertical li.toctree-l1.current li.toctree-l2 > ul, .wy-menu-vertical li.toctree-l2.current li.toctree-l3 > ul {
   display: none;
 }
 .wy-menu-vertical li.toctree-l1.current li.toctree-l2.current > ul, .wy-menu-vertical li.toctree-l2.current li.toctree-l3.current > ul {
   display: block;
 }
 .wy-menu-vertical li.toctree-l2.current > a {
   background: #c9c9c9;
   padding: 0.4045em 2.427em;
 }
 .wy-menu-vertical li.toctree-l2.current li.toctree-l3 > a {
   display: block;
   background: #c9c9c9;
   padding: 0.4045em 4.045em;
 }
 .wy-menu-vertical li.toctree-l2 a:hover span.toctree-expand {
   color: gray;
 }
 .wy-menu-vertical li.toctree-l2 span.toctree-expand {
   color: #a3a3a3;
 }
 .wy-menu-vertical li.toctree-l3 {
   font-size: 0.9em;
 }
 .wy-menu-vertical li.toctree-l3.current > a {
   background: #bdbdbd;
   padding: 0.4045em 4.045em;
 }
 .wy-menu-vertical li.toctree-l3.current li.toctree-l4 > a {
   display: block;
   background: #bdbdbd;
   padding: 0.4045em 5.663em;
   border-top: none;
   border-bottom: none;
 }
 .wy-menu-vertical li.toctree-l3 a:hover span.toctree-expand {
   color: gray;
 }
 .wy-menu-vertical li.toctree-l3 span.toctree-expand {
   color: #969696;
 }
 .wy-menu-vertical li.toctree-l4 {
   font-size: 0.9em;
 }
 .wy-menu-vertical li.current ul {
   display: block;
 }
 .wy-menu-vertical li ul {
   margin-bottom: 0;
   display: none;
 }
 .wy-menu-vertical .local-toc li ul {
   display: block;
 }
 .wy-menu-vertical li ul li a {
   margin-bottom: 0;
   color: #b3b3b3;
   font-weight: normal;
 }
 .wy-menu-vertical a {
   display: inline-block;
   line-height: 18px;
   padding: 0.4045em 1.618em;
   display: block;
   position: relative;
   font-size: 90%;
   color: #b3b3b3;
 }
 .wy-menu-vertical a:hover {
   background-color: #4e4a4a;
   cursor: pointer;
 }
 .wy-menu-vertical a:hover span.toctree-expand {
   color: #b3b3b3;
 }
 .wy-menu-vertical a:active {
   background-color: #2980B9;
   cursor: pointer;
   color: #fff;
 }
 .wy-menu-vertical a:active span.toctree-expand {
   color: #fff;
 }
 
 .wy-side-nav-search {
   z-index: 200;
   background-color: #2980B9;
   text-align: center;
   padding: 0.809em;
   display: block;
   color: #fcfcfc;
   margin-bottom: 0.809em;
 }
 .wy-side-nav-search input[type=text] {
   width: 100%;
   border-radius: 50px;
   padding: 6px 12px;
   border-color: #2472a4;
 }
 .wy-side-nav-search img {
   display: block;
   margin: auto auto 0.809em auto;
   height: 45px;
   width: 45px;
   background-color: #2980B9;
   padding: 5px;
   border-radius: 100%;
 }
 .wy-side-nav-search > a, .wy-side-nav-search .wy-dropdown > a {
   color: #fcfcfc;
   font-size: 100%;
   font-weight: bold;
   display: inline-block;
   padding: 4px 6px;
   margin-bottom: 0.809em;
 }
 .wy-side-nav-search > a:hover, .wy-side-nav-search .wy-dropdown > a:hover {
   background: rgba(255, 255, 255, 0.1);
 }
 .wy-side-nav-search > a img.logo, .wy-side-nav-search .wy-dropdown > a img.logo {
   display: block;
   margin: 0 auto;
   height: auto;
   width: auto;
   border-radius: 0;
   max-width: 100%;
   background: transparent;
 }
 .wy-side-nav-search > a.icon img.logo, .wy-side-nav-search .wy-dropdown > a.icon img.logo {
   margin-top: 0.85em;
 }
 .wy-side-nav-search > div.version {
   margin-top: -0.4045em;
   margin-bottom: 0.809em;
   font-weight: normal;
   color: rgba(255, 255, 255, 0.3);
 }
 
 .wy-nav .wy-menu-vertical header {
   color: #2980B9;
 }
 .wy-nav .wy-menu-vertical a {
   color: #b3b3b3;
 }
 .wy-nav .wy-menu-vertical a:hover {
   background-color: #2980B9;
   color: #fff;
 }
 
 [data-menu-wrap] {
   -webkit-transition: all 0.2s ease-in;
   -moz-transition: all 0.2s ease-in;
   transition: all 0.2s ease-in;
   position: absolute;
   opacity: 1;
   width: 100%;
   opacity: 0;
 }
 [data-menu-wrap].move-center {
   left: 0;
   right: auto;
   opacity: 1;
 }
 [data-menu-wrap].move-left {
   right: auto;
   left: -100%;
   opacity: 0;
 }
 [data-menu-wrap].move-right {
   right: -100%;
   left: auto;
   opacity: 0;
 }
 
 .wy-body-for-nav {
   background: left repeat-y #fcfcfc;
   background-image: url(data:image/png;base64,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);
   background-size: 300px 1px;
 }
 
 .wy-grid-for-nav {
   position: absolute;
   width: 100%;
   height: 100%;
 }
 
 .wy-nav-side {
   position: fixed;
   top: 0;
   bottom: 0;
   left: 0;
   padding-bottom: 2em;
   width: 300px;
   overflow-x: hidden;
   overflow-y: scroll;
   min-height: 100%;
   background: #343131;
   z-index: 200;
 }
 
 .wy-nav-top {
   display: none;
   background: #2980B9;
   color: #fff;
   padding: 0.4045em 0.809em;
   position: relative;
   line-height: 50px;
   text-align: center;
   font-size: 100%;
   *zoom: 1;
 }
 .wy-nav-top:before, .wy-nav-top:after {
   display: table;
   content: "";
 }
 .wy-nav-top:after {
   clear: both;
 }
 .wy-nav-top a {
   color: #fff;
   font-weight: bold;
 }
 .wy-nav-top img {
   margin-right: 12px;
   height: 45px;
   width: 45px;
   background-color: #2980B9;
   padding: 5px;
   border-radius: 100%;
 }
 .wy-nav-top i {
   font-size: 30px;
   float: left;
   cursor: pointer;
 }
 
 .wy-nav-content-wrap {
   margin-left: 300px;
   background: #fcfcfc;
   min-height: 100%;
 }
 
 .wy-nav-content {
   padding: 1.618em 3.236em;
   height: 100%;
   margin: auto;
 }
 
 .wy-body-mask {
   position: fixed;
   width: 100%;
   height: 100%;
   background: rgba(0, 0, 0, 0.2);
   display: none;
   z-index: 499;
 }
 .wy-body-mask.on {
   display: block;
 }
 
 footer {
   color: #999;
 }
 footer p {
   margin-bottom: 12px;
 }
 footer span.commit code, footer span.commit .rst-content tt, .rst-content footer span.commit tt {
   padding: 0px;
   font-family: Consolas, "Andale Mono WT", "Andale Mono", "Lucida Console", "Lucida Sans Typewriter", "DejaVu Sans Mono", "Bitstream Vera Sans Mono", "Liberation Mono", "Nimbus Mono L", Monaco, "Courier New", Courier, monospace;
   font-size: 1em;
   background: none;
   border: none;
   color: #999;
 }
 
 .rst-footer-buttons {
   *zoom: 1;
 }
 .rst-footer-buttons:before, .rst-footer-buttons:after {
   display: table;
   content: "";
 }
 .rst-footer-buttons:after {
   clear: both;
 }
 
 #search-results .search li {
   margin-bottom: 24px;
   border-bottom: solid 1px #e1e4e5;
   padding-bottom: 24px;
 }
 #search-results .search li:first-child {
   border-top: solid 1px #e1e4e5;
   padding-top: 24px;
 }
 #search-results .search li a {
   font-size: 120%;
   margin-bottom: 12px;
   display: inline-block;
 }
 #search-results .context {
   color: gray;
   font-size: 90%;
 }
 
 @media screen and (max-width: 768px) {
   .wy-body-for-nav {
     background: #fcfcfc;
   }
 
   .wy-nav-top {
     display: block;
   }
 
   .wy-nav-side {
     left: -300px;
   }
   .wy-nav-side.shift {
     width: 85%;
     left: 0;
   }
 
   .wy-nav-content-wrap {
     margin-left: 0;
   }
   .wy-nav-content-wrap .wy-nav-content {
     padding: 1.618em;
   }
   .wy-nav-content-wrap.shift {
     position: fixed;
     min-width: 100%;
     left: 85%;
     top: 0;
     height: 100%;
     overflow: hidden;
   }
 }
 @media screen and (min-width: 1400px) {
   .wy-nav-content-wrap {
     background: rgba(0, 0, 0, 0.05);
   }
 
   .wy-nav-content {
     margin: 0;
     background: #fcfcfc;
   }
 }
 @media print {
   .rst-versions, footer, .wy-nav-side {
     display: none;
   }
 
   .wy-nav-content-wrap {
     margin-left: 0;
   }
 }
 .rst-versions {
   position: fixed;
   bottom: 0;
   left: 0;
   width: 300px;
   color: #fcfcfc;
   background: #1f1d1d;
   border-top: solid 10px #343131;
   font-family: "Lato", "proxima-nova", "Helvetica Neue", Arial, sans-serif;
   z-index: 400;
 }
 .rst-versions a {
   color: #2980B9;
   text-decoration: none;
 }
 .rst-versions .rst-badge-small {
   display: none;
 }
 .rst-versions .rst-current-version {
   padding: 12px;
   background-color: #272525;
   display: block;
   text-align: right;
   font-size: 90%;
   cursor: pointer;
   color: #27AE60;
   *zoom: 1;
 }
 .rst-versions .rst-current-version:before, .rst-versions .rst-current-version:after {
   display: table;
   content: "";
 }
 .rst-versions .rst-current-version:after {
   clear: both;
 }
 .rst-versions .rst-current-version .fa, .rst-versions .rst-current-version .wy-menu-vertical li span.toctree-expand, .wy-menu-vertical li .rst-versions .rst-current-version span.toctree-expand, .rst-versions .rst-current-version .rst-content .admonition-title, .rst-content .rst-versions .rst-current-version .admonition-title, .rst-versions .rst-current-version .rst-content h1 .headerlink, .rst-content h1 .rst-versions .rst-current-version .headerlink, .rst-versions .rst-current-version .rst-content h2 .headerlink, .rst-content h2 .rst-versions .rst-current-version .headerlink, .rst-versions .rst-current-version .rst-content h3 .headerlink, .rst-content h3 .rst-versions .rst-current-version .headerlink, .rst-versions .rst-current-version .rst-content h4 .headerlink, .rst-content h4 .rst-versions .rst-current-version .headerlink, .rst-versions .rst-current-version .rst-content h5 .headerlink, .rst-content h5 .rst-versions .rst-current-version .headerlink, .rst-versions .rst-current-version .rst-content h6 .headerlink, .rst-content h6 .rst-versions .rst-current-version .headerlink, .rst-versions .rst-current-version .rst-content dl dt .headerlink, .rst-content dl dt .rst-versions .rst-current-version .headerlink, .rst-versions .rst-current-version .rst-content p.caption .headerlink, .rst-content p.caption .rst-versions .rst-current-version .headerlink, .rst-versions .rst-current-version .rst-content tt.download span:first-child, .rst-content tt.download .rst-versions .rst-current-version span:first-child, .rst-versions .rst-current-version .rst-content code.download span:first-child, .rst-content code.download .rst-versions .rst-current-version span:first-child, .rst-versions .rst-current-version .icon {
   color: #fcfcfc;
 }
 .rst-versions .rst-current-version .fa-book, .rst-versions .rst-current-version .icon-book {
   float: left;
 }
 .rst-versions .rst-current-version .icon-book {
   float: left;
 }
 .rst-versions .rst-current-version.rst-out-of-date {
   background-color: #E74C3C;
   color: #fff;
 }
 .rst-versions .rst-current-version.rst-active-old-version {
   background-color: #F1C40F;
   color: #000;
 }
 .rst-versions.shift-up .rst-other-versions {
   display: block;
 }
 .rst-versions .rst-other-versions {
   font-size: 90%;
   padding: 12px;
   color: gray;
   display: none;
 }
 .rst-versions .rst-other-versions hr {
   display: block;
   height: 1px;
   border: 0;
   margin: 20px 0;
   padding: 0;
   border-top: solid 1px #413d3d;
 }
 .rst-versions .rst-other-versions dd {
   display: inline-block;
   margin: 0;
 }
 .rst-versions .rst-other-versions dd a {
   display: inline-block;
   padding: 6px;
   color: #fcfcfc;
 }
 .rst-versions.rst-badge {
   width: auto;
   bottom: 20px;
   right: 20px;
   left: auto;
   border: none;
   max-width: 300px;
 }
 .rst-versions.rst-badge .icon-book {
   float: none;
 }
 .rst-versions.rst-badge .fa-book, .rst-versions.rst-badge .icon-book {
   float: none;
 }
 .rst-versions.rst-badge.shift-up .rst-current-version {
   text-align: right;
 }
 .rst-versions.rst-badge.shift-up .rst-current-version .fa-book, .rst-versions.rst-badge.shift-up .rst-current-version .icon-book {
   float: left;
 }
 .rst-versions.rst-badge.shift-up .rst-current-version .icon-book {
   float: left;
 }
 .rst-versions.rst-badge .rst-current-version {
   width: auto;
   height: 30px;
   line-height: 30px;
   padding: 0 6px;
   display: block;
   text-align: center;
 }
 
 @media screen and (max-width: 768px) {
   .rst-versions {
     width: 85%;
     display: none;
   }
   .rst-versions.shift {
     display: block;
   }
 
   img {
     width: 100%;
     height: auto;
   }
 }
 .rst-content img {
   max-width: 100%;
   height: auto !important;
 }
 .rst-content div.figure {
   margin-bottom: 24px;
 }
 .rst-content div.figure p.caption {
   font-style: italic;
 }
 .rst-content div.figure.align-center {
   text-align: center;
 }
 .rst-content .section > img, .rst-content .section > a > img {
   margin-bottom: 24px;
 }
 .rst-content blockquote {
   margin-left: 24px;
   line-height: 24px;
   margin-bottom: 24px;
 }
 .rst-content .note .last, .rst-content .attention .last, .rst-content .caution .last, .rst-content .danger .last, .rst-content .error .last, .rst-content .hint .last, .rst-content .important .last, .rst-content .tip .last, .rst-content .warning .last, .rst-content .seealso .last, .rst-content .admonition-todo .last {
   margin-bottom: 0;
 }
 .rst-content .admonition-title:before {
   margin-right: 4px;
 }
 .rst-content .admonition table {
   border-color: rgba(0, 0, 0, 0.1);
 }
 .rst-content .admonition table td, .rst-content .admonition table th {
   background: transparent !important;
   border-color: rgba(0, 0, 0, 0.1) !important;
 }
 .rst-content .section ol.loweralpha, .rst-content .section ol.loweralpha li {
   list-style: lower-alpha;
 }
 .rst-content .section ol.upperalpha, .rst-content .section ol.upperalpha li {
   list-style: upper-alpha;
 }
 .rst-content .section ol p, .rst-content .section ul p {
   margin-bottom: 12px;
 }
 .rst-content .line-block {
   margin-left: 24px;
 }
 .rst-content .topic-title {
   font-weight: bold;
   margin-bottom: 12px;
 }
 .rst-content .toc-backref {
   color: #404040;
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   <div class="section" id="atom-modify-command">
 <span id="index-0"></span><h1>atom_modify command<a class="headerlink" href="#atom-modify-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>atom_modify keyword values ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>one or more keyword/value pairs may be appended</li>
 <li>keyword = <em>id</em> or <em>map</em> or <em>first</em> or <em>sort</em></li>
 </ul>
 <pre class="literal-block">
 <em>id</em> value = <em>yes</em> or <em>no</em>
-   <em>map</em> value = <em>array</em> or <em>hash</em>
-   <em>first</em> value = group-ID = group whose atoms will appear first in internal atom lists
-   <em>sort</em> values = Nfreq binsize
-     Nfreq = sort atoms spatially every this many time steps
-     binsize = bin size for spatial sorting (distance units)
+<em>map</em> value = <em>array</em> or <em>hash</em>
+<em>first</em> value = group-ID = group whose atoms will appear first in internal atom lists
+<em>sort</em> values = Nfreq binsize
+  Nfreq = sort atoms spatially every this many time steps
+  binsize = bin size for spatial sorting (distance units)
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>atom_modify map hash
 atom_modify map array sort 10000 2.0
 atom_modify first colloid
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Modify certain attributes of atoms defined and stored within LAMMPS,
 in addition to what is specified by the <a class="reference internal" href="atom_style.html"><em>atom_style</em></a>
 command.  The <em>id</em> and <em>map</em> keywords must be specified before a
 simulation box is defined; other keywords can be specified any time.</p>
 <p>The <em>id</em> keyword determines whether non-zero atom IDs can be assigned
 to each atom.  If the value is <em>yes</em>, which is the default, IDs are
 assigned, whether you use the <a class="reference internal" href="create_atoms.html"><em>create atoms</em></a> or
 <a class="reference internal" href="read_data.html"><em>read_data</em></a> or <a class="reference internal" href="read_restart.html"><em>read_restart</em></a>
 commands to initialize atoms.  If the value is <em>no</em> the IDs for all
 atoms are assumed to be 0.</p>
 <p>If atom IDs are used, they must all be positive integers.  They should
 also be unique, though LAMMPS does not check for this.  Typically they
 should also be consecutively numbered (from 1 to Natoms), though this
 is not required.  Molecular <a class="reference internal" href="atom_style.html"><em>atom styles</em></a> are those
 that store bond topology information (styles bond, angle, molecular,
 full).  These styles require atom IDs since the IDs are used to encode
 the topology.  Some other LAMMPS commands also require the use of atom
 IDs.  E.g. some many-body pair styles use them to avoid double
 computation of the I-J interaction between two atoms.</p>
 <p>The only reason not to use atom IDs is if you are running an atomic
 simulation so large that IDs cannot be uniquely assigned.  For a
 default LAMMPS build this limit is 2^31 or about 2 billion atoms.
 However, even in this case, you can use 64-bit atom IDs, allowing 2^63
 or about 9e18 atoms, if you build LAMMPS with the - DLAMMPS_BIGBIG
 switch.  This is described in <a class="reference internal" href="Section_start.html#start-2"><span>Section 2.2</span></a>
 of the manual.  If atom IDs are not used, they must be specified as 0
 for all atoms, e.g. in a data or restart file.</p>
 <p>The <em>map</em> keyword determines how atom ID lookup is done for molecular
 atom styles.  Lookups are performed by bond (angle, etc) routines in
 LAMMPS to find the local atom index associated with a global atom ID.</p>
 <p>When the <em>array</em> value is used, each processor stores a lookup table
 of length N, where N is the largest atom ID in the system.  This is a
 fast, simple method for many simulations, but requires too much memory
 for large simulations.  The <em>hash</em> value uses a hash table to perform
 the lookups.  This can be slightly slower than the <em>array</em> method, but
 its memory cost is proportional to the number of atoms owned by a
 processor, i.e. N/P when N is the total number of atoms in the system
 and P is the number of processors.</p>
 <p>When this setting is not specified in your input script, LAMMPS
 creates a map, if one is needed, as an array or hash.  See the
 discussion of default values below for how LAMMPS chooses which kind
 of map to build.  Note that atomic systems do not normally need to
 create a map.  However, even in this case some LAMMPS commands will
 create a map to find atoms (and then destroy it), or require a
 permanent map.  An example of the former is the <a class="reference internal" href="velocity.html"><em>velocity loop all</em></a> command, which uses a map when looping over all
 atoms and insuring the same velocity values are assigned to an atom
 ID, no matter which processor owns it.</p>
 <p>The <em>first</em> keyword allows a <a class="reference internal" href="group.html"><em>group</em></a> to be specified whose
 atoms will be maintained as the first atoms in each processor&#8217;s list
 of owned atoms.  This in only useful when the specified group is a
 small fraction of all the atoms, and there are other operations LAMMPS
 is performing that will be sped-up significantly by being able to loop
 over the smaller set of atoms.  Otherwise the reordering required by
 this option will be a net slow-down.  The <a class="reference internal" href="neigh_modify.html"><em>neigh_modify include</em></a> and <a class="reference internal" href="comm_modify.html"><em>comm_modify group</em></a>
 commands are two examples of commands that require this setting to
 work efficiently.  Several <a class="reference internal" href="fix.html"><em>fixes</em></a>, most notably time
 integration fixes like <a class="reference internal" href="fix_nve.html"><em>fix nve</em></a>, also take advantage of
 this setting if the group they operate on is the group specified by
 this command.  Note that specifying &#8220;all&#8221; as the group-ID effectively
 turns off the <em>first</em> option.</p>
 <p>It is OK to use the <em>first</em> keyword with a group that has not yet been
 defined, e.g. to use the atom_modify first command at the beginning of
 your input script.  LAMMPS does not use the group until a simullation
 is run.</p>
 <p>The <em>sort</em> keyword turns on a spatial sorting or reordering of atoms
 within each processor&#8217;s sub-domain every <em>Nfreq</em> timesteps.  If
 <em>Nfreq</em> is set to 0, then sorting is turned off.  Sorting can improve
 cache performance and thus speed-up a LAMMPS simulation, as discussed
 in a paper by <a class="reference internal" href="#meloni"><span>(Meloni)</span></a>.  Its efficacy depends on the problem
 size (atoms/processor), how quickly the system becomes disordered, and
 various other factors.  As a general rule, sorting is typically more
 effective at speeding up simulations of liquids as opposed to solids.
 In tests we have done, the speed-up can range from zero to 3-4x.</p>
 <p>Reordering is peformed every <em>Nfreq</em> timesteps during a dynamics run
 or iterations during a minimization.  More precisely, reordering
 occurs at the first reneighboring that occurs after the target
 timestep.  The reordering is performed locally by each processor,
 using bins of the specified <em>binsize</em>.  If <em>binsize</em> is set to 0.0,
 then a binsize equal to half the <a class="reference internal" href="neighbor.html"><em>neighbor</em></a> cutoff
 distance (force cutoff plus skin distance) is used, which is a
 reasonable value.  After the atoms have been binned, they are
 reordered so that atoms in the same bin are adjacent to each other in
 the processor&#8217;s 1d list of atoms.</p>
 <p>The goal of this procedure is for atoms to put atoms close to each
 other in the processor&#8217;s one-dimensional list of atoms that are also
 near to each other spatially.  This can improve cache performance when
 pairwise intereractions and neighbor lists are computed.  Note that if
 bins are too small, there will be few atoms/bin.  Likewise if bins are
 too large, there will be many atoms/bin.  In both cases, the goal of
 cache locality will be undermined.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">Running a simulation with sorting on versus off should
 not change the simulation results in a statistical sense.  However, a
 different ordering will induce round-off differences, which will lead
 to diverging trajectories over time when comparing two simluations.
 Various commands, particularly those which use random numbers
 (e.g. <a class="reference internal" href="velocity.html"><em>velocity create</em></a>, and <a class="reference internal" href="fix_langevin.html"><em>fix langevin</em></a>), may generate (statistically identical)
 results which depend on the order in which atoms are processed.  The
 order of atoms in a <a class="reference internal" href="dump.html"><em>dump</em></a> file will also typically change
 if sorting is enabled.</p>
 </div>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>The <em>first</em> and <em>sort</em> options cannot be used together.  Since sorting
 is on by default, it will be turned off if the <em>first</em> keyword is
 used with a group-ID that is not &#8220;all&#8221;.</p>
 <p><strong>Related commands:</strong> none</p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>By default, <em>id</em> is yes.  By default, atomic systems (no bond topology
 info) do not use a map.  For molecular systems (with bond topology
 info), a map is used.  The default map style is array if no atom ID is
 larger than 1 million, otherwise the default is hash.  By default, a
 &#8220;first&#8221; group is not defined.  By default, sorting is enabled with a
 frequency of 1000 and a binsize of 0.0, which means the neighbor
 cutoff will be used to set the bin size.</p>
 <hr class="docutils" />
 <p id="meloni"><strong>(Meloni)</strong> Meloni, Rosati and Colombo, J Chem Phys, 126, 121102 (2007).</p>
 </div>
 </div>
 
 
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   <div class="section" id="atom-style-command">
 <span id="index-0"></span><h1>atom_style command<a class="headerlink" href="#atom-style-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>atom_style style args
 </pre></div>
 </div>
 <ul class="simple">
 <li>style = <em>angle</em> or <em>atomic</em> or <em>body</em> or <em>bond</em> or <em>charge</em> or <em>dipole</em> or         <em>electron</em> or <em>ellipsoid</em> or <em>full</em> or <em>line</em> or <em>meso</em> or         <em>molecular</em> or <em>peri</em> or <em>sphere</em> or <em>tri</em> or <em>template</em> or <em>hybrid</em></li>
 </ul>
 <pre class="literal-block">
 args = none for any style except <em>body</em> and <em>hybrid</em>
-  <em>body</em> args = bstyle bstyle-args
-    bstyle = style of body particles
-    bstyle-args = additional arguments specific to the bstyle
-                  see the <a class="reference internal" href="body.html"><em>body</em></a> doc page for details
-  <em>template</em> args = template-ID
-    template-ID = ID of molecule template specified in a separate <a class="reference internal" href="molecule.html"><em>molecule</em></a> command
-  <em>hybrid</em> args = list of one or more sub-styles, each with their args
+<em>body</em> args = bstyle bstyle-args
+  bstyle = style of body particles
+  bstyle-args = additional arguments specific to the bstyle
+                see the <a class="reference internal" href="body.html"><em>body</em></a> doc page for details
+<em>template</em> args = template-ID
+  template-ID = ID of molecule template specified in a separate <a class="reference internal" href="molecule.html"><em>molecule</em></a> command
+<em>hybrid</em> args = list of one or more sub-styles, each with their args
 </pre>
 <ul class="simple">
 <li>accelerated styles (with same args) = <em>angle/cuda</em> or <em>angle/kk</em> or <em>atomic/cuda</em> or <em>atomic/kk</em> or <em>bond/kk</em> or <em>charge/cuda</em> or <em>charge/kk</em> or <em>full/cuda</em> or <em>full/kk</em> or <em>molecular/kk</em></li>
 </ul>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>atom_style atomic
 atom_style bond
 atom_style full
 atom_style full/cuda
 atom_style body nparticle 2 10
 atom_style hybrid charge bond
 atom_style hybrid charge body nparticle 2 5
 atom_style template myMols
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Define what style of atoms to use in a simulation.  This determines
 what attributes are associated with the atoms.  This command must be
 used before a simulation is setup via a <a class="reference internal" href="read_data.html"><em>read_data</em></a>,
 <a class="reference internal" href="read_restart.html"><em>read_restart</em></a>, or <a class="reference internal" href="create_box.html"><em>create_box</em></a>
 command.</p>
 <p>Once a style is assigned, it cannot be changed, so use a style general
 enough to encompass all attributes.  E.g. with style <em>bond</em>, angular
 terms cannot be used or added later to the model.  It is OK to use a
 style more general than needed, though it may be slightly inefficient.</p>
 <p>The choice of style affects what quantities are stored by each atom,
 what quantities are communicated between processors to enable forces
 to be computed, and what quantities are listed in the data file read
 by the <a class="reference internal" href="read_data.html"><em>read_data</em></a> command.</p>
 <p>These are the additional attributes of each style and the typical
 kinds of physical systems they are used to model.  All styles store
 coordinates, velocities, atom IDs and types.  See the
 <a class="reference internal" href="read_data.html"><em>read_data</em></a>, <a class="reference internal" href="create_atoms.html"><em>create_atoms</em></a>, and
 <a class="reference internal" href="set.html"><em>set</em></a> commands for info on how to set these various
 quantities.</p>
 <table border="1" class="docutils">
 <colgroup>
 <col width="13%" />
 <col width="50%" />
 <col width="36%" />
 </colgroup>
 <tbody valign="top">
 <tr class="row-odd"><td><em>angle</em></td>
 <td>bonds and angles</td>
 <td>bead-spring polymers with stiffness</td>
 </tr>
 <tr class="row-even"><td><em>atomic</em></td>
 <td>only the default values</td>
 <td>coarse-grain liquids, solids, metals</td>
 </tr>
 <tr class="row-odd"><td><em>body</em></td>
 <td>mass, inertia moments, quaternion, angular momentum</td>
 <td>arbitrary bodies</td>
 </tr>
 <tr class="row-even"><td><em>bond</em></td>
 <td>bonds</td>
 <td>bead-spring polymers</td>
 </tr>
 <tr class="row-odd"><td><em>charge</em></td>
 <td>charge</td>
 <td>atomic system with charges</td>
 </tr>
 <tr class="row-even"><td><em>dipole</em></td>
 <td>charge and dipole moment</td>
 <td>system with dipolar particles</td>
 </tr>
 <tr class="row-odd"><td><em>electron</em></td>
 <td>charge and spin and eradius</td>
 <td>electronic force field</td>
 </tr>
 <tr class="row-even"><td><em>ellipsoid</em></td>
 <td>shape, quaternion, angular momentum</td>
 <td>aspherical particles</td>
 </tr>
 <tr class="row-odd"><td><em>full</em></td>
 <td>molecular + charge</td>
 <td>bio-molecules</td>
 </tr>
 <tr class="row-even"><td><em>line</em></td>
 <td>end points, angular velocity</td>
 <td>rigid bodies</td>
 </tr>
 <tr class="row-odd"><td><em>meso</em></td>
 <td>rho, e, cv</td>
 <td>SPH particles</td>
 </tr>
 <tr class="row-even"><td><em>molecular</em></td>
 <td>bonds, angles, dihedrals, impropers</td>
 <td>uncharged molecules</td>
 </tr>
 <tr class="row-odd"><td><em>peri</em></td>
 <td>mass, volume</td>
 <td>mesocopic Peridynamic models</td>
 </tr>
 <tr class="row-even"><td><em>sphere</em></td>
 <td>diameter, mass, angular velocity</td>
 <td>granular models</td>
 </tr>
 <tr class="row-odd"><td><em>template</em></td>
 <td>template index, template atom</td>
 <td>small molecules with fixed topology</td>
 </tr>
 <tr class="row-even"><td><em>tri</em></td>
 <td>corner points, angular momentum</td>
 <td>rigid bodies</td>
 </tr>
 <tr class="row-odd"><td><em>wavepacket</em></td>
 <td>charge, spin, eradius, etag, cs_re, cs_im</td>
 <td>AWPMD</td>
 </tr>
 </tbody>
 </table>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">It is possible to add some attributes, such as a
 molecule ID, to atom styles that do not have them via the <a class="reference internal" href="fix_property_atom.html"><em>fix property/atom</em></a> command.  This command also
 allows new custom attributes consisting of extra integer or
 floating-point values to be added to atoms.  See the <a class="reference internal" href="fix_property_atom.html"><em>fix property/atom</em></a> doc page for examples of cases
 where this is useful and details on how to initialize, access, and
 output the custom values.</p>
 </div>
 <p>All of the above styles define point particles, except the <em>sphere</em>,
 <em>ellipsoid</em>, <em>electron</em>, <em>peri</em>, <em>wavepacket</em>, <em>line</em>, <em>tri</em>, and
 <em>body</em> styles, which define finite-size particles.  See <a class="reference internal" href="Section_howto.html#howto-14"><span>Section_howto 14</span></a> for an overview of using finite-size
 particle models with LAMMPS.</p>
 <p>All of the point-particle styles assign mass to particles on a
 per-type basis, using the <a class="reference internal" href="mass.html"><em>mass</em></a> command, The finite-size
 particle styles assign mass to individual particles on a per-particle
 basis.</p>
 <p>For the <em>sphere</em> style, the particles are spheres and each stores a
 per-particle diameter and mass.  If the diameter &gt; 0.0, the particle
 is a finite-size sphere.  If the diameter = 0.0, it is a point
 particle.</p>
 <p>For the <em>ellipsoid</em> style, the particles are ellipsoids and each
 stores a flag which indicates whether it is a finite-size ellipsoid or
 a point particle.  If it is an ellipsoid, it also stores a shape
 vector with the 3 diamters of the ellipsoid and a quaternion 4-vector
 with its orientation.</p>
 <p>For the <em>electron</em> style, the particles representing electrons are 3d
 Gaussians with a specified position and bandwidth or uncertainty in
 position, which is represented by the eradius = electron size.</p>
 <p>For the <em>peri</em> style, the particles are spherical and each stores a
 per-particle mass and volume.</p>
 <p>The <em>meso</em> style is for smoothed particle hydrodynamics (SPH)
 particles which store a density (rho), energy (e), and heat capacity
 (cv).</p>
 <p>The <em>wavepacket</em> style is similar to <em>electron</em>, but the electrons may
 consist of several Gaussian wave packets, summed up with coefficients
 cs= (cs_re,cs_im).  Each of the wave packets is treated as a separate
 particle in LAMMPS, wave packets belonging to the same electron must
 have identical <em>etag</em> values.</p>
 <p>For the <em>line</em> style, the particles are idealized line segments and
 each stores a per-particle mass and length and orientation (i.e. the
 end points of the line segment).</p>
 <p>For the <em>tri</em> style, the particles are planar triangles and each
 stores a per-particle mass and size and orientation (i.e. the corner
 points of the triangle).</p>
 <p>The <em>template</em> style allows molecular topolgy (bonds,angles,etc) to be
 defined via a molecule template using the <a class="reference external" href="molecule.txt">molecule</a>
 command.  The template stores one or more molecules with a single copy
 of the topology info (bonds,angles,etc) of each.  Individual atoms
 only store a template index and template atom to identify which
 molecule and which atom-within-the-molecule they represent.  Using the
 <em>template</em> style instead of the <em>bond</em>, <em>angle</em>, <em>molecular</em> styles
 can save memory for systems comprised of a large number of small
 molecules, all of a single type (or small number of types).  See the
 paper by Grime and Voth, in <a class="reference internal" href="#grime"><span>(Grime)</span></a>, for examples of how this
 can be advantageous for large-scale coarse-grained systems.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">When using the <em>template</em> style with a <a class="reference internal" href="molecule.html"><em>molecule template</em></a> that contains multiple molecules, you should
 insure the atom types, bond types, angle_types, etc in all the
 molecules are consistent.  E.g. if one molecule represents H2O and
 another CO2, then you probably do not want each molecule file to
 define 2 atom types and a single bond type, because they will conflict
 with each other when a mixture system of H2O and CO2 molecules is
 defined, e.g. by the <a class="reference internal" href="read_data.html"><em>read_data</em></a> command.  Rather the
 H2O molecule should define atom types 1 and 2, and bond type 1.  And
 the CO2 molecule should define atom types 3 and 4 (or atom types 3 and
 2 if a single oxygen type is desired), and bond type 2.</p>
 </div>
 <p>For the <em>body</em> style, the particles are arbitrary bodies with internal
 attributes defined by the &#8220;style&#8221; of the bodies, which is specified by
 the <em>bstyle</em> argument.  Body particles can represent complex entities,
 such as surface meshes of discrete points, collections of
 sub-particles, deformable objects, etc.</p>
 <p>The <a class="reference internal" href="body.html"><em>body</em></a> doc page descibes the body styles LAMMPS
 currently supports, and provides more details as to the kind of body
 particles they represent.  For all styles, each body particle stores
 moments of inertia and a quaternion 4-vector, so that its orientation
 and position can be time integrated due to forces and torques.</p>
 <p>Note that there may be additional arguments required along with the
 <em>bstyle</em> specification, in the atom_style body command.  These
 arguments are described in the <a class="reference internal" href="body.html"><em>body</em></a> doc page.</p>
 <hr class="docutils" />
 <p>Typically, simulations require only a single (non-hybrid) atom style.
 If some atoms in the simulation do not have all the properties defined
 by a particular style, use the simplest style that defines all the
 needed properties by any atom.  For example, if some atoms in a
 simulation are charged, but others are not, use the <em>charge</em> style.
 If some atoms have bonds, but others do not, use the <em>bond</em> style.</p>
 <p>The only scenario where the <em>hybrid</em> style is needed is if there is no
 single style which defines all needed properties of all atoms.  For
 example, if you want dipolar particles which will rotate due to
 torque, you would need to use &#8220;atom_style hybrid sphere dipole&#8221;.  When
 a hybrid style is used, atoms store and communicate the union of all
 quantities implied by the individual styles.</p>
 <p>When using the <em>hybrid</em> style, you cannot combine the <em>template</em> style
 with another molecular style that stores bond,angle,etc info on a
 per-atom basis.</p>
 <p>LAMMPS can be extended with new atom styles as well as new body
 styles; see <a class="reference internal" href="Section_modify.html"><em>this section</em></a>.</p>
 <hr class="docutils" />
 <p>Styles with a <em>cuda</em> or <em>kk</em> suffix are functionally the same as the
 corresponding style without the suffix.  They have been optimized to
 run faster, depending on your available hardware, as discussed in
 <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a> of the manual.  The
 accelerated styles take the same arguments and should produce the same
 results, except for round-off and precision issues.</p>
 <p>Note that other acceleration packages in LAMMPS, specifically the GPU,
 USER-INTEL, USER-OMP, and OPT packages do not use accelerated atom
 styles.</p>
 <p>The accelerated styles are part of the USER-CUDA and KOKKOS packages
 respectively.  They are only enabled if LAMMPS was built with those
 packages.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section
 for more info.</p>
 <p>You can specify the accelerated styles explicitly in your input script
 by including their suffix, or you can use the <a class="reference internal" href="Section_start.html#start-7"><span>-suffix command-line switch</span></a> when you invoke LAMMPS, or you can
 use the <a class="reference internal" href="suffix.html"><em>suffix</em></a> command in your input script.</p>
 <p>See <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a> of the manual for
 more instructions on how to use the accelerated styles effectively.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>This command cannot be used after the simulation box is defined by a
 <a class="reference internal" href="read_data.html"><em>read_data</em></a> or <a class="reference internal" href="create_box.html"><em>create_box</em></a> command.</p>
 <p>The <em>angle</em>, <em>bond</em>, <em>full</em>, <em>molecular</em>, and <em>template</em> styles are
 part of the MOLECULE package.  The <em>line</em> and <em>tri</em> styles are part
 of the ASPHERE pacakge.  The <em>body</em> style is part of the BODY package.
 The <em>dipole</em> style is part of the DIPOLE package.  The <em>peri</em> style is
 part of the PERI package for Peridynamics.  The <em>electron</em> style is
 part of the USER-EFF package for <a class="reference internal" href="pair_eff.html"><em>electronic force fields</em></a>.  The <em>meso</em> style is part of the USER-SPH
 package for smoothed particle hydrodyanmics (SPH).  See <a class="reference external" href="USER/sph/SPH_LAMMPS_userguide.pdf">this PDF guide</a> to using SPH in LAMMPS.  The
 <em>wavepacket</em> style is part of the USER-AWPMD package for the
 <a class="reference internal" href="pair_awpmd.html"><em>antisymmetrized wave packet MD method</em></a>.  They are
 only enabled if LAMMPS was built with that package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="read_data.html"><em>read_data</em></a>, <a class="reference internal" href="pair_style.html"><em>pair_style</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>atom_style atomic</p>
 <hr class="docutils" />
 <p id="grime"><strong>(Grime)</strong> Grime and Voth, to appear in J Chem Theory &amp; Computation
 (2014).</p>
 </div>
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   <div class="section" id="balance-command">
 <span id="index-0"></span><h1>balance command<a class="headerlink" href="#balance-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>balance thresh style args ... keyword value ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>thresh = imbalance threshhold that must be exceeded to perform a re-balance</li>
 <li>one style/arg pair can be used (or multiple for <em>x</em>,*y*,*z*)</li>
 <li>style = <em>x</em> or <em>y</em> or <em>z</em> or <em>shift</em> or <em>rcb</em></li>
 </ul>
 <pre class="literal-block">
 <em>x</em> args = <em>uniform</em> or Px-1 numbers between 0 and 1
-    <em>uniform</em> = evenly spaced cuts between processors in x dimension
-    numbers = Px-1 ascending values between 0 and 1, Px - # of processors in x dimension
-    <em>x</em> can be specified together with <em>y</em> or <em>z</em>
-  <em>y</em> args = <em>uniform</em> or Py-1 numbers between 0 and 1
-    <em>uniform</em> = evenly spaced cuts between processors in y dimension
-    numbers = Py-1 ascending values between 0 and 1, Py - # of processors in y dimension
-    <em>y</em> can be specified together with <em>x</em> or <em>z</em>
-  <em>z</em> args = <em>uniform</em> or Pz-1 numbers between 0 and 1
-    <em>uniform</em> = evenly spaced cuts between processors in z dimension
-    numbers = Pz-1 ascending values between 0 and 1, Pz - # of processors in z dimension
-    <em>z</em> can be specified together with <em>x</em> or <em>y</em>
-  <em>shift</em> args = dimstr Niter stopthresh
-    dimstr = sequence of letters containing &quot;x&quot; or &quot;y&quot; or &quot;z&quot;, each not more than once
-    Niter = # of times to iterate within each dimension of dimstr sequence
-    stopthresh = stop balancing when this imbalance threshhold is reached
-  <em>rcb</em> args = none
+  <em>uniform</em> = evenly spaced cuts between processors in x dimension
+  numbers = Px-1 ascending values between 0 and 1, Px - # of processors in x dimension
+  <em>x</em> can be specified together with <em>y</em> or <em>z</em>
+<em>y</em> args = <em>uniform</em> or Py-1 numbers between 0 and 1
+  <em>uniform</em> = evenly spaced cuts between processors in y dimension
+  numbers = Py-1 ascending values between 0 and 1, Py - # of processors in y dimension
+  <em>y</em> can be specified together with <em>x</em> or <em>z</em>
+<em>z</em> args = <em>uniform</em> or Pz-1 numbers between 0 and 1
+  <em>uniform</em> = evenly spaced cuts between processors in z dimension
+  numbers = Pz-1 ascending values between 0 and 1, Pz - # of processors in z dimension
+  <em>z</em> can be specified together with <em>x</em> or <em>y</em>
+<em>shift</em> args = dimstr Niter stopthresh
+  dimstr = sequence of letters containing &quot;x&quot; or &quot;y&quot; or &quot;z&quot;, each not more than once
+  Niter = # of times to iterate within each dimension of dimstr sequence
+  stopthresh = stop balancing when this imbalance threshhold is reached
+<em>rcb</em> args = none
 </pre>
 <ul class="simple">
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>out</em></li>
 </ul>
 <pre class="literal-block">
 <em>out</em> value = filename
-    filename = write each processor's sub-domain to a file
+  filename = write each processor's sub-domain to a file
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>balance 0.9 x uniform y 0.4 0.5 0.6
 balance 1.2 shift xz 5 1.1
 balance 1.0 shift xz 5 1.1
 balance 1.1 rcb
 balance 1.0 shift x 20 1.0 out tmp.balance
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>This command adjusts the size and shape of processor sub-domains
 within the simulation box, to attempt to balance the number of
 particles and thus the computational cost (load) evenly across
 processors.  The load balancing is &#8220;static&#8221; in the sense that this
 command performs the balancing once, before or between simulations.
 The processor sub-domains will then remain static during the
 subsequent run.  To perform &#8220;dynamic&#8221; balancing, see the <a class="reference internal" href="fix_balance.html"><em>fix balance</em></a> command, which can adjust processor
 sub-domain sizes and shapes on-the-fly during a <a class="reference internal" href="run.html"><em>run</em></a>.</p>
 <p>Load-balancing is typically only useful if the particles in the
 simulation box have a spatially-varying density distribution.  E.g. a
 model of a vapor/liquid interface, or a solid with an irregular-shaped
 geometry containing void regions.  In this case, the LAMMPS default of
 dividing the simulation box volume into a regular-spaced grid of 3d
 bricks, with one equal-volume sub-domain per procesor, may assign very
 different numbers of particles per processor.  This can lead to poor
 performance when the simulation is run in parallel.</p>
 <p>Note that the <a class="reference internal" href="processors.html"><em>processors</em></a> command allows some control
 over how the box volume is split across processors.  Specifically, for
 a Px by Py by Pz grid of processors, it allows choice of Px, Py, and
 Pz, subject to the constraint that Px * Py * Pz = P, the total number
 of processors.  This is sufficient to achieve good load-balance for
 some problems on some processor counts.  However, all the processor
 sub-domains will still have the same shape and same volume.</p>
 <p>The requested load-balancing operation is only performed if the
 current &#8220;imbalance factor&#8221; in particles owned by each processor
 exceeds the specified <em>thresh</em> parameter.  The imbalance factor is
 defined as the maximum number of particles owned by any processor,
 divided by the average number of particles per processor.  Thus an
 imbalance factor of 1.0 is perfect balance.</p>
 <p>As an example, for 10000 particles running on 10 processors, if the
 most heavily loaded processor has 1200 particles, then the factor is
 1.2, meaning there is a 20% imbalance.  Note that a re-balance can be
 forced even if the current balance is perfect (1.0) be specifying a
 <em>thresh</em> &lt; 1.0.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">Balancing is performed even if the imbalance factor
 does not exceed the <em>thresh</em> parameter if a &#8220;grid&#8221; style is specified
 when the current partitioning is &#8220;tiled&#8221;.  The meaning of &#8220;grid&#8221; vs
 &#8220;tiled&#8221; is explained below.  This is to allow forcing of the
 partitioning to &#8220;grid&#8221; so that the <a class="reference internal" href="comm_style.html"><em>comm_style brick</em></a>
 command can then be used to replace a current <a class="reference internal" href="comm_style.html"><em>comm_style tiled</em></a> setting.</p>
 </div>
 <p>When the balance command completes, it prints statistics about the
 result, including the change in the imbalance factor and the change in
 the maximum number of particles on any processor.  For &#8220;grid&#8221; methods
 (defined below) that create a logical 3d grid of processors, the
 positions of all cutting planes in each of the 3 dimensions (as
 fractions of the box length) are also printed.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">This command attempts to minimize the imbalance
 factor, as defined above.  But depending on the method a perfect
 balance (1.0) may not be achieved.  For example, &#8220;grid&#8221; methods
 (defined below) that create a logical 3d grid cannot achieve perfect
 balance for many irregular distributions of particles.  Likewise, if a
 portion of the system is a perfect lattice, e.g. the intiial system is
 generated by the <a class="reference internal" href="create_atoms.html"><em>create_atoms</em></a> command, then &#8220;grid&#8221;
 methods may be unable to achieve exact balance.  This is because
 entire lattice planes will be owned or not owned by a single
 processor.</p>
 </div>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">The imbalance factor is also an estimate of the
 maximum speed-up you can hope to achieve by running a perfectly
 balanced simulation versus an imbalanced one.  In the example above,
 the 10000 particle simulation could run up to 20% faster if it were
 perfectly balanced, versus when imbalanced.  However, computational
 cost is not strictly proportional to particle count, and changing the
 relative size and shape of processor sub-domains may lead to
 additional computational and communication overheads, e.g. in the PPPM
 solver used via the <a class="reference internal" href="kspace_style.html"><em>kspace_style</em></a> command.  Thus
 you should benchmark the run times of a simulation before and after
 balancing.</p>
 </div>
 <hr class="docutils" />
 <p>The method used to perform a load balance is specified by one of the
 listed styles (or more in the case of <em>x</em>,*y*,*z*), which are
 described in detail below.  There are 2 kinds of styles.</p>
 <p>The <em>x</em>, <em>y</em>, <em>z</em>, and <em>shift</em> styles are &#8220;grid&#8221; methods which produce
 a logical 3d grid of processors.  They operate by changing the cutting
 planes (or lines) between processors in 3d (or 2d), to adjust the
 volume (area in 2d) assigned to each processor, as in the following 2d
 diagram where processor sub-domains are shown and atoms are colored by
 the processor that owns them.  The leftmost diagram is the default
 partitioning of the simulation box across processors (one sub-box for
 each of 16 processors); the middle diagram is after a &#8220;grid&#8221; method
 has been applied.</p>
 <a data-lightbox="group-default"
                    href="_images/balance_uniform.jpg"
                    class=""
                    title=""
                    data-title=""
                    ><img src="_images/balance_uniform.jpg"
                     class="align-center"
                     width="25%"
                     height="auto"
                     alt=""/>
                     </a><a data-lightbox="group-default"
                    href="_images/balance_nonuniform.jpg"
                    class=""
                    title=""
                    data-title=""
                    ><img src="_images/balance_nonuniform.jpg"
                     class="align-center"
                     width="25%"
                     height="auto"
                     alt=""/>
                     </a><a data-lightbox="group-default"
                    href="_images/balance_rcb.jpg"
                    class=""
                    title=""
                    data-title=""
                    ><img src="_images/balance_rcb.jpg"
                     class="align-center"
                     width="25%"
                     height="auto"
                     alt=""/>
                     </a><p>The <em>rcb</em> style is a &#8220;tiling&#8221; method which does not produce a logical
 3d grid of processors.  Rather it tiles the simulation domain with
 rectangular sub-boxes of varying size and shape in an irregular
 fashion so as to have equal numbers of particles in each sub-box, as
 in the rightmost diagram above.</p>
 <p>The &#8220;grid&#8221; methods can be used with either of the
 <a class="reference internal" href="comm_style.html"><em>comm_style</em></a> command options, <em>brick</em> or <em>tiled</em>.  The
 &#8220;tiling&#8221; methods can only be used with <a class="reference internal" href="comm_style.html"><em>comm_style tiled</em></a>.  Note that it can be useful to use a &#8220;grid&#8221;
 method with <a class="reference internal" href="comm_style.html"><em>comm_style tiled</em></a> to return the domain
 partitioning to a logical 3d grid of processors so that &#8220;comm_style
 brick&#8221; can afterwords be specified for subsequent <a class="reference internal" href="run.html"><em>run</em></a>
 commands.</p>
 <p>When a &#8220;grid&#8221; method is specified, the current domain partitioning can
 be either a logical 3d grid or a tiled partitioning.  In the former
 case, the current logical 3d grid is used as a starting point and
 changes are made to improve the imbalance factor.  In the latter case,
 the tiled partitioning is discarded and a logical 3d grid is created
 with uniform spacing in all dimensions.  This becomes the starting
 point for the balancing operation.</p>
 <p>When a &#8220;tiling&#8221; method is specified, the current domain partitioning
 (&#8220;grid&#8221; or &#8220;tiled&#8221;) is ignored, and a new partitioning is computed
 from scratch.</p>
 <hr class="docutils" />
 <p>The <em>x</em>, <em>y</em>, and <em>z</em> styles invoke a &#8220;grid&#8221; method for balancing, as
 described above.  Note that any or all of these 3 styles can be
 specified together, one after the other, but they cannot be used with
 any other style.  This style adjusts the position of cutting planes
 between processor sub-domains in specific dimensions.  Only the
 specified dimensions are altered.</p>
 <p>The <em>uniform</em> argument spaces the planes evenly, as in the left
 diagrams above.  The <em>numeric</em> argument requires listing Ps-1 numbers
 that specify the position of the cutting planes.  This requires
 knowing Ps = Px or Py or Pz = the number of processors assigned by
 LAMMPS to the relevant dimension.  This assignment is made (and the
 Px, Py, Pz values printed out) when the simulation box is created by
 the &#8220;create_box&#8221; or &#8220;read_data&#8221; or &#8220;read_restart&#8221; command and is
 influenced by the settings of the <a class="reference internal" href="processors.html"><em>processors</em></a>
 command.</p>
 <p>Each of the numeric values must be between 0 and 1, and they must be
 listed in ascending order.  They represent the fractional position of
 the cutting place.  The left (or lower) edge of the box is 0.0, and
 the right (or upper) edge is 1.0.  Neither of these values is
 specified.  Only the interior Ps-1 positions are specified.  Thus is
 there are 2 procesors in the x dimension, you specify a single value
 such as 0.75, which would make the left processor&#8217;s sub-domain 3x
 larger than the right processor&#8217;s sub-domain.</p>
 <hr class="docutils" />
 <p>The <em>shift</em> style invokes a &#8220;grid&#8221; method for balancing, as
 described above.  It changes the positions of cutting planes between
 processors in an iterative fashion, seeking to reduce the imbalance
 factor, similar to how the <a class="reference internal" href="fix_balance.html"><em>fix balance shift</em></a>
 command operates.</p>
 <p>The <em>dimstr</em> argument is a string of characters, each of which must be
 an &#8220;x&#8221; or &#8220;y&#8221; or &#8220;z&#8221;.  Eacn character can appear zero or one time,
 since there is no advantage to balancing on a dimension more than
 once.  You should normally only list dimensions where you expect there
 to be a density variation in the particles.</p>
 <p>Balancing proceeds by adjusting the cutting planes in each of the
 dimensions listed in <em>dimstr</em>, one dimension at a time.  For a single
 dimension, the balancing operation (described below) is iterated on up
 to <em>Niter</em> times.  After each dimension finishes, the imbalance factor
 is re-computed, and the balancing operation halts if the <em>stopthresh</em>
 criterion is met.</p>
 <p>A rebalance operation in a single dimension is performed using a
 recursive multisectioning algorithm, where the position of each
 cutting plane (line in 2d) in the dimension is adjusted independently.
 This is similar to a recursive bisectioning for a single value, except
 that the bounds used for each bisectioning take advantage of
 information from neighboring cuts if possible.  At each iteration, the
 count of particles on either side of each plane is tallied.  If the
 counts do not match the target value for the plane, the position of
 the cut is adjusted to be halfway between a low and high bound.  The
 low and high bounds are adjusted on each iteration, using new count
 information, so that they become closer together over time.  Thus as
 the recustion progresses, the count of particles on either side of the
 plane gets closer to the target value.</p>
 <p>Once the rebalancing is complete and final processor sub-domains
 assigned, particles are migrated to their new owning processor, and
 the balance procedure ends.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">At each rebalance operation, the bisectioning for each
 cutting plane (line in 2d) typcially starts with low and high bounds
 separated by the extent of a processor&#8217;s sub-domain in one dimension.
 The size of this bracketing region shrinks by 1/2 every iteration.
 Thus if <em>Niter</em> is specified as 10, the cutting plane will typically
 be positioned to 1 part in 1000 accuracy (relative to the perfect
 target position).  For <em>Niter</em> = 20, it will be accurate to 1 part in
 a million.  Thus there is no need ot set <em>Niter</em> to a large value.
 LAMMPS will check if the threshold accuracy is reached (in a
 dimension) is less iterations than <em>Niter</em> and exit early.  However,
 <em>Niter</em> should also not be set too small, since it will take roughly
 the same number of iterations to converge even if the cutting plane is
 initially close to the target value.</p>
 </div>
 <hr class="docutils" />
 <p>The <em>rcb</em> style invokes a &#8220;tiled&#8221; method for balancing, as described
 above.  It performs a recursive coordinate bisectioning (RCB) of the
 simulation domain. The basic idea is as follows.</p>
 <p>The simulation domain is cut into 2 boxes by an axis-aligned cut in
 the longest dimension, leaving one new box on either side of the cut.
 All the processors are also partitioned into 2 groups, half assigned
 to the box on the lower side of the cut, and half to the box on the
 upper side.  (If the processor count is odd, one side gets an extra
 processor.)  The cut is positioned so that the number of atoms in the
 lower box is exactly the number that the processors assigned to that
 box should own for load balance to be perfect.  This also makes load
 balance for the upper box perfect.  The positioning is done
 iteratively, by a bisectioning method.  Note that counting atoms on
 either side of the cut requires communication between all processors
 at each iteration.</p>
 <p>That is the procedure for the first cut.  Subsequent cuts are made
 recursively, in exactly the same manner.  The subset of processors
 assigned to each box make a new cut in the longest dimension of that
 box, splitting the box, the subset of processsors, and the atoms in
 the box in two.  The recursion continues until every processor is
 assigned a sub-box of the entire simulation domain, and owns the atoms
 in that sub-box.</p>
 <hr class="docutils" />
 <p>The <em>out</em> keyword writes a text file to the specified <em>filename</em> with
 the results of the balancing operation.  The file contains the bounds
 of the sub-domain for each processor after the balancing operation
 completes.  The format of the file is compatible with the
 <a class="reference external" href="pizza">Pizza.py</a> <em>mdump</em> tool which has support for manipulating and
 visualizing mesh files.  An example is shown here for a balancing by 4
 processors for a 2d problem:</p>
 <div class="highlight-python"><div class="highlight"><pre>ITEM: TIMESTEP
 0
 ITEM: NUMBER OF NODES
 16
 ITEM: BOX BOUNDS
 0 10
 0 10
 0 10
 ITEM: NODES
 1 1 0 0 0
 2 1 5 0 0
 3 1 5 5 0
 4 1 0 5 0
 5 1 5 0 0
 6 1 10 0 0
 7 1 10 5 0
 8 1 5 5 0
 9 1 0 5 0
 10 1 5 5 0
 11 1 5 10 0
 12 1 10 5 0
 13 1 5 5 0
 14 1 10 5 0
 15 1 10 10 0
 16 1 5 10 0
 ITEM: TIMESTEP
 0
 ITEM: NUMBER OF SQUARES
 4
 ITEM: SQUARES
 1 1 1 2 3 4
 2 1 5 6 7 8
 3 1 9 10 11 12
 4 1 13 14 15 16
 </pre></div>
 </div>
 <p>The coordinates of all the vertices are listed in the NODES section, 5
 per processor.  Note that the 4 sub-domains share vertices, so there
 will be duplicate nodes in the list.</p>
 <p>The &#8220;SQUARES&#8221; section lists the node IDs of the 4 vertices in a
 rectangle for each processor (1 to 4).</p>
 <p>For a 3d problem, the syntax is similar with 8 vertices listed for
 each processor, instead of 4, and &#8220;SQUARES&#8221; replaced by &#8220;CUBES&#8221;.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>For 2d simulations, the <em>z</em> style cannot be used.  Nor can a &#8220;z&#8221;
 appear in <em>dimstr</em> for the <em>shift</em> style.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="processors.html"><em>processors</em></a>, <a class="reference internal" href="fix_balance.html"><em>fix balance</em></a></p>
 <p><strong>Default:</strong> none</p>
 </div>
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   <div class="section" id="bond-style-command">
 <span id="index-0"></span><h1>bond_style command<a class="headerlink" href="#bond-style-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>bond_style style args
 </pre></div>
 </div>
 <ul class="simple">
 <li>style = <em>none</em> or <em>hybrid</em> or <em>class2</em> or <em>fene</em> or <em>fene/expand</em> or         <em>harmonic</em> or <em>morse</em> or <em>nonlinear</em> or <em>quartic</em></li>
 </ul>
 <pre class="literal-block">
 args = none for any style except <em>hybrid</em>
-  <em>hybrid</em> args = list of one or more styles
+<em>hybrid</em> args = list of one or more styles
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>bond_style harmonic
 bond_style fene
 bond_style hybrid harmonic fene
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Set the formula(s) LAMMPS uses to compute bond interactions between
 pairs of atoms.  In LAMMPS, a bond differs from a pairwise
 interaction, which are set via the <a class="reference internal" href="pair_style.html"><em>pair_style</em></a>
 command.  Bonds are defined between specified pairs of atoms and
 remain in force for the duration of the simulation (unless the bond
 breaks which is possible in some bond potentials).  The list of bonded
 atoms is read in by a <a class="reference internal" href="read_data.html"><em>read_data</em></a> or
 <a class="reference internal" href="read_restart.html"><em>read_restart</em></a> command from a data or restart file.
 By contrast, pair potentials are typically defined between all pairs
 of atoms within a cutoff distance and the set of active interactions
 changes over time.</p>
 <p>Hybrid models where bonds are computed using different bond potentials
 can be setup using the <em>hybrid</em> bond style.</p>
 <p>The coefficients associated with a bond style can be specified in a
 data or restart file or via the <a class="reference internal" href="bond_coeff.html"><em>bond_coeff</em></a> command.</p>
 <p>All bond potentials store their coefficient data in binary restart
 files which means bond_style and <a class="reference internal" href="bond_coeff.html"><em>bond_coeff</em></a> commands
 do not need to be re-specified in an input script that restarts a
 simulation.  See the <a class="reference internal" href="read_restart.html"><em>read_restart</em></a> command for
 details on how to do this.  The one exception is that bond_style
 <em>hybrid</em> only stores the list of sub-styles in the restart file; bond
 coefficients need to be re-specified.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">When both a bond and pair style is defined, the
 <a class="reference internal" href="special_bonds.html"><em>special_bonds</em></a> command often needs to be used to
 turn off (or weight) the pairwise interaction that would otherwise
 exist between 2 bonded atoms.</p>
 </div>
 <p>In the formulas listed for each bond style, <em>r</em> is the distance
 between the 2 atoms in the bond.</p>
 <hr class="docutils" />
 <p>Here is an alphabetic list of bond styles defined in LAMMPS.  Click on
 the style to display the formula it computes and coefficients
 specified by the associated <a class="reference internal" href="bond_coeff.html"><em>bond_coeff</em></a> command.</p>
 <p>Note that there are also additional bond styles submitted by users
 which are included in the LAMMPS distribution.  The list of these with
 links to the individual styles are given in the bond section of <a class="reference internal" href="Section_commands.html#cmd-5"><span>this page</span></a>.</p>
 <ul class="simple">
 <li><a class="reference internal" href="bond_none.html"><em>bond_style none</em></a> - turn off bonded interactions</li>
 <li><a class="reference internal" href="bond_hybrid.html"><em>bond_style hybrid</em></a> - define multiple styles of bond interactions</li>
 <li><a class="reference internal" href="bond_class2.html"><em>bond_style class2</em></a> - COMPASS (class 2) bond</li>
 <li><a class="reference internal" href="bond_fene.html"><em>bond_style fene</em></a> - FENE (finite-extensible non-linear elastic) bond</li>
 <li><a class="reference internal" href="bond_fene_expand.html"><em>bond_style fene/expand</em></a> - FENE bonds with variable size particles</li>
 <li><a class="reference internal" href="bond_harmonic.html"><em>bond_style harmonic</em></a> - harmonic bond</li>
 <li><a class="reference internal" href="bond_morse.html"><em>bond_style morse</em></a> - Morse bond</li>
 <li><a class="reference internal" href="bond_nonlinear.html"><em>bond_style nonlinear</em></a> - nonlinear bond</li>
 <li><a class="reference internal" href="bond_quartic.html"><em>bond_style quartic</em></a> - breakable quartic bond</li>
 <li><a class="reference internal" href="bond_table.html"><em>bond_style table</em></a> - tabulated by bond length</li>
 </ul>
 </div>
 <hr class="docutils" />
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>Bond styles can only be set for atom styles that allow bonds to be
 defined.</p>
 <p>Most bond styles are part of the MOLECULE package.  They are only
 enabled if LAMMPS was built with that package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info on packages.
 The doc pages for individual bond potentials tell if it is part of a
 package.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="bond_coeff.html"><em>bond_coeff</em></a>, <a class="reference internal" href="delete_bonds.html"><em>delete_bonds</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>bond_style none</p>
 </div>
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   <div class="section" id="boundary-command">
 <span id="index-0"></span><h1>boundary command<a class="headerlink" href="#boundary-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>boundary x y z
 </pre></div>
 </div>
 <ul class="simple">
 <li>x,y,z = <em>p</em> or <em>s</em> or <em>f</em> or <em>m</em>, one or two letters</li>
 </ul>
 <pre class="literal-block">
 <em>p</em> is periodic
-  <em>f</em> is non-periodic and fixed
-  <em>s</em> is non-periodic and shrink-wrapped
-  <em>m</em> is non-periodic and shrink-wrapped with a minimum value
+<em>f</em> is non-periodic and fixed
+<em>s</em> is non-periodic and shrink-wrapped
+<em>m</em> is non-periodic and shrink-wrapped with a minimum value
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>boundary p p f
 boundary p fs p
 boundary s f fm
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Set the style of boundaries for the global simulation box in each
 dimension.  A single letter assigns the same style to both the lower
 and upper face of the box.  Two letters assigns the first style to the
 lower face and the second style to the upper face.  The initial size
 of the simulation box is set by the <a class="reference internal" href="read_data.html"><em>read_data</em></a>,
 <a class="reference internal" href="read_restart.html"><em>read_restart</em></a>, or <a class="reference internal" href="create_box.html"><em>create_box</em></a>
 commands.</p>
 <p>The style <em>p</em> means the box is periodic, so that particles interact
 across the boundary, and they can exit one end of the box and re-enter
 the other end.  A periodic dimension can change in size due to
 constant pressure boundary conditions or box deformation (see the <a class="reference internal" href="fix_nh.html"><em>fix npt</em></a> and <a class="reference internal" href="fix_deform.html"><em>fix deform</em></a> commands).  The <em>p</em>
 style must be applied to both faces of a dimension.</p>
 <p>The styles <em>f</em>, <em>s</em>, and <em>m</em> mean the box is non-periodic, so that
 particles do not interact across the boundary and do not move from one
 side of the box to the other.</p>
 <p>For style <em>f</em>, the position of the face is fixed.  If an atom moves
 outside the face it will be deleted on the next timestep that
 reneighboring occurs.  This will typically generate an error unless
 you have set the <a class="reference internal" href="thermo_modify.html"><em>thermo_modify lost</em></a> option to
 allow for lost atoms.</p>
 <p>For style <em>s</em>, the position of the face is set so as to encompass the
 atoms in that dimension (shrink-wrapping), no matter how far they
 move.</p>
 <p>For style <em>m</em>, shrink-wrapping occurs, but is bounded by the value
 specified in the data or restart file or set by the
 <a class="reference internal" href="create_box.html"><em>create_box</em></a> command.  For example, if the upper z
 face has a value of 50.0 in the data file, the face will always be
 positioned at 50.0 or above, even if the maximum z-extent of all the
 atoms becomes less than 50.0.  This can be useful if you start a
 simulation with an empty box or if you wish to leave room on one side
 of the box, e.g. for atoms to evaporate from a surface.</p>
 <p>For triclinic (non-orthogonal) simulation boxes, if the 2nd dimension
 of a tilt factor (e.g. y for xy) is periodic, then the periodicity is
 enforced with the tilt factor offset.  If the 1st dimension is
 shrink-wrapped, then the shrink wrapping is applied to the tilted box
 face, to encompass the atoms.  E.g. for a positive xy tilt, the xlo
 and xhi faces of the box are planes tilting in the +y direction as y
 increases.  These tilted planes are shrink-wrapped around the atoms to
 determine the x extent of the box.</p>
 <p>See <a class="reference internal" href="Section_howto.html#howto-12"><span>Section_howto 12</span></a> of the doc pages
 for a geometric description of triclinic boxes, as defined by LAMMPS,
 and how to transform these parameters to and from other commonly used
 triclinic representations.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>This command cannot be used after the simulation box is defined by a
 <a class="reference internal" href="read_data.html"><em>read_data</em></a> or <a class="reference internal" href="create_box.html"><em>create_box</em></a> command or
 <a class="reference internal" href="read_restart.html"><em>read_restart</em></a> command.  See the
 <a class="reference internal" href="change_box.html"><em>change_box</em></a> command for how to change the simulation
 box boundaries after it has been defined.</p>
 <p>For 2d simulations, the z dimension must be periodic.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p>See the <a class="reference internal" href="thermo_modify.html"><em>thermo_modify</em></a> command for a discussion
 of lost atoms.</p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>boundary p p p
 </pre></div>
 </div>
 </div>
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   <div class="section" id="change-box-command">
 <span id="index-0"></span><h1>change_box command<a class="headerlink" href="#change-box-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>change_box group-ID parameter args ... keyword args ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>group-ID = ID of group of atoms to (optionally) displace</li>
 <li>one or more parameter/arg pairs may be appended</li>
 </ul>
 <pre class="literal-block">
 parameter = <em>x</em> or <em>y</em> or <em>z</em> or <em>xy</em> or <em>xz</em> or <em>yz</em> or <em>boundary</em> or <em>ortho</em> or <em>triclinic</em> or <em>set</em> or <em>remap</em>
   <em>x</em>, <em>y</em>, <em>z</em> args = style value(s)
     style = <em>final</em> or <em>delta</em> or <em>scale</em> or <em>volume</em>
       <em>final</em> values = lo hi
         lo hi = box boundaries after displacement (distance units)
       <em>delta</em> values = dlo dhi
         dlo dhi = change in box boundaries after displacement (distance units)
       <em>scale</em> values = factor
         factor = multiplicative factor for change in box length after displacement
       <em>volume</em> value = none = adjust this dim to preserve volume of system
   <em>xy</em>, <em>xz</em>, <em>yz</em> args = style value
     style = <em>final</em> or <em>delta</em>
       <em>final</em> value = tilt
         tilt = tilt factor after displacement (distance units)
       <em>delta</em> value = dtilt
         dtilt = change in tilt factor after displacement (distance units)
   <em>boundary</em> args = x y z
     x,y,z = <em>p</em> or <em>s</em> or <em>f</em> or <em>m</em>, one or two letters
     <em>p</em> is periodic
     <em>f</em> is non-periodic and fixed
     <em>s</em> is non-periodic and shrink-wrapped
     <em>m</em> is non-periodic and shrink-wrapped with a minimum value
   <em>ortho</em> args = none = change box to orthogonal
   <em>triclinic</em> args = none = change box to triclinic
   <em>set</em> args = none = store state of current box
   <em>remap</em> args = none = remap atom coords from last saved state to current box
 </pre>
 <ul class="simple">
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>units</em></li>
 </ul>
 <pre class="literal-block">
 <em>units</em> value = <em>lattice</em> or <em>box</em>
-    lattice = distances are defined in lattice units
-    box = distances are defined in simulation box units
+  lattice = distances are defined in lattice units
+  box = distances are defined in simulation box units
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>change_box all xy final -2.0 z final 0.0 5.0 boundary p p f remap units box
 change_box all x scale 1.1 y volume z volume remap
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Change the volume and/or shape and/or boundary conditions for the
 simulation box.  Orthogonal simulation boxes have 3 adjustable size
 parameters (x,y,z).  Triclinic (non-orthogonal) simulation boxes have
 6 adjustable size/shape parameters (x,y,z,xy,xz,yz).  Any or all of
 them can be adjusted independently by this command.  Thus it can be
 used to expand or contract a box, or to apply a shear strain to a
 non-orthogonal box.  It can also be used to change the boundary
 conditions for the simulation box, similar to the
 <a class="reference internal" href="boundary.html"><em>boundary</em></a> command.</p>
 <p>The size and shape of the initial simulation box are specified by the
 <a class="reference internal" href="create_box.html"><em>create_box</em></a> or <a class="reference internal" href="read_data.html"><em>read_data</em></a> or
 <a class="reference internal" href="read_restart.html"><em>read_restart</em></a> command used to setup the simulation.
 The size and shape may be altered by subsequent runs, e.g. by use of
 the <a class="reference internal" href="fix_nh.html"><em>fix npt</em></a> or <a class="reference internal" href="fix_deform.html"><em>fix deform</em></a> commands.
 The <a class="reference internal" href="create_box.html"><em>create_box</em></a>, <a class="reference internal" href="read_data.html"><em>read data</em></a>, and
 <a class="reference internal" href="read_restart.html"><em>read_restart</em></a> commands also determine whether the
 simulation box is orthogonal or triclinic and their doc pages explain
 the meaning of the xy,xz,yz tilt factors.</p>
 <p>See <a class="reference internal" href="Section_howto.html#howto-12"><span>Section_howto 12</span></a> of the doc pages
 for a geometric description of triclinic boxes, as defined by LAMMPS,
 and how to transform these parameters to and from other commonly used
 triclinic representations.</p>
 <p>The keywords used in this command are applied sequentially to the
 simulation box and the atoms in it, in the order specified.</p>
 <p>Before the sequence of keywords are invoked, the current box
 size/shape is stored, in case a <em>remap</em> keyword is used to map the
 atom coordinates from a previously stored box size/shape to the
 current one.</p>
 <p>After all the keywords have been processed, any shrink-wrap boundary
 conditions are invoked (see the <a class="reference internal" href="boundary.html"><em>boundary</em></a> command)
 which may change simulation box boundaries, and atoms are migrated to
 new owning processors.</p>
 <p>IMPORTANT_NOTE: This means that you cannot use the change_box command
 to enlarge a shrink-wrapped box, e.g. to make room to insert more
 atoms via the <a class="reference internal" href="create_atoms.html"><em>create_atoms</em></a> command, because the
 simulation box will be re-shrink-wrapped before the change_box command
 completes.  Instead you could do something like this, assuming the
 simulation box is non-periodic and atoms extend from 0 to 20 in all
 dimensions:</p>
 <div class="highlight-python"><div class="highlight"><pre>change_box all x final -10 20
 create_atoms 1 single -5 5 5   # this will fail to insert an atom
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>change_box all x final -10 20 boundary f s s
 create_atoms 1 single -5 5 5
 change_box boundary s s s      # this will work
 </pre></div>
 </div>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">Unlike the earlier &#8220;displace_box&#8221; version of this
 command, atom remapping is NOT performed by default.  This command
 allows remapping to be done in a more general way, exactly when you
 specify it (zero or more times) in the sequence of transformations.
 Thus if you do not use the <em>remap</em> keyword, atom coordinates will not
 be changed even if the box size/shape changes.  If a uniformly
 strained state is desired, the <em>remap</em> keyword should be specified.</p>
 </div>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">It is possible to lose atoms with this command.
 E.g. by changing the box without remapping the atoms, and having atoms
 end up outside of non-periodic boundaries.  It is also possible to
 alter bonds between atoms straddling a boundary in bad ways.  E.g. by
 converting a boundary from periodic to non-periodic.  It is also
 possible when remapping atoms to put them (nearly) on top of each
 other.  E.g. by converting a boundary from non-periodic to periodic.
 All of these will typically lead to bad dynamics and/or generate error
 messages.</p>
 </div>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">The simulation box size/shape can be changed by
 arbitrarily large amounts by this command.  This is not a problem,
 except that the mapping of processors to the simulation box is not
 changed from its initial 3d configuration; see the
 <a class="reference internal" href="processors.html"><em>processors</em></a> command.  Thus, if the box size/shape
 changes dramatically, the mapping of processors to the simulation box
 may not end up as optimal as the initial mapping attempted to be.</p>
 </div>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">Because the keywords used in this command are applied
 one at a time to the simulation box and the atoms in it, care must be
 taken with triclinic cells to avoid exceeding the limits on skew after
 each transformation in the sequence.  If skew is exceeded before the
 final transformation this can be avoided by changing the order of the
 sequence, or breaking the transformation into two or more smaller
 transformations.  For more information on the allowed limits for box
 skew see the discussion on triclinic boxes on <a class="reference internal" href="Section_howto.html#howto-12"><span>this page</span></a>.</p>
 </div>
 <hr class="docutils" />
 <p>For the <em>x</em>, <em>y</em>, and <em>z</em> parameters, this is the meaning of their
 styles and values.</p>
 <p>For style <em>final</em>, the final lo and hi box boundaries of a dimension
 are specified.  The values can be in lattice or box distance units.
 See the discussion of the units keyword below.</p>
 <p>For style <em>delta</em>, plus or minus changes in the lo/hi box boundaries
 of a dimension are specified.  The values can be in lattice or box
 distance units.  See the discussion of the units keyword below.</p>
 <p>For style <em>scale</em>, a multiplicative factor to apply to the box length
 of a dimension is specified.  For example, if the initial box length
 is 10, and the factor is 1.1, then the final box length will be 11.  A
 factor less than 1.0 means compression.</p>
 <p>The <em>volume</em> style changes the specified dimension in such a way that
 the overall box volume remains constant with respect to the operation
 performed by the preceding keyword.  The <em>volume</em> style can only be
 used following a keyword that changed the volume, which is any of the
 <em>x</em>, <em>y</em>, <em>z</em> keywords.  If the preceding keyword &#8220;key&#8221; had a <em>volume</em>
 style, then both it and the current keyword apply to the keyword
 preceding &#8220;key&#8221;.  I.e. this sequence of keywords is allowed:</p>
 <div class="highlight-python"><div class="highlight"><pre>change_box all x scale 1.1 y volume z volume
 </pre></div>
 </div>
 <p>The <em>volume</em> style changes the associated dimension so that the
 overall box volume is unchanged relative to its value before the
 preceding keyword was invoked.</p>
 <p>If the following command is used, then the z box length will shrink by
 the same 1.1 factor the x box length was increased by:</p>
 <div class="highlight-python"><div class="highlight"><pre>change_box all x scale 1.1 z volume
 </pre></div>
 </div>
 <p>If the following command is used, then the y,z box lengths will each
 shrink by sqrt(1.1) to keep the volume constant.  In this case, the
 y,z box lengths shrink so as to keep their relative aspect ratio
 constant:</p>
 <div class="highlight-python"><div class="highlight"><pre>change_box all&quot;x scale 1.1 y volume z volume
 </pre></div>
 </div>
 <p>If the following command is used, then the final box will be a factor
 of 10% larger in x and y, and a factor of 21% smaller in z, so as to
 keep the volume constant:</p>
 <div class="highlight-python"><div class="highlight"><pre>change_box all x scale 1.1 z volume y scale 1.1 z volume
 </pre></div>
 </div>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">For solids or liquids, when one dimension of the box
 is expanded, it may be physically undesirable to hold the other 2 box
 lengths constant since that implies a density change.  For solids,
 adjusting the other dimensions via the <em>volume</em> style may make
 physical sense (just as for a liquid), but may not be correct for
 materials and potentials whose Poisson ratio is not 0.5.</p>
 </div>
 <p>For the <em>scale</em> and <em>volume</em> styles, the box length is expanded or
 compressed around its mid point.</p>
 <hr class="docutils" />
 <p>For the <em>xy</em>, <em>xz</em>, and <em>yz</em> parameters, this is the meaning of their
 styles and values.  Note that changing the tilt factors of a triclinic
 box does not change its volume.</p>
 <p>For style <em>final</em>, the final tilt factor is specified.  The value
 can be in lattice or box distance units.  See the discussion of the
 units keyword below.</p>
 <p>For style <em>delta</em>, a plus or minus change in the tilt factor is
 specified.  The value can be in lattice or box distance units.  See
 the discussion of the units keyword below.</p>
 <p>All of these styles change the xy, xz, yz tilt factors.  In LAMMPS,
 tilt factors (xy,xz,yz) for triclinic boxes are required to be no more
 than half the distance of the parallel box length.  For example, if
 xlo = 2 and xhi = 12, then the x box length is 10 and the xy tilt
 factor must be between -5 and 5.  Similarly, both xz and yz must be
 between -(xhi-xlo)/2 and +(yhi-ylo)/2.  Note that this is not a
 limitation, since if the maximum tilt factor is 5 (as in this
 example), then configurations with tilt = ..., -15, -5, 5, 15, 25,
 ... are all equivalent.  Any tilt factor specified by this command
 must be within these limits.</p>
 <hr class="docutils" />
 <p>The <em>boundary</em> keyword takes arguments that have exactly the same
 meaning as they do for the <a class="reference internal" href="boundary.html"><em>boundary</em></a> command.  In each
 dimension, a single letter assigns the same style to both the lower
 and upper face of the box.  Two letters assigns the first style to the
 lower face and the second style to the upper face.</p>
 <p>The style <em>p</em> means the box is periodic; the other styles mean
 non-periodic. For style <em>f</em>, the position of the face is fixed.  For
 style <em>s</em>, the position of the face is set so as to encompass the
 atoms in that dimension (shrink-wrapping), no matter how far they
 move.  For style <em>m</em>, shrink-wrapping occurs, but is bounded by the
 current box edge in that dimension, so that the box will become no
 smaller.  See the <a class="reference internal" href="boundary.html"><em>boundary</em></a> command for more
 explanation of these style options.</p>
 <p>Note that the &#8220;boundary&#8221; command itself can only be used before the
 simulation box is defined via a <a class="reference internal" href="read_data.html"><em>read_data</em></a> or
 <a class="reference internal" href="create_box.html"><em>create_box</em></a> or <a class="reference internal" href="read_restart.html"><em>read_restart</em></a>
 command.  This command allows the boundary conditions to be changed
 later in your input script.  Also note that the
 <a class="reference internal" href="read_restart.html"><em>read_restart</em></a> will change boundary conditions to
 match what is stored in the restart file.  So if you wish to change
 them, you should use the change_box command after the read_restart
 command.</p>
 <hr class="docutils" />
 <p>The <em>ortho</em> and <em>triclinic</em> keywords convert the simulation box to be
 orthogonal or triclinic (non-orthongonal).  See <a class="reference internal" href="Section_howto.html#howto-13"><span>this section</span></a> for a discussion of how non-orthongal
 boxes are represented in LAMMPS.</p>
 <p>The simulation box is defined as either orthogonal or triclinic when
 it is created via the <a class="reference internal" href="create_box.html"><em>create_box</em></a>,
 <a class="reference internal" href="read_data.html"><em>read_data</em></a>, or <a class="reference internal" href="read_restart.html"><em>read_restart</em></a>
 commands.</p>
 <p>These keywords allow you to toggle the existing simulation box from
 orthogonal to triclinic and vice versa.  For example, an initial
 equilibration simulation can be run in an orthogonal box, the box can
 be toggled to triclinic, and then a <a class="reference internal" href="Section_howto.html#howto-13"><span>non-equilibrium MD (NEMD) simulation</span></a> can be run with deformation
 via the <a class="reference internal" href="fix_deform.html"><em>fix deform</em></a> command.</p>
 <p>If the simulation box is currently triclinic and has non-zero tilt in
 xy, yz, or xz, then it cannot be converted to an orthogonal box.</p>
 <hr class="docutils" />
 <p>The <em>set</em> keyword saves the current box size/shape.  This can be
 useful if you wish to use the <em>remap</em> keyword more than once or if you
 wish it to be applied to an intermediate box size/shape in a sequence
 of keyword operations.  Note that the box size/shape is saved before
 any of the keywords are processed, i.e. the box size/shape at the time
 the create_box command is encountered in the input script.</p>
 <p>The <em>remap</em> keyword remaps atom coordinates from the last saved box
 size/shape to the current box state.  For example, if you stretch the
 box in the x dimension or tilt it in the xy plane via the <em>x</em> and <em>xy</em>
 keywords, then the <em>remap</em> commmand will dilate or tilt the atoms to
 conform to the new box size/shape, as if the atoms moved with the box
 as it deformed.</p>
 <p>Note that this operation is performed without regard to periodic
 boundaries.  Also, any shrink-wrapping of non-periodic boundaries (see
 the <a class="reference internal" href="boundary.html"><em>boundary</em></a> command) occurs after all keywords,
 including this one, have been processed.</p>
 <p>Only atoms in the specified group are remapped.</p>
 <hr class="docutils" />
 <p>The <em>units</em> keyword determines the meaning of the distance units used
 to define various arguments.  A <em>box</em> value selects standard distance
 units as defined by the <a class="reference internal" href="units.html"><em>units</em></a> command, e.g. Angstroms for
 units = real or metal.  A <em>lattice</em> value means the distance units are
 in lattice spacings.  The <a class="reference internal" href="lattice.html"><em>lattice</em></a> command must have
 been previously used to define the lattice spacing.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>If you use the <em>ortho</em> or <em>triclinic</em> keywords, then at the point in
 the input script when this command is issued, no <a class="reference internal" href="dump.html"><em>dumps</em></a> can
 be active, nor can a <a class="reference internal" href="fix_ave_spatial.html"><em>fix ave/spatial</em></a> or <a class="reference internal" href="fix_deform.html"><em>fix deform</em></a> be active.  This is because these commands
 test whether the simulation box is orthogonal when they are first
 issued.  Note that these commands can be used in your script before a
 change_box command is issued, so long as an <a class="reference internal" href="undump.html"><em>undump</em></a> or
 <a class="reference internal" href="unfix.html"><em>unfix</em></a> command is also used to turn them off.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="fix_deform.html"><em>fix deform</em></a>, <a class="reference internal" href="boundary.html"><em>boundary</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The option default is units = lattice.</p>
 </div>
 </div>
 
 
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   <div class="section" id="comm-modify-command">
 <span id="index-0"></span><h1>comm_modify command<a class="headerlink" href="#comm-modify-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>comm_modify keyword value ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>mode</em> or <em>cutoff</em> or <em>group</em> or <em>vel</em></li>
 </ul>
 <pre class="literal-block">
 <em>mode</em> value = <em>single</em> or <em>multi</em> = communicate atoms within a single or multiple distances
-  <em>cutoff</em> value = Rcut (distance units) = communicate atoms from this far away
-  <em>group</em> value = group-ID = only communicate atoms in the group
-  <em>vel</em> value = <em>yes</em> or <em>no</em> = do or do not communicate velocity info with ghost atoms
+<em>cutoff</em> value = Rcut (distance units) = communicate atoms from this far away
+<em>group</em> value = group-ID = only communicate atoms in the group
+<em>vel</em> value = <em>yes</em> or <em>no</em> = do or do not communicate velocity info with ghost atoms
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>comm_modify mode multi
 comm_modify mode multi group solvent
 comm_modify vel yes
 comm_modify cutoff 5.0 vel yes
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>This command sets parameters that affect the inter-processor
 communication of atom information that occurs each timestep as
 coordinates and other properties are exchanged between neighboring
 processors and stored as properties of ghost atoms.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">These options apply to the currently defined comm
 style.  When you specify a <a class="reference internal" href="comm_style.html"><em>comm_style</em></a> command, all
 communication settings are restored to their default values, including
 those previously reset by a comm_modify command.  Thus if your input
 script specifies a comm_style command, you should use the comm_modify
 command after it.</p>
 </div>
 <p>The <em>mode</em> keyword determines whether a single or multiple cutoff
 distances are used to determine which atoms to communicate.</p>
 <p>The default mode is <em>single</em> which means each processor acquires
 information for ghost atoms that are within a single distance from its
 sub-domain.  The distance is the maximum of the neighbor cutoff for
 all atom type pairs.</p>
 <p>For many systems this is an efficient algorithm, but for systems with
 widely varying cutoffs for different type pairs, the <em>multi</em> mode can
 be faster.  In this case, each atom type is assigned its own distance
 cutoff for communication purposes, and fewer atoms will be
 communicated.  See the <a class="reference internal" href="neighbor.html"><em>neighbor multi</em></a> command for a
 neighbor list construction option that may also be beneficial for
 simulations of this kind.</p>
 <p>The <em>cutoff</em> keyword allows you to set a ghost cutoff distance, which
 is the distance from the borders of a processor&#8217;s sub-domain at which
 ghost atoms are acquired from other processors.  By default the ghost
 cutoff = neighbor cutoff = pairwise force cutoff + neighbor skin.  See
 the <a class="reference internal" href="neighbor.html"><em>neighbor</em></a> command for more information about the
 skin distance.  If the specified Rcut is greater than the neighbor
 cutoff, then extra ghost atoms will be acquired.  If it is smaller,
 the ghost cutoff is set to the neighbor cutoff.</p>
 <p>These are simulation scenarios in which it may be useful or even
 necessary to set a ghost cutoff &gt; neighbor cutoff:</p>
 <ul class="simple">
 <li>a single polymer chain with bond interactions, but no pairwise interactions</li>
 <li>bonded interactions (e.g. dihedrals) extend further than the pairwise cutoff</li>
 <li>ghost atoms beyond the pairwise cutoff are needed for some computation</li>
 </ul>
 <p>In the first scenario, a pairwise potential is not defined.  Thus the
 pairwise neighbor cutoff will be 0.0.  But ghost atoms are still
 needed for computing bond, angle, etc interactions between atoms on
 different processors, or when the interaction straddles a periodic
 boundary.</p>
 <p>The appropriate ghost cutoff depends on the <a class="reference internal" href="newton.html"><em>newton bond</em></a>
 setting.  For newton bond <em>off</em>, the distance needs to be the furthest
 distance between any two atoms in the bond, angle, etc.  E.g. the
 distance between 1-4 atoms in a dihedral.  For newton bond <em>on</em>, the
 distance between the central atom in the bond, angle, etc and any
 other atom is sufficient.  E.g. the distance between 2-4 atoms in a
 dihedral.</p>
 <p>In the second scenario, a pairwise potential is defined, but its
 neighbor cutoff is not sufficiently long enough to enable bond, angle,
 etc terms to be computed.  As in the previous scenario, an appropriate
 ghost cutoff should be set.</p>
 <p>In the last scenario, a <a class="reference internal" href="fix.html"><em>fix</em></a> or <a class="reference internal" href="compute.html"><em>compute</em></a> or
 <a class="reference internal" href="pair_style.html"><em>pairwise potential</em></a> needs to calculate with ghost
 atoms beyond the normal pairwise cutoff for some computation it
 performs (e.g. locate neighbors of ghost atoms in a multibody pair
 potential).  Setting the ghost cutoff appropriately can insure it will
 find the needed atoms.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">In these scenarios, if you do not set the ghost cutoff
 long enough, and if there is only one processor in a periodic
 dimension (e.g. you are running in serial), then LAMMPS may &#8220;find&#8221; the
 atom it is looking for (e.g. the partner atom in a bond), that is on
 the far side of the simulation box, across a periodic boundary.  This
 will typically lead to bad dynamics (i.e. the bond length is now the
 simulation box length).  To detect if this is happening, see the
 <a class="reference internal" href="neigh_modify.html"><em>neigh_modify cluster</em></a> command.</p>
 </div>
 <p>The <em>group</em> keyword will limit communication to atoms in the specified
 group.  This can be useful for models where no ghost atoms are needed
 for some kinds of particles.  All atoms (not just those in the
 specified group) will still migrate to new processors as they move.
 The group specified with this option must also be specified via the
 <a class="reference internal" href="atom_modify.html"><em>atom_modify first</em></a> command.</p>
 <p>The <em>vel</em> keyword enables velocity information to be communicated with
 ghost particles.  Depending on the <a class="reference internal" href="atom_style.html"><em>atom_style</em></a>,
 velocity info includes the translational velocity, angular velocity,
 and angular momentum of a particle.  If the <em>vel</em> option is set to
 <em>yes</em>, then ghost atoms store these quantities; if <em>no</em> then they do
 not.  The <em>yes</em> setting is needed by some pair styles which require
 the velocity state of both the I and J particles to compute a pairwise
 I,J interaction.</p>
 <p>Note that if the <a class="reference internal" href="fix_deform.html"><em>fix deform</em></a> command is being used
 with its &#8220;remap v&#8221; option enabled, then the velocities for ghost atoms
 (in the fix deform group) mirrored across a periodic boundary will
 also include components due to any velocity shift that occurs across
 that boundary (e.g. due to dilation or shear).</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <blockquote>
 <div>none</div></blockquote>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="comm_style.html"><em>comm_style</em></a>, <a class="reference internal" href="neighbor.html"><em>neighbor</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The option defauls are mode = single, group = all, cutoff = 0.0, vel =
 no.  The cutoff default of 0.0 means that ghost cutoff = neighbor
 cutoff = pairwise force cutoff + neighbor skin.</p>
 </div>
 </div>
 
 
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   <div class="section" id="compute-angle-local-command">
 <span id="index-0"></span><h1>compute angle/local command<a class="headerlink" href="#compute-angle-local-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>compute ID group-ID angle/local input1 input2 ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="compute.html"><em>compute</em></a> command</li>
 <li>angle/local = style name of this compute command</li>
 <li>one or more keywords may be appended</li>
 <li>keyword = <em>theta</em> or <em>eng</em></li>
 </ul>
 <pre class="literal-block">
 <em>theta</em> = tabulate angles
-  <em>eng</em> = tabulate angle energies
+<em>eng</em> = tabulate angle energies
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>compute 1 all angle/local theta
 compute 1 all angle/local eng theta
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Define a computation that calculates properties of individual angle
 interactions.  The number of datums generated, aggregated across all
 processors, equals the number of angles in the system, modified by the
 group parameter as explained below.</p>
 <p>The local data stored by this command is generated by looping over all
 the atoms owned on a processor and their angles.  An angle will only
 be included if all 3 atoms in the angle are in the specified compute
 group.  Any angles that have been broken (see the
 <a class="reference internal" href="angle_style.html"><em>angle_style</em></a> command) by setting their angle type to
 0 are not included.  Angles that have been turned off (see the <a class="reference internal" href="fix_shake.html"><em>fix shake</em></a> or <a class="reference internal" href="delete_bonds.html"><em>delete_bonds</em></a> commands) by
 setting their angle type negative are written into the file, but their
 energy will be 0.0.</p>
 <p>Note that as atoms migrate from processor to processor, there will be
 no consistent ordering of the entries within the local vector or array
 from one timestep to the next.  The only consistency that is
 guaranteed is that the ordering on a particular timestep will be the
 same for local vectors or arrays generated by other compute commands.
 For example, angle output from the <a class="reference internal" href="compute_property_local.html"><em>compute property/local</em></a> command can be combined
 with data from this command and output by the <a class="reference internal" href="dump.html"><em>dump local</em></a>
 command in a consistent way.</p>
 <p><strong>Output info:</strong></p>
 <p>This compute calculates a local vector or local array depending on the
 number of keywords.  The length of the vector or number of rows in the
 array is the number of angles.  If a single keyword is specified, a
 local vector is produced.  If two or more keywords are specified, a
 local array is produced where the number of columns = the number of
 keywords.  The vector or array can be accessed by any command that
 uses local values from a compute as input.  See <a class="reference internal" href="Section_howto.html#howto-15"><span>this section</span></a> for an overview of LAMMPS output
 options.</p>
 <p>The output for <em>theta</em> will be in degrees.  The output for <em>eng</em> will
 be in energy <a class="reference internal" href="units.html"><em>units</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <blockquote>
 <div>none</div></blockquote>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="dump.html"><em>dump local</em></a>, <a class="reference internal" href="compute_property_local.html"><em>compute property/local</em></a></p>
 <p><strong>Default:</strong> none</p>
 </div>
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   <div class="section" id="compute-body-local-command">
 <span id="index-0"></span><h1>compute body/local command<a class="headerlink" href="#compute-body-local-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>compute ID group-ID body/local input1 input2 ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="compute.html"><em>compute</em></a> command</li>
 <li>body/local = style name of this compute command</li>
 <li>one or more keywords may be appended</li>
 <li>keyword = <em>type</em> or <em>integer</em></li>
 </ul>
 <pre class="literal-block">
 <em>type</em> = atom type of the body particle
-  <em>integer</em> = 1,2,3,etc = index of fields defined by body style
+<em>integer</em> = 1,2,3,etc = index of fields defined by body style
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>compute 1 all body/local type 1 2 3
 compute 1 all body/local 3 6
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Define a computation that calculates properties of individual body
 sub-particles.  The number of datums generated, aggregated across all
 processors, equals the number of body sub-particles plus the number of
 non-body particles in the system, modified by the group parameter as
 explained below.  See <a class="reference internal" href="Section_howto.html#howto-14"><span>Section_howto 14</span></a>
 of the manual and the <a class="reference internal" href="body.html"><em>body</em></a> doc page for more details on
 using body particles.</p>
 <p>The local data stored by this command is generated by looping over all
 the atoms.  An atom will only be included if it is in the group.  If
 the atom is a body particle, then its N sub-particles will be looped
 over, and it will contribute N datums to the count of datums.  If it
 is not a body particle, it will contribute 1 datum.</p>
 <p>For both body particles and non-body particles, the <em>type</em> keyword
 will store the type of the atom.</p>
 <p>The <em>integer</em> keywords mean different things for body and non-body
 particles.  If the atom is not a body particle, only its <em>x</em>, <em>y</em>, <em>z</em>
 coordinates can be referenced, using the <em>integer</em> keywords 1,2,3.
 Note that this means that if you want to access more fields than this
 for body particles, then you cannot include non-body particles in the
 group.</p>
 <p>For a body particle, the <em>integer</em> keywords refer to fields calculated
 by the body style for each sub-particle.  The body style, as specified
 by the <a class="reference internal" href="atom_style.html"><em>atom_style body</em></a>, determines how many fields
 exist and what they are.  See the <a class="reference internal" href="body.html"><em>body</em></a> doc page for
 details of the different styles.</p>
 <p>Here is an example of how to output body information using the <a class="reference internal" href="dump.html"><em>dump local</em></a> command with this compute.  If fields 1,2,3 for the
 body sub-particles are x,y,z coordinates, then the dump file will be
 formatted similar to the output of a <a class="reference internal" href="dump.html"><em>dump atom or custom</em></a>
 command.</p>
 <div class="highlight-python"><div class="highlight"><pre>compute 1 all body/local type 1 2 3
 dump 1 all local 1000 tmp.dump index c_1[1] c_1[2] c_1[3] c_1[4]
 </pre></div>
 </div>
 <p><strong>Output info:</strong></p>
 <p>This compute calculates a local vector or local array depending on the
 number of keywords.  The length of the vector or number of rows in the
 array is the number of datums as described above.  If a single keyword
 is specified, a local vector is produced.  If two or more keywords are
 specified, a local array is produced where the number of columns = the
 number of keywords.  The vector or array can be accessed by any
 command that uses local values from a compute as input.  See <a class="reference internal" href="Section_howto.html#howto-15"><span>this section</span></a> for an overview of LAMMPS output
 options.</p>
 <p>The <a class="reference internal" href="units.html"><em>units</em></a> for output values depend on the body style.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <blockquote>
 <div>none</div></blockquote>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="dump.html"><em>dump local</em></a></p>
 <p><strong>Default:</strong> none</p>
 </div>
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   <div class="section" id="compute-bond-local-command">
 <span id="index-0"></span><h1>compute bond/local command<a class="headerlink" href="#compute-bond-local-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>compute ID group-ID bond/local input1 input2 ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="compute.html"><em>compute</em></a> command</li>
 <li>bond/local = style name of this compute command</li>
 <li>one or more keywords may be appended</li>
 <li>keyword = <em>dist</em> or <em>eng</em></li>
 </ul>
 <pre class="literal-block">
 <em>dist</em> = bond distance
-  <em>eng</em> = bond energy
-  <em>force</em> = bond force
+<em>eng</em> = bond energy
+<em>force</em> = bond force
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>compute 1 all bond/local eng
 compute 1 all bond/local dist eng force
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Define a computation that calculates properties of individual bond
 interactions.  The number of datums generated, aggregated across all
 processors, equals the number of bonds in the system, modified
 by the group parameter as explained below.</p>
 <p>The local data stored by this command is generated by looping over all
 the atoms owned on a processor and their bonds.  A bond will only be
 included if both atoms in the bond are in the specified compute group.
 Any bonds that have been broken (see the <a class="reference internal" href="bond_style.html"><em>bond_style</em></a>
 command) by setting their bond type to 0 are not included.  Bonds that
 have been turned off (see the <a class="reference internal" href="fix_shake.html"><em>fix shake</em></a> or
 <a class="reference internal" href="delete_bonds.html"><em>delete_bonds</em></a> commands) by setting their bond type
 negative are written into the file, but their energy will be 0.0.</p>
 <p>Note that as atoms migrate from processor to processor, there will be
 no consistent ordering of the entries within the local vector or array
 from one timestep to the next.  The only consistency that is
 guaranteed is that the ordering on a particular timestep will be the
 same for local vectors or arrays generated by other compute commands.
 For example, bond output from the <a class="reference internal" href="compute_property_local.html"><em>compute property/local</em></a> command can be combined
 with data from this command and output by the <a class="reference internal" href="dump.html"><em>dump local</em></a>
 command in a consistent way.</p>
 <p>Here is an example of how to do this:</p>
 <div class="highlight-python"><div class="highlight"><pre>compute 1 all property/local batom1 batom2 btype
 compute 2 all bond/local dist eng
 dump 1 all local 1000 tmp.dump index c_1[1] c_1[2] c_1[3] c_2[1] c_2[2]
 </pre></div>
 </div>
 <p><strong>Output info:</strong></p>
 <p>This compute calculates a local vector or local array depending on the
 number of keywords.  The length of the vector or number of rows in the
 array is the number of bonds.  If a single keyword is specified, a
 local vector is produced.  If two or more keywords are specified, a
 local array is produced where the number of columns = the number of
 keywords.  The vector or array can be accessed by any command that
 uses local values from a compute as input.  See <a class="reference internal" href="Section_howto.html#howto-15"><span>this section</span></a> for an overview of LAMMPS output
 options.</p>
 <p>The output for <em>dist</em> will be in distance <a class="reference internal" href="units.html"><em>units</em></a>.  The
 output for <em>eng</em> will be in energy <a class="reference internal" href="units.html"><em>units</em></a>.  The output for
 <em>force</em> will be in force <a class="reference internal" href="units.html"><em>units</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <blockquote>
 <div>none</div></blockquote>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="dump.html"><em>dump local</em></a>, <a class="reference internal" href="compute_property_local.html"><em>compute property/local</em></a></p>
 <p><strong>Default:</strong> none</p>
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   <div class="section" id="compute-chunk-atom-command">
 <span id="index-0"></span><h1>compute chunk/atom command<a class="headerlink" href="#compute-chunk-atom-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>compute ID group-ID chunk/atom style args keyword values ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="compute.html"><em>compute</em></a> command</li>
 <li>chunk/atom = style name of this compute command</li>
 </ul>
 <pre class="literal-block">
 style = <em>bin/1d</em> or <em>bin/2d</em> or <em>bin/3d</em> or <em>type</em> or <em>molecule</em> or <em>compute/fix/variable</em>
   <em>bin/1d</em> args = dim origin delta
     dim = <em>x</em> or <em>y</em> or <em>z</em>
     origin = <em>lower</em> or <em>center</em> or <em>upper</em> or coordinate value (distance units)
     delta = thickness of spatial bins in dim (distance units)
   <em>bin/2d</em> args = dim origin delta dim origin delta
     dim = <em>x</em> or <em>y</em> or <em>z</em>
     origin = <em>lower</em> or <em>center</em> or <em>upper</em> or coordinate value (distance units)
     delta = thickness of spatial bins in dim (distance units)
   <em>bin/3d</em> args = dim origin delta dim origin delta dim origin delta
     dim = <em>x</em> or <em>y</em> or <em>z</em>
     origin = <em>lower</em> or <em>center</em> or <em>upper</em> or coordinate value (distance units)
     delta = thickness of spatial bins in dim (distance units)
   <em>type</em> args = none
   <em>molecule</em> args = none
   <em>compute/fix/variable</em> = c_ID, c_ID[I], f_ID, f_ID[I], v_name with no args
     c_ID = per-atom vector calculated by a compute with ID
     c_ID[I] = Ith column of per-atom array calculated by a compute with ID
     f_ID = per-atom vector calculated by a fix with ID
     f_ID[I] = Ith column of per-atom array calculated by a fix with ID
     v_name = per-atom vector calculated by an atom-style variable with name
 </pre>
 <ul class="simple">
 <li>zero or more keyword/values pairs may be appended</li>
 <li>keyword = <em>region</em> or <em>nchunk</em> or <em>static</em> or <em>compress</em> or <em>bound</em> or <em>discard</em> or <em>units</em></li>
 </ul>
 <pre class="literal-block">
 <em>region</em> value = region-ID
-    region-ID = ID of region atoms must be in to be part of a chunk
-  <em>nchunk</em> value = <em>once</em> or <em>every</em>
-    once = only compute the number of chunks once
-    every = re-compute the number of chunks whenever invoked
-  <em>limit</em> values = 0 or Nc max or Nc exact
-    0 = no limit on the number of chunks
-    Nc max = limit number of chunks to be &lt;= Nc
-    Nc exact = set number of chunks to exactly Nc
-  <em>ids</em> value = <em>once</em> or <em>nfreq</em> or <em>every</em>
-    once = assign chunk IDs to atoms only once, they persist thereafter
-    nfreq = assign chunk IDs to atoms only once every Nfreq steps (if invoked by <a class="reference internal" href="fix_ave_chunk.html"><em>fix ave/chunk</em></a> which sets Nfreq)
-    every = assign chunk IDs to atoms whenever invoked
-  <em>compress</em> value = <em>yes</em> or <em>no</em>
-    yes = compress chunk IDs to eliminate IDs with no atoms
-    no = do not compress chunk IDs even if some IDs have no atoms
-  <em>discard</em> value = <em>yes</em> or <em>no</em> or <em>mixed</em>
-    yes = discard atoms with out-of-range chunk IDs by assigning a chunk ID = 0
-    no = keep atoms with out-of-range chunk IDs by assigning a valid chunk ID
-    mixed = keep or discard such atoms according to spatial binning rule
-  <em>bound</em> values = x/y/z lo hi
-    x/y/z = <em>x</em> or <em>y</em> or <em>z</em> to bound sptial bins in this dimension
-    lo = <em>lower</em> or coordinate value (distance units)
-    hi = <em>upper</em> or coordinate value (distance units)
-  <em>units</em> value = <em>box</em> or <em>lattice</em> or <em>reduced</em>
+  region-ID = ID of region atoms must be in to be part of a chunk
+<em>nchunk</em> value = <em>once</em> or <em>every</em>
+  once = only compute the number of chunks once
+  every = re-compute the number of chunks whenever invoked
+<em>limit</em> values = 0 or Nc max or Nc exact
+  0 = no limit on the number of chunks
+  Nc max = limit number of chunks to be &lt;= Nc
+  Nc exact = set number of chunks to exactly Nc
+<em>ids</em> value = <em>once</em> or <em>nfreq</em> or <em>every</em>
+  once = assign chunk IDs to atoms only once, they persist thereafter
+  nfreq = assign chunk IDs to atoms only once every Nfreq steps (if invoked by <a class="reference internal" href="fix_ave_chunk.html"><em>fix ave/chunk</em></a> which sets Nfreq)
+  every = assign chunk IDs to atoms whenever invoked
+<em>compress</em> value = <em>yes</em> or <em>no</em>
+  yes = compress chunk IDs to eliminate IDs with no atoms
+  no = do not compress chunk IDs even if some IDs have no atoms
+<em>discard</em> value = <em>yes</em> or <em>no</em> or <em>mixed</em>
+  yes = discard atoms with out-of-range chunk IDs by assigning a chunk ID = 0
+  no = keep atoms with out-of-range chunk IDs by assigning a valid chunk ID
+  mixed = keep or discard such atoms according to spatial binning rule
+<em>bound</em> values = x/y/z lo hi
+  x/y/z = <em>x</em> or <em>y</em> or <em>z</em> to bound sptial bins in this dimension
+  lo = <em>lower</em> or coordinate value (distance units)
+  hi = <em>upper</em> or coordinate value (distance units)
+<em>units</em> value = <em>box</em> or <em>lattice</em> or <em>reduced</em>
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>compute 1 all chunk/atom type
 compute 1 all chunk/atom bin/1d z lower 0.02 units reduced
 compute 1 all chunk/atom bin/2d z lower 1.0 y 0.0 2.5
 compute 1 all chunk/atom molecule region sphere nchunk once ids once compress yes
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Define a computation that calculates an integer chunk ID from 1 to
 Nchunk for each atom in the group.  Values of chunk IDs are determined
 by the <em>style</em> of chunk, which can be based on atom type or molecule
 ID or spatial binning or a per-atom property or value calculated by
 another <a class="reference internal" href="compute.html"><em>compute</em></a>, <a class="reference internal" href="fix.html"><em>fix</em></a>, or <a class="reference internal" href="variable.html"><em>atom-style variable</em></a>.  Per-atom chunk IDs can be used by other
 computes with &#8220;chunk&#8221; in their style name, such as <a class="reference internal" href="compute_com_chunk.html"><em>compute com/chunk</em></a> or <a class="reference internal" href="compute_msd_chunk.html"><em>compute msd/chunk</em></a>.  Or they can be used by the <a class="reference internal" href="fix_ave_chunk.html"><em>fix ave/chunk</em></a> command to sum and time average a
 variety of per-atom properties over the atoms in each chunk.  Or they
 can simply be accessed by any command that uses per-atom values from a
 compute as input, as discussed in <a class="reference internal" href="Section_howto.html#howto-15"><span>Section_howto 15</span></a>.</p>
 <p>See <a class="reference internal" href="Section_howto.html#howto-23"><span>Section_howto 23</span></a> for an overview of
 how this compute can be used with a variety of other commands to
 tabulate properties of a simulation.  The howto section gives several
 examples of input script commands that can be used to calculate
 interesting properties.</p>
 <p>Conceptually it is important to realize that this compute does two
 simple things.  First, it sets the value of <em>Nchunk</em> = the number of
 chunks, which can be a constant value or change over time.  Second, it
 assigns each atom to a chunk via a chunk ID.  Chunk IDs range from 1
 to <em>Nchunk</em> inclusive; some chunks may have no atoms assigned to them.
 Atoms that do not belong to any chunk are assigned a value of 0.  Note
 that the two operations are not always performed together.  For
 example, spatial bins can be setup once (which sets <em>Nchunk</em>), and
 atoms assigned to those bins many times thereafter (setting their
 chunk IDs).</p>
 <p>All other commands in LAMMPS that use chunk IDs assume there are
 <em>Nchunk</em> number of chunks, and that every atom is assigned to one of
 those chunks, or not assigned to any chunk.</p>
 <p>There are many options for specifying for how and when <em>Nchunk</em> is
 calculated, and how and when chunk IDs are assigned to atoms.  The
 details depend on the chunk <em>style</em> and its <em>args</em>, as well as
 optional keyword settings.  They can also depend on whether a <a class="reference internal" href="fix_ave_chunk.html"><em>fix ave/chunk</em></a> command is using this compute, since
 that command requires <em>Nchunk</em> to remain static across windows of
 timesteps it specifies, while it accumulates per-chunk averages.</p>
 <p>The details are described below.</p>
 <p>The different chunk styles operate as follows.  For each style, how it
 calculates <em>Nchunk</em> and assigns chunk IDs to atoms is explained.  Note
 that using the optional keywords can change both of those actions, as
 described further below where the keywords are discussed.</p>
 <hr class="docutils" />
 <p>The <em>binning</em> styles perform a spatial binning of atoms, and assign an
 atom the chunk ID corresponding to the bin number it is in.  <em>Nchunk</em>
 is set to the number of bins, which can change if the simulation box
 size changes.</p>
 <p>The <em>bin/1d</em>, <em>bin/2d</em>, and <em>bin/3d</em> styles define bins as 1d layers
 (slabs), 2d pencils, or 3d boxes.  The <em>dim</em>, <em>origin</em>, and <em>delta</em>
 settings are specified 1, 2, or 3 times.  For 2d or 3d bins, there is
 no restriction on specifying dim = x before dim = y or z, or dim = y
 before dim = z.  Bins in a particular <em>dim</em> have a bin size in that
 dimension given by <em>delta</em>.  In each dimension, bins are defined
 relative to a specified <em>origin</em>, which may be the lower/upper edge of
 the simulation box (in that dimension), or its center point, or a
 specified coordinate value.  Starting at the origin, sufficient bins
 are created in both directions to completely span the simulation box
 or the bounds specified by the optional <em>bounds</em> keyword.</p>
 <p>For orthogonal simulation boxes, the bins are layers, pencils, or
 boxes aligned with the xyz coordinate axes.  For triclinic
 (non-orthogonal) simulation boxes, the bin faces are parallel to the
 tilted faces of the simulation box.  See <a class="reference internal" href="Section_howto.html#howto-12"><span>this section</span></a> of the manual for a discussion of
 the geometry of triclinic boxes in LAMMPS.  As described there, a
 tilted simulation box has edge vectors a,b,c.  In that nomenclature,
 bins in the x dimension have faces with normals in the &#8220;b&#8221; cross &#8220;c&#8221;
 direction.  Bins in y have faces normal to the &#8220;a&#8221; cross &#8220;c&#8221;
 direction.  And bins in z have faces normal to the &#8220;a&#8221; cross &#8220;b&#8221;
 direction.  Note that in order to define the size and position of
 these bins in an unambiguous fashion, the <em>units</em> option must be set
 to <em>reduced</em> when using a triclinic simulation box, as noted below.</p>
 <p>The meaning of <em>origin</em> and <em>delta</em> for triclinic boxes is as follows.
 Consider a triclinic box with bins that are 1d layers or slabs in the
 x dimension.  No matter how the box is tilted, an <em>origin</em> of 0.0
 means start layers at the lower &#8220;b&#8221; cross &#8220;c&#8221; plane of the simulation
 box and an <em>origin</em> of 1.0 means to start layers at the upper &#8220;b&#8221;
 cross &#8220;c&#8221; face of the box.  A <em>delta</em> value of 0.1 in <em>reduced</em> units
 means there will be 10 layers from 0.0 to 1.0, regardless of the
 current size or shape of the simulation box.</p>
 <p>The created bins (and hence the chunk IDs) are numbered consecutively
 from 1 to the number of bins = <em>Nchunk</em>.  For 2d and 3d bins, the
 numbering varies most rapidly in the first dimension (which could be
 x, y, or z), next rapidly in the 2nd dimension, and most slowly in the
 3rd dimension.</p>
 <p>Each time this compute is invoked, each atom is mapped to a bin based
 on its current position.  Note that between reneighboring timesteps,
 atoms can move outside the current simulation box.  If the box is
 periodic (in that dimension) the atom is remapping into the periodic
 box for purposes of binning.  If the box in not periodic, the atom may
 have moved outside the bounds of all bins.  If an atom is not inside
 any bin, the <em>discard</em> keyword is used to determine how a chunk ID is
 assigned to the atom.</p>
 <hr class="docutils" />
 <p>The <em>type</em> style uses the atom type as the chunk ID.  <em>Nchunk</em> is set
 to the number of atom types defined for the simulation, e.g. via the
 <a class="reference internal" href="create_box.html"><em>create_box</em></a> or <a class="reference internal" href="read_data.html"><em>read_data</em></a> commands.</p>
 <hr class="docutils" />
 <p>The <em>molecule</em> style uses the molecule ID of each atom as its chunk
 ID.  <em>Nchunk</em> is set to the largest chunk ID.  Note that this excludes
 molecule IDs for atoms which are not in the specified group or
 optional region.</p>
 <p>There is no requirement that all atoms in a particular molecule are
 assigned the same chunk ID (zero or non-zero), though you probably
 want that to be the case, if you wish to compute a per-molecule
 property.  LAMMPS will issue a warning if that is not the case, but
 only the first time that <em>Nchunk</em> is calculated.</p>
 <p>Note that atoms with a molecule ID = 0, which may be non-molecular
 solvent atoms, have an out-of-range chunk ID.  These atoms are
 discarded (not assigned to any chunk) or assigned to <em>Nchunk</em>,
 depending on the value of the <em>discard</em> keyword.</p>
 <hr class="docutils" />
 <p>The <em>compute/fix/variable</em> styles set the chunk ID of each atom based
 on a quantity calculated and stored by a compute, fix, or variable.
 In each case, it must be a per-atom quantity.  In each case the
 referenced floating point values are converted to an integer chunk ID
 as follows.  The floating point value is truncated (rounded down) to
 an integer value.  If the integer value is &lt;= 0, then a chunk ID of 0
 is assigned to the atom.  If the integer value is &gt; 0, it becomes the
 chunk ID to the atom.  <em>Nchunk</em> is set to the largest chunk ID.  Note
 that this excludes atoms which are not in the specified group or
 optional region.</p>
 <p>If the style begins with &#8220;<a href="#id1"><span class="problematic" id="id2">c_</span></a>&#8221;, a compute ID must follow which has been
 previously defined in the input script.  If no bracketed integer is
 appended, the per-atom vector calculated by the compute is used.  If a
 bracketed integer is appended, the Ith column of the per-atom array
 calculated by the compute is used.  Users can also write code for
 their own compute styles and <a class="reference internal" href="Section_modify.html"><em>add them to LAMMPS</em></a>.</p>
 <p>If the style begins with &#8220;<a href="#id3"><span class="problematic" id="id4">f_</span></a>&#8221;, a fix ID must follow which has been
 previously defined in the input script.  If no bracketed integer is
 appended, the per-atom vector calculated by the fix is used.  If a
 bracketed integer is appended, the Ith column of the per-atom array
 calculated by the fix is used.  Note that some fixes only produce
 their values on certain timesteps, which must be compatible with the
 timestep on which this compute accesses the fix, else an error
 results.  Users can also write code for their own fix styles and <a class="reference internal" href="Section_modify.html"><em>add them to LAMMPS</em></a>.</p>
 <p>If a value begins with &#8220;<a href="#id5"><span class="problematic" id="id6">v_</span></a>&#8221;, a variable name for an <em>atom</em> or
 <em>atomfile</em> style <a class="reference internal" href="variable.html"><em>variable</em></a> must follow which has been
 previously defined in the input script.  Variables of style <em>atom</em> can
 reference thermodynamic keywords and various per-atom attributes, or
 invoke other computes, fixes, or variables when they are evaluated, so
 this is a very general means of generating per-atom quantities to
 treat as a chunk ID.</p>
 <p>Normally, <em>Nchunk</em> = the number of chunks, is re-calculated every time
 this fix is invoked, though the value may or may not change.  As
 explained below, the <em>nchunk</em> keyword can be set to <em>once</em> which means
 <em>Nchunk</em> will never change.</p>
 <p>If a <a class="reference internal" href="fix_ave_chunk.html"><em>fix ave/chunk</em></a> command uses this compute, it
 can also turn off the re-calculation of <em>Nchunk</em> for one or more
 windows of timesteps.  The extent of the windows, during which Nchunk
 is held constant, are determined by the <em>Nevery</em>, <em>Nrepeat</em>, <em>Nfreq</em>
 values and the <em>ave</em> keyword setting that are used by the <a class="reference internal" href="fix_ave_chunk.html"><em>fix ave/chunk</em></a> command.</p>
 <p>Specifically, if <em>ave</em> = <em>one</em>, then for each span of <em>Nfreq</em>
 timesteps, <em>Nchunk</em> is held constant between the first timestep when
 averaging is done (within the Nfreq-length window), and the last
 timestep when averaging is done (multiple of Nfreq).  If <em>ave</em> =
 <em>running</em> or <em>window</em>, then <em>Nchunk</em> is held constant forever,
 starting on the first timestep when the <a class="reference internal" href="fix_ave_chunk.html"><em>fix ave/chunk</em></a> command invokes this compute.</p>
 <p>Note that multiple <a class="reference internal" href="fix_ave_chunk.html"><em>fix ave/chunk</em></a> commands can use
 the same compute chunk/atom compute.  However, the time windows they
 induce for holding <em>Nchunk</em> constant must be identical, else an error
 will be generated.</p>
 <p>The various optional keywords operate as follows.  Note that some of
 them function differently or are ignored by different chunk styles.
 Some of them also have different default values, depending on
 the chunk style, as listed below.</p>
 <p>The <em>region</em> keyword applies to all chunk styles.  If used, an atom
 must be in both the specified group and the specified geometric
 <a class="reference internal" href="region.html"><em>region</em></a> to be assigned to a chunk.</p>
 <hr class="docutils" />
 <p>The <em>nchunk</em> keyword applies to all chunk styles.  It specifies how
 often <em>Nchunk</em> is recalculated, which in turn can affect the chunk IDs
 assigned to individual atoms.</p>
 <p>If <em>nchunk</em> is set to <em>once</em>, then <em>Nchunk</em> is only calculated once,
 the first time this compute is invoked.  If <em>nchunk</em> is set to
 <em>every</em>, then <em>Nchunk</em> is re-calculated every time the compute is
 invoked.  Note that, as described above, the use of this compute
 by the <a class="reference internal" href="fix_ave_chunk.html"><em>fix ave/chunk</em></a> command can override
 the <em>every</em> setting.</p>
 <p>The default values for <em>nchunk</em> are listed below and depend on the
 chunk style and other system and keyword settings.  They attempt to
 represent typical use cases for the various chunk styles.  The
 <em>nchunk</em> value can always be set explicitly if desired.</p>
 <hr class="docutils" />
 <p>The <em>limit</em> keyword can be used to limit the calculated value of
 <em>Nchunk</em> = the number of chunks.  The limit is applied each time
 <em>Nchunk</em> is calculated, which also limits the chunk IDs assigned to
 any atom.  The <em>limit</em> keyword is used by all chunk styles except the
 <em>binning</em> styles, which ignore it.  This is because the number of bins
 can be tailored using the <em>bound</em> keyword (described below) which
 effectively limits the size of <em>Nchunk</em>.</p>
 <p>If <em>limit</em> is set to <em>Nc</em> = 0, then no limit is imposed on <em>Nchunk</em>,
 though the <em>compress</em> keyword can still be used to reduce <em>Nchunk</em>, as
 described below.</p>
 <p>If <em>Nc</em> &gt; 0, then the effect of the <em>limit</em> keyword depends on whether
 the <em>compress</em> keyword is also used with a setting of <em>yes</em>, and
 whether the <em>compress</em> keyword is specified before the <em>limit</em> keyword
 or after.</p>
 <p>In all cases, <em>Nchunk</em> is first calculated in the usual way for each
 chunk style, as described above.</p>
 <p>First, here is what occurs if <em>compress yes</em> is not set.  If <em>limit</em>
 is set to <em>Nc max</em>, then <em>Nchunk</em> is reset to the smaller of <em>Nchunk</em>
 and <em>Nc</em>.  If <em>limit</em> is set to <em>Nc exact</em>, then <em>Nchunk</em> is reset to
 <em>Nc</em>, whether the original <em>Nchunk</em> was larger or smaller than <em>Nc</em>.
 If <em>Nchunk</em> shrank due to the <em>limit</em> setting, then atom chunk IDs &gt;
 <em>Nchunk</em> will be reset to 0 or <em>Nchunk</em>, depending on the setting of
 the <em>discard</em> keyword.  If <em>Nchunk</em> grew, there will simply be some
 chunks with no atoms assigned to them.</p>
 <p>If <em>compress yes</em> is set, and the <em>compress</em> keyword comes before the
 <em>limit</em> keyword, the compression operation is performed first, as
 described below, which resets <em>Nchunk</em>.  The <em>limit</em> keyword is then
 applied to the new <em>Nchunk</em> value, exactly as described in the
 preceeding paragraph.  Note that in this case, all atoms will end up
 with chunk IDs &lt;= <em>Nc</em>, but their original values (e.g. molecule ID or
 compute/fix/variable value) may have been &gt; <em>Nc</em>, because of the
 compression operation.</p>
 <p>If <em>compress yes</em> is set, and the <em>compress</em> keyword comes after the
 <em>limit</em> keyword, then the <em>limit</em> value of <em>Nc</em> is applied first to
 the uncompressed value of <em>Nchunk</em>, but only if <em>Nc</em> &lt; <em>Nchunk</em>
 (whether <em>Nc max</em> or <em>Nc exact</em> is used).  This effectively means all
 atoms with chunk IDs &gt; <em>Nc</em> have their chunk IDs reset to 0 or <em>Nc</em>,
 depending on the setting of the <em>discard</em> keyword.  The compression
 operation is then performed, which may shrink <em>Nchunk</em> further.  If
 the new <em>Nchunk</em> &lt; <em>Nc</em> and <em>limit</em> = <em>Nc exact</em> is specified, then
 <em>Nchunk</em> is reset to <em>Nc</em>, which results in extra chunks with no atoms
 assigned to them.  Note that in this case, all atoms will end up with
 chunk IDs &lt;= <em>Nc</em>, and their original values (e.g. molecule ID or
 compute/fix/variable value) will also have been &lt;= <em>Nc</em>.</p>
 <hr class="docutils" />
 <p>The <em>ids</em> keyword applies to all chunk styles.  If the setting is
 <em>once</em> then the chunk IDs assigned to atoms the first time this
 compute is invoked will be permanent, and never be re-computed.</p>
 <p>If the setting is <em>nfreq</em> and if a <a class="reference internal" href="fix_ave_chunk.html"><em>fix ave/chunk</em></a>
 command is using this compute, then in each of the <em>Nchunk</em> = constant
 time windows (discussed above), the chunk ID&#8217;s assigned to atoms on
 the first step of the time window will persist until the end of the
 time window.</p>
 <p>If the setting is <em>every</em>, which is the default, then chunk IDs are
 re-calculated on any timestep this compute is invoked.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">If you want the persistent chunk-IDs calculated by
 this compute to be continuous when running from a <a class="reference internal" href="read_restart.html"><em>restart file</em></a>, then you should use the same ID for this
 compute, as in the original run.  This is so that the fix this compute
 creates to store per-atom quantities will also have the same ID, and
 thus be initialized correctly with chunk IDs from the restart file.</p>
 </div>
 <hr class="docutils" />
 <p>The <em>compress</em> keyword applies to all chunk styles and affects how
 <em>Nchunk</em> is calculated, which in turn affects the chunk IDs assigned
 to each atom.  It is useful for converting a &#8220;sparse&#8221; set of chunk IDs
 (with many IDs that have no atoms assigned to them), into a &#8220;dense&#8221;
 set of IDs, where every chunk has one or more atoms assigned to it.</p>
 <p>Two possible use cases are as follows.  If a large simulation box is
 mostly empty space, then the <em>binning</em> style may produce many bins
 with no atoms.  If <em>compress</em> is set to <em>yes</em>, only bins with atoms
 will be contribute to <em>Nchunk</em>.  Likewise, the <em>molecule</em> or
 <em>compute/fix/variable</em> styles may produce large <em>Nchunk</em> values.  For
 example, the <a class="reference internal" href="compute_cluster_atom.html"><em>compute cluster/atom</em></a> command
 assigns every atom an atom ID for one of the atoms it is clustered
 with.  For a million-atom system with 5 clusters, there would only be
 5 unique chunk IDs, but the largest chunk ID might be 1 million,
 resulting in <em>Nchunk</em> = 1 million.  If <em>compress</em> is set to <em>yes</em>,
 <em>Nchunk</em> will be reset to 5.</p>
 <p>If <em>compress</em> is set to <em>no</em>, which is the default, no compression is
 done.  If it is set to <em>yes</em>, all chunk IDs with no atoms are removed
 from the list of chunk IDs, and the list is sorted.  The remaining
 chunk IDs are renumbered from 1 to <em>Nchunk</em> where <em>Nchunk</em> is the new
 length of the list.  The chunk IDs assigned to each atom reflect
 the new renumbering from 1 to <em>Nchunk</em>.</p>
 <p>The original chunk IDs (before renumbering) can be accessed by the
 <a class="reference internal" href="compute_property_chunk.html"><em>compute property/chunk</em></a> command and its
 <em>id</em> keyword, or by the <a class="reference internal" href="fix_ave_chunk.html"><em>fix ave/chunk</em></a> command
 which outputs the original IDs as one of the columns in its global
 output array.  For example, using the &#8220;compute cluster/atom&#8221; command
 discussed above, the original 5 unique chunk IDs might be atom IDs
 (27,4982,58374,857838,1000000).  After compresion, these will be
 renumbered to (1,2,3,4,5).  The original values (27,...,1000000) can
 be output to a file by the <a class="reference internal" href="fix_ave_chunk.html"><em>fix ave/chunk</em></a> command,
 or by using the <a class="reference internal" href="fix_ave_time.html"><em>fix ave/time</em></a> command in
 conjunction with the <a class="reference internal" href="compute_property_chunk.html"><em>compute property/chunk</em></a> command.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">The compression operation requires global
 communication across all processors to share their chunk ID values.
 It can require large memory on every processor to store them, even
 after they are compressed, if there are are a large number of unique
 chunk IDs with atoms assigned to them.  It uses a STL map to find
 unique chunk IDs and store them in sorted order.  Each time an atom is
 assigned a compressed chunk ID, it must access the STL map.  All of
 this means that compression can be expensive, both in memory and CPU
 time.  The use of the <em>limit</em> keyword in conjunction with the
 <em>compress</em> keyword can affect these costs, depending on which keyword
 is used first.  So use this option with care.</p>
 </div>
 <hr class="docutils" />
 <p>The <em>discard</em> keyword applies to all chunk styles.  It affects what
 chunk IDs are assigned to atoms that do not match one of the valid
 chunk IDs from 1 to <em>Nchunk</em>.  Note that it does not apply to atoms
 that are not in the specified group or optionally specified region.
 Those atoms are always assigned a chunk ID = 0.</p>
 <p>If the calculated chunk ID for an atom is not within the range 1 to
 <em>Nchunk</em> then it is a &#8220;discard&#8221; atom.  Note that <em>Nchunk</em> may have
 been shrunk by the <em>limit</em> keyword.  Or the <em>compress</em> keyword may
 have eliminated chunk IDs that were valid before the compression took
 place, and are now not in the compressed list.  Also note that for the
 <em>molecule</em> chunk style, if new molecules are added to the system,
 their chunk IDs may exceed a previously calculated <em>Nchunk</em>.
 Likewise, evaluation of a compute/fix/variable on a later timestep may
 return chunk IDs that are invalid for the previously calculated
 <em>Nchunk</em>.</p>
 <p>All the chunk styles except the <em>binning</em> styles, must use <em>discard</em>
 set to either <em>yes</em> or <em>no</em>.  If <em>discard</em> is set to <em>yes</em>, which is
 the default, then every &#8220;discard&#8221; atom has its chunk ID set to 0.  If
 <em>discard</em> is set to <em>no</em>, every &#8220;discard&#8221; atom has its chunk ID set to
 <em>Nchunk</em>.  I.e. it becomes part of the last chunk.</p>
 <p>The <em>binning</em> styles use the <em>discard</em> keyword to decide whether to
 discard atoms outside the spatial domain covered by bins, or to assign
 them to the bin they are nearest to.  Details are as follows.</p>
 <p>If <em>discard</em> is set to <em>yes</em>, an out-of-domain atom will have its
 chunk ID set to 0.  If <em>discard</em> is set to <em>no</em>, the atom will have
 its chunk ID set to the first or last bin in that dimension.  If
 (discard* is set to <em>mixed</em>, which is the default, it will only have
 its chunk ID set to the first or last bin if bins extend to the
 simulation box boundary in that dimension.  This is the case if the
 <em>bound</em> keyword settings are <em>lower</em> and <em>upper</em>, which is the
 default.  If the <em>bound</em> keyword settings are numeric values, then the
 atom will have its chunk ID set to 0 if it is outside the bounds of
 any bin.  Note that in this case, it is possible that the first or
 last bin extends beyond the numeric <em>bounds</em> settings, depending on
 the specified <em>origin</em>.  If this is the case, the chunk ID of the atom
 is only set to 0 if it is outside the first or last bin, not if it is
 simply outside the numeric <em>bounds</em> setting.</p>
 <hr class="docutils" />
 <p>The <em>bound</em> keyword only applies to the <em>binning</em> styles; otherwise it
 is ignored.  It can be used one or more times to limit the extent of
 bin coverage in a specified dimension, i.e. to only bin a portion of
 the box.  If the <em>lo</em> setting is <em>lower</em> or the <em>hi</em> setting is
 <em>upper</em>, the bin extent in that direction extends to the box boundary.
 If a numeric value is used for <em>lo</em> and/or <em>hi</em>, then the bin extent
 in the <em>lo</em> or <em>hi</em> direction extends only to that value, which is
 assumed to be inside (or at least near) the simulation box boundaries,
 though LAMMPS does not check for this.  Note that using the <em>bound</em>
 keyword typically reduces the total number of bins and thus the number
 of chunks <em>Nchunk</em>.</p>
 <p>The <em>units</em> keyword only applies to the <em>binning</em> styles; otherwise it
 is ignored.  It determines the meaning of the distance units used for
 the bin sizes <em>delta</em> and for <em>origin</em> and <em>bounds</em> values if they are
 coordinate values.  For orthogonal simulation boxes, any of the 3
 options may be used.  For non-orthogonal (triclinic) simulation boxes,
 only the <em>reduced</em> option may be used.</p>
 <p>A <em>box</em> value selects standard distance units as defined by the
 <a class="reference internal" href="units.html"><em>units</em></a> command, e.g. Angstroms for units = real or metal.
 A <em>lattice</em> value means the distance units are in lattice spacings.
 The <a class="reference internal" href="lattice.html"><em>lattice</em></a> command must have been previously used to
 define the lattice spacing.  A <em>reduced</em> value means normalized
 unitless values between 0 and 1, which represent the lower and upper
 faces of the simulation box respectively.  Thus an <em>origin</em> value of
 0.5 means the center of the box in any dimension.  A <em>delta</em> value of
 0.1 means 10 bins span the box in that dimension.</p>
 <p><strong>Output info:</strong></p>
 <p>This compute calculates a per-atom vector, which can be accessed by
 any command that uses per-atom values from a compute as input.  See
 <a class="reference internal" href="Section_howto.html#howto-15"><span>Section_howto 15</span></a> for an overview of
 LAMMPS output options.</p>
 <p>The per-atom vector values are unitless chunk IDs, ranging from 1 to
 <em>Nchunk</em> (inclusive) for atoms assigned to chunks, and 0 for atoms not
 belonging to a chunk.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>Even if the <em>nchunk</em> keyword is set to <em>once</em>, the chunk IDs assigned
 to each atom are not stored in a restart files.  This means you cannot
 expect those assignments to persist in a restarted simulation.
 Instead you must re-specify this command and assign atoms to chunks when
 the restarted simulation begins.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="fix_ave_chunk.html"><em>fix ave/chunk</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The option defaults are as follows:</p>
 <ul class="simple">
 <li>region = none</li>
 <li>nchunk = every if compress is yes, overriding other defaults listed here</li>
 <li>nchunk = once for type style</li>
 <li>nchunk = once for mol style if region is none</li>
 <li>nchunk = every for mol style if region is set</li>
 <li>nchunk = once for binning style if the simulation box size is static or units = reduced</li>
 <li>nchunk = every for binning style if the simulation box size is dynamic and units is lattice or box</li>
 <li>nchunk = every for compute/fix/variable style</li>
 <li>limit = 0</li>
 <li>ids = every</li>
 <li>compress = no</li>
 <li>discard = yes for all styles except binning</li>
 <li>discard = mixed for binning styles</li>
 <li>bound = lower and upper in all dimensions</li>
 <li>units = lattice</li>
 </ul>
 </div>
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diff --git a/doc/compute_fep.html b/doc/compute_fep.html
index baa065c87..04b631a92 100644
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   <div class="section" id="compute-fep-command">
 <span id="index-0"></span><h1>compute fep command<a class="headerlink" href="#compute-fep-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>compute ID group-ID fep temp attribute args ... keyword value ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in the <a class="reference internal" href="compute.html"><em>compute</em></a> command</li>
 <li>fep = name of this compute command</li>
 <li>temp = external temperature (as specified for constant-temperature run)</li>
 <li>one or more attributes with args may be appended</li>
 <li>attribute = <em>pair</em> or <em>atom</em></li>
 </ul>
 <pre class="literal-block">
 <em>pair</em> args = pstyle pparam I J v_delta
-    pstyle = pair style name, e.g. lj/cut
-    pparam = parameter to perturb
-    I,J = type pair(s) to set parameter for
-    v_delta = variable with perturbation to apply (in the units of the parameter)
-  <em>atom</em> args = aparam I v_delta
-    aparam = parameter to perturb
-    I = type to set parameter for
-    v_delta = variable with perturbation to apply (in the units of the parameter)
+  pstyle = pair style name, e.g. lj/cut
+  pparam = parameter to perturb
+  I,J = type pair(s) to set parameter for
+  v_delta = variable with perturbation to apply (in the units of the parameter)
+<em>atom</em> args = aparam I v_delta
+  aparam = parameter to perturb
+  I = type to set parameter for
+  v_delta = variable with perturbation to apply (in the units of the parameter)
 </pre>
 <ul class="simple">
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>tail</em> or <em>volume</em></li>
 </ul>
 <pre class="literal-block">
 <em>tail</em> value = <em>no</em> or <em>yes</em>
-    <em>no</em> = ignore tail correction to pair energies (usually small in fep)
-    <em>yes</em> = include tail correction to pair energies
-  <em>volume</em> value = <em>no</em> or <em>yes</em>
-    <em>no</em> = ignore volume changes (e.g. in <em>NVE</em> or <em>NVT</em> trajectories)
-    <em>yes</em> = include volume changes (e.g. in <em>NpT</em> trajectories)
+  <em>no</em> = ignore tail correction to pair energies (usually small in fep)
+  <em>yes</em> = include tail correction to pair energies
+<em>volume</em> value = <em>no</em> or <em>yes</em>
+  <em>no</em> = ignore volume changes (e.g. in <em>NVE</em> or <em>NVT</em> trajectories)
+  <em>yes</em> = include volume changes (e.g. in <em>NpT</em> trajectories)
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>compute 1 all fep 298 pair lj/cut epsilon 1 * v_delta pair lj/cut sigma 1 * v_delta volume yes
 compute 1 all fep 300 atom charge 2 v_delta
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Apply a perturbation to parameters of the interaction potential and
 recalculate the pair potential energy without changing the atomic
 coordinates from those of the reference, unperturbed system. This
 compute can be used to calculate free energy differences using several
 methods, such as free-energy perturbation (FEP), finite-difference
 thermodynamic integration (FDTI) or Bennet&#8217;s acceptance ratio method
 (BAR).</p>
 <p>The potential energy of the system is decomposed in three terms: a
 background term corresponding to interaction sites whose parameters
 remain constant, a reference term <a href="#id1"><span class="problematic" id="id2">*</span></a>U*&lt;sub&gt;0&lt;/sub&gt; corresponding to the
 initial interactions of the atoms that will undergo perturbation, and
 a term <a href="#id3"><span class="problematic" id="id4">*</span></a>U*&lt;sub&gt;1&lt;/sub&gt; corresponding to the final interactions of
 these atoms:</p>
 <img alt="_images/compute_fep_u.jpg" class="align-center" src="_images/compute_fep_u.jpg" />
 <p>A coupling parameter &amp;lambda; varying from 0 to 1 connects the
 reference and perturbed systems:</p>
 <img alt="_images/compute_fep_lambda.jpg" class="align-center" src="_images/compute_fep_lambda.jpg" />
 <p>It is possible but not necessary that the coupling parameter (or a
 function thereof) appears as a multiplication factor of the potential
 energy. Therefore, this compute can apply perturbations to interaction
 parameters that are not directly proportional to the potential energy
 (e.g. &amp;sigma; in Lennard-Jones potentials).</p>
 <p>This command can be combined with <a class="reference internal" href="fix_adapt.html"><em>fix adapt</em></a> to
 perform multistage free-energy perturbation calculations along
 stepwise alchemical transformations during a simulation run:</p>
 <img alt="_images/compute_fep_fep.jpg" class="align-center" src="_images/compute_fep_fep.jpg" />
 <p>This compute is suitable for the finite-difference thermodynamic
 integration (FDTI) method <a class="reference internal" href="#mezei"><span>(Mezei)</span></a>, which is based on an
 evaluation of the numerical derivative of the free energy by a
 perturbation method using a very small &amp;delta;:</p>
 <img alt="_images/compute_fep_fdti.jpg" class="align-center" src="_images/compute_fep_fdti.jpg" />
 <p>where <a href="#id5"><span class="problematic" id="id6">*</span></a>w*&lt;sub&gt;i&lt;/sub&gt; are weights of a numerical quadrature. The <a class="reference internal" href="fix_adapt.html"><em>fix adapt</em></a> command can be used to define the stages of
 &amp;lambda; at which the derivative is calculated and averaged.</p>
 <p>The compute fep calculates the exponential Boltzmann term and also the
 potential energy difference <a href="#id7"><span class="problematic" id="id8">*</span></a>U*&lt;sub&gt;1&lt;/sub&gt;-<a href="#id9"><span class="problematic" id="id10">*</span></a>U*&lt;sub&gt;0&lt;/sub&gt;. By
 choosing a very small perturbation &amp;delta; the thermodynamic
 integration method can be implemented using a numerical evaluation of
 the derivative of the potential energy with respect to &amp;lambda;:</p>
 <img alt="_images/compute_fep_ti.jpg" class="align-center" src="_images/compute_fep_ti.jpg" />
 <p>Another technique to calculate free energy differences is the
 acceptance ratio method <a class="reference internal" href="#bennet"><span>(Bennet)</span></a>, which can be implemented
 by calculating the potential energy differences with &amp;delta; = 1.0 on
 both the forward and reverse routes:</p>
 <img alt="_images/compute_fep_bar.jpg" class="align-center" src="_images/compute_fep_bar.jpg" />
 <p>The value of the free energy difference is determined by numerical
 root finding to establish the equality.</p>
 <p>Concerning the choice of how the atomic parameters are perturbed in
 order to setup an alchemical transformation route, several strategies
 are available, such as single-topology or double-topology strategies
 <a class="reference internal" href="#pearlman"><span>(Pearlman)</span></a>. The latter does not require modification of
 bond lengths, angles or other internal coordinates.</p>
 <p>IMPORTANT NOTES: This compute command does not take kinetic energy
 into account, therefore the masses of the particles should not be
 modified between the reference and perturbed states, or along the
 alchemical transformation route.  This compute command does not change
 bond lengths or other internal coordinates <a class="reference internal" href="#boreschkarplus"><span>(Boresch, Karplus)</span></a>.</p>
 <hr class="docutils" />
 <p>The <em>pair</em> attribute enables various parameters of potentials defined
 by the <a class="reference internal" href="pair_style.html"><em>pair_style</em></a> and <a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a>
 commands to be changed, if the pair style supports it.</p>
 <p>The <em>pstyle</em> argument is the name of the pair style. For example,
 <em>pstyle</em> could be specified as &#8220;lj/cut&#8221;.  The <em>pparam</em> argument is the
 name of the parameter to change.  This is a (non-exclusive) list of
 pair styles and parameters that can be used with this compute.  See
 the doc pages for individual pair styles and their energy formulas for
 the meaning of these parameters:</p>
 <table border="1" class="docutils">
 <colgroup>
 <col width="59%" />
 <col width="27%" />
 <col width="15%" />
 </colgroup>
 <tbody valign="top">
 <tr class="row-odd"><td><a class="reference internal" href="pair_lj.html"><em>lj/cut</em></a></td>
 <td>epsilon,sigma</td>
 <td>type pairs</td>
 </tr>
 <tr class="row-even"><td><a class="reference internal" href="pair_lj.html"><em>lj/cut/coul/cut</em></a></td>
 <td>epsilon,sigma</td>
 <td>type pairs</td>
 </tr>
 <tr class="row-odd"><td><a class="reference internal" href="pair_lj.html"><em>lj/cut/coul/long</em></a></td>
 <td>epsilon,sigma</td>
 <td>type pairs</td>
 </tr>
 <tr class="row-even"><td><a class="reference internal" href="pair_lj_soft.html"><em>lj/cut/soft</em></a></td>
 <td>epsilon,sigma,lambda</td>
 <td>type pairs</td>
 </tr>
 <tr class="row-odd"><td><a class="reference internal" href="pair_lj_soft.html"><em>coul/cut/soft</em></a></td>
 <td>lambda</td>
 <td>type pairs</td>
 </tr>
 <tr class="row-even"><td><a class="reference internal" href="pair_lj_soft.html"><em>coul/long/soft</em></a></td>
 <td>lambda</td>
 <td>type pairs</td>
 </tr>
 <tr class="row-odd"><td><a class="reference internal" href="pair_lj_soft.html"><em>lj/cut/coul/cut/soft</em></a></td>
 <td>epsilon,sigma,lambda</td>
 <td>type pairs</td>
 </tr>
 <tr class="row-even"><td><a class="reference internal" href="pair_lj_soft.html"><em>lj/cut/coul/long/soft</em></a></td>
 <td>epsilon,sigma,lambda</td>
 <td>type pairs</td>
 </tr>
 <tr class="row-odd"><td><a class="reference internal" href="pair_lj_soft.html"><em>lj/cut/tip4p/long/soft</em></a></td>
 <td>epsilon,sigma,lambda</td>
 <td>type pairs</td>
 </tr>
 <tr class="row-even"><td><a class="reference internal" href="pair_lj_soft.html"><em>tip4p/long/soft</em></a></td>
 <td>lambda</td>
 <td>type pairs</td>
 </tr>
 <tr class="row-odd"><td><a class="reference internal" href="pair_lj_soft.html"><em>lj/charmm/coul/long/soft</em></a></td>
 <td>epsilon,sigma,lambda</td>
 <td>type pairs</td>
 </tr>
 <tr class="row-even"><td><a class="reference internal" href="pair_born.html"><em>born</em></a></td>
 <td>a,b,c</td>
 <td>type pairs</td>
 </tr>
 <tr class="row-odd"><td><a class="reference internal" href="pair_buck.html"><em>buck</em></a></td>
 <td>a,c</td>
 <td>type pairs</td>
 </tr>
 </tbody>
 </table>
 <p>Note that it is easy to add new potentials and their parameters to
 this list.  All it typically takes is adding an extract() method to
 the pair_*.cpp file associated with the potential.</p>
 <p>Similar to the <a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a> command, I and J can be
 specified in one of two ways.  Explicit numeric values can be used for
 each, as in the 1st example above.  I &lt;= J is required.  LAMMPS sets
 the coefficients for the symmetric J,I interaction to the same
 values. A wild-card asterisk can be used in place of or in conjunction
 with the I,J arguments to set the coefficients for multiple pairs of
 atom types.  This takes the form &#8220;*&#8221; or &#8220;<em>n&#8221; or &#8220;n</em>&#8221; or &#8220;m*n&#8221;.  If N =
 the number of atom types, then an asterisk with no numeric values
 means all types from 1 to N.  A leading asterisk means all types from
 1 to n (inclusive).  A trailing asterisk means all types from n to N
 (inclusive).  A middle asterisk means all types from m to n
 (inclusive).  Note that only type pairs with I &lt;= J are considered; if
 asterisks imply type pairs where J &lt; I, they are ignored.</p>
 <p>If <a class="reference internal" href="pair_hybrid.html"><em>pair_style hybrid or hybrid/overlay</em></a> is being
 used, then the <em>pstyle</em> will be a sub-style name.  You must specify
 I,J arguments that correspond to type pair values defined (via the
 <a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a> command) for that sub-style.</p>
 <p>The <em>v_name</em> argument for keyword <em>pair</em> is the name of an
 <a class="reference internal" href="variable.html"><em>equal-style variable</em></a> which will be evaluated each time
 this compute is invoked.  It should be specified as v_name, where name
 is the variable name.</p>
 <hr class="docutils" />
 <p>The <em>atom</em> attribute enables atom properties to be changed.  The
 <em>aparam</em> argument is the name of the parameter to change.  This is the
 current list of atom parameters that can be used with this compute:</p>
 <ul class="simple">
 <li>charge = charge on particle</li>
 </ul>
 <p>The <em>v_name</em> argument for keyword <em>pair</em> is the name of an
 <a class="reference internal" href="variable.html"><em>equal-style variable</em></a> which will be evaluated each time
 this compute is invoked.  It should be specified as v_name, where name
 is the variable name.</p>
 <hr class="docutils" />
 <p>The <em>tail</em> keyword controls the calculation of the tail correction to
 &#8220;van der Waals&#8221; pair energies beyond the cutoff, if this has been
 activated via the <a class="reference internal" href="pair_modify.html"><em>pair_modify</em></a> command. If the
 perturbation is small, the tail contribution to the energy difference
 between the reference and perturbed systems should be negligible.</p>
 <p>If the keyword <em>volume</em> = <em>yes</em>, then the Boltzmann term is multiplied
 by the volume so that correct ensemble averaging can be performed over
 trajectories during which the volume fluctuates or changes <a class="reference internal" href="#allentildesley"><span>(Allen and Tildesley)</span></a>:</p>
 <img alt="_images/compute_fep_vol.jpg" class="align-center" src="_images/compute_fep_vol.jpg" />
 <hr class="docutils" />
 <p><strong>Output info:</strong></p>
 <p>This compute calculates a global vector of length 3 which contains the
 energy difference (<em>U*&lt;sub&gt;1&lt;/sub&gt;-*U*&lt;sub&gt;0&lt;/sub&gt;) as c_ID[1], the
 Boltzmann factor exp(-(*U*&lt;sub&gt;1&lt;/sub&gt;-*U*&lt;sub&gt;0&lt;/sub&gt;)/*kT</em>), or
 <em>V*exp(-(*U*&lt;sub&gt;1&lt;/sub&gt;-*U*&lt;sub&gt;0&lt;/sub&gt;)/*kT</em>), as c_ID[2] and the
 volume of the simulation box <em>V</em> as c_ID[3]. <a href="#id11"><span class="problematic" id="id12">*</span></a>U*&lt;sub&gt;1&lt;/sub&gt; is the
 pair potential energy obtained with the perturbed parameters and
 <a href="#id13"><span class="problematic" id="id14">*</span></a>U*&lt;sub&gt;0&lt;/sub&gt; is the pair potential energy obtained with the
 unperturbed parameters. The energies include kspace terms if these
 are used in the simulation.</p>
 <p>These output results can be used by any command that uses a global
 scalar or vector from a compute as input.  See <a class="reference internal" href="Section_howto.html#howto-15"><span>Section_howto 15</span></a> for an overview of LAMMPS output
 options. For example, the computed values can be averaged using <a class="reference internal" href="fix_ave_time.html"><em>fix ave/time</em></a>.</p>
 <p>The values calculated by this compute are &#8220;extensive&#8221;.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>This compute is distributed as the USER-FEP package.  It is only
 enabled if LAMMPS was built with that package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="fix_adapt_fep.html"><em>fix adapt/fep</em></a>, <a class="reference internal" href="fix_ave_time.html"><em>fix ave/time</em></a>,
 <a class="reference external" href="pair_lj_soft_coul_soft.txt">pair_lj_soft_coul_soft</a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The option defaults are <em>tail</em> = <em>no</em>, <em>volume</em> = <em>no</em>.</p>
 <hr class="docutils" />
 <p id="pearlman"><strong>(Pearlman)</strong> Pearlman, J Chem Phys, 98, 1487 (1994)</p>
 <p id="mezei"><strong>(Mezei)</strong> Mezei, J Chem Phys, 86, 7084 (1987)</p>
 <p id="bennet"><strong>(Bennet)</strong> Bennet, J Comput Phys, 22, 245 (1976)</p>
 <p id="boreschkarplus"><strong>(BoreschKarplus)</strong> Boresch and Karplus, J Phys Chem A, 103, 103 (1999)</p>
 <p id="allentildesley"><strong>(AllenTildesley)</strong> Allen and Tildesley, Computer Simulation of
 Liquids, Oxford University Press (1987)</p>
 </div>
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diff --git a/doc/compute_group_group.html b/doc/compute_group_group.html
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   <div class="section" id="compute-group-group-command">
 <span id="index-0"></span><h1>compute group/group command<a class="headerlink" href="#compute-group-group-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>compute ID group-ID group/group group2-ID keyword value ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="compute.html"><em>compute</em></a> command</li>
 <li>group/group = style name of this compute command</li>
 <li>group2-ID = group ID of second (or same) group</li>
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>pair</em> or <em>kspace</em> or <em>boundary</em></li>
 </ul>
 <pre class="literal-block">
 <em>pair</em> value = <em>yes</em> or <em>no</em>
-  <em>kspace</em> value = <em>yes</em> or <em>no</em>
-  <em>boundary</em> value = <em>yes</em> or <em>no</em>
+<em>kspace</em> value = <em>yes</em> or <em>no</em>
+<em>boundary</em> value = <em>yes</em> or <em>no</em>
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>compute 1 lower group/group upper
 compute 1 lower group/group upper kspace yes
 compute mine fluid group/group wall
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Define a computation that calculates the total energy and force
 interaction between two groups of atoms: the compute group and the
 specified group2.  The two groups can be the same.</p>
 <p>If the <em>pair</em> keyword is set to <em>yes</em>, which is the default, then the
 the interaction energy will include a pair component which is defined
 as the pairwise energy between all pairs of atoms where one atom in
 the pair is in the first group and the other is in the second group.
 Likewise, the interaction force calculated by this compute will
 include the force on the compute group atoms due to pairwise
 interactions with atoms in the specified group2.</p>
 <p>If the <em>kspace</em> keyword is set to <em>yes</em>, which is not the default, and
 if a <a class="reference internal" href="kspace_style.html"><em>kspace_style</em></a> is defined, then the interaction
 energy will include a Kspace component which is the long-range
 Coulombic energy between all the atoms in the first group and all the
 atoms in the 2nd group.  Likewise, the interaction force calculated by
 this compute will include the force on the compute group atoms due to
 long-range Coulombic interactions with atoms in the specified group2.</p>
 <p>Normally the long-range Coulombic energy converges only when the net
 charge of the unit cell is zero.  However, one can assume the net
 charge of the system is neutralized by a uniform background plasma,
 and a correction to the system energy can be applied to reduce
 artifacts. For more information see <a class="reference internal" href="#bogusz"><span>(Bogusz)</span></a>.  If the
 <em>boundary</em> keyword is set to <em>yes</em>, which is the default, and <em>kspace</em>
 contributions are included, then this energy correction term will be
 added to the total group-group energy.  This correction term does not
 affect the force calculation and will be zero if one or both of the
 groups are charge neutral.  This energy correction term is the same as
 that included in the regular Ewald and PPPM routines.</p>
 <p>This compute does not calculate any bond or angle or dihedral or
 improper interactions between atoms in the two groups.</p>
 <hr class="docutils" />
 <p>The pairwise contributions to the group-group interactions are
 calculated by looping over a neighbor list.  The Kspace contribution
 to the group-group interactions require essentially the same amount of
 work (FFTs, Ewald summation) as computing long-range forces for the
 entire system.  Thus it can be costly to invoke this compute too
 frequently.</p>
 <p>If you desire a breakdown of the interactions into a pairwise and
 Kspace component, simply invoke the compute twice with the appropriate
 yes/no settings for the <em>pair</em> and <em>kspace</em> keywords.  This is no more
 costly than using a single compute with both keywords set to <em>yes</em>.
 The individual contributions can be summed in a
 <a class="reference internal" href="variable.html"><em>variable</em></a> if desired.</p>
 <p>This <a class="reference external" href="PDF/kspace.pdf">document</a> describes how the long-range
 group-group calculations are performed.</p>
 <hr class="docutils" />
 <p><strong>Output info:</strong></p>
 <p>This compute calculates a global scalar (the energy) and a global
 vector of length 3 (force), which can be accessed by indices 1-3.
 These values can be used by any command that uses global scalar or
 vector values from a compute as input.  See <a class="reference internal" href="Section_howto.html#howto-15"><span>this section</span></a> for an overview of LAMMPS output
 options.</p>
 <p>Both the scalar and vector values calculated by this compute are
 &#8220;extensive&#8221;.  The scalar value will be in energy <a class="reference internal" href="units.html"><em>units</em></a>.
 The vector values will be in force <a class="reference internal" href="units.html"><em>units</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>Not all pair styles can be evaluated in a pairwise mode as required by
 this compute.  For example, 3-body and other many-body potentials,
 such as <a class="reference internal" href="pair_tersoff.html"><em>Tersoff</em></a> and
 <a class="reference internal" href="pair_sw.html"><em>Stillinger-Weber</em></a> cannot be used.  <a class="reference internal" href="pair_eam.html"><em>EAM</em></a>
 potentials only include the pair potential portion of the EAM
 interaction when used by this compute, not the embedding term.</p>
 <p>Not all Kspace styles support calculation of group/group interactions.
 The <em>ewald</em> and <em>pppm</em> styles do.</p>
 <p><strong>Related commands:</strong> none</p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The option defaults are pair = yes, kspace = no, and boundary = yes.</p>
 <hr class="docutils" />
 <p id="bogusz">Bogusz et al, J Chem Phys, 108, 7070 (1998)</p>
 </div>
 </div>
 
 
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   <div class="section" id="compute-modify-command">
 <span id="index-0"></span><h1>compute_modify command<a class="headerlink" href="#compute-modify-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>compute_modify compute-ID keyword value ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>compute-ID = ID of the compute to modify</li>
 <li>one or more keyword/value pairs may be listed</li>
 <li>keyword = <em>extra</em> or <em>dynamic</em></li>
 </ul>
 <pre class="literal-block">
 <em>extra</em> value = N
-    N = # of extra degrees of freedom to subtract
-  <em>dynamic</em> value = <em>yes</em> or <em>no</em>
-    yes/no = do or do not recompute the number of atoms contributing to the temperature
-  <em>thermo</em> value = <em>yes</em> or <em>no</em>
-    yes/no = do or do not add contributions from fixes to the potential energy
+  N = # of extra degrees of freedom to subtract
+<em>dynamic</em> value = <em>yes</em> or <em>no</em>
+  yes/no = do or do not recompute the number of atoms contributing to the temperature
+<em>thermo</em> value = <em>yes</em> or <em>no</em>
+  yes/no = do or do not add contributions from fixes to the potential energy
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>compute_modify myTemp extra 0
 compute_modify newtemp dynamic yes extra 600
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Modify one or more parameters of a previously defined compute.  Not
 all compute styles support all parameters.</p>
 <p>The <em>extra</em> keyword refers to how many degrees-of-freedom are
 subtracted (typically from 3N) as a normalizing factor in a
 temperature computation.  Only computes that compute a temperature use
 this option.  The default is 2 or 3 for <a class="reference internal" href="dimension.html"><em>2d or 3d systems</em></a> which is a correction factor for an ensemble
 of velocities with zero total linear momentum.  You can use a negative
 number for the <em>extra</em> parameter if you need to add
 degrees-of-freedom.  See the <a class="reference internal" href="compute_temp_asphere.html"><em>compute temp/asphere</em></a> command for an example.</p>
 <p>The <em>dynamic</em> keyword determines whether the number of atoms N in the
 compute group is re-computed each time a temperature is computed.
 Only compute styles that compute a temperature use this option.  By
 default, N is assumed to be constant.  If you are adding atoms to the
 system (see the <a class="reference internal" href="fix_pour.html"><em>fix pour</em></a> or <a class="reference internal" href="fix_deposit.html"><em>fix deposit</em></a> commands) or expect atoms to be lost
 (e.g. due to evaporation), then this option should be used to insure
 the temperature is correctly normalized.</p>
 <p>The <em>thermo</em> keyword determines whether the potential energy
 contribution calculated by some <a class="reference internal" href="fix.html"><em>fixes</em></a> is added to the
 potential energy calculated by the compute.  Currently, only the
 compute of style <em>pe</em> uses this option.  See the doc pages for
 <a class="reference internal" href="fix.html"><em>individual fixes</em></a> for details.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <blockquote>
 <div>none</div></blockquote>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="compute.html"><em>compute</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The option defaults are extra = 2 or 3 for 2d or 3d systems and
 dynamic = no.  Thermo is <em>yes</em> if the compute of style <em>pe</em> was
 defined with no extra keywords; otherwise it is <em>no</em>.</p>
 </div>
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   <div class="section" id="compute-pair-local-command">
 <span id="index-0"></span><h1>compute pair/local command<a class="headerlink" href="#compute-pair-local-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>compute ID group-ID pair/local input1 input2 ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="compute.html"><em>compute</em></a> command</li>
 <li>pair/local = style name of this compute command</li>
 <li>zero or more keywords may be appended</li>
 <li>keyword = <em>dist</em> or <em>eng</em> or <em>force</em> or <em>fx</em> or <em>fy</em> or <em>fz</em> or <em>pN</em></li>
 </ul>
 <pre class="literal-block">
 <em>dist</em> = pairwise distance
-  <em>eng</em> = pairwise energy
-  <em>force</em> = pairwise force
-  <em>fx</em>,*fy*,*fz* = components of pairwise force
-  <em>pN</em> = pair style specific quantities for allowed N values
+<em>eng</em> = pairwise energy
+<em>force</em> = pairwise force
+<em>fx</em>,*fy*,*fz* = components of pairwise force
+<em>pN</em> = pair style specific quantities for allowed N values
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>compute 1 all pair/local eng
 compute 1 all pair/local dist eng force
 compute 1 all pair/local dist eng fx fy fz
 compute 1 all pair/local dist fx fy fz p1 p2 p3
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Define a computation that calculates properties of individual pairwise
 interactions.  The number of datums generated, aggregated across all
 processors, equals the number of pairwise interactions in the system.</p>
 <p>The local data stored by this command is generated by looping over the
 pairwise neighbor list.  Info about an individual pairwise interaction
 will only be included if both atoms in the pair are in the specified
 compute group, and if the current pairwise distance is less than the
 force cutoff distance for that interaction, as defined by the
 <a class="reference internal" href="pair_style.html"><em>pair_style</em></a> and <a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a>
 commands.</p>
 <p>The output <em>dist</em> is the distance bewteen the pair of atoms.</p>
 <p>The output <em>eng</em> is the interaction energy for the pair of atoms.</p>
 <p>The output <em>force</em> is the force acting between the pair of atoms,
 which is positive for a repulsive force and negative for an attractive
 force.  The outputs <em>fx</em>, <em>fy</em>, and <em>fz</em> are the xyz components of
 <em>force</em> on atom I.</p>
 <p>A pair style may define additional pairwise quantities which can be
 accessed as <em>p1</em> to <em>pN</em>, where N is defined by the pair style.  Most
 pair styles do not define any additional quantities, so N = 0.  An
 example of ones that do are the <a class="reference internal" href="pair_gran.html"><em>granular pair styles</em></a>
 which calculate the tangential force between two particles and return
 its components and magnitude acting on atom I for N = 1,2,3,4.  See
 individual pair styles for detils.</p>
 <p>The output <em>dist</em> will be in distance <a class="reference internal" href="units.html"><em>units</em></a>.  The output
 <em>eng</em> will be in energy <a class="reference internal" href="units.html"><em>units</em></a>.  The outputs <em>force</em>,
 <em>fx</em>, <em>fy</em>, and <em>fz</em> will be in force <a class="reference internal" href="units.html"><em>units</em></a>.  The output
 <em>pN</em> will be in whatever units the pair style defines.</p>
 <p>Note that as atoms migrate from processor to processor, there will be
 no consistent ordering of the entries within the local vector or array
 from one timestep to the next.  The only consistency that is
 guaranteed is that the ordering on a particular timestep will be the
 same for local vectors or arrays generated by other compute commands.
 For example, pair output from the <a class="reference internal" href="compute_property_local.html"><em>compute property/local</em></a> command can be combined
 with data from this command and output by the <a class="reference internal" href="dump.html"><em>dump local</em></a>
 command in a consistent way.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">For pairs, if two atoms I,J are involved in 1-2, 1-3,
 1-4 interactions within the molecular topology, their pairwise
 interaction may be turned off, and thus they may not appear in the
 neighbor list, and will not be part of the local data created by this
 command.  More specifically, this will be true of I,J pairs with a
 weighting factor of 0.0; pairs with a non-zero weighting factor are
 included.  The weighting factors for 1-2, 1-3, and 1-4 pairwise
 interactions are set by the <a class="reference internal" href="special_bonds.html"><em>special_bonds</em></a>
 command.  An exception is if long-range Coulombics are being computed
 via the <a class="reference internal" href="kspace_style.html"><em>kspace_style</em></a> command, then atom pairs with
 weighting factors of zero are still included in the neighbor list, so
 that a portion of the long-range interaction contribution can be
 computed in the pair style.  Hence in that case, those atom pairs will
 be part of the local data created by this command.</p>
 </div>
 <p><strong>Output info:</strong></p>
 <p>This compute calculates a local vector or local array depending on the
 number of keywords.  The length of the vector or number of rows in the
 array is the number of pairs.  If a single keyword is specified, a
 local vector is produced.  If two or more keywords are specified, a
 local array is produced where the number of columns = the number of
 keywords.  The vector or array can be accessed by any command that
 uses local values from a compute as input.  See <a class="reference internal" href="Section_howto.html#howto-15"><span>this section</span></a> for an overview of LAMMPS output
 options.</p>
 <p>The output for <em>dist</em> will be in distance <a class="reference internal" href="units.html"><em>units</em></a>.  The
 output for <em>eng</em> will be in energy <a class="reference internal" href="units.html"><em>units</em></a>.  The output for
 <em>force</em> will be in force <a class="reference internal" href="units.html"><em>units</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <blockquote>
 <div>none</div></blockquote>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="dump.html"><em>dump local</em></a>, <a class="reference internal" href="compute_property_local.html"><em>compute property/local</em></a></p>
 <p><strong>Default:</strong> none</p>
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   <div class="section" id="compute-property-atom-command">
 <span id="index-0"></span><h1>compute property/atom command<a class="headerlink" href="#compute-property-atom-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>compute ID group-ID property/atom input1 input2 ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="compute.html"><em>compute</em></a> command</li>
 <li>property/atom = style name of this compute command</li>
 <li>input = one or more atom attributes</li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>possible attributes = id, mol, proc, type, mass,
-                     x, y, z, xs, ys, zs, xu, yu, zu, ix, iy, iz,
-                     vx, vy, vz, fx, fy, fz,
-                        q, mux, muy, muz, mu,
-                        radius, diameter, omegax, omegay, omegaz,
-                     angmomx, angmomy, angmomz,
-                     shapex,shapey, shapez,
-                     quatw, quati, quatj, quatk, tqx, tqy, tqz,
-                     end1x, end1y, end1z, end2x, end2y, end2z,
-                     corner1x, corner1y, corner1z,
-                     corner2x, corner2y, corner2z,
-                     corner3x, corner3y, corner3z,
-                     nbonds,
-                        vfrac, s0,
-                     spin, eradius, ervel, erforce,
-                        rho, drho, e, de, cv,
-                        i_name, d_name
+                   x, y, z, xs, ys, zs, xu, yu, zu, ix, iy, iz,
+                   vx, vy, vz, fx, fy, fz,
+                      q, mux, muy, muz, mu,
+                      radius, diameter, omegax, omegay, omegaz,
+                   angmomx, angmomy, angmomz,
+                   shapex,shapey, shapez,
+                   quatw, quati, quatj, quatk, tqx, tqy, tqz,
+                   end1x, end1y, end1z, end2x, end2y, end2z,
+                   corner1x, corner1y, corner1z,
+                   corner2x, corner2y, corner2z,
+                   corner3x, corner3y, corner3z,
+                   nbonds,
+                      vfrac, s0,
+                   spin, eradius, ervel, erforce,
+                      rho, drho, e, de, cv,
+                      i_name, d_name
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>id = atom ID
-      mol = molecule ID
-      proc = ID of processor that owns atom
-      type = atom type
-      mass = atom mass
-      x,y,z = unscaled atom coordinates
-      xs,ys,zs = scaled atom coordinates
-      xu,yu,zu = unwrapped atom coordinates
-      ix,iy,iz = box image that the atom is in
-      vx,vy,vz = atom velocities
-      fx,fy,fz = forces on atoms
-      q = atom charge
-      mux,muy,muz = orientation of dipole moment of atom
-      mu = magnitude of dipole moment of atom
-      radius,diameter = radius,diameter of spherical particle
-      omegax,omegay,omegaz = angular velocity of spherical particle
-      angmomx,angmomy,angmomz = angular momentum of aspherical particle
-      shapex,shapey,shapez = 3 diameters of aspherical particle
-      quatw,quati,quatj,quatk = quaternion components for aspherical or body particles
-      tqx,tqy,tqz = torque on finite-size particles
-      end12x, end12y, end12z = end points of line segment
-      corner123x, corner123y, corner123z = corner points of triangle
-      nbonds = number of bonds assigned to an atom
+mol = molecule ID
+proc = ID of processor that owns atom
+type = atom type
+mass = atom mass
+x,y,z = unscaled atom coordinates
+xs,ys,zs = scaled atom coordinates
+xu,yu,zu = unwrapped atom coordinates
+ix,iy,iz = box image that the atom is in
+vx,vy,vz = atom velocities
+fx,fy,fz = forces on atoms
+q = atom charge
+mux,muy,muz = orientation of dipole moment of atom
+mu = magnitude of dipole moment of atom
+radius,diameter = radius,diameter of spherical particle
+omegax,omegay,omegaz = angular velocity of spherical particle
+angmomx,angmomy,angmomz = angular momentum of aspherical particle
+shapex,shapey,shapez = 3 diameters of aspherical particle
+quatw,quati,quatj,quatk = quaternion components for aspherical or body particles
+tqx,tqy,tqz = torque on finite-size particles
+end12x, end12y, end12z = end points of line segment
+corner123x, corner123y, corner123z = corner points of triangle
+nbonds = number of bonds assigned to an atom
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>PERI package per-atom properties:
-      vfrac = ???
-      s0 = ???
+vfrac = ???
+s0 = ???
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>USER-EFF and USER-AWPMD package per-atom properties:
-      spin = electron spin
-      eradius = electron radius
-      ervel = electron radial velocity
-      erforce = electron radial force
+spin = electron spin
+eradius = electron radius
+ervel = electron radial velocity
+erforce = electron radial force
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>USER-SPH package per-atom properties:
-      rho = ???
-      drho = ???
-      e = ???
-      de = ???
-      cv = ???
+rho = ???
+drho = ???
+e = ???
+de = ???
+cv = ???
 </pre></div>
 </div>
 <pre class="literal-block">
 <a class="reference internal" href="fix_property_atom.html"><em>fix property/atom</em></a> per-atom properties:
-      i_name = custom integer vector with name
-      d_name = custom integer vector with name
+i_name = custom integer vector with name
+d_name = custom integer vector with name
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>compute 1 all property/atom xs vx fx mux
 compute 2 all property/atom type
 compute 1 all property/atom ix iy iz
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Define a computation that simply stores atom attributes for each atom
 in the group.  This is useful so that the values can be used by other
 <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a> that take computes as
 inputs.  See for example, the <a class="reference internal" href="compute_reduce.html"><em>compute reduce</em></a>,
 <a class="reference internal" href="fix_ave_atom.html"><em>fix ave/atom</em></a>, <a class="reference internal" href="fix_ave_histo.html"><em>fix ave/histo</em></a>,
 <a class="reference internal" href="fix_ave_spatial.html"><em>fix ave/spatial</em></a>, and <a class="reference internal" href="variable.html"><em>atom-style variable</em></a> commands.</p>
 <p>The list of possible attributes is the same as that used by the <a class="reference internal" href="dump.html"><em>dump custom</em></a> command, which describes their meaning, with some
 additional quantities that are only defined for certain <a class="reference internal" href="atom_style.html"><em>atom styles</em></a>.  Basically, this augmented list gives an
 input script access to any per-atom quantity stored by LAMMPS.</p>
 <p>The values are stored in a per-atom vector or array as discussed
 below.  Zeroes are stored for atoms not in the specified group or for
 quantities that are not defined for a particular particle in the group
 (e.g. <em>shapex</em> if the particle is not an ellipsoid).</p>
 <p>The additional quantities only accessible via this command, and not
 directly via the <a class="reference internal" href="dump.html"><em>dump custom</em></a> command, are as follows.</p>
 <p><em>Shapex</em>, <em>shapey</em>, and <em>shapez</em> are defined for ellipsoidal particles
 and define the 3d shape of each particle.</p>
 <p><em>Quatw</em>, <em>quati</em>, <em>quatj</em>, and <em>quatk</em> are defined for ellipsoidal
 particles and body particles and store the 4-vector quaternion
 representing the orientation of each particle.  See the <a class="reference internal" href="set.html"><em>set</em></a>
 command for an explanation of the quaternion vector.</p>
 <p><em>End1x</em>, <em>end1y</em>, <em>end1z</em>, <em>end2x</em>, <em>end2y</em>, <em>end2z</em>, are defined for
 line segment particles and define the end points of each line segment.</p>
 <p><em>Corner1x</em>, <em>corner1y</em>, <em>corner1z</em>, <em>corner2x</em>, <em>corner2y</em>,
 <em>corner2z</em>, <em>corner3x</em>, <em>corner3y</em>, <em>corner3z</em>, are defined for
 triangular particles and define the corner points of each triangle.</p>
 <p><em>Nbonds</em> is available for all molecular atom styles and refers to the
 number of explicit bonds assigned to an atom.  Note that if the
 <a class="reference internal" href="newton.html"><em>newton bond</em></a> command is set to <em>on</em>, which is the
 default, then every bond in the system is assigned to only one of the
 two atoms in the bond.  Thus a bond between atoms I,J may be tallied
 for either atom I or atom J.  If <a class="reference internal" href="newton.html"><em>newton bond off</em></a> is set,
 it will be tallied with both atom I and atom J.</p>
 <p>The <em>i_name</em> and <em>d_name</em> attributes refer to custom integer and
 floating-point properties that have been added to each atom via the
 <a class="reference internal" href="fix_property_atom.html"><em>fix property/atom</em></a> command.  When that command
 is used specific names are given to each attribute which are what is
 specified as the &#8220;name&#8221; portion of <em>i_name</em> or <em>d_name</em>.</p>
 <p><strong>Output info:</strong></p>
 <p>This compute calculates a per-atom vector or per-atom array depending
 on the number of input values.  If a single input is specified, a
 per-atom vector is produced.  If two or more inputs are specified, a
 per-atom array is produced where the number of columns = the number of
 inputs.  The vector or array can be accessed by any command that uses
 per-atom values from a compute as input.  See <a class="reference internal" href="Section_howto.html#howto-15"><span>this section</span></a> for an overview of LAMMPS output
 options.</p>
 <p>The vector or array values will be in whatever <a class="reference internal" href="units.html"><em>units</em></a> the
 corresponding attribute is in, e.g. velocity units for vx, charge
 units for q, etc.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <blockquote>
 <div>none</div></blockquote>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="dump.html"><em>dump custom</em></a>, <a class="reference internal" href="compute_reduce.html"><em>compute reduce</em></a>, <a class="reference internal" href="fix_ave_atom.html"><em>fix ave/atom</em></a>, <a class="reference internal" href="fix_ave_spatial.html"><em>fix ave/spatial</em></a>,
 <a class="reference internal" href="fix_property_atom.html"><em>fix property/atom</em></a></p>
 <p><strong>Default:</strong> none</p>
 </div>
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   <div class="section" id="compute-property-chunk-command">
 <span id="index-0"></span><h1>compute property/chunk command<a class="headerlink" href="#compute-property-chunk-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>compute ID group-ID property/chunk chunkID input1 input2 ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="compute.html"><em>compute</em></a> command</li>
 <li>property/chunk = style name of this compute command</li>
 <li>input = one or more attributes</li>
 </ul>
 <pre class="literal-block">
 attributes = count, id, coord1, coord2, coord3
-    count = # of atoms in chunk
-    id = original chunk IDs before compression by <a class="reference internal" href="compute_chunk_atom.html"><em>compute chunk/atom</em></a>
-    coord123 = coordinates for spatial bins calculated by <a class="reference internal" href="compute_chunk_atom.html"><em>compute chunk/atom</em></a>
+  count = # of atoms in chunk
+  id = original chunk IDs before compression by <a class="reference internal" href="compute_chunk_atom.html"><em>compute chunk/atom</em></a>
+  coord123 = coordinates for spatial bins calculated by <a class="reference internal" href="compute_chunk_atom.html"><em>compute chunk/atom</em></a>
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>compute 1 all property/chunk count
 compute 1 all property/chunk ID coord1
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Define a computation that stores the specified attributes of chunks of
 atoms.</p>
 <p>In LAMMPS, chunks are collections of atoms defined by a <a class="reference internal" href="compute_chunk_atom.html"><em>compute chunk/atom</em></a> command, which assigns each atom
 to a single chunk (or no chunk).  The ID for this command is specified
 as chunkID.  For example, a single chunk could be the atoms in a
 molecule or atoms in a spatial bin.  See the <a class="reference internal" href="compute_chunk_atom.html"><em>compute chunk/atom</em></a> doc page and &#8220;<a class="reference internal" href="Section_howto.html#howto-23"><span>Section_howto 23</span></a> for details of how chunks can be
 defined and examples of how they can be used to measure properties of
 a system.</p>
 <p>This compute calculates and stores the specified attributes of chunks
 as global data so they can be accessed by other <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a> and used in conjunction with
 other commands that generate per-chunk data, such as <a class="reference internal" href="compute_com_chunk.html"><em>compute com/chunk</em></a> or <a class="reference internal" href="compute_msd_chunk.html"><em>compute msd/chunk</em></a>.</p>
 <p>Note that only atoms in the specified group contribute to the
 calculation of the <em>count</em> attribute.  The <a class="reference internal" href="compute_chunk_atom.html"><em>compute chunk/atom</em></a> command defines its own group;
 atoms will have a chunk ID = 0 if they are not in that group,
 signifying they are not assigned to a chunk, and will thus also not
 contribute to this calculation.  You can specify the &#8220;all&#8221; group for
 this command if you simply want to include atoms with non-zero chunk
 IDs.</p>
 <p>The <em>count</em> attribute is the number of atoms in the chunk.</p>
 <p>The <em>id</em> attribute stores the original chunk ID for each chunk.  It
 can only be used if the <em>compress</em> keyword was set to <em>yes</em> for the
 <a class="reference internal" href="compute_chunk_atom.html"><em>compute chunk/atom</em></a> command referenced by
 chunkID.  This means that the original chunk IDs (e.g. molecule IDs)
 will have been compressed to remove chunk IDs with no atoms assigned
 to them.  Thus a compresed chunk ID of 3 may correspond to an original
 chunk ID (molecule ID in this case) of 415.  The <em>id</em> attribute will
 then be 415 for the 3rd chunk.</p>
 <p>The <em>coordN</em> attributes can only be used if a <em>binning</em> style was used
 in the <a class="reference internal" href="compute_chunk_atom.html"><em>compute chunk/atom</em></a> command referenced
 by chunkID.  For <em>bin/1d</em>, <em>bin/2d</em>, and <em>bin/3d</em> styles the attribute
 is the center point of the bin in the corresponding dimension.  Style
 <em>bin/1d</em> only defines a <em>coord1</em> attribute.  Style <em>bin/2d</em> adds a
 <em>coord2</em> attribute.  Style <em>bin/3d</em> adds a <em>coord3</em> attribute.</p>
 <p>Note that if the value of the <em>units</em> keyword used in the <a class="reference internal" href="compute_chunk_atom.html"><em>compute chunk/atom command</em></a> is <em>box</em> or <em>lattice</em>, the
 <em>coordN</em> attributes will be in distance <a class="reference internal" href="units.html"><em>units</em></a>.  If the
 value of the <em>units</em> keyword is <em>reduced</em>, the <em>coordN</em> attributes
 will be in unitless reduced units (0-1).</p>
 <p>The simplest way to output the results of the compute property/chunk
 calculation to a file is to use the <a class="reference internal" href="fix_ave_time.html"><em>fix ave/time</em></a>
 command, for example:</p>
 <div class="highlight-python"><div class="highlight"><pre>compute cc1 all chunk/atom molecule
 compute myChunk1 all property/chunk cc1
 compute myChunk2 all com/chunk cc1
 fix 1 all ave/time 100 1 100 c_myChunk1 c_myChunk2 file tmp.out mode vector
 </pre></div>
 </div>
 <p><strong>Output info:</strong></p>
 <p>This compute calculates a global vector or global array depending on
 the number of input values.  The length of the vector or number of
 rows in the array is the number of chunks.</p>
 <p>This compute calculates a global vector or global array where the
 number of rows = the number of chunks <em>Nchunk</em> as calculated by the
 specified <a class="reference internal" href="compute_chunk_atom.html"><em>compute chunk/atom</em></a> command.  If a
 single input is specified, a global vector is produced.  If two or
 more inputs are specified, a global array is produced where the number
 of columns = the number of inputs.  The vector or array can be
 accessed by any command that uses global values from a compute as
 input.  See <a class="reference internal" href="Section_howto.html#howto-15"><span>this section</span></a> for an overview
 of LAMMPS output options.</p>
 <p>The vector or array values are &#8220;intensive&#8221;.  The values will be
 unitless or in the units discussed above.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <blockquote>
 <div>none</div></blockquote>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="fix_ave_chunk.html"><em>fix ave/chunk</em></a></p>
 <p><strong>Default:</strong> none</p>
 </div>
 </div>
 
 
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diff --git a/doc/compute_property_local.html b/doc/compute_property_local.html
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   <div class="section" id="compute-property-local-command">
 <span id="index-0"></span><h1>compute property/local command<a class="headerlink" href="#compute-property-local-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>compute ID group-ID property/local input1 input2 ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="compute.html"><em>compute</em></a> command</li>
 <li>property/local = style name of this compute command</li>
 <li>input = one or more attributes</li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>possible attributes = natom1 natom2 ntype1 ntype2
-                     patom1 patom2 ptype1 ptype2
-                        batom1 batom2 btype
-                        aatom1 aatom2 aatom3 atype
-                        datom1 datom2 datom3 dtype
-                        iatom1 iatom2 iatom3 itype
+                   patom1 patom2 ptype1 ptype2
+                      batom1 batom2 btype
+                      aatom1 aatom2 aatom3 atype
+                      datom1 datom2 datom3 dtype
+                      iatom1 iatom2 iatom3 itype
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>natom1, natom2 = IDs of 2 atoms in each pair (within neighbor cutoff)
-     ntype1, ntype2 = type of 2 atoms in each pair (within neighbor cutoff)
-     patom1, patom2 = IDs of 2 atoms in each pair (within force cutoff)
-     ptype1, ptype2 = type of 2 atoms in each pair (within force cutoff)
-     batom1, batom2 = IDs of 2 atoms in each bond
-     btype = bond type of each bond
-     aatom1, aatom2, aatom3 = IDs of 3 atoms in each angle
-     atype = angle type of each angle
-     datom1, datom2, datom3, datom4 = IDs of 4 atoms in each dihedral
-     dtype = dihedral type of each dihedral
-     iatom1, iatom2, iatom3, iatom4 = IDs of 4 atoms in each improper
-     itype = improper type of each improper
+ntype1, ntype2 = type of 2 atoms in each pair (within neighbor cutoff)
+patom1, patom2 = IDs of 2 atoms in each pair (within force cutoff)
+ptype1, ptype2 = type of 2 atoms in each pair (within force cutoff)
+batom1, batom2 = IDs of 2 atoms in each bond
+btype = bond type of each bond
+aatom1, aatom2, aatom3 = IDs of 3 atoms in each angle
+atype = angle type of each angle
+datom1, datom2, datom3, datom4 = IDs of 4 atoms in each dihedral
+dtype = dihedral type of each dihedral
+iatom1, iatom2, iatom3, iatom4 = IDs of 4 atoms in each improper
+itype = improper type of each improper
 </pre></div>
 </div>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>compute 1 all property/local btype batom1 batom2
 compute 1 all property/local atype aatom2
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Define a computation that stores the specified attributes as local
 data so it can be accessed by other <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  If the input attributes refer
 to bond information, then the number of datums generated, aggregated
 across all processors, equals the number of bonds in the system.
 Ditto for pairs, angles, etc.</p>
 <p>If multiple input attributes are specified then they must all generate
 the same amount of information, so that the resulting local array has
 the same number of rows for each column.  This means that only bond
 attributes can be specified together, or angle attributes, etc.  Bond
 and angle attributes can not be mixed in the same compute
 property/local command.</p>
 <p>If the inputs are pair attributes, the local data is generated by
 looping over the pairwise neighbor list.  Info about an individual
 pairwise interaction will only be included if both atoms in the pair
 are in the specified compute group.  For <em>natom1</em> and <em>natom2</em>, all
 atom pairs in the neighbor list are considered (out to the neighbor
 cutoff = force cutoff + <a class="reference internal" href="neighbor.html"><em>neighbor skin</em></a>).  For <em>patom1</em>
 and <em>patom2</em>, the distance between the atoms must be less than the
 force cutoff distance for that pair to be included, as defined by the
 <a class="reference internal" href="pair_style.html"><em>pair_style</em></a> and <a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a>
 commands.</p>
 <p>If the inputs are bond, angle, etc attributes, the local data is
 generated by looping over all the atoms owned on a processor and
 extracting bond, angle, etc info.  For bonds, info about an individual
 bond will only be included if both atoms in the bond are in the
 specified compute group.  Likewise for angles, dihedrals, etc.</p>
 <p>For bonds and angles, a bonds/angles that have been broken by setting
 their bond/angle type to 0 will not be included.  Bonds/angles that
 have been turned off (see the <a class="reference internal" href="fix_shake.html"><em>fix shake</em></a> or
 <a class="reference internal" href="delete_bonds.html"><em>delete_bonds</em></a> commands) by setting their bond/angle
 type negative are written into the file.  This is consistent with the
 <a class="reference internal" href="compute_bond_local.html"><em>compute bond/local</em></a> and <a class="reference internal" href="compute_angle_local.html"><em>compute angle/local</em></a> commands</p>
 <p>Note that as atoms migrate from processor to processor, there will be
 no consistent ordering of the entries within the local vector or array
 from one timestep to the next.  The only consistency that is
 guaranteed is that the ordering on a particular timestep will be the
 same for local vectors or arrays generated by other compute commands.
 For example, output from the <a class="reference internal" href="compute_bond_local.html"><em>compute bond/local</em></a> command can be combined with bond
 atom indices from this command and output by the <a class="reference internal" href="dump.html"><em>dump local</em></a> command in a consistent way.</p>
 <p>The <em>natom1</em> and <em>natom2</em>, or <em>patom1</em> and <em>patom2</em> attributes refer
 to the atom IDs of the 2 atoms in each pairwise interaction computed
 by the <a class="reference internal" href="pair_style.html"><em>pair_style</em></a> command.  The <em>ntype1</em> and
 <em>ntype2</em>, or <em>ptype1</em> and <em>ptype2</em> attributes refer to the atom types
 of the 2 atoms in each pairwise interaction.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">For pairs, if two atoms I,J are involved in 1-2, 1-3,
 1-4 interactions within the molecular topology, their pairwise
 interaction may be turned off, and thus they may not appear in the
 neighbor list, and will not be part of the local data created by this
 command.  More specifically, this may be true of I,J pairs with a
 weighting factor of 0.0; pairs with a non-zero weighting factor are
 included.  The weighting factors for 1-2, 1-3, and 1-4 pairwise
 interactions are set by the <a class="reference internal" href="special_bonds.html"><em>special_bonds</em></a>
 command.</p>
 </div>
 <p>The <em>batom1</em> and <em>batom2</em> attributes refer to the atom IDs of the 2
 atoms in each <a class="reference internal" href="bond_style.html"><em>bond</em></a>.  The <em>btype</em> attribute refers to
 the type of the bond, from 1 to Nbtypes = # of bond types.  The number
 of bond types is defined in the data file read by the
 <a class="reference internal" href="read_data.html"><em>read_data</em></a> command.</p>
 <p>The attributes that start with &#8220;a&#8221;, &#8220;d&#8221;, &#8220;i&#8221;, refer to similar values
 for <a class="reference internal" href="angle_style.html"><em>angles</em></a>, <a class="reference internal" href="dihedral_style.html"><em>dihedrals</em></a>, and
 <a class="reference internal" href="improper_style.html"><em>impropers</em></a>.</p>
 <p><strong>Output info:</strong></p>
 <p>This compute calculates a local vector or local array depending on the
 number of input values.  The length of the vector or number of rows in
 the array is the number of bonds, angles, etc.  If a single input is
 specified, a local vector is produced.  If two or more inputs are
 specified, a local array is produced where the number of columns = the
 number of inputs.  The vector or array can be accessed by any command
 that uses local values from a compute as input.  See <a class="reference internal" href="Section_howto.html#howto-15"><span>this section</span></a> for an overview of LAMMPS output
 options.</p>
 <p>The vector or array values will be integers that correspond to the
 specified attribute.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <blockquote>
 <div>none</div></blockquote>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="dump.html"><em>dump local</em></a>, <a class="reference internal" href="compute_reduce.html"><em>compute reduce</em></a></p>
 <p><strong>Default:</strong> none</p>
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   <div class="section" id="compute-reduce-command">
 <span id="index-0"></span><h1>compute reduce command<a class="headerlink" href="#compute-reduce-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="compute-reduce-region-command">
 <h1>compute reduce/region command<a class="headerlink" href="#compute-reduce-region-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>compute ID group-ID style arg mode input1 input2 ... keyword args ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="compute.html"><em>compute</em></a> command</li>
 <li>style = <em>reduce</em> or <em>reduce/region</em></li>
 </ul>
 <pre class="literal-block">
 <em>reduce</em> arg = none
-  <em>reduce/region</em> arg = region-ID
-    region-ID = ID of region to use for choosing atoms
+<em>reduce/region</em> arg = region-ID
+  region-ID = ID of region to use for choosing atoms
 </pre>
 <ul class="simple">
 <li>mode = <em>sum</em> or <em>min</em> or <em>max</em> or <em>ave</em> or <em>sumsq</em> or <em>avesq</em></li>
 <li>one or more inputs can be listed</li>
 <li>input = x, y, z, vx, vy, vz, fx, fy, fz, c_ID, c_ID[N], f_ID, f_ID[N], v_name</li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>x,y,z,vx,vy,vz,fx,fy,fz = atom attribute (position, velocity, force component)
-  c_ID = per-atom or local vector calculated by a compute with ID
-  c_ID[I] = Ith column of per-atom or local array calculated by a compute with ID
-  f_ID = per-atom or local vector calculated by a fix with ID
-  f_ID[I] = Ith column of per-atom or local array calculated by a fix with ID
-  v_name = per-atom vector calculated by an atom-style variable with name
+c_ID = per-atom or local vector calculated by a compute with ID
+c_ID[I] = Ith column of per-atom or local array calculated by a compute with ID
+f_ID = per-atom or local vector calculated by a fix with ID
+f_ID[I] = Ith column of per-atom or local array calculated by a fix with ID
+v_name = per-atom vector calculated by an atom-style variable with name
 </pre></div>
 </div>
 <ul class="simple">
 <li>zero or more keyword/args pairs may be appended</li>
 <li>keyword = <em>replace</em></li>
 </ul>
 <pre class="literal-block">
 <em>replace</em> args = vec1 vec2
-    vec1 = reduced value from this input vector will be replaced
-    vec2 = replace it with vec1[N] where N is index of max/min value from vec2
+  vec1 = reduced value from this input vector will be replaced
+  vec2 = replace it with vec1[N] where N is index of max/min value from vec2
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>compute 1 all reduce sum c_force
 compute 1 all reduce/region subbox sum c_force
 compute 2 all reduce min c_press[2] f_ave v_myKE
 compute 3 fluid reduce max c_index[1] c_index[2] c_dist replace 1 3 replace 2 3
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Define a calculation that &#8220;reduces&#8221; one or more vector inputs into
 scalar values, one per listed input.  The inputs can be per-atom or
 local quantities; they cannot be global quantities.  Atom attributes
 are per-atom quantities, <a class="reference internal" href="compute.html"><em>computes</em></a> and <a class="reference internal" href="fix.html"><em>fixes</em></a>
 may generate any of the three kinds of quantities, and <a class="reference internal" href="variable.html"><em>atom-style variables</em></a> generate per-atom quantities.  See the
 <a class="reference external" href="variable">variable</a> command and its special functions which can
 perform the same operations as the compute reduce command on global
 vectors.</p>
 <p>The reduction operation is specified by the <em>mode</em> setting.  The <em>sum</em>
 option adds the values in the vector into a global total.  The <em>min</em>
 or <em>max</em> options find the minimum or maximum value across all vector
 values.  The <em>ave</em> setting adds the vector values into a global total,
 then divides by the number of values in the vector.  The <em>sumsq</em>
 option sums the square of the values in the vector into a global
 total.  The <em>avesq</em> setting does the same as <em>sumsq</em>, then divdes the
 sum of squares by the number of values.  The last two options can be
 useful for calculating the variance of some quantity, e.g. variance =
 sumsq - ave^2.</p>
 <p>Each listed input is operated on independently.  For per-atom inputs,
 the group specified with this command means only atoms within the
 group contribute to the result.  For per-atom inputs, if the compute
 reduce/region command is used, the atoms must also currently be within
 the region.  Note that an input that produces per-atom quantities may
 define its own group which affects the quantities it returns.  For
 example, if a compute is used as an input which generates a per-atom
 vector, it will generate values of 0.0 for atoms that are not in the
 group specified for that compute.</p>
 <p>Each listed input can be an atom attribute (position, velocity, force
 component) or can be the result of a <a class="reference internal" href="compute.html"><em>compute</em></a> or
 <a class="reference internal" href="fix.html"><em>fix</em></a> or the evaluation of an atom-style
 <a class="reference internal" href="variable.html"><em>variable</em></a>.</p>
 <p>The atom attribute values (x,y,z,vx,vy,vz,fx,fy,fz) are
 self-explanatory.  Note that other atom attributes can be used as
 inputs to this fix by using the <a class="reference internal" href="compute_property_atom.html"><em>compute property/atom</em></a> command and then specifying
 an input value from that compute.</p>
 <p>If a value begins with &#8220;<a href="#id1"><span class="problematic" id="id2">c_</span></a>&#8221;, a compute ID must follow which has been
 previously defined in the input script.  Computes can generate
 per-atom or local quantities.  See the individual
 <a class="reference internal" href="compute.html"><em>compute</em></a> doc page for details.  If no bracketed integer
 is appended, the vector calculated by the compute is used.  If a
 bracketed integer is appended, the Ith column of the array calculated
 by the compute is used.  Users can also write code for their own
 compute styles and <a class="reference internal" href="Section_modify.html"><em>add them to LAMMPS</em></a>.</p>
 <p>If a value begins with &#8220;<a href="#id3"><span class="problematic" id="id4">f_</span></a>&#8221;, a fix ID must follow which has been
 previously defined in the input script.  Fixes can generate per-atom
 or local quantities.  See the individual <a class="reference internal" href="fix.html"><em>fix</em></a> doc page for
 details.  Note that some fixes only produce their values on certain
 timesteps, which must be compatible with when compute reduce
 references the values, else an error results.  If no bracketed integer
 is appended, the vector calculated by the fix is used.  If a bracketed
 integer is appended, the Ith column of the array calculated by the fix
 is used.  Users can also write code for their own fix style and <a class="reference internal" href="Section_modify.html"><em>add them to LAMMPS</em></a>.</p>
 <p>If a value begins with &#8220;<a href="#id5"><span class="problematic" id="id6">v_</span></a>&#8221;, a variable name must follow which has
 been previously defined in the input script.  It must be an
 <a class="reference internal" href="variable.html"><em>atom-style variable</em></a>.  Atom-style variables can
 reference thermodynamic keywords and various per-atom attributes, or
 invoke other computes, fixes, or variables when they are evaluated, so
 this is a very general means of generating per-atom quantities to
 reduce.</p>
 <hr class="docutils" />
 <p>If the <em>replace</em> keyword is used, two indices <em>vec1</em> and <em>vec2</em> are
 specified, where each index ranges from 1 to the # of input values.
 The replace keyword can only be used if the <em>mode</em> is <em>min</em> or <em>max</em>.
 It works as follows.  A min/max is computed as usual on the <em>vec2</em>
 input vector.  The index N of that value within <em>vec2</em> is also stored.
 Then, instead of performing a min/max on the <em>vec1</em> input vector, the
 stored index is used to select the Nth element of the <em>vec1</em> vector.</p>
 <p>Thus, for example, if you wish to use this compute to find the bond
 with maximum stretch, you can do it as follows:</p>
 <div class="highlight-python"><div class="highlight"><pre>compute 1 all property/local batom1 batom2
 compute      2 all bond/local dist
 compute      3 all reduce max c_1[1] c_1[2] c_2 replace 1 3 replace 2 3
 thermo_style custom step temp c_3[1] c_3[2] c_3[3]
 </pre></div>
 </div>
 <p>The first two input values in the compute reduce command are vectors
 with the IDs of the 2 atoms in each bond, using the <a class="reference internal" href="compute_property_local.html"><em>compute property/local</em></a> command.  The last input
 value is bond distance, using the <a class="reference internal" href="compute_bond_local.html"><em>compute bond/local</em></a> command.  Instead of taking the
 max of the two atom ID vectors, which does not yield useful
 information in this context, the <em>replace</em> keywords will extract the
 atom IDs for the two atoms in the bond of maximum stretch.  These atom
 IDs and the bond stretch will be printed with thermodynamic output.</p>
 <hr class="docutils" />
 <p>If a single input is specified this compute produces a global scalar
 value.  If multiple inputs are specified, this compute produces a
 global vector of values, the length of which is equal to the number of
 inputs specified.</p>
 <p>As discussed below, for the <em>sum</em> and <em>sumsq</em> modes, the value(s)
 produced by this compute are all &#8220;extensive&#8221;, meaning their value
 scales linearly with the number of atoms involved.  If normalized
 values are desired, this compute can be accessed by the <a class="reference internal" href="thermo_style.html"><em>thermo_style custom</em></a> command with <a class="reference internal" href="thermo_modify.html"><em>thermo_modify norm yes</em></a> set as an option.  Or it can be accessed by a
 <a class="reference internal" href="variable.html"><em>variable</em></a> that divides by the appropriate atom count.</p>
 <hr class="docutils" />
 <p><strong>Output info:</strong></p>
 <p>This compute calculates a global scalar if a single input value is
 specified or a global vector of length N where N is the number of
 inputs, and which can be accessed by indices 1 to N.  These values can
 be used by any command that uses global scalar or vector values from a
 compute as input.  See <a class="reference internal" href="Section_howto.html#howto-15"><span>Section_howto 15</span></a>
 for an overview of LAMMPS output options.</p>
 <p>All the scalar or vector values calculated by this compute are
 &#8220;intensive&#8221;, except when the <em>sum</em> or <em>sumsq</em> modes are used on
 per-atom or local vectors, in which case the calculated values are
 &#8220;extensive&#8221;.</p>
 <p>The scalar or vector values will be in whatever <a class="reference internal" href="units.html"><em>units</em></a> the
 quantities being reduced are in.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <blockquote>
 <div>none</div></blockquote>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="compute.html"><em>compute</em></a>, <a class="reference internal" href="fix.html"><em>fix</em></a>, <a class="reference internal" href="variable.html"><em>variable</em></a></p>
 <p><strong>Default:</strong> none</p>
 </div>
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   <div class="section" id="compute-saed-command">
 <span id="index-0"></span><h1>compute saed command<a class="headerlink" href="#compute-saed-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>compute ID group-ID saed lambda type1 type2 ... typeN keyword value ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="compute.html"><em>compute</em></a> command</li>
 <li>saed = style name of this compute command</li>
 <li>lambda = wavelength of incident radiation (length units)</li>
 <li>type1 type2 ... typeN = chemical symbol of each atom type (see valid options below)</li>
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>Kmax</em> or <em>Zone</em> or <em>dR_Ewald</em> or <em>c</em> or <em>manual</em> or <em>echo</em></li>
 </ul>
 <pre class="literal-block">
 <em>Kmax</em> value = Maximum distance explored from reciprocal space origin
-                 (inverse length units)
-  <em>Zone</em> values = z1 z2 z3
-    z1,z2,z3 = Zone axis of incident radiation. If z1=z2=z3=0 all
-               reciprocal space will be meshed up to <em>Kmax</em>
-  <em>dR_Ewald</em> value = Thickness of Ewald sphere slice intercepting
-                     reciprocal space (inverse length units)
-  <em>c</em> values = c1 c2 c3
-    c1,c2,c3 = parameters to adjust the spacing of the reciprocal
-               lattice nodes in the h, k, and l directions respectively
-  <em>manual</em> = flag to use manual spacing of reciprocal lattice points
-             based on the values of the <em>c</em> parameters
-  <em>echo</em> = flag to provide extra output for debugging purposes
+               (inverse length units)
+<em>Zone</em> values = z1 z2 z3
+  z1,z2,z3 = Zone axis of incident radiation. If z1=z2=z3=0 all
+             reciprocal space will be meshed up to <em>Kmax</em>
+<em>dR_Ewald</em> value = Thickness of Ewald sphere slice intercepting
+                   reciprocal space (inverse length units)
+<em>c</em> values = c1 c2 c3
+  c1,c2,c3 = parameters to adjust the spacing of the reciprocal
+             lattice nodes in the h, k, and l directions respectively
+<em>manual</em> = flag to use manual spacing of reciprocal lattice points
+           based on the values of the <em>c</em> parameters
+<em>echo</em> = flag to provide extra output for debugging purposes
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>compute 1 all saed 0.0251 Al O Kmax 1.70 Zone 0 0 1 dR_Ewald 0.01 c 0.5 0.5 0.5
 compute 2 all saed 0.0251 Ni Kmax 1.70 Zone 0 0 0 c 0.05 0.05 0.05 manual echo
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>fix saed/vtk 1 1 1 c_1 file Al2O3_001.saed
 fix saed/vtk 1 1 1 c_2 file Ni_000.saed
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Define a computation that calculates electron diffraction intensity as
 described in <a class="reference internal" href="fix_saed_vtk.html#coleman"><span>(Coleman)</span></a> on a mesh of reciprocal lattice nodes
 defined by the entire simulation domain (or manually) using simulated
 radiation of wavelength lambda.</p>
 <p>The electron diffraction intensity I at each reciprocal lattice point
 is computed from the structure factor F using the equations:</p>
 <img alt="_images/compute_saed1.jpg" class="align-center" src="_images/compute_saed1.jpg" />
 <img alt="_images/compute_saed2.jpg" class="align-center" src="_images/compute_saed2.jpg" />
 <p>Here, K is the location of the reciprocal lattice node, rj is the
 position of each atom, fj are atomic scattering factors.</p>
 <p>Diffraction intensities are calculated on a three-dimensional mesh of
 reciprocal lattice nodes. The mesh spacing is defined either (a)  by
 the entire simulation domain or (b) manually using selected values as
 shown in the 2D diagram below.</p>
 <a data-lightbox="group-default"
                    href="_images/saed_mesh.jpg"
                    class=""
                    title=""
                    data-title=""
                    ><img src="_images/saed_mesh.jpg"
                     class="align-center"
                     width="25%"
                     height="auto"
                     alt=""/>
                     </a><p>For a mesh defined by the simulation domain, a rectilinear grid is
 constructed with spacing <a href="#id1"><span class="problematic" id="id2">*</span></a>c**inv(A) along each reciprocal lattice
 axis. Where A are the vectors corresponding to the edges of the
 simulation cell. If one or two directions has non-periodic boundary
 conditions, then the spacing in these directions is defined from the
 average of the (inversed) box lengths with periodic boundary conditions.
 Meshes defined by the simulation domain must contain at least one periodic
 boundary.</p>
 <p>If the <em>manual</em> flag is included, the mesh of reciprocal lattice nodes
 will defined using the <em>c</em> values for the spacing along each reciprocal
 lattice axis. Note that manual mapping of the reciprocal space mesh is
 good for comparing diffraction results from  multiple simulations; however
 it can reduce the likelihood that Bragg reflections will be satisfied
 unless small spacing parameters &lt;0.05 Angstrom^(-1) are implemented.
 Meshes with manual spacing do not require a periodic boundary.</p>
 <p>The limits of the reciprocal lattice mesh are determined by the use of
 the <em>Kmax</em>, <em>Zone</em>, and <em>dR_Ewald</em> parameters.  The rectilinear mesh
 created about the origin of reciprocal space is terminated at the
 boundary of a sphere of radius <em>Kmax</em> centered at the origin.  If
 <em>Zone</em> parameters z1=z2=z3=0 are used, diffraction intensities are
 computed throughout the entire spherical volume - note this can greatly
 increase the cost of computation.  Otherwise, <em>Zone</em> parameters will
 denote the z1=h, z2=k, and z3=l (in a global since) zone axis of an
 intersecting Ewald sphere.  Diffraction intensities will only be
 computed at the intersection of the reciprocal lattice mesh and a
 <em>dR_Ewald</em> thick surface of the Ewald sphere.  See the example 3D
 intestiety data and the intersection of a [010] zone axis in the below image.</p>
 <a data-lightbox="group-default"
                    href="_images/saed_ewald_intersect.jpg"
                    class=""
                    title=""
                    data-title=""
                    ><img src="_images/saed_ewald_intersect.jpg"
                     class="align-center"
                     width="25%"
                     height="auto"
                     alt=""/>
                     </a><p>The atomic scattering factors, fj, accounts for the reduction in
 diffraction intensity due to Compton scattering.  Compute saed uses
 analytical approximations of the atomic scattering factors that vary
 for each atom type (type1 type2 ... typeN) and angle of diffraction.
 The analytic approximation is computed using the formula
 <a class="reference internal" href="#brown"><span>(Brown)</span></a>:</p>
 <img alt="_images/compute_saed3.jpg" class="align-center" src="_images/compute_saed3.jpg" />
 <p>Coefficients parameterized by <a class="reference internal" href="#fox"><span>(Fox)</span></a> are assigned for each
 atom type designating the chemical symbol and charge of each atom
 type. Valid chemical symbols for compute saed are:</p>
 <dl class="docutils">
 <dt>H:      He:      Li:      Be:       B:</dt>
 <dd><blockquote class="first">
 <div>C:       N:       O:       F:      Ne:</div></blockquote>
 <dl class="docutils">
 <dt>Na:      Mg:      Al:      Si:       P:</dt>
 <dd>S:      Cl:      Ar:       K:      Ca:</dd>
 </dl>
 <p class="last">Sc:      Ti:       V:      Cr:      Mn:
 Fe:      Co:      Ni:      Cu:      Zn:
 Ga:      Ge:      As:      Se:      Br:
 Kr:      Rb:      Sr:       Y:      Zr:
 Nb:      Mo:      Tc:      Ru:      Rh:
 Pd:      Ag:      Cd:      In:      Sn:
 Sb:      Te:       I:      Xe:      Cs:
 Ba:      La:      Ce:      Pr:      Nd:
 Pm:      Sm:      Eu:      Gd:      Tb:
 Dy:      Ho:      Er:      Tm:      Yb:
 Lu:      Hf:      Ta:       W:      Re:
 Os:      Ir:      Pt:      Au:      Hg:
 Tl:      Pb:      Bi:      Po:      At:
 Rn:      Fr:      Ra:      Ac:      Th:
 Pa:       U:      Np:      Pu:      Am:
 Cm:      Bk:      Cf:tb(c=5,s=:)</p>
 </dd>
 </dl>
 <p>If the <em>echo</em> keyword is specified, compute saed will provide extra
 reporting information to the screen.</p>
 <p><strong>Output info:</strong></p>
 <p>This compute calculates a global vector.  The length of the vector is
 the number of reciprocal lattice nodes that are explored by the mesh.
 The entries of the global vector are the computed diffraction
 intensities as described above.</p>
 <p>The vector can be accessed by any command that uses global values
 from a compute as input.  See <a class="reference internal" href="Section_howto.html#howto-15"><span>this section</span></a> for an overview of LAMMPS output
 options.</p>
 <p>All array values calculated by this compute are &#8220;intensive&#8221;.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>The compute_saed command does not work for triclinic cells.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="fix_saed_vtk.html"><em>fix saed_vtk</em></a>, <a class="reference internal" href="compute_xrd.html"><em>compute xrd</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The option defaults are Kmax = 1.70, Zone 1 0 0, c 1 1 1, dR_Ewald =
 0.01.</p>
 <hr class="docutils" />
 <p id="coleman"><strong>(Coleman)</strong> Coleman, Spearot, Capolungo, MSMSE, 21, 055020
 (2013).</p>
 <p id="brown"><strong>(Brown)</strong> Brown et al. International Tables for Crystallography
 Volume C: Mathematical and Chemical Tables, 554-95 (2004).</p>
 <p id="fox"><strong>(Fox)</strong> Fox, O&#8217;Keefe, Tabbernor, Acta Crystallogr. A, 45, 786-93
 (1989).</p>
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   <div class="section" id="compute-slice-command">
 <span id="index-0"></span><h1>compute slice command<a class="headerlink" href="#compute-slice-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>compute ID group-ID slice Nstart Nstop Nskip input1 input2 ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="compute.html"><em>compute</em></a> command</li>
 <li>slice = style name of this compute command</li>
 <li>Nstart = starting index within input vector(s)</li>
 <li>Nstop = stopping index within input vector(s)</li>
 <li>Nskip = extract every Nskip elements from input vector(s)</li>
 <li>input = c_ID, c_ID[N], f_ID, f_ID[N]</li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>c_ID = global vector calculated by a compute with ID
-  c_ID[I] = Ith column of global array calculated by a compute with ID
-  f_ID = global vector calculated by a fix with ID
-  f_ID[I] = Ith column of global array calculated by a fix with ID
+c_ID[I] = Ith column of global array calculated by a compute with ID
+f_ID = global vector calculated by a fix with ID
+f_ID[I] = Ith column of global array calculated by a fix with ID
 </pre></div>
 </div>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>compute 1 all slice 1 100 10 c_msdmol[4]
 compute 1 all slice 301 400 1 c_msdmol[4]
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Define a calculation that &#8220;slices&#8221; one or more vector inputs into
 smaller vectors, one per listed input.  The inputs can be global
 quantities; they cannot be per-atom or local quantities.
 <a class="reference internal" href="compute.html"><em>Computes</em></a> and <a class="reference internal" href="fix.html"><em>fixes</em></a> may generate any of the
 three kinds of quantities.  <a class="reference internal" href="variable.html"><em>Variables</em></a> do not generate
 global vectors.  The group specified with this command is ignored.</p>
 <p>The values extracted from the input vector(s) are determined by the
 <em>Nstart</em>, <em>Nstop</em>, and <em>Nskip</em> parameters.  The elements of an input
 vector of length N are indexed from 1 to N.  Starting at element
 <em>Nstart</em>, every Mth element is extracted, where M = <em>Nskip</em>, until
 element <em>Nstop</em> is reached.  The extracted quantities are stored as a
 vector, which is typically shorter than the input vector.</p>
 <p>Each listed input is operated on independently to produce one output
 vector.  Each listed input must be a global vector or column of a
 global array calculated by another <a class="reference internal" href="compute.html"><em>compute</em></a> or
 <a class="reference internal" href="fix.html"><em>fix</em></a>.</p>
 <p>If an input value begins with &#8220;<a href="#id1"><span class="problematic" id="id2">c_</span></a>&#8221;, a compute ID must follow which has
 been previously defined in the input script and which generates a
 global vector or array.  See the individual <a class="reference internal" href="compute.html"><em>compute</em></a> doc
 page for details.  If no bracketed integer is appended, the vector
 calculated by the compute is used.  If a bracketed integer is
 appended, the Ith column of the array calculated by the compute is
 used.  Users can also write code for their own compute styles and <a class="reference internal" href="Section_modify.html"><em>add them to LAMMPS</em></a>.</p>
 <p>If a value begins with &#8220;<a href="#id3"><span class="problematic" id="id4">f_</span></a>&#8221;, a fix ID must follow which has been
 previously defined in the input script and which generates a global
 vector or array.  See the individual <a class="reference internal" href="fix.html"><em>fix</em></a> doc page for
 details.  Note that some fixes only produce their values on certain
 timesteps, which must be compatible with when compute slice references
 the values, else an error results.  If no bracketed integer is
 appended, the vector calculated by the fix is used.  If a bracketed
 integer is appended, the Ith column of the array calculated by the fix
 is used.  Users can also write code for their own fix style and <a class="reference internal" href="Section_modify.html"><em>add them to LAMMPS</em></a>.</p>
 <p>If a single input is specified this compute produces a global vector,
 even if the length of the vector is 1.  If multiple inputs are
 specified, then a global array of values is produced, with the number
 of columns equal to the number of inputs specified.</p>
 <hr class="docutils" />
 <p><strong>Output info:</strong></p>
 <p>This compute calculates a global vector if a single input value is
 specified or a global array with N columns where N is the number of
 inputs.  The length of the vector or the number of rows in the array
 is equal to the number of values extracted from each input vector.
 These values can be used by any command that uses global vector or
 array values from a compute as input.  See <a class="reference internal" href="Section_howto.html#howto-15"><span>this section</span></a> for an overview of LAMMPS output
 options.</p>
 <p>The vector or array values calculated by this compute are simply
 copies of values generated by computes or fixes that are input vectors
 to this compute.  If there is a single input vector of intensive
 and/or extensive values, then each value in the vector of values
 calculated by this compute will be &#8220;intensive&#8221; or &#8220;extensive&#8221;,
 depending on the corresponding input value.  If there are multiple
 input vectors, and all the values in them are intensive, then the
 array values calculated by this compute are &#8220;intensive&#8221;.  If there are
 multiple input vectors, and any value in them is extensive, then the
 array values calculated by this compute are &#8220;extensive&#8221;.</p>
 <p>The vector or array values will be in whatever <a class="reference internal" href="units.html"><em>units</em></a> the
 input quantities are in.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <blockquote>
 <div>none</div></blockquote>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="compute.html"><em>compute</em></a>, <a class="reference internal" href="fix.html"><em>fix</em></a>, <a class="reference internal" href="compute_reduce.html"><em>compute reduce</em></a></p>
 <p><strong>Default:</strong> none</p>
 </div>
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   <div class="section" id="compute-sna-atom-command">
 <span id="index-0"></span><h1>compute sna/atom command<a class="headerlink" href="#compute-sna-atom-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="compute-snad-atom-command">
 <h1>compute snad/atom command<a class="headerlink" href="#compute-snad-atom-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="compute-snav-atom-command">
 <h1>compute snav/atom command<a class="headerlink" href="#compute-snav-atom-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>compute ID group-ID sna/atom ntypes rcutfac rfac0 twojmax R_1 R_2 ... w_1 w_2 ... keyword values ...
 compute ID group-ID snad/atom ntypes rcutfac rfac0 twojmax R_1 R_2 ... w_1 w_2 ... keyword values ...
 compute ID group-ID snav/atom ntypes rcutfac rfac0 twojmax R_1 R_2 ... w_1 w_2 ... keyword values ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="compute.html"><em>compute</em></a> command</li>
 <li>sna/atom = style name of this compute command</li>
 <li>rcutfac = scale factor applied to all cutoff radii (positive real)</li>
 <li>rfac0 = parameter in distance to angle conversion (0 &lt; rcutfac &lt; 1)</li>
 <li>twojmax = band limit for bispectrum components (non-negative integer)</li>
 <li>R_1, R_2,... = list of cutoff radii, one for each type (distance units)</li>
 <li>w_1, w_2,... = list of neighbor weights, one for each type</li>
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>diagonal</em> or <em>rmin0</em> or <em>switchflag</em></li>
 </ul>
 <pre class="literal-block">
 <em>diagonal</em> value = <em>0</em> or <em>1</em> or <em>2</em> or <em>3</em>
-     <em>0</em> = all j1, j2, j &lt;= twojmax, j2 &lt;= j1
-     <em>1</em> = subset satisfying j1 == j2
-     <em>2</em> = subset satisfying j1 == j2 == j3
-     <em>3</em> = subset satisfying j2 &lt;= j1 &lt;= j
-  <em>rmin0</em> value = parameter in distance to angle conversion (distance units)
-  <em>switchflag</em> value = <em>0</em> or <em>1</em>
-     <em>0</em> = do not use switching function
-     <em>1</em> = use switching function
+   <em>0</em> = all j1, j2, j &lt;= twojmax, j2 &lt;= j1
+   <em>1</em> = subset satisfying j1 == j2
+   <em>2</em> = subset satisfying j1 == j2 == j3
+   <em>3</em> = subset satisfying j2 &lt;= j1 &lt;= j
+<em>rmin0</em> value = parameter in distance to angle conversion (distance units)
+<em>switchflag</em> value = <em>0</em> or <em>1</em>
+   <em>0</em> = do not use switching function
+   <em>1</em> = use switching function
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>compute b all sna/atom 1.4 0.99363 6 2.0 2.4 0.75 1.0 diagonal 3 rmin0 0.0
 compute db all sna/atom 1.4 0.95 6 2.0 1.0
 compute vb all sna/atom 1.4 0.95 6 2.0 1.0
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Define a computation that calculates a set of bispectrum components
 for each atom in a group.</p>
 <p>Bispectrum components of an atom are order parameters characterizing
 the radial and angular distribution of neighbor atoms. The detailed
 mathematical definition is given in the paper by Thompson et
 al. <a class="reference internal" href="pair_snap.html#thompson2014"><span>(Thompson)</span></a></p>
 <p>The position of a neighbor atom <em>i&#8217;</em> relative to a central atom <em>i</em> is
 a point within the 3D ball of radius <em>R_ii&#8217; = rcutfac*(R_i + R_i&#8217;)</em></p>
 <p>Bartok et al. <a class="reference internal" href="pair_snap.html#bartok2010"><span>(Bartok)</span></a>, proposed mapping this 3D ball
 onto the 3-sphere, the surface of the unit ball in a four-dimensional
 space.  The radial distance <em>r</em> within <em>R_ii&#8217;</em> is mapped on to a third
 polar angle <em>theta0</em> defined by,</p>
 <img alt="_images/compute_sna_atom1.jpg" class="align-center" src="_images/compute_sna_atom1.jpg" />
 <p>In this way, all possible neighbor positions are mapped on to a subset
 of the 3-sphere.  Points south of the latitude <em>theta0max=rfac0*Pi</em>
 are excluded.</p>
 <p>The natural basis for functions on the 3-sphere is formed by the 4D
 hyperspherical harmonics <em>U^j_m,m&#8217;(theta, phi, theta0).</em>  These
 functions are better known as <em>D^j_m,m&#8217;,</em> the elements of the Wigner
 <em>D</em>-matrices <a class="reference internal" href="#meremianin2006"><span>(Meremianin</span></a>,
 <a class="reference internal" href="#varshalovich1987"><span>Varshalovich)</span></a>.</p>
 <p>The density of neighbors on the 3-sphere can be written as a sum of
 Dirac-delta functions, one for each neighbor, weighted by species and
 radial distance. Expanding this density function as a generalized
 Fourier series in the basis functions, we can write each Fourier
 coefficient as</p>
 <img alt="_images/compute_sna_atom2.jpg" class="align-center" src="_images/compute_sna_atom2.jpg" />
 <p>The <em>w_i&#8217;</em> neighbor weights are dimensionless numbers that are chosen
 to distinguish atoms of different types, while the central atom is
 arbitrarily assigned a unit weight.  The function <em>fc(r)</em> ensures that
 the contribution of each neighbor atom goes smoothly to zero at
 <em>R_ii&#8217;</em>:</p>
 <img alt="_images/compute_sna_atom4.jpg" class="align-center" src="_images/compute_sna_atom4.jpg" />
 <p>The expansion coefficients <em>u^j_m,m&#8217;</em> are complex-valued and they are
 not directly useful as descriptors, because they are not invariant
 under rotation of the polar coordinate frame. However, the following
 scalar triple products of expansion coefficients can be shown to be
 real-valued and invariant under rotation <a class="reference internal" href="pair_snap.html#bartok2010"><span>(Bartok)</span></a>.</p>
 <img alt="_images/compute_sna_atom3.jpg" class="align-center" src="_images/compute_sna_atom3.jpg" />
 <p>The constants <em>H^jmm&#8217;_j1m1m1&#8217;_j2m2m2&#8217;</em> are coupling coefficients,
 analogous to Clebsch-Gordan coefficients for rotations on the
 2-sphere. These invariants are the components of the bispectrum and
 these are the quantities calculated by the compute <em>sna/atom</em>. They
 characterize the strength of density correlations at three points on
 the 3-sphere. The j2=0 subset form the power spectrum, which
 characterizes the correlations of two points. The lowest-order
 components describe the coarsest features of the density function,
 while higher-order components reflect finer detail.  Note that the
 central atom is included in the expansion, so three point-correlations
 can be either due to three neighbors, or two neighbors and the central
 atom.</p>
 <p>Compute <em>snad/atom</em> calculates the derivative of the bispectrum components
 summed separately for each atom type:</p>
 <img alt="_images/compute_sna_atom5.jpg" class="align-center" src="_images/compute_sna_atom5.jpg" />
 <p>The sum is over all atoms <em>i&#8217;</em> of atom type <em>I</em>.  For each atom <em>i</em>,
 this compute evaluates the above expression for each direction, each
 atom type, and each bispectrum component.  See section below on output
 for a detailed explanation.</p>
 <p>Compute <em>snav/atom</em> calculates the virial contribution due to the
 derivatives:</p>
 <img alt="_images/compute_sna_atom6.jpg" class="align-center" src="_images/compute_sna_atom6.jpg" />
 <p>Again, the sum is over all atoms <em>i&#8217;</em> of atom type <em>I</em>.  For each atom
 <em>i</em>, this compute evaluates the above expression for each of the six
 virial components, each atom type, and each bispectrum component.  See
 section below on output for a detailed explanation.</p>
 <p>The value of all bispectrum components will be zero for atoms not in
 the group. Neighbor atoms not in the group do not contribute to the
 bispectrum of atoms in the group.</p>
 <p>The neighbor list needed to compute this quantity is constructed each
 time the calculation is performed (i.e. each time a snapshot of atoms
 is dumped).  Thus it can be inefficient to compute/dump this quantity
 too frequently.</p>
 <p>The argument <em>rcutfac</em> is a scale factor that controls the ratio of
 atomic radius to radial cutoff distance.</p>
 <p>The argument <em>rfac0</em> and the optional keyword <em>rmin0</em> define the
 linear mapping from radial distance to polar angle <em>theta0</em> on the
 3-sphere.</p>
 <p>The argument <em>twojmax</em> and the keyword <em>diagonal</em> define which
 bispectrum components are generated. See section below on output for a
 detailed explanation of the number of bispectrum components and the
 ordered in which they are listed</p>
 <p>The keyword <em>switchflag</em> can be used to turn off the switching
 function.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">If you have a bonded system, then the settings of
 <a class="reference internal" href="special_bonds.html"><em>special_bonds</em></a> command can remove pairwise
 interactions between atoms in the same bond, angle, or dihedral.  This
 is the default setting for the <a class="reference internal" href="special_bonds.html"><em>special_bonds</em></a>
 command, and means those pairwise interactions do not appear in the
 neighbor list.  Because this fix uses the neighbor list, it also means
 those pairs will not be included in the calculation.  One way to get
 around this, is to write a dump file, and use the <a class="reference internal" href="rerun.html"><em>rerun</em></a>
 command to compute the bispectrum components for snapshots in the dump
 file.  The rerun script can use a <a class="reference internal" href="special_bonds.html"><em>special_bonds</em></a>
 command that includes all pairs in the neighbor list.</p>
 </div>
 <p>;line</p>
 <p><strong>Output info:</strong></p>
 <p>Compute <em>sna/atom</em> calculates a per-atom array, each column
 corresponding to a particular bispectrum component.  The total number
 of columns and the identities of the bispectrum component contained in
 each column depend on the values of <em>twojmax</em> and <em>diagonal</em>, as
 described by the following piece of python code:</p>
 <div class="highlight-python"><div class="highlight"><pre>for j1 in range(0,twojmax+1):
     if(diagonal==2):
         print j1/2,j1/2,j1/2
     elif(diagonal==1):
         for j in range(0,min(twojmax,2*j1)+1,2):
             print j1/2,j1/2,j/2
     elif(diagonal==0):
         for j2 in range(0,j1+1):
             for j in range(j1-j2,min(twojmax,j1+j2)+1,2):
                 print j1/2,j2/2,j/2
     elif(diagonal==3):
         for j2 in range(0,j1+1):
             for j in range(j1-j2,min(twojmax,j1+j2)+1,2):
                 if (j&gt;=j1): print j1/2,j2/2,j/2
 </pre></div>
 </div>
 <p>Compute <em>snad/atom</em> evaluates a per-atom array. The columns are
 arranged into <em>ntypes</em> blocks, listed in order of atom type <em>I</em>.  Each
 block contains three sub-blocks corresponding to the <em>x</em>, <em>y</em>, and <em>z</em>
 components of the atom position.  Each of these sub-blocks contains
 one column for each bispectrum component, the same as for compute
 <em>sna/atom</em></p>
 <p>Compute <em>snav/atom</em> evaluates a per-atom array. The columns are
 arranged into <em>ntypes</em> blocks, listed in order of atom type <em>I</em>.  Each
 block contains six sub-blocks corresponding to the <em>xx</em>, <em>yy</em>, <em>zz</em>,
 <em>yz</em>, <em>xz</em>, and <em>xy</em> components of the virial tensor in Voigt
 notation.  Each of these sub-blocks contains one column for each
 bispectrum component, the same as for compute <em>sna/atom</em></p>
 <p>These values can be accessed by any command that uses per-atom values
 from a compute as input.  See <a class="reference internal" href="Section_howto.html#howto-15"><span>Section_howto 15</span></a> for an overview of LAMMPS output
 options.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>These computes are part of the SNAP package.  They are only enabled if
 LAMMPS was built with that package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="pair_snap.html"><em>pair_style snap</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The optional keyword defaults are <em>diagonal</em> = 0, <em>rmin0</em> = 0,
 <em>switchflag</em> = 1.</p>
 <hr class="docutils" />
 <p id="thompson2014"><strong>(Thompson)</strong> Thompson, Swiler, Trott, Foiles, Tucker, under review, preprint
 available at <a class="reference external" href="http://arxiv.org/abs/1409.3880">arXiv:1409.3880</a></p>
 <p id="bartok2010"><strong>(Bartok)</strong> Bartok, Payne, Risi, Csanyi, Phys Rev Lett, 104, 136403 (2010).</p>
 <p id="meremianin2006"><strong>(Meremianin)</strong> Meremianin, J. Phys. A,  39, 3099 (2006).</p>
 <p id="varshalovich1987"><strong>(Varshalovich)</strong> Varshalovich, Moskalev, Khersonskii, Quantum Theory
 of Angular Momentum, World Scientific, Singapore (1987).</p>
 </div>
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diff --git a/doc/compute_temp_asphere.html b/doc/compute_temp_asphere.html
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   <div class="section" id="compute-temp-asphere-command">
 <span id="index-0"></span><h1>compute temp/asphere command<a class="headerlink" href="#compute-temp-asphere-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>compute ID group-ID temp/asphere keyword value ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="compute.html"><em>compute</em></a> command</li>
 <li>temp/asphere = style name of this compute command</li>
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>bias</em> or <em>dof</em></li>
 </ul>
 <pre class="literal-block">
 <em>bias</em> value = bias-ID
-    bias-ID = ID of a temperature compute that removes a velocity bias
-  <em>dof</em> value = <em>all</em> or <em>rotate</em>
-    all = compute temperature of translational and rotational degrees of freedom
-    rotate = compute temperature of just rotational degrees of freedom
+  bias-ID = ID of a temperature compute that removes a velocity bias
+<em>dof</em> value = <em>all</em> or <em>rotate</em>
+  all = compute temperature of translational and rotational degrees of freedom
+  rotate = compute temperature of just rotational degrees of freedom
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>compute 1 all temp/asphere
 compute myTemp mobile temp/asphere bias tempCOM
 compute myTemp mobile temp/asphere dof rotate
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Define a computation that calculates the temperature of a group of
 aspherical particles, including a contribution from both their
 translational and rotational kinetic energy.  This differs from the
 usual <a class="reference internal" href="compute_temp.html"><em>compute temp</em></a> command, which assumes point
 particles with only translational kinetic energy.</p>
 <p>Only finite-size particles (aspherical or spherical) can be included
 in the group.  For 3d finite-size particles, each has 6 degrees of
 freedom (3 translational, 3 rotational).  For 2d finite-size
 particles, each has 3 degrees of freedom (2 translational, 1
 rotational).</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">This choice for degrees of freedom (dof) assumes that
 all finite-size aspherical or spherical particles in your model will
 freely rotate, sampling all their rotational dof.  It is possible to
 use a combination of interaction potentials and fixes that induce no
 torque or otherwise constrain some of all of your particles so that
 this is not the case.  Then there are less dof and you should use the
 <a class="reference internal" href="compute_modify.html"><em>compute_modify extra</em></a> command to adjust the dof
 accordingly.</p>
 </div>
 <p>For example, an aspherical particle with all three of its shape
 parameters the same is a sphere.  If it does not rotate, then it
 should have 3 dof instead of 6 in 3d (or 2 instead of 3 in 2d).  A
 uniaxial aspherical particle has two of its three shape parameters the
 same.  If it does not rotate around the axis perpendicular to its
 circular cross section, then it should have 5 dof instead of 6 in 3d.
 The latter is the case for uniaxial ellipsoids in a <a class="reference internal" href="pair_gayberne.html"><em>GayBerne model</em></a> since there is no induced torque around the
 optical axis.  It will also be the case for biaxial ellipsoids when
 exactly two of the semiaxes have the same length and the corresponding
 relative well depths are equal.</p>
 <p>The translational kinetic energy is computed the same as is described
 by the <a class="reference internal" href="compute_temp.html"><em>compute temp</em></a> command.  The rotational
 kinetic energy is computed as 1/2 I w^2, where I is the inertia tensor
 for the aspherical particle and w is its angular velocity, which is
 computed from its angular momentum.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">For <a class="reference internal" href="dimension.html"><em>2d models</em></a>, particles are treated
 as ellipsoids, not ellipses, meaning their moments of inertia will be
 the same as in 3d.</p>
 </div>
 <p>A kinetic energy tensor, stored as a 6-element vector, is also
 calculated by this compute.  The formula for the components of the
 tensor is the same as the above formula, except that v^2 and w^2 are
 replaced by vx*vy and wx*wy for the xy component, and the appropriate
 elements of the inertia tensor are used.  The 6 components of the
 vector are ordered xx, yy, zz, xy, xz, yz.</p>
 <p>The number of atoms contributing to the temperature is assumed to be
 constant for the duration of the run; use the <em>dynamic</em> option of the
 <a class="reference internal" href="compute_modify.html"><em>compute_modify</em></a> command if this is not the case.</p>
 <p>This compute subtracts out translational degrees-of-freedom due to
 fixes that constrain molecular motion, such as <a class="reference internal" href="fix_shake.html"><em>fix shake</em></a> and <a class="reference internal" href="fix_rigid.html"><em>fix rigid</em></a>.  This means the
 temperature of groups of atoms that include these constraints will be
 computed correctly.  If needed, the subtracted degrees-of-freedom can
 be altered using the <em>extra</em> option of the
 <a class="reference internal" href="compute_modify.html"><em>compute_modify</em></a> command.</p>
 <p>See <a class="reference internal" href="Section_howto.html#howto-16"><span>this howto section</span></a> of the manual for
 a discussion of different ways to compute temperature and perform
 thermostatting.</p>
 <hr class="docutils" />
 <p>The keyword/value option pairs are used in the following ways.</p>
 <p>For the <em>bias</em> keyword, <em>bias-ID</em> refers to the ID of a temperature
 compute that removes a &#8220;bias&#8221; velocity from each atom.  This allows
 compute temp/sphere to compute its thermal temperature after the
 translational kinetic energy components have been altered in a
 prescribed way, e.g. to remove a flow velocity profile.  Thermostats
 that use this compute will work with this bias term.  See the doc
 pages for individual computes that calculate a temperature and the doc
 pages for fixes that perform thermostatting for more details.</p>
 <p>For the <em>dof</em> keyword, a setting of <em>all</em> calculates a temperature
 that includes both translational and rotational degrees of freedom.  A
 setting of <em>rotate</em> calculates a temperature that includes only
 rotational degrees of freedom.</p>
 <hr class="docutils" />
 <p><strong>Output info:</strong></p>
 <p>This compute calculates a global scalar (the temperature) and a global
 vector of length 6 (KE tensor), which can be accessed by indices 1-6.
 These values can be used by any command that uses global scalar or
 vector values from a compute as input.  See <a class="reference internal" href="Section_howto.html#howto-15"><span>this section</span></a> for an overview of LAMMPS output
 options.</p>
 <p>The scalar value calculated by this compute is &#8220;intensive&#8221;.  The
 vector values are &#8220;extensive&#8221;.</p>
 <p>The scalar value will be in temperature <a class="reference internal" href="units.html"><em>units</em></a>.  The
 vector values will be in energy <a class="reference internal" href="units.html"><em>units</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>This compute is part of the ASPHERE package.  It is only enabled if
 LAMMPS was built with that package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 <p>This compute requires that atoms store angular momementum and a
 quaternion as defined by the <a class="reference internal" href="atom_style.html"><em>atom_style ellipsoid</em></a>
 command.</p>
 <p>All particles in the group must be finite-size.  They cannot be point
 particles, but they can be aspherical or spherical as defined by their
 shape attribute.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="compute_temp.html"><em>compute temp</em></a></p>
 <p><strong>Default:</strong> none</p>
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   <div class="section" id="compute-temp-chunk-command">
 <span id="index-0"></span><h1>compute temp/chunk command<a class="headerlink" href="#compute-temp-chunk-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>compute ID group-ID temp/chunk chunkID value1 value2 ... keyword value ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="compute.html"><em>compute</em></a> command</li>
 <li>temp/chunk = style name of this compute command</li>
 <li>chunkID = ID of <a class="reference internal" href="compute_chunk_atom.html"><em>compute chunk/atom</em></a> command</li>
 <li>zero or more values can be listed as value1,value2,etc</li>
 <li>value = <em>temp</em> or <em>kecom</em> or <em>internal</em></li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>temp = temperature of each chunk
-  kecom = kinetic energy of each chunk based on velocity of center of mass
-  internal = internal kinetic energy of each chunk
+kecom = kinetic energy of each chunk based on velocity of center of mass
+internal = internal kinetic energy of each chunk
 </pre></div>
 </div>
 <ul class="simple">
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>com</em> or <em>bias</em> or <em>adof</em> or <em>cdof</em></li>
 </ul>
 <pre class="literal-block">
 <em>com</em> value = <em>yes</em> or <em>no</em>
-    yes = subtract center-of-mass velocity from each chunk before calculating temperature
-    no = do not subtract center-of-mass velocity
-  <em>bias</em> value = bias-ID
-    bias-ID = ID of a temperature compute that removes a velocity bias
-  <em>adof</em> value = dof_per_atom
-    dof_per_atom = define this many degrees-of-freedom per atom
-  <em>cdof</em> value = dof_per_chunk
-    dof_per_chunk = define this many degrees-of-freedom per chunk
+  yes = subtract center-of-mass velocity from each chunk before calculating temperature
+  no = do not subtract center-of-mass velocity
+<em>bias</em> value = bias-ID
+  bias-ID = ID of a temperature compute that removes a velocity bias
+<em>adof</em> value = dof_per_atom
+  dof_per_atom = define this many degrees-of-freedom per atom
+<em>cdof</em> value = dof_per_chunk
+  dof_per_chunk = define this many degrees-of-freedom per chunk
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>compute 1 fluid temp/chunk molchunk
 compute 1 fluid temp/chunk molchunk temp internal
 compute 1 fluid temp/chunk molchunk bias tpartial adof 2.0
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Define a computation that calculates the temperature of a group of
 atoms that are also in chunks, after optionally subtracting out the
 center-of-mass velocity of each chunk.  By specifying optional values,
 it can also calulate the per-chunk temperature or energies of the
 multiple chunks of atoms.</p>
 <p>In LAMMPS, chunks are collections of atoms defined by a <a class="reference internal" href="compute_chunk_atom.html"><em>compute chunk/atom</em></a> command, which assigns each atom
 to a single chunk (or no chunk).  The ID for this command is specified
 as chunkID.  For example, a single chunk could be the atoms in a
 molecule or atoms in a spatial bin.  See the <a class="reference internal" href="compute_chunk_atom.html"><em>compute chunk/atom</em></a> doc page and &#8220;<a class="reference internal" href="Section_howto.html#howto-23"><span>Section_howto 23</span></a> for details of how chunks can be
 defined and examples of how they can be used to measure properties of
 a system.</p>
 <p>The temperature is calculated by the formula KE = DOF/2 k T, where KE =
 total kinetic energy of all atoms assigned to chunks (sum of 1/2 m
 v^2), DOF = the total number of degrees of freedom for those atoms, k
 = Boltzmann constant, and T = temperature.</p>
 <p>The DOF is calculated as N*adof + Nchunk*cdof, where N = number of
 atoms contributing to the KE, adof = degrees of freedom per atom, and
 cdof = degrees of freedom per chunk.  By default adof = 2 or 3 =
 dimensionality of system, as set via the <a class="reference internal" href="dimension.html"><em>dimension</em></a>
 command, and cdof = 0.0.  This gives the usual formula for
 temperature.</p>
 <p>A kinetic energy tensor, stored as a 6-element vector, is also
 calculated by this compute for use in the computation of a pressure
 tensor.  The formula for the components of the tensor is the same as
 the above formula, except that v^2 is replaced by vx*vy for the xy
 component, etc.  The 6 components of the vector are ordered xx, yy,
 zz, xy, xz, yz.</p>
 <p>Note that the number of atoms contributing to the temperature is
 calculated each time the temperature is evaluated since it is assumed
 the atoms may be dynamically assigned to chunks.  Thus there is no
 need to use the <em>dynamic</em> option of the
 <a class="reference internal" href="compute_modify.html"><em>compute_modify</em></a> command for this compute style.</p>
 <p>If any optional values are specified, then per-chunk quantities are
 also calculated and stored in a global array, as described below.</p>
 <p>The <em>temp</em> value calculates the temperature for each chunk by the
 formula KE = DOF/2 k T, where KE = total kinetic energy of the chunk
 of atoms (sum of 1/2 m v^2), DOF = the total number of degrees of
 freedom for all atoms in the chunk, k = Boltzmann constant, and T =
 temperature.</p>
 <p>The DOF in this case is calculated as N*adof + cdof, where N = number
 of atoms in the chunk, adof = degrees of freedom per atom, and cdof =
 degrees of freedom per chunk.  By default adof = 2 or 3 =
 dimensionality of system, as set via the <a class="reference internal" href="dimension.html"><em>dimension</em></a>
 command, and cdof = 0.0.  This gives the usual formula for
 temperature.</p>
 <p>The <em>kecom</em> value calculates the kinetic energy of each chunk as if
 all its atoms were moving with the velocity of the center-of-mass of
 the chunk.</p>
 <p>The <em>internal</em> value calculates the internal kinetic energy of each
 chunk.  The interal KE is summed over the atoms in the chunk using an
 internal &#8220;thermal&#8221; velocity for each atom, which is its velocity minus
 the center-of-mass velocity of the chunk.</p>
 <hr class="docutils" />
 <p>Note that currently the global and per-chunk temperatures calculated
 by this compute only include translational degrees of freedom for each
 atom.  No rotational degrees of freedom are included for finite-size
 particles.  Also no degrees of freedom are subtracted for any velocity
 bias or constraints that are applied, such as <a class="reference internal" href="compute_temp_partial.html"><em>compute temp/partial</em></a>, or <a class="reference internal" href="fix_shake.html"><em>fix shake</em></a>
 or <a class="reference internal" href="fix_rigid.html"><em>fix rigid</em></a>.  This is because those degrees of
 freedom (e.g. a constrained bond) could apply to sets of atoms that
 are both included and excluded from a specific chunk, and hence the
 concept is somewhat ill-defined.  In some cases, you can use the
 <em>adof</em> and <em>cdof</em> keywords to adjust the calculated degress of freedom
 appropriately, as explained below.</p>
 <p>Note that the per-chunk temperature calulated by this compute and the
 <a class="reference internal" href="fix_ave_chunk.html"><em>fix ave/chunk temp</em></a> command can be different.
 This compute calculates the temperature for each chunk for a single
 snapshot.  Fix ave/chunk can do that but can also time average those
 values over many snapshots, or it can compute a temperature as if the
 atoms in the chunk on different timesteps were collected together as
 one set of atoms to calculate their temperature.  This compute allows
 the center-of-mass velocity of each chunk to be subtracted before
 calculating the temperature; fix ave/chunk does not.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">Only atoms in the specified group contribute to the
 calculations performed by this compute.  The <a class="reference internal" href="compute_chunk_atom.html"><em>compute chunk/atom</em></a> command defines its own group;
 atoms will have a chunk ID = 0 if they are not in that group,
 signifying they are not assigned to a chunk, and will thus also not
 contribute to this calculation.  You can specify the &#8220;all&#8221; group for
 this command if you simply want to include atoms with non-zero chunk
 IDs.</p>
 </div>
 <p>The simplest way to output the per-chunk results of the compute
 temp/chunk calculation to a file is to use the <a class="reference internal" href="fix_ave_time.html"><em>fix ave/time</em></a> command, for example:</p>
 <div class="highlight-python"><div class="highlight"><pre>compute cc1 all chunk/atom molecule
 compute myChunk all temp/chunk cc1 temp
 fix 1 all ave/time 100 1 100 c_myChunk file tmp.out mode vector
 </pre></div>
 </div>
 <hr class="docutils" />
 <p>The keyword/value option pairs are used in the following ways.</p>
 <p>The <em>com</em> keyword can be used with a value of <em>yes</em> to subtract the
 velocity of the center-of-mass for each chunk from the velocity of the
 atoms in that chunk, before calculating either the global or per-chunk
 temperature.  This can be useful if the atoms are streaming or
 otherwise moving collectively, and you wish to calculate only the
 thermal temperature.</p>
 <p>For the <em>bias</em> keyword, <em>bias-ID</em> refers to the ID of a temperature
 compute that removes a &#8220;bias&#8221; velocity from each atom.  This also
 allows calculation of the global or per-chunk temperature using only
 the thermal temperature of atoms in each chunk after the translational
 kinetic energy components have been altered in a prescribed way,
 e.g. to remove a velocity profile.  It also applies to the calculation
 of the other per-chunk values, such as <em>kecom</em> or <em>internal</em>, which
 involve the center-of-mass velocity of each chunk, which is calculated
 after the velocity bias is removed from each atom.  Note that the
 temperature compute will apply its bias globally to the entire system,
 not on a per-chunk basis.</p>
 <p>The <em>adof</em> and <em>cdof</em> keywords define the values used in the degree of
 freedom (DOF) formulas used for the global or per-chunk temperature,
 as described above.  They can be used to calculate a more appropriate
 temperature for some kinds of chunks.  Here are 3 examples:</p>
 <p>If spatially binned chunks contain some number of water molecules and
 <a class="reference internal" href="fix_shake.html"><em>fix shake</em></a> is used to make each molecule rigid, then
 you could calculate a temperature with 6 degrees of freedom (DOF) (3
 translational, 3 rotational) per molecule by setting <em>adof</em> to 2.0.</p>
 <p>If <a class="reference internal" href="compute_temp_partial.html"><em>compute temp/partial</em></a> is used with the
 <em>bias</em> keyword to only allow the x component of velocity to contribute
 to the temperature, then <em>adof</em> = 1.0 would be appropriate.</p>
 <p>If each chunk consists of a large molecule, with some number of its
 bonds constrained by <a class="reference internal" href="fix_shake.html"><em>fix shake</em></a> or the entire molecule
 by <a class="reference internal" href="fix_rigid.html"><em>fix rigid/small</em></a>, <em>adof</em> = 0.0 and <em>cdof</em> could be
 set to the remaining degrees of freedom for the entire molecule
 (entire chunk in this case), e.g. 6 for 3d, or 3 for 2d, for a rigid
 molecule.</p>
 <hr class="docutils" />
 <p><strong>Output info:</strong></p>
 <p>This compute calculates a global scalar (the temperature) and a global
 vector of length 6 (KE tensor), which can be accessed by indices 1-6.
 These values can be used by any command that uses global scalar or
 vector values from a compute as input.  See <a class="reference internal" href="Section_howto.html#howto-15"><span>this section</span></a> for an overview of LAMMPS output
 options.</p>
 <p>This compute also optionally calculates a global array, if one or more
 of the optional values are specified.  The number of rows in the array
 = the number of chunks <em>Nchunk</em> as calculated by the specified
 <a class="reference internal" href="compute_chunk_atom.html"><em>compute chunk/atom</em></a> command.  The number of
 columns is the number of specifed values (1 or more).  These values
 can be accessed by any command that uses global array values from a
 compute as input.  Again, see <a class="reference internal" href="Section_howto.html#howto-15"><span>Section_howto 15</span></a> for an overview of LAMMPS output
 options.</p>
 <p>The scalar value calculated by this compute is &#8220;intensive&#8221;.  The
 vector values are &#8220;extensive&#8221;.  The array values are &#8220;intensive&#8221;.</p>
 <p>The scalar value will be in temperature <a class="reference internal" href="units.html"><em>units</em></a>.  The
 vector values will be in energy <a class="reference internal" href="units.html"><em>units</em></a>.  The array values
 will be in temperature <a class="reference internal" href="units.html"><em>units</em></a> for the <em>temp</em> value, and in
 energy <a class="reference internal" href="units.html"><em>units</em></a> for the <em>kecom</em> and <em>internal</em> values.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>The <em>com</em> and <em>bias</em> keywords cannot be used together.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="compute_temp.html"><em>compute temp</em></a>, <a class="reference internal" href="fix_ave_chunk.html"><em>fix ave/chunk temp</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The option defaults are com no, no bias, adof = dimensionality of the
 system (2 or 3), and cdof = 0.0.</p>
 </div>
 </div>
 
 
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   <div class="section" id="compute-temp-profile-command">
 <span id="index-0"></span><h1>compute temp/profile command<a class="headerlink" href="#compute-temp-profile-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>compute ID group-ID temp/profile xflag yflag zflag binstyle args
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="compute.html"><em>compute</em></a> command</li>
 <li>temp/profile = style name of this compute command</li>
 <li>xflag,yflag,zflag = 0/1 for whether to exclude/include this dimension</li>
 <li>binstyle = <em>x</em> or <em>y</em> or <em>z</em> or <em>xy</em> or <em>yz</em> or <em>xz</em> or <em>xyz</em></li>
 </ul>
 <pre class="literal-block">
 <em>x</em> arg = Nx
-  <em>y</em> arg = Ny
-  <em>z</em> arg = Nz
-  <em>xy</em> args = Nx Ny
-  <em>yz</em> args = Ny Nz
-  <em>xz</em> args = Nx Nz
-  <em>xyz</em> args = Nx Ny Nz
-    Nx,Ny,Nz = number of velocity bins in x,y,z dimensions
+<em>y</em> arg = Ny
+<em>z</em> arg = Nz
+<em>xy</em> args = Nx Ny
+<em>yz</em> args = Ny Nz
+<em>xz</em> args = Nx Nz
+<em>xyz</em> args = Nx Ny Nz
+  Nx,Ny,Nz = number of velocity bins in x,y,z dimensions
 </pre>
 <ul class="simple">
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>out</em></li>
 </ul>
 <pre class="literal-block">
 <em>out</em> value = <em>tensor</em> or <em>bin</em>
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>compute myTemp flow temp/profile 1 1 1 x 10
 compute myTemp flow temp/profile 1 1 1 x 10 out bin
 compute myTemp flow temp/profile 0 1 1 xyz 20 20 20
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Define a computation that calculates the temperature of a group of
 atoms, after subtracting out a spatially-averaged center-of-mass
 velocity field, before computing the kinetic energy.  This can be
 useful for thermostatting a collection of atoms undergoing a complex
 flow, e.g. via a profile-unbiased thermostat (PUT) as described in
 <a class="reference internal" href="fix_nvt_sllod.html#evans"><span>(Evans)</span></a>.  A compute of this style can be used by any command
 that computes a temperature, e.g. <a class="reference internal" href="thermo_modify.html"><em>thermo_modify</em></a>,
 <a class="reference internal" href="fix_temp_rescale.html"><em>fix temp/rescale</em></a>, <a class="reference internal" href="fix_nh.html"><em>fix npt</em></a>, etc.</p>
 <p>The <em>xflag</em>, <em>yflag</em>, <em>zflag</em> settings determine which components of
 average velocity are subtracted out.</p>
 <p>The <em>binstyle</em> setting and its <em>Nx</em>, <em>Ny</em>, <em>Nz</em> arguments determine
 how bins are setup to perform spatial averaging.  &#8220;Bins&#8221; can be 1d
 slabs, 2d pencils, or 3d bricks depending on which <em>binstyle</em> is used.
 The simulation box is partitioned conceptually into <em>Nx</em> by <em>Ny</em> by
 <em>Nz</em> bins.  Depending on the <em>binstyle</em>, you may only specify one or
 two of these values; the others are effectively set to 1 (no binning
 in that dimension).  For non-orthogonal (triclinic) simulation boxes,
 the bins are &#8220;tilted&#8221; slabs or pencils or bricks that are parallel to
 the tilted faces of the box.  See the <a class="reference internal" href="region.html"><em>region prism</em></a>
 command for a discussion of the geometry of tilted boxes in LAMMPS.</p>
 <p>When a temperature is computed, the center-of-mass velocity for the
 set of atoms that are both in the compute group and in the same
 spatial bin is calculated.  This bias velocity is then subtracted from
 the velocities of individual atoms in the bin to yield a thermal
 velocity for each atom.  Note that if there is only one atom in the
 bin, its thermal velocity will thus be 0.0.</p>
 <p>After the spatially-averaged velocity field has been subtracted from
 each atom, the temperature is calculated by the formula KE = (dim/2 N
 - dim*Nx*Ny*Nz) k T, where KE = total kinetic energy of the group of
 atoms (sum of 1/2 m v^2), dim = 2 or 3 = dimensionality of the
 simulation, N = number of atoms in the group, k = Boltzmann constant,
 and T = temperature.  The dim*Nx*Ny*Nz term are degrees of freedom
 subtracted to adjust for the removal of the center-of-mass velocity in
 each of Nx*Ny*Nz bins, as discussed in the <a class="reference internal" href="fix_nvt_sllod.html#evans"><span>(Evans)</span></a> paper.</p>
 <p>If the <em>out</em> keyword is used with a <em>tensor</em> value, which is the
 default, a kinetic energy tensor, stored as a 6-element vector, is
 also calculated by this compute for use in the computation of a
 pressure tensor.  The formula for the components of the tensor is the
 same as the above formula, except that v^2 is replaced by vx*vy for
 the xy component, etc.  The 6 components of the vector are ordered xx,
 yy, zz, xy, xz, yz.</p>
 <p>If the <em>out</em> keyword is used with a <em>bin</em> value, the count of atoms
 and computed temperature for each bin are stored for output, as an
 array of values, as described below.  The temperature of each bin is
 calculated as described above, where the bias velocity is subtracted
 and only the remaining thermal velocity of atoms in the bin
 contributes to the temperature.  See the note below for how the
 temperature is normalized by the degrees-of-freedom of atoms in the
 bin.</p>
 <p>The number of atoms contributing to the temperature is assumed to be
 constant for the duration of the run; use the <em>dynamic</em> option of the
 <a class="reference internal" href="compute_modify.html"><em>compute_modify</em></a> command if this is not the case.</p>
 <p>The removal of the spatially-averaged velocity field by this fix is
 essentially computing the temperature after a &#8220;bias&#8221; has been removed
 from the velocity of the atoms.  If this compute is used with a fix
 command that performs thermostatting then this bias will be subtracted
 from each atom, thermostatting of the remaining thermal velocity will
 be performed, and the bias will be added back in.  Thermostatting
 fixes that work in this way include <a class="reference internal" href="fix_nh.html"><em>fix nvt</em></a>, <a class="reference internal" href="fix_temp_rescale.html"><em>fix temp/rescale</em></a>, <a class="reference internal" href="fix_temp_berendsen.html"><em>fix temp/berendsen</em></a>, and <a class="reference internal" href="fix_langevin.html"><em>fix langevin</em></a>.</p>
 <p>This compute subtracts out degrees-of-freedom due to fixes that
 constrain molecular motion, such as <a class="reference internal" href="fix_shake.html"><em>fix shake</em></a> and
 <a class="reference internal" href="fix_rigid.html"><em>fix rigid</em></a>.  This means the temperature of groups of
 atoms that include these constraints will be computed correctly.  If
 needed, the subtracted degrees-of-freedom can be altered using the
 <em>extra</em> option of the <a class="reference internal" href="compute_modify.html"><em>compute_modify</em></a> command.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">When using the <em>out</em> keyword with a value of <em>bin</em>,
 the calculated temperature for each bin does not include the
 degrees-of-freedom adjustment described in the preceeding paragraph,
 for fixes that constrain molecular motion.  It does include the
 adjustment due to the <em>extra</em> option, which is applied to each bin.</p>
 </div>
 <p>See <a class="reference internal" href="Section_howto.html#howto-16"><span>this howto section</span></a> of the manual for
 a discussion of different ways to compute temperature and perform
 thermostatting.  Using this compute in conjunction with a
 thermostatting fix, as explained there, will effectively implement a
 profile-unbiased thermostat (PUT), as described in <a class="reference internal" href="fix_nvt_sllod.html#evans"><span>(Evans)</span></a>.</p>
 <p><strong>Output info:</strong></p>
 <p>This compute calculates a global scalar (the temperature).  Depending
 on the setting of the <em>out</em> keyword, it also calculates a global
 vector or array.  For <em>out</em> = <em>tensor</em>, it calculates a vector of
 length 6 (KE tensor), which can be accessed by indices 1-6.  For <em>out</em>
 = <em>bin</em> it calculates a global array which has 2 columns and N rows,
 where N is the number of bins.  The first column contains the number
 of atoms in that bin.  The second contains the temperature of that
 bin, calculated as described above.  The ordering of rows in the array
 is as follows.  Bins in x vary fastest, then y, then z.  Thus for a
 10x10x10 3d array of bins, there will be 1000 rows.  The bin with
 indices ix,iy,iz = 2,3,4 would map to row M = (iz-1)*10*10 + (iy-1)*10
 + ix = 322, where the rows are numbered from 1 to 1000 and the bin
 indices are numbered from 1 to 10 in each dimension.</p>
 <p>These values can be used by any command that uses global scalar or
 vector or array values from a compute as input.  See <a class="reference internal" href="Section_howto.html#howto-15"><span>this section</span></a> for an overview of LAMMPS output
 options.</p>
 <p>The scalar value calculated by this compute is &#8220;intensive&#8221;.  The
 vector values are &#8220;extensive&#8221;.  The array values are &#8220;intensive&#8221;.</p>
 <p>The scalar value will be in temperature <a class="reference internal" href="units.html"><em>units</em></a>.  The
 vector values will be in energy <a class="reference internal" href="units.html"><em>units</em></a>.  The first column
 of array values are counts; the values in the second column will be in
 temperature <a class="reference internal" href="units.html"><em>units</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>You should not use too large a velocity-binning grid, especially in
 3d.  In the current implementation, the binned velocity averages are
 summed across all processors, so this will be inefficient if the grid
 is too large, and the operation is performed every timestep, as it
 will be for most thermostats.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="compute_temp.html"><em>compute temp</em></a>, <a class="reference internal" href="compute_temp_ramp.html"><em>compute temp/ramp</em></a>, <a class="reference internal" href="compute_temp_deform.html"><em>compute temp/deform</em></a>, <a class="reference internal" href="compute_pressure.html"><em>compute pressure</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The option default is out = tensor.</p>
 <hr class="docutils" />
 <p id="evans"><strong>(Evans)</strong> Evans and Morriss, Phys Rev Lett, 56, 2172-2175 (1986).</p>
 </div>
 </div>
 
 
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index c08fa3f9a..9ab859208 100644
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   <div class="section" id="compute-temp-sphere-command">
 <span id="index-0"></span><h1>compute temp/sphere command<a class="headerlink" href="#compute-temp-sphere-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>compute ID group-ID temp/sphere keyword value ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="compute.html"><em>compute</em></a> command</li>
 <li>temp/sphere = style name of this compute command</li>
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>bias</em> or <em>dof</em></li>
 </ul>
 <pre class="literal-block">
 <em>bias</em> value = bias-ID
-    bias-ID = ID of a temperature compute that removes a velocity bias
-  <em>dof</em> value = <em>all</em> or <em>rotate</em>
-    all = compute temperature of translational and rotational degrees of freedom
-    rotate = compute temperature of just rotational degrees of freedom
+  bias-ID = ID of a temperature compute that removes a velocity bias
+<em>dof</em> value = <em>all</em> or <em>rotate</em>
+  all = compute temperature of translational and rotational degrees of freedom
+  rotate = compute temperature of just rotational degrees of freedom
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>compute 1 all temp/sphere
 compute myTemp mobile temp/sphere bias tempCOM
 compute myTemp mobile temp/sphere dof rotate
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Define a computation that calculates the temperature of a group of
 spherical particles, including a contribution from both their
 translational and rotational kinetic energy.  This differs from the
 usual <a class="reference internal" href="compute_temp.html"><em>compute temp</em></a> command, which assumes point
 particles with only translational kinetic energy.</p>
 <p>Both point and finite-size particles can be included in the group.
 Point particles do not rotate, so they have only 3 translational
 degrees of freedom.  For 3d spherical particles, each has 6 degrees of
 freedom (3 translational, 3 rotational).  For 2d spherical particles,
 each has 3 degrees of freedom (2 translational, 1 rotational).</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">This choice for degrees of freedom (dof) assumes that
 all finite-size spherical particles in your model will freely rotate,
 sampling all their rotational dof.  It is possible to use a
 combination of interaction potentials and fixes that induce no torque
 or otherwise constrain some of all of your particles so that this is
 not the case.  Then there are less dof and you should use the
 <a class="reference internal" href="compute_modify.html"><em>compute_modify extra</em></a> command to adjust the dof
 accordingly.</p>
 </div>
 <p>The translational kinetic energy is computed the same as is described
 by the <a class="reference internal" href="compute_temp.html"><em>compute temp</em></a> command.  The rotational
 kinetic energy is computed as 1/2 I w^2, where I is the moment of
 inertia for a sphere and w is the particle&#8217;s angular velocity.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">For <a class="reference internal" href="dimension.html"><em>2d models</em></a>, particles are treated
 as spheres, not disks, meaning their moment of inertia will be the
 same as in 3d.</p>
 </div>
 <p>A kinetic energy tensor, stored as a 6-element vector, is also
 calculated by this compute.  The formula for the components of the
 tensor is the same as the above formulas, except that v^2 and w^2 are
 replaced by vx*vy and wx*wy for the xy component.  The 6 components of
 the vector are ordered xx, yy, zz, xy, xz, yz.</p>
 <p>The number of atoms contributing to the temperature is assumed to be
 constant for the duration of the run; use the <em>dynamic</em> option of the
 <a class="reference internal" href="compute_modify.html"><em>compute_modify</em></a> command if this is not the case.</p>
 <p>This compute subtracts out translational degrees-of-freedom due to
 fixes that constrain molecular motion, such as <a class="reference internal" href="fix_shake.html"><em>fix shake</em></a> and <a class="reference internal" href="fix_rigid.html"><em>fix rigid</em></a>.  This means the
 temperature of groups of atoms that include these constraints will be
 computed correctly.  If needed, the subtracted degrees-of-freedom can
 be altered using the <em>extra</em> option of the
 <a class="reference internal" href="compute_modify.html"><em>compute_modify</em></a> command.</p>
 <p>See <a class="reference internal" href="Section_howto.html#howto-16"><span>this howto section</span></a> of the manual for
 a discussion of different ways to compute temperature and perform
 thermostatting.</p>
 <hr class="docutils" />
 <p>The keyword/value option pairs are used in the following ways.</p>
 <p>For the <em>bias</em> keyword, <em>bias-ID</em> refers to the ID of a temperature
 compute that removes a &#8220;bias&#8221; velocity from each atom.  This allows
 compute temp/sphere to compute its thermal temperature after the
 translational kinetic energy components have been altered in a
 prescribed way, e.g. to remove a flow velocity profile.  Thermostats
 that use this compute will work with this bias term.  See the doc
 pages for individual computes that calculate a temperature and the doc
 pages for fixes that perform thermostatting for more details.</p>
 <p>For the <em>dof</em> keyword, a setting of <em>all</em> calculates a temperature
 that includes both translational and rotational degrees of freedom.  A
 setting of <em>rotate</em> calculates a temperature that includes only
 rotational degrees of freedom.</p>
 <hr class="docutils" />
 <p><strong>Output info:</strong></p>
 <p>This compute calculates a global scalar (the temperature) and a global
 vector of length 6 (KE tensor), which can be accessed by indices 1-6.
 These values can be used by any command that uses global scalar or
 vector values from a compute as input.  See <a class="reference internal" href="Section_howto.html#howto-15"><span>this section</span></a> for an overview of LAMMPS output
 options.</p>
 <p>The scalar value calculated by this compute is &#8220;intensive&#8221;.  The
 vector values are &#8220;extensive&#8221;.</p>
 <p>The scalar value will be in temperature <a class="reference internal" href="units.html"><em>units</em></a>.  The
 vector values will be in energy <a class="reference internal" href="units.html"><em>units</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>This fix requires that atoms store torque and angular velocity (omega)
 and a radius as defined by the <a class="reference internal" href="atom_style.html"><em>atom_style sphere</em></a>
 command.</p>
 <p>All particles in the group must be finite-size spheres, or point
 particles with radius = 0.0.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="compute_temp.html"><em>compute temp</em></a>, <a class="reference internal" href="compute_temp.html"><em>compute temp/asphere</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The option defaults are no bias and dof = all.</p>
 </div>
 </div>
 
 
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   <div class="section" id="compute-ti-command">
 <span id="index-0"></span><h1>compute ti command<a class="headerlink" href="#compute-ti-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>compute ID group ti keyword args ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="compute.html"><em>compute</em></a> command</li>
 <li>ti = style name of this compute command</li>
 <li>one or more attribute/arg pairs may be appended</li>
 <li>keyword = pair style (lj/cut, gauss, born, etc) or <em>tail</em> or <em>kspace</em></li>
 </ul>
 <pre class="literal-block">
 pair style args = atype v_name1 v_name2
-    atype = atom type (see asterisk form below)
-    v_name1 = variable with name1 that is energy scale factor and function of lambda
-    v_name2 = variable with name2 that is derivative of v_name1 with respect to lambda
-  <em>tail</em> args = atype v_name1 v_name2
-    atype = atom type (see asterisk form below)
-    v_name1 = variable with name1 that is energy tail correction scale factor and function of lambda
-    v_name2 = variable with name2 that is derivative of v_name1 with respect to lambda
-  <em>kspace</em> args = atype v_name1 v_name2
-    atype = atom type (see asterisk form below)
-    v_name1 = variable with name1 that is K-Space scale factor and function of lambda
-    v_name2 = variable with name2 that is derivative of v_name1 with respect to lambda
+  atype = atom type (see asterisk form below)
+  v_name1 = variable with name1 that is energy scale factor and function of lambda
+  v_name2 = variable with name2 that is derivative of v_name1 with respect to lambda
+<em>tail</em> args = atype v_name1 v_name2
+  atype = atom type (see asterisk form below)
+  v_name1 = variable with name1 that is energy tail correction scale factor and function of lambda
+  v_name2 = variable with name2 that is derivative of v_name1 with respect to lambda
+<em>kspace</em> args = atype v_name1 v_name2
+  atype = atom type (see asterisk form below)
+  v_name1 = variable with name1 that is K-Space scale factor and function of lambda
+  v_name2 = variable with name2 that is derivative of v_name1 with respect to lambda
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>compute 1 all ti lj/cut 1 v_lj v_dlj coul/long 2 v_c v_dc kspace 1 v_ks v_dks
 compute 1 all ti lj/cut 1*3 v_lj v_dlj coul/long * v_c v_dc kspace * v_ks v_dks
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Define a computation that calculates the derivative of the interaction
 potential with respect to <em>lambda</em>, the coupling parameter used in a
 thermodynamic integration.  This derivative can be used to infer a
 free energy difference resulting from an alchemical simulation, as
 described in <a class="reference internal" href="#eike"><span>Eike</span></a>.</p>
 <p>Typically this compute will be used in conjunction with the <a class="reference internal" href="fix_adapt.html"><em>fix adapt</em></a> command which can perform alchemical
 transformations by adusting the strength of an interaction potential
 as a simulation runs, as defined by one or more
 <a class="reference internal" href="pair_style.html"><em>pair_style</em></a> or <a class="reference internal" href="kspace_style.html"><em>kspace_style</em></a>
 commands.  This scaling is done via a prefactor on the energy, forces,
 virial calculated by the pair or K-Space style.  The prefactor is
 often a function of a <em>lambda</em> parameter which may be adjusted from 0
 to 1 (or vice versa) over the course of a <a class="reference internal" href="run.html"><em>run</em></a>.  The
 time-dependent adjustment is what the <a class="reference internal" href="fix_adapt.html"><em>fix adapt</em></a>
 command does.</p>
 <p>Assume that the unscaled energy of a pair_style or kspace_style is
 given by U.  Then the scaled energy is</p>
 <div class="highlight-python"><div class="highlight"><pre>Us = f(lambda) U
 </pre></div>
 </div>
 <p>where f() is some function of lambda.  What this compute calculates is</p>
 <div class="highlight-python"><div class="highlight"><pre>dUs / d(lambda) = U df(lambda)/dlambda = Us / f(lambda) df(lambda)/dlambda
 </pre></div>
 </div>
 <p>which is the derivative of the system&#8217;s scaled potential energy Us
 with respect to <em>lambda</em>.</p>
 <p>To perform this calculation, you provide one or more atom types as
 <em>atype</em>.  <em>Atype</em> can be specified in one of two ways.  An explicit
 numeric values can be used, as in the 1st example above.  Or a
 wildcard asterisk can be used in place of or in conjunction with the
 <em>atype</em> argument to select multiple atom types.  This takes the form
 &#8220;*&#8221; or &#8220;<em>n&#8221; or &#8220;n</em>&#8221; or &#8220;m*n&#8221;.  If N = the number of atom types, then
 an asterisk with no numeric values means all types from 1 to N.  A
 leading asterisk means all types from 1 to n (inclusive).  A trailing
 asterisk means all types from n to N (inclusive).  A middle asterisk
 means all types from m to n (inclusive).</p>
 <p>You also specify two functions, as <a class="reference internal" href="variable.html"><em>equal-style variables</em></a>.  The first is specified as <em>v_name1</em>, where
 <em>name1</em> is the name of the variable, and is f(lambda) in the notation
 above.  The second is specified as <em>v_name2</em>, where <em>name2</em> is the
 name of the variable, and is df(lambda) / dlambda in the notation
 above.  I.e. it is the analytic derivative of f() with respect to
 lambda.  Note that the <em>name1</em> variable is also typically given as an
 argument to the <a class="reference internal" href="fix_adapt.html"><em>fix adapt</em></a> command.</p>
 <p>An alchemical simulation may use several pair potentials together,
 invoked via the <a class="reference internal" href="pair_hybrid.html"><em>pair_style hybrid or hybrid/overlay</em></a>
 command.  The total dUs/dlambda for the overall system is calculated
 as the sum of each contributing term as listed by the keywords in the
 compute ti command.  Individual pair potentials can be listed, which
 will be sub-styles in the hybrid case.  You can also include a K-space
 term via the <em>kspace</em> keyword.  You can also include a pairwise
 long-range tail correction to the energy via the <em>tail</em> keyword.</p>
 <p>For each term you can specify a different (or the same) scale factor
 by the two variables that you list.  Again, these will typically
 correspond toe the scale factors applied to these various potentials
 and the K-Space contribution via the <a class="reference internal" href="fix_adapt.html"><em>fix_adapt</em></a>
 command.</p>
 <p>More details about the exact functional forms for the computation of
 du/dl can be found in the paper by <a class="reference internal" href="#eike"><span>Eike</span></a>.</p>
 <hr class="docutils" />
 <p><strong>Output info:</strong></p>
 <p>This compute calculates a global scalar, namely dUs/dlambda.  This
 value can be used by any command that uses a global scalar value from
 a compute as input.  See <a class="reference internal" href="Section_howto.html#howto-15"><span>Section_howto 15</span></a> for an overview of LAMMPS output
 options.</p>
 <p>The scalar value calculated by this compute is &#8220;extensive&#8221;.</p>
 <p>The scalar value will be in energy <a class="reference internal" href="units.html"><em>units</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>This compute is part of the MISC package.  It is only enabled if
 LAMMPS was built with that package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="fix_adapt.html"><em>fix adapt</em></a></p>
 <p><strong>Default:</strong> none</p>
 <hr class="docutils" />
 <p id="eike"><strong>(Eike)</strong> Eike and Maginn, Journal of Chemical Physics, 124, 164503 (2006).</p>
 </div>
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   <div class="section" id="compute-voronoi-atom-command">
 <span id="index-0"></span><h1>compute voronoi/atom command<a class="headerlink" href="#compute-voronoi-atom-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>compute ID group-ID voronoi/atom keyword arg ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="compute.html"><em>compute</em></a> command</li>
 <li>voronoi/atom = style name of this compute command</li>
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>only_group</em> or <em>surface</em> or <em>radius</em> or <em>edge_histo</em> or <em>edge_threshold</em> or <em>face_threshold</em></li>
 </ul>
 <pre class="literal-block">
 <em>only_group</em> = no arg
-  <em>occupation</em> = no arg
-  <em>surface</em> arg = sgroup-ID
-    sgroup-ID = compute the dividing surface between group-ID and sgroup-ID
-      this keyword adds a third column to the compute output
-  <em>radius</em> arg = v_r
-    v_r = radius atom style variable for a poly-disperse Voronoi tessellation
-  <em>edge_histo</em> arg = maxedge
-    maxedge = maximum number of Voronoi cell edges to be accounted in the histogram
-  <em>edge_threshold</em> arg = minlength
-    minlength = minimum length for an edge to be counted
-  <em>face_threshold</em> arg = minarea
-    minarea = minimum area for a face to be counted
+<em>occupation</em> = no arg
+<em>surface</em> arg = sgroup-ID
+  sgroup-ID = compute the dividing surface between group-ID and sgroup-ID
+    this keyword adds a third column to the compute output
+<em>radius</em> arg = v_r
+  v_r = radius atom style variable for a poly-disperse Voronoi tessellation
+<em>edge_histo</em> arg = maxedge
+  maxedge = maximum number of Voronoi cell edges to be accounted in the histogram
+<em>edge_threshold</em> arg = minlength
+  minlength = minimum length for an edge to be counted
+<em>face_threshold</em> arg = minarea
+  minarea = minimum area for a face to be counted
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>compute 1 all voronoi/atom
 compute 2 precipitate voronoi/atom surface matrix
 compute 3b precipitate voronoi/atom radius v_r
 compute 4 solute voronoi/atom only_group
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>compute 5 defects voronoi/atom occupation
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Define a computation that calculates the Voronoi tessellation of the
 atoms in the simulation box.  The tessellation is calculated using all
 atoms in the simulation, but non-zero values are only stored for atoms
 in the group.</p>
 <p>By default two quantities per atom are calculated by this compute.
 The first is the volume of the Voronoi cell around each atom.  Any
 point in an atom&#8217;s Voronoi cell is closer to that atom than any other.
 The second is the number of faces of the Voronoi cell, which is also
 the number of nearest neighbors of the atom in the middle of the cell.</p>
 <hr class="docutils" />
 <p>If the <em>only_group</em> keyword is specified the tessellation is performed
 only with respect to the atoms contained in the compute group. This is
 equivalent to deleting all atoms not contained in the group prior to
 evaluating the tessellation.</p>
 <p>If the <em>surface</em> keyword is specified a third quantity per atom is
 computed: the Voronoi cell surface of the given atom. <em>surface</em> takes
 a group ID as an argument. If a group other than <em>all</em> is specified,
 only the Voronoi cell facets facing a neighbor atom from the specified
 group are counted towards the surface area.</p>
 <p>In the example above, a precipitate embedded in a matrix, only atoms
 at the surface of the precipitate will have non-zero surface area, and
 only the outward facing facets of the Voronoi cells are counted (the
 hull of the precipitate). The total surface area of the precipitate
 can be obtained by running a &#8220;reduce sum&#8221; compute on c_2[3]</p>
 <p>If the <em>radius</em> keyword is specified with an atom style variable as
 the argument, a poly-disperse Voronoi tessellation is
 performed. Examples for radius variables are</p>
 <div class="highlight-python"><div class="highlight"><pre>variable r1 atom (type==1)*0.1+(type==2)*0.4
 compute radius all property/atom radius
 variable r2 atom c_radius
 </pre></div>
 </div>
 <p>Here v_r1 specifies a per-type radius of 0.1 units for type 1 atoms
 and 0.4 units for type 2 atoms, and v_r2 accesses the radius property
 present in atom_style sphere for granular models.</p>
 <p>The <em>edge_histo</em> keyword activates the compilation of a histogram of
 number of edges on the faces of the Voronoi cells in the compute
 group. The argument maxedge of the this keyword is the largest number
 of edges on a single Voronoi cell face expected to occur in the
 sample. This keyword adds the generation of a global vector with
 maxedge+1 entries. The last entry in the vector contains the number of
 faces with with more than maxedge edges. Since the polygon with the
 smallest amount of edges is a triangle, entries 1 and 2 of the vector
 will always be zero.</p>
 <p>The <em>edge_threshold</em> and <em>face_threshold</em> keywords allow the
 suppression of edges below a given minimum length and faces below a
 given minimum area. Ultra short edges and ultra small faces can occur
 as artifacts of the Voronoi tessellation. These keywords will affect
 the neighbor count and edge histogram outputs.</p>
 <p>If the <em>occupation</em> keyword is specified the tessellation is only
 performed for the first invocation of the compute and then stored.
 For all following invocations of the compute the number of atoms in
 each Voronoi cell in the stored tessellation is counted. In this mode
 the compute returns a per-atom array with 2 columns. The first column
 is the number of atoms currently in the Voronoi volume defined by this
 atom at the time of the first invocation of the compute (note that the
 atom may have moved significantly). The second column contains the
 total number of atoms sharing the Voronoi cell of the stored
 tessellation at the location of the current atom. Numbers in column
 one can be any positive integer including zero, while column two
 values will always be greater than zero. Column one data can be used
 to locate vacancies (the coordinates are given by the atom coordinates
 at the time step when the compute was first invoked), while column two
 data can be used to identify interstitial atoms.</p>
 <hr class="docutils" />
 <p>The Voronoi calculation is performed by the freely available <a class="reference external" href="http://math.lbl.gov/voro++">Voro++ package</a>, written by Chris Rycroft at UC Berkeley and LBL,
 which must be installed on your system when building LAMMPS for use
 with this compute.  See instructions on obtaining and installing the
 Voro++ software in the src/VORONOI/README file.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">The calculation of Voronoi volumes is performed by
 each processor for the atoms it owns, and includes the effect of ghost
 atoms stored by the processor.  This assumes that the Voronoi cells of
 owned atoms are not affected by atoms beyond the ghost atom cut-off
 distance.  This is usually a good assumption for liquid and solid
 systems, but may lead to underestimation of Voronoi volumes in low
 density systems.  By default, the set of ghost atoms stored by each
 processor is determined by the cutoff used for
 <a class="reference internal" href="pair_style.html"><em>pair_style</em></a> interactions.  The cutoff can be set
 explicitly via the <a class="reference internal" href="comm_modify.html"><em>comm_modify cutoff</em></a> command.</p>
 </div>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">The Voro++ package performs its calculation in 3d.
 This should still work for a 2d LAMMPS simulation, to effectively
 compute Voronoi &#8220;areas&#8221;, so long as the z-dimension of the box is
 roughly the same (or smaller) compared to the separation of the atoms.
 Typical values for the z box dimensions in a 2d LAMMPS model are -0.5
 to 0.5, which satisfies the criterion for most <a class="reference internal" href="units.html"><em>units</em></a>
 systems.  Note that you define the z extent of the simulation box for
 2d simulations when using the <a class="reference internal" href="create_box.html"><em>create_box</em></a> or
 <a class="reference internal" href="read_data.html"><em>read_data</em></a> commands.</p>
 </div>
 <p><strong>Output info:</strong></p>
 <p>This compute calculates a per-atom array with 2 columns. In regular
 dynamic tessellation mode the first column is the Voronoi volume, the
 second is the neighbor count, as described above (read above for the
 output data in case the <em>occupation</em> keyword is specified).
 These values can be accessed by any command that
 uses per-atom values from a compute as input.  See <a class="reference internal" href="Section_howto.html#howto-15"><span>Section_howto 15</span></a> for an overview of LAMMPS output
 options.</p>
 <p>The Voronoi cell volume will be in distance <a class="reference internal" href="units.html"><em>units</em></a> cubed.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>This compute is part of the VORONOI package.  It is only enabled if
 LAMMPS was built with that package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="dump.html"><em>dump custom</em></a></p>
 <p><strong>Default:</strong> none</p>
 </div>
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   <div class="section" id="compute-xrd-command">
 <span id="index-0"></span><h1>compute xrd command<a class="headerlink" href="#compute-xrd-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>compute ID group-ID xrd lambda type1 type2 ... typeN keyword value ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="compute.html"><em>compute</em></a> command</li>
 <li>xrd = style name of this compute command</li>
 <li>lambda = wavelength of incident radiation (length units)</li>
 <li>type1 type2 ... typeN = chemical symbol of each atom type (see valid options below)</li>
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>2Theta</em> or <em>c</em> or <em>LP</em> or <em>manual</em> or <em>echo</em></li>
 </ul>
 <pre class="literal-block">
 <em>2Theta</em> values = Min2Theta Max2Theta
-    Min2Theta,Max2Theta = minimum and maximum 2 theta range to explore
-    (radians or degrees)
-  <em>c</em> values = c1 c2 c3
-    c1,c2,c3 = parameters to adjust the spacing of the reciprocal
-               lattice nodes in the h, k, and l directions respectively
-  <em>LP</em> value = switch to apply Lorentz-polarization factor
-    0/1 = off/on
-  <em>manual</em> = flag to use manual spacing of reciprocal lattice points
-             based on the values of the <em>c</em> parameters
-  <em>echo</em> = flag to provide extra output for debugging purposes
+  Min2Theta,Max2Theta = minimum and maximum 2 theta range to explore
+  (radians or degrees)
+<em>c</em> values = c1 c2 c3
+  c1,c2,c3 = parameters to adjust the spacing of the reciprocal
+             lattice nodes in the h, k, and l directions respectively
+<em>LP</em> value = switch to apply Lorentz-polarization factor
+  0/1 = off/on
+<em>manual</em> = flag to use manual spacing of reciprocal lattice points
+           based on the values of the <em>c</em> parameters
+<em>echo</em> = flag to provide extra output for debugging purposes
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>compute 1 all xrd 1.541838 Al O 2Theta 0.087 0.87 c 1 1 1 LP 1 echo
 compute 2 all xrd 1.541838 Al O 2Theta 10 100 c 0.05 0.05 0.05 LP 1 manual
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>fix 1 all ave/histo/weights 1 1 1 0.087 0.87 250 c_1[1] c_1[2] mode vector file Rad2Theta.xrd
 fix 2 all ave/histo/weights 1 1 1 10 100 250 c_2[1] c_2[2] mode vector file Deg2Theta.xrd
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Define a computation that calculates x-ray diffraction intensity as described
 in <a class="reference internal" href="fix_saed_vtk.html#coleman"><span>(Coleman)</span></a> on a mesh of reciprocal lattice nodes defined
 by the entire simulation domain (or manually) using a simulated radiation
 of wavelength lambda.</p>
 <p>The x-ray diffraction intensity, I, at each reciprocal lattice point, k,
 is computed from the structure factor, F, using the equations:</p>
 <img alt="_images/compute_xrd1.jpg" class="align-center" src="_images/compute_xrd1.jpg" />
 <img alt="_images/compute_xrd2.jpg" class="align-center" src="_images/compute_xrd2.jpg" />
 <img alt="_images/compute_xrd3.jpg" class="align-center" src="_images/compute_xrd3.jpg" />
 <img alt="_images/compute_xrd4.jpg" class="align-center" src="_images/compute_xrd4.jpg" />
 <p>Here, K is the location of the reciprocal lattice node, rj is the
 position of each atom, fj are atomic scattering factors, LP is the
 Lorentz-polarization factor, and theta is the scattering angle of
 diffraction.  The Lorentz-polarization factor can be turned off using
 the optional <em>LP</em> keyword.</p>
 <p>Diffraction intensities are calculated on a three-dimensional mesh of
 reciprocal lattice nodes. The mesh spacing is defined either (a)
 by the entire simulation domain or (b) manually using selected values as
 shown in the 2D diagram below.</p>
 <a data-lightbox="group-default"
                    href="_images/xrd_mesh.jpg"
                    class=""
                    title=""
                    data-title=""
                    ><img src="_images/xrd_mesh.jpg"
                     class="align-center"
                     width="25%"
                     height="auto"
                     alt=""/>
                     </a><p>For a mesh defined by the simulation domain, a rectilinear grid is
 constructed with spacing <a href="#id1"><span class="problematic" id="id2">*</span></a>c**inv(A) along each reciprocal lattice
 axis. Where A are the vectors corresponding to the edges of the
 simulation cell. If one or two directions has non-periodic boundary
 conditions, then the spacing in these directions is defined from the
 average of the (inversed) box lengths with periodic boundary conditions.
 Meshes defined by the simulation domain must contain at least one periodic
 boundary.</p>
 <p>If the <em>manual</em> flag is included, the mesh of reciprocal lattice nodes
 will defined using the <em>c</em> values for the spacing along each
 reciprocal lattice axis. Note that manual mapping of the reciprocal
 space mesh is good for comparing diffraction results from multiple
 simulations; however it can reduce the likelihood that Bragg
 reflections will be satisfied unless small spacing parameters (&lt; 0.05
 Angstrom^(-1)) are implemented.  Meshes with manual spacing do not
 require a periodic boundary.</p>
 <p>The limits of the reciprocal lattice mesh are determined by range of
 scattering angles explored.  The <em>2Theta</em> parameters allows the user
 to reduce the scattering angle range to only the region of interest
 which reduces the cost of the computation.</p>
 <p>The atomic scattering factors, fj, accounts for the reduction in
 diffraction intensity due to Compton scattering.  Compute xrd uses
 analytical approximations of the atomic scattering factors that vary
 for each atom type (type1 type2 ... typeN) and angle of diffraction.
 The analytic approximation is computed using the formula
 <a class="reference internal" href="#colliex"><span>(Colliex)</span></a>:</p>
 <img alt="_images/compute_xrd5.jpg" class="align-center" src="_images/compute_xrd5.jpg" />
 <p>Coefficients parameterized by <a class="reference internal" href="#peng"><span>(Peng)</span></a> are assigned for each
 atom type designating the chemical symbol and charge of each atom
 type. Valid chemical symbols for compute xrd are:</p>
 <dl class="docutils">
 <dt>H:    He1-:      He:      Li:    Li1+:</dt>
 <dd><blockquote class="first">
 <div><blockquote>
 <div><dl class="docutils">
 <dt>Be:    Be2+:       B:       C:    Cval:</dt>
 <dd>N:       O:     O1-:       F:     F1-:</dd>
 </dl>
 <p>Ne:      Na:    Na1+:      Mg:    Mg2+:
 Al:    Al3+:      Si:    Sival:   Si4+:</p>
 <blockquote>
 <div>P:       S:      Cl:    Cl1-:      Ar:
 K:      Ca:    Ca2+:      Sc:    Sc3+:</div></blockquote>
 <p>Ti:    Ti2+:    Ti3+:    Ti4+:       V:</p>
 </div></blockquote>
 <p>V2+:     V3+:     V5+:      Cr:    Cr2+:</p>
 </div></blockquote>
 <dl class="docutils">
 <dt>Cr3+:      Mn:    Mn2+:    Mn3+:    Mn4+:</dt>
 <dd>Fe:    Fe2+:    Fe3+:      Co:    Co2+:
 Co:      Ni:    Ni2+:    Ni3+:      Cu:</dd>
 </dl>
 <p>Cu1+:    Cu2+:      Zn:    Zn2+:      Ga:
 Ga3+:      Ge:    Ge4+:      As:      Se:</p>
 <blockquote>
 <div>Br:    Br1-:      Kr:      Rb:    Rb1+:
 Sr:    Sr2+:       Y:     Y3+:      Zr:</div></blockquote>
 <p>Zr4+:      Nb:    Nb3+:    Nb5+:      Mo:
 Mo3+:    Mo5+:    Mo6+:      Tc:      Ru:
 Ru3+:    Ru4+:      Rh:    Rh3+:    Rh4+:</p>
 <blockquote>
 <div>Pd:    Pd2+:    Pd4+:      Ag:    Ag1+:</div></blockquote>
 <dl class="docutils">
 <dt>Ag2+:      Cd:    Cd2+:      In:    In3+:</dt>
 <dd>Sn:    Sn2+:    Sn4+:      Sb:    Sb3+:</dd>
 <dt>Sb5+:      Te:       I:     I1-:      Xe:</dt>
 <dd>Cs:    Cs1+:      Ba:    Ba2+:      La:</dd>
 </dl>
 <p>La3+:      Ce:    Ce3+:    Ce4+:      Pr:
 Pr3+:    Pr4+:      Nd:    Nd3+:      Pm:
 Pm3+:      Sm:    Sm3+:      Eu:    Eu2+:
 Eu3+:      Gd:    Gd3+:      Tb:    Tb3+:</p>
 <blockquote>
 <div>Dy:    Dy3+:      Ho:    Ho3+:      Er:</div></blockquote>
 <p>Er3+:      Tm:    Tm3+:      Yb:    Yb2+:
 Yb3+:      Lu:    Lu3+:      Hf:    Hf4+:</p>
 <blockquote>
 <div>Ta:    Ta5+:       W:     W6+:      Re:
 Os:    Os4+:      Ir:    Ir3+:    Ir4+:
 Pt:    Pt2+:    Pt4+:      Au:    Au1+:</div></blockquote>
 <p>Au3+:      Hg:    Hg1+:    Hg2+:      Tl:
 Tl1+:    Tl3+:      Pb:    Pb2+:    Pb4+:</p>
 <blockquote>
 <div>Bi:    Bi3+:    Bi5+:      Po:      At:
 Rn:      Fr:      Ra:    Ra2+:      Ac:</div></blockquote>
 <dl class="docutils">
 <dt>Ac3+:      Th:    Th4+:      Pa:       U:</dt>
 <dd>U3+:     U4+:     U6+:      Np:    Np3+:</dd>
 </dl>
 <p class="last">Np4+:    Np6+:      Pu:    Pu3+:    Pu4+:
 Pu6+:      Am:      Cm:      Bk:      Cf:tb(c=5,s=:)</p>
 </dd>
 </dl>
 <p>If the <em>echo</em> keyword is specified, compute xrd will provide extra
 reporting information to the screen.</p>
 <p><strong>Output info:</strong></p>
 <p>This compute calculates a global array.  The number of rows in the
 array is the number of reciprocal lattice nodes that are explored
 which by the mesh.  The global array has 2 columns.</p>
 <p>The first column contains the diffraction angle in the units (radians
 or degrees) provided with the <em>2Theta</em> values. The second column contains
 the computed diffraction intensities as described above.</p>
 <p>The array can be accessed by any command that uses global values
 from a compute as input.  See <a class="reference internal" href="Section_howto.html#howto-15"><span>this section</span></a> for an overview of LAMMPS output
 options.</p>
 <p>All array values calculated by this compute are &#8220;intensive&#8221;.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>The compute_xrd command does not work for triclinic cells.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="fix_ave_histo.html"><em>fix ave/histo</em></a>,
 <a class="reference internal" href="compute_saed.html"><em>compute saed</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The option defaults are 2Theta = 1 179 (degrees), c = 1 1 1, LP = 1,
 no manual flag, no echo flag.</p>
 <hr class="docutils" />
 <p id="coleman"><strong>(Coleman)</strong> Coleman, Spearot, Capolungo, MSMSE, 21, 055020
 (2013).</p>
 <p id="colliex"><strong>(Colliex)</strong> Colliex et al. International Tables for Crystallography
 Volume C: Mathematical and Chemical Tables, 249-429 (2004).</p>
 <p id="peng"><strong>(Peng)</strong> Peng, Ren, Dudarev, Whelan, Acta Crystallogr. A, 52, 257-76
 (1996).</p>
 </div>
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diff --git a/doc/create_atoms.html b/doc/create_atoms.html
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   <div class="section" id="create-atoms-command">
 <span id="index-0"></span><h1>create_atoms command<a class="headerlink" href="#create-atoms-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>create_atoms type style args keyword values ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>type = atom type (1-Ntypes) of atoms to create (offset for molecule creation)</li>
 <li>style = <em>box</em> or <em>region</em> or <em>single</em> or <em>random</em></li>
 </ul>
 <pre class="literal-block">
 <em>box</em> args = none
-  <em>region</em> args = region-ID
-    region-ID = particles will only be created if contained in the region
-  <em>single</em> args = x y z
-    x,y,z = coordinates of a single particle (distance units)
-  <em>random</em> args = N seed region-ID
-    N = number of particles to create
-    seed = random # seed (positive integer)
-    region-ID = create atoms within this region, use NULL for entire simulation box
+<em>region</em> args = region-ID
+  region-ID = particles will only be created if contained in the region
+<em>single</em> args = x y z
+  x,y,z = coordinates of a single particle (distance units)
+<em>random</em> args = N seed region-ID
+  N = number of particles to create
+  seed = random # seed (positive integer)
+  region-ID = create atoms within this region, use NULL for entire simulation box
 </pre>
 <ul class="simple">
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>mol</em> or <em>basis</em> or <em>remap</em> or <em>var</em> or <em>set</em> or <em>units</em></li>
 </ul>
 <pre class="literal-block">
 <em>mol</em> value = template-ID seed
-    template-ID = ID of molecule template specified in a separate <a class="reference internal" href="molecule.html"><em>molecule</em></a> command
-    seed = random # seed (positive integer)
-  <em>basis</em> values = M itype
-    M = which basis atom
-    itype = atom type (1-N) to assign to this basis atom
-  <em>remap</em> value = <em>yes</em> or <em>no</em>
-  <em>var</em> value = name = variable name to evaluate for test of atom creation
-  <em>set</em> values = dim vname
-    dim = <em>x</em> or <em>y</em> or <em>z</em>
-    name = name of variable to set with x,y,z atom position
-  <em>rotate</em> values = Rx Ry Rz theta
-    Rx,Ry,Rz = rotation vector for single molecule
-    theta = rotation angle for single molecule (degrees)
-  <em>units</em> value = <em>lattice</em> or <em>box</em>
-    <em>lattice</em> = the geometry is defined in lattice units
-    <em>box</em> = the geometry is defined in simulation box units
+  template-ID = ID of molecule template specified in a separate <a class="reference internal" href="molecule.html"><em>molecule</em></a> command
+  seed = random # seed (positive integer)
+<em>basis</em> values = M itype
+  M = which basis atom
+  itype = atom type (1-N) to assign to this basis atom
+<em>remap</em> value = <em>yes</em> or <em>no</em>
+<em>var</em> value = name = variable name to evaluate for test of atom creation
+<em>set</em> values = dim vname
+  dim = <em>x</em> or <em>y</em> or <em>z</em>
+  name = name of variable to set with x,y,z atom position
+<em>rotate</em> values = Rx Ry Rz theta
+  Rx,Ry,Rz = rotation vector for single molecule
+  theta = rotation angle for single molecule (degrees)
+<em>units</em> value = <em>lattice</em> or <em>box</em>
+  <em>lattice</em> = the geometry is defined in lattice units
+  <em>box</em> = the geometry is defined in simulation box units
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>create_atoms 1 box
 create_atoms 3 region regsphere basis 2 3
 create_atoms 3 single 0 0 5
 create_atoms 1 box var v set x xpos set y ypos
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>This command creates atoms (or molecules) on a lattice, or a single
 atom (or molecule), or a random collection of atoms (or molecules), as
 an alternative to reading in their coordinates explicitly via a
 <a class="reference internal" href="read_data.html"><em>read_data</em></a> or <a class="reference internal" href="read_restart.html"><em>read_restart</em></a>
 command.  A simulation box must already exist, which is typically
 created via the <a class="reference internal" href="create_box.html"><em>create_box</em></a> command.  Before using
 this command, a lattice must also be defined using the
 <a class="reference internal" href="lattice.html"><em>lattice</em></a> command, unless you specify the <em>single</em> style
 with units = box or the <em>random</em> style.  For the remainder of this doc
 page, a created atom or molecule is referred to as a &#8220;particle&#8221;.</p>
 <p>If created particles are individual atoms, they are assigned the
 specified atom <em>type</em>, though this can be altered via the <em>basis</em>
 keyword as discussed below.  If molecules are being created, the type
 of each atom in the created molecule is specified in the file read by
 the <a class="reference internal" href="molecule.html"><em>molecule</em></a> command, and those values are added to
 the specified atom <em>type</em>.  E.g. if <em>type</em> = 2, and the file specifies
 atom types 1,2,3, then each created molecule will have atom types
 3,4,5.</p>
 <p>For the <em>box</em> style, the create_atoms command fills the entire
 simulation box with particles on the lattice.  If your simulation box
 is periodic, you should insure its size is a multiple of the lattice
 spacings, to avoid unwanted atom overlaps at the box boundaries.  If
 your box is periodic and a multiple of the lattice spacing in a
 particular dimension, LAMMPS is careful to put exactly one particle at
 the boundary (on either side of the box), not zero or two.</p>
 <p>For the <em>region</em> style, a geometric volume is filled with particles on
 the lattice.  This volume what is inside the simulation box and is
 also consistent with the region volume.  See the <a class="reference internal" href="region.html"><em>region</em></a>
 command for details.  Note that a region can be specified so that its
 &#8220;volume&#8221; is either inside or outside a geometric boundary.  Also note
 that if your region is the same size as a periodic simulation box (in
 some dimension), LAMMPS does not implement the same logic described
 above as for the <em>box</em> style, to insure exactly one particle at
 periodic boundaries.  if this is what you desire, you should either
 use the <em>box</em> style, or tweak the region size to get precisely the
 particles you want.</p>
 <p>For the <em>single</em> style, a single particle is added to the system at
 the specified coordinates.  This can be useful for debugging purposes
 or to create a tiny system with a handful of particles at specified
 positions.</p>
 <p>For the <em>random</em> style, N particles are added to the system at
 randomly generated coordinates, which can be useful for generating an
 amorphous system.  The particles are created one by one using the
 speficied random number <em>seed</em>, resulting in the same set of particles
 coordinates, independent of how many processors are being used in the
 simulation.  If the <em>region-ID</em> argument is specified as NULL, then
 the created particles will be anywhere in the simulation box.  If a
 <em>region-ID</em> is specified, a geometric volume is filled which is both
 inside the simulation box and is also consistent with the region
 volume.  See the <a class="reference internal" href="region.html"><em>region</em></a> command for details.  Note that
 a region can be specified so that its &#8220;volume&#8221; is either inside or
 outside a geometric boundary.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">Particles generated by the <em>random</em> style will
 typically be highly overlapped which will cause many interatomic
 potentials to compute large energies and forces.  Thus you should
 either perform an <a class="reference internal" href="minimize.html"><em>energy minimization</em></a> or run dynamics
 with <a class="reference internal" href="fix_nve_limit.html"><em>fix nve/limit</em></a> to equilibrate such a system,
 before running normal dynamics.</p>
 </div>
 <p>Note that this command adds particles to those that already exist.
 This means it can be used to add particles to a system previously read
 in from a data or restart file.  Or the create_atoms command can be
 used multiple times, to add multiple sets of particles to the
 simulation.  For example, grain boundaries can be created, by
 interleaving create_atoms with <a class="reference internal" href="lattice.html"><em>lattice</em></a> commands
 specifying different orientations.  By using the create_atoms command
 in conjunction with the <a class="reference internal" href="delete_atoms.html"><em>delete_atoms</em></a> command,
 reasonably complex geometries can be created, or a protein can be
 solvated with a surrounding box of water molecules.</p>
 <p>In all these cases, care should be taken to insure that new atoms do
 not overlap existing atoms inappropriately, especially if molecules
 are being added.  The <a class="reference internal" href="delete_atoms.html"><em>delete_atoms</em></a> command can be
 used to remove overlapping atoms or molecules.</p>
 <hr class="docutils" />
 <p>Individual atoms are inserted by this command, unless the <em>mol</em>
 keyword is used.  It specifies a <em>template-ID</em> previously defined
 using the <a class="reference internal" href="molecule.html"><em>molecule</em></a> command, which reads a file that
 defines the molecule.  The coordinates, atom types, charges, etc, as
 well as any bond/angle/etc and special neighbor information for the
 molecule can be specified in the molecule file.  See the
 <a class="reference internal" href="molecule.html"><em>molecule</em></a> command for details.  The only settings
 required to be in this file are the coordinates and types of atoms in
 the molecule.</p>
 <p>Using a lattice to add molecules, e.g. via the <em>box</em> or <em>region</em> or
 <em>single</em> styles, is exactly the same as adding atoms on lattice
 points, except that entire molecules are added at each point, i.e. on
 the point defined by each basis atom in the unit cell as it tiles the
 simulation box or region.  This is done by placing the geometric
 center of the molecule at the lattice point, and giving the molecule a
 random orientation about the point.  The random <em>seed</em> specified with
 the <em>mol</em> keyword is used for this operation, and the random numbers
 generated by each processor are different.  This means the coordinates
 of individual atoms (in the molecules) will be different when running
 on different numbers of processors, unlike when atoms are being
 created in parallel.</p>
 <p>Also note that because of the random rotations, it may be important to
 use a lattice with a large enough spacing that adjacent molecules will
 not overlap, regardless of their relative orientations.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">If the <a class="reference internal" href="create_box.html"><em>create_box</em></a> command is used to
 create the simulation box, followed by the create_atoms command with
 its <em>mol</em> option for adding molecules, then you typically need to use
 the optional keywords allowed by the <a class="reference internal" href="create_box.html"><em>create_box</em></a>
 command for extra bonds (angles,etc) or extra special neighbors.  This
 is because by default, the <a class="reference internal" href="create_box.html"><em>create_box</em></a> command sets
 up a non-molecular system which doesn&#8217;t allow molecules to be added.</p>
 </div>
 <hr class="docutils" />
 <p>This is the meaning of the other allowed keywords.</p>
 <p>The <em>basis</em> keyword is only used when atoms (not molecules) are being
 created.  It specifies an atom type that will be assigned to specific
 basis atoms as they are created.  See the <a class="reference internal" href="lattice.html"><em>lattice</em></a>
 command for specifics on how basis atoms are defined for the unit cell
 of the lattice.  By default, all created atoms are assigned the
 argument <em>type</em> as their atom type.</p>
 <p>The <em>remap</em> keyword only applies to the <em>single</em> style.  If it is set
 to <em>yes</em>, then if the specified position is outside the simulation
 box, it will mapped back into the box, assuming the relevant
 dimensions are periodic.  If it is set to <em>no</em>, no remapping is done
 and no particle is created if its position is outside the box.</p>
 <p>The <em>var</em> and <em>set</em> keywords can be used to provide a criterion for
 accepting or rejecting the addition of an individual atom, based on
 its coordinates.  The <em>vname</em> specified for the <em>var</em> keyword is the
 name of an <a class="reference internal" href="variable.html"><em>equal-style variable</em></a> which should evaluate
 to a zero or non-zero value based on one or two or three variables
 which will store the x, y, or z coordinates of an atom (one variable
 per coordinate).  These other variables must be <a class="reference internal" href="variable.html"><em>equal-style variables</em></a> defined in the input script, but their
 formula can by anything.  The <em>set</em> keyword is used to identify the
 names of these other variables, one variable for the x-coordinate of a
 created atom, one for y, and one for z.</p>
 <p>When an atom is created, its x, y, or z coordinates override the
 formula for any <em>set</em> variable that is defined.  The <em>var</em> variable is
 then evaluated.  If the returned value is 0.0, the atom is not
 created.  If it is non-zero, the atom is created.  After all atoms are
 created, the formulas defined for all of the <em>set</em> variables are
 restored to their original strings.</p>
 <p>As an example, these commands can be used in a 2d simulation, to
 create a sinusoidal surface.  Note that the surface is &#8220;rough&#8221; due to
 individual lattice points being &#8220;above&#8221; or &#8220;below&#8221; the mathematical
 expression for the sinusoidal curve.  If a finer lattice were used,
 the sinusoid would appear to be &#8220;smoother&#8221;.  Also note the use of the
 &#8220;xlat&#8221; and &#8220;ylat&#8221; <a class="reference internal" href="thermo_style.html"><em>thermo_style</em></a> keywords which
 converts lattice spacings to distance.  Click on the image for a
 larger version.</p>
 <div class="highlight-python"><div class="highlight"><pre>variable        x equal 100
 variable        y equal 25
 lattice              hex 0.8442
 region               box block 0 $x 0 $y -0.5 0.5
 create_box   1 box
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>variable        xx equal 0.0
 variable        yy equal 0.0
 variable        v equal &quot;(0.2*v_y*ylat * cos(v_xx/xlat * 2.0*PI*4.0/v_x) + 0.5*v_y*ylat - v_yy) &gt; 0.0&quot;
 create_atoms 1 box var v set x xx set y yy
 </pre></div>
 </div>
 <a data-lightbox="group-default"
                    href="_images/sinusoid.jpg"
                    class=""
                    title=""
                    data-title=""
                    ><img src="_images/sinusoid.jpg"
                     class="align-center"
                     width="25%"
                     height="auto"
                     alt=""/>
                     </a><p>The <em>rotate</em> keyword can be used with the <em>single</em> style, when adding
 a single molecule to specify the orientation at which the molecule is
 inserted.  The axis of rotation is determined by the rotation vector
 (Rx,Ry,Rz) that goes through the insertion point.  The specified
 <em>theta</em> determines the angle of rotation around that axis.  Note that
 the direction of rotation for the atoms around the rotation axis is
 consistent with the right-hand rule: if your right-hand&#8217;s thumb points
 along <em>R</em>, then your fingers wrap around the axis in the direction of
 rotation.</p>
 <p>The <em>units</em> keyword determines the meaning of the distance units used
 to specify the coordinates of the one particle created by the <em>single</em>
 style.  A <em>box</em> value selects standard distance units as defined by
 the <a class="reference internal" href="units.html"><em>units</em></a> command, e.g. Angstroms for units = real or
 metal.  A <em>lattice</em> value means the distance units are in lattice
 spacings.</p>
 <hr class="docutils" />
 <p>Atom IDs are assigned to created atoms in the following way.  The
 collection of created atoms are assigned consecutive IDs that start
 immediately following the largest atom ID existing before the
 create_atoms command was invoked.  When a simulation is performed on
 different numbers of processors, there is no guarantee a particular
 created atom will be assigned the same ID.  If molecules are being
 created, molecule IDs are assigned to created molecules in a similar
 fashion.</p>
 <p>Aside from their ID, atom type, and xyz position, other properties of
 created atoms are set to default values, depending on which quantities
 are defined by the chosen <a class="reference internal" href="atom_style.html"><em>atom style</em></a>.  See the <a class="reference internal" href="atom_style.html"><em>atom style</em></a> command for more details.  See the
 <a class="reference internal" href="set.html"><em>set</em></a> and <a class="reference internal" href="velocity.html"><em>velocity</em></a> commands for info on how
 to change these values.</p>
 <ul class="simple">
 <li>charge = 0.0</li>
 <li>dipole moment magnitude = 0.0</li>
 <li>diameter = 1.0</li>
 <li>shape = 0.0 0.0 0.0</li>
 <li>density = 1.0</li>
 <li>volume = 1.0</li>
 <li>velocity = 0.0 0.0 0.0</li>
 <li>angular velocity = 0.0 0.0 0.0</li>
 <li>angular momentum = 0.0 0.0 0.0</li>
 <li>quaternion = (1,0,0,0)</li>
 <li>bonds, angles, dihedrals, impropers = none</li>
 </ul>
 <p>If molecules are being created, these defaults can be overridden by
 values specified in the file read by the <a class="reference internal" href="molecule.html"><em>molecule</em></a>
 command.  E.g. the file typically defines bonds (angles,etc) between
 atoms in the molecule, and can optionally define charges on each atom.</p>
 <p>Note that the <em>sphere</em> atom style sets the default particle diameter
 to 1.0 as well as the density.  This means the mass for the particle
 is not 1.0, but is PI/6 * diameter^3 = 0.5236.</p>
 <p>Note that the <em>ellipsoid</em> atom style sets the default particle shape
 to (0.0 0.0 0.0) and the density to 1.0 which means it is a point
 particle, not an ellipsoid, and has a mass of 1.0.</p>
 <p>Note that the <em>peri</em> style sets the default volume and density to 1.0
 and thus also set the mass for the particle to 1.0.</p>
 <p>The <a class="reference internal" href="set.html"><em>set</em></a> command can be used to override many of these
 default settings.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>An <a class="reference internal" href="atom_style.html"><em>atom_style</em></a> must be previously defined to use this
 command.</p>
 <p>A rotation vector specified for a single molecule must be in
 the z-direction for a 2d model.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="lattice.html"><em>lattice</em></a>, <a class="reference internal" href="region.html"><em>region</em></a>, <a class="reference internal" href="create_box.html"><em>create_box</em></a>,
 <a class="reference internal" href="read_data.html"><em>read_data</em></a>, <a class="reference internal" href="read_restart.html"><em>read_restart</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The default for the <em>basis</em> keyword is that all created atoms are
 assigned the argument <em>type</em> as their atom type (when single atoms are
 being created).  The other defaults are <em>remap</em> = no, <em>rotate</em> =
 random, and <em>units</em> = lattice.</p>
 </div>
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   <div class="section" id="create-box-command">
 <span id="index-0"></span><h1>create_box command<a class="headerlink" href="#create-box-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>create_box N region-ID keyword value ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>N = # of atom types to use in this simulation</li>
 <li>region-ID = ID of region to use as simulation domain</li>
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>bond/types</em> or <em>angle/types</em> or <em>dihedral/types</em> or <em>improper/types</em> or <em>extra/bond/per/atom</em> or <em>extra/angle/per/atom</em> or <em>extra/dihedral/per/atom</em> or <em>extra/improper/per/atom</em></li>
 </ul>
 <pre class="literal-block">
 <em>bond/types</em> value = # of bond types
-  <em>angle/types</em> value = # of angle types
-  <em>dihedral/types</em> value = # of dihedral types
-  <em>improper/types</em> value = # of improper types
-  <em>extra/bond/per/atom</em> value = # of bonds per atom
-  <em>extra/angle/per/atom</em> value = # of angles per atom
-  <em>extra/dihedral/per/atom</em> value = # of dihedrals per atom
-  <em>extra/improper/per/atom</em> value = # of impropers per atom
-  <em>extra/special/per/atom</em> value = # of special neighbors per atom
+<em>angle/types</em> value = # of angle types
+<em>dihedral/types</em> value = # of dihedral types
+<em>improper/types</em> value = # of improper types
+<em>extra/bond/per/atom</em> value = # of bonds per atom
+<em>extra/angle/per/atom</em> value = # of angles per atom
+<em>extra/dihedral/per/atom</em> value = # of dihedrals per atom
+<em>extra/improper/per/atom</em> value = # of impropers per atom
+<em>extra/special/per/atom</em> value = # of special neighbors per atom
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>create_box 2 mybox
 create_box 2 mybox bond/types 2 extra/bond/per/atom 1
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>This command creates a simulation box based on the specified region.
 Thus a <a class="reference internal" href="region.html"><em>region</em></a> command must first be used to define a
 geometric domain.  It also partitions the simulation box into a
 regular 3d grid of rectangular bricks, one per processor, based on the
 number of processors being used and the settings of the
 <a class="reference internal" href="processors.html"><em>processors</em></a> command.  The partitioning can later be
 changed by the <a class="reference internal" href="balance.html"><em>balance</em></a> or <a class="reference internal" href="fix_balance.html"><em>fix balance</em></a> commands.</p>
 <p>The argument N is the number of atom types that will be used in the
 simulation.</p>
 <p>If the region is not of style <em>prism</em>, then LAMMPS encloses the region
 (block, sphere, etc) with an axis-aligned orthogonal bounding box
 which becomes the simulation domain.</p>
 <p>If the region is of style <em>prism</em>, LAMMPS creates a non-orthogonal
 simulation domain shaped as a parallelepiped with triclinic symmetry.
 As defined by the <a class="reference internal" href="region.html"><em>region prism</em></a> command, the
 parallelepiped has its &#8220;origin&#8221; at (xlo,ylo,zlo) and is defined by 3
 edge vectors starting from the origin given by A = (xhi-xlo,0,0); B =
 (xy,yhi-ylo,0); C = (xz,yz,zhi-zlo).  <em>Xy,xz,yz</em> can be 0.0 or
 positive or negative values and are called &#8220;tilt factors&#8221; because they
 are the amount of displacement applied to faces of an originally
 orthogonal box to transform it into the parallelipiped.</p>
 <p>By default, a <em>prism</em> region used with the create_box command must
 have tilt factors (xy,xz,yz) that do not skew the box more than half
 the distance of the parallel box length.  For example, if xlo = 2 and
 xhi = 12, then the x box length is 10 and the xy tilt factor must be
 between -5 and 5.  Similarly, both xz and yz must be between
 -(xhi-xlo)/2 and +(yhi-ylo)/2.  Note that this is not a limitation,
 since if the maximum tilt factor is 5 (as in this example), then
 configurations with tilt = ..., -15, -5, 5, 15, 25, ... are all
 geometrically equivalent.  If you wish to define a box with tilt
 factors that exceed these limits, you can use the <a class="reference internal" href="box.html"><em>box tilt</em></a>
 command, with a setting of <em>large</em>; a setting of <em>small</em> is the
 default.</p>
 <p>See <a class="reference internal" href="Section_howto.html#howto-12"><span>Section_howto 12</span></a> of the doc pages
 for a geometric description of triclinic boxes, as defined by LAMMPS,
 and how to transform these parameters to and from other commonly used
 triclinic representations.</p>
 <p>When a prism region is used, the simulation domain should normally be
 periodic in the dimension that the tilt is applied to, which is given
 by the second dimension of the tilt factor (e.g. y for xy tilt).  This
 is so that pairs of atoms interacting across that boundary will have
 one of them shifted by the tilt factor.  Periodicity is set by the
 <a class="reference internal" href="boundary.html"><em>boundary</em></a> command.  For example, if the xy tilt factor
 is non-zero, then the y dimension should be periodic.  Similarly, the
 z dimension should be periodic if xz or yz is non-zero.  LAMMPS does
 not require this periodicity, but you may lose atoms if this is not
 the case.</p>
 <p>Also note that if your simulation will tilt the box, e.g. via the <a class="reference internal" href="fix_deform.html"><em>fix deform</em></a> command, the simulation box must be setup to
 be triclinic, even if the tilt factors are initially 0.0.  You can
 also change an orthogonal box to a triclinic box or vice versa by
 using the <a class="reference internal" href="change_box.html"><em>change box</em></a> command with its <em>ortho</em> and
 <em>triclinic</em> options.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">If the system is non-periodic (in a dimension), then
 you should not make the lo/hi box dimensions (as defined in your
 <a class="reference internal" href="region.html"><em>region</em></a> command) radically smaller/larger than the extent
 of the atoms you eventually plan to create, e.g. via the
 <a class="reference internal" href="create_atoms.html"><em>create_atoms</em></a> command.  For example, if your atoms
 extend from 0 to 50, you should not specify the box bounds as -10000
 and 10000. This is because as described above, LAMMPS uses the
 specified box size to layout the 3d grid of processors.  A huge
 (mostly empty) box will be sub-optimal for performance when using
 &#8220;fixed&#8221; boundary conditions (see the <a class="reference internal" href="boundary.html"><em>boundary</em></a>
 command).  When using &#8220;shrink-wrap&#8221; boundary conditions (see the
 <a class="reference internal" href="boundary.html"><em>boundary</em></a> command), a huge (mostly empty) box may cause
 a parallel simulation to lose atoms the first time that LAMMPS
 shrink-wraps the box around the atoms.</p>
 </div>
 <hr class="docutils" />
 <p>The optional keywords can be used to create a system that allows for
 bond (angle, dihedral, improper) interactions, or for molecules with
 special 1-2,1-3,1-4 neighbors to be added later.  These optional
 keywords serve the same purpose as the analogous keywords that can be
 used in a data file which are recognized by the
 <a class="reference internal" href="read_data.html"><em>read_data</em></a> command when it sets up a system.</p>
 <p>Note that if these keywords are not used, then the create_box command
 creates an atomic (non-molecular) simulation that does not allow bonds
 between pairs of atoms to be defined, or a <a class="reference internal" href="bond_style.html"><em>bond potential</em></a> to be specified, or for molecules with
 special neighbors to be added to the system by commands such as
 <a class="reference internal" href="create_atoms.html"><em>create_atoms mol</em></a>, <a class="reference internal" href="fix_deposit.html"><em>fix deposit</em></a>
 or <a class="reference internal" href="fix_pour.html"><em>fix pour</em></a>.</p>
 <p>As an example, see the examples/deposit/in.deposit.molecule script,
 which deposits molecules onto a substrate.  Initially there are no
 molecules in the system, but they are added later by the <a class="reference internal" href="fix_deposit.html"><em>fix deposit</em></a> command.  The create_box command in the
 script uses the bond/types and extra/bond/per/atom keywords to allow
 this.  If the added molecule contained more than 1 special bond
 (allowed by default), an extra/special/per/atom keyword would also
 need to be specified.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>An <a class="reference internal" href="atom_style.html"><em>atom_style</em></a> and <a class="reference internal" href="region.html"><em>region</em></a> must have
 been previously defined to use this command.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="read_data.html"><em>read_data</em></a>, <a class="reference internal" href="create_atoms.html"><em>create_atoms</em></a>,
 <a class="reference internal" href="region.html"><em>region</em></a></p>
 <p><strong>Default:</strong> none</p>
 </div>
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   <div class="section" id="delete-atoms-command">
 <span id="index-0"></span><h1>delete_atoms command<a class="headerlink" href="#delete-atoms-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>delete_atoms style args keyword value ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>style = <em>group</em> or <em>region</em> or <em>overlap</em> or <em>porosity</em></li>
 </ul>
 <pre class="literal-block">
 <em>group</em> args = group-ID
-  <em>region</em> args = region-ID
-  <em>overlap</em> args = cutoff group1-ID group2-ID
-    cutoff = delete one atom from pairs of atoms within the cutoff (distance units)
-    group1-ID = one atom in pair must be in this group
-    group2-ID = other atom in pair must be in this group
-  <em>porosity</em> args = region-ID fraction seed
-    region-ID = region within which to perform deletions
-    fraction = delete this fraction of atoms
-    seed = random number seed (positive integer)
+<em>region</em> args = region-ID
+<em>overlap</em> args = cutoff group1-ID group2-ID
+  cutoff = delete one atom from pairs of atoms within the cutoff (distance units)
+  group1-ID = one atom in pair must be in this group
+  group2-ID = other atom in pair must be in this group
+<em>porosity</em> args = region-ID fraction seed
+  region-ID = region within which to perform deletions
+  fraction = delete this fraction of atoms
+  seed = random number seed (positive integer)
 </pre>
 <ul class="simple">
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>compress</em> or <em>bond</em> or <em>mol</em></li>
 </ul>
 <pre class="literal-block">
 <em>compress</em> value = <em>no</em> or <em>yes</em>
-  <em>bond</em> value = <em>no</em> or <em>yes</em>
-  <em>mol</em> value = <em>no</em> or <em>yes</em>
+<em>bond</em> value = <em>no</em> or <em>yes</em>
+<em>mol</em> value = <em>no</em> or <em>yes</em>
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>delete_atoms group edge
 delete_atoms region sphere compress no
 delete_atoms overlap 0.3 all all
 delete_atoms overlap 0.5 solvent colloid
 delete_atoms porosity cube 0.1 482793 bond yes
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Delete the specified atoms.  This command can be used to carve out
 voids from a block of material or to delete created atoms that are too
 close to each other (e.g. at a grain boundary).</p>
 <p>For style <em>group</em>, all atoms belonging to the group are deleted.</p>
 <p>For style <em>region</em>, all atoms in the region volume are deleted.
 Additional atoms can be deleted if they are in a molecule for which
 one or more atoms were deleted within the region; see the <em>mol</em>
 keyword discussion below.</p>
 <p>For style <em>overlap</em> pairs of atoms whose distance of separation is
 within the specified cutoff distance are searched for, and one of the
 2 atoms is deleted.  Only pairs where one of the two atoms is in the
 first group specified and the other atom is in the second group are
 considered.  The atom that is in the first group is the one that is
 deleted.</p>
 <p>Note that it is OK for the two group IDs to be the same (e.g. group
 <em>all</em>), or for some atoms to be members of both groups.  In these
 cases, either atom in the pair may be deleted.  Also note that if
 there are atoms which are members of both groups, the only guarantee
 is that at the end of the deletion operation, enough deletions will
 have occurred that no atom pairs within the cutoff will remain
 (subject to the group restriction).  There is no guarantee that the
 minimum number of atoms will be deleted, or that the same atoms will
 be deleted when running on different numbers of processors.</p>
 <p>For style <em>porosity</em> a specified <em>fraction</em> of atoms are deleted
 within the specified region.  For example, if fraction is 0.1, then
 10% of the atoms will be deleted.  The atoms to delete are chosen
 randomly.  There is no guarantee that the exact fraction of atoms will
 be deleted, or that the same atoms will be deleted when running on
 different numbers of processors.</p>
 <p>If the <em>compress</em> keyword is set to <em>yes</em>, then after atoms are
 deleted, then atom IDs are re-assigned so that they run from 1 to the
 number of atoms in the system.  Note that this is not done for
 molecular systems (see the <a class="reference internal" href="atom_style.html"><em>atom_style</em></a> command),
 regardless of the <em>compress</em> setting, since it would foul up the bond
 connectivity that has already been assigned.</p>
 <p>A molecular system with fixed bonds, angles, dihedrals, or improper
 interactions, is one where the topology of the interactions is
 typically defined in the data file read by the
 <a class="reference internal" href="read_data.html"><em>read_data</em></a> command, and where the interactions
 themselves are defined with the <a class="reference internal" href="bond_style.html"><em>bond_style</em></a>,
 <a class="reference internal" href="angle_style.html"><em>angle_style</em></a>, etc commands.  If you delete atoms
 from such a system, you must be careful not to end up with bonded
 interactions that are stored by remaining atoms but which include
 deleted atoms.  This will cause LAMMPS to generate a &#8220;missing atoms&#8221;
 error when the bonded interaction is computed.  The <em>bond</em> and <em>mol</em>
 keywords offer two ways to do that.</p>
 <p>It the <em>bond</em> keyword is set to <em>yes</em> then any bond or angle or
 dihedral or improper interaction that includes a deleted atom is also
 removed from the lists of such interactions stored by non-deleted
 atoms.  Note that simply deleting interactions due to dangling bonds
 (e.g. at a surface) may result in a inaccurate or invalid model for
 the remaining atoms.</p>
 <p>It the <em>mol</em> keyword is set to <em>yes</em>, then for every atom that is
 deleted, all other atoms in the same molecule (with the same molecule
 ID) will also be deleted.  This is not done for atoms with molecule ID
 = 0, since such an ID is assumed to flag isolated atoms that are not
 part of molecules.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">The molecule deletion operation in invoked after all
 individual atoms have been deleted using the rules described above for
 each style.  This means additional atoms may be deleted that are not
 in the group or region, that are not required by the overlap cutoff
 criterion, or that will create a higher fraction of porosity than was
 requested.</p>
 </div>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>The <em>overlap</em> styles requires inter-processor communication to acquire
 ghost atoms and build a neighbor list.  This means that your system
 must be ready to perform a simulation before using this command (force
 fields setup, atom masses set, etc).  Since a neighbor list is used to
 find overlapping atom pairs, it also means that you must define a
 <a class="reference internal" href="pair_style.html"><em>pair style</em></a> with the minimum force cutoff distance
 between any pair of atoms types (plus the <a class="reference internal" href="neighbor.html"><em>neighbor</em></a>
 skin) &gt;= the specified overlap cutoff.</p>
 <p>If the <a class="reference internal" href="special_bonds.html"><em>special_bonds</em></a> command is used with a
 setting of 0, then a pair of bonded atoms (1-2, 1-3, or 1-4) will not
 appear in the neighbor list, and thus will not be considered for
 deletion by the <em>overlap</em> styles.  You probably don&#8217;t want to be
 deleting one atom in a bonded pair anyway.</p>
 <p>The <em>bond yes</em> option cannot be used with molecular systems defined
 using molecule template files via the <code class="xref doc docutils literal"><span class="pre">molecule</span></code> and
 <a class="reference internal" href="atom_style.html"><em>atom_style template</em></a> commands.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="create_atoms.html"><em>create_atoms</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The option defaults are compress = yes, bond = no, mol = no.</p>
 </div>
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   <div class="section" id="delete-bonds-command">
 <span id="index-0"></span><h1>delete_bonds command<a class="headerlink" href="#delete-bonds-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>delete_bonds group-ID style arg keyword ...
 </pre></div>
 </div>
 <ul>
 <li><p class="first">group-ID = group ID</p>
 </li>
 <li><dl class="first docutils">
 <dt>style = <em>multi</em> or <em>atom</em> or <em>bond</em> or <em>angle</em> or <em>dihedral</em> or</dt>
 <dd><p class="first last"><em>improper</em> or <em>stats</em></p>
 </dd>
 </dl>
 </li>
 </ul>
 <pre class="literal-block">
 <em>multi</em> arg = none
-  <em>atom</em> arg = an atom type or range of types (see below)
-  <em>bond</em> arg = a bond type or range of types (see below)
-  <em>angle</em> arg = an angle type or range of types (see below)
-  <em>dihedral</em> arg = a dihedral type or range of types (see below)
-  <em>improper</em> arg = an improper type or range of types (see below)
-  <em>stats</em> arg = none
+<em>atom</em> arg = an atom type or range of types (see below)
+<em>bond</em> arg = a bond type or range of types (see below)
+<em>angle</em> arg = an angle type or range of types (see below)
+<em>dihedral</em> arg = a dihedral type or range of types (see below)
+<em>improper</em> arg = an improper type or range of types (see below)
+<em>stats</em> arg = none
 </pre>
 <ul class="simple">
 <li>zero or more keywords may be appended</li>
 <li>keyword = <em>any</em> or <em>undo</em> or <em>remove</em> or <em>special</em></li>
 </ul>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>delete_bonds frozen multi remove
 delete_bonds all atom 4 special
 delete_bonds all bond 0*3 special
 delete_bonds all stats
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Turn off (or on) molecular topology interactions, i.e. bonds, angles,
 dihedrals, impropers.  This command is useful for deleting
 interactions that have been previously turned off by bond-breaking
 potentials.  It is also useful for turning off topology interactions
 between frozen or rigid atoms.  Pairwise interactions can be turned
 off via the <a class="reference internal" href="neigh_modify.html"><em>neigh_modify exclude</em></a> command.  The
 <a class="reference internal" href="fix_shake.html"><em>fix shake</em></a> command also effectively turns off certain
 bond and angle interactions.</p>
 <p>For all styles, by default, an interaction is only turned off (or on)
 if all the atoms involved are in the specified group.  See the <em>any</em>
 keyword to change the behavior.</p>
 <p>Several of the styles (<em>atom</em>, <em>bond</em>, <em>angle</em>, <em>dihedral</em>,
 <em>improper</em>) take a <em>type</em> as an argument.  The specified <em>type</em> should
 be an integer from 0 to N, where N is the number of relevant types
 (atom types, bond types, etc).  A value of 0 is only relevant for
 style <em>bond</em>; see details below.  In all cases, a wildcard asterisk
 can be used in place of or in conjunction with the <em>type</em> argument to
 specify a range of types.  This takes the form &#8220;*&#8221; or &#8220;<em>n&#8221; or &#8220;n</em>&#8221; or
 &#8220;m*n&#8221;.  If N = the number of types, then an asterisk with no numeric
 values means all types from 0 to N.  A leading asterisk means all
 types from 0 to n (inclusive).  A trailing asterisk means all types
 from n to N (inclusive).  A middle asterisk means all types from m to
 n (inclusive).  Note that it is fine to include a type of 0 for
 non-bond styles; it will simply be ignored.</p>
 <p>For style <em>multi</em> all bond, angle, dihedral, and improper interactions
 of any type, involving atoms in the group, are turned off.</p>
 <p>Style <em>atom</em> is the same as style <em>multi</em> except that in addition, one
 or more of the atoms involved in the bond, angle, dihedral, or
 improper interaction must also be of the specified atom type.</p>
 <p>For style <em>bond</em>, only bonds are candidates for turn-off, and the bond
 must also be of the specified type.  Styles <em>angle</em>, <em>dihedral</em>, and
 <em>improper</em> are treated similarly.</p>
 <p>For style <em>bond</em>, you can set the type to 0 to delete bonds that have
 been previously broken by a bond-breaking potential (which sets the
 bond type to 0 when a bond is broken); e.g. see the <a class="reference internal" href="bond_style.html"><em>bond_style quartic</em></a> command.</p>
 <p>For style <em>stats</em> no interactions are turned off (or on); the status
 of all interactions in the specified group is simply reported.  This
 is useful for diagnostic purposes if bonds have been turned off by a
 bond-breaking potential during a previous run.</p>
 <p>The default behavior of the delete_bonds command is to turn off
 interactions by toggling their type to a negative value, but not to
 permanently remove the interaction.  E.g. a bond_type of 2 is set to
 -2.  The neighbor list creation routines will not include such an
 interaction in their interaction lists.  The default is also to not
 alter the list of 1-2, 1-3, 1-4 neighbors computed by the
 <a class="reference internal" href="special_bonds.html"><em>special_bonds</em></a> command and used to weight pairwise
 force and energy calculations.  This means that pairwise computations
 will proceed as if the bond (or angle, etc) were still turned on.</p>
 <p>Several keywords can be appended to the argument list to alter the
 default behaviors.</p>
 <p>The <em>any</em> keyword changes the requirement that all atoms in the bond
 (angle, etc) must be in the specified group in order to turn-off the
 interaction.  Instead, if any of the atoms in the interaction are in
 the specified group, it will be turned off (or on if the <em>undo</em>
 keyword is used).</p>
 <p>The <em>undo</em> keyword inverts the delete_bonds command so that the
 specified bonds, angles, etc are turned on if they are currently
 turned off.  This means a negative value is toggled to positive.  For
 example, for style <em>angle</em>, if <em>type</em> is specified as 2, then all
 angles with current type = -2, are reset to type = 2.  Note that the
 <a class="reference internal" href="fix_shake.html"><em>fix shake</em></a> command also sets bond and angle types
 negative, so this option should not be used on those interactions.</p>
 <p>The <em>remove</em> keyword is invoked at the end of the delete_bonds
 operation.  It causes turned-off bonds (angles, etc) to be removed
 from each atom&#8217;s data structure and then adjusts the global bond
 (angle, etc) counts accordingly.  Removal is a permanent change;
 removed bonds cannot be turned back on via the <em>undo</em> keyword.
 Removal does not alter the pairwise 1-2, 1-3, 1-4 weighting list.</p>
 <p>The <em>special</em> keyword is invoked at the end of the delete_bonds
 operation, after (optional) removal.  It re-computes the pairwise 1-2,
 1-3, 1-4 weighting list.  The weighting list computation treats
 turned-off bonds the same as turned-on.  Thus, turned-off bonds must
 be removed if you wish to change the weighting list.</p>
 <p>Note that the choice of <em>remove</em> and <em>special</em> options affects how
 1-2, 1-3, 1-4 pairwise interactions will be computed across bonds that
 have been modified by the delete_bonds command.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>This command requires inter-processor communication to coordinate the
 deleting of bonds.  This means that your system must be ready to
 perform a simulation before using this command (force fields setup,
 atom masses set, etc).</p>
 <p>If deleted bonds (angles, etc) are removed but the 1-2, 1-3, 1-4
 weighting list is not recomputed, this can cause a later <a class="reference internal" href="fix_shake.html"><em>fix shake</em></a> command to fail due to an atom&#8217;s bonds being
 inconsistent with the weighting list.  This should only happen if the
 group used in the fix command includes both atoms in the bond, in
 which case you probably should be recomputing the weighting list.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="neigh_modify.html"><em>neigh_modify</em></a> exclude,
 <a class="reference internal" href="special_bonds.html"><em>special_bonds</em></a>, <a class="reference internal" href="fix_shake.html"><em>fix shake</em></a></p>
 <p><strong>Default:</strong> none</p>
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   <div class="section" id="displace-atoms-command">
 <span id="index-0"></span><h1>displace_atoms command<a class="headerlink" href="#displace-atoms-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>displace_atoms group-ID style args keyword value ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>group-ID = ID of group of atoms to displace</li>
 <li>style = <em>move</em> or <em>ramp</em> or <em>random</em> or <em>rotate</em></li>
 </ul>
 <pre class="literal-block">
 <em>move</em> args = delx dely delz
-    delx,dely,delz = distance to displace in each dimension (distance units)
-  <em>ramp</em> args = ddim dlo dhi dim clo chi
-    ddim = <em>x</em> or <em>y</em> or <em>z</em>
-    dlo,dhi = displacement distance between dlo and dhi (distance units)
-    dim = <em>x</em> or <em>y</em> or <em>z</em>
-    clo,chi = lower and upper bound of domain to displace (distance units)
-  <em>random</em> args = dx dy dz seed
-    dx,dy,dz = random displacement magnitude in each dimension (distance units)
-    seed = random # seed (positive integer)
-  <em>rotate</em> args = Px Py Pz Rx Ry Rz theta
-    Px,Py,Pz = origin point of axis of rotation (distance units)
-    Rx,Ry,Rz = axis of rotation vector
-    theta = angle of rotation (degrees)
+  delx,dely,delz = distance to displace in each dimension (distance units)
+<em>ramp</em> args = ddim dlo dhi dim clo chi
+  ddim = <em>x</em> or <em>y</em> or <em>z</em>
+  dlo,dhi = displacement distance between dlo and dhi (distance units)
+  dim = <em>x</em> or <em>y</em> or <em>z</em>
+  clo,chi = lower and upper bound of domain to displace (distance units)
+<em>random</em> args = dx dy dz seed
+  dx,dy,dz = random displacement magnitude in each dimension (distance units)
+  seed = random # seed (positive integer)
+<em>rotate</em> args = Px Py Pz Rx Ry Rz theta
+  Px,Py,Pz = origin point of axis of rotation (distance units)
+  Rx,Ry,Rz = axis of rotation vector
+  theta = angle of rotation (degrees)
 </pre>
 <ul class="simple">
 <li>zero or more keyword/value pairs may be appended</li>
 </ul>
 <pre class="literal-block">
 keyword = <em>units</em>
-    value = <em>box</em> or <em>lattice</em>
+  value = <em>box</em> or <em>lattice</em>
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>displace_atoms top move 0 -5 0 units box
 displace_atoms flow ramp x 0.0 5.0 y 2.0 20.5
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Displace a group of atoms.  This can be used to move atoms a large
 distance before beginning a simulation or to randomize atoms initially
 on a lattice.  For example, in a shear simulation, an initial strain
 can be imposed on the system.  Or two groups of atoms can be brought
 into closer proximity.</p>
 <p>The <em>move</em> style displaces the group of atoms by the specified 3d
 distance.</p>
 <p>The <em>ramp</em> style displaces atoms a variable amount in one dimension
 depending on the atom&#8217;s coordinate in a (possibly) different
 dimension.  For example, the second example command displaces atoms in
 the x-direction an amount between 0.0 and 5.0 distance units.  Each
 atom&#8217;s displacement depends on the fractional distance its y
 coordinate is between 2.0 and 20.5.  Atoms with y-coordinates outside
 those bounds will be moved the minimum (0.0) or maximum (5.0) amount.</p>
 <p>The <em>random</em> style independently moves each atom in the group by a
 random displacement, uniformly sampled from a value between -dx and
 +dx in the x dimension, and similarly for y and z.  Random numbers are
 used in such a way that the displacement of a particular atom is the
 same, regardless of how many processors are being used.</p>
 <p>The <em>rotate</em> style rotates each atom in the group by the angle <em>theta</em>
 around a rotation axis <em>R</em> = (Rx,Ry,Rz) that goes thru a point <em>P</em> =
 (Px,Py,Pz).  The direction of rotation for the atoms around the
 rotation axis is consistent with the right-hand rule: if your
 right-hand&#8217;s thumb points along <em>R</em>, then your fingers wrap around the
 axis in the direction of positive theta.</p>
 <p>Distance units for displacements and the origin point of the <em>rotate</em>
 style are determined by the setting of <em>box</em> or <em>lattice</em> for the
 <em>units</em> keyword.  <em>Box</em> means distance units as defined by the
 <a class="reference internal" href="units.html"><em>units</em></a> command - e.g. Angstroms for <em>real</em> units.
 <em>Lattice</em> means distance units are in lattice spacings.  The
 <a class="reference internal" href="lattice.html"><em>lattice</em></a> command must have been previously used to
 define the lattice spacing.</p>
 <hr class="docutils" />
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">Care should be taken not to move atoms on top of other
 atoms.  After the move, atoms are remapped into the periodic
 simulation box if needed, and any shrink-wrap boundary conditions (see
 the <a class="reference internal" href="boundary.html"><em>boundary</em></a> command) are enforced which may change
 the box size.  Other than this effect, this command does not change
 the size or shape of the simulation box.  See the
 <a class="reference internal" href="change_box.html"><em>change_box</em></a> command if that effect is desired.</p>
 </div>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">Atoms can be moved arbitrarily long distances by this
 command.  If the simulation box is non-periodic and shrink-wrapped
 (see the <a class="reference internal" href="boundary.html"><em>boundary</em></a> command), this can change its size
 or shape.  This is not a problem, except that the mapping of
 processors to the simulation box is not changed by this command from
 its initial 3d configuration; see the <a class="reference internal" href="processors.html"><em>processors</em></a>
 command.  Thus, if the box size/shape changes dramatically, the
 mapping of processors to the simulation box may not end up as optimal
 as the initial mapping attempted to be.</p>
 </div>
 </div>
 <hr class="docutils" />
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>You cannot rotate around any rotation vector except the z-axis for a
 2d simulation.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="lattice.html"><em>lattice</em></a>, <a class="reference internal" href="change_box.html"><em>change_box</em></a>,
 <a class="reference internal" href="fix_move.html"><em>fix_move</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The option defaults are units = lattice.</p>
 </div>
 </div>
 
 
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   <div class="section" id="dump-command">
 <span id="index-0"></span><h1>dump command<a class="headerlink" href="#dump-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="dump-image-command">
 <h1><a class="reference internal" href="dump_image.html"><em>dump image</em></a> command<a class="headerlink" href="#dump-image-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="dump-movie-command">
 <h1><a class="reference internal" href="dump_image.html"><em>dump movie</em></a> command<a class="headerlink" href="#dump-movie-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="dump-molfile-command">
 <h1><a class="reference internal" href="dump_molfile.html"><em>dump molfile</em></a> command<a class="headerlink" href="#dump-molfile-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>dump ID group-ID style N file args
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID = user-assigned name for the dump</li>
 <li>group-ID = ID of the group of atoms to be dumped</li>
 <li>style = <em>atom</em> or <em>atom/mpiio</em> or <em>cfg</em> or <em>cfg/mpiio</em> or <em>dcd</em> or <em>xtc</em> or <em>xyz</em> or <em>xyz/mpiio</em> or <em>image</em> or <em>movie</em> or <em>molfile</em> or <em>local</em> or <em>custom</em> or <em>custom/mpiio</em></li>
 <li>N = dump every this many timesteps</li>
 <li>file = name of file to write dump info to</li>
 <li>args = list of arguments for a particular style</li>
 </ul>
 <pre class="literal-block">
 <em>atom</em> args = none
-  <em>atom/mpiio</em> args = none
-  <em>cfg</em> args = same as <em>custom</em> args, see below
-  <em>cfg/mpiio</em> args = same as <em>custom</em> args, see below
-  <em>dcd</em> args = none
-  <em>xtc</em> args = none
-  <em>xyz</em> args = none
+<em>atom/mpiio</em> args = none
+<em>cfg</em> args = same as <em>custom</em> args, see below
+<em>cfg/mpiio</em> args = same as <em>custom</em> args, see below
+<em>dcd</em> args = none
+<em>xtc</em> args = none
+<em>xyz</em> args = none
 </pre>
 <pre class="literal-block">
 <em>xyz/mpiio</em> args = none
 </pre>
 <pre class="literal-block">
 <em>image</em> args = discussed on <a class="reference internal" href="dump_image.html"><em>dump image</em></a> doc page
 </pre>
 <pre class="literal-block">
 <em>movie</em> args = discussed on <a class="reference internal" href="dump_image.html"><em>dump image</em></a> doc page
 </pre>
 <pre class="literal-block">
 <em>molfile</em> args = discussed on <a class="reference internal" href="dump_molfile.html"><em>dump molfile</em></a> doc page
 </pre>
 <pre class="literal-block">
 <em>local</em> args = list of local attributes
-    possible attributes = index, c_ID, c_ID[N], f_ID, f_ID[N]
-      index = enumeration of local values
-      c_ID = local vector calculated by a compute with ID
-      c_ID[N] = Nth column of local array calculated by a compute with ID
-      f_ID = local vector calculated by a fix with ID
-      f_ID[N] = Nth column of local array calculated by a fix with ID
+  possible attributes = index, c_ID, c_ID[N], f_ID, f_ID[N]
+    index = enumeration of local values
+    c_ID = local vector calculated by a compute with ID
+    c_ID[N] = Nth column of local array calculated by a compute with ID
+    f_ID = local vector calculated by a fix with ID
+    f_ID[N] = Nth column of local array calculated by a fix with ID
 </pre>
 <pre class="literal-block">
 <em>custom</em> or <em>custom/mpiio</em> args = list of atom attributes
-    possible attributes = id, mol, proc, procp1, type, element, mass,
-                       x, y, z, xs, ys, zs, xu, yu, zu,
-                       xsu, ysu, zsu, ix, iy, iz,
-                       vx, vy, vz, fx, fy, fz,
-                          q, mux, muy, muz, mu,
-                          radius, diameter, omegax, omegay, omegaz,
-                       angmomx, angmomy, angmomz, tqx, tqy, tqz,
-                       c_ID, c_ID[N], f_ID, f_ID[N], v_name
+  possible attributes = id, mol, proc, procp1, type, element, mass,
+                     x, y, z, xs, ys, zs, xu, yu, zu,
+                     xsu, ysu, zsu, ix, iy, iz,
+                     vx, vy, vz, fx, fy, fz,
+                        q, mux, muy, muz, mu,
+                        radius, diameter, omegax, omegay, omegaz,
+                     angmomx, angmomy, angmomz, tqx, tqy, tqz,
+                     c_ID, c_ID[N], f_ID, f_ID[N], v_name
 </pre>
 <pre class="literal-block">
 id = atom ID
-      mol = molecule ID
-      proc = ID of processor that owns atom
-      procp1 = ID+1 of processor that owns atom
-      type = atom type
-      element = name of atom element, as defined by <a class="reference internal" href="dump_modify.html"><em>dump_modify</em></a> command
-      mass = atom mass
-      x,y,z = unscaled atom coordinates
-      xs,ys,zs = scaled atom coordinates
-      xu,yu,zu = unwrapped atom coordinates
-      xsu,ysu,zsu = scaled unwrapped atom coordinates
-      ix,iy,iz = box image that the atom is in
-      vx,vy,vz = atom velocities
-      fx,fy,fz = forces on atoms
-      q = atom charge
-      mux,muy,muz = orientation of dipole moment of atom
-      mu = magnitude of dipole moment of atom
-      radius,diameter = radius,diameter of spherical particle
-      omegax,omegay,omegaz = angular velocity of spherical particle
-      angmomx,angmomy,angmomz = angular momentum of aspherical particle
-      tqx,tqy,tqz = torque on finite-size particles
-      c_ID = per-atom vector calculated by a compute with ID
-      c_ID[N] = Nth column of per-atom array calculated by a compute with ID
-      f_ID = per-atom vector calculated by a fix with ID
-      f_ID[N] = Nth column of per-atom array calculated by a fix with ID
-      v_name = per-atom vector calculated by an atom-style variable with name
-      d_name = per-atom floating point vector with name, managed by fix property/atom
-      i_name = per-atom integer vector with name, managed by fix property/atom
+mol = molecule ID
+proc = ID of processor that owns atom
+procp1 = ID+1 of processor that owns atom
+type = atom type
+element = name of atom element, as defined by <a class="reference internal" href="dump_modify.html"><em>dump_modify</em></a> command
+mass = atom mass
+x,y,z = unscaled atom coordinates
+xs,ys,zs = scaled atom coordinates
+xu,yu,zu = unwrapped atom coordinates
+xsu,ysu,zsu = scaled unwrapped atom coordinates
+ix,iy,iz = box image that the atom is in
+vx,vy,vz = atom velocities
+fx,fy,fz = forces on atoms
+q = atom charge
+mux,muy,muz = orientation of dipole moment of atom
+mu = magnitude of dipole moment of atom
+radius,diameter = radius,diameter of spherical particle
+omegax,omegay,omegaz = angular velocity of spherical particle
+angmomx,angmomy,angmomz = angular momentum of aspherical particle
+tqx,tqy,tqz = torque on finite-size particles
+c_ID = per-atom vector calculated by a compute with ID
+c_ID[N] = Nth column of per-atom array calculated by a compute with ID
+f_ID = per-atom vector calculated by a fix with ID
+f_ID[N] = Nth column of per-atom array calculated by a fix with ID
+v_name = per-atom vector calculated by an atom-style variable with name
+d_name = per-atom floating point vector with name, managed by fix property/atom
+i_name = per-atom integer vector with name, managed by fix property/atom
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>dump myDump all atom 100 dump.atom
 dump myDump all atom/mpiio 100 dump.atom.mpiio
 dump 2 subgroup atom 50 dump.run.bin
 dump 2 subgroup atom 50 dump.run.mpiio.bin
 dump 4a all custom 100 dump.myforce.* id type x y vx fx
 dump 4b flow custom 100 dump.%.myforce id type c_myF[3] v_ke
 dump 2 inner cfg 10 dump.snap.*.cfg mass type xs ys zs vx vy vz
 dump snap all cfg 100 dump.config.*.cfg mass type xs ys zs id type c_Stress[2]
 dump 1 all xtc 1000 file.xtc
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Dump a snapshot of atom quantities to one or more files every N
 timesteps in one of several styles.  The <em>image</em> and <em>movie</em> styles are
 the exception: the <em>image</em> style renders a JPG, PNG, or PPM image file
 of the atom configuration every N timesteps while the <em>movie</em> style
 combines and compresses them into a movie file; both are discussed in
 detail on the <a class="reference internal" href="dump_image.html"><em>dump image</em></a> doc page.  The timesteps on
 which dump output is written can also be controlled by a variable.
 See the <a class="reference internal" href="dump_modify.html"><em>dump_modify every</em></a> command.</p>
 <p>Only information for atoms in the specified group is dumped.  The
 <a class="reference internal" href="dump_modify.html"><em>dump_modify thresh and region</em></a> commands can also
 alter what atoms are included.  Not all styles support all these
 options; see details below.</p>
 <p>As described below, the filename determines the kind of output (text
 or binary or gzipped, one big file or one per timestep, one big file
 or multiple smaller files).</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">Because periodic boundary conditions are enforced only
 on timesteps when neighbor lists are rebuilt, the coordinates of an
 atom written to a dump file may be slightly outside the simulation
 box.</p>
 </div>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">Unless the <a class="reference internal" href="dump_modify.html"><em>dump_modify sort</em></a> option
 is invoked, the lines of atom information written to dump files
 (typically one line per atom) will be in an indeterminate order for
 each snapshot.  This is even true when running on a single processor,
 if the <a class="reference internal" href="atom_modify.html"><em>atom_modify sort</em></a> option is on, which it is
 by default.  In this case atoms are re-ordered periodically during a
 simulation, due to spatial sorting.  It is also true when running in
 parallel, because data for a single snapshot is collected from
 multiple processors, each of which owns a subset of the atoms.</p>
 </div>
 <p>For the <em>atom</em>, <em>custom</em>, <em>cfg</em>, and <em>local</em> styles, sorting is off by
 default.  For the <em>dcd</em>, <em>xtc</em>, <em>xyz</em>, and <em>molfile</em> styles, sorting by
 atom ID is on by default. See the <a class="reference internal" href="dump_modify.html"><em>dump_modify</em></a> doc
 page for details.</p>
 <p>As explained below, the <em>atom/mpiio</em>, <em>cfg/mpiio</em>, <em>custom/mpiio</em>, and
 <em>xyz/mpiio</em> styles are identical in command syntax and in the format
 of the dump files they create, to the corresponding styles without
 &#8220;mpiio&#8221;, except the single dump file they produce is written in
 parallel via the MPI-IO library.  For the remainder of this doc page,
 you should thus consider the <em>atom</em> and <em>atom/mpiio</em> styles (etc) to
 be inter-changeable.  The one exception is how the filename is
 specified for the MPI-IO styles, as explained below.</p>
 <hr class="docutils" />
 <p>The <em>style</em> keyword determines what atom quantities are written to the
 file and in what format.  Settings made via the
 <a class="reference internal" href="dump_modify.html"><em>dump_modify</em></a> command can also alter the format of
 individual values and the file itself.</p>
 <p>The <em>atom</em>, <em>local</em>, and <em>custom</em> styles create files in a simple text
 format that is self-explanatory when viewing a dump file.  Many of the
 LAMMPS <a class="reference internal" href="Section_tools.html"><em>post-processing tools</em></a>, including
 <a class="reference external" href="http://www.sandia.gov/~sjplimp/pizza.html">Pizza.py</a>, work with this
 format, as does the <a class="reference internal" href="rerun.html"><em>rerun</em></a> command.</p>
 <p>For post-processing purposes the <em>atom</em>, <em>local</em>, and <em>custom</em> text
 files are self-describing in the following sense.</p>
 <p>The dimensions of the simulation box are included in each snapshot.
 For an orthogonal simulation box this information is is formatted as:</p>
 <div class="highlight-python"><div class="highlight"><pre>ITEM: BOX BOUNDS xx yy zz
 xlo xhi
 ylo yhi
 zlo zhi
 </pre></div>
 </div>
 <p>where xlo,xhi are the maximum extents of the simulation box in the
 x-dimension, and similarly for y and z.  The &#8220;xx yy zz&#8221; represent 6
 characters that encode the style of boundary for each of the 6
 simulation box boundaries (xlo,xhi and ylo,yhi and zlo,zhi).  Each of
 the 6 characters is either p = periodic, f = fixed, s = shrink wrap,
 or m = shrink wrapped with a minimum value.  See the
 <a class="reference internal" href="boundary.html"><em>boundary</em></a> command for details.</p>
 <p>For triclinic simulation boxes (non-orthogonal), an orthogonal
 bounding box which encloses the triclinic simulation box is output,
 along with the 3 tilt factors (xy, xz, yz) of the triclinic box,
 formatted as follows:</p>
 <div class="highlight-python"><div class="highlight"><pre>ITEM: BOX BOUNDS xy xz yz xx yy zz
 xlo_bound xhi_bound xy
 ylo_bound yhi_bound xz
 zlo_bound zhi_bound yz
 </pre></div>
 </div>
 <p>The presence of the text &#8220;xy xz yz&#8221; in the ITEM line indicates that
 the 3 tilt factors will be included on each of the 3 following lines.
 This bounding box is convenient for many visualization programs.  The
 meaning of the 6 character flags for &#8220;xx yy zz&#8221; is the same as above.</p>
 <p>Note that the first two numbers on each line are now xlo_bound instead
 of xlo, etc, since they repesent a bounding box.  See <a class="reference internal" href="Section_howto.html#howto-12"><span>this section</span></a> of the doc pages for a geometric
 description of triclinic boxes, as defined by LAMMPS, simple formulas
 for how the 6 bounding box extents (xlo_bound,xhi_bound,etc) are
 calculated from the triclinic parameters, and how to transform those
 parameters to and from other commonly used triclinic representations.</p>
 <p>The &#8220;ITEM: ATOMS&#8221; line in each snapshot lists column descriptors for
 the per-atom lines that follow.  For example, the descriptors would be
 &#8220;id type xs ys zs&#8221; for the default <em>atom</em> style, and would be the atom
 attributes you specify in the dump command for the <em>custom</em> style.</p>
 <p>For style <em>atom</em>, atom coordinates are written to the file, along with
 the atom ID and atom type.  By default, atom coords are written in a
 scaled format (from 0 to 1).  I.e. an x value of 0.25 means the atom
 is at a location 1/4 of the distance from xlo to xhi of the box
 boundaries.  The format can be changed to unscaled coords via the
 <a class="reference internal" href="dump_modify.html"><em>dump_modify</em></a> settings.  Image flags can also be
 added for each atom via dump_modify.</p>
 <p>Style <em>custom</em> allows you to specify a list of atom attributes to be
 written to the dump file for each atom.  Possible attributes are
 listed above and will appear in the order specified.  You cannot
 specify a quantity that is not defined for a particular simulation -
 such as <em>q</em> for atom style <em>bond</em>, since that atom style doesn&#8217;t
 assign charges.  Dumps occur at the very end of a timestep, so atom
 attributes will include effects due to fixes that are applied during
 the timestep.  An explanation of the possible dump custom attributes
 is given below.</p>
 <p>For style <em>local</em>, local output generated by <a class="reference internal" href="compute.html"><em>computes</em></a>
 and <a class="reference internal" href="fix.html"><em>fixes</em></a> is used to generate lines of output that is
 written to the dump file.  This local data is typically calculated by
 each processor based on the atoms it owns, but there may be zero or
 more entities per atom, e.g. a list of bond distances.  An explanation
 of the possible dump local attributes is given below.  Note that by
 using input from the <a class="reference internal" href="compute_property_local.html"><em>compute property/local</em></a> command with dump local,
 it is possible to generate information on bonds, angles, etc that can
 be cut and pasted directly into a data file read by the
 <a class="reference internal" href="read_data.html"><em>read_data</em></a> command.</p>
 <p>Style <em>cfg</em> has the same command syntax as style <em>custom</em> and writes
 extended CFG format files, as used by the
 <a class="reference external" href="http://mt.seas.upenn.edu/Archive/Graphics/A">AtomEye</a> visualization
 package.  Since the extended CFG format uses a single snapshot of the
 system per file, a wildcard &#8220;*&#8221; must be included in the filename, as
 discussed below.  The list of atom attributes for style <em>cfg</em> must
 begin with either &#8220;mass type xs ys zs&#8221; or &#8220;mass type xsu ysu zsu&#8221;
 since these quantities are needed to write the CFG files in the
 appropriate format (though the &#8220;mass&#8221; and &#8220;type&#8221; fields do not appear
 explicitly in the file).  Any remaining attributes will be stored as
 &#8220;auxiliary properties&#8221; in the CFG files.  Note that you will typically
 want to use the <a class="reference internal" href="dump_modify.html"><em>dump_modify element</em></a> command with
 CFG-formatted files, to associate element names with atom types, so
 that AtomEye can render atoms appropriately. When unwrapped
 coordinates <em>xsu</em>, <em>ysu</em>, and <em>zsu</em> are requested, the nominal AtomEye
 periodic cell dimensions are expanded by a large factor UNWRAPEXPAND =
 10.0, which ensures atoms that are displayed correctly for up to
 UNWRAPEXPAND/2 periodic boundary crossings in any direction.  Beyond
 this, AtomEye will rewrap the unwrapped coordinates.  The expansion
 causes the atoms to be drawn farther away from the viewer, but it is
 easy to zoom the atoms closer, and the interatomic distances are
 unaffected.</p>
 <p>The <em>dcd</em> style writes DCD files, a standard atomic trajectory format
 used by the CHARMM, NAMD, and XPlor molecular dynamics packages.  DCD
 files are binary and thus may not be portable to different machines.
 The number of atoms per snapshot cannot change with the <em>dcd</em> style.
 The <em>unwrap</em> option of the <a class="reference internal" href="dump_modify.html"><em>dump_modify</em></a> command
 allows DCD coordinates to be written &#8220;unwrapped&#8221; by the image flags
 for each atom.  Unwrapped means that if the atom has passed through
 a periodic boundary one or more times, the value is printed for what
 the coordinate would be if it had not been wrapped back into the
 periodic box.  Note that these coordinates may thus be far outside
 the box size stored with the snapshot.</p>
 <p>The <em>xtc</em> style writes XTC files, a compressed trajectory format used
 by the GROMACS molecular dynamics package, and described
 <a class="reference external" href="http://manual.gromacs.org/current/online/xtc.html">here</a>.
 The precision used in XTC files can be adjusted via the
 <a class="reference internal" href="dump_modify.html"><em>dump_modify</em></a> command.  The default value of 1000
 means that coordinates are stored to 1/1000 nanometer accuracy.  XTC
 files are portable binary files written in the NFS XDR data format,
 so that any machine which supports XDR should be able to read them.
 The number of atoms per snapshot cannot change with the <em>xtc</em> style.
 The <em>unwrap</em> option of the <a class="reference internal" href="dump_modify.html"><em>dump_modify</em></a> command allows
 XTC coordinates to be written &#8220;unwrapped&#8221; by the image flags for each
 atom.  Unwrapped means that if the atom has passed thru a periodic
 boundary one or more times, the value is printed for what the
 coordinate would be if it had not been wrapped back into the periodic
 box.  Note that these coordinates may thus be far outside the box size
 stored with the snapshot.</p>
 <p>The <em>xyz</em> style writes XYZ files, which is a simple text-based
 coordinate format that many codes can read. Specifically it has
 a line with the number of atoms, then a comment line that is
 usually ignored followed by one line per atom with the atom type
 and the x-, y-, and z-coordinate of that atom. You can use the
 <a class="reference internal" href="dump_modify.html"><em>dump_modify element</em></a> option to change the output
 from using the (numerical) atom type to an element name (or some
 other label). This will help many visualization programs to guess
 bonds and colors.</p>
 <p>Note that <em>atom</em>, <em>custom</em>, <em>dcd</em>, <em>xtc</em>, and <em>xyz</em> style dump files
 can be read directly by <a class="reference external" href="http://www.ks.uiuc.edu/Research/vmd">VMD</a>, a
 popular molecular viewing program.  See <a class="reference internal" href="Section_tools.html#vmd"><span>Section tools</span></a> of the manual and the
 tools/lmp2vmd/README.txt file for more information about support in
 VMD for reading and visualizing LAMMPS dump files.</p>
 <hr class="docutils" />
 <p>Dumps are performed on timesteps that are a multiple of N (including
 timestep 0) and on the last timestep of a minimization if the
 minimization converges.  Note that this means a dump will not be
 performed on the initial timestep after the dump command is invoked,
 if the current timestep is not a multiple of N.  This behavior can be
 changed via the <a class="reference internal" href="dump_modify.html"><em>dump_modify first</em></a> command, which
 can also be useful if the dump command is invoked after a minimization
 ended on an arbitrary timestep.  N can be changed between runs by
 using the <a class="reference internal" href="dump_modify.html"><em>dump_modify every</em></a> command (not allowed
 for <em>dcd</em> style).  The <a class="reference internal" href="dump_modify.html"><em>dump_modify every</em></a> command
 also allows a variable to be used to determine the sequence of
 timesteps on which dump files are written.  In this mode a dump on the
 first timestep of a run will also not be written unless the
 <a class="reference internal" href="dump_modify.html"><em>dump_modify first</em></a> command is used.</p>
 <p>The specified filename determines how the dump file(s) is written.
 The default is to write one large text file, which is opened when the
 dump command is invoked and closed when an <a class="reference internal" href="undump.html"><em>undump</em></a>
 command is used or when LAMMPS exits.  For the <em>dcd</em> and <em>xtc</em> styles,
 this is a single large binary file.</p>
 <p>Dump filenames can contain two wildcard characters.  If a &#8220;*&#8221;
 character appears in the filename, then one file per snapshot is
 written and the &#8220;*&#8221; character is replaced with the timestep value.
 For example, tmp.dump.* becomes tmp.dump.0, tmp.dump.10000,
 tmp.dump.20000, etc.  This option is not available for the <em>dcd</em> and
 <em>xtc</em> styles.  Note that the <a class="reference internal" href="dump_modify.html"><em>dump_modify pad</em></a>
 command can be used to insure all timestep numbers are the same length
 (e.g. 00010), which can make it easier to read a series of dump files
 in order with some post-processing tools.</p>
 <p>If a &#8220;%&#8221; character appears in the filename, then each of P processors
 writes a portion of the dump file, and the &#8220;%&#8221; character is replaced
 with the processor ID from 0 to P-1.  For example, tmp.dump.% becomes
 tmp.dump.0, tmp.dump.1, ... tmp.dump.P-1, etc.  This creates smaller
 files and can be a fast mode of output on parallel machines that
 support parallel I/O for output. This option is not available for the
 <em>dcd</em>, <em>xtc</em>, and <em>xyz</em> styles.</p>
 <p>By default, P = the number of processors meaning one file per
 processor, but P can be set to a smaller value via the <em>nfile</em> or
 <em>fileper</em> keywords of the <a class="reference internal" href="dump_modify.html"><em>dump_modify</em></a> command.
 These options can be the most efficient way of writing out dump files
 when running on large numbers of processors.</p>
 <p>Note that using the &#8220;*&#8221; and &#8220;%&#8221; characters together can produce a
 large number of small dump files!</p>
 <p>For the <em>atom/mpiio</em>, <em>cfg/mpiio</em>, <em>custom/mpiio</em>, and <em>xyz/mpiio</em>
 styles, a single dump file is written in parallel via the MPI-IO
 library, which is part of the MPI standard for versions 2.0 and above.
 Using MPI-IO requires two steps.  First, build LAMMPS with its MPIIO
 package installed, e.g.</p>
 <div class="highlight-python"><div class="highlight"><pre>make yes-mpiio    # installs the MPIIO package
 make g++          # build LAMMPS for your platform
 </pre></div>
 </div>
 <p>Second, use a dump filename which contains &#8221;.mpiio&#8221;.  Note that it
 does not have to end in &#8221;.mpiio&#8221;, just contain those characters.
 Unlike MPI-IO restart files, which must be both written and read using
 MPI-IO, the dump files produced by these MPI-IO styles are identical
 in format to the files produced by their non-MPI-IO style
 counterparts.  This means you can write a dump file using MPI-IO and
 use the <a class="reference internal" href="read_dump.html"><em>read_dump</em></a> command or perform other
 post-processing, just as if the dump file was not written using
 MPI-IO.</p>
 <p>Note that MPI-IO dump files are one large file which all processors
 write to.  You thus cannot use the &#8220;%&#8221; wildcard character described
 above in the filename since that specifies generation of multiple
 files.  You can use the &#8221;.bin&#8221; suffix described below in an MPI-IO
 dump file; again this file will be written in parallel and have the
 same binary format as if it were written without MPI-IO.</p>
 <p>If the filename ends with &#8221;.bin&#8221;, the dump file (or files, if &#8220;*&#8221; or
 &#8220;%&#8221; is also used) is written in binary format.  A binary dump file
 will be about the same size as a text version, but will typically
 write out much faster.  Of course, when post-processing, you will need
 to convert it back to text format (see the <a class="reference internal" href="Section_tools.html#binary"><span>binary2txt tool</span></a>) or write your own code to read the
 binary file.  The format of the binary file can be understood by
 looking at the tools/binary2txt.cpp file.  This option is only
 available for the <em>atom</em> and <em>custom</em> styles.</p>
 <p>If the filename ends with &#8221;.gz&#8221;, the dump file (or files, if &#8220;*&#8221; or &#8220;%&#8221;
 is also used) is written in gzipped format.  A gzipped dump file will
 be about 3x smaller than the text version, but will also take longer
 to write.  This option is not available for the <em>dcd</em> and <em>xtc</em>
 styles.</p>
 <hr class="docutils" />
 <p>This section explains the local attributes that can be specified as
 part of the <em>local</em> style.</p>
 <p>The <em>index</em> attribute can be used to generate an index number from 1
 to N for each line written into the dump file, where N is the total
 number of local datums from all processors, or lines of output that
 will appear in the snapshot.  Note that because data from different
 processors depend on what atoms they currently own, and atoms migrate
 between processor, there is no guarantee that the same index will be
 used for the same info (e.g. a particular bond) in successive
 snapshots.</p>
 <p>The <em>c_ID</em> and <em>c_ID[N]</em> attributes allow local vectors or arrays
 calculated by a <a class="reference internal" href="compute.html"><em>compute</em></a> to be output.  The ID in the
 attribute should be replaced by the actual ID of the compute that has
 been defined previously in the input script.  See the
 <a class="reference internal" href="compute.html"><em>compute</em></a> command for details.  There are computes for
 calculating local information such as indices, types, and energies for
 bonds and angles.</p>
 <p>Note that computes which calculate global or per-atom quantities, as
 opposed to local quantities, cannot be output in a dump local command.
 Instead, global quantities can be output by the <a class="reference internal" href="thermo_style.html"><em>thermo_style custom</em></a> command, and per-atom quantities can be
 output by the dump custom command.</p>
 <p>If <em>c_ID</em> is used as a attribute, then the local vector calculated by
 the compute is printed.  If <em>c_ID[N]</em> is used, then N must be in the
 range from 1-M, which will print the Nth column of the M-length local
 array calculated by the compute.</p>
 <p>The <em>f_ID</em> and <em>f_ID[N]</em> attributes allow local vectors or arrays
 calculated by a <a class="reference internal" href="fix.html"><em>fix</em></a> to be output.  The ID in the attribute
 should be replaced by the actual ID of the fix that has been defined
 previously in the input script.</p>
 <p>If <em>f_ID</em> is used as a attribute, then the local vector calculated by
 the fix is printed.  If <em>f_ID[N]</em> is used, then N must be in the
 range from 1-M, which will print the Nth column of the M-length local
 array calculated by the fix.</p>
 <p>Here is an example of how to dump bond info for a system,
 including the distance and energy of each bond:</p>
 <div class="highlight-python"><div class="highlight"><pre>compute 1 all property/local batom1 batom2 btype
 compute 2 all bond/local dist eng
 dump 1 all local 1000 tmp.dump index c_1[1] c_1[2] c_1[3] c_2[1] c_2[2]
 </pre></div>
 </div>
 <hr class="docutils" />
 <p>This section explains the atom attributes that can be specified as
 part of the <em>custom</em> and <em>cfg</em> styles.</p>
 <p>The <em>id</em>, <em>mol</em>, <em>proc</em>, <em>procp1</em>, <em>type</em>, <em>element</em>, <em>mass</em>, <em>vx</em>,
 <em>vy</em>, <em>vz</em>, <em>fx</em>, <em>fy</em>, <em>fz</em>, <em>q</em> attributes are self-explanatory.</p>
 <p><em>Id</em> is the atom ID.  <em>Mol</em> is the molecule ID, included in the data
 file for molecular systems.  <em>Proc</em> is the ID of the processor (0 to
 Nprocs-1) that currently owns the atom.  <em>Procp1</em> is the proc ID+1,
 which can be convenient in place of a <em>type</em> attribute (1 to Ntypes)
 for coloring atoms in a visualization program.  <em>Type</em> is the atom
 type (1 to Ntypes).  <em>Element</em> is typically the chemical name of an
 element, which you must assign to each type via the <a class="reference internal" href="dump_modify.html"><em>dump_modify element</em></a> command.  More generally, it can be any
 string you wish to associated with an atom type.  <em>Mass</em> is the atom
 mass.  <em>Vx</em>, <em>vy</em>, <em>vz</em>, <em>fx</em>, <em>fy</em>, <em>fz</em>, and <em>q</em> are components of
 atom velocity and force and atomic charge.</p>
 <p>There are several options for outputting atom coordinates.  The <em>x</em>,
 <em>y</em>, <em>z</em> attributes write atom coordinates &#8220;unscaled&#8221;, in the
 appropriate distance <a class="reference internal" href="units.html"><em>units</em></a> (Angstroms, sigma, etc).  Use
 <em>xs</em>, <em>ys</em>, <em>zs</em> if you want the coordinates &#8220;scaled&#8221; to the box size,
 so that each value is 0.0 to 1.0.  If the simulation box is triclinic
 (tilted), then all atom coords will still be between 0.0 and 1.0.  Use
 <em>xu</em>, <em>yu</em>, <em>zu</em> if you want the coordinates &#8220;unwrapped&#8221; by the image
 flags for each atom.  Unwrapped means that if the atom has passed thru
 a periodic boundary one or more times, the value is printed for what
 the coordinate would be if it had not been wrapped back into the
 periodic box.  Note that using <em>xu</em>, <em>yu</em>, <em>zu</em> means that the
 coordinate values may be far outside the box bounds printed with the
 snapshot.  Using <em>xsu</em>, <em>ysu</em>, <em>zsu</em> is similar to using <em>xu</em>, <em>yu</em>, <em>zu</em>,
 except that the unwrapped coordinates are scaled by the box size. Atoms
 that have passed through a periodic boundary will have the corresponding
 cooordinate increased or decreased by 1.0.</p>
 <p>The image flags can be printed directly using the <em>ix</em>, <em>iy</em>, <em>iz</em>
 attributes.  For periodic dimensions, they specify which image of the
 simulation box the atom is considered to be in.  An image of 0 means
 it is inside the box as defined.  A value of 2 means add 2 box lengths
 to get the true value.  A value of -1 means subtract 1 box length to
 get the true value.  LAMMPS updates these flags as atoms cross
 periodic boundaries during the simulation.</p>
 <p>The <em>mux</em>, <em>muy</em>, <em>muz</em> attributes are specific to dipolar systems
 defined with an atom style of <em>dipole</em>.  They give the orientation of
 the atom&#8217;s point dipole moment.  The <em>mu</em> attribute gives the
 magnitude of the atom&#8217;s dipole moment.</p>
 <p>The <em>radius</em> and <em>diameter</em> attributes are specific to spherical
 particles that have a finite size, such as those defined with an atom
 style of <em>sphere</em>.</p>
 <p>The <em>omegax</em>, <em>omegay</em>, and <em>omegaz</em> attributes are specific to
 finite-size spherical particles that have an angular velocity.  Only
 certain atom styles, such as <em>sphere</em> define this quantity.</p>
 <p>The <em>angmomx</em>, <em>angmomy</em>, and <em>angmomz</em> attributes are specific to
 finite-size aspherical particles that have an angular momentum.  Only
 the <em>ellipsoid</em> atom style defines this quantity.</p>
 <p>The <em>tqx</em>, <em>tqy</em>, <em>tqz</em> attributes are for finite-size particles that
 can sustain a rotational torque due to interactions with other
 particles.</p>
 <p>The <em>c_ID</em> and <em>c_ID[N]</em> attributes allow per-atom vectors or arrays
 calculated by a <a class="reference internal" href="compute.html"><em>compute</em></a> to be output.  The ID in the
 attribute should be replaced by the actual ID of the compute that has
 been defined previously in the input script.  See the
 <a class="reference internal" href="compute.html"><em>compute</em></a> command for details.  There are computes for
 calculating the per-atom energy, stress, centro-symmetry parameter,
 and coordination number of individual atoms.</p>
 <p>Note that computes which calculate global or local quantities, as
 opposed to per-atom quantities, cannot be output in a dump custom
 command.  Instead, global quantities can be output by the
 <a class="reference internal" href="thermo_style.html"><em>thermo_style custom</em></a> command, and local quantities
 can be output by the dump local command.</p>
 <p>If <em>c_ID</em> is used as a attribute, then the per-atom vector calculated
 by the compute is printed.  If <em>c_ID[N]</em> is used, then N must be in
 the range from 1-M, which will print the Nth column of the M-length
 per-atom array calculated by the compute.</p>
 <p>The <em>f_ID</em> and <em>f_ID[N]</em> attributes allow vector or array per-atom
 quantities calculated by a <a class="reference internal" href="fix.html"><em>fix</em></a> to be output.  The ID in the
 attribute should be replaced by the actual ID of the fix that has been
 defined previously in the input script.  The <a class="reference internal" href="fix_ave_atom.html"><em>fix ave/atom</em></a> command is one that calculates per-atom
 quantities.  Since it can time-average per-atom quantities produced by
 any <a class="reference internal" href="compute.html"><em>compute</em></a>, <a class="reference internal" href="fix.html"><em>fix</em></a>, or atom-style
 <a class="reference internal" href="variable.html"><em>variable</em></a>, this allows those time-averaged results to
 be written to a dump file.</p>
 <p>If <em>f_ID</em> is used as a attribute, then the per-atom vector calculated
 by the fix is printed.  If <em>f_ID[N]</em> is used, then N must be in the
 range from 1-M, which will print the Nth column of the M-length
 per-atom array calculated by the fix.</p>
 <p>The <em>v_name</em> attribute allows per-atom vectors calculated by a
 <a class="reference internal" href="variable.html"><em>variable</em></a> to be output.  The name in the attribute
 should be replaced by the actual name of the variable that has been
 defined previously in the input script.  Only an atom-style variable
 can be referenced, since it is the only style that generates per-atom
 values.  Variables of style <em>atom</em> can reference individual atom
 attributes, per-atom atom attributes, thermodynamic keywords, or
 invoke other computes, fixes, or variables when they are evaluated, so
 this is a very general means of creating quantities to output to a
 dump file.</p>
 <p>The <em>d_name</em> and <em>i_name</em> attributes allow to output custom per atom
 floating point or integer properties that are managed by
 <a class="reference internal" href="fix_property_atom.html"><em>fix property/atom</em></a>.</p>
 <p>See <a class="reference internal" href="Section_modify.html"><em>Section_modify</em></a> of the manual for information
 on how to add new compute and fix styles to LAMMPS to calculate
 per-atom quantities which could then be output into dump files.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>To write gzipped dump files, you must compile LAMMPS with the
 -DLAMMPS_GZIP option - see the <a class="reference internal" href="Section_start.html#start-2"><span>Making LAMMPS</span></a> section of the documentation.</p>
 <p>The <em>atom/mpiio</em>, <em>cfg/mpiio</em>, <em>custom/mpiio</em>, and <em>xyz/mpiio</em> styles
 are part of the MPIIO package.  They are only enabled if LAMMPS was
 built with that package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 <p>The <em>xtc</em> style is part of the XTC package.  It is only enabled if
 LAMMPS was built with that package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.  This is
 because some machines may not support the low-level XDR data format
 that XTC files are written with, which will result in a compile-time
 error when a low-level include file is not found.  Putting this style
 in a package makes it easy to exclude from a LAMMPS build for those
 machines.  However, the XTC package also includes two compatibility
 header files and associated functions, which should be a suitable
 substitute on machines that do not have the appropriate native header
 files.  This option can be invoked at build time by adding
 -DLAMMPS_XDR to the CCFLAGS variable in the appropriate low-level
 Makefile, e.g. src/MAKE/Makefile.foo.  This compatibility mode has
 been tested successfully on Cray XT3/XT4/XT5 and IBM BlueGene/L
 machines and should also work on IBM BG/P, and Windows XP/Vista/7
 machines.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="dump_image.html"><em>dump image</em></a>, <a class="reference internal" href="dump_modify.html"><em>dump_modify</em></a>,
 <a class="reference internal" href="undump.html"><em>undump</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The defaults for the <em>image</em> and <em>movie</em> styles are listed on the
 <a class="reference internal" href="dump_image.html"><em>dump image</em></a> doc page.</p>
 </div>
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   <div class="section" id="dump-image-command">
 <span id="index-0"></span><h1>dump image command<a class="headerlink" href="#dump-image-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="dump-movie-command">
 <h1>dump movie command<a class="headerlink" href="#dump-movie-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>dump ID group-ID style N file color diameter keyword value ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID = user-assigned name for the dump</li>
 <li>group-ID = ID of the group of atoms to be imaged</li>
 <li>style = <em>image</em> or <em>movie</em> = style of dump command (other styles <em>atom</em> or <em>cfg</em> or <em>dcd</em> or <em>xtc</em> or <em>xyz</em> or <em>local</em> or <em>custom</em> are discussed on the <a class="reference internal" href="dump.html"><em>dump</em></a> doc page)</li>
 <li>N = dump every this many timesteps</li>
 <li>file = name of file to write image to</li>
 <li>color = atom attribute that determines color of each atom</li>
 <li>diameter = atom attribute that determines size of each atom</li>
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>adiam</em> or <em>atom</em> or <em>bond</em> or <em>size</em> or <em>view</em> or <em>center</em> or <em>up</em> or <em>zoom</em> or <em>persp</em> or <em>box</em> or <em>axes</em> or <em>subbox</em> or <em>shiny</em> or <em>ssao</em></li>
 </ul>
 <pre class="literal-block">
 <em>adiam</em> value = number = numeric value for atom diameter (distance units)
-  <em>atom</em> = yes/no = do or do not draw atoms
-  <em>bond</em> values = color width = color and width of bonds
-    color = <em>atom</em> or <em>type</em> or <em>none</em>
-    width = number or <em>atom</em> or <em>type</em> or <em>none</em>
-      number = numeric value for bond width (distance units)
-  <em>size</em> values = width height = size of images
-    width = width of image in # of pixels
-    height = height of image in # of pixels
-  <em>view</em> values = theta phi = view of simulation box
-    theta = view angle from +z axis (degrees)
-    phi = azimuthal view angle (degrees)
-    theta or phi can be a variable (see below)
-  <em>center</em> values = flag Cx Cy Cz = center point of image
-    flag = &quot;s&quot; for static, &quot;d&quot; for dynamic
-    Cx,Cy,Cz = center point of image as fraction of box dimension (0.5 = center of box)
-    Cx,Cy,Cz can be variables (see below)
-  <em>up</em> values = Ux Uy Uz = direction that is &quot;up&quot; in image
-    Ux,Uy,Uz = components of up vector
-    Ux,Uy,Uz can be variables (see below)
-  <em>zoom</em> value = zfactor = size that simulation box appears in image
-    zfactor = scale image size by factor &gt; 1 to enlarge, factor &lt; 1 to shrink
-    zfactor can be a variable (see below)
-  <em>persp</em> value = pfactor = amount of &quot;perspective&quot; in image
-    pfactor = amount of perspective (0 = none, &lt; 1 = some, &gt; 1 = highly skewed)
-    pfactor can be a variable (see below)
-  <em>box</em> values = yes/no diam = draw outline of simulation box
-    yes/no = do or do not draw simulation box lines
-    diam = diameter of box lines as fraction of shortest box length
-  <em>axes</em> values = yes/no length diam = draw xyz axes
-    yes/no = do or do not draw xyz axes lines next to simulation box
-    length = length of axes lines as fraction of respective box lengths
-    diam = diameter of axes lines as fraction of shortest box length
-  <em>subbox</em> values = yes/no diam = draw outline of processor sub-domains
-    yes/no = do or do not draw sub-domain lines
-    diam = diameter of sub-domain lines as fraction of shortest box length
-  <em>shiny</em> value = sfactor = shinyness of spheres and cylinders
-    sfactor = shinyness of spheres and cylinders from 0.0 to 1.0
-  <em>ssao</em> value = yes/no seed dfactor = SSAO depth shading
-    yes/no = turn depth shading on/off
-    seed = random # seed (positive integer)
-    dfactor = strength of shading from 0.0 to 1.0
+<em>atom</em> = yes/no = do or do not draw atoms
+<em>bond</em> values = color width = color and width of bonds
+  color = <em>atom</em> or <em>type</em> or <em>none</em>
+  width = number or <em>atom</em> or <em>type</em> or <em>none</em>
+    number = numeric value for bond width (distance units)
+<em>size</em> values = width height = size of images
+  width = width of image in # of pixels
+  height = height of image in # of pixels
+<em>view</em> values = theta phi = view of simulation box
+  theta = view angle from +z axis (degrees)
+  phi = azimuthal view angle (degrees)
+  theta or phi can be a variable (see below)
+<em>center</em> values = flag Cx Cy Cz = center point of image
+  flag = &quot;s&quot; for static, &quot;d&quot; for dynamic
+  Cx,Cy,Cz = center point of image as fraction of box dimension (0.5 = center of box)
+  Cx,Cy,Cz can be variables (see below)
+<em>up</em> values = Ux Uy Uz = direction that is &quot;up&quot; in image
+  Ux,Uy,Uz = components of up vector
+  Ux,Uy,Uz can be variables (see below)
+<em>zoom</em> value = zfactor = size that simulation box appears in image
+  zfactor = scale image size by factor &gt; 1 to enlarge, factor &lt; 1 to shrink
+  zfactor can be a variable (see below)
+<em>persp</em> value = pfactor = amount of &quot;perspective&quot; in image
+  pfactor = amount of perspective (0 = none, &lt; 1 = some, &gt; 1 = highly skewed)
+  pfactor can be a variable (see below)
+<em>box</em> values = yes/no diam = draw outline of simulation box
+  yes/no = do or do not draw simulation box lines
+  diam = diameter of box lines as fraction of shortest box length
+<em>axes</em> values = yes/no length diam = draw xyz axes
+  yes/no = do or do not draw xyz axes lines next to simulation box
+  length = length of axes lines as fraction of respective box lengths
+  diam = diameter of axes lines as fraction of shortest box length
+<em>subbox</em> values = yes/no diam = draw outline of processor sub-domains
+  yes/no = do or do not draw sub-domain lines
+  diam = diameter of sub-domain lines as fraction of shortest box length
+<em>shiny</em> value = sfactor = shinyness of spheres and cylinders
+  sfactor = shinyness of spheres and cylinders from 0.0 to 1.0
+<em>ssao</em> value = yes/no seed dfactor = SSAO depth shading
+  yes/no = turn depth shading on/off
+  seed = random # seed (positive integer)
+  dfactor = strength of shading from 0.0 to 1.0
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>dump d0 all image 100 dump.*.jpg type type
 dump d1 mobile image 500 snap.*.png element element ssao yes 4539 0.6
 dump d2 all image 200 img-*.ppm type type zoom 2.5 adiam 1.5 size 1280 720
 dump m0 all movie 1000 movie.mpg type type size 640 480
 dump m1 all movie 1000 movie.avi type type size 640 480
 dump m2 all movie 100 movie.m4v type type zoom 1.8 adiam v_value size 1280 720
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Dump a high-quality rendered image of the atom configuration every N
 timesteps and save the images either as a sequence of JPEG or PNG or
 PPM files, or as a single movie file.  The options for this command as
 well as the <a class="reference internal" href="dump_modify.html"><em>dump_modify</em></a> command control what is
 included in the image or movie and how it appears.  A series of such
 images can easily be manually converted into an animated movie of your
 simulation or the process can be automated without writing the
 intermediate files using the dump movie style; see further details
 below.  Other dump styles store snapshots of numerical data asociated
 with atoms in various formats, as discussed on the <a class="reference internal" href="dump.html"><em>dump</em></a>
 doc page.</p>
 <p>Note that a set of images or a movie can be made after a simulation
 has been run, using the <a class="reference internal" href="rerun.html"><em>rerun</em></a> command to read snapshots
 from an existing dump file, and using these dump commands in the rerun
 script to generate the images/movie.</p>
 <p>Here are two sample images, rendered as 1024x1024 JPEG files.  Click
 to see the full-size images:</p>
 <DIV ALIGN=center><a data-lightbox="group-default"
                    href="_images/dump1.jpg"
                    class=""
                    title=""
                    data-title=""
                    ><img src="_images/dump1.jpg"
                     class=""
                     width="25%"
                     height="auto"
                     alt=""/>
                     </a><a data-lightbox="group-default"
                    href="_images/dump2.jpg"
                    class=""
                    title=""
                    data-title=""
                    ><img src="_images/dump2.jpg"
                     class=""
                     width="25%"
                     height="auto"
                     alt=""/>
                     </a></DIV><p>Only atoms in the specified group are rendered in the image.  The
 <a class="reference internal" href="dump_modify.html"><em>dump_modify region and thresh</em></a> commands can also
 alter what atoms are included in the image.
 The filename suffix determines whether a JPEG, PNG, or PPM file is
 created with the <em>image</em> dump style.  If the suffix is &#8221;.jpg&#8221; or
 &#8221;.jpeg&#8221;, then a JPEG format file is created, if the suffix is &#8221;.png&#8221;,
 then a PNG format is created, else a PPM (aka NETPBM) format file is
 created.  The JPEG and PNG files are binary; PPM has a text mode
 header followed by binary data. JPEG images have lossy compression;
 PNG has lossless compression; and PPM files are uncompressed but can
 be compressed with gzip, if LAMMPS has been compiled with
 -DLAMMPS_GZIP and a &#8221;.gz&#8221; suffix is used.</p>
 <p>Similarly, the format of the resulting movie is chosen with the
 <em>movie</em> dump style. This is handled by the underlying FFmpeg converter
 and thus details have to be looked up in the FFmpeg documentation.
 Typical examples are: .avi, .mpg, .m4v, .mp4, .mkv, .flv, .mov, .gif
 Additional settings of the movie compression like bitrate and
 framerate can be set using the <a class="reference internal" href="dump_modify.html"><em>dump_modify</em></a> command.</p>
 <p>To write out JPEG and PNG format files, you must build LAMMPS with
 support for the corresponding JPEG or PNG library. To convert images
 into movies, LAMMPS has to be compiled with the -DLAMMPS_FFMPEG
 flag. See <a class="reference internal" href="Section_start.html#start-2-4"><span>this section</span></a> of the manual
 for instructions on how to do this.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">Because periodic boundary conditions are enforced only
 on timesteps when neighbor lists are rebuilt, the coordinates of an
 atom in the image may be slightly outside the simulation box.</p>
 </div>
 <hr class="docutils" />
 <p>Dumps are performed on timesteps that are a multiple of N (including
 timestep 0) and on the last timestep of a minimization if the
 minimization converges.  Note that this means a dump will not be
 performed on the initial timestep after the dump command is invoked,
 if the current timestep is not a multiple of N.  This behavior can be
 changed via the <a class="reference internal" href="dump_modify.html"><em>dump_modify first</em></a> command, which
 can be useful if the dump command is invoked after a minimization
 ended on an arbitrary timestep.  N can be changed between runs by
 using the <a class="reference internal" href="dump_modify.html"><em>dump_modify every</em></a> command.</p>
 <p>Dump <em>image</em> filenames must contain a wildcard character &#8220;*&#8221;, so that
 one image file per snapshot is written.  The &#8220;*&#8221; character is replaced
 with the timestep value.  For example, tmp.dump.*.jpg becomes
 tmp.dump.0.jpg, tmp.dump.10000.jpg, tmp.dump.20000.jpg, etc.  Note
 that the <a class="reference internal" href="dump_modify.html"><em>dump_modify pad</em></a> command can be used to
 insure all timestep numbers are the same length (e.g. 00010), which
 can make it easier to convert a series of images into a movie in the
 correct ordering.</p>
 <p>Dump <em>movie</em> filenames on the other hand, must not have any wildcard
 character since only one file combining all images into a single
 movie will be written by the movie encoder.</p>
 <hr class="docutils" />
 <p>The <em>color</em> and <em>diameter</em> settings determine the color and size of
 atoms rendered in the image.  They can be any atom attribute defined
 for the <a class="reference internal" href="dump.html"><em>dump custom</em></a> command, including <em>type</em> and
 <em>element</em>.  This includes per-atom quantities calculated by a
 <a class="reference internal" href="compute.html"><em>compute</em></a>, <a class="reference internal" href="fix.html"><em>fix</em></a>, or <a class="reference internal" href="variable.html"><em>variable</em></a>,
 which are prefixed by &#8220;<a href="#id9"><span class="problematic" id="id10">c_</span></a>&#8221;, &#8220;<a href="#id11"><span class="problematic" id="id12">f_</span></a>&#8221;, or &#8220;<a href="#id13"><span class="problematic" id="id14">v_</span></a>&#8221; respectively.  Note that the
 <em>diameter</em> setting can be overridden with a numeric value by the
 optional <em>adiam</em> keyword, in which case you can specify the <em>diameter</em>
 setting with any valid atom attribute.</p>
 <p>If <em>type</em> is specified for the <em>color</em> setting, then the color of each
 atom is determined by its atom type.  By default the mapping of types
 to colors is as follows:</p>
 <ul class="simple">
 <li>type 1 = red</li>
 <li>type 2 = green</li>
 <li>type 3 = blue</li>
 <li>type 4 = yellow</li>
 <li>type 5 = aqua</li>
 <li>type 6 = cyan</li>
 </ul>
 <p>and repeats itself for types &gt; 6.  This mapping can be changed by the
 <a class="reference internal" href="dump_modify.html"><em>dump_modify acolor</em></a> command.</p>
 <p>If <em>type</em> is specified for the <em>diameter</em> setting then the diameter of
 each atom is determined by its atom type.  By default all types have
 diameter 1.0.  This mapping can be changed by the <a class="reference internal" href="dump_modify.html"><em>dump_modify adiam</em></a> command.</p>
 <p>If <em>element</em> is specified for the <em>color</em> and/or <em>diameter</em> setting,
 then the color and/or diameter of each atom is determined by which
 element it is, which in turn is specified by the element-to-type
 mapping specified by the &#8220;dump_modify element&#8221; command.  By default
 every atom type is C (carbon).  Every element has a color and diameter
 associated with it, which is the same as the colors and sizes used by
 the <a class="reference external" href="http://mt.seas.upenn.edu/Archive/Graphics/A">AtomEye</a> visualization package.</p>
 <p>If other atom attributes are used for the <em>color</em> or <em>diameter</em>
 settings, they are interpreted in the following way.</p>
 <p>If &#8220;vx&#8221;, for example, is used as the <em>color</em> setting, then the color
 of the atom will depend on the x-component of its velocity.  The
 association of a per-atom value with a specific color is determined by
 a &#8220;color map&#8221;, which can be specified via the
 <a class="reference internal" href="dump_modify.html"><em>dump_modify</em></a> command.  The basic idea is that the
 atom-attribute will be within a range of values, and every value
 within the range is mapped to a specific color.  Depending on how the
 color map is defined, that mapping can take place via interpolation so
 that a value of -3.2 is halfway between &#8220;red&#8221; and &#8220;blue&#8221;, or
 discretely so that the value of -3.2 is &#8220;orange&#8221;.</p>
 <p>If &#8220;vx&#8221;, for example, is used as the <em>diameter</em> setting, then the atom
 will be rendered using the x-component of its velocity as the
 diameter.  If the per-atom value &lt;= 0.0, them the atom will not be
 drawn.  Note that finite-size spherical particles, as defined by
 <a class="reference internal" href="atom_style.html"><em>atom_style sphere</em></a> define a per-particle radius or
 diameter, which can be used as the <em>diameter</em> setting.</p>
 <hr class="docutils" />
 <p>The various kewords listed above control how the image is rendered.
 As listed below, all of the keywords have defaults, most of which you
 will likely not need to change.  The <a class="reference internal" href="dump_modify.html"><em>dump modify</em></a>
 also has options specific to the dump image style, particularly for
 assigning colors to atoms, bonds, and other image features.</p>
 <hr class="docutils" />
 <p>The <em>adiam</em> keyword allows you to override the <em>diameter</em> setting to a
 per-atom attribute with a specified numeric value.  All atoms will be
 drawn with that diameter, e.g. 1.5, which is in whatever distance
 <a class="reference internal" href="units.html"><em>units</em></a> the input script defines, e.g. Angstroms.</p>
 <p>The <em>atom</em> keyword allow you to turn off the drawing of all atoms,
 if the specified value is <em>no</em>.</p>
 <p>The <em>bond</em> keyword allows to you to alter how bonds are drawn.  A bond
 is only drawn if both atoms in the bond are being drawn due to being
 in the specified group and due to other selection criteria
 (e.g. region, threshhold settings of the
 <a class="reference internal" href="dump_modify.html"><em>dump_modify</em></a> command).  By default, bonds are drawn
 if they are defined in the input data file as read by the
 <a class="reference internal" href="read_data.html"><em>read_data</em></a> command.  Using <em>none</em> for both the bond
 <em>color</em> and <em>width</em> value will turn off the drawing of all bonds.</p>
 <p>If <em>atom</em> is specified for the bond <em>color</em> value, then each bond is
 drawn in 2 halves, with the color of each half being the color of the
 atom at that end of the bond.</p>
 <p>If <em>type</em> is specified for the <em>color</em> value, then the color of each
 bond is determined by its bond type.  By default the mapping of bond
 types to colors is as follows:</p>
 <ul class="simple">
 <li>type 1 = red</li>
 <li>type 2 = green</li>
 <li>type 3 = blue</li>
 <li>type 4 = yellow</li>
 <li>type 5 = aqua</li>
 <li>type 6 = cyan</li>
 </ul>
 <p>and repeats itself for bond types &gt; 6.  This mapping can be changed by
 the <a class="reference internal" href="dump_modify.html"><em>dump_modify bcolor</em></a> command.</p>
 <p>The bond <em>width</em> value can be a numeric value or <em>atom</em> or <em>type</em> (or
 <em>none</em> as indicated above).</p>
 <p>If a numeric value is specified, then all bonds will be drawn as
 cylinders with that diameter, e.g. 1.0, which is in whatever distance
 <a class="reference internal" href="units.html"><em>units</em></a> the input script defines, e.g. Angstroms.</p>
 <p>If <em>atom</em> is specified for the <em>width</em> value, then each bond
 will be drawn with a width corresponding to the minimum diameter
 of the 2 atoms in the bond.</p>
 <p>If <em>type</em> is specified for the <em>width</em> value then the diameter of each
 bond is determined by its bond type.  By default all types have
 diameter 0.5.  This mapping can be changed by the <a class="reference internal" href="dump_modify.html"><em>dump_modify bdiam</em></a> command.</p>
 <hr class="docutils" />
 <p>The <em>size</em> keyword sets the width and height of the created images,
 i.e. the number of pixels in each direction.</p>
 <hr class="docutils" />
 <p>The <em>view</em>, <em>center</em>, <em>up</em>, <em>zoom</em>, and <em>persp</em> values determine how
 3d simulation space is mapped to the 2d plane of the image.  Basically
 they control how the simulation box appears in the image.</p>
 <p>All of the <em>view</em>, <em>center</em>, <em>up</em>, <em>zoom</em>, and <em>persp</em> values can be
 specified as numeric quantities, whose meaning is explained below.
 Any of them can also be specified as an <a class="reference internal" href="variable.html"><em>equal-style variable</em></a>, by using v_name as the value, where &#8220;name&#8221; is
 the variable name.  In this case the variable will be evaluated on the
 timestep each image is created to create a new value.  If the
 equal-style variable is time-dependent, this is a means of changing
 the way the simulation box appears from image to image, effectively
 doing a pan or fly-by view of your simulation.</p>
 <p>The <em>view</em> keyword determines the viewpoint from which the simulation
 box is viewed, looking towards the <em>center</em> point.  The <em>theta</em> value
 is the vertical angle from the +z axis, and must be an angle from 0 to
 180 degrees.  The <em>phi</em> value is an azimuthal angle around the z axis
 and can be positive or negative.  A value of 0.0 is a view along the
 +x axis, towards the <em>center</em> point.  If <em>theta</em> or <em>phi</em> are
 specified via variables, then the variable values should be in
 degrees.</p>
 <p>The <em>center</em> keyword determines the point in simulation space that
 will be at the center of the image.  <em>Cx</em>, <em>Cy</em>, and <em>Cz</em> are
 speficied as fractions of the box dimensions, so that (0.5,0.5,0.5) is
 the center of the simulation box.  These values do not have to be
 between 0.0 and 1.0, if you want the simulation box to be offset from
 the center of the image.  Note, however, that if you choose strange
 values for <em>Cx</em>, <em>Cy</em>, or <em>Cz</em> you may get a blank image.  Internally,
 <em>Cx</em>, <em>Cy</em>, and <em>Cz</em> are converted into a point in simulation space.
 If <em>flag</em> is set to &#8220;s&#8221; for static, then this conversion is done once,
 at the time the dump command is issued.  If <em>flag</em> is set to &#8220;d&#8221; for
 dynamic then the conversion is performed every time a new image is
 created.  If the box size or shape is changing, this will adjust the
 center point in simulation space.</p>
 <p>The <em>up</em> keyword determines what direction in simulation space will be
 &#8220;up&#8221; in the image.  Internally it is stored as a vector that is in the
 plane perpendicular to the view vector implied by the <em>theta</em> and
 <em>pni</em> values, and which is also in the plane defined by the view
 vector and user-specified up vector.  Thus this internal vector is
 computed from the user-specified <em>up</em> vector as</p>
 <div class="highlight-python"><div class="highlight"><pre>up_internal = view cross (up cross view)
 </pre></div>
 </div>
 <p>This means the only restriction on the specified <em>up</em> vector is that
 it cannot be parallel to the <em>view</em> vector, implied by the <em>theta</em> and
 <em>phi</em> values.</p>
 <p>The <em>zoom</em> keyword scales the size of the simulation box as it appears
 in the image.  The default <em>zfactor</em> value of 1 should display an
 image mostly filled by the atoms in the simulation box.  A <em>zfactor</em> &gt;
 1 will make the simulation box larger; a <em>zfactor</em> &lt; 1 will make it
 smaller.  <em>Zfactor</em> must be a value &gt; 0.0.</p>
 <p>The <em>persp</em> keyword determines how much depth perspective is present
 in the image.  Depth perspective makes lines that are parallel in
 simulation space appear non-parallel in the image.  A <em>pfactor</em> value
 of 0.0 means that parallel lines will meet at infininty (1.0/pfactor),
 which is an orthographic rendering with no persepctive.  A <em>pfactor</em>
 value between 0.0 and 1.0 will introduce more perspective.  A <em>pfactor</em>
 value &gt; 1 will create a highly skewed image with a large amount of
 perspective.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">The <em>persp</em> keyword is not yet supported as an option.</p>
 </div>
 <hr class="docutils" />
 <p>The <em>box</em> keyword determines if and how the simulation box boundaries
 are rendered as thin cylinders in the image.  If <em>no</em> is set, then the
 box boundaries are not drawn and the <em>diam</em> setting is ignored.  If
 <em>yes</em> is set, the 12 edges of the box are drawn, with a diameter that
 is a fraction of the shortest box length in x,y,z (for 3d) or x,y (for
 2d).  The color of the box boundaries can be set with the <a class="reference internal" href="dump_modify.html"><em>dump_modify boxcolor</em></a> command.</p>
 <p>The <em>axes</em> keyword determines if and how the coordinate axes are
 rendered as thin cylinders in the image.  If <em>no</em> is set, then the
 axes are not drawn and the <em>length</em> and <em>diam</em> settings are ignored.
 If <em>yes</em> is set, 3 thin cylinders are drawn to represent the x,y,z
 axes in colors red,green,blue.  The origin of these cylinders will be
 offset from the lower left corner of the box by 10%.  The <em>length</em>
 setting determines how long the cylinders will be as a fraction of the
 respective box lengths.  The <em>diam</em> setting determines their thickness
 as a fraction of the shortest box length in x,y,z (for 3d) or x,y (for
 2d).</p>
 <p>The <em>subbox</em> keyword determines if and how processor sub-domain
 boundaries are rendered as thin cylinders in the image.  If <em>no</em> is
 set (default), then the sub-domain boundaries are not drawn and the
 <em>diam</em> setting is ignored.  If <em>yes</em> is set, the 12 edges of each
 processor sub-domain are drawn, with a diameter that is a fraction of
 the shortest box length in x,y,z (for 3d) or x,y (for 2d).  The color
 of the sub-domain boundaries can be set with the <a class="reference internal" href="dump_modify.html"><em>dump_modify boxcolor</em></a> command.</p>
 <hr class="docutils" />
 <p>The <em>shiny</em> keyword determines how shiny the objects rendered in the
 image will appear.  The <em>sfactor</em> value must be a value 0.0 &lt;=
 <em>sfactor</em> &lt;= 1.0, where <em>sfactor</em> = 1 is a highly reflective surface
 and <em>sfactor</em> = 0 is a rough non-shiny surface.</p>
 <p>The <em>ssao</em> keyword turns on/off a screen space ambient occlusion
 (SSAO) model for depth shading.  If <em>yes</em> is set, then atoms further
 away from the viewer are darkened via a randomized process, which is
 perceived as depth.  The calculation of this effect can increase the
 cost of computing the image by roughly 2x.  The strength of the effect
 can be scaled by the <em>dfactor</em> parameter.  If <em>no</em> is set, no depth
 shading is performed.</p>
 <hr class="docutils" />
 <p>A series of JPEG, PNG, or PPM images can be converted into a movie
 file and then played as a movie using commonly available tools. Using
 dump style <em>movie</em> automates this step and avoids the intermediate
 step of writing (many) image snapshot file. But LAMMPS has to be
 compiled with -DLAMMPS_FFMPEG and an FFmpeg executable have to be
 installed.</p>
 <p>To manually convert JPEG, PNG or PPM files into an animated GIF or
 MPEG or other movie file you can use:</p>
 <ul class="simple">
 <li><ol class="first loweralpha">
 <li>Use the ImageMagick convert program.</li>
 </ol>
 </li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>% convert *.jpg foo.gif
 % convert -loop 1 *.ppm foo.mpg
 </pre></div>
 </div>
 <p>Animated GIF files from ImageMagick are unoptimized. You can use a
 program like gifsicle to optimize and massively shrink them.
 MPEG files created by ImageMagick are in MPEG-1 format with rather
 inefficient compression and low quality.</p>
 <ul class="simple">
 <li><ol class="first loweralpha" start="2">
 <li>Use QuickTime.</li>
 </ol>
 </li>
 </ul>
 <p>Select &#8220;Open Image Sequence&#8221; under the File menu Load the images into
 QuickTime to animate them Select &#8220;Export&#8221; under the File menu Save the
 movie as a QuickTime movie (<a href="#id7"><span class="problematic" id="id8">*</span></a>.mov) or in another format.  QuickTime
 can generate very high quality and efficiently compressed movie
 files. Some of the supported formats require to buy a license and some
 are not readable on all platforms until specific runtime libraries are
 installed.</p>
 <ul class="simple">
 <li><ol class="first loweralpha" start="3">
 <li>Use FFmpeg</li>
 </ol>
 </li>
 </ul>
 <p>FFmpeg is a command line tool that is available on many platforms and
 allows extremely flexible encoding and decoding of movies.</p>
 <div class="highlight-python"><div class="highlight"><pre>cat snap.*.jpg | ffmpeg -y -f image2pipe -c:v mjpeg -i - -b:v 2000k movie.m4v
 cat snap.*.ppm | ffmpeg -y -f image2pipe -c:v ppm -i - -b:v 2400k movie.avi
 </pre></div>
 </div>
 <p>Frontends for FFmpeg exist for multiple platforms. For more
 information see the <a class="reference external" href="http://www.ffmpeg.org/">FFmpeg homepage</a></p>
 <hr class="docutils" />
 <p>Play the movie:</p>
 <ul class="simple">
 <li><ol class="first loweralpha">
 <li>Use your browser to view an animated GIF movie.</li>
 </ol>
 </li>
 </ul>
 <p>Select &#8220;Open File&#8221; under the File menu
 Load the animated GIF file</p>
 <ul class="simple">
 <li>b) Use the freely available mplayer or ffplay tool to view a
 movie. Both are available for multiple OSes and support a large
 variety of file formats and decoders.</li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>% mplayer foo.mpg
 % ffplay bar.avi
 </pre></div>
 </div>
 <ul class="simple">
 <li>c) Use the <a class="reference external" href="http://www.sandia.gov/~sjplimp/pizza.html">Pizza.py</a>
 <a class="reference external" href="http://www.sandia.gov/~sjplimp/pizza/doc/animate.html">animate tool</a>,
 which works directly on a series of image files.</li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre><span class="n">a</span> <span class="o">=</span> <span class="n">animate</span><span class="p">(</span><span class="s">&quot;foo*.jpg&quot;</span><span class="p">)</span>
 </pre></div>
 </div>
 <ul class="simple">
 <li>d) QuickTime and other Windows- or MacOS-based media players can
 obviously play movie files directly. Similarly for corresponding tools
 bundled with Linux desktop environments.  However, due to licensing
 issues with some file formats, the formats may require installing
 additional libraries, purchasing a license, or may not be
 supported.</li>
 </ul>
 <hr class="docutils" />
 <p>See <a class="reference internal" href="Section_modify.html"><em>Section_modify</em></a> of the manual for information
 on how to add new compute and fix styles to LAMMPS to calculate
 per-atom quantities which could then be output into dump files.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>To write JPEG images, you must use the -DLAMMPS_JPEG switch when
 building LAMMPS and link with a JPEG library. To write PNG images, you
 must use the -DLAMMPS_PNG switch when building LAMMPS and link with a
 PNG library.</p>
 <p>To write <em>movie</em> dumps, you must use the -DLAMMPS_FFMPEG switch when
 building LAMMPS and have the FFmpeg executable available on the
 machine where LAMMPS is being run.  Typically it&#8217;s name is lowercase,
 i.e. ffmpeg.</p>
 <p>See the <a class="reference internal" href="Section_start.html#start-2-4"><span>Making LAMMPS</span></a> section of the
 documentation for details on how to compile with optional switches.</p>
 <p>Note that since FFmpeg is run as an external program via a pipe,
 LAMMPS has limited control over its execution and no knowledge about
 errors and warnings printed by it. Those warnings and error messages
 will be printed to the screen only. Due to the way image data is
 communicated to FFmpeg, it will often print the message</p>
 <div class="highlight-python"><div class="highlight"><pre>pipe:: Input/output error
 </pre></div>
 </div>
 <p>which can be safely ignored. Other warnings
 and errors have to be addressed according to the FFmpeg documentation.
 One known issue is that certain movie file formats (e.g. MPEG level 1
 and 2 format streams) have video bandwith limits that can be crossed
 when rendering too large of image sizes. Typical warnings look like
 this:</p>
 <div class="highlight-python"><div class="highlight"><pre>[mpeg @ 0x98b5e0] packet too large, ignoring buffer limits to mux it
 [mpeg @ 0x98b5e0] buffer underflow st=0 bufi=281407 size=285018
 [mpeg @ 0x98b5e0] buffer underflow st=0 bufi=283448 size=285018
 </pre></div>
 </div>
 <p>In this case it is recommended to either reduce the size of the image
 or encode in a different format that is also supported by your copy of
 FFmpeg, and which does not have this limitation (e.g. .avi, .mkv,
 mp4).</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="dump.html"><em>dump</em></a>, <a class="reference internal" href="dump_modify.html"><em>dump_modify</em></a>, <a class="reference internal" href="undump.html"><em>undump</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The defaults for the keywords are as follows:</p>
 <ul class="simple">
 <li>adiam = not specified (use diameter setting)</li>
 <li>atom = yes</li>
 <li>bond = none none (if no bonds in system)</li>
 <li>bond = atom 0.5 (if bonds in system)</li>
 <li>size = 512 512</li>
 <li>view = 60 30 (for 3d)</li>
 <li>view = 0 0 (for 2d)</li>
 <li>center = s 0.5 0.5 0.5</li>
 <li>up = 0 0 1 (for 3d)</li>
 <li>up = 0 1 0 (for 2d)</li>
 <li>zoom = 1.0</li>
 <li>persp = 0.0</li>
 <li>box = yes 0.02</li>
 <li>axes = no 0.0 0.0</li>
 <li>subbox no 0.0</li>
 <li>shiny = 1.0</li>
 <li>ssao = no</li>
 </ul>
 </div>
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   <div class="section" id="dump-modify-command">
 <span id="index-0"></span><h1>dump_modify command<a class="headerlink" href="#dump-modify-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>dump_modify dump-ID keyword values ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>dump-ID = ID of dump to modify</li>
 <li>one or more keyword/value pairs may be appended</li>
 <li>these keywords apply to various dump styles</li>
 <li>keyword = <em>append</em> or <em>buffer</em> or <em>element</em> or <em>every</em> or <em>fileper</em> or <em>first</em> or <em>flush</em> or <em>format</em> or <em>image</em> or <em>label</em> or <em>nfile</em> or <em>pad</em> or <em>precision</em> or <em>region</em> or <em>scale</em> or <em>sort</em> or <em>thresh</em> or <em>unwrap</em></li>
 </ul>
 <pre class="literal-block">
 <em>append</em> arg = <em>yes</em> or <em>no</em>
-  <em>buffer</em> arg = <em>yes</em> or <em>no</em>
-  <em>element</em> args = E1 E2 ... EN, where N = # of atom types
-    E1,...,EN = element name, e.g. C or Fe or Ga
-  <em>every</em> arg = N
-    N = dump every this many timesteps
-    N can be a variable (see below)
-  <em>fileper</em> arg = Np
-    Np = write one file for every this many processors
-  <em>first</em> arg = <em>yes</em> or <em>no</em>
-  <em>format</em> arg = C-style format string for one line of output
-  <em>flush</em> arg = <em>yes</em> or <em>no</em>
-  <em>image</em> arg = <em>yes</em> or <em>no</em>
-  <em>label</em> arg = string
-    string = character string (e.g. BONDS) to use in header of dump local file
-  <em>nfile</em> arg = Nf
-    Nf = write this many files, one from each of Nf processors
-  <em>pad</em> arg = Nchar = # of characters to convert timestep to
-  <em>precision</em> arg = power-of-10 value from 10 to 1000000
-  <em>region</em> arg = region-ID or &quot;none&quot;
-  <em>scale</em> arg = <em>yes</em> or <em>no</em>
-  <em>sfactor</em> arg = coordinate scaling factor (&gt; 0.0)
-  <em>tfactor</em> arg = time scaling factor (&gt; 0.0)
-  <em>sort</em> arg = <em>off</em> or <em>id</em> or N or -N
-     off = no sorting of per-atom lines within a snapshot
-     id = sort per-atom lines by atom ID
-     N = sort per-atom lines in ascending order by the Nth column
-     -N = sort per-atom lines in descending order by the Nth column
-  <em>thresh</em> args = attribute operation value
-    attribute = same attributes (x,fy,etotal,sxx,etc) used by dump custom style
-    operation = &quot;&lt;&quot; or &quot;&lt;=&quot; or &quot;&gt;&quot; or &quot;&gt;=&quot; or &quot;==&quot; or &quot;!=&quot;
-    value = numeric value to compare to
-    these 3 args can be replaced by the word &quot;none&quot; to turn off thresholding
-  <em>unwrap</em> arg = <em>yes</em> or <em>no</em>
+<em>buffer</em> arg = <em>yes</em> or <em>no</em>
+<em>element</em> args = E1 E2 ... EN, where N = # of atom types
+  E1,...,EN = element name, e.g. C or Fe or Ga
+<em>every</em> arg = N
+  N = dump every this many timesteps
+  N can be a variable (see below)
+<em>fileper</em> arg = Np
+  Np = write one file for every this many processors
+<em>first</em> arg = <em>yes</em> or <em>no</em>
+<em>format</em> arg = C-style format string for one line of output
+<em>flush</em> arg = <em>yes</em> or <em>no</em>
+<em>image</em> arg = <em>yes</em> or <em>no</em>
+<em>label</em> arg = string
+  string = character string (e.g. BONDS) to use in header of dump local file
+<em>nfile</em> arg = Nf
+  Nf = write this many files, one from each of Nf processors
+<em>pad</em> arg = Nchar = # of characters to convert timestep to
+<em>precision</em> arg = power-of-10 value from 10 to 1000000
+<em>region</em> arg = region-ID or &quot;none&quot;
+<em>scale</em> arg = <em>yes</em> or <em>no</em>
+<em>sfactor</em> arg = coordinate scaling factor (&gt; 0.0)
+<em>tfactor</em> arg = time scaling factor (&gt; 0.0)
+<em>sort</em> arg = <em>off</em> or <em>id</em> or N or -N
+   off = no sorting of per-atom lines within a snapshot
+   id = sort per-atom lines by atom ID
+   N = sort per-atom lines in ascending order by the Nth column
+   -N = sort per-atom lines in descending order by the Nth column
+<em>thresh</em> args = attribute operation value
+  attribute = same attributes (x,fy,etotal,sxx,etc) used by dump custom style
+  operation = &quot;&lt;&quot; or &quot;&lt;=&quot; or &quot;&gt;&quot; or &quot;&gt;=&quot; or &quot;==&quot; or &quot;!=&quot;
+  value = numeric value to compare to
+  these 3 args can be replaced by the word &quot;none&quot; to turn off thresholding
+<em>unwrap</em> arg = <em>yes</em> or <em>no</em>
 </pre>
 <ul class="simple">
 <li>these keywords apply only to the <em>image</em> and <em>movie</em> <a class="reference internal" href="dump_image.html"><em>styles</em></a></li>
 <li>keyword = <em>acolor</em> or <em>adiam</em> or <em>amap</em> or <em>backcolor</em> or <em>bcolor</em> or <em>bdiam</em> or <em>boxcolor</em> or <em>color</em> or <em>bitrate</em> or <em>framerate</em></li>
 </ul>
 <pre class="literal-block">
 <em>acolor</em> args = type color
-    type = atom type or range of types (see below)
-    color = name of color or color1/color2/...
-  <em>adiam</em> args = type diam
-    type = atom type or range of types (see below)
-    diam = diameter of atoms of that type (distance units)
-  <em>amap</em> args = lo hi style delta N entry1 entry2 ... entryN
-    lo = number or <em>min</em> = lower bound of range of color map
-    hi = number or <em>max</em> = upper bound of range of color map
-    style = 2 letters = &quot;c&quot; or &quot;d&quot; or &quot;s&quot; plus &quot;a&quot; or &quot;f&quot;
-      &quot;c&quot; for continuous
-      &quot;d&quot; for discrete
-      &quot;s&quot; for sequential
-      &quot;a&quot; for absolute
-      &quot;f&quot; for fractional
-    delta = binsize (only used for style &quot;s&quot;, otherwise ignored)
-      binsize = range is divided into bins of this width
-    N = # of subsequent entries
-    entry = value color (for continuous style)
-      value = number or <em>min</em> or <em>max</em> = single value within range
-      color = name of color used for that value
-    entry = lo hi color (for discrete style)
-      lo/hi = number or <em>min</em> or <em>max</em> = lower/upper bound of subset of range
-      color = name of color used for that subset of values
-    entry = color (for sequential style)
-      color = name of color used for a bin of values
-  <em>backcolor</em> arg = color
-    color = name of color for background
-  <em>bcolor</em> args = type color
-    type = bond type or range of types (see below)
-    color = name of color or color1/color2/...
-  <em>bdiam</em> args = type diam
-    type = bond type or range of types (see below)
-    diam = diameter of bonds of that type (distance units)
-  <em>boxcolor</em> arg = color
-    color = name of color for simulation box lines and processor sub-domain lines
-  <em>color</em> args = name R G B
-    name = name of color
-    R,G,B = red/green/blue numeric values from 0.0 to 1.0
-  <em>bitrate</em> arg = rate
-    rate = target bitrate for movie in kbps
-  <em>framerate</em> arg = fps
-    fps = frames per second for movie
+  type = atom type or range of types (see below)
+  color = name of color or color1/color2/...
+<em>adiam</em> args = type diam
+  type = atom type or range of types (see below)
+  diam = diameter of atoms of that type (distance units)
+<em>amap</em> args = lo hi style delta N entry1 entry2 ... entryN
+  lo = number or <em>min</em> = lower bound of range of color map
+  hi = number or <em>max</em> = upper bound of range of color map
+  style = 2 letters = &quot;c&quot; or &quot;d&quot; or &quot;s&quot; plus &quot;a&quot; or &quot;f&quot;
+    &quot;c&quot; for continuous
+    &quot;d&quot; for discrete
+    &quot;s&quot; for sequential
+    &quot;a&quot; for absolute
+    &quot;f&quot; for fractional
+  delta = binsize (only used for style &quot;s&quot;, otherwise ignored)
+    binsize = range is divided into bins of this width
+  N = # of subsequent entries
+  entry = value color (for continuous style)
+    value = number or <em>min</em> or <em>max</em> = single value within range
+    color = name of color used for that value
+  entry = lo hi color (for discrete style)
+    lo/hi = number or <em>min</em> or <em>max</em> = lower/upper bound of subset of range
+    color = name of color used for that subset of values
+  entry = color (for sequential style)
+    color = name of color used for a bin of values
+<em>backcolor</em> arg = color
+  color = name of color for background
+<em>bcolor</em> args = type color
+  type = bond type or range of types (see below)
+  color = name of color or color1/color2/...
+<em>bdiam</em> args = type diam
+  type = bond type or range of types (see below)
+  diam = diameter of bonds of that type (distance units)
+<em>boxcolor</em> arg = color
+  color = name of color for simulation box lines and processor sub-domain lines
+<em>color</em> args = name R G B
+  name = name of color
+  R,G,B = red/green/blue numeric values from 0.0 to 1.0
+<em>bitrate</em> arg = rate
+  rate = target bitrate for movie in kbps
+<em>framerate</em> arg = fps
+  fps = frames per second for movie
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>dump_modify 1 format &quot;%d %d %20.15g %g %g&quot; scale yes
 dump_modify myDump image yes scale no flush yes
 dump_modify 1 region mySphere thresh x &lt; 0.0 thresh epair &gt;= 3.2
 dump_modify xtcdump precision 10000 sfactor 0.1
 dump_modify 1 every 1000 nfile 20
 dump_modify 1 every v_myVar
 dump_modify 1 amap min max cf 0.0 3 min green 0.5 yellow max blue boxcolor red
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Modify the parameters of a previously defined dump command.  Not all
 parameters are relevant to all dump styles.</p>
 <p>As explained on the <a class="reference internal" href="dump.html"><em>dump</em></a> doc page, the <em>atom/mpiio</em>,
 <em>custom/mpiio</em>, and <em>xyz/mpiio</em> dump styles are identical in command
 syntax and in the format of the dump files they create, to the
 corresponding styles without &#8220;mpiio&#8221;, except the single dump file they
 produce is written in parallel via the MPI-IO library.  Thus if a
 dump_modify option below is valid for the <em>atom</em> style, it is also
 valid for the <em>atom/mpiio</em> style, and similarly for the other styles
 which allow for use of MPI-IO.</p>
 <p>These keywords apply to various dump styles, including the <a class="reference internal" href="dump_image.html"><em>dump image</em></a> and <a class="reference internal" href="dump_image.html"><em>dump movie</em></a> styles.  The
 description gives details.</p>
 <hr class="docutils" />
 <p>The <em>append</em> keyword applies to all dump styles except <em>cfg</em> and <em>xtc</em>
 and <em>dcd</em>.  It also applies only to text output files, not to binary
 or gzipped or image/movie files.  If specified as <em>yes</em>, then dump
 snapshots are appended to the end of an existing dump file.  If
 specified as <em>no</em>, then a new dump file will be created which will
 overwrite an existing file with the same name.  This keyword can only
 take effect if the dump_modify command is used after the
 <a class="reference internal" href="dump.html"><em>dump</em></a> command, but before the first command that causes
 dump snapshots to be output, e.g. a <a class="reference internal" href="run.html"><em>run</em></a> or
 <a class="reference internal" href="minimize.html"><em>minimize</em></a> command.  Once the dump file has been opened,
 this keyword has no further effect.</p>
 <hr class="docutils" />
 <p>The <em>buffer</em> keyword applies only to dump styles <em>atom</em>, <em>cfg</em>,
 <em>custom</em>, <em>local</em>, and <em>xyz</em>.  It also applies only to text output
 files, not to binary or gzipped files.  If specified as <em>yes</em>, which
 is the default, then each processor writes its output into an internal
 text buffer, which is then sent to the processor(s) which perform file
 writes, and written by those processors(s) as one large chunk of text.
 If specified as <em>no</em>, each processor sends its per-atom data in binary
 format to the processor(s) which perform file wirtes, and those
 processor(s) format and write it line by line into the output file.</p>
 <p>The buffering mode is typically faster since each processor does the
 relatively expensive task of formatting the output for its own atoms.
 However it requires about twice the memory (per processor) for the
 extra buffering.</p>
 <hr class="docutils" />
 <p>The <em>element</em> keyword applies only to the the dump <em>cfg</em>, <em>xyz</em>, and
 <em>image</em> styles.  It associates element names (e.g. H, C, Fe) with
 LAMMPS atom types.  See the list of element names at the bottom of
 this page.</p>
 <p>In the case of dump <em>cfg</em>, this allows the <a class="reference external" href="http://mt.seas.upenn.edu/Archive/Graphics/A">AtomEye</a>
 visualization package to read the dump file and render atoms with the
 appropriate size and color.</p>
 <p>In the case of dump <em>image</em>, the output images will follow the same
 <a class="reference external" href="http://mt.seas.upenn.edu/Archive/Graphics/A">AtomEye</a> convention.  An element name is specified for each
 atom type (1 to Ntype) in the simulation.  The same element name can
 be given to multiple atom types.</p>
 <p>In the case of <em>xyz</em> format dumps, there are no restrictions to what
 label can be used as an element name.  Any whitespace separated text
 will be accepted.</p>
 <hr class="docutils" />
 <p>The <em>every</em> keyword changes the dump frequency originally specified by
 the <a class="reference internal" href="dump.html"><em>dump</em></a> command to a new value.  The every keyword can be
 specified in one of two ways.  It can be a numeric value in which case
 it must be &gt; 0.  Or it can be an <a class="reference internal" href="variable.html"><em>equal-style variable</em></a>,
 which should be specified as v_name, where name is the variable name.</p>
 <p>In this case, the variable is evaluated at the beginning of a run to
 determine the next timestep at which a dump snapshot will be written
 out.  On that timestep the variable will be evaluated again to
 determine the next timestep, etc.  Thus the variable should return
 timestep values.  See the stagger() and logfreq() and stride() math
 functions for <a class="reference internal" href="variable.html"><em>equal-style variables</em></a>, as examples of
 useful functions to use in this context.  Other similar math functions
 could easily be added as options for <a class="reference internal" href="variable.html"><em>equal-style variables</em></a>.  Also see the next() function, which allows
 use of a file-style variable which reads successive values from a
 file, each time the variable is evaluated.  Used with the <em>every</em>
 keyword, if the file contains a list of ascending timesteps, you can
 output snapshots whenever you wish.</p>
 <p>Note that when using the variable option with the <em>every</em> keyword, you
 need to use the <em>first</em> option if you want an initial snapshot written
 to the dump file.  The <em>every</em> keyword cannot be used with the dump
 <em>dcd</em> style.</p>
 <p>For example, the following commands will
 write snapshots at timesteps 0,10,20,30,100,200,300,1000,2000,etc:</p>
 <div class="highlight-python"><div class="highlight"><pre>variable     s equal logfreq(10,3,10)
 dump         1 all atom 100 tmp.dump
 dump_modify  1 every v_s first yes
 </pre></div>
 </div>
 <p>The following commands would write snapshots at the timesteps listed
 in file tmp.times:</p>
 <div class="highlight-python"><div class="highlight"><pre>variable        f file tmp.times
 variable     s equal next(f)
 dump         1 all atom 100 tmp.dump
 dump_modify  1 every v_s
 </pre></div>
 </div>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">When using a file-style variable with the <em>every</em>
 keyword, the file of timesteps must list a first timestep that is
 beyond the current timestep (e.g. it cannot be 0).  And it must list
 one or more timesteps beyond the length of the run you perform.  This
 is because the dump command will generate an error if the next
 timestep it reads from the file is not a value greater than the
 current timestep.  Thus if you wanted output on steps 0,15,100 of a
 100-timestep run, the file should contain the values 15,100,101 and
 you should also use the dump_modify first command.  Any final value &gt;
 100 could be used in place of 101.</p>
 </div>
 <hr class="docutils" />
 <p>The <em>first</em> keyword determines whether a dump snapshot is written on
 the very first timestep after the dump command is invoked.  This will
 always occur if the current timestep is a multiple of N, the frequency
 specified in the <a class="reference internal" href="dump.html"><em>dump</em></a> command, including timestep 0.  But
 if this is not the case, a dump snapshot will only be written if the
 setting of this keyword is <em>yes</em>.  If it is <em>no</em>, which is the
 default, then it will not be written.</p>
 <hr class="docutils" />
 <p>The <em>flush</em> keyword determines whether a flush operation is invoked
 after a dump snapshot is written to the dump file.  A flush insures
 the output in that file is current (no buffering by the OS), even if
 LAMMPS halts before the simulation completes.  Flushes cannot be
 performed with dump style <em>xtc</em>.</p>
 <hr class="docutils" />
 <p>The text-based dump styles have a default C-style format string which
 simply specifies %d for integers and %g for floating-point values.
 The <em>format</em> keyword can be used to override the default with a new
 C-style format string.  Do not include a trailing &#8220;n&#8221; newline
 character in the format string.  This option has no effect on the
 <em>dcd</em> and <em>xtc</em> dump styles since they write binary files.  Note that
 for the <em>cfg</em> style, the first two fields (atom id and type) are not
 actually written into the CFG file, though you must include formats
 for them in the format string.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">Any value written to a text-based dump file that is a
 per-atom quantity calculated by a <a class="reference internal" href="compute.html"><em>compute</em></a> or
 <a class="reference internal" href="fix.html"><em>fix</em></a> is stored internally as a floating-point value.  If the
 value is actually an integer and you wish it to appear in the text
 dump file as a (large) integer, then you need to use an appropriate
 format.  For example, these commands:</p>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>compute     1 all property/local batom1 batom2
 dump        1 all local 100 tmp.bonds index c_1[1] c_1[2]
 dump_modify 1 format &quot;%d %0.0f %0.0f&quot;
 </pre></div>
 </div>
 <p>will output the two atom IDs for atoms in each bond as integers.  If
 the dump_modify command were omitted, they would appear as
 floating-point values, assuming they were large integers (more than 6
 digits).  The &#8220;index&#8221; keyword should use the &#8220;%d&#8221; format since it is
 not generated by a compute or fix, and is stored internally as an
 integer.</p>
 <hr class="docutils" />
 <p>The <em>fileper</em> keyword is documented below with the <em>nfile</em> keyword.</p>
 <hr class="docutils" />
 <p>The <em>image</em> keyword applies only to the dump <em>atom</em> style.  If the
 image value is <em>yes</em>, 3 flags are appended to each atom&#8217;s coords which
 are the absolute box image of the atom in each dimension.  For
 example, an x image flag of -2 with a normalized coord of 0.5 means
 the atom is in the center of the box, but has passed thru the box
 boundary 2 times and is really 2 box lengths to the left of its
 current coordinate.  Note that for dump style <em>custom</em> these various
 values can be printed in the dump file by using the appropriate atom
 attributes in the dump command itself.</p>
 <hr class="docutils" />
 <p>The <em>label</em> keyword applies only to the dump <em>local</em> style.  When
 it writes local information, such as bond or angle topology
 to a dump file, it will use the specified <em>label</em> to format
 the header.  By default this includes 2 lines:</p>
 <div class="highlight-python"><div class="highlight"><pre>ITEM: NUMBER OF ENTRIES
 ITEM: ENTRIES ...
 </pre></div>
 </div>
 <p>The word &#8220;ENTRIES&#8221; will be replaced with the string specified,
 e.g. BONDS or ANGLES.</p>
 <hr class="docutils" />
 <p>The <em>nfile</em> or <em>fileper</em> keywords can be used in conjunction with the
 &#8220;%&#8221; wildcard character in the specified dump file name, for all dump
 styles except the <em>dcd</em>, <em>image</em>, <em>movie</em>, <em>xtc</em>, and <em>xyz</em> styles
 (for which &#8220;%&#8221; is not allowed).  As explained on the <a class="reference internal" href="dump.html"><em>dump</em></a>
 command doc page, the &#8220;%&#8221; character causes the dump file to be written
 in pieces, one piece for each of P processors.  By default P = the
 number of processors the simulation is running on.  The <em>nfile</em> or
 <em>fileper</em> keyword can be used to set P to a smaller value, which can
 be more efficient when running on a large number of processors.</p>
 <p>The <em>nfile</em> keyword sets P to the specified Nf value.  For example, if
 Nf = 4, and the simulation is running on 100 processors, 4 files will
 be written, by processors 0,25,50,75.  Each will collect information
 from itself and the next 24 processors and write it to a dump file.</p>
 <p>For the <em>fileper</em> keyword, the specified value of Np means write one
 file for every Np processors.  For example, if Np = 4, every 4th
 processor (0,4,8,12,etc) will collect information from itself and the
 next 3 processors and write it to a dump file.</p>
 <hr class="docutils" />
 <p>The <em>pad</em> keyword only applies when the dump filename is specified
 with a wildcard &#8220;*&#8221; character which becomes the timestep.  If <em>pad</em> is
 0, which is the default, the timestep is converted into a string of
 unpadded length, e.g. 100 or 12000 or 2000000.  When <em>pad</em> is
 specified with <em>Nchar</em> &gt; 0, the string is padded with leading zeroes
 so they are all the same length = <em>Nchar</em>.  For example, pad 7 would
 yield 0000100, 0012000, 2000000.  This can be useful so that
 post-processing programs can easily read the files in ascending
 timestep order.</p>
 <hr class="docutils" />
 <p>The <em>precision</em> keyword only applies to the dump <em>xtc</em> style.  A
 specified value of N means that coordinates are stored to 1/N
 nanometer accuracy, e.g. for N = 1000, the coordinates are written to
 1/1000 nanometer accuracy.</p>
 <hr class="docutils" />
 <p>The <em>sfactor</em> and <em>tfactor</em> keywords only apply to the dump <em>xtc</em>
 style.  They allow customization of the unit conversion factors used
 when writing to XTC files.  By default they are initialized for
 whatever <a class="reference internal" href="units.html"><em>units</em></a> style is being used, to write out
 coordinates in nanometers and time in picoseconds.  I.e. for <em>real</em>
 units, LAMMPS defines <em>sfactor</em> = 0.1 and <em>tfactor</em> = 0.001, since the
 Angstroms and fmsec used by <em>real</em> units are 0.1 nm and 0.001 psec
 respectively.  If you are using a units system with distance and time
 units far from nm and psec, you may wish to write XTC files with
 different units, since the compression algorithm used in XTC files is
 most effective when the typical magnitude of position data is between
 10.0 and 0.1.</p>
 <hr class="docutils" />
 <p>The <em>region</em> keyword only applies to the dump <em>custom</em>, <em>cfg</em>,
 <em>image</em>, and <em>movie</em> styles.  If specified, only atoms in the region
 will be written to the dump file or included in the image/movie.  Only
 one region can be applied as a filter (the last one specified).  See
 the <a class="reference internal" href="region.html"><em>region</em></a> command for more details.  Note that a region
 can be defined as the &#8220;inside&#8221; or &#8220;outside&#8221; of a geometric shape, and
 it can be the &#8220;union&#8221; or &#8220;intersection&#8221; of a series of simpler
 regions.</p>
 <hr class="docutils" />
 <p>The <em>scale</em> keyword applies only to the dump <em>atom</em> style.  A scale
 value of <em>yes</em> means atom coords are written in normalized units from
 0.0 to 1.0 in each box dimension.  If the simluation box is triclinic
 (tilted), then all atom coords will still be between 0.0 and 1.0.  A
 value of <em>no</em> means they are written in absolute distance units
 (e.g. Angstroms or sigma).</p>
 <hr class="docutils" />
 <p>The <em>sort</em> keyword determines whether lines of per-atom output in a
 snapshot are sorted or not.  A sort value of <em>off</em> means they will
 typically be written in indeterminate order, either in serial or
 parallel.  This is the case even in serial if the <a class="reference internal" href="atom_modify.html"><em>atom_modify sort</em></a> option is turned on, which it is by default, to
 improve performance.  A sort value of <em>id</em> means sort the output by
 atom ID.  A sort value of N or -N means sort the output by the value
 in the Nth column of per-atom info in either ascending or descending
 order.</p>
 <p>The dump <em>local</em> style cannot be sorted by atom ID, since there are
 typically multiple lines of output per atom.  Some dump styles, such
 as <em>dcd</em> and <em>xtc</em>, require sorting by atom ID to format the output
 file correctly.  If multiple processors are writing the dump file, via
 the &#8220;%&#8221; wildcard in the dump filename, then sorting cannot be
 performed.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">Unless it is required by the dump style, sorting dump
 file output requires extra overhead in terms of CPU and communication
 cost, as well as memory, versus unsorted output.</p>
 </div>
 <hr class="docutils" />
 <p>The <em>thresh</em> keyword only applies to the dump <em>custom</em>, <em>cfg</em>,
 <em>image</em>, and <em>movie</em> styles.  Multiple thresholds can be specified.
 Specifying &#8220;none&#8221; turns off all threshold criteria.  If thresholds are
 specified, only atoms whose attributes meet all the threshold criteria
 are written to the dump file or included in the image.  The possible
 attributes that can be tested for are the same as those that can be
 specified in the <a class="reference internal" href="dump.html"><em>dump custom</em></a> command, with the exception
 of the <em>element</em> attribute, since it is not a numeric value.  Note
 that different attributes can be output by the dump custom command
 than are used as threshold criteria by the dump_modify command.
 E.g. you can output the coordinates and stress of atoms whose energy
 is above some threshold.</p>
 <hr class="docutils" />
 <p>The <em>unwrap</em> keyword only applies to the dump <em>dcd</em> and <em>xtc</em> styles.
 If set to <em>yes</em>, coordinates will be written &#8220;unwrapped&#8221; by the image
 flags for each atom.  Unwrapped means that if the atom has passed thru
 a periodic boundary one or more times, the value is printed for what
 the coordinate would be if it had not been wrapped back into the
 periodic box.  Note that these coordinates may thus be far outside the
 box size stored with the snapshot.</p>
 <p>These keywords apply only to the <a class="reference internal" href="dump_image.html"><em>dump image</em></a> and
 <a class="reference internal" href="dump_image.html"><em>dump movie</em></a> styles.  Any keyword that affects an
 image, also affects a movie, since the movie is simply a collection of
 images.  Some of the keywords only affect the <a class="reference internal" href="dump_image.html"><em>dump movie</em></a> style.  The descriptions give details.</p>
 <hr class="docutils" />
 <p>The <em>acolor</em> keyword can be used with the <a class="reference internal" href="dump_image.html"><em>dump image</em></a>
 command, when its atom color setting is <em>type</em>, to set the color that
 atoms of each type will be drawn in the image.</p>
 <p>The specified <em>type</em> should be an integer from 1 to Ntypes = the
 number of atom types.  A wildcard asterisk can be used in place of or
 in conjunction with the <em>type</em> argument to specify a range of atom
 types.  This takes the form &#8220;*&#8221; or &#8220;<em>n&#8221; or &#8220;n</em>&#8221; or &#8220;m*n&#8221;.  If N = the
 number of atom types, then an asterisk with no numeric values means
 all types from 1 to N.  A leading asterisk means all types from 1 to n
 (inclusive).  A trailing asterisk means all types from n to N
 (inclusive).  A middle asterisk means all types from m to n
 (inclusive).</p>
 <p>The specified <em>color</em> can be a single color which is any of the 140
 pre-defined colors (see below) or a color name defined by the
 dump_modify color option.  Or it can be two or more colors separated
 by a &#8220;/&#8221; character, e.g. red/green/blue.  In the former case, that
 color is assigned to all the specified atom types.  In the latter
 case, the list of colors are assigned in a round-robin fashion to each
 of the specified atom types.</p>
 <hr class="docutils" />
 <p>The <em>adiam</em> keyword can be used with the <a class="reference internal" href="dump_image.html"><em>dump image</em></a>
 command, when its atom diameter setting is <em>type</em>, to set the size
 that atoms of each type will be drawn in the image.  The specified
 <em>type</em> should be an integer from 1 to Ntypes.  As with the <em>acolor</em>
 keyword, a wildcard asterisk can be used as part of the <em>type</em>
 argument to specify a range of atomt types.  The specified <em>diam</em> is
 the size in whatever distance <a class="reference internal" href="units.html"><em>units</em></a> the input script is
 using, e.g. Angstroms.</p>
 <hr class="docutils" />
 <p>The <em>amap</em> keyword can be used with the <a class="reference internal" href="dump_image.html"><em>dump image</em></a>
 command, with its <em>atom</em> keyword, when its atom setting is an
 atom-attribute, to setup a color map.  The color map is used to assign
 a specific RGB (red/green/blue) color value to an individual atom when
 it is drawn, based on the atom&#8217;s attribute, which is a numeric value,
 e.g. its x-component of velocity if the atom-attribute &#8220;vx&#8221; was
 specified.</p>
 <p>The basic idea of a color map is that the atom-attribute will be
 within a range of values, and that range is associated with a a series
 of colors (e.g. red, blue, green).  An atom&#8217;s specific value (vx =
 -3.2) can then mapped to the series of colors (e.g. halfway between
 red and blue), and a specific color is determined via an interpolation
 procedure.</p>
 <p>There are many possible options for the color map, enabled by the
 <em>amap</em> keyword.  Here are the details.</p>
 <p>The <em>lo</em> and <em>hi</em> settings determine the range of values allowed for
 the atom attribute.  If numeric values are used for <em>lo</em> and/or <em>hi</em>,
 then values that are lower/higher than that value are set to the
 value.  I.e. the range is static.  If <em>lo</em> is specified as <em>min</em> or
 <em>hi</em> as <em>max</em> then the range is dynamic, and the lower and/or
 upper bound will be calculated each time an image is drawn, based
 on the set of atoms being visualized.</p>
 <p>The <em>style</em> setting is two letters, such as &#8220;ca&#8221;.  The first letter is
 either &#8220;c&#8221; for continuous, &#8220;d&#8221; for discrete, or &#8220;s&#8221; for sequential.
 The second letter is either &#8220;a&#8221; for absolute, or &#8220;f&#8221; for fractional.</p>
 <p>A continuous color map is one in which the color changes continuously
 from value to value within the range.  A discrete color map is one in
 which discrete colors are assigned to sub-ranges of values within the
 range.  A sequential color map is one in which discrete colors are
 assigned to a sequence of sub-ranges of values covering the entire
 range.</p>
 <p>An absolute color map is one in which the values to which colors are
 assigned are specified explicitly as values within the range.  A
 fractional color map is one in which the values to which colors are
 assigned are specified as a fractional portion of the range.  For
 example if the range is from -10.0 to 10.0, and the color red is to be
 assigned to atoms with a value of 5.0, then for an absolute color map
 the number 5.0 would be used.  But for a fractional map, the number
 0.75 would be used since 5.0 is 3/4 of the way from -10.0 to 10.0.</p>
 <p>The <em>delta</em> setting must be specified for all styles, but is only used
 for the sequential style; otherwise the value is ignored.  It
 specifies the bin size to use within the range for assigning
 consecutive colors to.  For example, if the range is from -10.0 to
 10.0 and a <em>delta</em> of 1.0 is used, then 20 colors will be assigned to
 the range.  The first will be from -10.0 &lt;= color1 &lt; -9.0, then 2nd
 from -9.0 &lt;= color2 &lt; -8.0, etc.</p>
 <p>The <em>N</em> setting is how many entries follow.  The format of the entries
 depends on whether the color map style is continuous, discrete or
 sequential.  In all cases the <em>color</em> setting can be any of the 140
 pre-defined colors (see below) or a color name defined by the
 dump_modify color option.</p>
 <p>For continuous color maps, each entry has a <em>value</em> and a <em>color</em>.
 The <em>value</em> is either a number within the range of values or <em>min</em> or
 <em>max</em>.  The <em>value</em> of the first entry must be <em>min</em> and the <em>value</em>
 of the last entry must be <em>max</em>.  Any entries in between must have
 increasing values.  Note that numeric values can be specified either
 as absolute numbers or as fractions (0.0 to 1.0) of the range,
 depending on the &#8220;a&#8221; or &#8220;f&#8221; in the style setting for the color map.</p>
 <p>Here is how the entries are used to determine the color of an
 individual atom, given the value X of its atom attribute.  X will fall
 between 2 of the entry values.  The color of the atom is linearly
 interpolated (in each of the RGB values) between the 2 colors
 associated with those entries.  For example, if X = -5.0 and the 2
 surrounding entries are &#8220;red&#8221; at -10.0 and &#8220;blue&#8221; at 0.0, then the
 atom&#8217;s color will be halfway between &#8220;red&#8221; and &#8220;blue&#8221;, which happens
 to be &#8220;purple&#8221;.</p>
 <p>For discrete color maps, each entry has a <em>lo</em> and <em>hi</em> value and a
 <em>color</em>.  The <em>lo</em> and <em>hi</em> settings are either numbers within the
 range of values or <em>lo</em> can be <em>min</em> or <em>hi</em> can be <em>max</em>.  The <em>lo</em>
 and <em>hi</em> settings of the last entry must be <em>min</em> and <em>max</em>.  Other
 entries can have any <em>lo</em> and <em>hi</em> values and the sub-ranges of
 different values can overlap.  Note that numeric <em>lo</em> and <em>hi</em> values
 can be specified either as absolute numbers or as fractions (0.0 to
 1.0) of the range, depending on the &#8220;a&#8221; or &#8220;f&#8221; in the style setting
 for the color map.</p>
 <p>Here is how the entries are used to determine the color of an
 individual atom, given the value X of its atom attribute.  The entries
 are scanned from first to last.  The first time that <em>lo</em> &lt;= X &lt;=
 <em>hi</em>, X is assigned the color associated with that entry.  You can
 think of the last entry as assigning a default color (since it will
 always be matched by X), and the earlier entries as colors that
 override the default.  Also note that no interpolation of a color RGB
 is done.  All atoms will be drawn with one of the colors in the list
 of entries.</p>
 <p>For sequential color maps, each entry has only a <em>color</em>.  Here is how
 the entries are used to determine the color of an individual atom,
 given the value X of its atom attribute.  The range is partitioned
 into N bins of width <em>binsize</em>.  Thus X will fall in a specific bin
 from 1 to N, say the Mth bin.  If it falls on a boundary between 2
 bins, it is considered to be in the higher of the 2 bins.  Each bin is
 assigned a color from the E entries.  If E &lt; N, then the colors are
 repeated.  For example if 2 entries with colors red and green are
 specified, then the odd numbered bins will be red and the even bins
 green.  The color of the atom is the color of its bin.  Note that the
 sequential color map is really a shorthand way of defining a discrete
 color map without having to specify where all the bin boundaries are.</p>
 <p>Here is an example of using a sequential color map to color all the
 atoms in individual molecules with a different color.  See the
 examples/pour/in.pour.2d.molecule input script for an example of how
 this is used.</p>
 <div class="highlight-python"><div class="highlight"><pre>variable        colors string &amp;
                 &quot;red green blue yellow white &amp;
                 purple pink orange lime gray&quot;
 variable     mol atom mol%10
 dump         1 all image 250 image.*.jpg v_mol type &amp;
              zoom 1.6 adiam 1.5
 dump_modify  1 pad 5 amap 0 10 sa 1 10 ${colors}
 </pre></div>
 </div>
 <p>In this case, 10 colors are defined, and molecule IDs are
 mapped to one of the colors, even if there are 1000s of molecules.</p>
 <hr class="docutils" />
 <p>The <em>backcolor</em> sets the background color of the images.  The color
 name can be any of the 140 pre-defined colors (see below) or a color
 name defined by the dump_modify color option.</p>
 <hr class="docutils" />
 <p>The <em>bcolor</em> keyword can be used with the <a class="reference internal" href="dump_image.html"><em>dump image</em></a>
 command, with its <em>bond</em> keyword, when its color setting is <em>type</em>, to
 set the color that bonds of each type will be drawn in the image.</p>
 <p>The specified <em>type</em> should be an integer from 1 to Nbondtypes = the
 number of bond types.  A wildcard asterisk can be used in place of or
 in conjunction with the <em>type</em> argument to specify a range of bond
 types.  This takes the form &#8220;*&#8221; or &#8220;<em>n&#8221; or &#8220;n</em>&#8221; or &#8220;m*n&#8221;.  If N = the
 number of bond types, then an asterisk with no numeric values means
 all types from 1 to N.  A leading asterisk means all types from 1 to n
 (inclusive).  A trailing asterisk means all types from n to N
 (inclusive).  A middle asterisk means all types from m to n
 (inclusive).</p>
 <p>The specified <em>color</em> can be a single color which is any of the 140
 pre-defined colors (see below) or a color name defined by the
 dump_modify color option.  Or it can be two or more colors separated
 by a &#8220;/&#8221; character, e.g. red/green/blue.  In the former case, that
 color is assigned to all the specified bond types.  In the latter
 case, the list of colors are assigned in a round-robin fashion to each
 of the specified bond types.</p>
 <hr class="docutils" />
 <p>The <em>bdiam</em> keyword can be used with the <a class="reference internal" href="dump_image.html"><em>dump image</em></a>
 command, with its <em>bond</em> keyword, when its diam setting is <em>type</em>, to
 set the diameter that bonds of each type will be drawn in the image.
 The specified <em>type</em> should be an integer from 1 to Nbondtypes.  As
 with the <em>bcolor</em> keyword, a wildcard asterisk can be used as part of
 the <em>type</em> argument to specify a range of bond types.  The specified
 <em>diam</em> is the size in whatever distance <a class="reference internal" href="units.html"><em>units</em></a> you are
 using, e.g. Angstroms.</p>
 <hr class="docutils" />
 <p>The <em>bitrate</em> keyword can be used with the <a class="reference internal" href="dump_image.html"><em>dump movie</em></a> command to define the size of the resulting
 movie file and its quality via setting how many kbits per second are
 to be used for the movie file. Higher bitrates require less
 compression and will result in higher quality movies.  The quality is
 also determined by the compression format and encoder.  The default
 setting is 2000 kbit/s, which will result in average quality with
 older compression formats.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">Not all movie file formats supported by dump movie
 allow the bitrate to be set.  If not, the setting is silently ignored.</p>
 </div>
 <hr class="docutils" />
 <p>The <em>boxcolor</em> keyword sets the color of the simulation box drawn
 around the atoms in each image as well as the color of processor
 sub-domain boundaries.  See the &#8220;dump image box&#8221; command for how to
 specify that a box be drawn via the <em>box</em> keyword, and the sub-domain
 boundaries via the <em>subbox</em> keyword.  The color name can be any of the
 140 pre-defined colors (see below) or a color name defined by the
 dump_modify color option.</p>
 <hr class="docutils" />
 <p>The <em>color</em> keyword allows definition of a new color name, in addition
 to the 140-predefined colors (see below), and associates 3
 red/green/blue RGB values with that color name.  The color name can
 then be used with any other dump_modify keyword that takes a color
 name as a value.  The RGB values should each be floating point values
 between 0.0 and 1.0 inclusive.</p>
 <p>When a color name is converted to RGB values, the user-defined color
 names are searched first, then the 140 pre-defined color names.  This
 means you can also use the <em>color</em> keyword to overwrite one of the
 pre-defined color names with new RBG values.</p>
 <hr class="docutils" />
 <p>The <em>framerate</em> keyword can be used with the <a class="reference internal" href="dump_image.html"><em>dump movie</em></a> command to define the duration of the resulting
 movie file.  Movie files written by the dump <em>movie</em> command have a
 default frame rate of 24 frames per second and the images generated
 will be converted at that rate.  Thus a sequence of 1000 dump images
 will result in a movie of about 42 seconds.  To make a movie run
 longer you can either generate images more frequently or lower the
 frame rate.  To speed a movie up, you can do the inverse.  Using a
 frame rate higher than 24 is not recommended, as it will result in
 simply dropping the rendered images. It is more efficient to dump
 images less frequently.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <blockquote>
 <div>none</div></blockquote>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="dump.html"><em>dump</em></a>, <a class="reference internal" href="dump_image.html"><em>dump image</em></a>, <a class="reference internal" href="undump.html"><em>undump</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The option defaults are</p>
 <ul class="simple">
 <li>append = no</li>
 <li>buffer = yes for dump styles <em>atom</em>, <em>custom</em>, <em>loca</em>, and <em>xyz</em></li>
 <li>element = &#8220;C&#8221; for every atom type</li>
 <li>every = whatever it was set to via the <a class="reference internal" href="dump.html"><em>dump</em></a> command</li>
 <li>fileper = # of processors</li>
 <li>first = no</li>
 <li>flush = yes</li>
 <li>format = %d and %g for each integer or floating point value</li>
 <li>image = no</li>
 <li>label = ENTRIES</li>
 <li>nfile = 1</li>
 <li>pad = 0</li>
 <li>precision = 1000</li>
 <li>region = none</li>
 <li>scale = yes</li>
 <li>sort = off for dump styles <em>atom</em>, <em>custom</em>, <em>cfg</em>, and <em>local</em></li>
 <li>sort = id for dump styles <em>dcd</em>, <em>xtc</em>, and <em>xyz</em></li>
 <li>thresh = none</li>
 <li>unwrap = no</li>
 <li>acolor = * red/green/blue/yellow/aqua/cyan</li>
 <li>adiam = * 1.0</li>
 <li>amap = min max cf 0.0 2 min blue max red</li>
 <li>backcolor = black</li>
 <li>bcolor = * red/green/blue/yellow/aqua/cyan</li>
 <li>bdiam = * 0.5</li>
 <li>bitrate = 2000</li>
 <li>boxcolor = yellow</li>
 <li>color = 140 color names are pre-defined as listed below</li>
 <li>framerate = 24</li>
 </ul>
 <hr class="docutils" />
 <p>These are the standard 109 element names that LAMMPS pre-defines for
 use with the <a class="reference internal" href="dump_image.html"><em>dump image</em></a> and dump_modify commands.</p>
 <ul class="simple">
 <li>1-10 = &#8220;H&#8221;, &#8220;He&#8221;, &#8220;Li&#8221;, &#8220;Be&#8221;, &#8220;B&#8221;, &#8220;C&#8221;, &#8220;N&#8221;, &#8220;O&#8221;, &#8220;F&#8221;, &#8220;Ne&#8221;</li>
 <li>11-20 = &#8220;Na&#8221;, &#8220;Mg&#8221;, &#8220;Al&#8221;, &#8220;Si&#8221;, &#8220;P&#8221;, &#8220;S&#8221;, &#8220;Cl&#8221;, &#8220;Ar&#8221;, &#8220;K&#8221;, &#8220;Ca&#8221;</li>
 <li>21-30 = &#8220;Sc&#8221;, &#8220;Ti&#8221;, &#8220;V&#8221;, &#8220;Cr&#8221;, &#8220;Mn&#8221;, &#8220;Fe&#8221;, &#8220;Co&#8221;, &#8220;Ni&#8221;, &#8220;Cu&#8221;, &#8220;Zn&#8221;</li>
 <li>31-40 = &#8220;Ga&#8221;, &#8220;Ge&#8221;, &#8220;As&#8221;, &#8220;Se&#8221;, &#8220;Br&#8221;, &#8220;Kr&#8221;, &#8220;Rb&#8221;, &#8220;Sr&#8221;, &#8220;Y&#8221;, &#8220;Zr&#8221;</li>
 <li>41-50 = &#8220;Nb&#8221;, &#8220;Mo&#8221;, &#8220;Tc&#8221;, &#8220;Ru&#8221;, &#8220;Rh&#8221;, &#8220;Pd&#8221;, &#8220;Ag&#8221;, &#8220;Cd&#8221;, &#8220;In&#8221;, &#8220;Sn&#8221;</li>
 <li>51-60 = &#8220;Sb&#8221;, &#8220;Te&#8221;, &#8220;I&#8221;, &#8220;Xe&#8221;, &#8220;Cs&#8221;, &#8220;Ba&#8221;, &#8220;La&#8221;, &#8220;Ce&#8221;, &#8220;Pr&#8221;, &#8220;Nd&#8221;</li>
 <li>61-70 = &#8220;Pm&#8221;, &#8220;Sm&#8221;, &#8220;Eu&#8221;, &#8220;Gd&#8221;, &#8220;Tb&#8221;, &#8220;Dy&#8221;, &#8220;Ho&#8221;, &#8220;Er&#8221;, &#8220;Tm&#8221;, &#8220;Yb&#8221;</li>
 <li>71-80 = &#8220;Lu&#8221;, &#8220;Hf&#8221;, &#8220;Ta&#8221;, &#8220;W&#8221;, &#8220;Re&#8221;, &#8220;Os&#8221;, &#8220;Ir&#8221;, &#8220;Pt&#8221;, &#8220;Au&#8221;, &#8220;Hg&#8221;</li>
 <li>81-90 = &#8220;Tl&#8221;, &#8220;Pb&#8221;, &#8220;Bi&#8221;, &#8220;Po&#8221;, &#8220;At&#8221;, &#8220;Rn&#8221;, &#8220;Fr&#8221;, &#8220;Ra&#8221;, &#8220;Ac&#8221;, &#8220;Th&#8221;</li>
 <li>91-100 = &#8220;Pa&#8221;, &#8220;U&#8221;, &#8220;Np&#8221;, &#8220;Pu&#8221;, &#8220;Am&#8221;, &#8220;Cm&#8221;, &#8220;Bk&#8221;, &#8220;Cf&#8221;, &#8220;Es&#8221;, &#8220;Fm&#8221;</li>
 <li>101-109 = &#8220;Md&#8221;, &#8220;No&#8221;, &#8220;Lr&#8221;, &#8220;Rf&#8221;, &#8220;Db&#8221;, &#8220;Sg&#8221;, &#8220;Bh&#8221;, &#8220;Hs&#8221;, &#8220;Mt&#8221;</li>
 </ul>
 <hr class="docutils" />
 <p>These are the 140 colors that LAMMPS pre-defines for use with the
 <a class="reference internal" href="dump_image.html"><em>dump image</em></a> and dump_modify commands.  Additional
 colors can be defined with the dump_modify color command.  The 3
 numbers listed for each name are the RGB (red/green/blue) values.
 Divide each value by 255 to get the equivalent 0.0 to 1.0 value.</p>
 <table border="1" class="docutils">
 <colgroup>
 <col width="19%" />
 <col width="23%" />
 <col width="20%" />
 <col width="19%" />
 <col width="19%" />
 </colgroup>
 <tbody valign="top">
 <tr class="row-odd"><td>aliceblue = 240, 248, 255</td>
 <td>antiquewhite = 250, 235, 215</td>
 <td>aqua = 0, 255, 255</td>
 <td>aquamarine = 127, 255, 212</td>
 <td>azure = 240, 255, 255</td>
 </tr>
 <tr class="row-even"><td>beige = 245, 245, 220</td>
 <td>bisque = 255, 228, 196</td>
 <td>black = 0, 0, 0</td>
 <td>blanchedalmond = 255, 255, 205</td>
 <td>blue = 0, 0, 255</td>
 </tr>
 <tr class="row-odd"><td>blueviolet = 138, 43, 226</td>
 <td>brown = 165, 42, 42</td>
 <td>burlywood = 222, 184, 135</td>
 <td>cadetblue = 95, 158, 160</td>
 <td>chartreuse = 127, 255, 0</td>
 </tr>
 <tr class="row-even"><td>chocolate = 210, 105, 30</td>
 <td>coral = 255, 127, 80</td>
 <td>cornflowerblue = 100, 149, 237</td>
 <td>cornsilk = 255, 248, 220</td>
 <td>crimson = 220, 20, 60</td>
 </tr>
 <tr class="row-odd"><td>cyan = 0, 255, 255</td>
 <td>darkblue = 0, 0, 139</td>
 <td>darkcyan = 0, 139, 139</td>
 <td>darkgoldenrod = 184, 134, 11</td>
 <td>darkgray = 169, 169, 169</td>
 </tr>
 <tr class="row-even"><td>darkgreen = 0, 100, 0</td>
 <td>darkkhaki = 189, 183, 107</td>
 <td>darkmagenta = 139, 0, 139</td>
 <td>darkolivegreen = 85, 107, 47</td>
 <td>darkorange = 255, 140, 0</td>
 </tr>
 <tr class="row-odd"><td>darkorchid = 153, 50, 204</td>
 <td>darkred = 139, 0, 0</td>
 <td>darksalmon = 233, 150, 122</td>
 <td>darkseagreen = 143, 188, 143</td>
 <td>darkslateblue = 72, 61, 139</td>
 </tr>
 <tr class="row-even"><td>darkslategray = 47, 79, 79</td>
 <td>darkturquoise = 0, 206, 209</td>
 <td>darkviolet = 148, 0, 211</td>
 <td>deeppink = 255, 20, 147</td>
 <td>deepskyblue = 0, 191, 255</td>
 </tr>
 <tr class="row-odd"><td>dimgray = 105, 105, 105</td>
 <td>dodgerblue = 30, 144, 255</td>
 <td>firebrick = 178, 34, 34</td>
 <td>floralwhite = 255, 250, 240</td>
 <td>forestgreen = 34, 139, 34</td>
 </tr>
 <tr class="row-even"><td>fuchsia = 255, 0, 255</td>
 <td>gainsboro = 220, 220, 220</td>
 <td>ghostwhite = 248, 248, 255</td>
 <td>gold = 255, 215, 0</td>
 <td>goldenrod = 218, 165, 32</td>
 </tr>
 <tr class="row-odd"><td>gray = 128, 128, 128</td>
 <td>green = 0, 128, 0</td>
 <td>greenyellow = 173, 255, 47</td>
 <td>honeydew = 240, 255, 240</td>
 <td>hotpink = 255, 105, 180</td>
 </tr>
 <tr class="row-even"><td>indianred = 205, 92, 92</td>
 <td>indigo = 75, 0, 130</td>
 <td>ivory = 255, 240, 240</td>
 <td>khaki = 240, 230, 140</td>
 <td>lavender = 230, 230, 250</td>
 </tr>
 <tr class="row-odd"><td>lavenderblush = 255, 240, 245</td>
 <td>lawngreen = 124, 252, 0</td>
 <td>lemonchiffon = 255, 250, 205</td>
 <td>lightblue = 173, 216, 230</td>
 <td>lightcoral = 240, 128, 128</td>
 </tr>
 <tr class="row-even"><td>lightcyan = 224, 255, 255</td>
 <td>lightgoldenrodyellow = 250, 250, 210</td>
 <td>lightgreen = 144, 238, 144</td>
 <td>lightgrey = 211, 211, 211</td>
 <td>lightpink = 255, 182, 193</td>
 </tr>
 <tr class="row-odd"><td>lightsalmon = 255, 160, 122</td>
 <td>lightseagreen = 32, 178, 170</td>
 <td>lightskyblue = 135, 206, 250</td>
 <td>lightslategray = 119, 136, 153</td>
 <td>lightsteelblue = 176, 196, 222</td>
 </tr>
 <tr class="row-even"><td>lightyellow = 255, 255, 224</td>
 <td>lime = 0, 255, 0</td>
 <td>limegreen = 50, 205, 50</td>
 <td>linen = 250, 240, 230</td>
 <td>magenta = 255, 0, 255</td>
 </tr>
 <tr class="row-odd"><td>maroon = 128, 0, 0</td>
 <td>mediumaquamarine = 102, 205, 170</td>
 <td>mediumblue = 0, 0, 205</td>
 <td>mediumorchid = 186, 85, 211</td>
 <td>mediumpurple = 147, 112, 219</td>
 </tr>
 <tr class="row-even"><td>mediumseagreen = 60, 179, 113</td>
 <td>mediumslateblue = 123, 104, 238</td>
 <td>mediumspringgreen = 0, 250, 154</td>
 <td>mediumturquoise = 72, 209, 204</td>
 <td>mediumvioletred = 199, 21, 133</td>
 </tr>
 <tr class="row-odd"><td>midnightblue = 25, 25, 112</td>
 <td>mintcream = 245, 255, 250</td>
 <td>mistyrose = 255, 228, 225</td>
 <td>moccasin = 255, 228, 181</td>
 <td>navajowhite = 255, 222, 173</td>
 </tr>
 <tr class="row-even"><td>navy = 0, 0, 128</td>
 <td>oldlace = 253, 245, 230</td>
 <td>olive = 128, 128, 0</td>
 <td>olivedrab = 107, 142, 35</td>
 <td>orange = 255, 165, 0</td>
 </tr>
 <tr class="row-odd"><td>orangered = 255, 69, 0</td>
 <td>orchid = 218, 112, 214</td>
 <td>palegoldenrod = 238, 232, 170</td>
 <td>palegreen = 152, 251, 152</td>
 <td>paleturquoise = 175, 238, 238</td>
 </tr>
 <tr class="row-even"><td>palevioletred = 219, 112, 147</td>
 <td>papayawhip = 255, 239, 213</td>
 <td>peachpuff = 255, 239, 213</td>
 <td>peru = 205, 133, 63</td>
 <td>pink = 255, 192, 203</td>
 </tr>
 <tr class="row-odd"><td>plum = 221, 160, 221</td>
 <td>powderblue = 176, 224, 230</td>
 <td>purple = 128, 0, 128</td>
 <td>red = 255, 0, 0</td>
 <td>rosybrown = 188, 143, 143</td>
 </tr>
 <tr class="row-even"><td>royalblue = 65, 105, 225</td>
 <td>saddlebrown = 139, 69, 19</td>
 <td>salmon = 250, 128, 114</td>
 <td>sandybrown = 244, 164, 96</td>
 <td>seagreen = 46, 139, 87</td>
 </tr>
 <tr class="row-odd"><td>seashell = 255, 245, 238</td>
 <td>sienna = 160, 82, 45</td>
 <td>silver = 192, 192, 192</td>
 <td>skyblue = 135, 206, 235</td>
 <td>slateblue = 106, 90, 205</td>
 </tr>
 <tr class="row-even"><td>slategray = 112, 128, 144</td>
 <td>snow = 255, 250, 250</td>
 <td>springgreen = 0, 255, 127</td>
 <td>steelblue = 70, 130, 180</td>
 <td>tan = 210, 180, 140</td>
 </tr>
 <tr class="row-odd"><td>teal = 0, 128, 128</td>
 <td>thistle = 216, 191, 216</td>
 <td>tomato = 253, 99, 71</td>
 <td>turquoise = 64, 224, 208</td>
 <td>violet = 238, 130, 238</td>
 </tr>
 <tr class="row-even"><td>wheat = 245, 222, 179</td>
 <td>white = 255, 255, 255</td>
 <td>whitesmoke = 245, 245, 245</td>
 <td>yellow = 255, 255, 0</td>
 <td>yellowgreen = 154, 205, 50</td>
 </tr>
 </tbody>
 </table>
 </div>
 </div>
 
 
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   <div class="section" id="fix-adapt-command">
 <span id="index-0"></span><h1>fix adapt command<a class="headerlink" href="#fix-adapt-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID adapt N attribute args ... keyword value ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>adapt = style name of this fix command</li>
 <li>N = adapt simulation settings every this many timesteps</li>
 <li>one or more attribute/arg pairs may be appended</li>
 <li>attribute = <em>pair</em> or <em>kspace</em> or <em>atom</em></li>
 </ul>
 <pre class="literal-block">
 <em>pair</em> args = pstyle pparam I J v_name
-    pstyle = pair style name, e.g. lj/cut
-    pparam = parameter to adapt over time
-    I,J = type pair(s) to set parameter for
-    v_name = variable with name that calculates value of pparam
-  <em>kspace</em> arg = v_name
-    v_name = variable with name that calculates scale factor on K-space terms
-  <em>atom</em> args = aparam v_name
-    aparam = parameter to adapt over time
-    v_name = variable with name that calculates value of aparam
+  pstyle = pair style name, e.g. lj/cut
+  pparam = parameter to adapt over time
+  I,J = type pair(s) to set parameter for
+  v_name = variable with name that calculates value of pparam
+<em>kspace</em> arg = v_name
+  v_name = variable with name that calculates scale factor on K-space terms
+<em>atom</em> args = aparam v_name
+  aparam = parameter to adapt over time
+  v_name = variable with name that calculates value of aparam
 </pre>
 <ul class="simple">
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>scale</em> or <em>reset</em></li>
 </ul>
 <pre class="literal-block">
 <em>scale</em> value = <em>no</em> or <em>yes</em>
-    <em>no</em> = the variable value is the new setting
-    <em>yes</em> = the variable value multiplies the original setting
-  <em>reset</em> value = <em>no</em> or <em>yes</em>
-    <em>no</em> = values will remain altered at the end of a run
-    <em>yes</em> = reset altered values to their original values at the end of a run
+  <em>no</em> = the variable value is the new setting
+  <em>yes</em> = the variable value multiplies the original setting
+<em>reset</em> value = <em>no</em> or <em>yes</em>
+  <em>no</em> = values will remain altered at the end of a run
+  <em>yes</em> = reset altered values to their original values at the end of a run
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix 1 all adapt 1 pair soft a 1 1 v_prefactor
 fix 1 all adapt 1 pair soft a 2* 3 v_prefactor
 fix 1 all adapt 1 pair lj/cut epsilon * * v_scale1 coul/cut scale 3 3 v_scale2 scale yes reset yes
 fix 1 all adapt 10 atom diameter v_size
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Change or adapt one or more specific simulation attributes or settings
 over time as a simulation runs.  Pair potential and K-space and atom
 attributes which can be varied by this fix are discussed below.  Many
 other fixes can also be used to time-vary simulation parameters,
 e.g. the &#8220;fix deform&#8221; command will change the simulation box
 size/shape and the &#8220;fix move&#8221; command will change atom positions and
 velocities in a prescribed manner.  Also note that many commands allow
 variables as arguments for specific parameters, if described in that
 manner on their doc pages.  An equal-style variable can calculate a
 time-dependent quantity, so this is another way to vary a simulation
 parameter over time.</p>
 <p>If <em>N</em> is specified as 0, the specified attributes are only changed
 once, before the simulation begins.  This is all that is needed if the
 associated variables are not time-dependent.  If <em>N</em> &gt; 0, then changes
 are made every <em>N</em> steps during the simulation, presumably with a
 variable that is time-dependent.</p>
 <p>Depending on the value of the <em>reset</em> keyword, attributes changed by
 this fix will or will not be reset back to their original values at
 the end of a simulation.  Even if <em>reset</em> is specified as <em>yes</em>, a
 restart file written during a simulation will contain the modified
 settings.</p>
 <p>If the <em>scale</em> keyword is set to <em>no</em>, then the value the parameter is
 set to will be whatever the variable generates.  If the <em>scale</em>
 keyword is set to <em>yes</em>, then the value of the altered parameter will
 be the initial value of that parameter multiplied by whatever the
 variable generates.  I.e. the variable is now a &#8220;scale factor&#8221; applied
 in (presumably) a time-varying fashion to the parameter.</p>
 <p>Note that whether scale is <em>no</em> or <em>yes</em>, internally, the parameters
 themselves are actually altered by this fix.  Make sure you use the
 <em>reset yes</em> option if you want the parameters to be restored to their
 initial values after the run.</p>
 <hr class="docutils" />
 <p>The <em>pair</em> keyword enables various parameters of potentials defined by
 the <a class="reference internal" href="pair_style.html"><em>pair_style</em></a> command to be changed, if the pair
 style supports it.  Note that the <a class="reference internal" href="pair_style.html"><em>pair_style</em></a> and
 <a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a> commands must be used in the usual manner
 to specify these parameters initially; the fix adapt command simply
 overrides the parameters.</p>
 <p>The <em>pstyle</em> argument is the name of the pair style.  If <a class="reference internal" href="pair_hybrid.html"><em>pair_style hybrid or hybrid/overlay</em></a> is used, <em>pstyle</em> should be
 a sub-style name.  For example, <em>pstyle</em> could be specified as &#8220;soft&#8221;
 or &#8220;lubricate&#8221;.  The <em>pparam</em> argument is the name of the parameter to
 change.  This is the current list of pair styles and parameters that
 can be varied by this fix.  See the doc pages for individual pair
 styles and their energy formulas for the meaning of these parameters:</p>
 <table border="1" class="docutils">
 <colgroup>
 <col width="51%" />
 <col width="31%" />
 <col width="18%" />
 </colgroup>
 <tbody valign="top">
 <tr class="row-odd"><td><a class="reference internal" href="pair_born.html"><em>born</em></a></td>
 <td>a,b,c</td>
 <td>type pairs</td>
 </tr>
 <tr class="row-even"><td><a class="reference internal" href="pair_buck.html"><em>buck</em></a></td>
 <td>a,c</td>
 <td>type pairs</td>
 </tr>
 <tr class="row-odd"><td><a class="reference internal" href="pair_coul.html"><em>coul/cut</em></a></td>
 <td>scale</td>
 <td>type pairs</td>
 </tr>
 <tr class="row-even"><td><a class="reference internal" href="pair_coul.html"><em>coul/debye</em></a></td>
 <td>scale</td>
 <td>type pairs</td>
 </tr>
 <tr class="row-odd"><td><a class="reference internal" href="pair_coul.html"><em>coul/long</em></a></td>
 <td>scale</td>
 <td>type pairs</td>
 </tr>
 <tr class="row-even"><td><a class="reference internal" href="pair_lj.html"><em>lj/cut</em></a></td>
 <td>epsilon,sigma</td>
 <td>type pairs</td>
 </tr>
 <tr class="row-odd"><td><a class="reference internal" href="pair_lj_expand.html"><em>lj/expand</em></a></td>
 <td>epsilon,sigma,delta</td>
 <td>type pairs</td>
 </tr>
 <tr class="row-even"><td><a class="reference internal" href="pair_lubricate.html"><em>lubricate</em></a></td>
 <td>mu</td>
 <td>global</td>
 </tr>
 <tr class="row-odd"><td><a class="reference internal" href="pair_gauss.html"><em>gauss</em></a></td>
 <td>a</td>
 <td>type pairs</td>
 </tr>
 <tr class="row-even"><td><a class="reference internal" href="pair_morse.html"><em>morse</em></a></td>
 <td>d0,r0,alpha</td>
 <td>type pairs</td>
 </tr>
 <tr class="row-odd"><td><a class="reference internal" href="pair_soft.html"><em>soft</em></a></td>
 <td>a</td>
 <td>type pairs</td>
 </tr>
 </tbody>
 </table>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">It is easy to add new potentials and their parameters
 to this list.  All it typically takes is adding an extract() method to
 the pair_*.cpp file associated with the potential.</p>
 </div>
 <p>Some parameters are global settings for the pair style, e.g. the
 viscosity setting &#8220;mu&#8221; for <a class="reference internal" href="pair_lubricate.html"><em>pair_style lubricate</em></a>.
 Other parameters apply to atom type pairs within the pair style,
 e.g. the prefactor &#8220;a&#8221; for <a class="reference internal" href="pair_soft.html"><em>pair_style soft</em></a>.</p>
 <p>Note that for many of the potentials, the parameter that can be varied
 is effectively a prefactor on the entire energy expression for the
 potential, e.g. the lj/cut epsilon.  The parameters listed as &#8220;scale&#8221;
 are exactly that, since the energy expression for the
 <a class="reference internal" href="pair_coul.html"><em>coul/cut</em></a> potential (for example) has no labeled
 prefactor in its formula.  To apply an effective prefactor to some
 potentials, multiple parameters need to be altered.  For example, the
 <a class="reference internal" href="pair_buck.html"><em>Buckingham potential</em></a> needs both the A and C terms
 altered together.  To scale the Buckingham potential, you should thus
 list the pair style twice, once for A and once for C.</p>
 <p>If a type pair parameter is specified, the <em>I</em> and <em>J</em> settings should
 be specified to indicate which type pairs to apply it to.  If a global
 parameter is specified, the <em>I</em> and <em>J</em> settings still need to be
 specified, but are ignored.</p>
 <p>Similar to the <a class="reference internal" href="pair_coeff.html"><em>pair_coeff command</em></a>, I and J can be
 specified in one of two ways.  Explicit numeric values can be used for
 each, as in the 1st example above.  I &lt;= J is required.  LAMMPS sets
 the coefficients for the symmetric J,I interaction to the same values.</p>
 <p>A wild-card asterisk can be used in place of or in conjunction with
 the I,J arguments to set the coefficients for multiple pairs of atom
 types.  This takes the form &#8220;*&#8221; or &#8220;<em>n&#8221; or &#8220;n</em>&#8221; or &#8220;m*n&#8221;.  If N = the
 number of atom types, then an asterisk with no numeric values means
 all types from 1 to N.  A leading asterisk means all types from 1 to n
 (inclusive).  A trailing asterisk means all types from n to N
 (inclusive).  A middle asterisk means all types from m to n
 (inclusive).  Note that only type pairs with I &lt;= J are considered; if
 asterisks imply type pairs where J &lt; I, they are ignored.</p>
 <p>IMPROTANT NOTE: If <a class="reference internal" href="pair_hybrid.html"><em>pair_style hybrid or hybrid/overlay</em></a> is being used, then the <em>pstyle</em> will
 be a sub-style name.  You must specify I,J arguments that correspond
 to type pair values defined (via the <a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a>
 command) for that sub-style.</p>
 <p>The <em>v_name</em> argument for keyword <em>pair</em> is the name of an
 <a class="reference internal" href="variable.html"><em>equal-style variable</em></a> which will be evaluated each time
 this fix is invoked to set the parameter to a new value.  It should be
 specified as v_name, where name is the variable name.  Equal-style
 variables can specify formulas with various mathematical functions,
 and include <a class="reference internal" href="thermo_style.html"><em>thermo_style</em></a> command keywords for the
 simulation box parameters and timestep and elapsed time.  Thus it is
 easy to specify parameters that change as a function of time or span
 consecutive runs in a continuous fashion.  For the latter, see the
 <em>start</em> and <em>stop</em> keywords of the <a class="reference internal" href="run.html"><em>run</em></a> command and the
 <em>elaplong</em> keyword of <a class="reference internal" href="thermo_style.html"><em>thermo_style custom</em></a> for
 details.</p>
 <p>For example, these commands would change the prefactor coefficient of
 the <a class="reference internal" href="pair_soft.html"><em>pair_style soft</em></a> potential from 10.0 to 30.0 in a
 linear fashion over the course of a simulation:</p>
 <div class="highlight-python"><div class="highlight"><pre>variable prefactor equal ramp(10,30)
 fix 1 all adapt 1 pair soft a * * v_prefactor
 </pre></div>
 </div>
 <hr class="docutils" />
 <p>The <em>kspace</em> keyword used the specified variable as a scale factor on
 the energy, forces, virial calculated by whatever K-Space solver is
 defined by the <a class="reference internal" href="kspace_style.html"><em>kspace_style</em></a> command.  If the
 variable has a value of 1.0, then the solver is unaltered.</p>
 <p>The <em>kspace</em> keyword works this way whether the <em>scale</em> keyword
 is set to <em>no</em> or <em>yes</em>.</p>
 <hr class="docutils" />
 <p>The <em>atom</em> keyword enables various atom properties to be changed.  The
 <em>aparam</em> argument is the name of the parameter to change.  This is the
 current list of atom parameters that can be varied by this fix:</p>
 <ul class="simple">
 <li>charge = charge on particle</li>
 <li>diameter = diameter of particle</li>
 </ul>
 <p>The <em>v_name</em> argument of the <em>atom</em> keyword is the name of an
 <a class="reference internal" href="variable.html"><em>equal-style variable</em></a> which will be evaluated each time
 this fix is invoked to set the parameter to a new value.  It should be
 specified as v_name, where name is the variable name.  See the
 discussion above describing the formulas associated with equal-style
 variables.  The new value is assigned to the corresponding attribute
 for all atoms in the fix group.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">The <em>atom</em> keyword works this way whether the <em>scale</em>
 keyword is set to <em>no</em> or <em>yes</em>.  I.e. the use of scale yes is not yet
 supported by the <em>atom</em> keyword.</p>
 </div>
 <p>If the atom parameter is <em>diameter</em> and per-atom density and per-atom
 mass are defined for particles (e.g. <a class="reference internal" href="atom_style.html"><em>atom_style granular</em></a>), then the mass of each particle is also
 changed when the diameter changes (density is assumed to stay
 constant).</p>
 <p>For example, these commands would shrink the diameter of all granular
 particles in the &#8220;center&#8221; group from 1.0 to 0.1 in a linear fashion
 over the course of a 1000-step simulation:</p>
 <div class="highlight-python"><div class="highlight"><pre>variable size equal ramp(1.0,0.1)
 fix 1 center adapt 10 atom diameter v_size
 </pre></div>
 </div>
 </div>
 <hr class="docutils" />
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.  None of the <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> options
 are relevant to this fix.  No global or per-atom quantities are stored
 by this fix for access by various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  No parameter of this fix can
 be used with the <em>start/stop</em> keywords of the <a class="reference internal" href="run.html"><em>run</em></a> command.
 This fix is not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 <p>For <a class="reference internal" href="run_style.html"><em>rRESPA time integration</em></a>, this fix changes
 parameters on the outermost rRESPA level.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <blockquote>
 <div>none</div></blockquote>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="compute_ti.html"><em>compute ti</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The option defaults are scale = no, reset = no.</p>
 </div>
 </div>
 
 
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   <div class="section" id="fix-adapt-fep-command">
 <span id="index-0"></span><h1>fix adapt/fep command<a class="headerlink" href="#fix-adapt-fep-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID adapt/fep N attribute args ... keyword value ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>adapt/fep = style name of this fix command</li>
 <li>N = adapt simulation settings every this many timesteps</li>
 <li>one or more attribute/arg pairs may be appended</li>
 <li>attribute = <em>pair</em> or <em>kspace</em> or <em>atom</em></li>
 </ul>
 <pre class="literal-block">
 <em>pair</em> args = pstyle pparam I J v_name
-    pstyle = pair style name, e.g. lj/cut
-    pparam = parameter to adapt over time
-    I,J = type pair(s) to set parameter for
-    v_name = variable with name that calculates value of pparam
-  <em>kspace</em> arg = v_name
-    v_name = variable with name that calculates scale factor on K-space terms
-  <em>atom</em> args = aparam v_name
-    aparam = parameter to adapt over time
-    I = type(s) to set parameter for
-    v_name = variable with name that calculates value of aparam
+  pstyle = pair style name, e.g. lj/cut
+  pparam = parameter to adapt over time
+  I,J = type pair(s) to set parameter for
+  v_name = variable with name that calculates value of pparam
+<em>kspace</em> arg = v_name
+  v_name = variable with name that calculates scale factor on K-space terms
+<em>atom</em> args = aparam v_name
+  aparam = parameter to adapt over time
+  I = type(s) to set parameter for
+  v_name = variable with name that calculates value of aparam
 </pre>
 <ul class="simple">
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>scale</em> or <em>reset</em> or <em>after</em></li>
 </ul>
 <pre class="literal-block">
 <em>scale</em> value = <em>no</em> or <em>yes</em>
-    <em>no</em> = the variable value is the new setting
-    <em>yes</em> = the variable value multiplies the original setting
-  <em>reset</em> value = <em>no</em> or <em>yes</em>
-    <em>no</em> = values will remain altered at the end of a run
-    <em>yes</em> = reset altered values to their original values at the end
-    of a run
-  <em>after</em> value = <em>no</em> or <em>yes</em>
-    <em>no</em> = parameters are adapted at timestep N
-    <em>yes</em> = parameters are adapted one timestep after N
+  <em>no</em> = the variable value is the new setting
+  <em>yes</em> = the variable value multiplies the original setting
+<em>reset</em> value = <em>no</em> or <em>yes</em>
+  <em>no</em> = values will remain altered at the end of a run
+  <em>yes</em> = reset altered values to their original values at the end
+  of a run
+<em>after</em> value = <em>no</em> or <em>yes</em>
+  <em>no</em> = parameters are adapted at timestep N
+  <em>yes</em> = parameters are adapted one timestep after N
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix 1 all adapt/fep 1 pair soft a 1 1 v_prefactor
 fix 1 all adapt/fep 1 pair soft a 2* 3 v_prefactor
 fix 1 all adapt/fep 1 pair lj/cut epsilon * * v_scale1 coul/cut scale 3 3 v_scale2 scale yes reset yes
 fix 1 all adapt/fep 10 atom diameter 1 v_size
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Change or adapt one or more specific simulation attributes or settings
 over time as a simulation runs.</p>
 <p>This is an enhanced version of the <a class="reference internal" href="fix_adapt.html"><em>fix_adapt</em></a> command
 with two differences,</p>
 <ul class="simple">
 <li>It is possible to modify the charges of chosen atom types only,
 instead of scaling all the charges in the system.</li>
 <li>There is a new option <em>after</em> for better compatibility with &#8220;fix
 ave/time&#8221;.</li>
 </ul>
 <p>This version is suited for free energy calculations using
 <a class="reference internal" href="compute_ti.html"><em>compute_ti</em></a> or <a class="reference internal" href="compute_fep.html"><em>compute_fep</em></a>.</p>
 <p>If <em>N</em> is specified as 0, the specified attributes are only changed
 once, before the simulation begins.  This is all that is needed if the
 associated variables are not time-dependent.  If <em>N</em> &gt; 0, then changes
 are made every <em>N</em> steps during the simulation, presumably with a
 variable that is time-dependent.</p>
 <p>Depending on the value of the <em>reset</em> keyword, attributes changed by
 this fix will or will not be reset back to their original values at
 the end of a simulation.  Even if <em>reset</em> is specified as <em>yes</em>, a
 restart file written during a simulation will contain the modified
 settings.</p>
 <p>If the <em>scale</em> keyword is set to <em>no</em>, then the value the parameter is
 set to will be whatever the variable generates.  If the <em>scale</em>
 keyword is set to <em>yes</em>, then the value of the altered parameter will
 be the initial value of that parameter multiplied by whatever the
 variable generates.  I.e. the variable is now a &#8220;scale factor&#8221; applied
 in (presumably) a time-varying fashion to the parameter.  Internally,
 the parameters themselves are actually altered; make sure you use the
 <em>reset yes</em> option if you want the parameters to be restored to their
 initial values after the run.</p>
 <p>If the <em>after</em> keyword is set to <em>yes</em>, then the parameters are
 changed one timestep after the multiple of N. In this manner, if a fix
 such as &#8220;fix ave/time&#8221; is used to calculate averages at every N
 timesteps, all the contributions to the average will be obtained with
 the same values of the parameters.</p>
 <hr class="docutils" />
 <p>The <em>pair</em> keyword enables various parameters of potentials defined by
 the <a class="reference internal" href="pair_style.html"><em>pair_style</em></a> command to be changed, if the pair
 style supports it.  Note that the <a class="reference internal" href="pair_style.html"><em>pair_style</em></a> and
 <a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a> commands must be used in the usual manner
 to specify these parameters initially; the fix adapt command simply
 overrides the parameters.</p>
 <p>The <em>pstyle</em> argument is the name of the pair style.  If <a class="reference internal" href="pair_hybrid.html"><em>pair_style hybrid or hybrid/overlay</em></a> is used, <em>pstyle</em> should be
 a sub-style name.  For example, <em>pstyle</em> could be specified as &#8220;soft&#8221;
 or &#8220;lubricate&#8221;.  The <em>pparam</em> argument is the name of the parameter to
 change.  This is the current list of pair styles and parameters that
 can be varied by this fix.  See the doc pages for individual pair
 styles and their energy formulas for the meaning of these parameters:</p>
 <table border="1" class="docutils">
 <colgroup>
 <col width="51%" />
 <col width="31%" />
 <col width="18%" />
 </colgroup>
 <tbody valign="top">
 <tr class="row-odd"><td><a class="reference internal" href="pair_born.html"><em>born</em></a></td>
 <td>a,b,c</td>
 <td>type pairs</td>
 </tr>
 <tr class="row-even"><td><a class="reference internal" href="pair_buck.html"><em>buck</em></a></td>
 <td>a,c</td>
 <td>type pairs</td>
 </tr>
 <tr class="row-odd"><td><a class="reference internal" href="pair_coul.html"><em>coul/cut</em></a></td>
 <td>scale</td>
 <td>type pairs</td>
 </tr>
 <tr class="row-even"><td><a class="reference internal" href="pair_coul.html"><em>coul/debye</em></a></td>
 <td>scale</td>
 <td>type pairs</td>
 </tr>
 <tr class="row-odd"><td><a class="reference internal" href="pair_coul.html"><em>coul/long</em></a></td>
 <td>scale</td>
 <td>type pairs</td>
 </tr>
 <tr class="row-even"><td><a class="reference internal" href="pair_lj.html"><em>lj/cut</em></a></td>
 <td>epsilon,sigma</td>
 <td>type pairs</td>
 </tr>
 <tr class="row-odd"><td><a class="reference internal" href="pair_lj_expand.html"><em>lj/expand</em></a></td>
 <td>epsilon,sigma,delta</td>
 <td>type pairs</td>
 </tr>
 <tr class="row-even"><td><a class="reference internal" href="pair_lubricate.html"><em>lubricate</em></a></td>
 <td>mu</td>
 <td>global</td>
 </tr>
 <tr class="row-odd"><td><a class="reference internal" href="pair_gauss.html"><em>gauss</em></a></td>
 <td>a</td>
 <td>type pairs</td>
 </tr>
 <tr class="row-even"><td><a class="reference internal" href="pair_soft.html"><em>soft</em></a></td>
 <td>a</td>
 <td>type pairs</td>
 </tr>
 </tbody>
 </table>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">It is easy to add new potentials and their parameters
 to this list.  All it typically takes is adding an extract() method to
 the pair_*.cpp file associated with the potential.</p>
 </div>
 <p>Some parameters are global settings for the pair style, e.g. the
 viscosity setting &#8220;mu&#8221; for <a class="reference internal" href="pair_lubricate.html"><em>pair_style lubricate</em></a>.
 Other parameters apply to atom type pairs within the pair style,
 e.g. the prefactor &#8220;a&#8221; for <a class="reference internal" href="pair_soft.html"><em>pair_style soft</em></a>.</p>
 <p>Note that for many of the potentials, the parameter that can be varied
 is effectively a prefactor on the entire energy expression for the
 potential, e.g. the lj/cut epsilon.  The parameters listed as &#8220;scale&#8221;
 are exactly that, since the energy expression for the
 <a class="reference internal" href="pair_coul.html"><em>coul/cut</em></a> potential (for example) has no labeled
 prefactor in its formula.  To apply an effective prefactor to some
 potentials, multiple parameters need to be altered.  For example, the
 <a class="reference internal" href="pair_buck.html"><em>Buckingham potential</em></a> needs both the A and C terms
 altered together.  To scale the Buckingham potential, you should thus
 list the pair style twice, once for A and once for C.</p>
 <p>If a type pair parameter is specified, the <em>I</em> and <em>J</em> settings should
 be specified to indicate which type pairs to apply it to.  If a global
 parameter is specified, the <em>I</em> and <em>J</em> settings still need to be
 specified, but are ignored.</p>
 <p>Similar to the <a class="reference internal" href="pair_coeff.html"><em>pair_coeff command</em></a>, I and J can be
 specified in one of two ways.  Explicit numeric values can be used for
 each, as in the 1st example above.  I &lt;= J is required.  LAMMPS sets
 the coefficients for the symmetric J,I interaction to the same values.</p>
 <p>A wild-card asterisk can be used in place of or in conjunction with
 the I,J arguments to set the coefficients for multiple pairs of atom
 types.  This takes the form &#8220;*&#8221; or &#8220;<em>n&#8221; or &#8220;n</em>&#8221; or &#8220;m*n&#8221;.  If N = the
 number of atom types, then an asterisk with no numeric values means
 all types from 1 to N.  A leading asterisk means all types from 1 to n
 (inclusive).  A trailing asterisk means all types from n to N
 (inclusive).  A middle asterisk means all types from m to n
 (inclusive).  Note that only type pairs with I &lt;= J are considered; if
 asterisks imply type pairs where J &lt; I, they are ignored.</p>
 <p>IMPROTANT NOTE: If <a class="reference internal" href="pair_hybrid.html"><em>pair_style hybrid or hybrid/overlay</em></a> is being used, then the <em>pstyle</em> will
 be a sub-style name.  You must specify I,J arguments that correspond
 to type pair values defined (via the <a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a>
 command) for that sub-style.</p>
 <p>The <em>v_name</em> argument for keyword <em>pair</em> is the name of an
 <a class="reference internal" href="variable.html"><em>equal-style variable</em></a> which will be evaluated each time
 this fix is invoked to set the parameter to a new value.  It should be
 specified as v_name, where name is the variable name.  Equal-style
 variables can specify formulas with various mathematical functions,
 and include <a class="reference internal" href="thermo_style.html"><em>thermo_style</em></a> command keywords for the
 simulation box parameters and timestep and elapsed time.  Thus it is
 easy to specify parameters that change as a function of time or span
 consecutive runs in a continuous fashion.  For the latter, see the
 <em>start</em> and <em>stop</em> keywords of the <a class="reference internal" href="run.html"><em>run</em></a> command and the
 <em>elaplong</em> keyword of <a class="reference internal" href="thermo_style.html"><em>thermo_style custom</em></a> for
 details.</p>
 <p>For example, these commands would change the prefactor coefficient of
 the <a class="reference internal" href="pair_soft.html"><em>pair_style soft</em></a> potential from 10.0 to 30.0 in a
 linear fashion over the course of a simulation:</p>
 <div class="highlight-python"><div class="highlight"><pre>variable prefactor equal ramp(10,30)
 fix 1 all adapt 1 pair soft a * * v_prefactor
 </pre></div>
 </div>
 <hr class="docutils" />
 <p>The <em>kspace</em> keyword used the specified variable as a scale factor on
 the energy, forces, virial calculated by whatever K-Space solver is
 defined by the <a class="reference internal" href="kspace_style.html"><em>kspace_style</em></a> command.  If the
 variable has a value of 1.0, then the solver is unaltered.</p>
 <p>The <em>kspace</em> keyword works this way whether the <em>scale</em> keyword
 is set to <em>no</em> or <em>yes</em>.</p>
 <hr class="docutils" />
 <p>The <em>atom</em> keyword enables various atom properties to be changed.  The
 <em>aparam</em> argument is the name of the parameter to change.  This is the
 current list of atom parameters that can be varied by this fix:</p>
 <ul class="simple">
 <li>charge = charge on particle</li>
 <li>diameter = diameter of particle</li>
 </ul>
 <p>The <em>I</em> argument indicates which atom types are affected. A wild-card
 asterisk can be used in place of or in conjunction with the I argument
 to set the coefficients for multiple atom types.</p>
 <p>The <em>v_name</em> argument of the <em>atom</em> keyword is the name of an
 <a class="reference internal" href="variable.html"><em>equal-style variable</em></a> which will be evaluated each time
 this fix is invoked to set the parameter to a new value.  It should be
 specified as v_name, where name is the variable name.  See the
 discussion above describing the formulas associated with equal-style
 variables.  The new value is assigned to the corresponding attribute
 for all atoms in the fix group.</p>
 <p>If the atom parameter is <em>diameter</em> and per-atom density and per-atom
 mass are defined for particles (e.g. <a class="reference internal" href="atom_style.html"><em>atom_style granular</em></a>), then the mass of each particle is also
 changed when the diameter changes (density is assumed to stay
 constant).</p>
 <p>For example, these commands would shrink the diameter of all granular
 particles in the &#8220;center&#8221; group from 1.0 to 0.1 in a linear fashion
 over the course of a 1000-step simulation:</p>
 <div class="highlight-python"><div class="highlight"><pre>variable size equal ramp(1.0,0.1)
 fix 1 center adapt 10 atom diameter * v_size
 </pre></div>
 </div>
 <p>For <a class="reference internal" href="run_style.html"><em>rRESPA time integration</em></a>, this fix changes
 parameters on the outermost rRESPA level.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.  None of the <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> options
 are relevant to this fix.  No global or per-atom quantities are stored
 by this fix for access by various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  No parameter of this fix can
 be used with the <em>start/stop</em> keywords of the <a class="reference internal" href="run.html"><em>run</em></a> command.
 This fix is not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <blockquote>
 <div>none</div></blockquote>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="compute_fep.html"><em>compute fep</em></a>, <a class="reference internal" href="fix_adapt.html"><em>fix_adapt</em></a>, <a class="reference internal" href="compute_ti.html"><em>compute ti</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The option defaults are scale = no, reset = no, after = no.</p>
 </div>
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   <div class="section" id="fix-addforce-command">
 <span id="index-0"></span><h1>fix addforce command<a class="headerlink" href="#fix-addforce-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="fix-addforce-cuda-command">
 <h1>fix addforce/cuda command<a class="headerlink" href="#fix-addforce-cuda-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID addforce fx fy fz keyword value ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>addforce = style name of this fix command</li>
 <li>fx,fy,fz = force component values (force units)</li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>any of fx,fy,fz can be a variable (see below)
 </pre></div>
 </div>
 <ul class="simple">
 <li>zero or more keyword/value pairs may be appended to args</li>
 <li>keyword = <em>every</em> or <em>region</em> or <em>energy</em></li>
 </ul>
 <pre class="literal-block">
 <em>every</em> value = Nevery
-    Nevery = add force every this many timesteps
-  <em>region</em> value = region-ID
-    region-ID = ID of region atoms must be in to have added force
-  <em>energy</em> value = v_name
-    v_name = variable with name that calculates the potential energy of each atom in the added force field
+  Nevery = add force every this many timesteps
+<em>region</em> value = region-ID
+  region-ID = ID of region atoms must be in to have added force
+<em>energy</em> value = v_name
+  v_name = variable with name that calculates the potential energy of each atom in the added force field
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix kick flow addforce 1.0 0.0 0.0
 fix kick flow addforce 1.0 0.0 v_oscillate
 fix ff boundary addforce 0.0 0.0 v_push energy v_espace
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Add fx,fy,fz to the corresponding component of force for each atom in
 the group.  This command can be used to give an additional push to
 atoms in a simulation, such as for a simulation of Poiseuille flow in
 a channel.</p>
 <p>Any of the 3 quantities defining the force components can be specified
 as an equal-style or atom-style <a class="reference internal" href="variable.html"><em>variable</em></a>, namely <em>fx</em>,
 <em>fy</em>, <em>fz</em>.  If the value is a variable, it should be specified as
 v_name, where name is the variable name.  In this case, the variable
 will be evaluated each timestep, and its value(s) used to determine
 the force component.</p>
 <p>Equal-style variables can specify formulas with various mathematical
 functions, and include <a class="reference internal" href="thermo_style.html"><em>thermo_style</em></a> command
 keywords for the simulation box parameters and timestep and elapsed
 time.  Thus it is easy to specify a time-dependent force field.</p>
 <p>Atom-style variables can specify the same formulas as equal-style
 variables but can also include per-atom values, such as atom
 coordinates.  Thus it is easy to specify a spatially-dependent force
 field with optional time-dependence as well.</p>
 <p>If the <em>every</em> keyword is used, the <em>Nevery</em> setting determines how
 often the forces are applied.  The default value is 1, for every
 timestep.</p>
 <p>If the <em>region</em> keyword is used, the atom must also be in the
 specified geometric <a class="reference internal" href="region.html"><em>region</em></a> in order to have force added
 to it.</p>
 <hr class="docutils" />
 <p>Adding a force to atoms implies a change in their potential energy as
 they move due to the applied force field.  For dynamics via the &#8220;run&#8221;
 command, this energy can be optionally added to the system&#8217;s potential
 energy for thermodynamic output (see below).  For energy minimization
 via the &#8220;minimize&#8221; command, this energy must be added to the system&#8217;s
 potential energy to formulate a self-consistent minimization problem
 (see below).</p>
 <p>The <em>energy</em> keyword is not allowed if the added force is a constant
 vector F = (fx,fy,fz), with all components defined as numeric
 constants and not as variables.  This is because LAMMPS can compute
 the energy for each atom directly as E = -x dot F = -(x*fx + y*fy +
 z*fz), so that -Grad(E) = F.</p>
 <p>The <em>energy</em> keyword is optional if the added force is defined with
 one or more variables, and if you are performing dynamics via the
 <a class="reference internal" href="run.html"><em>run</em></a> command.  If the keyword is not used, LAMMPS will set
 the energy to 0.0, which is typically fine for dynamics.</p>
 <p>The <em>energy</em> keyword is required if the added force is defined with
 one or more variables, and you are performing energy minimization via
 the &#8220;minimize&#8221; command.  The keyword specifies the name of an
 atom-style <a class="reference internal" href="variable.html"><em>variable</em></a> which is used to compute the
 energy of each atom as function of its position.  Like variables used
 for <em>fx</em>, <em>fy</em>, <em>fz</em>, the energy variable is specified as v_name,
 where name is the variable name.</p>
 <p>Note that when the <em>energy</em> keyword is used during an energy
 minimization, you must insure that the formula defined for the
 atom-style <a class="reference internal" href="variable.html"><em>variable</em></a> is consistent with the force
 variable formulas, i.e. that -Grad(E) = F.  For example, if the force
 were a spring-like F = kx, then the energy formula should be E =
 -0.5kx^2.  If you don&#8217;t do this correctly, the minimization will not
 converge properly.</p>
 <hr class="docutils" />
 <p>Styles with a <em>cuda</em> suffix are functionally the same as the
 corresponding style without the suffix.  They have been optimized to
 run faster, depending on your available hardware, as discussed in
 <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a> of the manual.  The
 accelerated styles take the same arguments and should produce the same
 results, except for round-off and precision issues.</p>
 <p>These accelerated styles are part of the USER-CUDA package.  They are
 only enabled if LAMMPS was built with that package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 <p>You can specify the accelerated styles explicitly in your input script
 by including their suffix, or you can use the <a class="reference internal" href="Section_start.html#start-7"><span>-suffix command-line switch</span></a> when you invoke LAMMPS, or you can
 use the <a class="reference internal" href="suffix.html"><em>suffix</em></a> command in your input script.</p>
 <p>See <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a> of the manual for
 more instructions on how to use the accelerated styles effectively.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.</p>
 <p>The <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> <em>energy</em> option is supported by this
 fix to add the potential &#8220;energy&#8221; inferred by the added force to the
 system&#8217;s potential energy as part of <a class="reference internal" href="thermo_style.html"><em>thermodynamic output</em></a>.  This is a fictitious quantity but is
 needed so that the <a class="reference internal" href="minimize.html"><em>minimize</em></a> command can include the
 forces added by this fix in a consistent manner.  I.e. there is a
 decrease in potential energy when atoms move in the direction of the
 added force.</p>
 <p>This fix computes a global scalar and a global 3-vector of forces,
 which can be accessed by various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  The scalar is the potential
 energy discussed above.  The vector is the total force on the group of
 atoms before the forces on individual atoms are changed by the fix.
 The scalar and vector values calculated by this fix are &#8220;extensive&#8221;.</p>
 <p>No parameter of this fix can be used with the <em>start/stop</em> keywords of
 the <a class="reference internal" href="run.html"><em>run</em></a> command.</p>
 <p>The forces due to this fix are imposed during an energy minimization,
 invoked by the <a class="reference internal" href="minimize.html"><em>minimize</em></a> command.  You should not
 specify force components with a variable that has time-dependence for
 use with a minimizer, since the minimizer increments the timestep as
 the iteration count during the minimization.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">If you want the fictitious potential energy associated
 with the added forces to be included in the total potential energy of
 the system (the quantity being minimized), you MUST enable the
 <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> <em>energy</em> option for this fix.</p>
 </div>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <blockquote>
 <div>none</div></blockquote>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="fix_setforce.html"><em>fix setforce</em></a>, <a class="reference internal" href="fix_aveforce.html"><em>fix aveforce</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The option default for the every keyword is every = 1.</p>
 </div>
 </div>
 
 
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diff --git a/doc/fix_append_atoms.html b/doc/fix_append_atoms.html
index 009f8b510..375d6dc71 100644
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   <div class="section" id="fix-append-atoms-command">
 <span id="index-0"></span><h1>fix append/atoms command<a class="headerlink" href="#fix-append-atoms-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID append/atoms face ... keyword value ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>append/atoms = style name of this fix command</li>
 <li>face = <em>zhi</em></li>
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>basis</em> or <em>size</em> or <em>freq</em> or <em>temp</em> or <em>random</em> or <em>units</em></li>
 </ul>
 <pre class="literal-block">
 <em>basis</em> values = M itype
-    M = which basis atom
-    itype = atom type (1-N) to assign to this basis atom
-  <em>size</em> args = Lz
-    Lz = z size of lattice region appended in a single event(distance units)
-  <em>freq</em> args = freq
-    freq = the number of timesteps between append events
-  <em>temp</em> args = target damp seed extent
-    target = target temperature for the region between zhi-extent and zhi (temperature units)
-    damp = damping parameter (time units)
-    seed = random number seed for langevin kicks
-    extent = extent of thermostated region (distance units)
-  <em>random</em> args = xmax ymax zmax seed
-    <em>xmax</em>, <em>ymax</em>, <em>zmax</em> = maximum displacement in particular direction (distance units)
-    <em>seed</em> = random number seed for random displacement
-  <em>units</em> value = <em>lattice</em> or <em>box</em>
-    <em>lattice</em> = the wall position is defined in lattice units
-    <em>box</em> = the wall position is defined in simulation box units
+  M = which basis atom
+  itype = atom type (1-N) to assign to this basis atom
+<em>size</em> args = Lz
+  Lz = z size of lattice region appended in a single event(distance units)
+<em>freq</em> args = freq
+  freq = the number of timesteps between append events
+<em>temp</em> args = target damp seed extent
+  target = target temperature for the region between zhi-extent and zhi (temperature units)
+  damp = damping parameter (time units)
+  seed = random number seed for langevin kicks
+  extent = extent of thermostated region (distance units)
+<em>random</em> args = xmax ymax zmax seed
+  <em>xmax</em>, <em>ymax</em>, <em>zmax</em> = maximum displacement in particular direction (distance units)
+  <em>seed</em> = random number seed for random displacement
+<em>units</em> value = <em>lattice</em> or <em>box</em>
+  <em>lattice</em> = the wall position is defined in lattice units
+  <em>box</em> = the wall position is defined in simulation box units
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix 1 all append/atoms zhi size 5.0 freq 295 units lattice
 fix 4 all append/atoms zhi size 15.0 freq 5 units box
 fix A all append/atoms zhi size 1.0 freq 1000 units lattice
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>This fix creates atoms on a lattice, appended on the zhi edge of the
 system box.  This can be useful when a shock or wave is propagating
 from zlo.  This allows the system to grow with time to accommodate an
 expanding wave.  A simulation box must already exist, which is
 typically created via the <a class="reference internal" href="create_box.html"><em>create_box</em></a> command.
 Before using this command, a lattice must also be defined using the
 <a class="reference internal" href="lattice.html"><em>lattice</em></a> command.</p>
 <p>This fix will automatically freeze atoms on the zhi edge of the
 system, so that overlaps are avoided when new atoms are appended.</p>
 <p>The <em>basis</em> keyword specifies an atom type that will be assigned to
 specific basis atoms as they are created.  See the
 <a class="reference internal" href="lattice.html"><em>lattice</em></a> command for specifics on how basis atoms are
 defined for the unit cell of the lattice.  By default, all created
 atoms are assigned type = 1 unless this keyword specifies differently.</p>
 <p>The <em>size</em> keyword defines the size in z of the chunk of material to
 be added.</p>
 <p>The <em>random</em> keyword will give the atoms random displacements around
 their lattice points to simulate some initial temperature.</p>
 <p>The <em>temp</em> keyword will cause a region to be thermostated with a
 Langevin thermostat on the zhi boundary.  The size of the region is
 measured from zhi and is set with the <em>extent</em> argument.</p>
 <p>The <em>units</em> keyword determines the meaning of the distance units used
 to define a wall position, but only when a numeric constant is used.
 A <em>box</em> value selects standard distance units as defined by the
 <a class="reference internal" href="units.html"><em>units</em></a> command, e.g. Angstroms for units = real or metal.
 A <em>lattice</em> value means the distance units are in lattice spacings.
 The <a class="reference internal" href="lattice.html"><em>lattice</em></a> command must have been previously used to
 define the lattice spacings.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.  None of the <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> options
 are relevant to this fix.  No global or per-atom quantities are stored
 by this fix for access by various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  No parameter of this fix can
 be used with the <em>start/stop</em> keywords of the <a class="reference internal" href="run.html"><em>run</em></a> command.
 This fix is not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>This fix style is part of the SHOCK package.  It is only enabled if
 LAMMPS was built with that package. See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 <p>The boundary on which atoms are added with append/atoms must be
 shrink/minimum.  The opposite boundary may be any boundary type other
 than periodic.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="fix_wall_piston.html"><em>fix wall/piston</em></a> command</p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The keyword defaults are size = 0.0, freq = 0, units = lattice.  All
 added atoms are of type 1 unless the basis keyword is used.</p>
 </div>
 </div>
 
 
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   <div class="section" id="fix-atc-command">
 <span id="index-0"></span><h1>fix atc command<a class="headerlink" href="#fix-atc-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix &lt;fixID&gt; &lt;group&gt; atc &lt;type&gt; &lt;parameter_file&gt;
 </pre></div>
 </div>
 <ul class="simple">
 <li>fixID = name of fix</li>
 <li>group = name of group fix is to be applied</li>
 <li>type = <em>thermal</em> or <em>two_temperature</em> or <em>hardy</em> or <em>field</em></li>
 </ul>
 <pre class="literal-block">
 <em>thermal</em> = thermal coupling with fields: temperature
- <em>two_temperature</em> = electron-phonon coupling with field: temperature and electron_temperature
- <em>hardy</em> = on-the-fly post-processing using kernel localization functions (see &quot;related&quot; section for possible fields)
- <em>field</em> = on-the-fly post-processing using mesh-based localization functions (see &quot;related&quot; section for possible fields)
+<em>two_temperature</em> = electron-phonon coupling with field: temperature and electron_temperature
+<em>hardy</em> = on-the-fly post-processing using kernel localization functions (see &quot;related&quot; section for possible fields)
+<em>field</em> = on-the-fly post-processing using mesh-based localization functions (see &quot;related&quot; section for possible fields)
 </pre>
 <ul class="simple">
 <li>parameter_file = name of the file with material parameters. Note: Neither hardy nor field requires a parameter file</li>
 </ul>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix AtC internal atc thermal Ar_thermal.dat
 fix AtC internal atc two_temperature Ar_ttm.mat
 fix AtC internal atc hardy
 fix AtC internal atc field
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>This fix is the beginning to creating a coupled FE/MD simulation and/or an on-the-fly estimation of continuum fields. The coupled versions of this fix do Verlet integration and the post-processing does not. After instantiating this fix, several other fix_modify commands will be needed to set up the problem, e.g. define the finite element mesh and prescribe initial and boundary conditions.</p>
 <img alt="_images/atc_nanotube.jpg" class="align-center" src="_images/atc_nanotube.jpg" />
 <div class="highlight-python"><div class="highlight"><pre>The following coupling example is typical, but non-exhaustive:
  # ... commands to create and initialize the MD system
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre># initial fix to designate coupling type and group to apply it to
- # tag group physics material_file
- fix AtC internal atc thermal Ar_thermal.mat
+# tag group physics material_file
+fix AtC internal atc thermal Ar_thermal.mat
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre># create a uniform 12 x 2 x 2 mesh that covers region contain the group
- # nx ny nz region periodicity
- fix_modify AtC mesh create 12 2 2 mdRegion f p p
+# nx ny nz region periodicity
+fix_modify AtC mesh create 12 2 2 mdRegion f p p
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre># specify the control method for the type of coupling
- # physics control_type
- fix_modify AtC thermal control flux
+# physics control_type
+fix_modify AtC thermal control flux
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre># specify the initial values for the empirical field &quot;temperature&quot;
- # field node_group value
- fix_modify AtC initial temperature all 30
+# field node_group value
+fix_modify AtC initial temperature all 30
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre># create an output stream for nodal fields
- # filename output_frequency
- fix_modify AtC output atc_fe_output 100
+# filename output_frequency
+fix_modify AtC output atc_fe_output 100
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>run 1000
 </pre></div>
 </div>
 <p>likewise for this post-processing example:</p>
 <div class="highlight-python"><div class="highlight"><pre><span class="c"># ... commands to create and initialize the MD system</span>
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre># initial fix to designate post-processing and the group to apply it to
- # no material file is allowed nor required
- fix AtC internal atc hardy
+# no material file is allowed nor required
+fix AtC internal atc hardy
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre># for hardy fix, specific kernel function (function type and range) to # be used as a localization function
- fix AtC kernel quartic_sphere 10.0
+fix AtC kernel quartic_sphere 10.0
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre># create a uniform 1 x 1 x 1 mesh that covers region contain the group
- # with periodicity this effectively creats a system average
- fix_modify AtC mesh create 1 1 1 box p p p
+# with periodicity this effectively creats a system average
+fix_modify AtC mesh create 1 1 1 box p p p
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre># change from default lagrangian map to eulerian
- # refreshed every 100 steps
- fix_modify AtC atom_element_map eulerian 100
+# refreshed every 100 steps
+fix_modify AtC atom_element_map eulerian 100
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre># start with no field defined
- # add mass density, potential energy density, stress and temperature
- fix_modify AtC fields add density energy stress temperature
+# add mass density, potential energy density, stress and temperature
+fix_modify AtC fields add density energy stress temperature
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre># create an output stream for nodal fields
- # filename output_frequency
- fix_modify AtC output nvtFE 100 text
+# filename output_frequency
+fix_modify AtC output nvtFE 100 text
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>run 1000
 </pre></div>
 </div>
 <dl class="docutils">
 <dt>the mesh&#8217;s linear interpolation functions can be used as the localization function</dt>
 <dd>by using the field option:</dd>
 </dl>
 <p>fix AtC internal atc field</p>
 <p>fix_modify AtC mesh create 1 1 1 box p p p</p>
 <p>...</p>
 <p>Note coupling and post-processing can be combined in the same simulations using separate fixes.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.  The <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> options relevant to this fix are listed below.  No global scalar or vector or per-atom quantities are stored by this fix for access by various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  No parameter of this fix can be used with the <em>start/stop</em> keywords of the <a class="reference internal" href="run.html"><em>run</em></a> command.  This fix is not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>Thermal and two_temperature (coupling) types use a Verlet time-integration algorithm. The hardy type does not contain its own time-integrator and must be used with a separate fix that does contain one, e.g. nve, nvt, etc.</p>
 <ul class="simple">
 <li>Currently,</li>
 <li><ul class="first">
 <li>the coupling is restricted to thermal physics</li>
 </ul>
 </li>
 <li><ul class="first">
 <li>the FE computations are done in serial on each processor.</li>
 </ul>
 </li>
 </ul>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p>After specifying this fix in your input script, several other <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> commands are used to setup the problem, e.g. define the finite element mesh and prescribe initial and boundary conditions.</p>
 <p>fix_modify commands for setup:</p>
 <ul class="simple">
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">mesh</span> <span class="pre">create</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">mesh</span> <span class="pre">quadrature</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">mesh</span> <span class="pre">read</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">mesh</span> <span class="pre">write</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">mesh</span> <span class="pre">create_nodeset</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">mesh</span> <span class="pre">add_to_nodeset</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">mesh</span> <span class="pre">create_faceset</span> <span class="pre">box</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">mesh</span> <span class="pre">create_faceset</span> <span class="pre">plane</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">mesh</span> <span class="pre">create_elementset</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">mesh</span> <span class="pre">delete_elements</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">mesh</span> <span class="pre">nodeset_to_elementset</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">boundary</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">internal_quadrature</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">time_integration</span> <span class="pre">(thermal)</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">time_integration</span> <span class="pre">(momentum)</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">extrinsic</span> <span class="pre">electron_integration</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">internal_element_set</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">decomposition</span></code></li>
 </ul>
 <p>fix_modify commands for boundary and initial conditions:</p>
 <ul class="simple">
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">initial</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">fix</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">unfix</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">fix_flux</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">unfix_flux</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">source</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">remove_source</span></code></li>
 </ul>
 <p>fix_modify commands for control and filtering:</p>
 <ul class="simple">
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">control</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">control</span> <span class="pre">thermal</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">control</span> <span class="pre">thermal</span> <span class="pre">correction_max_iterations</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">control</span> <span class="pre">momentum</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">control</span> <span class="pre">localized_lambda</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">control</span> <span class="pre">lumped_lambda_solve</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">control</span> <span class="pre">mask_direction</span></code> control</li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">filter</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">filter</span> <span class="pre">scale</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">filter</span> <span class="pre">type</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">equilibrium_start</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">extrinsic</span> <span class="pre">exchange</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">poisson_solver</span></code></li>
 </ul>
 <p>fix_modify commands for output:</p>
 <ul class="simple">
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">output</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">output</span> <span class="pre">nodeset</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">output</span> <span class="pre">elementset</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">output</span> <span class="pre">boundary_integral</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">output</span> <span class="pre">contour_integral</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">mesh</span> <span class="pre">output</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">write_restart</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">read_restart</span></code></li>
 </ul>
 <p>fix_modify commands for post-processing:</p>
 <ul class="simple">
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">kernel</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">fields</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">grdients</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">rates</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">computes</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">on_the_fly</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">pair_interactions/bond_interactions</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">sample_frequency</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">set</span></code></li>
 </ul>
 <p>miscellaneous fix_modify commands:</p>
 <ul class="simple">
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">atom_element_map</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">atom_weight</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">write_atom_weights</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">reset_time</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">reset_atomic_reference_positions</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">fe_md_boundary</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">boundary_faceset</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">consistent_fe_initialization</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">mass_matrix</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">material</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">atomic_charge</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">source_integration</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">temperature_definition</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">track_displacement</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">boundary_dynamics</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">add_species</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">add_molecule</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">remove_species</span></code></li>
 <li><code class="xref doc docutils literal"><span class="pre">fix_modify</span> <span class="pre">AtC</span> <span class="pre">remove_molecule</span></code></li>
 </ul>
 <p>Note: a set of example input files with the attendant material files are included with this package</p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>None</p>
 <hr class="docutils" />
 <p>For detailed exposition of the theory and algorithms please see:</p>
 <p id="wagner"><strong>(Wagner)</strong> Wagner, GJ; Jones, RE; Templeton, JA; Parks, MA, &#8220;An atomistic-to-continuum coupling method for heat transfer in solids.&#8221; Special Issue of Computer Methods and Applied Mechanics (2008) 197:3351.</p>
 <p id="zimmeman2004"><strong>(Zimmerman2004)</strong> Zimmerman, JA; Webb, EB; Hoyt, JJ;. Jones, RE; Klein, PA; Bammann, DJ, &#8220;Calculation of stress in atomistic simulation.&#8221; Special Issue of Modelling and Simulation in Materials Science and Engineering (2004), 12:S319.</p>
 <p id="zimmerman2010"><strong>(Zimmerman2010)</strong> Zimmerman, JA; Jones, RE; Templeton, JA, &#8220;A material frame approach for evaluating continuum variables in atomistic simulations.&#8221; Journal of Computational Physics (2010), 229:2364.</p>
 <p id="templeton2010"><strong>(Templeton2010)</strong> Templeton, JA; Jones, RE; Wagner, GJ, &#8220;Application of a field-based method to spatially varying thermal transport problems in molecular dynamics.&#8221; Modelling and Simulation in Materials Science and Engineering (2010), 18:085007.</p>
 <p id="jones"><strong>(Jones)</strong> Jones, RE; Templeton, JA; Wagner, GJ; Olmsted, D; Modine, JA, &#8220;Electron transport enhanced molecular dynamics for metals and semi-metals.&#8221; International Journal for Numerical Methods in Engineering (2010), 83:940.</p>
 <p id="templeton2011"><strong>(Templeton2011)</strong> Templeton, JA; Jones, RE; Lee, JW; Zimmerman, JA; Wong, BM, &#8220;A long-range electric field solver for molecular dynamics based on atomistic-to-continuum modeling.&#8221; Journal of Chemical Theory and Computation (2011), 7:1736.</p>
 <p id="mandadapu"><strong>(Mandadapu)</strong> Mandadapu, KK; Templeton, JA; Lee, JW, &#8220;Polarization as a field variable from molecular dynamics simulations.&#8221; Journal of Chemical Physics (2013), 139:054115.</p>
 <p>Please refer to the standard finite element (FE) texts, e.g. T.J.R Hughes &#8221; The finite element method &#8221;, Dover 2003, for the basics of FE simulation.</p>
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diff --git a/doc/fix_atom_swap.html b/doc/fix_atom_swap.html
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   <div class="section" id="fix-atom-swap-command">
 <span id="index-0"></span><h1>fix atom/swap command<a class="headerlink" href="#fix-atom-swap-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID atom/swap N X seed T keyword values ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>atom/swap = style name of this fix command</li>
 <li>N = invoke this fix every N steps</li>
 <li>X = number of swaps to attempt every N steps</li>
 <li>seed = random # seed (positive integer)</li>
 <li>T = scaling temperature of the MC swaps (temperature units)</li>
 <li>one or more keyword/value pairs may be appended to args</li>
 <li>keyword = <em>types</em> or <em>delta_mu</em> or <em>ke</em> or <em>semi-grand</em> or <em>region</em></li>
 </ul>
 <pre class="literal-block">
 <em>types</em> values = two or more atom types
-  <em>delta_mu</em> values = number_of_types-1 relative chemical potentials (energy units)
-  <em>ke</em> value = <em>no</em> or <em>yes</em>
-    <em>no</em> = no conservation of kinetic energy after atom swaps
-    <em>yes</em> = kinetic energy is conserved after atom swaps
-  <em>semi-grand</em> value = <em>no</em> or <em>yes</em>
-    <em>no</em> = particle type counts and fractions conserved
-    <em>yes</em> = semi-grand canonical ensemble, particle fractions not conserved
-  <em>region</em> value = region-ID
-    region-ID = ID of region to use as an exchange/move volume
+<em>delta_mu</em> values = number_of_types-1 relative chemical potentials (energy units)
+<em>ke</em> value = <em>no</em> or <em>yes</em>
+  <em>no</em> = no conservation of kinetic energy after atom swaps
+  <em>yes</em> = kinetic energy is conserved after atom swaps
+<em>semi-grand</em> value = <em>no</em> or <em>yes</em>
+  <em>no</em> = particle type counts and fractions conserved
+  <em>yes</em> = semi-grand canonical ensemble, particle fractions not conserved
+<em>region</em> value = region-ID
+  region-ID = ID of region to use as an exchange/move volume
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix 2 all atom/swap 1 1 29494 300.0 ke no types 1 2
 fix myFix all atom/swap 100 1 12345 298.0 region my_swap_region types 5 6
 fix SGMC all atom/swap 1 100 345 1.0 semi-grand yes types 1 2 3 delta_mu 4.3 -5.0
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>This fix performs Monte Carlo swaps of atoms of one given atom type
 with atoms of the other given atom types. The specified T is used in
 the Metropolis criterion dictating swap probabilities.</p>
 <p>Perform X swaps of atoms of one type with atoms of another type
 according to a Monte Carlo probability. Swap candidates must be in the
 fix group, must be in the region (if specified), and must be of one of
 the listed types. Swaps are attempted between candidates that are
 chosen randomly with equal probability among the candidate
 atoms. Swaps are not attempted between atoms of the same type since
 nothing would happen.</p>
 <p>All atoms in the simulation domain can be moved using regular time
 integration displacements, e.g. via <code class="xref doc docutils literal"><span class="pre">fix_nvt</span></code>, resulting
 in a hybrid MC+MD simulation. A smaller-than-usual timestep size may
 be needed when running such a hybrid simulation, especially if the
 swapped atoms are not well equilibrated.</p>
 <p>The <em>types</em> keyword is required. At least two atom types must be
 specified.</p>
 <p>The <em>ke</em> keyword can be set to <em>no</em> to turn off kinetic energy
 conservation for swaps. The default is <em>yes</em>, which means that swapped
 atoms have their velocities scaled by the ratio of the masses of the
 swapped atom types. This ensures that the kinetic energy of each atom
 is the same after the swap as it was before the swap, even though the
 atom masses have changed.</p>
 <p>The <em>semi-grand</em> keyword can be set to <em>yes</em> to switch to the
 semi-grand canonical ensemble as discussed in <a class="reference internal" href="#sadigh"><span>(Sadigh)</span></a>. This
 means that the total number of each particle type does not need to be
 conserved. The default is <em>no</em>, which means that the only kind of swap
 allowed exchanges an atom of one type with an atom of a different
 given type. In other words, the relative mole fractions of the swapped
 atoms remains constant. Whereas in the semi-grand canonical ensemble,
 the composition of the system can change. Note that when using
 <em>semi-grand</em>, all atoms in the fix group are eligible for attempted
 conversion to one of the given types, even if its current type is not
 one of the given types. An attempt is made to switch the selected atom
 to one of the listed <em>types</em> with equal probability. Acceptance of
 each attempt depends upon the Metropolis criterion.</p>
 <p>The <em>delta_mu</em> keyword allows users to specify non-zero chemical
 potentials for each of the atom types. All chemical potentials are
 relative to the first atom type, so no value is given for the first
 atom type. These parameters are useful for semi-grand canonical
 ensemble simulations where it may be desirable to actively control the
 composition of the system. When given, there must be ntypes-1 values
 given, where ntypes is the number of atom types in the simulated
 system. Note that a value for delta_mu is required for all atom types
 when using <em>semi-grand</em>, even for atom types not listed following the
 <em>types</em> keyword. This is because when using <em>semi-grand</em>, it is
 possible that any of the atom types in the system could be part of the
 fix group and therefore are eligible for swapping to one of the listed
 atom types.</p>
 <p>This command may optionally use the <em>region</em> keyword to define swap
 volume.  The specified region must have been previously defined with a
 <a class="reference internal" href="region.html"><em>region</em></a> command.  It must be defined with side = <em>in</em>.
 Swap attempts occur only between atoms that are both within the
 specified region. Swaps are not otherwise attempted.</p>
 <p>You should ensure you do not swap atoms belonging to a molecule, or
 LAMMPS will soon generate an error when it tries to find those atoms.
 LAMMPS will warn you if any of the atoms eligible for swapping have a
 non-zero molecule ID, but does not check for this at the time of
 swapping.</p>
 <p>This fix checks to ensure all atoms of the given types have the same
 atomic charge. LAMMPS doesn&#8217;t enforce this in general, but it is
 needed for this fix to simplify the swapping procedure. Successful
 swaps will swap the atom type and charge of the swapped atoms.</p>
 <p>Since this fix computes total potential energies before and after
 proposed swaps, so even complicated potential energy calculations are
 OK, including the following:</p>
 <ul class="simple">
 <li>long-range electrostatics (kspace)</li>
 <li>many body pair styles</li>
 <li>hybrid pair styles</li>
 <li>eam pair styles</li>
 <li>triclinic systems</li>
 <li>need to include potential energy contributions from other fixes</li>
 </ul>
 <p>Some fixes have an associated potential energy. Examples of such fixes
 include: <a class="reference internal" href="fix_efield.html"><em>efield</em></a>, <a class="reference internal" href="fix_gravity.html"><em>gravity</em></a>,
 <a class="reference internal" href="fix_addforce.html"><em>addforce</em></a>, <a class="reference internal" href="fix_langevin.html"><em>langevin</em></a>,
 <a class="reference internal" href="fix_restrain.html"><em>restrain</em></a>, <a class="reference internal" href="fix_temp_berendsen.html"><em>temp/berendsen</em></a>,
 <a class="reference internal" href="fix_temp_rescale.html"><em>temp/rescale</em></a>, and <a class="reference internal" href="fix_wall.html"><em>wall fixes</em></a>.
 For that energy to be included in the total potential energy of the
 system (the quantity used when performing GCMC moves),
 you MUST enable the <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> <em>energy</em> option for
 that fix.  The doc pages for individual <a class="reference internal" href="fix.html"><em>fix</em></a> commands
 specify if this should be done.</p>
 </div>
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>This fix writes the state of the fix to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.  This includes information about the random
 number generator seed, the next timestep for MC exchanges, etc.  See
 the <a class="reference internal" href="read_restart.html"><em>read_restart</em></a> command for info on how to
 re-specify a fix in an input script that reads a restart file, so that
 the operation of the fix continues in an uninterrupted fashion.</p>
 <p>None of the <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> options are relevant to this
 fix.</p>
 <p>This fix computes a global vector of length 2, which can be accessed
 by various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  The vector
 values are the following global cumulative quantities:</p>
 <ul class="simple">
 <li>1 = swap attempts</li>
 <li>2 = swap successes</li>
 </ul>
 <p>The vector values calculated by this fix are &#8220;extensive&#8221;.</p>
 <p>No parameter of this fix can be used with the <em>start/stop</em> keywords of
 the <a class="reference internal" href="run.html"><em>run</em></a> command.  This fix is not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>This fix is part of the MC package.  It is only enabled if LAMMPS was
 built with that package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><code class="xref doc docutils literal"><span class="pre">fix_nvt</span></code>, <a class="reference internal" href="neighbor.html"><em>neighbor</em></a>,
 <a class="reference internal" href="fix_deposit.html"><em>fix_deposit</em></a>, <a class="reference internal" href="fix_evaporate.html"><em>fix_evaporate</em></a>,
 <a class="reference internal" href="delete_atoms.html"><em>delete_atoms</em></a>, <a class="reference internal" href="fix_gcmc.html"><em>fix_gcmc</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The option defaults are ke = yes, semi-grand = no, delta_mu = 0.0 for
 all atom types.</p>
 <hr class="docutils" />
 <p id="sadigh"><strong>(Sadigh)</strong> B Sadigh, P Erhart, A Stukowski, A Caro, E Martinez, and
 L Zepeda-Ruiz, Phys. Rev. B, 85, 184203 (2012).</p>
 </div>
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diff --git a/doc/fix_ave_atom.html b/doc/fix_ave_atom.html
index 5efc53bd2..925beefe1 100644
--- a/doc/fix_ave_atom.html
+++ b/doc/fix_ave_atom.html
@@ -1,320 +1,320 @@
 
 
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   <div class="section" id="fix-ave-atom-command">
 <span id="index-0"></span><h1>fix ave/atom command<a class="headerlink" href="#fix-ave-atom-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID ave/atom Nevery Nrepeat Nfreq value1 value2 ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>ave/atom = style name of this fix command</li>
 <li>Nevery = use input values every this many timesteps</li>
 <li>Nrepeat = # of times to use input values for calculating averages</li>
 <li>Nfreq = calculate averages every this many timesteps
 one or more input values can be listed</li>
 <li>value = x, y, z, vx, vy, vz, fx, fy, fz, c_ID, c_ID[i], f_ID, f_ID[i], v_name</li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>x,y,z,vx,vy,vz,fx,fy,fz = atom attribute (position, velocity, force component)
-  c_ID = per-atom vector calculated by a compute with ID
-  c_ID[I] = Ith column of per-atom array calculated by a compute with ID
-  f_ID = per-atom vector calculated by a fix with ID
-  f_ID[I] = Ith column of per-atom array calculated by a fix with ID
-  v_name = per-atom vector calculated by an atom-style variable with name
+c_ID = per-atom vector calculated by a compute with ID
+c_ID[I] = Ith column of per-atom array calculated by a compute with ID
+f_ID = per-atom vector calculated by a fix with ID
+f_ID[I] = Ith column of per-atom array calculated by a fix with ID
+v_name = per-atom vector calculated by an atom-style variable with name
 </pre></div>
 </div>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix 1 all ave/atom 1 100 100 vx vy vz
 fix 1 all ave/atom 10 20 1000 c_my_stress[1]
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Use one or more per-atom vectors as inputs every few timesteps, and
 average them atom by atom over longer timescales.  The resulting
 per-atom averages can be used by other <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a> such as the <a class="reference internal" href="fix_ave_spatial.html"><em>fix ave/spatial</em></a> or <a class="reference internal" href="dump.html"><em>dump custom</em></a> commands.</p>
 <p>The group specified with the command means only atoms within the group
 have their averages computed.  Results are set to 0.0 for atoms not in
 the group.</p>
 <p>Each input value can be an atom attribute (position, velocity, force
 component) or can be the result of a <a class="reference internal" href="compute.html"><em>compute</em></a> or
 <a class="reference internal" href="fix.html"><em>fix</em></a> or the evaluation of an atom-style
 <a class="reference internal" href="variable.html"><em>variable</em></a>.  In the latter cases, the compute, fix, or
 variable must produce a per-atom vector, not a global quantity or
 local quantity.  If you wish to time-average global quantities from a
 compute, fix, or variable, then see the <a class="reference internal" href="fix_ave_time.html"><em>fix ave/time</em></a> command.</p>
 <p><a class="reference internal" href="compute.html"><em>Computes</em></a> that produce per-atom vectors or arrays are
 those which have the word <em>atom</em> in their style name.  See the doc
 pages for individual <a class="reference internal" href="fix.html"><em>fixes</em></a> to determine which ones produce
 per-atom vectors or arrays.  <a class="reference internal" href="variable.html"><em>Variables</em></a> of style <em>atom</em>
 are the only ones that can be used with this fix since they produce
 per-atom vectors.</p>
 <p>Each per-atom value of each input vector is averaged independently.</p>
 <hr class="docutils" />
 <p>The <em>Nevery</em>, <em>Nrepeat</em>, and <em>Nfreq</em> arguments specify on what
 timesteps the input values will be used in order to contribute to the
 average.  The final averaged quantities are generated on timesteps
 that are a multiple of <em>Nfreq</em>.  The average is over <em>Nrepeat</em>
 quantities, computed in the preceding portion of the simulation every
 <em>Nevery</em> timesteps.  <em>Nfreq</em> must be a multiple of <em>Nevery</em> and
 <em>Nevery</em> must be non-zero even if <em>Nrepeat</em> is 1.  Also, the timesteps
 contributing to the average value cannot overlap, i.e. Nfreq &gt;
 (Nrepeat-1)*Nevery is required.</p>
 <p>For example, if Nevery=2, Nrepeat=6, and Nfreq=100, then values on
 timesteps 90,92,94,96,98,100 will be used to compute the final average
 on timestep 100.  Similarly for timesteps 190,192,194,196,198,200 on
 timestep 200, etc.</p>
 <hr class="docutils" />
 <p>The atom attribute values (x,y,z,vx,vy,vz,fx,fy,fz) are
 self-explanatory.  Note that other atom attributes can be used as
 inputs to this fix by using the <a class="reference internal" href="compute_property_atom.html"><em>compute property/atom</em></a> command and then specifying
 an input value from that compute.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">The x,y,z attributes are values that are re-wrapped
 inside the periodic box whenever an atom crosses a periodic boundary.
 Thus if you time average an atom that spends half its time on either
 side of the periodic box, you will get a value in the middle of the
 box.  If this is not what you want, consider averaging unwrapped
 coordinates, which can be provided by the <a class="reference internal" href="compute_property_atom.html"><em>compute property/atom</em></a> command via its xu,yu,zu
 attributes.</p>
 </div>
 <p>If a value begins with &#8220;<a href="#id1"><span class="problematic" id="id2">c_</span></a>&#8221;, a compute ID must follow which has been
 previously defined in the input script.  If no bracketed term is
 appended, the per-atom vector calculated by the compute is used.  If a
 bracketed term containing an index I is appended, the Ith column of
 the per-atom array calculated by the compute is used.  Users can also
 write code for their own compute styles and <a class="reference internal" href="Section_modify.html"><em>add them to LAMMPS</em></a>.</p>
 <p>If a value begins with &#8220;<a href="#id3"><span class="problematic" id="id4">f_</span></a>&#8221;, a fix ID must follow which has been
 previously defined in the input script.  If no bracketed term is
 appended, the per-atom vector calculated by the fix is used.  If a
 bracketed term containing an index I is appended, the Ith column of
 the per-atom array calculated by the fix is used.  Note that some
 fixes only produce their values on certain timesteps, which must be
 compatible with <em>Nevery</em>, else an error will result.  Users can also
 write code for their own fix styles and <a class="reference internal" href="Section_modify.html"><em>add them to LAMMPS</em></a>.</p>
 <p>If a value begins with &#8220;<a href="#id5"><span class="problematic" id="id6">v_</span></a>&#8221;, a variable name must follow which has
 been previously defined in the input script as an <a class="reference internal" href="variable.html"><em>atom-style variable</em></a> Variables of style <em>atom</em> can reference
 thermodynamic keywords, or invoke other computes, fixes, or variables
 when they are evaluated, so this is a very general means of generating
 per-atom quantities to time average.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.  None of the <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> options
 are relevant to this fix.  No global scalar or vector quantities are
 stored by this fix for access by various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.</p>
 <p>This fix produces a per-atom vector or array which can be accessed by
 various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  A vector is
 produced if only a single quantity is averaged by this fix.  If two or
 more quantities are averaged, then an array of values is produced.
 The per-atom values can only be accessed on timesteps that are
 multiples of <em>Nfreq</em> since that is when averaging is performed.</p>
 <p>No parameter of this fix can be used with the <em>start/stop</em> keywords of
 the <a class="reference internal" href="run.html"><em>run</em></a> command.  This fix is not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <blockquote>
 <div>none</div></blockquote>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="compute.html"><em>compute</em></a>, <a class="reference internal" href="fix_ave_histo.html"><em>fix ave/histo</em></a>, <a class="reference internal" href="fix_ave_spatial.html"><em>fix ave/spatial</em></a>, <a class="reference internal" href="fix_ave_time.html"><em>fix ave/time</em></a>,
 <a class="reference internal" href="variable.html"><em>variable</em></a>,</p>
 <p><strong>Default:</strong> none</p>
 </div>
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   <div class="section" id="fix-ave-chunk-command">
 <span id="index-0"></span><h1>fix ave/chunk command<a class="headerlink" href="#fix-ave-chunk-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID ave/chunk Nevery Nrepeat Nfreq chunkID value1 value2 ... keyword args ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>ave/chunk = style name of this fix command</li>
 <li>Nevery = use input values every this many timesteps</li>
 <li>Nrepeat = # of times to use input values for calculating averages</li>
 <li>Nfreq = calculate averages every this many timesteps</li>
 <li>chunkID = ID of <a class="reference internal" href="compute_chunk_atom.html"><em>compute chunk/atom</em></a> command</li>
 <li>one or more input values can be listed</li>
 <li>value = vx, vy, vz, fx, fy, fz, density/mass, density/number, temp, c_ID, c_ID[I], f_ID, f_ID[I], v_name</li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>vx,vy,vz,fx,fy,fz = atom attribute (velocity, force component)
-  density/number, density/mass = number or mass density
-  temp = temperature
-  c_ID = per-atom vector calculated by a compute with ID
-  c_ID[I] = Ith column of per-atom array calculated by a compute with ID
-  f_ID = per-atom vector calculated by a fix with ID
-  f_ID[I] = Ith column of per-atom array calculated by a fix with ID
-  v_name = per-atom vector calculated by an atom-style variable with name
+density/number, density/mass = number or mass density
+temp = temperature
+c_ID = per-atom vector calculated by a compute with ID
+c_ID[I] = Ith column of per-atom array calculated by a compute with ID
+f_ID = per-atom vector calculated by a fix with ID
+f_ID[I] = Ith column of per-atom array calculated by a fix with ID
+v_name = per-atom vector calculated by an atom-style variable with name
 </pre></div>
 </div>
 <ul class="simple">
 <li>zero or more keyword/arg pairs may be appended</li>
 <li>keyword = <em>norm</em> or <em>ave</em> or <em>bias</em> or <em>adof</em> or <em>cdof</em> or <em>file</em> or <em>overwrite</em> or <em>title1</em> or <em>title2</em> or <em>title3</em></li>
 </ul>
 <pre class="literal-block">
 <em>norm</em> arg = <em>all</em> or <em>sample</em> or <em>none</em> = how output on <em>Nfreq</em> steps is normalized
-    all = output is sum of atoms across all <em>Nrepeat</em> samples, divided by atom count
-    sample = output is sum of <em>Nrepeat</em> sample averages, divided by <em>Nrepeat</em>
-    none = output is sum of <em>Nrepeat</em> sums, divided by <em>Nrepeat</em>
-  <em>ave</em> args = <em>one</em> or <em>running</em> or <em>window M</em>
-    one = output new average value every Nfreq steps
-    running = output cumulative average of all previous Nfreq steps
-    window M = output average of M most recent Nfreq steps
-  <em>bias</em> arg = bias-ID
-    bias-ID = ID of a temperature compute that removes a velocity bias for temperature calculation
-  <em>adof</em> value = dof_per_atom
-    dof_per_atom = define this many degrees-of-freedom per atom for temperature calculation
-  <em>cdof</em> value = dof_per_chunk
-    dof_per_chunk = define this many degrees-of-freedom per chunk for temperature calculation
-  <em>file</em> arg = filename
-    filename = file to write results to
-  <em>overwrite</em> arg = none = overwrite output file with only latest output
-  <em>title1</em> arg = string
-    string = text to print as 1st line of output file
-  <em>title2</em> arg = string
-    string = text to print as 2nd line of output file
-  <em>title3</em> arg = string
-    string = text to print as 3rd line of output file
+  all = output is sum of atoms across all <em>Nrepeat</em> samples, divided by atom count
+  sample = output is sum of <em>Nrepeat</em> sample averages, divided by <em>Nrepeat</em>
+  none = output is sum of <em>Nrepeat</em> sums, divided by <em>Nrepeat</em>
+<em>ave</em> args = <em>one</em> or <em>running</em> or <em>window M</em>
+  one = output new average value every Nfreq steps
+  running = output cumulative average of all previous Nfreq steps
+  window M = output average of M most recent Nfreq steps
+<em>bias</em> arg = bias-ID
+  bias-ID = ID of a temperature compute that removes a velocity bias for temperature calculation
+<em>adof</em> value = dof_per_atom
+  dof_per_atom = define this many degrees-of-freedom per atom for temperature calculation
+<em>cdof</em> value = dof_per_chunk
+  dof_per_chunk = define this many degrees-of-freedom per chunk for temperature calculation
+<em>file</em> arg = filename
+  filename = file to write results to
+<em>overwrite</em> arg = none = overwrite output file with only latest output
+<em>title1</em> arg = string
+  string = text to print as 1st line of output file
+<em>title2</em> arg = string
+  string = text to print as 2nd line of output file
+<em>title3</em> arg = string
+  string = text to print as 3rd line of output file
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix 1 all ave/chunk 10000 1 10000 binchunk c_myCentro title1 &quot;My output values&quot;
 fix 1 flow ave/chunk 100 10 1000 molchunk vx vz norm sample file vel.profile
 fix 1 flow ave/chunk 100 5 1000 binchunk density/mass ave running
 fix 1 flow ave/chunk 100 5 1000 binchunk density/mass ave running
 </pre></div>
 </div>
 <p><strong>IMPORTANT NOTE:</strong></p>
 <p>If you are trying to replace an older fix ave/spatial command with the
 newer, more flexible fix ave/chunk and <a class="reference internal" href="compute_chunk_atom.html"><em>compute chunk/atom</em></a> commands, you simply need to split
 the fix ave/spatial arguments across the two new commands.  For
 example, this command:</p>
 <div class="highlight-python"><div class="highlight"><pre>fix 1 flow ave/spatial 100 10 1000 y 0.0 1.0 vx vz norm sample file vel.profile
 </pre></div>
 </div>
 <p>could be replaced by:</p>
 <div class="highlight-python"><div class="highlight"><pre>compute cc1 flow chunk/atom bin/1d y 0.0 1.0
 fix 1 flow ave/chunk 100 10 1000 cc1 vx vz norm sample file vel.profile
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Use one or more per-atom vectors as inputs every few timesteps, sum
 the values over the atoms in each chunk at each timestep, then average
 the per-chunk values over longer timescales.  The resulting chunk
 averages can be used by other <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a> such as <a class="reference internal" href="thermo_style.html"><em>thermo_style custom</em></a>, and can also be written to a file.</p>
 <p>In LAMMPS, chunks are collections of atoms defined by a <a class="reference internal" href="compute_chunk_atom.html"><em>compute chunk/atom</em></a> command, which assigns each atom
 to a single chunk (or no chunk).  The ID for this command is specified
 as chunkID.  For example, a single chunk could be the atoms in a
 molecule or atoms in a spatial bin.  See the <a class="reference internal" href="compute_chunk_atom.html"><em>compute chunk/atom</em></a> doc page and &#8220;<a class="reference internal" href="Section_howto.html#howto-23"><span>Section_howto 23</span></a> for details of how chunks can be
 defined and examples of how they can be used to measure properties of
 a system.</p>
 <p>Note that only atoms in the specified group contribute to the summing
 and averaging calculations.  The <a class="reference internal" href="compute_chunk_atom.html"><em>compute chunk/atom</em></a> command defines its own group as
 well as an optional region.  Atoms will have a chunk ID = 0, meaning
 they belong to no chunk, if they are not in that group or region.
 Thus you can specify the &#8220;all&#8221; group for this command if you simply
 want to use the chunk definitions provided by chunkID.</p>
 <p>Each specified per-atom value can be an atom attribute (position,
 velocity, force component), a mass or number density, or the result of
 a <a class="reference internal" href="compute.html"><em>compute</em></a> or <a class="reference internal" href="fix.html"><em>fix</em></a> or the evaluation of an
 atom-style <a class="reference internal" href="variable.html"><em>variable</em></a>.  In the latter cases, the
 compute, fix, or variable must produce a per-atom quantity, not a
 global quantity.  Note that the <a class="reference internal" href="compute_property_atom.html"><em>compute property/atom</em></a> command provides access to
 any attribute defined and stored by atoms.  If you wish to
 time-average global quantities from a compute, fix, or variable, then
 see the <a class="reference internal" href="fix_ave_time.html"><em>fix ave/time</em></a> command.</p>
 <p><a class="reference internal" href="compute.html"><em>Computes</em></a> that produce per-atom quantities are those
 which have the word <em>atom</em> in their style name.  See the doc pages for
 individual <a class="reference internal" href="fix.html"><em>fixes</em></a> to determine which ones produce per-atom
 quantities.  <a class="reference internal" href="variable.html"><em>Variables</em></a> of style <em>atom</em> are the only
 ones that can be used with this fix since all other styles of variable
 produce global quantities.</p>
 <p>The per-atom values of each input vector are summed and averaged
 independently of the per-atom values in other input vectors.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">This fix works by creating an array of size <em>Nchunk</em>
 by Nvalues on each processor.  <em>Nchunk</em> is the number of chunks which
 is defined by the <code class="xref doc docutils literal"><span class="pre">compute</span> <span class="pre">chunk/atom</span></code>
 command.  Nvalues is the number of input values specified.  Each
 processor loops over its atoms, tallying its values to the appropriate
 chunk.  Then the entire array is summed across all processors.  This
 means that using a large number of chunks will incur an overhead in
 memory and computational cost (summing across processors), so be
 careful to define a reasonable number of chunks.</p>
 </div>
 <hr class="docutils" />
 <p>The <em>Nevery</em>, <em>Nrepeat</em>, and <em>Nfreq</em> arguments specify on what
 timesteps the input values will be accessed and contribute to the
 average.  The final averaged quantities are generated on timesteps
 that are a multiples of <em>Nfreq</em>.  The average is over <em>Nrepeat</em>
 quantities, computed in the preceding portion of the simulation every
 <em>Nevery</em> timesteps.  <em>Nfreq</em> must be a multiple of <em>Nevery</em> and
 <em>Nevery</em> must be non-zero even if <em>Nrepeat</em> is 1.  Also, the timesteps
 contributing to the average value cannot overlap, i.e. Nfreq &gt;
 (Nrepeat-1)*Nevery is required.</p>
 <p>For example, if Nevery=2, Nrepeat=6, and Nfreq=100, then values on
 timesteps 90,92,94,96,98,100 will be used to compute the final average
 on timestep 100.  Similarly for timesteps 190,192,194,196,198,200 on
 timestep 200, etc.  If Nrepeat=1 and Nfreq = 100, then no time
 averaging is done; values are simply generated on timesteps
 100,200,etc.</p>
 <p>Each input value can also be averaged over the atoms in each chunk.
 The way the averaging is done across the <em>Nrepeat</em> timesteps to
 produce output on the <em>Nfreq</em> timesteps, and across multiple <em>Nfreq</em>
 outputs, is determined by the <em>norm</em> and <em>ave</em> keyword settings, as
 discussed below.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">To perform per-chunk averaging within a <em>Nfreq</em> time
 window, the number of chunks <em>Nchunk</em> defined by the <a class="reference internal" href="compute_chunk_atom.html"><em>compute chunk/atom</em></a> command must remain constant.  If
 the <em>ave</em> keyword is set to <em>running</em> or <em>window</em> then <em>Nchunk</em> must
 remain constant for the duration of the simulation.  This fix forces
 the chunk/atom compute specified by chunkID to hold <em>Nchunk</em> constant
 for the appropriate time windows, by not allowing it to re-calcualte
 <em>Nchunk</em>, which can also affect how it assigns chunk IDs to atoms.
 More details are given on the <a class="reference internal" href="compute_chunk_atom.html"><em>compute chunk/atom</em></a> doc page.</p>
 </div>
 <hr class="docutils" />
 <p>The atom attribute values (vx,vy,vz,fx,fy,fz) are self-explanatory.
 As noted above, any other atom attributes can be used as input values
 to this fix by using the <a class="reference internal" href="compute_property_atom.html"><em>compute property/atom</em></a> command and then specifying
 an input value from that compute.</p>
 <p>The <em>density/number</em> value means the number density is computed for
 each chunk, i.e. number/volume.  The <em>density/mass</em> value means the
 mass density is computed for each chunk, i.e. total-mass/volume.  The
 output values are in units of 1/volume or density (mass/volume).  See
 the <a class="reference internal" href="units.html"><em>units</em></a> command doc page for the definition of density
 for each choice of units, e.g. gram/cm^3.  If the chunks defined by
 the <a class="reference internal" href="compute_chunk_atom.html"><em>compute chunk/atom</em></a> command are spatial
 bins, the volume is the bin volume.  Otherwise it is the volume of the
 entire simulation box.</p>
 <p>The <em>temp</em> value means the temperature is computed for each chunk, by
 the formula KE = DOF/2 k T, where KE = total kinetic energy of the
 chunk of atoms (sum of 1/2 m v^2), DOF = the total number of degrees
 of freedom for all atoms in the chunk, k = Boltzmann constant, and T =
 temperature.</p>
 <p>The DOF is calculated as N*adof + cdof, where N = number of atoms in
 the chunk, adof = degrees of freedom per atom, and cdof = degrees of
 freedom per chunk.  By default adof = 2 or 3 = dimensionality of
 system, as set via the <a class="reference internal" href="dimension.html"><em>dimension</em></a> command, and cdof =
 0.0.  This gives the usual formula for temperature.</p>
 <p>Note that currently this temperature only includes translational
 degrees of freedom for each atom.  No rotational degrees of freedom
 are included for finite-size particles.  Also no degrees of freedom
 are subtracted for any velocity bias or constraints that are applied,
 such as <a class="reference internal" href="compute_temp_partial.html"><em>compute temp/partial</em></a>, or <a class="reference internal" href="fix_shake.html"><em>fix shake</em></a> or <a class="reference internal" href="fix_rigid.html"><em>fix rigid</em></a>.  This is because
 those degrees of freedom (e.g. a constrained bond) could apply to sets
 of atoms that are both included and excluded from a specific chunk,
 and hence the concept is somewhat ill-defined.  In some cases, you can
 use the <em>adof</em> and <em>cdof</em> keywords to adjust the calculated degress of
 freedom appropriately, as explained below.</p>
 <p>Also note that a bias can be subtracted from atom velocities before
 they are used in the above formula for KE, by using the <em>bias</em>
 keyword.  This allows, for example, a thermal temperature to be
 computed after removal of a flow velocity profile.</p>
 <p>Note that the per-chunk temperature calculated by this fix and the
 <a class="reference internal" href="compute_temp_chunk.html"><em>compute temp/chunk</em></a> command can be different.
 The compute calculates the temperature for each chunk for a single
 snapshot.  This fix can do that but can also time average those values
 over many snapshots, or it can compute a temperature as if the atoms
 in the chunk on different timesteps were collected together as one set
 of atoms to calculate their temperature.  The compute allows the
 center-of-mass velocity of each chunk to be subtracted before
 calculating the temperature; this fix does not.</p>
 <p>If a value begins with &#8220;<a href="#id1"><span class="problematic" id="id2">c_</span></a>&#8221;, a compute ID must follow which has been
 previously defined in the input script.  If no bracketed integer is
 appended, the per-atom vector calculated by the compute is used.  If a
 bracketed integer is appended, the Ith column of the per-atom array
 calculated by the compute is used.  Users can also write code for
 their own compute styles and <a class="reference internal" href="Section_modify.html"><em>add them to LAMMPS</em></a>.</p>
 <p>If a value begins with &#8220;<a href="#id3"><span class="problematic" id="id4">f_</span></a>&#8221;, a fix ID must follow which has been
 previously defined in the input script.  If no bracketed integer is
 appended, the per-atom vector calculated by the fix is used.  If a
 bracketed integer is appended, the Ith column of the per-atom array
 calculated by the fix is used.  Note that some fixes only produce
 their values on certain timesteps, which must be compatible with
 <em>Nevery</em>, else an error results.  Users can also write code for their
 own fix styles and <a class="reference internal" href="Section_modify.html"><em>add them to LAMMPS</em></a>.</p>
 <p>If a value begins with &#8220;<a href="#id5"><span class="problematic" id="id6">v_</span></a>&#8221;, a variable name must follow which has
 been previously defined in the input script.  Variables of style
 <em>atom</em> can reference thermodynamic keywords and various per-atom
 attributes, or invoke other computes, fixes, or variables when they
 are evaluated, so this is a very general means of generating per-atom
 quantities to average within chunks.</p>
 <hr class="docutils" />
 <p>Additional optional keywords also affect the operation of this fix
 and its outputs.</p>
 <p>The <em>norm</em> keyword affects how averaging is done for the per-chunk
 values that are output every <em>Nfreq</em> timesteps.</p>
 <p>It the <em>norm</em> setting is <em>all</em>, which is the default, a chunk value is
 summed over all atoms in all <em>Nrepeat</em> samples, as is the count of
 atoms in the chunk.  The averaged output value for the chunk on the
 <em>Nfreq</em> timesteps is Total-sum / Total-count.  In other words it is an
 average over atoms across the entire <em>Nfreq</em> timescale.</p>
 <p>If the <em>norm</em> setting is <em>sample</em>, the chunk value is summed over atoms
 for each sample, as is the count, and an &#8220;average sample value&#8221; is
 computed for each sample, i.e. Sample-sum / Sample-count.  The outuput
 value for the chunk on the <em>Nfreq</em> timesteps is the average of the
 <em>Nrepeat</em> &#8220;average sample values&#8221;, i.e. the sum of <em>Nrepeat</em> &#8220;average
 sample values&#8221; divided by <em>Nrepeat</em>.  In other words it is an average
 of an average.</p>
 <p>If the <em>norm</em> setting is <em>none</em>, a similar computation as for the
 <em>sample</em> seting is done, except the individual &#8220;average sample values&#8221;
 are &#8220;summed sample values&#8221;.  A summed sample value is simply the chunk
 value summed over atoms in the sample, without dividing by the number
 of atoms in the sample.  The outuput value for the chunk on the
 <em>Nfreq</em> timesteps is the average of the <em>Nrepeat</em> &#8220;summed sample
 values&#8221;, i.e. the sum of <em>Nrepeat</em> &#8220;summed sample values&#8221; divided by
 <em>Nrepeat</em>.</p>
 <p>The <em>ave</em> keyword determines how the per-chunk values produced every
 <em>Nfreq</em> steps are averaged with values produced on previous steps that
 were multiples of <em>Nfreq</em>, before they are accessed by another output
 command or written to a file.</p>
 <p>If the <em>ave</em> setting is <em>one</em>, which is the default, then the chunk
 values produced on timesteps that are multiples of <em>Nfreq</em> are
 independent of each other; they are output as-is without further
 averaging.</p>
 <p>If the <em>ave</em> setting is <em>running</em>, then the chunk values produced on
 timesteps that are multiples of <em>Nfreq</em> are summed and averaged in a
 cumulative sense before being output.  Each output chunk value is thus
 the average of the chunk value produced on that timestep with all
 preceding values for the same chunk.  This running average begins when
 the fix is defined; it can only be restarted by deleting the fix via
 the <a class="reference internal" href="unfix.html"><em>unfix</em></a> command, or re-defining the fix by
 re-specifying it.</p>
 <p>If the <em>ave</em> setting is <em>window</em>, then the chunk values produced on
 timesteps that are multiples of <em>Nfreq</em> are summed and averaged within
 a moving &#8220;window&#8221; of time, so that the last M values for the same
 chunk are used to produce the output.  E.g. if M = 3 and Nfreq = 1000,
 then the output on step 10000 will be the average of the individual
 chunk values on steps 8000,9000,10000.  Outputs on early steps will
 average over less than M values if they are not available.</p>
 <p>The <em>bias</em> keyword specifies the ID of a temperature compute that
 removes a &#8220;bias&#8221; velocity from each atom, specified as <em>bias-ID</em>.  It
 is only used when the <em>temp</em> value is calculated, to compute the
 thermal temperature of each chunk after the translational kinetic
 energy components have been altered in a prescribed way, e.g.  to
 remove a flow velocity profile.  See the doc pages for individual
 computes that calculate a temperature to see which ones implement a
 bias.</p>
 <p>The <em>adof</em> and <em>cdof</em> keywords define the values used in the degree of
 freedom (DOF) formula described above for for temperature calculation
 for each chunk.  They are only used when the <em>temp</em> value is
 calculated.  They can be used to calculate a more appropriate
 temperature for some kinds of chunks.  Here are 3 examples:</p>
 <p>If spatially binned chunks contain some number of water molecules and
 <a class="reference internal" href="fix_shake.html"><em>fix shake</em></a> is used to make each molecule rigid, then
 you could calculate a temperature with 6 degrees of freedom (DOF) (3
 translational, 3 rotational) per molecule by setting <em>adof</em> to 2.0.</p>
 <p>If <a class="reference internal" href="compute_temp_partial.html"><em>compute temp/partial</em></a> is used with the
 <em>bias</em> keyword to only allow the x component of velocity to contribute
 to the temperature, then <em>adof</em> = 1.0 would be appropriate.</p>
 <p>If each chunk consists of a large molecule, with some number of its
 bonds constrained by <a class="reference internal" href="fix_shake.html"><em>fix shake</em></a> or the entire molecule
 by <a class="reference internal" href="fix_rigid.html"><em>fix rigid/small</em></a>, <em>adof</em> = 0.0 and <em>cdof</em> could be
 set to the remaining degrees of freedom for the entire molecule
 (entire chunk in this case), e.g. 6 for 3d, or 3 for 2d, for a rigid
 molecule.</p>
 <p>The <em>file</em> keyword allows a filename to be specified.  Every <em>Nfreq</em>
 timesteps, a section of chunk info will be written to a text file in
 the following format.  A line with the timestep and number of chunks
 is written.  Then one line per chunk is written, containing the chunk
 ID (1-Nchunk), an optional original ID value, optional coordinate
 values for chunks that represent spatial bins, the number of atoms in
 the chunk, and one or more calculated values.  More explanation of the
 optional values is given below.  The number of values in each line
 corresponds to the number of values specified in the fix ave/chunk
 command.  The number of atoms and the value(s) are summed or average
 quantities, as explained above.</p>
 <p>The <em>overwrite</em> keyword will continuously overwrite the output file
 with the latest output, so that it only contains one timestep worth of
 output.  This option can only be used with the <em>ave running</em> setting.</p>
 <p>The <em>title1</em> and <em>title2</em> and <em>title3</em> keywords allow specification of
 the strings that will be printed as the first 3 lines of the output
 file, assuming the <em>file</em> keyword was used.  LAMMPS uses default
 values for each of these, so they do not need to be specified.</p>
 <p>By default, these header lines are as follows:</p>
 <div class="highlight-python"><div class="highlight"><pre><span class="c"># Chunk-averaged data for fix ID and group name</span>
 <span class="c"># Timestep Number-of-chunks</span>
 <span class="c"># Chunk (OrigID) (Coord1) (Coord2) (Coord3) Ncount value1 value2 ...</span>
 </pre></div>
 </div>
 <p>In the first line, ID and name are replaced with the fix-ID and group
 name.  The second line describes the two values that are printed at
 the first of each section of output.  In the third line the values are
 replaced with the appropriate value names, e.g. fx or c_myCompute**2**.</p>
 <p>The words in parenthesis only appear with corresponding columns if the
 chunk style specified for the <a class="reference internal" href="compute_chunk_atom.html"><em>compute chunk/atom</em></a> command supports them.  The OrigID
 column is only used if the <em>compress</em> keyword was set to <em>yes</em> for the
 <a class="reference internal" href="compute_chunk_atom.html"><em>compute chunk/atom</em></a> command.  This means that
 the original chunk IDs (e.g. molecule IDs) will have been compressed
 to remove chunk IDs with no atoms assigned to them.  Thus a compresed
 chunk ID of 3 may correspond to an original chunk ID or molecule ID of
 415.  The OrigID column will list 415 for the 3rd chunk.</p>
 <p>The CoordN columns only appear if a <em>binning</em> style was used in the
 <a class="reference internal" href="compute_chunk_atom.html"><em>compute chunk/atom</em></a> command.  For <em>bin/1d</em>,
 <em>bin/2d</em>, and <em>bin/3d</em> styles the column values are the center point
 of the bin in the corresponding dimension.  Just Coord1 is used for
 <em>bin/1d</em>, Coord2 is added for <em>bin/2d</em>, Coord3 is added for <em>bin/3d</em>.</p>
 <p>Note that if the value of the <em>units</em> keyword used in the <a class="reference internal" href="compute_chunk_atom.html"><em>compute chunk/atom command</em></a> is <em>box</em> or <em>lattice</em>, the
 coordinate values will be in distance <a class="reference internal" href="units.html"><em>units</em></a>.  If the
 value of the <em>units</em> keyword is <em>reduced</em>, the coordinate values will
 be in unitless reduced units (0-1).</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.  None of the <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> options
 are relevant to this fix.</p>
 <p>This fix computes a global array of values which can be accessed by
 various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  The values can
 only be accessed on timesteps that are multiples of <em>Nfreq</em> since that
 is when averaging is performed.  The global array has # of rows =
 the number of chunks <em>Nchunk</em> as calculated by the specified <a class="reference internal" href="compute_chunk_atom.html"><em>compute chunk/atom</em></a> command.  The # of columns =
 M+1+Nvalues, where M = 1 to 4, depending on whether the optional
 columns for OrigID and CoordN are used, as explained above.
 Following the optional columns, the next column contains the count of
 atoms in the chunk, and the remaining columns are the Nvalue
 quantities.  When the array is accessed with a row I that exceeds the
 current number of chunks, than a 0.0 is returned by the fix instead of
 an error, since the number of chunks can vary as a simulation runs
 depending on how that value is computed by the compute chunk/atom
 command.</p>
 <p>The array values calculated by this fix are treated as &#8220;intensive&#8221;,
 since they are typically already normalized by the count of atoms in
 each chunk.</p>
 <p>No parameter of this fix can be used with the <em>start/stop</em> keywords of
 the <a class="reference internal" href="run.html"><em>run</em></a> command.  This fix is not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <blockquote>
 <div>none</div></blockquote>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="compute.html"><em>compute</em></a>, <a class="reference internal" href="fix_ave_atom.html"><em>fix ave/atom</em></a>, <a class="reference internal" href="fix_ave_histo.html"><em>fix ave/histo</em></a>, <a class="reference internal" href="fix_ave_time.html"><em>fix ave/time</em></a>,
 <a class="reference internal" href="variable.html"><em>variable</em></a>, <a class="reference internal" href="fix_ave_correlate.html"><em>fix ave/correlate</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The option defaults are norm = all, ave = one, bias = none, no file output, and
 title 1,2,3 = strings as described above.</p>
 </div>
 </div>
 
 
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   <div class="section" id="fix-ave-correlate-command">
 <span id="index-0"></span><h1>fix ave/correlate command<a class="headerlink" href="#fix-ave-correlate-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID ave/correlate Nevery Nrepeat Nfreq value1 value2 ... keyword args ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>ave/correlate = style name of this fix command</li>
 <li>Nevery = use input values every this many timesteps</li>
 <li>Nrepeat = # of correlation time windows to accumulate</li>
 <li>Nfreq = calculate tine window averages every this many timesteps</li>
 <li>one or more input values can be listed</li>
 <li>value = c_ID, c_ID[N], f_ID, f_ID[N], v_name</li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>c_ID = global scalar calculated by a compute with ID
-  c_ID[I] = Ith component of global vector calculated by a compute with ID
-  f_ID = global scalar calculated by a fix with ID
-  f_ID[I] = Ith component of global vector calculated by a fix with ID
-  v_name = global value calculated by an equal-style variable with name
+c_ID[I] = Ith component of global vector calculated by a compute with ID
+f_ID = global scalar calculated by a fix with ID
+f_ID[I] = Ith component of global vector calculated by a fix with ID
+v_name = global value calculated by an equal-style variable with name
 </pre></div>
 </div>
 <ul class="simple">
 <li>zero or more keyword/arg pairs may be appended</li>
 <li>keyword = <em>type</em> or <em>ave</em> or <em>start</em> or <em>prefactor</em> or <em>file</em> or <em>overwrite</em> or <em>title1</em> or <em>title2</em> or <em>title3</em></li>
 </ul>
 <pre class="literal-block">
 <em>type</em> arg = <em>auto</em> or <em>upper</em> or <em>lower</em> or <em>auto/upper</em> or <em>auto/lower</em> or <em>full</em>
-    auto = correlate each value with itself
-    upper = correlate each value with each succeeding value
-    lower = correlate each value with each preceding value
-    auto/upper = auto + upper
-    auto/lower = auto + lower
-    full = correlate each value with every other value, including itself = auto + upper + lower
-  <em>ave</em> args = <em>one</em> or <em>running</em>
-    one = zero the correlation accumulation every Nfreq steps
-    running = accumulate correlations continuously
-  <em>start</em> args = Nstart
-    Nstart = start accumulating correlations on this timestep
-  <em>prefactor</em> args = value
-    value = prefactor to scale all the correlation data by
-  <em>file</em> arg = filename
-    filename = name of file to output correlation data to
-  <em>overwrite</em> arg = none = overwrite output file with only latest output
-  <em>title1</em> arg = string
-    string = text to print as 1st line of output file
-  <em>title2</em> arg = string
-    string = text to print as 2nd line of output file
-  <em>title3</em> arg = string
-    string = text to print as 3rd line of output file
+  auto = correlate each value with itself
+  upper = correlate each value with each succeeding value
+  lower = correlate each value with each preceding value
+  auto/upper = auto + upper
+  auto/lower = auto + lower
+  full = correlate each value with every other value, including itself = auto + upper + lower
+<em>ave</em> args = <em>one</em> or <em>running</em>
+  one = zero the correlation accumulation every Nfreq steps
+  running = accumulate correlations continuously
+<em>start</em> args = Nstart
+  Nstart = start accumulating correlations on this timestep
+<em>prefactor</em> args = value
+  value = prefactor to scale all the correlation data by
+<em>file</em> arg = filename
+  filename = name of file to output correlation data to
+<em>overwrite</em> arg = none = overwrite output file with only latest output
+<em>title1</em> arg = string
+  string = text to print as 1st line of output file
+<em>title2</em> arg = string
+  string = text to print as 2nd line of output file
+<em>title3</em> arg = string
+  string = text to print as 3rd line of output file
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix 1 all ave/correlate 5 100 1000 c_myTemp file temp.correlate
 fix 1 all ave/correlate 1 50 10000 &amp;
           c_thermo_press[1] c_thermo_press[2] c_thermo_press[3] &amp;
        type upper ave running title1 &quot;My correlation data&quot;
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Use one or more global scalar values as inputs every few timesteps,
 calculate time correlations bewteen them at varying time intervals,
 and average the correlation data over longer timescales.  The
 resulting correlation values can be time integrated by
 <a class="reference internal" href="variable.html"><em>variables</em></a> or used by other <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a> such as <a class="reference internal" href="thermo_style.html"><em>thermo_style custom</em></a>, and can also be written to a file.</p>
 <p>The group specified with this command is ignored.  However, note that
 specified values may represent calculations performed by computes and
 fixes which store their own &#8220;group&#8221; definitions.</p>
 <p>Each listed value can be the result of a <a class="reference internal" href="compute.html"><em>compute</em></a> or
 <a class="reference internal" href="fix.html"><em>fix</em></a> or the evaluation of an equal-style
 <a class="reference internal" href="variable.html"><em>variable</em></a>.  In each case, the compute, fix, or variable
 must produce a global quantity, not a per-atom or local quantity.  If
 you wish to spatial- or time-average or histogram per-atom quantities
 from a compute, fix, or variable, then see the <a class="reference internal" href="fix_ave_spatial.html"><em>fix ave/spatial</em></a>, <a class="reference internal" href="fix_ave_atom.html"><em>fix ave/atom</em></a>,
 or <a class="reference internal" href="fix_ave_histo.html"><em>fix ave/histo</em></a> commands.  If you wish to sum a
 per-atom quantity into a single global quantity, see the <a class="reference internal" href="compute_reduce.html"><em>compute reduce</em></a> command.</p>
 <p><a class="reference internal" href="compute.html"><em>Computes</em></a> that produce global quantities are those which
 do not have the word <em>atom</em> in their style name.  Only a few
 <a class="reference internal" href="fix.html"><em>fixes</em></a> produce global quantities.  See the doc pages for
 individual fixes for info on which ones produce such values.
 <a class="reference internal" href="variable.html"><em>Variables</em></a> of style <em>equal</em> are the only ones that can
 be used with this fix.  Variables of style <em>atom</em> cannot be used,
 since they produce per-atom values.</p>
 <p>The input values must either be all scalars.  What kinds of
 correlations between input values are calculated is determined by the
 <em>type</em> keyword as discussed below.</p>
 <hr class="docutils" />
 <p>The <em>Nevery</em>, <em>Nrepeat</em>, and <em>Nfreq</em> arguments specify on what
 timesteps the input values will be used to calculate correlation data.
 The input values are sampled every <em>Nevery</em> timesteps.  The
 correlation data for the preceding samples is computed on timesteps
 that are a multiple of <em>Nfreq</em>.  Consider a set of samples from some
 initial time up to an output timestep.  The initial time could be the
 beginning of the simulation or the last output time; see the <em>ave</em>
 keyword for options.  For the set of samples, the correlation value
 Cij is calculated as:</p>
 <div class="highlight-python"><div class="highlight"><pre><span class="n">Cij</span><span class="p">(</span><span class="n">delta</span><span class="p">)</span> <span class="o">=</span> <span class="n">ave</span><span class="p">(</span><span class="n">Vi</span><span class="p">(</span><span class="n">t</span><span class="p">)</span><span class="o">*</span><span class="n">Vj</span><span class="p">(</span><span class="n">t</span><span class="o">+</span><span class="n">delta</span><span class="p">))</span>
 </pre></div>
 </div>
 <p>which is the correlation value between input values Vi and Vj,
 separated by time delta.  Note that the second value Vj in the pair is
 always the one sampled at the later time.  The ave() represents an
 average over every pair of samples in the set that are separated by
 time delta.  The maximum delta used is of size (<em>Nrepeat</em>-1)**Nevery*.
 Thus the correlation between a pair of input values yields <em>Nrepeat</em>
 correlation datums:</p>
 <div class="highlight-python"><div class="highlight"><pre><span class="n">Cij</span><span class="p">(</span><span class="mi">0</span><span class="p">),</span> <span class="n">Cij</span><span class="p">(</span><span class="n">Nevery</span><span class="p">),</span> <span class="n">Cij</span><span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">Nevery</span><span class="p">),</span> <span class="o">...</span><span class="p">,</span> <span class="n">Cij</span><span class="p">((</span><span class="n">Nrepeat</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="o">*</span><span class="n">Nevery</span><span class="p">)</span>
 </pre></div>
 </div>
 <p>For example, if Nevery=5, Nrepeat=6, and Nfreq=100, then values on
 timesteps 0,5,10,15,...,100 will be used to compute the final averages
 on timestep 100.  Six averages will be computed: Cij(0), Cij(5),
 Cij(10), Cij(15), Cij(20), and Cij(25).  Cij(10) on timestep 100 will
 be the average of 19 samples, namely Vi(0)*Vj(10), Vi(5)*Vj(15),
 Vi(10)*V j20), Vi(15)*Vj(25), ..., Vi(85)*Vj(95), Vi(90)*Vj(100).</p>
 <p><em>Nfreq</em> must be a multiple of <em>Nevery</em>; <em>Nevery</em> and <em>Nrepeat</em> must be
 non-zero.  Also, if the <em>ave</em> keyword is set to <em>one</em> which is the
 default, then <em>Nfreq</em> &gt;= (<em>Nrepeat</em>-1)**Nevery* is required.</p>
 <hr class="docutils" />
 <p>If a value begins with &#8220;<a href="#id3"><span class="problematic" id="id4">c_</span></a>&#8221;, a compute ID must follow which has been
 previously defined in the input script.  If no bracketed term is
 appended, the global scalar calculated by the compute is used.  If a
 bracketed term is appended, the Ith element of the global vector
 calculated by the compute is used.</p>
 <p>Note that there is a <a class="reference internal" href="compute_reduce.html"><em>compute reduce</em></a> command
 which can sum per-atom quantities into a global scalar or vector which
 can thus be accessed by fix ave/correlate.  Or it can be a compute
 defined not in your input script, but by <a class="reference internal" href="thermo_style.html"><em>thermodynamic output</em></a> or other fixes such as <a class="reference internal" href="fix_nh.html"><em>fix nvt</em></a>
 or <a class="reference internal" href="fix_temp_rescale.html"><em>fix temp/rescale</em></a>.  See the doc pages for
 these commands which give the IDs of these computes.  Users can also
 write code for their own compute styles and <a class="reference internal" href="Section_modify.html"><em>add them to LAMMPS</em></a>.</p>
 <p>If a value begins with &#8220;<a href="#id5"><span class="problematic" id="id6">f_</span></a>&#8221;, a fix ID must follow which has been
 previously defined in the input script.  If no bracketed term is
 appended, the global scalar calculated by the fix is used.  If a
 bracketed term is appended, the Ith element of the global vector
 calculated by the fix is used.</p>
 <p>Note that some fixes only produce their values on certain timesteps,
 which must be compatible with <em>Nevery</em>, else an error will result.
 Users can also write code for their own fix styles and <a class="reference internal" href="Section_modify.html"><em>add them to LAMMPS</em></a>.</p>
 <p>If a value begins with &#8220;<a href="#id7"><span class="problematic" id="id8">v_</span></a>&#8221;, a variable name must follow which has
 been previously defined in the input script.  Only equal-style
 variables can be referenced.  See the <a class="reference internal" href="variable.html"><em>variable</em></a> command
 for details.  Note that variables of style <em>equal</em> define a formula
 which can reference individual atom properties or thermodynamic
 keywords, or they can invoke other computes, fixes, or variables when
 they are evaluated, so this is a very general means of specifying
 quantities to time correlate.</p>
 <hr class="docutils" />
 <p>Additional optional keywords also affect the operation of this fix.</p>
 <p>The <em>type</em> keyword determines which pairs of input values are
 correlated with each other.  For N input values Vi, for i = 1 to N,
 let the number of pairs = Npair.  Note that the second value in the
 pair Vi(t)*Vj(t+delta) is always the one sampled at the later time.</p>
 <ul class="simple">
 <li>If <em>type</em> is set to <em>auto</em> then each input value is correlated with
 itself.  I.e. Cii = Vi*Vi, for i = 1 to N, so Npair = N.</li>
 <li>If <em>type</em> is set
 to <em>upper</em> then each input value is correlated with every succeeding
 value.  I.e. Cij = Vi*Vj, for i &lt; j, so Npair = N*(N-1)/2.</li>
 <li>If <em>type</em> is set
 to <em>lower</em> then each input value is correlated with every preceeding
 value.  I.e. Cij = Vi*Vj, for i &gt; j, so Npair = N*(N-1)/2.</li>
 <li>If <em>type</em> is set to <em>auto/upper</em> then each input value is correlated
 with itself and every succeeding value.  I.e. Cij = Vi*Vj, for i &gt;= j,
 so Npair = N*(N+1)/2.</li>
 <li>If <em>type</em> is set to <em>auto/lower</em> then each input value is correlated
 with itself and every preceding value.  I.e. Cij = Vi*Vj, for i &lt;= j,
 so Npair = N*(N+1)/2.</li>
 <li>If <em>type</em> is set to <em>full</em> then each input value is correlated with
 itself and every other value.  I.e. Cij = Vi*Vj, for i,j = 1,N so
 Npair = N^2.</li>
 </ul>
 <p>The <em>ave</em> keyword determines what happens to the accumulation of
 correlation samples every <em>Nfreq</em> timesteps.  If the <em>ave</em> setting is
 <em>one</em>, then the accumulation is restarted or zeroed every <em>Nfreq</em>
 timesteps.  Thus the outputs on successive <em>Nfreq</em> timesteps are
 essentially independent of each other.  The exception is that the
 Cij(0) = Vi(T)*Vj(T) value at a timestep T, where T is a multiple of
 <em>Nfreq</em>, contributes to the correlation output both at time T and at
 time T+Nfreq.</p>
 <p>If the <em>ave</em> setting is <em>running</em>, then the accumulation is never
 zeroed.  Thus the output of correlation data at any timestep is the
 average over samples accumulated every <em>Nevery</em> steps since the fix
 was defined.  it can only be restarted by deleting the fix via the
 <a class="reference internal" href="unfix.html"><em>unfix</em></a> command, or by re-defining the fix by re-specifying
 it.</p>
 <p>The <em>start</em> keyword specifies what timestep the accumulation of
 correlation samples will begin on.  The default is step 0.  Setting it
 to a larger value can avoid adding non-equilibrated data to the
 correlation averages.</p>
 <p>The <em>prefactor</em> keyword specifies a constant which will be used as a
 multiplier on the correlation data after it is averaged.  It is
 effectively a scale factor on Vi*Vj, which can be used to account for
 the size of the time window or other unit conversions.</p>
 <p>The <em>file</em> keyword allows a filename to be specified.  Every <em>Nfreq</em>
 steps, an array of correlation data is written to the file.  The
 number of rows is <em>Nrepeat</em>, as described above.  The number of
 columns is the Npair+2, also as described above.  Thus the file ends
 up to be a series of these array sections.</p>
 <p>The <em>overwrite</em> keyword will continuously overwrite the output file
 with the latest output, so that it only contains one timestep worth of
 output.  This option can only be used with the <em>ave running</em> setting.</p>
 <p>The <em>title1</em> and <em>title2</em> and <em>title3</em> keywords allow specification of
 the strings that will be printed as the first 3 lines of the output
 file, assuming the <em>file</em> keyword was used.  LAMMPS uses default
 values for each of these, so they do not need to be specified.</p>
 <p>By default, these header lines are as follows:</p>
 <div class="highlight-python"><div class="highlight"><pre><span class="c"># Time-correlated data for fix ID</span>
 <span class="c"># TimeStep Number-of-time-windows</span>
 <span class="c"># Index TimeDelta Ncount valueI*valueJ valueI*valueJ ...</span>
 </pre></div>
 </div>
 <p>In the first line, ID is replaced with the fix-ID.  The second line
 describes the two values that are printed at the first of each section
 of output.  In the third line the value pairs are replaced with the
 appropriate fields from the fix ave/correlate command.</p>
 <hr class="docutils" />
 <p>Let Sij = a set of time correlation data for input values I and J,
 namely the <em>Nrepeat</em> values:</p>
 <div class="highlight-python"><div class="highlight"><pre>Sij = Cij(0), Cij(Nevery), Cij(2*Nevery), ..., Cij(*Nrepeat-1)*Nevery)
 </pre></div>
 </div>
 <p>As explained below, these datums are output as one column of a global
 array, which is effectively the correlation matrix.</p>
 <p>The <em>trap</em> function defined for <a class="reference internal" href="variable.html"><em>equal-style variables</em></a>
 can be used to perform a time integration of this vector of datums,
 using a trapezoidal rule.  This is useful for calculating various
 quantities which can be derived from time correlation data.  If a
 normalization factor is needed for the time integration, it can be
 included in the variable formula or via the <em>prefactor</em> keyword.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.  None of the <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> options
 are relevant to this fix.</p>
 <p>This fix computes a global array of values which can be accessed by
 various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  The values can
 only be accessed on timesteps that are multiples of <em>Nfreq</em> since that
 is when averaging is performed.  The global array has # of rows =
 <em>Nrepeat</em> and # of columns = Npair+2.  The first column has the time
 delta (in timesteps) between the pairs of input values used to
 calculate the correlation, as described above.  The 2nd column has the
 number of samples contributing to the correlation average, as
 described above.  The remaining Npair columns are for I,J pairs of the
 N input values, as determined by the <em>type</em> keyword, as described
 above.</p>
 <ul class="simple">
 <li>For <em>type</em> = <em>auto</em>, the Npair = N columns are ordered: C11, C22, ...,
 CNN.</li>
 <li>For <em>type</em> = <em>upper</em>, the Npair = N*(N-1)/2 columns are ordered: C12,
 C13, ..., C1N, C23, ..., C2N, C34, ..., CN-1N.</li>
 <li>For <em>type</em> = <em>lower</em>, the Npair = N*(N-1)/2 columns are ordered: C21,
 C31, C32, C41, C42, C43, ..., CN1, CN2, ..., CNN-1.</li>
 <li>For <em>type</em> = <em>auto/upper</em>, the Npair = N*(N+1)/2 columns are ordered:
 C11, C12, C13, ..., C1N, C22, C23, ..., C2N, C33, C34, ..., CN-1N,
 CNN.</li>
 <li>For <em>type</em> = <em>auto/lower</em>, the Npair = N*(N+1)/2 columns are ordered:
 C11, C21, C22, C31, C32, C33, C41, ..., C44, CN1, CN2, ..., CNN-1,
 CNN.</li>
 <li>For <em>type</em> = <em>full</em>, the Npair = N^2 columns are ordered: C11, C12,
 ..., C1N, C21, C22, ..., C2N, C31, ..., C3N, ..., CN1, ..., CNN-1,
 CNN.</li>
 </ul>
 <p>The array values calculated by this fix are treated as &#8220;intensive&#8221;.
 If you need to divide them by the number of atoms, you must do this in
 a later processing step, e.g. when using them in a
 <a class="reference internal" href="variable.html"><em>variable</em></a>.</p>
 <p>No parameter of this fix can be used with the <em>start/stop</em> keywords of
 the <a class="reference internal" href="run.html"><em>run</em></a> command.  This fix is not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <blockquote>
 <div>none</div></blockquote>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="compute.html"><em>compute</em></a>, <a class="reference internal" href="fix_ave_time.html"><em>fix ave/time</em></a>, <a class="reference internal" href="fix_ave_atom.html"><em>fix ave/atom</em></a>, <a class="reference internal" href="fix_ave_spatial.html"><em>fix ave/spatial</em></a>,
 <a class="reference internal" href="fix_ave_histo.html"><em>fix ave/histo</em></a>, <a class="reference internal" href="variable.html"><em>variable</em></a></p>
 <p><strong>Default:</strong> none</p>
 <p>The option defaults are ave = one, type = auto, start = 0, no file
 output, title 1,2,3 = strings as described above, and prefactor = 1.0.</p>
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   <div class="section" id="fix-ave-histo-command">
 <span id="index-0"></span><h1>fix ave/histo command<a class="headerlink" href="#fix-ave-histo-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="fix-ave-histo-weight-command">
 <h1>fix ave/histo/weight command<a class="headerlink" href="#fix-ave-histo-weight-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID style Nevery Nrepeat Nfreq lo hi Nbin value1 value2 ... keyword args ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>style = <em>ave/histo</em> or <em>ave/histo/weight</em> = style name of this fix command</li>
 <li>Nevery = use input values every this many timesteps</li>
 <li>Nrepeat = # of times to use input values for calculating histogram</li>
 <li>Nfreq = calculate histogram every this many timesteps</li>
 <li>lo,hi = lo/hi bounds within which to histogram</li>
 <li>Nbin = # of histogram bins</li>
 <li>one or more input values can be listed</li>
 <li>value = x, y, z, vx, vy, vz, fx, fy, fz, c_ID, c_ID[N], f_ID, f_ID[N], v_name</li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>x,y,z,vx,vy,vz,fx,fy,fz = atom attribute (position, velocity, force component)
-  c_ID = scalar or vector calculated by a compute with ID
-  c_ID[I] = Ith component of vector or Ith column of array calculated by a compute with ID
-  f_ID = scalar or vector calculated by a fix with ID
-  f_ID[I] = Ith component of vector or Ith column of array calculated by a fix with ID
-  v_name = value(s) calculated by an equal-style or atom-style variable with name
+c_ID = scalar or vector calculated by a compute with ID
+c_ID[I] = Ith component of vector or Ith column of array calculated by a compute with ID
+f_ID = scalar or vector calculated by a fix with ID
+f_ID[I] = Ith component of vector or Ith column of array calculated by a fix with ID
+v_name = value(s) calculated by an equal-style or atom-style variable with name
 </pre></div>
 </div>
 <ul class="simple">
 <li>zero or more keyword/arg pairs may be appended</li>
 <li>keyword = <em>mode</em> or <em>file</em> or <em>ave</em> or <em>start</em> or <em>beyond</em> or <em>overwrite</em> or <em>title1</em> or <em>title2</em> or <em>title3</em></li>
 </ul>
 <pre class="literal-block">
 <em>mode</em> arg = <em>scalar</em> or <em>vector</em>
-    scalar = all input values are scalars
-    vector = all input values are vectors
-  <em>file</em> arg = filename
-    filename = name of file to output histogram(s) to
-  <em>ave</em> args = <em>one</em> or <em>running</em> or <em>window</em>
-    one = output a new average value every Nfreq steps
-    running = output cumulative average of all previous Nfreq steps
-    window M = output average of M most recent Nfreq steps
-  <em>start</em> args = Nstart
-    Nstart = start averaging on this timestep
-  <em>beyond</em> arg = <em>ignore</em> or <em>end</em> or <em>extra</em>
-    ignore = ignore values outside histogram lo/hi bounds
-    end = count values outside histogram lo/hi bounds in end bins
-    extra = create 2 extra bins for value outside histogram lo/hi bounds
-  <em>overwrite</em> arg = none = overwrite output file with only latest output
-  <em>title1</em> arg = string
-    string = text to print as 1st line of output file
-  <em>title2</em> arg = string
-    string = text to print as 2nd line of output file
-  <em>title3</em> arg = string
-    string = text to print as 3rd line of output file, only for vector mode
+  scalar = all input values are scalars
+  vector = all input values are vectors
+<em>file</em> arg = filename
+  filename = name of file to output histogram(s) to
+<em>ave</em> args = <em>one</em> or <em>running</em> or <em>window</em>
+  one = output a new average value every Nfreq steps
+  running = output cumulative average of all previous Nfreq steps
+  window M = output average of M most recent Nfreq steps
+<em>start</em> args = Nstart
+  Nstart = start averaging on this timestep
+<em>beyond</em> arg = <em>ignore</em> or <em>end</em> or <em>extra</em>
+  ignore = ignore values outside histogram lo/hi bounds
+  end = count values outside histogram lo/hi bounds in end bins
+  extra = create 2 extra bins for value outside histogram lo/hi bounds
+<em>overwrite</em> arg = none = overwrite output file with only latest output
+<em>title1</em> arg = string
+  string = text to print as 1st line of output file
+<em>title2</em> arg = string
+  string = text to print as 2nd line of output file
+<em>title3</em> arg = string
+  string = text to print as 3rd line of output file, only for vector mode
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix 1 all ave/histo 100 5 1000 0.5 1.5 50 c_myTemp file temp.histo ave running
 fix 1 all ave/histo 100 5 1000 -5 5 100 c_thermo_press[2] c_thermo_press[3] title1 &quot;My output values&quot;
 fix 1 all ave/histo 1 100 1000 -2.0 2.0 18 vx vy vz mode vector ave running beyond extra
 fix 1 all ave/histo/weight 1 1 1 10 100 2000 c_XRD[1] c_XRD[2]
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Use one or more values as inputs every few timesteps, histogram them,
 and average the histogram over longer timescales.  The resulting
 histogram can be used by other <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>, and can also be written to a
 file.  The fix ave/histo/weight command has identical syntax to fix
 ave/histo, except that exactly two values must be specified.  See
 details below.</p>
 <p>The group specified with this command is ignored for global and local
 input values.  For per-atom input values, only atoms in the group
 contribute to the histogram.  Note that regardless of the specified
 group, specified values may represent calculations performed by
 computes and fixes which store their own &#8220;group&#8221; definition.</p>
 <p>A histogram is simply a count of the number of values that fall within
 a histogram bin.  <em>Nbins</em> are defined, with even spacing between <em>lo</em>
 and <em>hi</em>.  Values that fall outside the lo/hi bounds can be treated in
 different ways; see the discussion of the <em>beyond</em> keyword below.</p>
 <p>Each input value can be an atom attribute (position, velocity, force
 component) or can be the result of a <a class="reference internal" href="compute.html"><em>compute</em></a> or
 <a class="reference internal" href="fix.html"><em>fix</em></a> or the evaluation of an equal-style or atom-style
 <a class="reference internal" href="variable.html"><em>variable</em></a>.  The set of input values can be either all
 global, all per-atom, or all local quantities.  Inputs of different
 kinds (e.g. global and per-atom) cannot be mixed.  Atom attributes are
 per-atom vector values.  See the doc page for individual &#8220;compute&#8221; and
 &#8220;fix&#8221; commands to see what kinds of quantities they generate.</p>
 <p>The input values must either be all scalars or all vectors (or
 arrays), depending on the setting of the <em>mode</em> keyword.</p>
 <p>Note that the output of this command is a single histogram for all
 input values combined together, not one histogram per input value.
 See below for details on the format of the output of this fix.</p>
 <p>If <em>mode</em> = vector, then the input values may either be vectors or
 arrays.  If a global array is listed, then it is the same as if the
 individual columns of the array had been listed one by one.
 E.g. these 2 fix ave/histo commands are equivalent, since the <a class="reference internal" href="compute_com_chunk.html"><em>compute com/chunk</em></a> command creates a global array
 with 3 columns:</p>
 <div class="highlight-python"><div class="highlight"><pre>compute myCOM all com/chunk
 fix 1 all ave/histo 100 1 100 c_myCOM file tmp1.com mode vector
 fix 2 all ave/histo 100 1 100 c_myCOM[1] c_myCOM[2] c_myCOM[3] file tmp2.com mode vector
 </pre></div>
 </div>
 <p>If the fix ave/histo/weight command is used, exactly two values must
 be specified.  If the values are vectors, they must be the same
 length.  The first value (a scalar or vector) is what is histogrammed
 into bins, in the same manner the fix ave/histo command operates.  The
 second value (a scalar or vector) is used as a &#8220;weight&#8221;.  This means
 that instead of each value tallying a &#8220;1&#8221; to its bin, the
 corresponding weight is tallied.  E.g. the Nth entry in the first
 vector tallies the Nth entry (weight) in the second vector.</p>
 <hr class="docutils" />
 <p>The <em>Nevery</em>, <em>Nrepeat</em>, and <em>Nfreq</em> arguments specify on what
 timesteps the input values will be used in order to contribute to the
 histogram.  The final histogram is generated on timesteps that are
 multiple of <em>Nfreq</em>.  It is averaged over <em>Nrepeat</em> histograms,
 computed in the preceding portion of the simulation every <em>Nevery</em>
 timesteps.  <em>Nfreq</em> must be a multiple of <em>Nevery</em> and <em>Nevery</em> must
 be non-zero even if <em>Nrepeat</em> is 1.  Also, the timesteps contributing
 to the histogram cannot overlap, i.e. Nfreq &gt; (Nrepeat-1)*Nevery is
 required.</p>
 <p>For example, if Nevery=2, Nrepeat=6, and Nfreq=100, then input values
 on timesteps 90,92,94,96,98,100 will be used to compute the final
 histogram on timestep 100.  Similarly for timesteps
 190,192,194,196,198,200 on timestep 200, etc.  If Nrepeat=1 and Nfreq
 = 100, then no time averaging of the histogram is done; a histogram is
 simply generated on timesteps 100,200,etc.</p>
 <hr class="docutils" />
 <p>The atom attribute values (x,y,z,vx,vy,vz,fx,fy,fz) are
 self-explanatory.  Note that other atom attributes can be used as
 inputs to this fix by using the <a class="reference internal" href="compute_property_atom.html"><em>compute property/atom</em></a> command and then specifying
 an input value from that compute.</p>
 <p>If a value begins with &#8220;<a href="#id1"><span class="problematic" id="id2">c_</span></a>&#8221;, a compute ID must follow which has been
 previously defined in the input script.  If <em>mode</em> = scalar, then if
 no bracketed term is appended, the global scalar calculated by the
 compute is used.  If a bracketed term is appended, the Ith element of
 the global vector calculated by the compute is used.  If <em>mode</em> =
 vector, then if no bracketed term is appended, the global or per-atom
 or local vector calculated by the compute is used.  Or if the compute
 calculates an array, all of the columns of the array are used as if
 they had been specified as individual vectors (see description above).
 If a bracketed term is appended, the Ith column of the global or
 per-atom or local array calculated by the compute is used.</p>
 <p>Note that there is a <a class="reference internal" href="compute_reduce.html"><em>compute reduce</em></a> command
 which can sum per-atom quantities into a global scalar or vector which
 can thus be accessed by fix ave/histo.  Or it can be a compute defined
 not in your input script, but by <a class="reference internal" href="thermo_style.html"><em>thermodynamic output</em></a> or other fixes such as <a class="reference internal" href="fix_nh.html"><em>fix nvt</em></a> or <a class="reference internal" href="fix_temp_rescale.html"><em>fix temp/rescale</em></a>.  See
 the doc pages for these commands which give the IDs of these computes.
 Users can also write code for their own compute styles and <a class="reference internal" href="Section_modify.html"><em>add them to LAMMPS</em></a>.</p>
 <p>If a value begins with &#8220;<a href="#id3"><span class="problematic" id="id4">f_</span></a>&#8221;, a fix ID must follow which has been
 previously defined in the input script.  If <em>mode</em> = scalar, then if
 no bracketed term is appended, the global scalar calculated by the fix
 is used.  If a bracketed term is appended, the Ith element of the
 global vector calculated by the fix is used.  If <em>mode</em> = vector, then
 if no bracketed term is appended, the global or per-atom or local
 vector calculated by the fix is used.  Or if the fix calculates an
 array, all of the columns of the array are used as if they had been
 specified as individual vectors (see description above).  If a
 bracketed term is appended, the Ith column of the global or per-atom
 or local array calculated by the fix is used.</p>
 <p>Note that some fixes only produce their values on certain timesteps,
 which must be compatible with <em>Nevery</em>, else an error will result.
 Users can also write code for their own fix styles and <a class="reference internal" href="Section_modify.html"><em>add them to LAMMPS</em></a>.</p>
 <p>If a value begins with &#8220;<a href="#id5"><span class="problematic" id="id6">v_</span></a>&#8221;, a variable name must follow which has
 been previously defined in the input script.  If <em>mode</em> = scalar, then
 only equal-style variables can be used, which produce a global value.
 If <em>mode</em> = vector, then only atom-style variables can be used, which
 produce a per-atom vector.  See the <a class="reference internal" href="variable.html"><em>variable</em></a> command
 for details.  Note that variables of style <em>equal</em> and <em>atom</em> define a
 formula which can reference individual atom properties or
 thermodynamic keywords, or they can invoke other computes, fixes, or
 variables when they are evaluated, so this is a very general means of
 specifying quantities to histogram.</p>
 <hr class="docutils" />
 <p>Additional optional keywords also affect the operation of this fix.</p>
 <p>If the <em>mode</em> keyword is set to <em>scalar</em>, then all input values must
 be global scalars, or elements of global vectors.  If the <em>mode</em>
 keyword is set to <em>vector</em>, then all input values must be global or
 per-atom or local vectors, or columns of global or per-atom or local
 arrays.</p>
 <p>The <em>beyond</em> keyword determines how input values that fall outside the
 <em>lo</em> to <em>hi</em> bounds are treated.  Values such that <em>lo</em> &lt;= value &lt;=
 <em>hi</em> are assigned to one bin.  Values on a bin boundary are assigned
 to the lower of the 2 bins.  If <em>beyond</em> is set to <em>ignore</em> then
 values &lt; <em>lo</em> and values &gt; <em>hi</em> are ignored, i.e. they are not binned.
 If <em>beyond</em> is set to <em>end</em> then values &lt; <em>lo</em> are counted in the
 first bin and values &gt; <em>hi</em> are counted in the last bin.  If <em>beyond</em>
 is set to <em>extend</em> then two extra bins are created, so that there are
 Nbins+2 total bins.  Values &lt; <em>lo</em> are counted in the first bin and
 values &gt; <em>hi</em> are counted in the last bin (Nbins+1).  Values between
 <em>lo</em> and <em>hi</em> (inclusive) are counted in bins 2 thru Nbins+1.  The
 &#8220;coordinate&#8221; stored and printed for these two extra bins is <em>lo</em> and
 <em>hi</em>.</p>
 <p>The <em>ave</em> keyword determines how the histogram produced every <em>Nfreq</em>
 steps are averaged with histograms produced on previous steps that
 were multiples of <em>Nfreq</em>, before they are accessed by another output
 command or written to a file.</p>
 <p>If the <em>ave</em> setting is <em>one</em>, then the histograms produced on
 timesteps that are multiples of <em>Nfreq</em> are independent of each other;
 they are output as-is without further averaging.</p>
 <p>If the <em>ave</em> setting is <em>running</em>, then the histograms produced on
 timesteps that are multiples of <em>Nfreq</em> are summed and averaged in a
 cumulative sense before being output.  Each bin value in the histogram
 is thus the average of the bin value produced on that timestep with
 all preceding values for the same bin.  This running average begins
 when the fix is defined; it can only be restarted by deleting the fix
 via the <a class="reference internal" href="unfix.html"><em>unfix</em></a> command, or by re-defining the fix by
 re-specifying it.</p>
 <p>If the <em>ave</em> setting is <em>window</em>, then the histograms produced on
 timesteps that are multiples of <em>Nfreq</em> are summed within a moving
 &#8220;window&#8221; of time, so that the last M histograms are used to produce
 the output.  E.g. if M = 3 and Nfreq = 1000, then the output on step
 10000 will be the combined histogram of the individual histograms on
 steps 8000,9000,10000.  Outputs on early steps will be sums over less
 than M histograms if they are not available.</p>
 <p>The <em>start</em> keyword specifies what timestep histogramming will begin
 on.  The default is step 0.  Often input values can be 0.0 at time 0,
 so setting <em>start</em> to a larger value can avoid including a 0.0 in
 a running or windowed histogram.</p>
 <p>The <em>file</em> keyword allows a filename to be specified.  Every <em>Nfreq</em>
 steps, one histogram is written to the file.  This includes a leading
 line that contains the timestep, number of bins, the total count of
 values contributing to the histogram, the count of values that were
 not histogrammed (see the <em>beyond</em> keyword), the minimum value
 encountered, and the maximum value encountered.  The min/max values
 include values that were not histogrammed.  Following the leading
 line, one line per bin is written into the file.  Each line contains
 the bin #, the coordinate for the center of the bin (between <em>lo</em> and
 <em>hi</em>), the count of values in the bin, and the normalized count.  The
 normalized count is the bin count divided by the total count (not
 including values not histogrammed), so that the normalized values sum
 to 1.0 across all bins.</p>
 <p>The <em>overwrite</em> keyword will continuously overwrite the output file
 with the latest output, so that it only contains one timestep worth of
 output.  This option can only be used with the <em>ave running</em> setting.</p>
 <p>The <em>title1</em> and <em>title2</em> and <em>title3</em> keywords allow specification of
 the strings that will be printed as the first 3 lines of the output
 file, assuming the <em>file</em> keyword was used.  LAMMPS uses default
 values for each of these, so they do not need to be specified.</p>
 <p>By default, these header lines are as follows:</p>
 <div class="highlight-python"><div class="highlight"><pre><span class="c"># Histogram for fix ID</span>
 <span class="c"># TimeStep Number-of-bins Total-counts Missing-counts Min-value Max-value</span>
 <span class="c"># Bin Coord Count Count/Total</span>
 </pre></div>
 </div>
 <p>In the first line, ID is replaced with the fix-ID.  The second line
 describes the six values that are printed at the first of each section
 of output.  The third describes the 4 values printed for each bin in
 the histogram.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.  None of the <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> options
 are relevant to this fix.</p>
 <p>This fix produces a global vector and global array which can be
 accessed by various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.
 The values can only be accessed on timesteps that are multiples of
 <em>Nfreq</em> since that is when a histogram is generated.  The global
 vector has 4 values:</p>
 <ul class="simple">
 <li>1 = total counts in the histogram</li>
 <li>2 = values that were not histogrammed (see <em>beyond</em> keyword)</li>
 <li>3 = min value of all input values, including ones not histogrammed</li>
 <li>4 = max value of all input values, including ones not histogrammed</li>
 </ul>
 <p>The global array has # of rows = Nbins and # of columns = 3.  The
 first column has the bin coordinate, the 2nd column has the count of
 values in that histogram bin, and the 3rd column has the bin count
 divided by the total count (not including missing counts), so that the
 values in the 3rd column sum to 1.0.</p>
 <p>The vector and array values calculated by this fix are all treated as
 &#8220;intensive&#8221;.  If this is not the case, e.g. due to histogramming
 per-atom input values, then you will need to account for that when
 interpreting the values produced by this fix.</p>
 <p>No parameter of this fix can be used with the <em>start/stop</em> keywords of
 the <a class="reference internal" href="run.html"><em>run</em></a> command.  This fix is not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <blockquote>
 <div>none</div></blockquote>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="compute.html"><em>compute</em></a>, <a class="reference internal" href="fix_ave_atom.html"><em>fix ave/atom</em></a>, <a class="reference internal" href="fix_ave_spatial.html"><em>fix ave/spatial</em></a>, <a class="reference internal" href="fix_ave_time.html"><em>fix ave/time</em></a>,
 <a class="reference internal" href="variable.html"><em>variable</em></a>, <a class="reference internal" href="fix_ave_correlate.html"><em>fix ave/correlate</em></a>,</p>
 <p><strong>Default:</strong> none</p>
 <p>The option defaults are mode = scalar, ave = one, start = 0, no file
 output, beyond = ignore, and title 1,2,3 = strings as described above.</p>
 </div>
 </div>
 
 
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   <div class="section" id="fix-ave-spatial-command">
 <span id="index-0"></span><h1>fix ave/spatial command<a class="headerlink" href="#fix-ave-spatial-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID ave/spatial Nevery Nrepeat Nfreq dim origin delta ... value1 value2 ... keyword args ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>ave/spatial = style name of this fix command</li>
 <li>Nevery = use input values every this many timesteps</li>
 <li>Nrepeat = # of times to use input values for calculating averages</li>
 <li>Nfreq = calculate averages every this many timesteps</li>
 <li>dim, origin, delta can be repeated 1, 2, or 3 times for 1d, 2d, or 3d bins</li>
 </ul>
 <pre class="literal-block">
 dim = <em>x</em> or <em>y</em> or <em>z</em>
-  origin = <em>lower</em> or <em>center</em> or <em>upper</em> or coordinate value (distance units)
-  delta = thickness of spatial bins in dim (distance units)
+origin = <em>lower</em> or <em>center</em> or <em>upper</em> or coordinate value (distance units)
+delta = thickness of spatial bins in dim (distance units)
 </pre>
 <ul class="simple">
 <li>one or more input values can be listed</li>
 <li>value = vx, vy, vz, fx, fy, fz, density/mass, density/number, c_ID, c_ID[I], f_ID, f_ID[I], v_name</li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>vx,vy,vz,fx,fy,fz = atom attribute (velocity, force component)
-  density/number, density/mass = number or mass density
-  c_ID = per-atom vector calculated by a compute with ID
-  c_ID[I] = Ith column of per-atom array calculated by a compute with ID
-  f_ID = per-atom vector calculated by a fix with ID
-  f_ID[I] = Ith column of per-atom array calculated by a fix with ID
-  v_name = per-atom vector calculated by an atom-style variable with name
+density/number, density/mass = number or mass density
+c_ID = per-atom vector calculated by a compute with ID
+c_ID[I] = Ith column of per-atom array calculated by a compute with ID
+f_ID = per-atom vector calculated by a fix with ID
+f_ID[I] = Ith column of per-atom array calculated by a fix with ID
+v_name = per-atom vector calculated by an atom-style variable with name
 </pre></div>
 </div>
 <ul class="simple">
 <li>zero or more keyword/arg pairs may be appended</li>
 <li>keyword = <em>region</em> or <em>bound</em> or <em>discard</em> or <em>norm</em> or <em>ave</em> or <em>units</em> or <em>file</em> or <em>overwrite</em> or <em>title1</em> or <em>title2</em> or <em>title3</em></li>
 </ul>
 <pre class="literal-block">
 <em>region</em> arg = region-ID
-  <em>bound</em> args = x/y/z lo hi
-    x/y/z = <em>x</em> or <em>y</em> or <em>z</em> to bound bins in this dimension
-    lo = <em>lower</em> or coordinate value (distance units)
-    hi = <em>upper</em> or coordinate value (distance units)
-  <em>discard</em> arg = <em>mixed</em> or <em>no</em> or <em>yes</em>
-    mixed = discard atoms outside bins only if bin bounds are explicitly set
-    no = always keep out-of-bounds atoms
-    yes = always discard out-of-bounds atoms
-  <em>norm</em> arg = <em>all</em> or <em>sample</em>
-    region-ID = ID of region atoms must be in to contribute to spatial averaging
-  <em>ave</em> args = <em>one</em> or <em>running</em> or <em>window M</em>
-    one = output new average value every Nfreq steps
-    running = output cumulative average of all previous Nfreq steps
-    window M = output average of M most recent Nfreq steps
-  <em>units</em> arg = <em>box</em> or <em>lattice</em> or <em>reduced</em>
-  <em>file</em> arg = filename
-    filename = file to write results to
-  <em>overwrite</em> arg = none = overwrite output file with only latest output
-  <em>title1</em> arg = string
-    string = text to print as 1st line of output file
-  <em>title2</em> arg = string
-    string = text to print as 2nd line of output file
-  <em>title3</em> arg = string
-    string = text to print as 3rd line of output file
+<em>bound</em> args = x/y/z lo hi
+  x/y/z = <em>x</em> or <em>y</em> or <em>z</em> to bound bins in this dimension
+  lo = <em>lower</em> or coordinate value (distance units)
+  hi = <em>upper</em> or coordinate value (distance units)
+<em>discard</em> arg = <em>mixed</em> or <em>no</em> or <em>yes</em>
+  mixed = discard atoms outside bins only if bin bounds are explicitly set
+  no = always keep out-of-bounds atoms
+  yes = always discard out-of-bounds atoms
+<em>norm</em> arg = <em>all</em> or <em>sample</em>
+  region-ID = ID of region atoms must be in to contribute to spatial averaging
+<em>ave</em> args = <em>one</em> or <em>running</em> or <em>window M</em>
+  one = output new average value every Nfreq steps
+  running = output cumulative average of all previous Nfreq steps
+  window M = output average of M most recent Nfreq steps
+<em>units</em> arg = <em>box</em> or <em>lattice</em> or <em>reduced</em>
+<em>file</em> arg = filename
+  filename = file to write results to
+<em>overwrite</em> arg = none = overwrite output file with only latest output
+<em>title1</em> arg = string
+  string = text to print as 1st line of output file
+<em>title2</em> arg = string
+  string = text to print as 2nd line of output file
+<em>title3</em> arg = string
+  string = text to print as 3rd line of output file
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix 1 all ave/spatial 10000 1 10000 z lower 0.02 c_myCentro units reduced &amp;
                       title1 &quot;My output values&quot;
 fix 1 flow ave/spatial 100 10 1000 y 0.0 1.0 vx vz norm sample file vel.profile
 fix 1 flow ave/spatial 100 5 1000 z lower 1.0 y 0.0 2.5 density/mass ave running
 fix 1 flow ave/spatial 100 5 1000 z lower 1.0 y 0.0 2.5 density/mass bound y 5.0 20.0 discard yes ave running
 </pre></div>
 </div>
 <p><strong>IMPORTANT NOTE:</strong></p>
 <p>The fix ave/spatial command has been replaced by the more flexible
 <a class="reference internal" href="fix_ave_chunk.html"><em>fix ave/chunk</em></a> and <a class="reference internal" href="compute_chunk_atom.html"><em>compute chunk/atom</em></a> commands.  The fix ave/spatial
 command will be removed from LAMMPS sometime in the summer of 2015.</p>
 <p>Any fix ave/spatial command can be replaced by the two new commands.
 You simply need to split the fix ave/spatial arguments across the two
 new commands.  For example, this command:</p>
 <div class="highlight-python"><div class="highlight"><pre>fix 1 flow ave/spatial 100 10 1000 y 0.0 1.0 vx vz norm sample file vel.profile
 </pre></div>
 </div>
 <p>could be replaced by:</p>
 <div class="highlight-python"><div class="highlight"><pre>compute cc1 flow chunk/atom bin/1d y 0.0 1.0
 fix 1 flow ave/chunk 100 10 1000 cc1 vx vz norm sample file vel.profile
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Use one or more per-atom vectors as inputs every few timesteps, bin
 their values spatially into 1d, 2d, or 3d bins based on current atom
 coordinates, and average the bin values over longer timescales.  The
 resulting bin averages can be used by other <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a> such as <a class="reference internal" href="thermo_style.html"><em>thermo_style custom</em></a>, and can also be written to a file.</p>
 <p>The group specified with the command means only atoms within the group
 contribute to bin averages.  If the <em>region</em> keyword is used, the atom
 must be in both the specified group and the specified geometric
 <a class="reference internal" href="region.html"><em>region</em></a> in order to contribute to bin averages.</p>
 <p>Each listed value can be an atom attribute (position, velocity, force
 component), a mass or number density, or the result of a
 <a class="reference internal" href="compute.html"><em>compute</em></a> or <a class="reference internal" href="fix.html"><em>fix</em></a> or the evaluation of an
 atom-style <a class="reference internal" href="variable.html"><em>variable</em></a>.  In the latter cases, the
 compute, fix, or variable must produce a per-atom quantity, not a
 global quantity.  If you wish to time-average global quantities from a
 compute, fix, or variable, then see the <a class="reference internal" href="fix_ave_time.html"><em>fix ave/time</em></a> command.</p>
 <p><a class="reference internal" href="compute.html"><em>Computes</em></a> that produce per-atom quantities are those
 which have the word <em>atom</em> in their style name.  See the doc pages for
 individual <a class="reference internal" href="fix.html"><em>fixes</em></a> to determine which ones produce per-atom
 quantities.  <a class="reference internal" href="variable.html"><em>Variables</em></a> of style <em>atom</em> are the only
 ones that can be used with this fix since all other styles of variable
 produce global quantities.</p>
 <p>The per-atom values of each input vector are binned and averaged
 independently of the per-atom values in other input vectors.</p>
 <p>The size and dimensionality of the bins (1d = layers or slabs, 2d =
 pencils, 3d = boxes) are determined by the <em>dim</em>, <em>origin</em>, and
 <em>delta</em> settings and how many times they are specified (1, 2, or 3).
 See details below.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">This fix works by creating an array of size Nbins by
 Nvalues on each processor.  Nbins is the total number of bins; Nvalues
 is the number of input values specified.  Each processor loops over
 its atoms, tallying its values to the appropriate bin.  Then the
 entire array is summed across all processors.  This means that using a
 large number of bins (easy to do for 2d or 3d bins) will incur an
 overhead in memory and computational cost (summing across processors),
 so be careful to use reasonable numbers of bins.</p>
 </div>
 <hr class="docutils" />
 <p>The <em>Nevery</em>, <em>Nrepeat</em>, and <em>Nfreq</em> arguments specify on what
 timesteps the input values will be used to bin them and contribute to
 the average.  The final averaged quantities are generated on timesteps
 that are a multiples of <em>Nfreq</em>.  The average is over <em>Nrepeat</em>
 quantities, computed in the preceding portion of the simulation every
 <em>Nevery</em> timesteps.  <em>Nfreq</em> must be a multiple of <em>Nevery</em> and
 <em>Nevery</em> must be non-zero even if <em>Nrepeat</em> is 1.  Also, the timesteps
 contributing to the average value cannot overlap, i.e. Nfreq &gt;
 (Nrepeat-1)*Nevery is required.</p>
 <p>For example, if Nevery=2, Nrepeat=6, and Nfreq=100, then values on
 timesteps 90,92,94,96,98,100 will be used to compute the final average
 on timestep 100.  Similarly for timesteps 190,192,194,196,198,200 on
 timestep 200, etc.  If Nrepeat=1 and Nfreq = 100, then no time
 averaging is done; values are simply generated on timesteps
 100,200,etc.</p>
 <hr class="docutils" />
 <p>Each per-atom property is also averaged over atoms in each bin.  The
 way the averaging is one across the <em>Nrepeat</em> timesteps to produce
 output on the <em>Nfreq</em> timesteps, and across multiple <em>Nfreq</em> outputs,
 is determined by the <em>norm</em> and <em>av</em> keyword settings, as discussed
 below.</p>
 <p>Bins can be 1d layers or slabs, 2d pencils, or 3d boxes.  This depends
 on how many times (1, 2, or 3) the <em>dim</em>, <em>origin</em>, and <em>delta</em>
 settings are specified in the fix ave/spatial command.  For 2d or 3d
 bins, there is no restriction on specifying dim = x before dim = y, or
 dim = y before dim = z.  Bins in a particular <em>dim</em> have a bin size in
 that dimension given by <em>delta</em>.  Every Nfreq steps, when averaging is
 being performed and the per-atom property is calculated for the first
 time, the number of bins and the bin sizes and boundaries are
 computed.  Thus if the simulation box changes size during a
 simulation, the number of bins and their boundaries may also change.
 In each dimension, bins are defined relative to a specified <em>origin</em>,
 which may be the lower/upper edge of the simulation box in that
 dimension, or its center point, or a specified coordinate value.
 Starting at the origin, sufficient bins are created in both directions
 to completely span the bin extent in that dimension.  By default the
 bin extent is the entire simulation box.</p>
 <p>The <em>bound</em> keyword can be used one or more times to limit the extent
 of bin coverage in specified dimensions, i.e. to only bin a portion of
 the box.  If the <em>lo</em> setting is <em>lower</em> or the <em>hi</em> setting is
 <em>upper</em>, the bin extent in that direction extends to the box boundary.
 If a numeric value is used for <em>lo</em> and/or <em>hi</em>, then the bin extent
 in the <em>lo</em> or <em>hi</em> direction extends only to that value, which is
 assumed to be inside (or at least near) the simulation box boundaries,
 though LAMMPS does not check for this.</p>
 <p>On each sampling timestep, each atom is mapped to the bin it currently
 belongs to, based on its current position.  Note that the group-ID and
 region keyword can exclude specific atoms from this operation, as
 discussed above.  Note that between reneighboring timesteps, atoms can
 move outside the current simulation box.  If the box is periodic (in
 that dimension) the atom is remapping into the periodic box for
 purposes of binning.  If the box in not periodic, the atom may have
 moved outside the bounds of any bin.</p>
 <p>The <em>discard</em> keyword determines what is done with any atom which is
 outside the bounds of any bin.  If <em>discard</em> is set to <em>yes</em>, the atom
 will be ignored and not contribute to any bin averages.  If <em>discard</em>
 is set to <em>no</em>, the atom will be counted as if it were in the first or
 last bin in that dimension.  If (discard* is set to <em>mixed</em>, which is
 the default, it will only be counted in the first or last bin if bins
 extend to the box boundary in that dimension.  This is the case if the
 <em>bound</em> keyword settings are <em>lower</em> and <em>upper</em>, which is the
 default.  If the <em>bound</em> keyword settings are numeric values, then the
 atom will be ignored if it is outside the bounds of any bin.  Note
 that in this case, it is possible that the first or last bin extends
 beyond the numeric <em>bounds</em> settings, depending on the specified
 <em>origin</em>.  If this is the case, the atom is only ignored if it is
 outside the first or last bin, not if it is simply outside the numeric
 <em>bounds</em> setting.</p>
 <p>For orthogonal simulation boxes, the bins are also layers, pencils, or
 boxes aligned with the xyz coordinate axes.  For triclinic
 (non-orthogonal) simulation boxes, the bins are so that they are
 parallel to the tilted faces of the simulation box.  See <a class="reference internal" href="Section_howto.html#howto-12"><span>this section</span></a> of the manual for a discussion of
 the geometry of triclinic boxes in LAMMPS.  As described there, a
 tilted simulation box has edge vectors a,b,c.  In that nomenclature,
 bins in the x dimension have faces with normals in the &#8220;b&#8221; cross &#8220;c&#8221;
 direction.  Bins in y have faces normal to the &#8220;a&#8221; cross &#8220;c&#8221;
 direction.  And bins in z have faces normal to the &#8220;a&#8221; cross &#8220;b&#8221;
 direction.  Note that in order to define the size and position of
 these bins in an unambiguous fashion, the <em>units</em> option must be set
 to <em>reduced</em> when using a triclinic simulation box, as noted below.</p>
 <hr class="docutils" />
 <p>The atom attribute values (vx,vy,vz,fx,fy,fz) are self-explanatory.
 Note that other atom attributes (including atom postitions x,y,z) can
 be used as inputs to this fix by using the <a class="reference internal" href="compute_property_atom.html"><em>compute property/atom</em></a> command and then specifying
 an input value from that compute.</p>
 <p>The <em>density/number</em> value means the number density is computed in
 each bin, i.e. a weighting of 1 for each atom.  The <em>density/mass</em>
 value means the mass density is computed in each bind, i.e. each atom
 is weighted by its mass.  The resulting density is normalized by the
 volume of the bin so that units of number/volume or density are
 output.  See the <a class="reference internal" href="units.html"><em>units</em></a> command doc page for the
 definition of density for each choice of units, e.g. gram/cm^3.</p>
 <p>If a value begins with &#8220;<a href="#id1"><span class="problematic" id="id2">c_</span></a>&#8221;, a compute ID must follow which has been
 previously defined in the input script.  If no bracketed integer is
 appended, the per-atom vector calculated by the compute is used.  If a
 bracketed integer is appended, the Ith column of the per-atom array
 calculated by the compute is used.  Users can also write code for
 their own compute styles and <a class="reference internal" href="Section_modify.html"><em>add them to LAMMPS</em></a>.</p>
 <p>If a value begins with &#8220;<a href="#id3"><span class="problematic" id="id4">f_</span></a>&#8221;, a fix ID must follow which has been
 previously defined in the input script.  If no bracketed integer is
 appended, the per-atom vector calculated by the fix is used.  If a
 bracketed integer is appended, the Ith column of the per-atom array
 calculated by the fix is used.  Note that some fixes only produce
 their values on certain timesteps, which must be compatible with
 <em>Nevery</em>, else an error results.  Users can also write code for their
 own fix styles and <a class="reference internal" href="Section_modify.html"><em>add them to LAMMPS</em></a>.</p>
 <p>If a value begins with &#8220;<a href="#id5"><span class="problematic" id="id6">v_</span></a>&#8221;, a variable name must follow which has
 been previously defined in the input script.  Variables of style
 <em>atom</em> can reference thermodynamic keywords and various per-atom
 attributes, or invoke other computes, fixes, or variables when they
 are evaluated, so this is a very general means of generating per-atom
 quantities to spatially average.</p>
 <hr class="docutils" />
 <p>Additional optional keywords also affect the operation of this fix.
 The <em>region</em>, <em>bound</em>, and <em>discard</em> keywords were discussed above.</p>
 <p>The <em>norm</em> keyword affects how averaging is done for the output
 produced every <em>Nfreq</em> timesteps.  For an <em>all</em> setting, a bin
 quantity is summed over all atoms in all <em>Nrepeat</em> samples, as is the
 count of atoms in the bin.  The printed value for the bin is
 Total-quantity / Total-count.  In other words it is an average over
 the entire <em>Nfreq</em> timescale.</p>
 <p>For a <em>sample</em> setting, the bin quantity is summed over atoms for only
 a single sample, as is the count, and a &#8220;average sample value&#8221; is
 computed, i.e. Sample-quantity / Sample-count.  The printed value for
 the bin is the average of the <em>Nrepeat</em> &#8220;average sample values&#8221;, In
 other words it is an average of an average.</p>
 <p>The <em>ave</em> keyword determines how the bin values produced every <em>Nfreq</em>
 steps are averaged with bin values produced on previous steps that
 were multiples of <em>Nfreq</em>, before they are accessed by another output
 command or written to a file.</p>
 <p>If the <em>ave</em> setting is <em>one</em>, then the bin values produced on
 timesteps that are multiples of <em>Nfreq</em> are independent of each other;
 they are output as-is without further averaging.</p>
 <p>If the <em>ave</em> setting is <em>running</em>, then the bin values produced on
 timesteps that are multiples of <em>Nfreq</em> are summed and averaged in a
 cumulative sense before being output.  Each output bin value is thus
 the average of the bin value produced on that timestep with all
 preceding values for the same bin.  This running average begins when
 the fix is defined; it can only be restarted by deleting the fix via
 the <a class="reference internal" href="unfix.html"><em>unfix</em></a> command, or re-defining the fix by
 re-specifying it.</p>
 <p>If the <em>ave</em> setting is <em>window</em>, then the bin values produced on
 timesteps that are multiples of <em>Nfreq</em> are summed and averaged within
 a moving &#8220;window&#8221; of time, so that the last M values for the same bin
 are used to produce the output.  E.g. if M = 3 and Nfreq = 1000, then
 the output on step 10000 will be the average of the individual bin
 values on steps 8000,9000,10000.  Outputs on early steps will average
 over less than M values if they are not available.</p>
 <p>The <em>units</em> keyword determines the meaning of the distance units used
 for the bin size <em>delta</em> and for <em>origin</em> and <em>bounds</em> values if they
 are coordinate value.  For orthogonal simulation boxes, any of the 3
 options may be used.  For non-orthogonal (triclinic) simulation boxes,
 only the <em>reduced</em> option may be used.</p>
 <p>A <em>box</em> value selects standard distance units as defined by the
 <a class="reference internal" href="units.html"><em>units</em></a> command, e.g. Angstroms for units = real or metal.
 A <em>lattice</em> value means the distance units are in lattice spacings.
 The <a class="reference internal" href="lattice.html"><em>lattice</em></a> command must have been previously used to
 define the lattice spacing.  A <em>reduced</em> value means normalized
 unitless values between 0 and 1, which represent the lower and upper
 faces of the simulation box respectively.  Thus an <em>origin</em> value of
 0.5 means the center of the box in any dimension.  A <em>delta</em> value of
 0.1 means 10 bins span the box in that dimension.</p>
 <p>Consider a non-orthogonal box, with bins that are 1d layers or slabs
 in the x dimension.  No matter how the box is tilted, an <em>origin</em> of
 0.0 means start layers at the lower &#8220;b&#8221; cross &#8220;c&#8221; plane of the
 simulation box and an <em>origin</em> of 1.0 means to start layers at the
 upper &#8220;b&#8221; cross &#8220;c&#8221; face of the box.  A <em>delta</em> value of 0.1 means
 there will be 10 layers from 0.0 to 1.0, regardless of the current
 size or shape of the simulation box.</p>
 <p>The <em>file</em> keyword allows a filename to be specified.  Every <em>Nfreq</em>
 timesteps, a section of bin info will be written to a text file in the
 following format.  A line with the timestep and number of bin is
 written.  Then one line per bin is written, containing the bin ID
 (1-N), the coordinate of the center of the bin, the number of atoms
 in the bin, and one or more calculated values.  The number of values
 in each line corresponds to the number of values specified in the fix
 ave/spatial command.  The number of atoms and the value(s) are average
 quantities.  If the value of the <em>units</em> keyword is <em>box</em> or
 <em>lattice</em>, the &#8220;coord&#8221; is printed in box units.  If the value of the
 <em>units</em> keyword is <em>reduced</em>, the &#8220;coord&#8221; is printed in reduced units
 (0-1).</p>
 <p>The <em>overwrite</em> keyword will continuously overwrite the output file
 with the latest output, so that it only contains one timestep worth of
 output.  This option can only be used with the <em>ave running</em> setting.</p>
 <p>The <em>title1</em> and <em>title2</em> and <em>title3</em> keywords allow specification of
 the strings that will be printed as the first 3 lines of the output
 file, assuming the <em>file</em> keyword was used.  LAMMPS uses default
 values for each of these, so they do not need to be specified.</p>
 <p>By default, these header lines are as follows:</p>
 <div class="highlight-python"><div class="highlight"><pre><span class="c"># Spatial-averaged data for fix ID and group name</span>
 <span class="c"># Timestep Number-of-bins</span>
 <span class="c"># Bin Coord1 Coord2 Coord3 Count value1 value2 ...</span>
 </pre></div>
 </div>
 <p>In the first line, ID and name are replaced with the fix-ID and group
 name.  The second line describes the two values that are printed at
 the first of each section of output.  In the third line the values are
 replaced with the appropriate fields from the fix ave/spatial command.
 The Coord2 and Coord3 entries in the third line only appear for 2d and
 3d bins respectively.  For 1d bins, the word Coord1 is replaced by
 just Coord.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.  None of the <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> options
 are relevant to this fix.</p>
 <p>This fix computes a global array of values which can be accessed by
 various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  The values can
 only be accessed on timesteps that are multiples of <em>Nfreq</em> since that
 is when averaging is performed.  The global array has # of rows =
 Nbins and # of columns = Ndim+1+Nvalues, where Ndim = 1,2,3 for
 1d,2d,3d bins.  The first 1 or 2 or 3 columns have the bin coordinates
 (center of the bin) in the appropriate dimensions, the next column has
 the count of atoms in that bin, and the remaining columns are the
 Nvalue quantities.  When the array is accessed with an I that exceeds
 the current number of bins, than a 0.0 is returned by the fix instead
 of an error, since the number of bins can vary as a simulation runs,
 depending on the simulation box size.  2d or 3d bins are ordered so
 that the last dimension(s) vary fastest.  The array values calculated
 by this fix are &#8220;intensive&#8221;, since they are already normalized by the
 count of atoms in each bin.</p>
 <p>No parameter of this fix can be used with the <em>start/stop</em> keywords of
 the <a class="reference internal" href="run.html"><em>run</em></a> command.  This fix is not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>When the <em>ave</em> keyword is set to <em>running</em> or <em>window</em> then the number
 of bins must remain the same during the simulation, so that the
 appropriate averaging can be done.  This will be the case if the
 simulation box size doesn&#8217;t change or if the <em>units</em> keyword is set to
 <em>reduced</em>.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="compute.html"><em>compute</em></a>, <a class="reference internal" href="fix_ave_atom.html"><em>fix ave/atom</em></a>, <a class="reference internal" href="fix_ave_histo.html"><em>fix ave/histo</em></a>, <a class="reference internal" href="fix_ave_time.html"><em>fix ave/time</em></a>,
 <a class="reference internal" href="variable.html"><em>variable</em></a>, <a class="reference internal" href="fix_ave_correlate.html"><em>fix ave/correlate</em></a>,
 <a class="reference internal" href="fix_ave_spatial_sphere.html"><em>fix ave/spatial/sphere</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The option defaults are bound = lower and upper in all dimensions,
 discard = mixed, norm = all, ave = one, units = lattice, no file
 output, and title 1,2,3 = strings as described above.</p>
 </div>
 </div>
 
 
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diff --git a/doc/fix_ave_spatial_sphere.html b/doc/fix_ave_spatial_sphere.html
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   <div class="section" id="fix-ave-spatial-sphere-command">
 <span id="index-0"></span><h1>fix ave/spatial/sphere command<a class="headerlink" href="#fix-ave-spatial-sphere-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID ave/spatial/sphere Nevery Nrepeat Nfreq origin_x origin_y origin_z r_min r_max nbins value1 value2 ... keyword args ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>ave/spatial = style name of this fix command</li>
 <li>Nevery = use input values every this many timesteps</li>
 <li>Nrepeat = # of times to use input values for calculating averages</li>
 <li>Nfreq = calculate averages every this many timesteps</li>
 <li>origin_x, origin_y, origin_z = center of the sphere. can be the result of variables or computes (see below)</li>
 <li>r_min = radial distance at which binning begins</li>
 <li>r_max = radial distance at which binning ends</li>
 <li>nbins = number of spherical shells to create between r_min and r_max</li>
 <li>one or more input values can be listed</li>
 <li>value = vx, vy, vz, fx, fy, fz, density/mass, density/number, c_ID, c_ID[I], f_ID, f_ID[I], v_name</li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>vx,vy,vz,fx,fy,fz = atom attribute (velocity, force component)
-  density/number, density/mass = number or mass density
-  c_ID = per-atom vector calculated by a compute with ID
-  c_ID[I] = Ith column of per-atom array calculated by a compute with ID
-  f_ID = per-atom vector calculated by a fix with ID
-  f_ID[I] = Ith column of per-atom array calculated by a fix with ID
-  v_name = per-atom vector calculated by an atom-style variable with name
+density/number, density/mass = number or mass density
+c_ID = per-atom vector calculated by a compute with ID
+c_ID[I] = Ith column of per-atom array calculated by a compute with ID
+f_ID = per-atom vector calculated by a fix with ID
+f_ID[I] = Ith column of per-atom array calculated by a fix with ID
+v_name = per-atom vector calculated by an atom-style variable with name
 </pre></div>
 </div>
 <ul class="simple">
 <li>zero or more keyword/arg pairs may be appended</li>
 <li>keyword = <em>region</em> or <em>norm</em> or <em>units</em> or <em>ave</em> or <em>file</em> or <em>overwrite</em> or <em>title1</em> or <em>title2</em> or <em>title3</em></li>
 </ul>
 <pre class="literal-block">
 <em>region</em> arg = region-ID
-    region-ID = ID of region atoms must be in to contribute to spatial averaging
-  <em>norm</em> arg = <em>all</em> or <em>sample</em>
-  <em>units</em> arg = <em>box</em> or <em>lattice</em> or <em>reduced</em>
-  <em>ave</em> args = <em>one</em> or <em>running</em> or <em>window M</em>
-    one = output new average value every Nfreq steps
-    running = output cumulative average of all previous Nfreq steps
-    window M = output average of M most recent Nfreq steps
-  <em>file</em> arg = filename
-    filename = file to write results to
-  <em>overwrite</em> arg = none = overwrite output file with only latest output
-  <em>title1</em> arg = string
-    string = text to print as 1st line of output file
-  <em>title2</em> arg = string
-    string = text to print as 2nd line of output file
-  <em>title3</em> arg = string
-    string = text to print as 3rd line of output file
+  region-ID = ID of region atoms must be in to contribute to spatial averaging
+<em>norm</em> arg = <em>all</em> or <em>sample</em>
+<em>units</em> arg = <em>box</em> or <em>lattice</em> or <em>reduced</em>
+<em>ave</em> args = <em>one</em> or <em>running</em> or <em>window M</em>
+  one = output new average value every Nfreq steps
+  running = output cumulative average of all previous Nfreq steps
+  window M = output average of M most recent Nfreq steps
+<em>file</em> arg = filename
+  filename = file to write results to
+<em>overwrite</em> arg = none = overwrite output file with only latest output
+<em>title1</em> arg = string
+  string = text to print as 1st line of output file
+<em>title2</em> arg = string
+  string = text to print as 2nd line of output file
+<em>title3</em> arg = string
+  string = text to print as 3rd line of output file
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix 1 all ave/spatial/sphere 10000 1 10000 0.5 0.5 0.5 0.1 0.5 5 density/number vx vy vz units reduced title1 &quot;My output values&quot;
 fix 1 flow ave/spatial/sphere 100 10 1000 20.0 20.0 20.0 0.0 20.0 20 vx vz norm sample file vel.profile
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Use one or more per-atom vectors as inputs every few timesteps, bin
 their values spatially into spherical shells based on current atom
 coordinates, and average the bin values over longer timescales.  The
 resulting bin averages can be used by other <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a> such as <a class="reference internal" href="thermo_style.html"><em>thermo_style custom</em></a>, and can also be written to a file.</p>
 <p>The group specified with the command means only atoms within the group
 contribute to bin averages.  If the <em>region</em> keyword is used, the atom
 must be in both the group and the specified geometric
 <a class="reference internal" href="region.html"><em>region</em></a> in order to contribute to bin averages.</p>
 <p>Each listed value can be an atom attribute (position, velocity, force
 component), a mass or number density, or the result of a
 <a class="reference internal" href="compute.html"><em>compute</em></a> or <a class="reference internal" href="fix.html"><em>fix</em></a> or the evaluation of an
 atom-style <a class="reference internal" href="variable.html"><em>variable</em></a>.  In the latter cases, the
 compute, fix, or variable must produce a per-atom quantity, not a
 global quantity.  If you wish to time-average global quantities from a
 compute, fix, or variable, then see the <a class="reference internal" href="fix_ave_time.html"><em>fix ave/time</em></a> command.</p>
 <p><a class="reference internal" href="compute.html"><em>Computes</em></a> that produce per-atom quantities are those
 which have the word <em>atom</em> in their style name.  See the doc pages for
 individual <a class="reference internal" href="fix.html"><em>fixes</em></a> to determine which ones produce per-atom
 quantities.  <a class="reference internal" href="variable.html"><em>Variables</em></a> of style <em>atom</em> are the only
 ones that can be used with this fix since all other styles of variable
 produce global quantities.</p>
 <p>The per-atom values of each input vector are binned and averaged
 independently of the per-atom values in other input vectors.</p>
 <p><em>Nbins</em> specifies the number of spherical shells which will be created
 between r_min and r_max centered at (origin_x, origin_y, origin_z).</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">This fix works by creating an array of size Nbins by
 Nvalues on each processor.  Nbins is the total number of bins; Nvalues
 is the number of input values specified.  Each processor loops over
 its atoms, tallying its values to the appropriate bin.  Then the
 entire array is summed across all processors.  This means that using a
 large number of bins will incur an overhead in memory and computational
 cost (summing across processors), so be careful to use reasonable numbers
 of bins.</p>
 </div>
 <hr class="docutils" />
 <p>The <em>Nevery</em>, <em>Nrepeat</em>, and <em>Nfreq</em> arguments specify on what
 timesteps the input values will be used to bin them and contribute to
 the average.  The final averaged quantities are generated on timesteps
 that are a multiples of <em>Nfreq</em>.  The average is over <em>Nrepeat</em>
 quantities, computed in the preceding portion of the simulation every
 <em>Nevery</em> timesteps.  <em>Nfreq</em> must be a multiple of <em>Nevery</em> and
 <em>Nevery</em> must be non-zero even if <em>Nrepeat</em> is 1.  Also, the timesteps
 contributing to the average value cannot overlap, i.e. Nfreq &gt;
 (Nrepeat-1)*Nevery is required.</p>
 <p>For example, if Nevery=2, Nrepeat=6, and Nfreq=100, then values on
 timesteps 90,92,94,96,98,100 will be used to compute the final average
 on timestep 100.  Similarly for timesteps 190,192,194,196,198,200 on
 timestep 200, etc.  If Nrepeat=1 and Nfreq = 100, then no time
 averaging is done; values are simply generated on timesteps
 100,200,etc.</p>
 <hr class="docutils" />
 <p>The <em>origin_x</em>, <em>origin_y</em>, and <em>origin_z</em> parameters may be specified
 by either a compute or a variable. This allows, for example, the
 center of the spherical bins to be attached to the center of mass of a
 group of atoms. If a variable origin is used and periodic boundary
 conditions are in effect, then the origin will be wrapped across
 periodic boundaries whenever it changes so that it is always inside
 the simulation box.</p>
 <hr class="docutils" />
 <p>The atom attribute values (vx,vy,vz,fx,fy,fz) are self-explanatory.
 Note that other atom attributes (including atom postitions x,y,z) can
 be used as inputs to this fix by using the <a class="reference internal" href="compute_property_atom.html"><em>compute property/atom</em></a> command and then specifying
 an input value from that compute.</p>
 <p>The <em>density/number</em> value means the number density is computed in
 each bin, i.e. a weighting of 1 for each atom.  The <em>density/mass</em>
 value means the mass density is computed in each bin, i.e. each atom
 is weighted by its mass.  The resulting density is normalized by the
 volume of the bin so that units of number/volume or density are
 output.  See the <a class="reference internal" href="units.html"><em>units</em></a> command doc page for the
 definition of density for each choice of units, e.g. gram/cm^3.
 The bin volume will always be calculated in box units, independent
 of the use of the <em>units</em> keyword in this command.</p>
 <p>If a value begins with &#8220;<a href="#id1"><span class="problematic" id="id2">c_</span></a>&#8221;, a compute ID must follow which has been
 previously defined in the input script.  If no bracketed integer is
 appended, the per-atom vector calculated by the compute is used.  If a
 bracketed integer is appended, the Ith column of the per-atom array
 calculated by the compute is used.  Users can also write code for
 their own compute styles and <a class="reference internal" href="Section_modify.html"><em>add them to LAMMPS</em></a>.</p>
 <p>If a value begins with &#8220;<a href="#id3"><span class="problematic" id="id4">f_</span></a>&#8221;, a fix ID must follow which has been
 previously defined in the input script.  If no bracketed integer is
 appended, the per-atom vector calculated by the fix is used.  If a
 bracketed integer is appended, the Ith column of the per-atom array
 calculated by the fix is used.  Note that some fixes only produce
 their values on certain timesteps, which must be compatible with
 <em>Nevery</em>, else an error results.  Users can also write code for their
 own fix styles and <a class="reference internal" href="Section_modify.html"><em>add them to LAMMPS</em></a>.</p>
 <p>If a value begins with &#8220;<a href="#id5"><span class="problematic" id="id6">v_</span></a>&#8221;, a variable name must follow which has
 been previously defined in the input script.  Variables of style
 <em>atom</em> can reference thermodynamic keywords and various per-atom
 attributes, or invoke other computes, fixes, or variables when they
 are evaluated, so this is a very general means of generating per-atom
 quantities to spatially average.</p>
 <hr class="docutils" />
 <p>Additional optional keywords also affect the operation of this fix.
 The <em>region</em> keyword was discussed above.</p>
 <p>The <em>norm</em> keyword affects how averaging is done for the output
 produced every <em>Nfreq</em> timesteps.  For an <em>all</em> setting, a bin
 quantity is summed over all atoms in all <em>Nrepeat</em> samples, as is the
 count of atoms in the bin.  The printed value for the bin is
 Total-quantity / Total-count.  In other words it is an average over
 the entire <em>Nfreq</em> timescale.</p>
 <p>For a <em>sample</em> setting, the bin quantity is summed over atoms for only
 a single sample, as is the count, and a &#8220;average sample value&#8221; is
 computed, i.e. Sample-quantity / Sample-count.  The printed value for
 the bin is the average of the <em>Nrepeat</em> &#8220;average sample values&#8221;, In
 other words it is an average of an average.</p>
 <p>The <em>ave</em> keyword determines how the bin values produced every <em>Nfreq</em>
 steps are averaged with bin values produced on previous steps that
 were multiples of <em>Nfreq</em>, before they are accessed by another output
 command or written to a file.</p>
 <p>If the <em>ave</em> setting is <em>one</em>, then the bin values produced on
 timesteps that are multiples of <em>Nfreq</em> are independent of each other;
 they are output as-is without further averaging.</p>
 <p>If the <em>ave</em> setting is <em>running</em>, then the bin values produced on
 timesteps that are multiples of <em>Nfreq</em> are summed and averaged in a
 cumulative sense before being output.  Each output bin value is thus
 the average of the bin value produced on that timestep with all
 preceding values for the same bin.  This running average begins when
 the fix is defined; it can only be restarted by deleting the fix via
 the <a class="reference internal" href="unfix.html"><em>unfix</em></a> command, or re-defining the fix by
 re-specifying it.</p>
 <p>If the <em>ave</em> setting is <em>window</em>, then the bin values produced on
 timesteps that are multiples of <em>Nfreq</em> are summed and averaged within
 a moving &#8220;window&#8221; of time, so that the last M values for the same bin
 are used to produce the output.  E.g. if M = 3 and Nfreq = 1000, then
 the output on step 10000 will be the average of the individual bin
 values on steps 8000,9000,10000.  Outputs on early steps will average
 over less than M values if they are not available.</p>
 <p>The <em>units</em> keyword determines the meaning of the distance units used
 for the sphere origin and the two radial lengths.  For orthogonal
 simulation boxes, any of the 3 options may be used.  For
 non-orthogonal (triclinic) simulation boxes, only the <em>reduced</em> option
 may be used.</p>
 <p>A <em>box</em> value selects standard distance units as defined by the
 <a class="reference internal" href="units.html"><em>units</em></a> command, e.g. Angstroms for units = real or metal.
 A <em>lattice</em> value means the distance units are in lattice spacings.
 The <a class="reference internal" href="lattice.html"><em>lattice</em></a> command must have been previously used to
 define the lattice spacing.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">The <em>lattice</em> style may only be used if the lattice
 spacing is the same in each direction.</p>
 </div>
 <p>A <em>reduced</em> value means normalized unitless values between 0 and 1,
 which represent the lower and upper faces of the simulation box
 respectively.  Thus an <em>origin</em> value of 0.5 means the center of the
 box in any dimension.</p>
 <p>The <em>file</em> keyword allows a filename to be specified.  Every <em>Nfreq</em>
 timesteps, a section of bin info will be written to a text file in the
 following format.  A line with the timestep and number of bin is
 written.  Then one line per bin is written, containing the bin ID
 (1-N), the coordinate of the center of the bin, the number of atoms in
 the bin, and one or more calculated values.  The number of values in
 each line corresponds to the number of values specified in the fix
 ave/spatial command.  The number of atoms and the value(s) are average
 quantities.  If the value of the <em>units</em> keyword is <em>box</em> or
 <em>lattice</em>, the &#8220;coord&#8221; is printed in box units.  If the value of the
 <em>units</em> keyword is <em>reduced</em>, the &#8220;coord&#8221; is printed in reduced units
 (0-1).</p>
 <p>The <em>overwrite</em> keyword will continuously overwrite the output file
 with the latest output, so that it only contains one timestep worth of
 output.  This option can only be used with the <em>ave running</em> setting.</p>
 <p>The <em>title1</em> and <em>title2</em> and <em>title3</em> keywords allow specification of
 the strings that will be printed as the first 3 lines of the output
 file, assuming the <em>file</em> keyword was used.  LAMMPS uses default
 values for each of these, so they do not need to be specified.</p>
 <p>By default, these header lines are as follows:</p>
 <div class="highlight-python"><div class="highlight"><pre><span class="c"># Spatial-averaged data for fix ID and group name</span>
 <span class="c"># Timestep Number-of-bins</span>
 <span class="c"># Bin r Count value1 value2 ...</span>
 </pre></div>
 </div>
 <p>In the first line, ID and name are replaced with the fix-ID and group
 name.  The second line describes the two values that are printed at
 the first of each section of output.  In the third line the values are
 replaced with the appropriate fields from the fix ave/spatial command.
 The Coord2 and Coord3 entries in the third line only appear for 2d and
 3d bins respectively.  For 1d bins, the word Coord1 is replaced by
 just Coord.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.  None of the <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> options
 are relevant to this fix.</p>
 <p>This fix computes a global array of values which can be accessed by
 various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  The values can
 only be accessed on timesteps that are multiples of <em>Nfreq</em> since that
 is when averaging is performed.  The global array has # of rows =
 Nbins and # of columns = 2+Nvalues.  The first column contains the
 radius at the center of the shell. For units <em>reduced</em>, this is in
 reduced units, while for units <em>box</em> and <em>lattice</em> this is in box
 units. The next column has the count of atoms in that bin, and the
 remaining columns are the Nvalue quantities.  When the array is
 accessed with an I that exceeds the current number of bins, than a 0.0
 is returned by the fix instead of an error.  The array values
 calculated by this fix are &#8220;intensive&#8221;, since they are already
 normalized by the count of atoms in each bin.</p>
 <p>No parameter of this fix can be used with the <em>start/stop</em> keywords of
 the <a class="reference internal" href="run.html"><em>run</em></a> command.  This fix is not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>When the <em>ave</em> keyword is set to <em>running</em> or <em>window</em> then the number
 of bins must remain the same during the simulation, so that the
 appropriate averaging can be done.  This will be the case if the
 simulation box size doesn&#8217;t change or if the <em>units</em> keyword is set to
 <em>reduced</em>.</p>
 <p>This style is part of the USER-MISC package. It is only enabled if
 LAMMPS is build with that package. See the <span class="xref std std-ref">Making of LAMMPS</span> section for more info.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="compute.html"><em>compute</em></a>, <a class="reference internal" href="fix_ave_atom.html"><em>fix ave/atom</em></a>, <a class="reference internal" href="fix_ave_histo.html"><em>fix ave/histo</em></a>, <a class="reference internal" href="fix_ave_time.html"><em>fix ave/time</em></a>,
 <a class="reference internal" href="variable.html"><em>variable</em></a>, <a class="reference internal" href="fix_ave_correlate.html"><em>fix ave/correlate</em></a>,
 <a class="reference internal" href="fix_ave_spatial.html"><em>fix ave/spatial</em></a>,</p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The option defaults are norm = all, ave = one, units = lattice, no
 file output, and title 1,2,3 = strings as described above.</p>
 </div>
 </div>
 
 
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   <div class="section" id="fix-ave-time-command">
 <span id="index-0"></span><h1>fix ave/time command<a class="headerlink" href="#fix-ave-time-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID ave/time Nevery Nrepeat Nfreq value1 value2 ... keyword args ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>ave/time = style name of this fix command</li>
 <li>Nevery = use input values every this many timesteps</li>
 <li>Nrepeat = # of times to use input values for calculating averages</li>
 <li>Nfreq = calculate averages every this many timesteps</li>
 <li>one or more input values can be listed</li>
 <li>value = c_ID, c_ID[N], f_ID, f_ID[N], v_name</li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>c_ID = global scalar, vector, or array calculated by a compute with ID
-  c_ID[I] = Ith component of global vector or Ith column of global array calculated by a compute with ID
-  f_ID = global scalar, vector, or array calculated by a fix with ID
-  f_ID[I] = Ith component of global vector or Ith column of global array calculated by a fix with ID
-  v_name = global value calculated by an equal-style variable with name
+c_ID[I] = Ith component of global vector or Ith column of global array calculated by a compute with ID
+f_ID = global scalar, vector, or array calculated by a fix with ID
+f_ID[I] = Ith component of global vector or Ith column of global array calculated by a fix with ID
+v_name = global value calculated by an equal-style variable with name
 </pre></div>
 </div>
 <ul class="simple">
 <li>zero or more keyword/arg pairs may be appended</li>
 <li>keyword = <em>mode</em> or <em>file</em> or <em>ave</em> or <em>start</em> or <em>off</em> or <em>overwrite</em> or <em>title1</em> or <em>title2</em> or <em>title3</em></li>
 </ul>
 <pre class="literal-block">
 <em>mode</em> arg = <em>scalar</em> or <em>vector</em>
-    scalar = all input values are global scalars
-    vector = all input values are global vectors or global arrays
-  <em>ave</em> args = <em>one</em> or <em>running</em> or <em>window M</em>
-    one = output a new average value every Nfreq steps
-    running = output cummulative average of all previous Nfreq steps
-    window M = output average of M most recent Nfreq steps
-  <em>start</em> args = Nstart
-    Nstart = start averaging on this timestep
-  <em>off</em> arg = M = do not average this value
-    M = value # from 1 to Nvalues
-  <em>file</em> arg = filename
-    filename = name of file to output time averages to
-  <em>overwrite</em> arg = none = overwrite output file with only latest output
-  <em>title1</em> arg = string
-    string = text to print as 1st line of output file
-  <em>title2</em> arg = string
-    string = text to print as 2nd line of output file
-  <em>title3</em> arg = string
-    string = text to print as 3rd line of output file, only for vector mode
+  scalar = all input values are global scalars
+  vector = all input values are global vectors or global arrays
+<em>ave</em> args = <em>one</em> or <em>running</em> or <em>window M</em>
+  one = output a new average value every Nfreq steps
+  running = output cummulative average of all previous Nfreq steps
+  window M = output average of M most recent Nfreq steps
+<em>start</em> args = Nstart
+  Nstart = start averaging on this timestep
+<em>off</em> arg = M = do not average this value
+  M = value # from 1 to Nvalues
+<em>file</em> arg = filename
+  filename = name of file to output time averages to
+<em>overwrite</em> arg = none = overwrite output file with only latest output
+<em>title1</em> arg = string
+  string = text to print as 1st line of output file
+<em>title2</em> arg = string
+  string = text to print as 2nd line of output file
+<em>title3</em> arg = string
+  string = text to print as 3rd line of output file, only for vector mode
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix 1 all ave/time 100 5 1000 c_myTemp c_thermo_temp file temp.profile
 fix 1 all ave/time 100 5 1000 c_thermo_press[2] ave window 20 &amp;
                               title1 &quot;My output values&quot;
 fix 1 all ave/time 1 100 1000 f_indent f_indent[1] file temp.indent off 1
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Use one or more global values as inputs every few timesteps, and
 average them over longer timescales.  The resulting averages can be
 used by other <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a> such as
 <a class="reference internal" href="thermo_style.html"><em>thermo_style custom</em></a>, and can also be written to a
 file.  Note that if no time averaging is done, this command can be
 used as a convenient way to simply output one or more global values to
 a file.</p>
 <p>The group specified with this command is ignored.  However, note that
 specified values may represent calculations performed by computes and
 fixes which store their own &#8220;group&#8221; definitions.</p>
 <p>Each listed value can be the result of a <a class="reference internal" href="compute.html"><em>compute</em></a> or
 <a class="reference internal" href="fix.html"><em>fix</em></a> or the evaluation of an equal-style
 <a class="reference internal" href="variable.html"><em>variable</em></a>.  In each case, the compute, fix, or variable
 must produce a global quantity, not a per-atom or local quantity.  If
 you wish to spatial- or time-average or histogram per-atom quantities
 from a compute, fix, or variable, then see the <a class="reference internal" href="fix_ave_spatial.html"><em>fix ave/spatial</em></a>, <a class="reference internal" href="fix_ave_atom.html"><em>fix ave/atom</em></a>,
 or <a class="reference internal" href="fix_ave_histo.html"><em>fix ave/histo</em></a> commands.  If you wish to sum a
 per-atom quantity into a single global quantity, see the <a class="reference internal" href="compute_reduce.html"><em>compute reduce</em></a> command.</p>
 <p><a class="reference internal" href="compute.html"><em>Computes</em></a> that produce global quantities are those which
 do not have the word <em>atom</em> in their style name.  Only a few
 <a class="reference internal" href="fix.html"><em>fixes</em></a> produce global quantities.  See the doc pages for
 individual fixes for info on which ones produce such values.
 <a class="reference internal" href="variable.html"><em>Variables</em></a> of style <em>equal</em> are the only ones that can
 be used with this fix.  Variables of style <em>atom</em> cannot be used,
 since they produce per-atom values.</p>
 <p>The input values must either be all scalars or all vectors (or
 arrays), depending on the setting of the <em>mode</em> keyword.  In both
 cases, the averaging is performed independently on each input value.
 I.e. each input scalar is averaged independently and each element of
 each input vector (or array) is averaged independently.</p>
 <p>If <em>mode</em> = vector, then the input values may either be vectors or
 arrays and all must be the same &#8220;length&#8221;, which is the length of the
 vector or number of rows in the array.  If a global array is listed,
 then it is the same as if the individual columns of the array had been
 listed one by one.  E.g. these 2 fix ave/time commands are equivalent,
 since the <a class="reference internal" href="compute_rdf.html"><em>compute rdf</em></a> command creates, in this
 case, a global array with 3 columns, each of length 50:</p>
 <div class="highlight-python"><div class="highlight"><pre>compute myRDF all rdf 50 1 2
 fix 1 all ave/time 100 1 100 c_myRDF file tmp1.rdf mode vector
 fix 2 all ave/time 100 1 100 c_myRDF[1] c_myRDF[2] c_myRDF[3] file tmp2.rdf mode vector
 </pre></div>
 </div>
 <hr class="docutils" />
 <p>The <em>Nevery</em>, <em>Nrepeat</em>, and <em>Nfreq</em> arguments specify on what
 timesteps the input values will be used in order to contribute to the
 average.  The final averaged quantities are generated on timesteps
 that are a mlutiple of <em>Nfreq</em>.  The average is over <em>Nrepeat</em>
 quantities, computed in the preceding portion of the simulation every
 <em>Nevery</em> timesteps.  <em>Nfreq</em> must be a multiple of <em>Nevery</em> and
 <em>Nevery</em> must be non-zero even if <em>Nrepeat</em> is 1.  Also, the timesteps
 contributing to the average value cannot overlap, i.e. Nfreq &gt;
 (Nrepeat-1)*Nevery is required.</p>
 <p>For example, if Nevery=2, Nrepeat=6, and Nfreq=100, then values on
 timesteps 90,92,94,96,98,100 will be used to compute the final average
 on timestep 100.  Similarly for timesteps 190,192,194,196,198,200 on
 timestep 200, etc.  If Nrepeat=1 and Nfreq = 100, then no time
 averaging is done; values are simply generated on timesteps
 100,200,etc.</p>
 <hr class="docutils" />
 <p>If a value begins with &#8220;<a href="#id1"><span class="problematic" id="id2">c_</span></a>&#8221;, a compute ID must follow which has been
 previously defined in the input script.  If <em>mode</em> = scalar, then if
 no bracketed term is appended, the global scalar calculated by the
 compute is used.  If a bracketed term is appended, the Ith element of
 the global vector calculated by the compute is used.  If <em>mode</em> =
 vector, then if no bracketed term is appended, the global vector
 calculated by the compute is used.  Or if the compute calculates an
 array, all of the columns of the global array are used as if they had
 been specified as individual vectors (see description above).  If a
 bracketed term is appended, the Ith column of the global array
 calculated by the compute is used.</p>
 <p>Note that there is a <a class="reference internal" href="compute_reduce.html"><em>compute reduce</em></a> command
 which can sum per-atom quantities into a global scalar or vector which
 can thus be accessed by fix ave/time.  Or it can be a compute defined
 not in your input script, but by <a class="reference internal" href="thermo_style.html"><em>thermodynamic output</em></a> or other fixes such as <a class="reference internal" href="fix_nh.html"><em>fix nvt</em></a> or <a class="reference internal" href="fix_temp_rescale.html"><em>fix temp/rescale</em></a>.  See
 the doc pages for these commands which give the IDs of these computes.
 Users can also write code for their own compute styles and <a class="reference internal" href="Section_modify.html"><em>add them to LAMMPS</em></a>.</p>
 <p>If a value begins with &#8220;<a href="#id3"><span class="problematic" id="id4">f_</span></a>&#8221;, a fix ID must follow which has been
 previously defined in the input script.  If <em>mode</em> = scalar, then if
 no bracketed term is appended, the global scalar calculated by the fix
 is used.  If a bracketed term is appended, the Ith element of the
 global vector calculated by the fix is used.  If <em>mode</em> = vector, then
 if no bracketed term is appended, the global vector calculated by the
 fix is used.  Or if the fix calculates an array, all of the columns of
 the global array are used as if they had been specified as individual
 vectors (see description above).  If a bracketed term is appended, the
 Ith column of the global array calculated by the fix is used.</p>
 <p>Note that some fixes only produce their values on certain timesteps,
 which must be compatible with <em>Nevery</em>, else an error will result.
 Users can also write code for their own fix styles and <a class="reference internal" href="Section_modify.html"><em>add them to LAMMPS</em></a>.</p>
 <p>If a value begins with &#8220;<a href="#id5"><span class="problematic" id="id6">v_</span></a>&#8221;, a variable name must follow which has
 been previously defined in the input script.  Variables can only be
 used as input for <em>mode</em> = scalar.  Only equal-style variables can be
 referenced.  See the <a class="reference internal" href="variable.html"><em>variable</em></a> command for details.
 Note that variables of style <em>equal</em> define a formula which can
 reference individual atom properties or thermodynamic keywords, or
 they can invoke other computes, fixes, or variables when they are
 evaluated, so this is a very general means of specifying quantities to
 time average.</p>
 <hr class="docutils" />
 <p>Additional optional keywords also affect the operation of this fix.</p>
 <p>If the <em>mode</em> keyword is set to <em>scalar</em>, then all input values must
 be global scalars, or elements of global vectors.  If the <em>mode</em>
 keyword is set to <em>vector</em>, then all input values must be global
 vectors, or columns of global arrays.  They can also be global arrays,
 which are converted into a series of global vectors (one per column),
 as explained above.</p>
 <p>The <em>ave</em> keyword determines how the values produced every <em>Nfreq</em>
 steps are averaged with values produced on previous steps that were
 multiples of <em>Nfreq</em>, before they are accessed by another output
 command or written to a file.</p>
 <p>If the <em>ave</em> setting is <em>one</em>, then the values produced on timesteps
 that are multiples of <em>Nfreq</em> are independent of each other; they are
 output as-is without further averaging.</p>
 <p>If the <em>ave</em> setting is <em>running</em>, then the values produced on
 timesteps that are multiples of <em>Nfreq</em> are summed and averaged in a
 cummulative sense before being output.  Each output value is thus the
 average of the value produced on that timestep with all preceding
 values.  This running average begins when the fix is defined; it can
 only be restarted by deleting the fix via the <a class="reference internal" href="unfix.html"><em>unfix</em></a>
 command, or by re-defining the fix by re-specifying it.</p>
 <p>If the <em>ave</em> setting is <em>window</em>, then the values produced on
 timesteps that are multiples of <em>Nfreq</em> are summed and averaged within
 a moving &#8220;window&#8221; of time, so that the last M values are used to
 produce the output.  E.g. if M = 3 and Nfreq = 1000, then the output
 on step 10000 will be the average of the individual values on steps
 8000,9000,10000.  Outputs on early steps will average over less than M
 values if they are not available.</p>
 <p>The <em>start</em> keyword specifies what timestep averaging will begin on.
 The default is step 0.  Often input values can be 0.0 at time 0, so
 setting <em>start</em> to a larger value can avoid including a 0.0 in a
 running or windowed average.</p>
 <p>The <em>off</em> keyword can be used to flag any of the input values.  If a
 value is flagged, it will not be time averaged.  Instead the most
 recent input value will always be stored and output.  This is useful
 if one of more of the inputs produced by a compute or fix or variable
 are effectively constant or are simply current values.  E.g. they are
 being written to a file with other time-averaged values for purposes
 of creating well-formatted output.</p>
 <p>The <em>file</em> keyword allows a filename to be specified.  Every <em>Nfreq</em>
 steps, one quantity or vector of quantities is written to the file for
 each input value specified in the fix ave/time command.  For <em>mode</em> =
 scalar, this means a single line is written each time output is
 performed.  Thus the file ends up to be a series of lines, i.e. one
 column of numbers for each input value.  For <em>mode</em> = vector, an array
 of numbers is written each time output is performed.  The number of
 rows is the length of the input vectors, and the number of columns is
 the number of values.  Thus the file ends up to be a series of these
 array sections.</p>
 <p>The <em>overwrite</em> keyword will continuously overwrite the output file
 with the latest output, so that it only contains one timestep worth of
 output.  This option can only be used with the <em>ave running</em> setting.</p>
 <p>The <em>title1</em> and <em>title2</em> and <em>title3</em> keywords allow specification of
 the strings that will be printed as the first 2 or 3 lines of the
 output file, assuming the <em>file</em> keyword was used.  LAMMPS uses
 default values for each of these, so they do not need to be specified.</p>
 <p>By default, these header lines are as follows for <em>mode</em> = scalar:</p>
 <div class="highlight-python"><div class="highlight"><pre><span class="c"># Time-averaged data for fix ID</span>
 <span class="c"># TimeStep value1 value2 ...</span>
 </pre></div>
 </div>
 <p>In the first line, ID is replaced with the fix-ID.  In the second line
 the values are replaced with the appropriate fields from the fix
 ave/time command.  There is no third line in the header of the file,
 so the <em>title3</em> setting is ignored when <em>mode</em> = scalar.</p>
 <p>By default, these header lines are as follows for <em>mode</em> = vector:</p>
 <div class="highlight-python"><div class="highlight"><pre><span class="c"># Time-averaged data for fix ID</span>
 <span class="c"># TimeStep Number-of-rows</span>
 <span class="c"># Row value1 value2 ...</span>
 </pre></div>
 </div>
 <p>In the first line, ID is replaced with the fix-ID.  The second line
 describes the two values that are printed at the first of each section
 of output.  In the third line the values are replaced with the
 appropriate fields from the fix ave/time command.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.  None of the <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> options
 are relevant to this fix.</p>
 <p>This fix produces a global scalar or global vector or global array
 which can be accessed by various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  The values can only be
 accessed on timesteps that are multiples of <em>Nfreq</em> since that is when
 averaging is performed.</p>
 <p>A scalar is produced if only a single input value is averaged and
 <em>mode</em> = scalar.  A vector is produced if multiple input values are
 averaged for <em>mode</em> = scalar, or a single input value for <em>mode</em> =
 vector.  In the first case, the length of the vector is the number of
 inputs.  In the second case, the length of the vector is the same as
 the length of the input vector.  An array is produced if multiple
 input values are averaged and <em>mode</em> = vector.  The global array has #
 of rows = length of the input vectors and # of columns = number of
 inputs.</p>
 <p>If the fix prouduces a scalar or vector, then the scalar and each
 element of the vector can be either &#8220;intensive&#8221; or &#8220;extensive&#8221;,
 depending on whether the values contributing to the scalar or vector
 element are &#8220;intensive&#8221; or &#8220;extensive&#8221;.  If the fix produces an array,
 then all elements in the array must be the same, either &#8220;intensive&#8221; or
 &#8220;extensive&#8221;.  If a compute or fix provides the value being time
 averaged, then the compute or fix determines whether the value is
 intensive or extensive; see the doc page for that compute or fix for
 further info.  Values produced by a variable are treated as intensive.</p>
 <p>No parameter of this fix can be used with the <em>start/stop</em> keywords of
 the <a class="reference internal" href="run.html"><em>run</em></a> command.  This fix is not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <blockquote>
 <div>none</div></blockquote>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="compute.html"><em>compute</em></a>, <a class="reference internal" href="fix_ave_atom.html"><em>fix ave/atom</em></a>, <a class="reference internal" href="fix_ave_spatial.html"><em>fix ave/spatial</em></a>, <a class="reference internal" href="fix_ave_histo.html"><em>fix ave/histo</em></a>,
 <a class="reference internal" href="variable.html"><em>variable</em></a>, <a class="reference internal" href="fix_ave_correlate.html"><em>fix ave/correlate</em></a>,</p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The option defaults are mode = scalar, ave = one, start = 0, no file
 output, title 1,2,3 = strings as described above, and no off settings
 for any input values.</p>
 </div>
 </div>
 
 
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diff --git a/doc/fix_aveforce.html b/doc/fix_aveforce.html
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   <div class="section" id="fix-aveforce-command">
 <span id="index-0"></span><h1>fix aveforce command<a class="headerlink" href="#fix-aveforce-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="fix-aveforce-cuda-command">
 <h1>fix aveforce/cuda command<a class="headerlink" href="#fix-aveforce-cuda-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID aveforce fx fy fz keyword value ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>aveforce = style name of this fix command</li>
 <li>fx,fy,fz = force component values (force units)</li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>any of fx,fy,fz can be a variable (see below)
 </pre></div>
 </div>
 <ul class="simple">
 <li>zero or more keyword/value pairs may be appended to args</li>
 <li>keyword = <em>region</em></li>
 </ul>
 <pre class="literal-block">
 <em>region</em> value = region-ID
-    region-ID = ID of region atoms must be in to have added force
+  region-ID = ID of region atoms must be in to have added force
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix pressdown topwall aveforce 0.0 -1.0 0.0
 fix 2 bottomwall aveforce NULL -1.0 0.0 region top
 fix 2 bottomwall aveforce NULL -1.0 v_oscillate region top
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Apply an additional external force to a group of atoms in such a way
 that every atom experiences the same force.  This is useful for
 pushing on wall or boundary atoms so that the structure of the wall
 does not change over time.</p>
 <p>The existing force is averaged for the group of atoms, component by
 component.  The actual force on each atom is then set to the average
 value plus the component specified in this command.  This means each
 atom in the group receives the same force.</p>
 <p>Any of the fx,fy,fz values can be specified as NULL which means the
 force in that dimension is not changed.  Note that this is not the
 same as specifying a 0.0 value, since that sets all forces to the same
 average value without adding in any additional force.</p>
 <p>Any of the 3 quantities defining the force components can be specified
 as an equal-style <a class="reference internal" href="variable.html"><em>variable</em></a>, namely <em>fx</em>, <em>fy</em>, <em>fz</em>.
 If the value is a variable, it should be specified as v_name, where
 name is the variable name.  In this case, the variable will be
 evaluated each timestep, and its value used to determine the average
 force.</p>
 <p>Equal-style variables can specify formulas with various mathematical
 functions, and include <a class="reference internal" href="thermo_style.html"><em>thermo_style</em></a> command
 keywords for the simulation box parameters and timestep and elapsed
 time.  Thus it is easy to specify a time-dependent average force.</p>
 <p>If the <em>region</em> keyword is used, the atom must also be in the
 specified geometric <a class="reference internal" href="region.html"><em>region</em></a> in order to have force added
 to it.</p>
 <hr class="docutils" />
 <p>Styles with a <em>cuda</em> suffix are functionally the same as the
 corresponding style without the suffix.  They have been optimized to
 run faster, depending on your available hardware, as discussed in
 <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a> of the manual.  The
 accelerated styles take the same arguments and should produce the same
 results, except for round-off and precision issues.</p>
 <p>These accelerated styles are part of the USER-CUDA package.  They are
 only enabled if LAMMPS was built with that package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 <p>You can specify the accelerated styles explicitly in your input script
 by including their suffix, or you can use the <a class="reference internal" href="Section_start.html#start-7"><span>-suffix command-line switch</span></a> when you invoke LAMMPS, or you can
 use the <a class="reference internal" href="suffix.html"><em>suffix</em></a> command in your input script.</p>
 <p>See <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a> of the manual for
 more instructions on how to use the accelerated styles effectively.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.  None of the <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> options
 are relevant to this fix.</p>
 <p>This fix computes a global 3-vector of forces, which can be accessed
 by various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  This is the
 total force on the group of atoms before the forces on individual
 atoms are changed by the fix.  The vector values calculated by this
 fix are &#8220;extensive&#8221;.</p>
 <p>No parameter of this fix can be used with the <em>start/stop</em> keywords of
 the <a class="reference internal" href="run.html"><em>run</em></a> command.</p>
 <p>The forces due to this fix are imposed during an energy minimization,
 invoked by the <a class="reference internal" href="minimize.html"><em>minimize</em></a> command.  You should not
 specify force components with a variable that has time-dependence for
 use with a minimizer, since the minimizer increments the timestep as
 the iteration count during the minimization.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <blockquote>
 <div>none</div></blockquote>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="fix_setforce.html"><em>fix setforce</em></a>, <a class="reference internal" href="fix_addforce.html"><em>fix addforce</em></a></p>
 <p><strong>Default:</strong> none</p>
 </div>
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   <div class="section" id="fix-balance-command">
 <span id="index-0"></span><h1>fix balance command<a class="headerlink" href="#fix-balance-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID balance Nfreq thresh style args keyword value ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>balance = style name of this fix command</li>
 <li>Nfreq = perform dynamic load balancing every this many steps</li>
 <li>thresh = imbalance threshhold that must be exceeded to perform a re-balance</li>
 <li>style = <em>shift</em> or <em>rcb</em></li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>shift args = dimstr Niter stopthresh
-    dimstr = sequence of letters containing &quot;x&quot; or &quot;y&quot; or &quot;z&quot;, each not more than once
-    Niter = # of times to iterate within each dimension of dimstr sequence
-    stopthresh = stop balancing when this imbalance threshhold is reached
-  rcb args = none
+  dimstr = sequence of letters containing &quot;x&quot; or &quot;y&quot; or &quot;z&quot;, each not more than once
+  Niter = # of times to iterate within each dimension of dimstr sequence
+  stopthresh = stop balancing when this imbalance threshhold is reached
+rcb args = none
 </pre></div>
 </div>
 <ul class="simple">
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>out</em></li>
 </ul>
 <pre class="literal-block">
 <em>out</em> value = filename
-    filename = write each processor's sub-domain to a file, at each re-balancing
+  filename = write each processor's sub-domain to a file, at each re-balancing
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix 2 all balance 1000 1.05 shift x 10 1.05
 fix 2 all balance 100 0.9 shift xy 20 1.1 out tmp.balance
 fix 2 all balance 1000 1.1 rcb
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>This command adjusts the size and shape of processor sub-domains
 within the simulation box, to attempt to balance the number of
 particles and thus the computational cost (load) evenly across
 processors.  The load balancing is &#8220;dynamic&#8221; in the sense that
 rebalancing is performed periodically during the simulation.  To
 perform &#8220;static&#8221; balancing, before or between runs, see the
 <a class="reference internal" href="balance.html"><em>balance</em></a> command.</p>
 <p>Load-balancing is typically only useful if the particles in the
 simulation box have a spatially-varying density distribution.  E.g. a
 model of a vapor/liquid interface, or a solid with an irregular-shaped
 geometry containing void regions.  In this case, the LAMMPS default of
 dividing the simulation box volume into a regular-spaced grid of 3d
 bricks, with one equal-volume sub-domain per processor, may assign
 very different numbers of particles per processor.  This can lead to
 poor performance when the simulation is run in parallel.</p>
 <p>Note that the <a class="reference internal" href="processors.html"><em>processors</em></a> command allows some control
 over how the box volume is split across processors.  Specifically, for
 a Px by Py by Pz grid of processors, it allows choice of Px, Py, and
 Pz, subject to the constraint that Px * Py * Pz = P, the total number
 of processors.  This is sufficient to achieve good load-balance for
 some problems on some processor counts.  However, all the processor
 sub-domains will still have the same shape and same volume.</p>
 <p>On a particular timestep, a load-balancing operation is only performed
 if the current &#8220;imbalance factor&#8221; in particles owned by each processor
 exceeds the specified <em>thresh</em> parameter.  The imbalance factor is
 defined as the maximum number of particles owned by any processor,
 divided by the average number of particles per processor.  Thus an
 imbalance factor of 1.0 is perfect balance.</p>
 <p>As an example, for 10000 particles running on 10 processors, if the
 most heavily loaded processor has 1200 particles, then the factor is
 1.2, meaning there is a 20% imbalance.  Note that re-balances can be
 forced even if the current balance is perfect (1.0) be specifying a
 <em>thresh</em> &lt; 1.0.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">This command attempts to minimize the imbalance
 factor, as defined above.  But depending on the method a perfect
 balance (1.0) may not be achieved.  For example, &#8220;grid&#8221; methods
 (defined below) that create a logical 3d grid cannot achieve perfect
 balance for many irregular distributions of particles.  Likewise, if a
 portion of the system is a perfect lattice, e.g. the initial system is
 generated by the <a class="reference internal" href="create_atoms.html"><em>create_atoms</em></a> command, then &#8220;grid&#8221;
 methods may be unable to achieve exact balance.  This is because
 entire lattice planes will be owned or not owned by a single
 processor.</p>
 </div>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">The imbalance factor is also an estimate of the
 maximum speed-up you can hope to achieve by running a perfectly
 balanced simulation versus an imbalanced one.  In the example above,
 the 10000 particle simulation could run up to 20% faster if it were
 perfectly balanced, versus when imbalanced.  However, computational
 cost is not strictly proportional to particle count, and changing the
 relative size and shape of processor sub-domains may lead to
 additional computational and communication overheads, e.g. in the PPPM
 solver used via the <a class="reference internal" href="kspace_style.html"><em>kspace_style</em></a> command.  Thus
 you should benchmark the run times of a simulation before and after
 balancing.</p>
 </div>
 <hr class="docutils" />
 <p>The method used to perform a load balance is specified by one of the
 listed styles, which are described in detail below.  There are 2 kinds
 of styles.</p>
 <p>The <em>shift</em> style is a &#8220;grid&#8221; method which produces a logical 3d grid
 of processors.  It operates by changing the cutting planes (or lines)
 between processors in 3d (or 2d), to adjust the volume (area in 2d)
 assigned to each processor, as in the following 2d diagram where
 processor sub-domains are shown and atoms are colored by the processor
 that owns them.  The leftmost diagram is the default partitioning of
 the simulation box across processors (one sub-box for each of 16
 processors); the middle diagram is after a &#8220;grid&#8221; method has been
 applied.</p>
 <a data-lightbox="group-default"
                    href="_images/balance_uniform.jpg"
                    class=""
                    title=""
                    data-title=""
                    ><img src="_images/balance_uniform.jpg"
                     class="align-center"
                     width="25%"
                     height="auto"
                     alt=""/>
                     </a><a data-lightbox="group-default"
                    href="_images/balance_nonuniform.jpg"
                    class=""
                    title=""
                    data-title=""
                    ><img src="_images/balance_nonuniform.jpg"
                     class="align-center"
                     width="25%"
                     height="auto"
                     alt=""/>
                     </a><a data-lightbox="group-default"
                    href="_images/balance_rcb.jpg"
                    class=""
                    title=""
                    data-title=""
                    ><img src="_images/balance_rcb.jpg"
                     class="align-center"
                     width="25%"
                     height="auto"
                     alt=""/>
                     </a><p>The <em>rcb</em> style is a &#8220;tiling&#8221; method which does not produce a logical
 3d grid of processors.  Rather it tiles the simulation domain with
 rectangular sub-boxes of varying size and shape in an irregular
 fashion so as to have equal numbers of particles in each sub-box, as
 in the rightmost diagram above.</p>
 <p>The &#8220;grid&#8221; methods can be used with either of the
 <a class="reference internal" href="comm_style.html"><em>comm_style</em></a> command options, <em>brick</em> or <em>tiled</em>.  The
 &#8220;tiling&#8221; methods can only be used with <a class="reference internal" href="comm_style.html"><em>comm_style tiled</em></a>.</p>
 <p>When a &#8220;grid&#8221; method is specified, the current domain partitioning can
 be either a logical 3d grid or a tiled partitioning.  In the former
 case, the current logical 3d grid is used as a starting point and
 changes are made to improve the imbalance factor.  In the latter case,
 the tiled partitioning is discarded and a logical 3d grid is created
 with uniform spacing in all dimensions.  This is the starting point
 for the balancing operation.</p>
 <p>When a &#8220;tiling&#8221; method is specified, the current domain partitioning
 (&#8220;grid&#8221; or &#8220;tiled&#8221;) is ignored, and a new partitioning is computed
 from scratch.</p>
 <hr class="docutils" />
 <p>The <em>group-ID</em> is currently ignored.  In the future it may be used to
 determine what particles are considered for balancing.  Normally it
 would only makes sense to use the <em>all</em> group.  But in some cases it
 may be useful to balance on a subset of the particles, e.g. when
 modeling large nanoparticles in a background of small solvent
 particles.</p>
 <p>The <em>Nfreq</em> setting determines how often a rebalance is performed.  If
 <em>Nfreq</em> &gt; 0, then rebalancing will occur every <em>Nfreq</em> steps.  Each
 time a rebalance occurs, a reneighboring is triggered, so <em>Nfreq</em>
 should not be too small.  If <em>Nfreq</em> = 0, then rebalancing will be
 done every time reneighboring normally occurs, as determined by the
 the <a class="reference internal" href="neighbor.html"><em>neighbor</em></a> and <a class="reference internal" href="neigh_modify.html"><em>neigh_modify</em></a>
 command settings.</p>
 <p>On rebalance steps, rebalancing will only be attempted if the current
 imbalance factor, as defined above, exceeds the <em>thresh</em> setting.</p>
 <hr class="docutils" />
 <p>The <em>shift</em> style invokes a &#8220;grid&#8221; method for balancing, as described
 above.  It changes the positions of cutting planes between processors
 in an iterative fashion, seeking to reduce the imbalance factor.</p>
 <p>The <em>dimstr</em> argument is a string of characters, each of which must be
 an &#8220;x&#8221; or &#8220;y&#8221; or &#8220;z&#8221;.  Eacn character can appear zero or one time,
 since there is no advantage to balancing on a dimension more than
 once.  You should normally only list dimensions where you expect there
 to be a density variation in the particles.</p>
 <p>Balancing proceeds by adjusting the cutting planes in each of the
 dimensions listed in <em>dimstr</em>, one dimension at a time.  For a single
 dimension, the balancing operation (described below) is iterated on up
 to <em>Niter</em> times.  After each dimension finishes, the imbalance factor
 is re-computed, and the balancing operation halts if the <em>stopthresh</em>
 criterion is met.</p>
 <p>A rebalance operation in a single dimension is performed using a
 density-dependent recursive multisectioning algorithm, where the
 position of each cutting plane (line in 2d) in the dimension is
 adjusted independently.  This is similar to a recursive bisectioning
 for a single value, except that the bounds used for each bisectioning
 take advantage of information from neighboring cuts if possible, as
 well as counts of particles at the bounds on either side of each cuts,
 which themselves were cuts in previous iterations.  The latter is used
 to infer a density of pariticles near each of the current cuts.  At
 each iteration, the count of particles on either side of each plane is
 tallied.  If the counts do not match the target value for the plane,
 the position of the cut is adjusted based on the local density.  The
 low and high bounds are adjusted on each iteration, using new count
 information, so that they become closer together over time.  Thus as
 the recursion progresses, the count of particles on either side of the
 plane gets closer to the target value.</p>
 <p>The density-dependent part of this algorithm is often an advantage
 when you rebalance a system that is already nearly balanced.  It
 typically converges more quickly than the geometric bisectioning
 algorithm used by the <a class="reference internal" href="balance.html"><em>balance</em></a> command.  However, if can
 be a disadvantage if you attempt to rebalance a system that is far
 from balanced, and converge more slowly.  In this case you probably
 want to use the <a class="reference internal" href="balance.html"><em>balance</em></a> command before starting a run,
 so that you begin the run with a balanced system.</p>
 <p>Once the rebalancing is complete and final processor sub-domains
 assigned, particles migrate to their new owning processor as part of
 the normal reneighboring procedure.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">At each rebalance operation, the bisectioning for each
 cutting plane (line in 2d) typcially starts with low and high bounds
 separated by the extent of a processor&#8217;s sub-domain in one dimension.
 The size of this bracketing region shrinks based on the local density,
 as described above, which should typically be 1/2 or more every
 iteration.  Thus if <em>Niter</em> is specified as 10, the cutting plane will
 typically be positioned to better than 1 part in 1000 accuracy
 (relative to the perfect target position).  For <em>Niter</em> = 20, it will
 be accurate to better than 1 part in a million.  Thus there is no need
 to set <em>Niter</em> to a large value.  This is especially true if you are
 rebalancing often enough that each time you expect only an incremental
 adjustement in the cutting planes is necessary.  LAMMPS will check if
 the threshold accuracy is reached (in a dimension) is less iterations
 than <em>Niter</em> and exit early.</p>
 </div>
 <hr class="docutils" />
 <p>The <em>rcb</em> style invokes a &#8220;tiled&#8221; method for balancing, as described
 above.  It performs a recursive coordinate bisectioning (RCB) of the
 simulation domain.  The basic idea is as follows.</p>
 <p>The simulation domain is cut into 2 boxes by an axis-aligned cut in
 the longest dimension, leaving one new box on either side of the cut.
 All the processors are also partitioned into 2 groups, half assigned
 to the box on the lower side of the cut, and half to the box on the
 upper side.  (If the processor count is odd, one side gets an extra
 processor.)  The cut is positioned so that the number of atoms in the
 lower box is exactly the number that the processors assigned to that
 box should own for load balance to be perfect.  This also makes load
 balance for the upper box perfect.  The positioning is done
 iteratively, by a bisectioning method.  Note that counting atoms on
 either side of the cut requires communication between all processors
 at each iteration.</p>
 <p>That is the procedure for the first cut.  Subsequent cuts are made
 recursively, in exactly the same manner.  The subset of processors
 assigned to each box make a new cut in the longest dimension of that
 box, splitting the box, the subset of processsors, and the atoms in
 the box in two.  The recursion continues until every processor is
 assigned a sub-box of the entire simulation domain, and owns the atoms
 in that sub-box.</p>
 <hr class="docutils" />
 <p>The <em>out</em> keyword writes a text file to the specified <em>filename</em> with
 the results of each rebalancing operation.  The file contains the
 bounds of the sub-domain for each processor after the balancing
 operation completes.  The format of the file is compatible with the
 <a class="reference external" href="pizza">Pizza.py</a> <em>mdump</em> tool which has support for manipulating and
 visualizing mesh files.  An example is shown here for a balancing by 4
 processors for a 2d problem:</p>
 <div class="highlight-python"><div class="highlight"><pre>ITEM: TIMESTEP
 0
 ITEM: NUMBER OF NODES
 16
 ITEM: BOX BOUNDS
 0 10
 0 10
 0 10
 ITEM: NODES
 1 1 0 0 0
 2 1 5 0 0
 3 1 5 5 0
 4 1 0 5 0
 5 1 5 0 0
 6 1 10 0 0
 7 1 10 5 0
 8 1 5 5 0
 9 1 0 5 0
 10 1 5 5 0
 11 1 5 10 0
 12 1 10 5 0
 13 1 5 5 0
 14 1 10 5 0
 15 1 10 10 0
 16 1 5 10 0
 ITEM: TIMESTEP
 0
 ITEM: NUMBER OF SQUARES
 4
 ITEM: SQUARES
 1 1 1 2 3 4
 2 1 5 6 7 8
 3 1 9 10 11 12
 4 1 13 14 15 16
 </pre></div>
 </div>
 <p>The coordinates of all the vertices are listed in the NODES section, 5
 per processor.  Note that the 4 sub-domains share vertices, so there
 will be duplicate nodes in the list.</p>
 <p>The &#8220;SQUARES&#8221; section lists the node IDs of the 4 vertices in a
 rectangle for each processor (1 to 4).</p>
 <p>For a 3d problem, the syntax is similar with 8 vertices listed for
 each processor, instead of 4, and &#8220;SQUARES&#8221; replaced by &#8220;CUBES&#8221;.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.  None of the <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> options
 are relevant to this fix.</p>
 <p>This fix computes a global scalar which is the imbalance factor
 after the most recent rebalance and a global vector of length 3 with
 additional information about the most recent rebalancing.  The 3
 values in the vector are as follows:</p>
 <ul class="simple">
 <li>1 = max # of particles per processor</li>
 <li>2 = total # iterations performed in last rebalance</li>
 <li>3 = imbalance factor right before the last rebalance was performed</li>
 </ul>
 <p>As explained above, the imbalance factor is the ratio of the maximum
 number of particles on any processor to the average number of
 particles per processor.</p>
 <p>These quantities can be accessed by various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  The scalar and vector values
 calculated by this fix are &#8220;intensive&#8221;.</p>
 <p>No parameter of this fix can be used with the <em>start/stop</em> keywords of
 the <a class="reference internal" href="run.html"><em>run</em></a> command.  This fix is not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>For 2d simulations, a &#8220;z&#8221; cannot appear in <em>dimstr</em> for the <em>shift</em>
 style.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="processors.html"><em>processors</em></a>, <a class="reference internal" href="balance.html"><em>balance</em></a></p>
 <p><strong>Default:</strong> none</p>
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   <div class="section" id="fix-bond-break-command">
 <span id="index-0"></span><h1>fix bond/break command<a class="headerlink" href="#fix-bond-break-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID bond/break Nevery bondtype Rmax keyword values ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>bond/break = style name of this fix command</li>
 <li>Nevery = attempt bond breaking every this many steps</li>
 <li>bondtype = type of bonds to break</li>
 <li>Rmax = bond longer than Rmax can break (distance units)</li>
 <li>zero or more keyword/value pairs may be appended to args</li>
 <li>keyword = <em>prob</em></li>
 </ul>
 <pre class="literal-block">
 <em>prob</em> values = fraction seed
-    fraction = break a bond with this probability if otherwise eligible
-    seed = random number seed (positive integer)
+  fraction = break a bond with this probability if otherwise eligible
+  seed = random number seed (positive integer)
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix 5 all bond/break 10 2 1.2
 fix 5 polymer bond/break 1 1 2.0 prob 0.5 49829
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Break bonds between pairs of atoms as a simulation runs according to
 specified criteria.  This can be used to model the dissolution of a
 polymer network due to stretching of the simulation box or other
 deformations.  In this context, a bond means an interaction between a
 pair of atoms computed by the <a class="reference internal" href="bond_style.html"><em>bond_style</em></a> command.
 Once the bond is broken it will be permanently deleted, as will all
 angle, dihedral, and improper interactions that bond is part of.</p>
 <p>This is different than a <a class="reference internal" href="pair_style.html"><em>pairwise</em></a> bond-order
 potential such as Tersoff or AIREBO which infers bonds and many-body
 interactions based on the current geometry of a small cluster of atoms
 and effectively creates and destroys bonds and higher-order many-body
 interactions from timestep to timestep as atoms move.</p>
 <p>A check for possible bond breakage is performed every <em>Nevery</em>
 timesteps.  If two bonded atoms I,J are further than a distance <em>Rmax</em>
 of each other, if the bond is of type <em>bondtype</em>, and if both I and J
 are in the specified fix group, then I,J is labeled as a &#8220;possible&#8221;
 bond to break.</p>
 <p>If several bonds involving an atom are stretched, it may have multiple
 possible bonds to break.  Every atom checks its list of possible bonds
 to break and labels the longest such bond as its &#8220;sole&#8221; bond to break.
 After this is done, if atom I is bonded to atom J in its sole bond,
 and atom J is bonded to atom I in its sole bond, then the I,J bond is
 &#8220;eligible&#8221; to be broken.</p>
 <p>Note that these rules mean an atom will only be part of at most one
 broken bond on a given timestep.  It also means that if atom I chooses
 atom J as its sole partner, but atom J chooses atom K is its sole
 partner (due to Rjk &gt; Rij), then this means atom I will not be part of
 a broken bond on this timestep, even if it has other possible bond
 partners.</p>
 <p>The <em>prob</em> keyword can effect whether an eligible bond is actually
 broken.  The <em>fraction</em> setting must be a value between 0.0 and 1.0.
 A uniform random number between 0.0 and 1.0 is generated and the
 eligible bond is only broken if the random number &lt; fraction.</p>
 <p>When a bond is broken, data structures within LAMMPS that store bond
 topology are updated to reflect the breakage.  Likewise, if the bond
 is part of a 3-body (angle) or 4-body (dihedral, improper)
 interaction, that interaction is removed as well.  These changes
 typically affect pairwise interactions between atoms that used to be
 part of bonds, angles, etc.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">One data structure that is not updated when a bond
 breaks are the molecule IDs stored by each atom.  Even though
 one molecule becomes two moleclues due to the broken bond, all atoms
 in both new moleclues retain their original molecule IDs.</p>
 </div>
 <p>Computationally, each timestep this fix operates, it loops over all
 the bonds in the system and computes distances between pairs of bonded
 atoms.  It also communicates between neighboring processors to
 coordinate which bonds are broken.  Moreover, if any bonds are broken,
 neighbor lists must be immediately updated on the same timestep.  This
 is to insure that any pairwise interactions that should be turned &#8220;on&#8221;
 due to a bond breaking, because they are no longer excluded by the
 presence of the bond and the settings of the
 <a class="reference internal" href="special_bonds.html"><em>special_bonds</em></a> command, will be immediately
 recognized.  All of these operations increase the cost of a timestep.
 Thus you should be cautious about invoking this fix too frequently.</p>
 <p>You can dump out snapshots of the current bond topology via the <a class="reference internal" href="dump.html"><em>dump local</em></a> command.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">Breaking a bond typically alters the energy of a
 system.  You should be careful not to choose bond breaking criteria
 that induce a dramatic change in energy.  For example, if you define a
 very stiff harmonic bond and break it when 2 atoms are separated by a
 distance far from the equilibribum bond length, then the 2 atoms will
 be dramatically released when the bond is broken.  More generally, you
 may need to thermostat your system to compensate for energy changes
 resulting from broken bonds (and angles, dihedrals, impropers).</p>
 </div>
 </div>
 <hr class="docutils" />
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.  None of the <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> options
 are relevant to this fix.</p>
 <p>This fix computes two statistics which it stores in a global vector of
 length 2, which can be accessed by various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  The vector values calculated
 by this fix are &#8220;intensive&#8221;.</p>
 <p>These are the 2 quantities:</p>
 <ul class="simple">
 <li><ol class="first arabic">
 <li># of bonds broken on the most recent breakage timestep</li>
 </ol>
 </li>
 <li><ol class="first arabic" start="2">
 <li>cummulative # of bonds broken</li>
 </ol>
 </li>
 </ul>
 <p>No parameter of this fix can be used with the <em>start/stop</em> keywords of
 the <a class="reference internal" href="run.html"><em>run</em></a> command.  This fix is not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>This fix is part of the MC package.  It is only enabled if LAMMPS was
 built with that package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="fix_bond_create.html"><em>fix bond/create</em></a>, <a class="reference internal" href="fix_bond_swap.html"><em>fix bond/swap</em></a>, <a class="reference internal" href="dump.html"><em>dump local</em></a>,
 <a class="reference internal" href="special_bonds.html"><em>special_bonds</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The option defaults are prob = 1.0.</p>
 </div>
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   <div class="section" id="fix-bond-create-command">
 <span id="index-0"></span><h1>fix bond/create command<a class="headerlink" href="#fix-bond-create-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID bond/create Nevery itype jtype Rmin bondtype keyword values ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>bond/create = style name of this fix command</li>
 <li>Nevery = attempt bond creation every this many steps</li>
 <li>itype,jtype = atoms of itype can bond to atoms of jtype</li>
 <li>Rmin = 2 atoms separated by less than Rmin can bond (distance units)</li>
 <li>bondtype = type of created bonds</li>
 <li>zero or more keyword/value pairs may be appended to args</li>
 <li>keyword = <em>iparam</em> or <em>jparam</em> or <em>prob</em> or <em>atype</em> or <em>dtype</em> or <em>itype</em></li>
 </ul>
 <pre class="literal-block">
 <em>iparam</em> values = maxbond, newtype
-    maxbond = max # of bonds of bondtype the itype atom can have
-    newtype = change the itype atom to this type when maxbonds exist
-  <em>jparam</em> values = maxbond, newtype
-    maxbond = max # of bonds of bondtype the jtype atom can have
-    newtype = change the jtype atom to this type when maxbonds exist
-  <em>prob</em> values = fraction seed
-    fraction = create a bond with this probability if otherwise eligible
-    seed = random number seed (positive integer)
-  <em>atype</em> value = angletype
-    angletype = type of created angles
-  <em>dtype</em> value = dihedraltype
-    dihedraltype = type of created dihedrals
-  <em>itype</em> value = impropertype
-    impropertype = type of created impropers
+  maxbond = max # of bonds of bondtype the itype atom can have
+  newtype = change the itype atom to this type when maxbonds exist
+<em>jparam</em> values = maxbond, newtype
+  maxbond = max # of bonds of bondtype the jtype atom can have
+  newtype = change the jtype atom to this type when maxbonds exist
+<em>prob</em> values = fraction seed
+  fraction = create a bond with this probability if otherwise eligible
+  seed = random number seed (positive integer)
+<em>atype</em> value = angletype
+  angletype = type of created angles
+<em>dtype</em> value = dihedraltype
+  dihedraltype = type of created dihedrals
+<em>itype</em> value = impropertype
+  impropertype = type of created impropers
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix 5 all bond/create 10 1 2 0.8 1
 fix 5 all bond/create 1 3 3 0.8 1 prob 0.5 85784 iparam 2 3
 fix 5 all bond/create 1 3 3 0.8 1 prob 0.5 85784 iparam 2 3 atype 1 dtype 2
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Create bonds between pairs of atoms as a simulation runs according to
 specified criteria.  This can be used to model cross-linking of
 polymers, the formation of a percolation network, etc.  In this
 context, a bond means an interaction between a pair of atoms computed
 by the <a class="reference internal" href="bond_style.html"><em>bond_style</em></a> command.  Once the bond is created
 it will be permanently in place.  Optionally, the creation of a bond
 can also create angle, dihedral, and improper interactions that bond
 is part of.  See the discussion of the <em>atype</em>, <em>dtype</em>, and <em>itype</em>
 keywords below.</p>
 <p>This is different than a <a class="reference internal" href="pair_style.html"><em>pairwise</em></a> bond-order
 potential such as Tersoff or AIREBO which infers bonds and many-body
 interactions based on the current geometry of a small cluster of atoms
 and effectively creates and destroys bonds and higher-order many-body
 interactions from timestep to timestep as atoms move.</p>
 <p>A check for possible new bonds is performed every <em>Nevery</em> timesteps.
 If two atoms I,J are within a distance <em>Rmin</em> of each other, if I is
 of atom type <em>itype</em>, if J is of atom type <em>jtype</em>, if both I and J
 are in the specified fix group, if a bond does not already exist
 between I and J, and if both I and J meet their respective <em>maxbond</em>
 requirement (explained below), then I,J is labeled as a &#8220;possible&#8221;
 bond pair.</p>
 <p>If several atoms are close to an atom, it may have multiple possible
 bond partners.  Every atom checks its list of possible bond partners
 and labels the closest such partner as its &#8220;sole&#8221; bond partner.  After
 this is done, if atom I has atom J as its sole partner, and atom J has
 atom I as its sole partner, then the I,J bond is &#8220;eligible&#8221; to be
 formed.</p>
 <p>Note that these rules mean an atom will only be part of at most one
 created bond on a given timestep.  It also means that if atom I
 chooses atom J as its sole partner, but atom J chooses atom K is its
 sole partner (due to Rjk &lt; Rij), then this means atom I will not form
 a bond on this timestep, even if it has other possible bond partners.</p>
 <p>It is permissible to have <em>itype</em> = <em>jtype</em>.  <em>Rmin</em> must be &lt;= the
 pairwise cutoff distance between <em>itype</em> and <em>jtype</em> atoms, as defined
 by the <a class="reference internal" href="pair_style.html"><em>pair_style</em></a> command.</p>
 <p>The <em>iparam</em> and <em>jparam</em> keywords can be used to limit the bonding
 functionality of the participating atoms.  Each atom keeps track of
 how many bonds of <em>bondtype</em> it already has.  If atom I of
 itype already has <em>maxbond</em> bonds (as set by the <em>iparam</em>
 keyword), then it will not form any more.  Likewise for atom J.  If
 <em>maxbond</em> is set to 0, then there is no limit on the number of bonds
 that can be formed with that atom.</p>
 <p>The <em>newtype</em> value for <em>iparam</em> and <em>jparam</em> can be used to change
 the atom type of atom I or J when it reaches <em>maxbond</em> number of bonds
 of type <em>bondtype</em>.  This means it can now interact in a pairwise
 fashion with other atoms in a different way by specifying different
 <a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a> coefficients.  If you do not wish the
 atom type to change, simply specify <em>newtype</em> as <em>itype</em> or <em>jtype</em>.</p>
 <p>The <em>prob</em> keyword can also effect whether an eligible bond is
 actually created.  The <em>fraction</em> setting must be a value between 0.0
 and 1.0.  A uniform random number between 0.0 and 1.0 is generated and
 the eligible bond is only created if the random number &lt; fraction.</p>
 <p>Any bond that is created is assigned a bond type of <em>bondtype</em></p>
 <p>When a bond is created, data structures within LAMMPS that store bond
 topology are updated to reflect the creation.  If the bond is part of
 new 3-body (angle) or 4-body (dihedral, improper) interactions, you
 can choose to create new angles, dihedrals, impropers as well, using
 the <em>atype</em>, <em>dtype</em>, and <em>itype</em> keywords.  All of these changes
 typically affect pairwise interactions between atoms that are now part
 of new bonds, angles, etc.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">One data structure that is not updated when a bond
 breaks are the molecule IDs stored by each atom.  Even though two
 molecules become one moleclue due to the created bond, all atoms in
 the new moleclue retain their original molecule IDs.</p>
 </div>
 <p>If the <em>atype</em> keyword is used and if an angle potential is defined
 via the <code class="xref doc docutils literal"><span class="pre">angle_style</span></code> command, then any new 3-body
 interactions inferred by the creation of a bond will create new angles
 of type <em>angletype</em>, with parameters assigned by the corresponding
 <a class="reference internal" href="angle_coeff.html"><em>angle_coeff</em></a> command.  Likewise, the <em>dtype</em> and
 <em>itype</em> keywords will create new dihedrals and impropers of type
 <em>dihedraltype</em> and <em>impropertype</em>.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">To create a new bond, the internal LAMMPS data
 structures that store this information must have space for it.  When
 LAMMPS is initialized from a data file, the list of bonds is scanned
 and the maximum number of bonds per atom is tallied.  If some atom
 will acquire more bonds than this limit as this fix operates, then the
 &#8220;extra bond per atom&#8221; parameter must be set to allow for it.  Ditto
 for &#8220;extra angle per atom&#8221;, &#8220;extra dihedral per atom&#8221;, and &#8220;extra
 improper per atom&#8221; if angles, dihedrals, or impropers are being added
 when bonds are created.  See the <a class="reference internal" href="read_data.html"><em>read_data</em></a> or
 <a class="reference internal" href="create_box.html"><em>create_box</em></a> command for more details.  Note that a
 data file with no atoms can be used if you wish to add unbonded atoms
 via the <a class="reference internal" href="create_atoms.html"><em>create atoms</em></a> command, e.g. for a
 percolation simulation.</p>
 </div>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">LAMMPS stores and maintains a data structure with a
 list of the 1st, 2nd, and 3rd neighbors of each atom (within the bond
 topology of the system) for use in weighting pairwise interactions for
 bonded atoms.  Note that adding a single bond always adds a new 1st
 neighbor but may also induce <em>many</em> new 2nd and 3rd neighbors,
 depending on the molecular topology of your system.  The &#8220;extra
 special per atom&#8221; parameter must typically be set to allow for the new
 maximum total size (1st + 2nd + 3rd neighbors) of this per-atom list.
 There are 3 ways to do this.  See the <a class="reference internal" href="read_data.html"><em>read_data</em></a> or
 <a class="reference internal" href="create_box.html"><em>create_box</em></a> or &#8220;special_bonds extra&#8221; commands for
 details.</p>
 </div>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">Even if you do not use the <em>atype</em>, <em>dtype</em>, or
 <em>itype</em> keywords, the list of topological neighbors is updated for
 atoms affected by the new bond.  This in turn affects which neighbors
 are considered for pairwise interactions, using the weighting rules
 set by the <a class="reference internal" href="special_bonds.html"><em>special_bonds</em></a> command.  Consider a new
 bond created between atoms I,J.  If J has a bonded neighbor K, then K
 becomes a 2nd neighbor of I.  Even if the <em>atype</em> keyword is not used
 to create angle I-J-K, the pairwise interaction between I and K will
 be potentially turned off or weighted by the 1-3 weighting specified
 by the <a class="reference internal" href="special_bonds.html"><em>special_bonds</em></a> command.  This is the case
 even if the &#8220;angle yes&#8221; option was used with that command.  The same
 is true for 3rd neighbors (1-4 interactions), the <em>dtype</em> keyword, and
 the &#8220;dihedral yes&#8221; option used with the
 <a class="reference internal" href="special_bonds.html"><em>special_bonds</em></a> command.</p>
 </div>
 <p>Note that even if your simulation starts with no bonds, you must
 define a <a class="reference internal" href="bond_style.html"><em>bond_style</em></a> and use the
 <a class="reference internal" href="bond_coeff.html"><em>bond_coeff</em></a> command to specify coefficients for the
 <em>bondtype</em>.  Similarly, if new atom types are specified by the
 <em>iparam</em> or <em>jparam</em> keywords, they must be within the range of atom
 types allowed by the simulation and pairwise coefficients must be
 specified for the new types.</p>
 <p>Computationally, each timestep this fix operates, it loops over
 neighbor lists and computes distances between pairs of atoms in the
 list.  It also communicates between neighboring processors to
 coordinate which bonds are created.  Moreover, if any bonds are
 created, neighbor lists must be immediately updated on the same
 timestep.  This is to insure that any pairwise interactions that
 should be turned &#8220;off&#8221; due to a bond creation, because they are now
 excluded by the presence of the bond and the settings of the
 <a class="reference internal" href="special_bonds.html"><em>special_bonds</em></a> command, will be immediately
 recognized.  All of these operations increase the cost of a timestep.
 Thus you should be cautious about invoking this fix too frequently.</p>
 <p>You can dump out snapshots of the current bond topology via the <a class="reference internal" href="dump.html"><em>dump local</em></a> command.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">Creating a bond typically alters the energy of a
 system.  You should be careful not to choose bond creation criteria
 that induce a dramatic change in energy.  For example, if you define a
 very stiff harmonic bond and create it when 2 atoms are separated by a
 distance far from the equilibribum bond length, then the 2 atoms will
 oscillate dramatically when the bond is formed.  More generally, you
 may need to thermostat your system to compensate for energy changes
 resulting from created bonds (and angles, dihedrals, impropers).</p>
 </div>
 </div>
 <hr class="docutils" />
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.  None of the <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> options
 are relevant to this fix.</p>
 <p>This fix computes two statistics which it stores in a global vector of
 length 2, which can be accessed by various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  The vector values calculated
 by this fix are &#8220;intensive&#8221;.</p>
 <p>These are the 2 quantities:</p>
 <ul class="simple">
 <li><ol class="first arabic">
 <li># of bonds created on the most recent creation timestep</li>
 </ol>
 </li>
 <li><ol class="first arabic" start="2">
 <li>cummulative # of bonds created</li>
 </ol>
 </li>
 </ul>
 <p>No parameter of this fix can be used with the <em>start/stop</em> keywords of
 the <a class="reference internal" href="run.html"><em>run</em></a> command.  This fix is not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>This fix is part of the MC package.  It is only enabled if LAMMPS was
 built with that package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="fix_bond_break.html"><em>fix bond/break</em></a>, <a class="reference internal" href="fix_bond_swap.html"><em>fix bond/swap</em></a>, <a class="reference internal" href="dump.html"><em>dump local</em></a>,
 <a class="reference internal" href="special_bonds.html"><em>special_bonds</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The option defaults are iparam = (0,itype), jparam = (0,jtype), and
 prob = 1.0.</p>
 </div>
 </div>
 
 
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   <div class="section" id="fix-colvars-command">
 <span id="index-0"></span><h1>fix colvars command<a class="headerlink" href="#fix-colvars-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID colvars configfile keyword values ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>colvars = style name of this fix command</li>
 <li>configfile = the configuration file for the colvars module</li>
 <li>keyword = <em>input</em> or <em>output</em> or <em>seed</em> or <em>tstat</em></li>
 </ul>
 <pre class="literal-block">
 <em>input</em> arg = colvars.state file name or prefix or NULL (default: NULL)
-  <em>output</em> arg = output filename prefix (default: out)
-  <em>seed</em> arg = seed for random number generator (default: 1966)
-  <em>unwrap</em> arg = <em>yes</em> or <em>no</em>
-    use unwrapped coordinates in collective variables (default: yes)
-  <em>tstat</em> arg = fix id of a thermostat or NULL (default: NULL)
+<em>output</em> arg = output filename prefix (default: out)
+<em>seed</em> arg = seed for random number generator (default: 1966)
+<em>unwrap</em> arg = <em>yes</em> or <em>no</em>
+  use unwrapped coordinates in collective variables (default: yes)
+<em>tstat</em> arg = fix id of a thermostat or NULL (default: NULL)
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix mtd all colvars peptide.colvars.inp seed 2122 input peptide.colvars.state output peptide
 fix abf all colvars colvars.inp tstat 1
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>This fix interfaces LAMMPS to a &#8220;collective variables&#8221; or &#8220;colvars&#8221;
 module library which allows to calculate potentials of mean force
 (PMFs) for any set of colvars, using different sampling methods:
 currently implemented are the Adaptive Biasing Force (ABF) method,
 metadynamics, Steered Molecular Dynamics (SMD) and Umbrella Sampling
 (US) via a flexible harmonic restraint bias. The colvars library is
 hosted at <a class="reference external" href="http://colvars.github.io/">http://colvars.github.io/</a></p>
 <p>This documentation describes only the fix colvars command itself and
 LAMMPS specific parts of the code.  The full documentation of the
 colvars library is available as <a class="reference external" href="PDF/colvars-refman-lammps.pdf">this supplementary PDF document</a></p>
 <p>A detailed discussion of the implementation of the portable collective
 variable library is in <a class="reference internal" href="#fiorin"><span>(Fiorin)</span></a>. Additional information can
 be found in <a class="reference internal" href="#henin"><span>(Henin)</span></a>.</p>
 <p>There are some example scripts for using this package with LAMMPS in the
 examples/USER/colvars directory.</p>
 <hr class="docutils" />
 <p>The only mandatory argument to the fix is the filename to the colvars
 input file that contains the input that is independent from the MD
 program in which the colvars library has been integrated.</p>
 <p>The <em>group-ID</em> entry is ignored. The collective variable module will
 always apply to the entire system and there can only be one instance
 of the colvars fix at a time. The colvars fix will only communicate
 the minimum information necessary and the colvars library supports
 multiple, completely independent collective variables, so there is
 no restriction to functionaliry by limiting the number of colvars fixes.</p>
 <p>The <em>input</em> keyword allows to specify a state file that would contain
 the restart information required in order to continue a calculation from
 a prerecorded state. Fix colvars records it state in <a class="reference internal" href="restart.html"><em>binary restart</em></a>
 files, so when using the <a class="reference internal" href="read_restart.html"><em>read_restart</em></a> command,
 this is usually not needed.</p>
 <p>The <em>output</em> keyword allows to specify the output prefix. All output
 files generated will use this prefix followed by the &#8221;.colvars.&#8221; and
 a word like &#8220;state&#8221; or &#8220;traj&#8221;.</p>
 <p>The <em>seed</em> keyword contains the seed for the random number generator
 that will be used in the colvars module.</p>
 <p>The <em>unwrap</em> keyword controls whether wrapped or unwrapped coordinates
 are passed to the colvars library for calculation of the collective
 variables and the resulting forces. The default is <em>yes</em>, i.e. to use
 the image flags to reconstruct the absolute atom positions.
 Setting this to <em>no</em> will use the current local coordinates that are
 wrapped back into the simulation cell at each re-neighboring instead.</p>
 <p>The <em>tstat</em> keyword can be either NULL or the label of a thermostating
 fix that thermostats all atoms in the fix colvars group. This will be
 used to provide the colvars module with the current thermostat target
 temperature.</p>
 </div>
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>This fix writes the current status of the colvars module into
 <a class="reference internal" href="restart.html"><em>binary restart files</em></a>. This is in addition to the text
 mode status file that is written by the colvars module itself and the
 kind of information in both files is identical.</p>
 <p>The <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> <em>energy</em> option is supported by this
 fix to add the energy change from the biasing force added by the fix
 to the system&#8217;s potential energy as part of <a class="reference internal" href="thermo_style.html"><em>thermodynamic output</em></a>.</p>
 <p>This fix computes a global scalar which can be accessed by various
 <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  The scalar is the
 cummulative energy change due to this fix.  The scalar value
 calculated by this fix is &#8220;extensive&#8221;.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>This fix is part of the USER-COLVARS package.  It is only enabled if
 LAMMPS was built with that package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 <p>There can only be one colvars fix active at a time. Since the interface
 communicates only the minimum amount of information and colvars module
 itself can handle an arbitrary number of collective variables, this is
 not a limitation of functionality.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="fix_smd.html"><em>fix smd</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The default options are input = NULL, output = out, seed = 1966, unwrap yes,
 and tstat = NULL.</p>
 <hr class="docutils" />
 <p id="fiorin"><strong>(Fiorin)</strong> Fiorin , Klein, Henin, Mol. Phys., DOI:10.1080/00268976.2013.813594</p>
 <p id="henin"><strong>(Henin)</strong> Henin, Fiorin, Chipot, Klein, J. Chem. Theory Comput., 6,
 35-47 (2010)</p>
 </div>
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   <div class="section" id="fix-deform-command">
 <span id="index-0"></span><h1>fix deform command<a class="headerlink" href="#fix-deform-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID deform N parameter args ... keyword value ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>deform = style name of this fix command</li>
 <li>N = perform box deformation every this many timesteps</li>
 <li>one or more parameter/arg pairs may be appended</li>
 </ul>
 <pre class="literal-block">
 parameter = <em>x</em> or <em>y</em> or <em>z</em> or <em>xy</em> or <em>xz</em> or <em>yz</em>
   <em>x</em>, <em>y</em>, <em>z</em> args = style value(s)
     style = <em>final</em> or <em>delta</em> or <em>scale</em> or <em>vel</em> or <em>erate</em> or <em>trate</em> or <em>volume</em> or <em>wiggle</em> or <em>variable</em>
       <em>final</em> values = lo hi
         lo hi = box boundaries at end of run (distance units)
       <em>delta</em> values = dlo dhi
         dlo dhi = change in box boundaries at end of run (distance units)
       <em>scale</em> values = factor
         factor = multiplicative factor for change in box length at end of run
       <em>vel</em> value = V
         V = change box length at this velocity (distance/time units),
          effectively an engineering strain rate
       <em>erate</em> value = R
         R = engineering strain rate (1/time units)
       <em>trate</em> value = R
         R = true strain rate (1/time units)
       <em>volume</em> value = none = adjust this dim to preserve volume of system
       <em>wiggle</em> values = A Tp
         A = amplitude of oscillation (distance units)
      Tp = period of oscillation (time units)
       <em>variable</em> values = v_name1 v_name2
         v_name1 = variable with name1 for box length change as function of time
      v_name2 = variable with name2 for change rate as function of time
   <em>xy</em>, <em>xz</em>, <em>yz</em> args = style value
     style = <em>final</em> or <em>delta</em> or <em>vel</em> or <em>erate</em> or <em>trate</em> or <em>wiggle</em>
       <em>final</em> value = tilt
         tilt = tilt factor at end of run (distance units)
       <em>delta</em> value = dtilt
         dtilt = change in tilt factor at end of run (distance units)
       <em>vel</em> value = V
         V = change tilt factor at this velocity (distance/time units),
          effectively an engineering shear strain rate
       <em>erate</em> value = R
         R = engineering shear strain rate (1/time units)
       <em>trate</em> value = R
         R = true shear strain rate (1/time units)
       <em>wiggle</em> values = A Tp
         A = amplitude of oscillation (distance units)
      Tp = period of oscillation (time units)
       <em>variable</em> values = v_name1 v_name2
         v_name1 = variable with name1 for tilt change as function of time
      v_name2 = variable with name2 for change rate as function of time
 </pre>
 <ul class="simple">
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>remap</em> or <em>flip</em> or <em>units</em></li>
 </ul>
 <pre class="literal-block">
 <em>remap</em> value = <em>x</em> or <em>v</em> or <em>none</em>
-    x = remap coords of atoms in group into deforming box
-    v = remap velocities of all atoms when they cross periodic boundaries
-    none = no remapping of x or v
-  <em>flip</em> value = <em>yes</em> or <em>no</em>
-    allow or disallow box flips when it becomes highly skewed
-  <em>units</em> value = <em>lattice</em> or <em>box</em>
-    lattice = distances are defined in lattice units
-    box = distances are defined in simulation box units
+  x = remap coords of atoms in group into deforming box
+  v = remap velocities of all atoms when they cross periodic boundaries
+  none = no remapping of x or v
+<em>flip</em> value = <em>yes</em> or <em>no</em>
+  allow or disallow box flips when it becomes highly skewed
+<em>units</em> value = <em>lattice</em> or <em>box</em>
+  lattice = distances are defined in lattice units
+  box = distances are defined in simulation box units
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix 1 all deform 1 x final 0.0 9.0 z final 0.0 5.0 units box
 fix 1 all deform 1 x trate 0.1 y volume z volume
 fix 1 all deform 1 xy erate 0.001 remap v
 fix 1 all deform 10 y delta -0.5 0.5 xz vel 1.0
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Change the volume and/or shape of the simulation box during a dynamics
 run.  Orthogonal simulation boxes have 3 adjustable parameters
 (x,y,z).  Triclinic (non-orthogonal) simulation boxes have 6
 adjustable parameters (x,y,z,xy,xz,yz).  Any or all of them can be
 adjusted independently and simultaneously by this command.  This fix
 can be used to perform non-equilibrium MD (NEMD) simulations of a
 continuously strained system.  See the <a class="reference internal" href="fix_nvt_sllod.html"><em>fix nvt/sllod</em></a> and <a class="reference internal" href="compute_temp_deform.html"><em>compute temp/deform</em></a> commands for more details.</p>
 <p>For the <em>x</em>, <em>y</em>, <em>z</em> parameters, the associated dimension cannot be
 shrink-wrapped.  For the <em>xy</em>, <em>yz</em>, <em>xz</em> parameters, the associated
 2nd dimension cannot be shrink-wrapped.  Dimensions not varied by this
 command can be periodic or non-periodic.  Dimensions corresponding to
 unspecified parameters can also be controlled by a <a class="reference internal" href="fix_nh.html"><em>fix npt</em></a> or <a class="reference internal" href="fix_nh.html"><em>fix nph</em></a> command.</p>
 <p>The size and shape of the simulation box at the beginning of the
 simulation run were either specified by the
 <a class="reference internal" href="create_box.html"><em>create_box</em></a> or <a class="reference internal" href="read_data.html"><em>read_data</em></a> or
 <a class="reference internal" href="read_restart.html"><em>read_restart</em></a> command used to setup the simulation
 initially if it is the first run, or they are the values from the end
 of the previous run.  The <a class="reference internal" href="create_box.html"><em>create_box</em></a>, <a class="reference internal" href="read_data.html"><em>read data</em></a>, and <a class="reference internal" href="read_restart.html"><em>read_restart</em></a> commands
 specify whether the simulation box is orthogonal or non-orthogonal
 (triclinic) and explain the meaning of the xy,xz,yz tilt factors.  If
 fix deform changes the xy,xz,yz tilt factors, then the simulation box
 must be triclinic, even if its initial tilt factors are 0.0.</p>
 <p>As described below, the desired simulation box size and shape at the
 end of the run are determined by the parameters of the fix deform
 command.  Every Nth timestep during the run, the simulation box is
 expanded, contracted, or tilted to ramped values between the initial
 and final values.</p>
 <hr class="docutils" />
 <p>For the <em>x</em>, <em>y</em>, and <em>z</em> parameters, this is the meaning of their
 styles and values.</p>
 <p>The <em>final</em>, <em>delta</em>, <em>scale</em>, <em>vel</em>, and <em>erate</em> styles all change
 the specified dimension of the box via &#8220;constant displacement&#8221; which
 is effectively a &#8220;constant engineering strain rate&#8221;.  This means the
 box dimension changes linearly with time from its initial to final
 value.</p>
 <p>For style <em>final</em>, the final lo and hi box boundaries of a dimension
 are specified.  The values can be in lattice or box distance units.
 See the discussion of the units keyword below.</p>
 <p>For style <em>delta</em>, plus or minus changes in the lo/hi box boundaries
 of a dimension are specified.  The values can be in lattice or box
 distance units.  See the discussion of the units keyword below.</p>
 <p>For style <em>scale</em>, a multiplicative factor to apply to the box length
 of a dimension is specified.  For example, if the initial box length
 is 10, and the factor is 1.1, then the final box length will be 11.  A
 factor less than 1.0 means compression.</p>
 <p>For style <em>vel</em>, a velocity at which the box length changes is
 specified in units of distance/time.  This is effectively a &#8220;constant
 engineering strain rate&#8221;, where rate = V/L0 and L0 is the initial box
 length.  The distance can be in lattice or box distance units.  See
 the discussion of the units keyword below.  For example, if the
 initial box length is 100 Angstroms, and V is 10 Angstroms/psec, then
 after 10 psec, the box length will have doubled.  After 20 psec, it
 will have tripled.</p>
 <p>The <em>erate</em> style changes a dimension of the the box at a &#8220;constant
 engineering strain rate&#8221;.  The units of the specified strain rate are
 1/time.  See the <a class="reference internal" href="units.html"><em>units</em></a> command for the time units
 associated with different choices of simulation units,
 e.g. picoseconds for &#8220;metal&#8221; units).  Tensile strain is unitless and
 is defined as delta/L0, where L0 is the original box length and delta
 is the change relative to the original length.  The box length L as a
 function of time will change as</p>
 <div class="highlight-python"><div class="highlight"><pre><span class="n">L</span><span class="p">(</span><span class="n">t</span><span class="p">)</span> <span class="o">=</span> <span class="n">L0</span> <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="n">erate</span><span class="o">*</span><span class="n">dt</span><span class="p">)</span>
 </pre></div>
 </div>
 <p>where dt is the elapsed time (in time units).  Thus if <em>erate</em> R is
 specified as 0.1 and time units are picoseconds, this means the box
 length will increase by 10% of its original length every picosecond.
 I.e. strain after 1 psec = 0.1, strain after 2 psec = 0.2, etc.  R =
 -0.01 means the box length will shrink by 1% of its original length
 every picosecond.  Note that for an &#8220;engineering&#8221; rate the change is
 based on the original box length, so running with R = 1 for 10
 picoseconds expands the box length by a factor of 11 (strain of 10),
 which is different that what the <em>trate</em> style would induce.</p>
 <p>The <em>trate</em> style changes a dimension of the box at a &#8220;constant true
 strain rate&#8221;.  Note that this is not an &#8220;engineering strain rate&#8221;, as
 the other styles are.  Rather, for a &#8220;true&#8221; rate, the rate of change
 is constant, which means the box dimension changes non-linearly with
 time from its initial to final value.  The units of the specified
 strain rate are 1/time.  See the <a class="reference internal" href="units.html"><em>units</em></a> command for the
 time units associated with different choices of simulation units,
 e.g. picoseconds for &#8220;metal&#8221; units).  Tensile strain is unitless and
 is defined as delta/L0, where L0 is the original box length and delta
 is the change relative to the original length.</p>
 <p>The box length L as a function of time will change as</p>
 <div class="highlight-python"><div class="highlight"><pre>L(t) = L0 exp(trate*dt)
 </pre></div>
 </div>
 <p>where dt is the elapsed time (in time units).  Thus if <em>trate</em> R is
 specified as ln(1.1) and time units are picoseconds, this means the
 box length will increase by 10% of its current (not original) length
 every picosecond.  I.e. strain after 1 psec = 0.1, strain after 2 psec
 = 0.21, etc.  R = ln(2) or ln(3) means the box length will double or
 triple every picosecond.  R = ln(0.99) means the box length will
 shrink by 1% of its current length every picosecond.  Note that for a
 &#8220;true&#8221; rate the change is continuous and based on the current length,
 so running with R = ln(2) for 10 picoseconds does not expand the box
 length by a factor of 11 as it would with <em>erate</em>, but by a factor of
 1024 since the box length will double every picosecond.</p>
 <p>Note that to change the volume (or cross-sectional area) of the
 simulation box at a constant rate, you can change multiple dimensions
 via <em>erate</em> or <em>trate</em>.  E.g. to double the box volume in a picosecond
 picosecond, you could set &#8220;x erate M&#8221;, &#8220;y erate M&#8221;, &#8220;z erate M&#8221;, with
 M = pow(2,1/3) - 1 = 0.26, since if each box dimension grows by 26%,
 the box volume doubles.  Or you could set &#8220;x trate M&#8221;, &#8220;y trate M&#8221;, &#8220;z
 trate M&#8221;, with M = ln(1.26) = 0.231, and the box volume would double
 every picosecond.</p>
 <p>The <em>volume</em> style changes the specified dimension in such a way that
 the box volume remains constant while other box dimensions are changed
 explicitly via the styles discussed above.  For example, &#8220;x scale 1.1
 y scale 1.1 z volume&#8221; will shrink the z box length as the x,y box
 lengths increase, to keep the volume constant (product of x,y,z
 lengths).  If &#8220;x scale 1.1 z volume&#8221; is specified and parameter <em>y</em> is
 unspecified, then the z box length will shrink as x increases to keep
 the product of x,z lengths constant.  If &#8220;x scale 1.1 y volume z
 volume&#8221; is specified, then both the y,z box lengths will shrink as x
 increases to keep the volume constant (product of x,y,z lengths).  In
 this case, the y,z box lengths shrink so as to keep their relative
 aspect ratio constant.</p>
 <p>For solids or liquids, note that when one dimension of the box is
 expanded via fix deform (i.e. tensile strain), it may be physically
 undesirable to hold the other 2 box lengths constant (unspecified by
 fix deform) since that implies a density change.  Using the <em>volume</em>
 style for those 2 dimensions to keep the box volume constant may make
 more physical sense, but may also not be correct for materials and
 potentials whose Poisson ratio is not 0.5.  An alternative is to use
 <a class="reference internal" href="fix_nh.html"><em>fix npt aniso</em></a> with zero applied pressure on those 2
 dimensions, so that they respond to the tensile strain dynamically.</p>
 <p>The <em>wiggle</em> style oscillates the specified box length dimension
 sinusoidally with the specified amplitude and period.  I.e. the box
 length L as a function of time is given by</p>
 <div class="highlight-python"><div class="highlight"><pre>L(t) = L0 + A sin(2*pi t/Tp)
 </pre></div>
 </div>
 <p>where L0 is its initial length.  If the amplitude A is a positive
 number the box initially expands, then contracts, etc.  If A is
 negative then the box initially contracts, then expands, etc.  The
 amplitude can be in lattice or box distance units.  See the discussion
 of the units keyword below.</p>
 <p>The <em>variable</em> style changes the specified box length dimension by
 evaluating a variable, which presumably is a function of time.  The
 variable with <em>name1</em> must be an <a class="reference internal" href="variable.html"><em>equal-style variable</em></a>
 and should calculate a change in box length in units of distance.
 Note that this distance is in box units, not lattice units; see the
 discussion of the <em>units</em> keyword below.  The formula associated with
 variable <em>name1</em> can reference the current timestep.  Note that it
 should return the &#8220;change&#8221; in box length, not the absolute box length.
 This means it should evaluate to 0.0 when invoked on the initial
 timestep of the run following the definition of fix deform.  It should
 evaluate to a value &gt; 0.0 to dilate the box at future times, or a
 value &lt; 0.0 to compress the box.</p>
 <p>The variable <em>name2</em> must also be an <a class="reference internal" href="variable.html"><em>equal-style variable</em></a> and should calculate the rate of box length
 change, in units of distance/time, i.e. the time-derivative of the
 <em>name1</em> variable.  This quantity is used internally by LAMMPS to reset
 atom velocities when they cross periodic boundaries.  It is computed
 internally for the other styles, but you must provide it when using an
 arbitrary variable.</p>
 <p>Here is an example of using the <em>variable</em> style to perform the same
 box deformation as the <em>wiggle</em> style formula listed above, where we
 assume that the current timestep = 0.</p>
 <div class="highlight-python"><div class="highlight"><pre>variable A equal 5.0
 variable Tp equal 10.0
 variable displace equal &quot;v_A * sin(2*PI * step*dt/v_Tp)&quot;
 variable rate equal &quot;2*PI*v_A/v_Tp * cos(2*PI * step*dt/v_Tp)&quot;
 fix 2 all deform 1 x variable v_displace v_rate remap v
 </pre></div>
 </div>
 <p>For the <em>scale</em>, <em>vel</em>, <em>erate</em>, <em>trate</em>, <em>volume</em>, <em>wiggle</em>, and
 <em>variable</em> styles, the box length is expanded or compressed around its
 mid point.</p>
 <hr class="docutils" />
 <p>For the <em>xy</em>, <em>xz</em>, and <em>yz</em> parameters, this is the meaning of their
 styles and values.  Note that changing the tilt factors of a triclinic
 box does not change its volume.</p>
 <p>The <em>final</em>, <em>delta</em>, <em>vel</em>, and <em>erate</em> styles all change the shear
 strain at a &#8220;constant engineering shear strain rate&#8221;.  This means the
 tilt factor changes linearly with time from its initial to final
 value.</p>
 <p>For style <em>final</em>, the final tilt factor is specified.  The value
 can be in lattice or box distance units.  See the discussion of the
 units keyword below.</p>
 <p>For style <em>delta</em>, a plus or minus change in the tilt factor is
 specified.  The value can be in lattice or box distance units.  See
 the discussion of the units keyword below.</p>
 <p>For style <em>vel</em>, a velocity at which the tilt factor changes is
 specified in units of distance/time.  This is effectively an
 &#8220;engineering shear strain rate&#8221;, where rate = V/L0 and L0 is the
 initial box length perpendicular to the direction of shear.  The
 distance can be in lattice or box distance units.  See the discussion
 of the units keyword below.  For example, if the initial tilt factor
 is 5 Angstroms, and the V is 10 Angstroms/psec, then after 1 psec, the
 tilt factor will be 15 Angstroms.  After 2 psec, it will be 25
 Angstroms.</p>
 <p>The <em>erate</em> style changes a tilt factor at a &#8220;constant engineering
 shear strain rate&#8221;.  The units of the specified shear strain rate are
 1/time.  See the <a class="reference internal" href="units.html"><em>units</em></a> command for the time units
 associated with different choices of simulation units,
 e.g. picoseconds for &#8220;metal&#8221; units).  Shear strain is unitless and is
 defined as offset/length, where length is the box length perpendicular
 to the shear direction (e.g. y box length for xy deformation) and
 offset is the displacement distance in the shear direction (e.g. x
 direction for xy deformation) from the unstrained orientation.</p>
 <p>The tilt factor T as a function of time will change as</p>
 <div class="highlight-python"><div class="highlight"><pre><span class="n">T</span><span class="p">(</span><span class="n">t</span><span class="p">)</span> <span class="o">=</span> <span class="n">T0</span> <span class="o">+</span> <span class="n">L0</span><span class="o">*</span><span class="n">erate</span><span class="o">*</span><span class="n">dt</span>
 </pre></div>
 </div>
 <p>where T0 is the initial tilt factor, L0 is the original length of the
 box perpendicular to the shear direction (e.g. y box length for xy
 deformation), and dt is the elapsed time (in time units).  Thus if
 <em>erate</em> R is specified as 0.1 and time units are picoseconds, this
 means the shear strain will increase by 0.1 every picosecond.  I.e. if
 the xy shear strain was initially 0.0, then strain after 1 psec = 0.1,
 strain after 2 psec = 0.2, etc.  Thus the tilt factor would be 0.0 at
 time 0, 0.1*ybox at 1 psec, 0.2*ybox at 2 psec, etc, where ybox is the
 original y box length.  R = 1 or 2 means the tilt factor will increase
 by 1 or 2 every picosecond.  R = -0.01 means a decrease in shear
 strain by 0.01 every picosecond.</p>
 <p>The <em>trate</em> style changes a tilt factor at a &#8220;constant true shear
 strain rate&#8221;.  Note that this is not an &#8220;engineering shear strain
 rate&#8221;, as the other styles are.  Rather, for a &#8220;true&#8221; rate, the rate
 of change is constant, which means the tilt factor changes
 non-linearly with time from its initial to final value.  The units of
 the specified shear strain rate are 1/time.  See the
 <a class="reference internal" href="units.html"><em>units</em></a> command for the time units associated with
 different choices of simulation units, e.g. picoseconds for &#8220;metal&#8221;
 units).  Shear strain is unitless and is defined as offset/length,
 where length is the box length perpendicular to the shear direction
 (e.g. y box length for xy deformation) and offset is the displacement
 distance in the shear direction (e.g. x direction for xy deformation)
 from the unstrained orientation.</p>
 <p>The tilt factor T as a function of time will change as</p>
 <div class="highlight-python"><div class="highlight"><pre>T(t) = T0 exp(trate*dt)
 </pre></div>
 </div>
 <p>where T0 is the initial tilt factor and dt is the elapsed time (in
 time units).  Thus if <em>trate</em> R is specified as ln(1.1) and time units
 are picoseconds, this means the shear strain or tilt factor will
 increase by 10% every picosecond.  I.e. if the xy shear strain was
 initially 0.1, then strain after 1 psec = 0.11, strain after 2 psec =
 0.121, etc.  R = ln(2) or ln(3) means the tilt factor will double or
 triple every picosecond.  R = ln(0.99) means the tilt factor will
 shrink by 1% every picosecond.  Note that the change is continuous, so
 running with R = ln(2) for 10 picoseconds does not change the tilt
 factor by a factor of 10, but by a factor of 1024 since it doubles
 every picosecond.  Note that the initial tilt factor must be non-zero
 to use the <em>trate</em> option.</p>
 <p>Note that shear strain is defined as the tilt factor divided by the
 perpendicular box length.  The <em>erate</em> and <em>trate</em> styles control the
 tilt factor, but assume the perpendicular box length remains constant.
 If this is not the case (e.g. it changes due to another fix deform
 parameter), then this effect on the shear strain is ignored.</p>
 <p>The <em>wiggle</em> style oscillates the specified tilt factor sinusoidally
 with the specified amplitude and period.  I.e. the tilt factor T as a
 function of time is given by</p>
 <div class="highlight-python"><div class="highlight"><pre>T(t) = T0 + A sin(2*pi t/Tp)
 </pre></div>
 </div>
 <p>where T0 is its initial value.  If the amplitude A is a positive
 number the tilt factor initially becomes more positive, then more
 negative, etc.  If A is negative then the tilt factor initially
 becomes more negative, then more positive, etc.  The amplitude can be
 in lattice or box distance units.  See the discussion of the units
 keyword below.</p>
 <p>The <em>variable</em> style changes the specified tilt factor by evaluating a
 variable, which presumably is a function of time.  The variable with
 <em>name1</em> must be an <a class="reference internal" href="variable.html"><em>equal-style variable</em></a> and should
 calculate a change in tilt in units of distance.  Note that this
 distance is in box units, not lattice units; see the discussion of the
 <em>units</em> keyword below.  The formula associated with variable <em>name1</em>
 can reference the current timestep.  Note that it should return the
 &#8220;change&#8221; in tilt factor, not the absolute tilt factor.  This means it
 should evaluate to 0.0 when invoked on the initial timestep of the run
 following the definition of fix deform.</p>
 <p>The variable <em>name2</em> must also be an <a class="reference internal" href="variable.html"><em>equal-style variable</em></a> and should calculate the rate of tilt change,
 in units of distance/time, i.e. the time-derivative of the <em>name1</em>
 variable.  This quantity is used internally by LAMMPS to reset atom
 velocities when they cross periodic boundaries.  It is computed
 internally for the other styles, but you must provide it when using an
 arbitrary variable.</p>
 <p>Here is an example of using the <em>variable</em> style to perform the same
 box deformation as the <em>wiggle</em> style formula listed above, where we
 assume that the current timestep = 0.</p>
 <div class="highlight-python"><div class="highlight"><pre>variable A equal 5.0
 variable Tp equal 10.0
 variable displace equal &quot;v_A * sin(2*PI * step*dt/v_Tp)&quot;
 variable rate equal &quot;2*PI*v_A/v_Tp * cos(2*PI * step*dt/v_Tp)&quot;
 fix 2 all deform 1 xy variable v_displace v_rate remap v
 </pre></div>
 </div>
 <hr class="docutils" />
 <p>All of the tilt styles change the xy, xz, yz tilt factors during a
 simulation.  In LAMMPS, tilt factors (xy,xz,yz) for triclinic boxes
 are normally bounded by half the distance of the parallel box length.
 See the discussion of the <em>flip</em> keyword below, to allow this bound to
 be exceeded, if desired.</p>
 <p>For example, if xlo = 2 and xhi = 12, then the x box length is 10 and
 the xy tilt factor must be between -5 and 5.  Similarly, both xz and
 yz must be between -(xhi-xlo)/2 and +(yhi-ylo)/2.  Note that this is
 not a limitation, since if the maximum tilt factor is 5 (as in this
 example), then configurations with tilt = ..., -15, -5, 5, 15, 25,
 ... are all equivalent.</p>
 <p>To obey this constraint and allow for large shear deformations to be
 applied via the <em>xy</em>, <em>xz</em>, or <em>yz</em> parameters, the following
 algorithm is used.  If <em>prd</em> is the associated parallel box length (10
 in the example above), then if the tilt factor exceeds the accepted
 range of -5 to 5 during the simulation, then the box is flipped to the
 other limit (an equivalent box) and the simulation continues.  Thus
 for this example, if the initial xy tilt factor was 0.0 and &#8220;xy final
 100.0&#8221; was specified, then during the simulation the xy tilt factor
 would increase from 0.0 to 5.0, the box would be flipped so that the
 tilt factor becomes -5.0, the tilt factor would increase from -5.0 to
 5.0, the box would be flipped again, etc.  The flip occurs 10 times
 and the final tilt factor at the end of the simulation would be 0.0.
 During each flip event, atoms are remapped into the new box in the
 appropriate manner.</p>
 <p>The one exception to this rule is if the 1st dimension in the tilt
 factor (x for xy) is non-periodic.  In that case, the limits on the
 tilt factor are not enforced, since flipping the box in that dimension
 does not change the atom positions due to non-periodicity.  In this
 mode, if you tilt the system to extreme angles, the simulation will
 simply become inefficient due to the highly skewed simulation box.</p>
 <hr class="docutils" />
 <p>Each time the box size or shape is changed, the <em>remap</em> keyword
 determines whether atom positions are remapped to the new box.  If
 <em>remap</em> is set to <em>x</em> (the default), atoms in the fix group are
 remapped; otherwise they are not.  Note that their velocities are not
 changed, just their positions are altered.  If <em>remap</em> is set to <em>v</em>,
 then any atom in the fix group that crosses a periodic boundary will
 have a delta added to its velocity equal to the difference in
 velocities between the lo and hi boundaries.  Note that this velocity
 difference can include tilt components, e.g. a delta in the x velocity
 when an atom crosses the y periodic boundary.  If <em>remap</em> is set to
 <em>none</em>, then neither of these remappings take place.</p>
 <p>Conceptually, setting <em>remap</em> to <em>x</em> forces the atoms to deform via an
 affine transformation that exactly matches the box deformation.  This
 setting is typically appropriate for solids.  Note that though the
 atoms are effectively &#8220;moving&#8221; with the box over time, it is not due
 to their having a velocity that tracks the box change, but only due to
 the remapping.  By contrast, setting <em>remap</em> to <em>v</em> is typically
 appropriate for fluids, where you want the atoms to respond to the
 change in box size/shape on their own and acquire a velocity that
 matches the box change, so that their motion will naturally track the
 box without explicit remapping of their coordinates.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">When non-equilibrium MD (NEMD) simulations are
 performed using this fix, the option &#8220;remap v&#8221; should normally be
 used.  This is because <a class="reference internal" href="fix_nvt_sllod.html"><em>fix nvt/sllod</em></a> adjusts the
 atom positions and velocities to induce a velocity profile that
 matches the changing box size/shape.  Thus atom coordinates should NOT
 be remapped by fix deform, but velocities SHOULD be when atoms cross
 periodic boundaries, since that is consistent with maintaining the
 velocity profile already created by fix nvt/sllod.  LAMMPS will warn
 you if the <em>remap</em> setting is not consistent with fix nvt/sllod.</p>
 </div>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">For non-equilibrium MD (NEMD) simulations using &#8220;remap
 v&#8221; it is usually desirable that the fluid (or flowing material,
 e.g. granular particles) stream with a velocity profile consistent
 with the deforming box.  As mentioned above, using a thermostat such
 as <a class="reference internal" href="fix_nvt_sllod.html"><em>fix nvt/sllod</em></a> or <code class="xref doc docutils literal"><span class="pre">fix</span> <span class="pre">lavgevin</span></code> (with a bias provided by <a class="reference internal" href="compute_temp_deform.html"><em>compute temp/deform</em></a>), will typically accomplish
 that.  If you do not use a thermostat, then there is no driving force
 pushing the atoms to flow in a manner consistent with the deforming
 box.  E.g. for a shearing system the box deformation velocity may vary
 from 0 at the bottom to 10 at the top of the box.  But the stream
 velocity profile of the atoms may vary from -5 at the bottom to +5 at
 the top.  You can monitor these effects using the <a class="reference internal" href="fix_ave_spatial.html"><em>fix ave/spatial</em></a>, <a class="reference internal" href="compute_temp_deform.html"><em>compute temp/deform</em></a>, and <a class="reference internal" href="compute_temp_profile.html"><em>compute temp/profile</em></a> commands.  One way to induce
 atoms to stream consistent with the box deformation is to give them an
 initial velocity profile, via the <a class="reference internal" href="velocity.html"><em>velocity ramp</em></a>
 command, that matches the box deformation rate.  This also typically
 helps the system come to equilibrium more quickly, even if a
 thermostat is used.</p>
 </div>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">If a <a class="reference internal" href="fix_rigid.html"><em>fix rigid</em></a> is defined for rigid
 bodies, and <em>remap</em> is set to <em>x</em>, then the center-of-mass coordinates
 of rigid bodies will be remapped to the changing simulation box.  This
 will be done regardless of whether atoms in the rigid bodies are in
 the fix deform group or not.  The velocity of the centers of mass are
 not remapped even if <em>remap</em> is set to <em>v</em>, since <a class="reference internal" href="fix_nvt_sllod.html"><em>fix nvt/sllod</em></a> does not currently do anything special
 for rigid particles.  If you wish to perform a NEMD simulation of
 rigid particles, you can either thermostat them independently or
 include a background fluid and thermostat the fluid via <a class="reference internal" href="fix_nvt_sllod.html"><em>fix nvt/sllod</em></a>.</p>
 </div>
 <p>The <em>flip</em> keyword allows the tilt factors for a triclinic box to
 exceed half the distance of the parallel box length, as discussed
 above.  If the <em>flip</em> value is set to <em>yes</em>, the bound is enforced by
 flipping the box when it is exceeded.  If the <em>flip</em> value is set to
 <em>no</em>, the tilt will continue to change without flipping.  Note that if
 you apply large deformations, this means the box shape can tilt
 dramatically LAMMPS will run less efficiently, due to the large volume
 of communication needed to acquire ghost atoms around a processor&#8217;s
 irregular-shaped sub-domain.  For extreme values of tilt, LAMMPS may
 also lose atoms and generate an error.</p>
 <p>The <em>units</em> keyword determines the meaning of the distance units used
 to define various arguments.  A <em>box</em> value selects standard distance
 units as defined by the <a class="reference internal" href="units.html"><em>units</em></a> command, e.g. Angstroms for
 units = real or metal.  A <em>lattice</em> value means the distance units are
 in lattice spacings.  The <a class="reference internal" href="lattice.html"><em>lattice</em></a> command must have
 been previously used to define the lattice spacing.  Note that the
 units choice also affects the <em>vel</em> style parameters since it is
 defined in terms of distance/time.  Also note that the units keyword
 does not affect the <em>variable</em> style.  You should use the <em>xlat</em>,
 <em>ylat</em>, <em>zlat</em> keywords of the <a class="reference internal" href="thermo_style.html"><em>thermo_style</em></a>
 command if you want to include lattice spacings in a variable formula.</p>
 </div>
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.  None of the <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> options
 are relevant to this fix.  No global or per-atom quantities are stored
 by this fix for access by various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.</p>
 <p>This fix can perform deformation over multiple runs, using the <em>start</em>
 and <em>stop</em> keywords of the <a class="reference internal" href="run.html"><em>run</em></a> command.  See the
 <a class="reference internal" href="run.html"><em>run</em></a> command for details of how to do this.</p>
 <p>This fix is not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>You cannot apply x, y, or z deformations to a dimension that is
 shrink-wrapped via the <a class="reference internal" href="boundary.html"><em>boundary</em></a> comamnd.</p>
 <p>You cannot apply xy, yz, or xz deformations to a 2nd dimension (y in
 xy) that is shrink-wrapped via the <a class="reference internal" href="boundary.html"><em>boundary</em></a> comamnd.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="change_box.html"><em>change_box</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The option defaults are remap = x, flip = yes, and units = lattice.</p>
 </div>
 </div>
 
 
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diff --git a/doc/fix_deposit.html b/doc/fix_deposit.html
index e586ff546..1f38c377e 100644
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   <div class="section" id="fix-deposit-command">
 <span id="index-0"></span><h1>fix deposit command<a class="headerlink" href="#fix-deposit-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID deposit N type M seed keyword values ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>deposit = style name of this fix command</li>
 <li>N = # of atoms or molecules to insert</li>
 <li>type = atom type to assign to inserted atoms (offset for moleclue insertion)</li>
 <li>M = insert a single atom or molecule every M steps</li>
 <li>seed = random # seed (positive integer)</li>
 <li>one or more keyword/value pairs may be appended to args</li>
 <li>keyword = <em>region</em> or <em>id</em> or <em>global</em> or <em>local</em> or <em>near</em> or <em>attempt</em> or <em>rate</em> or <em>vx</em> or <em>vy</em> or <em>vz</em> or <em>mol</em> or <em>rigid</em> or <em>shake</em> or <em>units</em></li>
 </ul>
 <pre class="literal-block">
 <em>region</em> value = region-ID
-    region-ID = ID of region to use as insertion volume
-  <em>id</em> value = <em>max</em> or <em>next</em>
-    max = atom ID for new atom(s) is max ID of all current atoms plus one
-    next = atom ID for new atom(s) increments by one for every deposition
-  <em>global</em> values = lo hi
-    lo,hi = put new atom/molecule a distance lo-hi above all other atoms (distance units)
-  <em>local</em> values = lo hi delta
-    lo,hi = put new atom/molecule a distance lo-hi above any nearby atom beneath it (distance units)
-    delta = lateral distance within which a neighbor is considered &quot;nearby&quot; (distance units)
-  <em>near</em> value = R
-    R = only insert atom/molecule if further than R from existing particles (distance units)
-  <em>attempt</em> value = Q
-    Q = attempt a single insertion up to Q times
-  <em>rate</em> value = V
-    V = z velocity (y in 2d) at which insertion volume moves (velocity units)
-  <em>vx</em> values = vxlo vxhi
-    vxlo,vxhi = range of x velocities for inserted atom/molecule (velocity units)
-  <em>vy</em> values = vylo vyhi
-    vylo,vyhi = range of y velocities for inserted atom/molecule (velocity units)
-  <em>vz</em> values = vzlo vzhi
-    vzlo,vzhi = range of z velocities for inserted atom/molecule (velocity units)
-  <em>target</em> values = tx ty tz
-    tx,ty,tz = location of target point (distance units)
-  <em>mol</em> value = template-ID
-    template-ID = ID of molecule template specified in a separate <a class="reference internal" href="molecule.html"><em>molecule</em></a> command
-  <em>molfrac</em> values = f1 f2 ... fN
-    f1 to fN = relative probability of creating each of N molecules in template-ID
-  <em>rigid</em> value = fix-ID
-    fix-ID = ID of <a class="reference internal" href="fix_rigid.html"><em>fix rigid/small</em></a> command
-  <em>shake</em> value = fix-ID
-    fix-ID = ID of <a class="reference internal" href="fix_shake.html"><em>fix shake</em></a> command
-  <em>units</em> value = <em>lattice</em> or <em>box</em>
-    lattice = the geometry is defined in lattice units
-    box = the geometry is defined in simulation box units
+  region-ID = ID of region to use as insertion volume
+<em>id</em> value = <em>max</em> or <em>next</em>
+  max = atom ID for new atom(s) is max ID of all current atoms plus one
+  next = atom ID for new atom(s) increments by one for every deposition
+<em>global</em> values = lo hi
+  lo,hi = put new atom/molecule a distance lo-hi above all other atoms (distance units)
+<em>local</em> values = lo hi delta
+  lo,hi = put new atom/molecule a distance lo-hi above any nearby atom beneath it (distance units)
+  delta = lateral distance within which a neighbor is considered &quot;nearby&quot; (distance units)
+<em>near</em> value = R
+  R = only insert atom/molecule if further than R from existing particles (distance units)
+<em>attempt</em> value = Q
+  Q = attempt a single insertion up to Q times
+<em>rate</em> value = V
+  V = z velocity (y in 2d) at which insertion volume moves (velocity units)
+<em>vx</em> values = vxlo vxhi
+  vxlo,vxhi = range of x velocities for inserted atom/molecule (velocity units)
+<em>vy</em> values = vylo vyhi
+  vylo,vyhi = range of y velocities for inserted atom/molecule (velocity units)
+<em>vz</em> values = vzlo vzhi
+  vzlo,vzhi = range of z velocities for inserted atom/molecule (velocity units)
+<em>target</em> values = tx ty tz
+  tx,ty,tz = location of target point (distance units)
+<em>mol</em> value = template-ID
+  template-ID = ID of molecule template specified in a separate <a class="reference internal" href="molecule.html"><em>molecule</em></a> command
+<em>molfrac</em> values = f1 f2 ... fN
+  f1 to fN = relative probability of creating each of N molecules in template-ID
+<em>rigid</em> value = fix-ID
+  fix-ID = ID of <a class="reference internal" href="fix_rigid.html"><em>fix rigid/small</em></a> command
+<em>shake</em> value = fix-ID
+  fix-ID = ID of <a class="reference internal" href="fix_shake.html"><em>fix shake</em></a> command
+<em>units</em> value = <em>lattice</em> or <em>box</em>
+  lattice = the geometry is defined in lattice units
+  box = the geometry is defined in simulation box units
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix 3 all deposit 1000 2 100 29494 region myblock local 1.0 1.0 1.0 units box
 fix 2 newatoms deposit 10000 1 500 12345 region disk near 2.0 vz -1.0 -0.8
 fix 4 sputter deposit 1000 2 500 12235 region sphere vz -1.0 -1.0 target 5.0 5.0 0.0 units lattice
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Insert a single atom or molecule into the simulation domain every M
 timesteps until N atoms or molecules have been inserted.  This is
 useful for simulating deposition onto a surface.  For the remainder of
 this doc page, a single inserted atom or molecule is referred to as a
 &#8220;particle&#8221;.</p>
 <p>If inserted particles are individual atoms, they are assigned the
 specified atom type.  If they are molecules, the type of each atom in
 the inserted molecule is specified in the file read by the
 <a class="reference internal" href="molecule.html"><em>molecule</em></a> command, and those values are added to the
 specified atom type.  E.g. if the file specifies atom types 1,2,3, and
 those are the atom types you want for inserted molecules, then specify
 <em>type</em> = 0.  If you specify <em>type</em> = 2, the in the inserted molecule
 will have atom types 3,4,5.</p>
 <p>All atoms in the inserted particle are assigned to two groups: the
 default group &#8220;all&#8221; and the group specified in the fix deposit command
 (which can also be &#8220;all&#8221;).</p>
 <p>If you are computing temperature values which include inserted
 particles, you will want to use the
 <a class="reference internal" href="compute_modify.html"><em>compute_modify</em></a> dynamic option, which insures the
 current number of atoms is used as a normalizing factor each time the
 temperature is computed.</p>
 <p>Care must be taken that inserted particles are not too near existing
 atoms, using the options described below.  When inserting particles
 above a surface in a non-periodic box (see the
 <a class="reference internal" href="boundary.html"><em>boundary</em></a> command), the possibility of a particle
 escaping the surface and flying upward should be considered, since the
 particle may be lost or the box size may grow infinitely large.  A
 <a class="reference internal" href="fix_wall_reflect.html"><em>fix wall/reflect</em></a> command can be used to
 prevent this behavior.  Note that if a shrink-wrap boundary is used,
 it is OK to insert the new particle outside the box, however the box
 will immediately be expanded to include the new particle. When
 simulating a sputtering experiment it is probably more realistic to
 ignore those atoms using the <a class="reference internal" href="thermo_modify.html"><em>thermo_modify</em></a>
 command with the <em>lost ignore</em> option and a fixed
 <a class="reference internal" href="boundary.html"><em>boundary</em></a>.</p>
 <p>The fix deposit command must use the <em>region</em> keyword to define an
 insertion volume.  The specified region must have been previously
 defined with a <a class="reference internal" href="region.html"><em>region</em></a> command.  It must be defined with
 side = <em>in</em>.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">LAMMPS checks that the specified region is wholly
 inside the simulation box.  It can do this correctly for orthonormal
 simulation boxes.  However for <a class="reference internal" href="Section_howto.html#howto-12"><span>triclinic boxes</span></a>, it only tests against the larger
 orthonormal box that bounds the tilted simulation box.  If the
 specified region includes volume outside the tilted box, then an
 insertion will likely fail, leading to a &#8220;lost atoms&#8221; error.  Thus for
 triclinic boxes you should insure the specified region is wholly
 inside the simulation box.</p>
 </div>
 <p>Individual atoms are inserted, unless the <em>mol</em> keyword is used.  It
 specifies a <em>template-ID</em> previously defined using the
 <a class="reference internal" href="molecule.html"><em>molecule</em></a> command, which reads files that define one or
 more molecules.  The coordinates, atom types, charges, etc, as well as
 any bond/angle/etc and special neighbor information for the molecule
 can be specified in the molecule file.  See the
 <a class="reference internal" href="molecule.html"><em>molecule</em></a> command for details.  The only settings
 required to be in each file are the coordinates and types of atoms in
 the molecule.</p>
 <p>If the molecule template contains more than one molecule, the relative
 probability of depositing each molecule can be specified by the
 <em>molfrac</em> keyword.  N relative probablities, each from 0.0 to 1.0, are
 specified, where N is the number of molecules in the template.  Each
 time a molecule is deposited, a random number is used to sample from
 the list of relative probabilities.  The N values must sum to 1.0.</p>
 <p>If you wish to insert molecules via the <em>mol</em> keyword, that will be
 treated as rigid bodies, use the <em>rigid</em> keyword, specifying as its
 value the ID of a separate <code class="xref doc docutils literal"><span class="pre">fix</span> <span class="pre">rigid/small</span></code>
 command which also appears in your input script.</p>
 <p>If you wish to insert molecules via the <em>mol</em> keyword, that will have
 their bonds or angles constrained via SHAKE, use the <em>shake</em> keyword,
 specifying as its value the ID of a separate <a class="reference internal" href="fix_shake.html"><em>fix shake</em></a> command which also appears in your input script.</p>
 <p>Each timestep a particle is inserted, the coordinates for its atoms
 are chosen as follows.  For insertion of individual atoms, the
 &#8220;position&#8221; referred to in the following description is the coordinate
 of the atom.  For insertion of molecule, the &#8220;position&#8221; is the
 geometric center of the molecule; see the <a class="reference internal" href="molecule.html"><em>molecule</em></a> doc
 page for details.  A random rotation of the molecule around its center
 point is performed, which determines the coordinates all the
 individual atoms.</p>
 <p>A random position within the region insertion volume is generated.  If
 neither the <em>global</em> or <em>local</em> keyword is used, the random position
 is the trial position.  If the <em>global</em> keyword is used, the random
 x,y values are used, but the z position of the new particle is set
 above the highest current atom in the simulation by a distance
 randomly chosen between lo/hi.  (For a 2d simulation, this is done for
 the y position.)  If the <em>local</em> keyword is used, the z position is
 set a distance between lo/hi above the highest current atom in the
 simulation that is &#8220;nearby&#8221; the chosen x,y position.  In this context,
 &#8220;nearby&#8221; means the lateral distance (in x,y) between the new and old
 particles is less than the <em>delta</em> setting.</p>
 <p>Once a trial x,y,z position has been selected, the insertion is only
 performed if no current atom in the simulation is within a distance R
 of any atom in the new particle, including the effect of periodic
 boundary conditions if applicable.  R is defined by the <em>near</em>
 keyword.  Note that the default value for R is 0.0, which will allow
 atoms to strongly overlap if you are inserting where other atoms are
 present.  This distance test is performed independently for each atom
 in an inserted molecule, based on the randomly rotated configuration
 of the molecule.  If this test fails, a new random position within the
 insertion volume is chosen and another trial is made.  Up to Q
 attempts are made.  If the particle is not successfully inserted,
 LAMMPS prints a warning message.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">If you are inserting finite size particles or a
 molecule or rigid body consisting of finite-size particles, then you
 should typically set R larger than the distance at which any inserted
 particle may overlap with either a previouly inserted particle or an
 existing particle.  LAMMPS will issue a warning if R is smaller than
 this value, based on the radii of existing and inserted particles.</p>
 </div>
 <p>The <em>rate</em> option moves the insertion volume in the z direction (3d)
 or y direction (2d).  This enables particles to be inserted from a
 successively higher height over time.  Note that this parameter is
 ignored if the <em>global</em> or <em>local</em> keywords are used, since those
 options choose a z-coordinate for insertion independently.</p>
 <p>The vx, vy, and vz components of velocity for the inserted particle
 are set using the values specified for the <em>vx</em>, <em>vy</em>, and <em>vz</em>
 keywords.  Note that normally, new particles should be a assigned a
 negative vertical velocity so that they move towards the surface.  For
 molecules, the same velocity is given to every particle (no rotation
 or bond vibration).</p>
 <p>If the <em>target</em> option is used, the velocity vector of the inserted
 particle is changed so that it points from the insertion position
 towards the specified target point.  The magnitude of the velocity is
 unchanged.  This can be useful, for example, for simulating a
 sputtering process.  E.g. the target point can be far away, so that
 all incident particles strike the surface as if they are in an
 incident beam of particles at a prescribed angle.</p>
 <p>The <em>id</em> keyword determines how atom IDs and molecule IDs are assigned
 to newly deposited particles.  Molecule IDs are only assigned if
 molecules are being inserted.  For the <em>max</em> setting, the atom and
 molecule IDs of all current atoms are checked.  Atoms in the new
 particle are assigned IDs starting with the current maximum plus one.
 If a molecule is inserted it is assigned an ID = current maximum plus
 one.  This means that if particles leave the system, the new IDs may
 replace the lost ones.  For the <em>next</em> setting, the maximum ID of any
 atom and molecule is stored at the time the fix is defined.  Each time
 a new particle is added, this value is incremented to assign IDs to
 the new atom(s) or molecule.  Thus atom and molecule IDs for deposited
 particles will be consecutive even if particles leave the system over
 time.</p>
 <p>The <em>units</em> keyword determines the meaning of the distance units used
 for the other deposition parameters.  A <em>box</em> value selects standard
 distance units as defined by the <a class="reference internal" href="units.html"><em>units</em></a> command,
 e.g. Angstroms for units = real or metal.  A <em>lattice</em> value means the
 distance units are in lattice spacings.  The <a class="reference internal" href="lattice.html"><em>lattice</em></a>
 command must have been previously used to define the lattice spacing.
 Note that the units choice affects all the keyword values that have
 units of distance or velocity.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">If you are monitoring the temperature of a system
 where the atom count is changing due to adding particles, you
 typically should use the <a class="reference internal" href="compute_modify.html"><em>compute_modify dynamic yes</em></a> command for the temperature compute you are
 using.</p>
 </div>
 </div>
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>This fix writes the state of the deposition to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.  This includes information about how many
 particles have been depositied, the random number generator seed, the
 next timestep for deposition, etc.  See the
 <a class="reference internal" href="read_restart.html"><em>read_restart</em></a> command for info on how to re-specify
 a fix in an input script that reads a restart file, so that the
 operation of the fix continues in an uninterrupted fashion.</p>
 <p>None of the <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> options are relevant to this
 fix.  No global or per-atom quantities are stored by this fix for
 access by various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  No
 parameter of this fix can be used with the <em>start/stop</em> keywords of
 the <a class="reference internal" href="run.html"><em>run</em></a> command.  This fix is not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>This fix is part of the MISC package.  It is only enabled if LAMMPS
 was built with that package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 <p>The specified insertion region cannot be a &#8220;dynamic&#8221; region, as
 defined by the <a class="reference internal" href="region.html"><em>region</em></a> command.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="fix_pour.html"><em>fix_pour</em></a>, <a class="reference internal" href="region.html"><em>region</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>Insertions are performed for individual atoms, i.e. no <em>mol</em> setting
 is defined.  If the <em>mol</em> keyword is used, the default for <em>molfrac</em>
 is an equal probabilities for all molecules in the template.
 Additional option defaults are id = max, delta = 0.0, near = 0.0,
 attempt = 10, rate = 0.0, vx = 0.0 0.0, vy = 0.0 0.0, vz = 0.0 0.0,
 and units = lattice.</p>
 </div>
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   <div class="section" id="fix-dt-reset-command">
 <span id="index-0"></span><h1>fix dt/reset command<a class="headerlink" href="#fix-dt-reset-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID dt/reset N Tmin Tmax Xmax keyword values ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>dt/reset = style name of this fix command</li>
 <li>N = recompute dt every N timesteps</li>
 <li>Tmin = minimum dt allowed which can be NULL (time units)</li>
 <li>Tmax = maximum dt allowed which can be NULL (time units)</li>
 <li>Xmax = maximum distance for an atom to move in one timestep (distance units)</li>
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>units</em></li>
 </ul>
 <pre class="literal-block">
 <em>units</em> value = <em>lattice</em> or <em>box</em>
-    lattice = Xmax is defined in lattice units
-    box = Xmax is defined in simulation box units
+  lattice = Xmax is defined in lattice units
+  box = Xmax is defined in simulation box units
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix 5 all dt/reset 10 1.0e-5 0.01 0.1
 fix 5 all dt/reset 10 0.01 2.0 0.2 units box
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Reset the timestep size every N steps during a run, so that no atom
 moves further than Xmax, based on current atom velocities and forces.
 This can be useful when starting from a configuration with overlapping
 atoms, where forces will be large.  Or it can be useful when running
 an impact simulation where one or more high-energy atoms collide with
 a solid, causing a damage cascade.</p>
 <p>This fix overrides the timestep size setting made by the
 <a class="reference internal" href="timestep.html"><em>timestep</em></a> command.  The new timestep size <em>dt</em> is
 computed in the following manner.</p>
 <p>For each atom, the timestep is computed that would cause it to
 displace <em>Xmax</em> on the next integration step, as a function of its
 current velocity and force.  Since performing this calculation exactly
 would require the solution to a quartic equation, a cheaper estimate
 is generated.  The estimate is conservative in that the atom&#8217;s
 displacement is guaranteed not to exceed <em>Xmax</em>, though it may be
 smaller.</p>
 <p>Given this putative timestep for each atom, the minimum timestep value
 across all atoms is computed.  Then the <em>Tmin</em> and <em>Tmax</em> bounds are
 applied, if specified.  If one (or both) is specified as NULL, it is
 not applied.</p>
 <p>When the <a class="reference internal" href="run_style.html"><em>run style</em></a> is <em>respa</em>, this fix resets the
 outer loop (largest) timestep, which is the same timestep that the
 <a class="reference internal" href="timestep.html"><em>timestep</em></a> command sets.</p>
 <p>Note that the cumulative simulation time (in time units), which
 accounts for changes in the timestep size as a simulation proceeds,
 can be accessed by the <a class="reference internal" href="thermo_style.html"><em>thermo_style time</em></a> keyword.</p>
 </div>
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.  None of the <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> options
 are relevant to this fix.</p>
 <p>This fix computes a global scalar which can be accessed by various
 <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  The scalar stores
 the last timestep on which the timestep was reset to a new value.</p>
 <p>The scalar value calculated by this fix is &#8220;intensive&#8221;.</p>
 <p>No parameter of this fix can be used with the <em>start/stop</em> keywords of
 the <a class="reference internal" href="run.html"><em>run</em></a> command.  This fix is not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <blockquote>
 <div>none</div></blockquote>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="timestep.html"><em>timestep</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The option defaults is units = lattice.</p>
 </div>
 </div>
 
 
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diff --git a/doc/fix_efield.html b/doc/fix_efield.html
index c89f9c011..78fbc2ddb 100644
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   <div class="section" id="fix-efield-command">
 <span id="index-0"></span><h1>fix efield command<a class="headerlink" href="#fix-efield-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID efield ex ey ez keyword value ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>efield = style name of this fix command</li>
 <li>ex,ey,ez = E-field component values (electric field units)</li>
 <li>any of ex,ey,ez can be a variable (see below)</li>
 <li>zero or more keyword/value pairs may be appended to args</li>
 <li>keyword = <em>region</em> or <em>energy</em></li>
 </ul>
 <pre class="literal-block">
 <em>region</em> value = region-ID
-    region-ID = ID of region atoms must be in to have added force
-  <em>energy</em> value = v_name
-    v_name = variable with name that calculates the potential energy of each atom in the added E-field
+  region-ID = ID of region atoms must be in to have added force
+<em>energy</em> value = v_name
+  v_name = variable with name that calculates the potential energy of each atom in the added E-field
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix kick external-field efield 1.0 0.0 0.0
 fix kick external-field efield 0.0 0.0 v_oscillate
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Add a force F = qE to each charged atom in the group due to an
 external electric field being applied to the system.  If the system
 contains point-dipoles, also add a torque on the dipoles due to the
 external electric field.</p>
 <p>For charges, any of the 3 quantities defining the E-field components
 can be specified as an equal-style or atom-style
 <a class="reference internal" href="variable.html"><em>variable</em></a>, namely <em>ex</em>, <em>ey</em>, <em>ez</em>.  If the value is a
 variable, it should be specified as v_name, where name is the variable
 name.  In this case, the variable will be evaluated each timestep, and
 its value used to determine the E-field component.</p>
 <p>For point-dipoles, equal-style variables can be used, but atom-style
 variables are not currently supported, since they imply a spatial
 gradient in the electric field which means additional terms with
 gradients of the field are required for the force and torque on
 dipoles.</p>
 <p>Equal-style variables can specify formulas with various mathematical
 functions, and include <a class="reference internal" href="thermo_style.html"><em>thermo_style</em></a> command
 keywords for the simulation box parameters and timestep and elapsed
 time.  Thus it is easy to specify a time-dependent E-field.</p>
 <p>Atom-style variables can specify the same formulas as equal-style
 variables but can also include per-atom values, such as atom
 coordinates.  Thus it is easy to specify a spatially-dependent E-field
 with optional time-dependence as well.</p>
 <p>If the <em>region</em> keyword is used, the atom must also be in the
 specified geometric <a class="reference internal" href="region.html"><em>region</em></a> in order to have force added
 to it.</p>
 <hr class="docutils" />
 <p>Adding a force or torque to atoms implies a change in their potential
 energy as they move or rotate due to the applied E-field.</p>
 <p>For dynamics via the &#8220;run&#8221; command, this energy can be optionally
 added to the system&#8217;s potential energy for thermodynamic output (see
 below).  For energy minimization via the &#8220;minimize&#8221; command, this
 energy must be added to the system&#8217;s potential energy to formulate a
 self-consistent minimization problem (see below).</p>
 <p>The <em>energy</em> keyword is not allowed if the added field is a constant
 vector (ex,ey,ez), with all components defined as numeric constants
 and not as variables.  This is because LAMMPS can compute the energy
 for each charged particle directly as E = -x dot qE = -q (x*ex + y*ey
 + z*ez), so that -Grad(E) = F.  Similarly for point-dipole particles
 the energy can be computed as E = -mu dot E = -(mux*ex + muy*ey +
 muz*ez).</p>
 <p>The <em>energy</em> keyword is optional if the added force is defined with
 one or more variables, and if you are performing dynamics via the
 <a class="reference internal" href="run.html"><em>run</em></a> command.  If the keyword is not used, LAMMPS will set
 the energy to 0.0, which is typically fine for dynamics.</p>
 <p>The <em>energy</em> keyword is required if the added force is defined with
 one or more variables, and you are performing energy minimization via
 the &#8220;minimize&#8221; command for charged particles.  It is not required for
 point-dipoles, but a warning is issued since the minimizer in LAMMPS
 does not rotate dipoles, so you should not expect to be able to
 minimize the orientation of dipoles in an applied electric field.</p>
 <p>The <em>energy</em> keyword specifies the name of an atom-style
 <a class="reference internal" href="variable.html"><em>variable</em></a> which is used to compute the energy of each
 atom as function of its position.  Like variables used for <em>ex</em>, <em>ey</em>,
 <em>ez</em>, the energy variable is specified as v_name, where name is the
 variable name.</p>
 <p>Note that when the <em>energy</em> keyword is used during an energy
 minimization, you must insure that the formula defined for the
 atom-style <a class="reference internal" href="variable.html"><em>variable</em></a> is consistent with the force
 variable formulas, i.e. that -Grad(E) = F.  For example, if the force
 due to the electric field were a spring-like F = kx, then the energy
 formula should be E = -0.5kx^2.  If you don&#8217;t do this correctly, the
 minimization will not converge properly.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.</p>
 <p>The <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> <em>energy</em> option is supported by this
 fix to add the potential &#8220;energy&#8221; inferred by the added force due to
 the electric field to the system&#8217;s potential energy as part of
 <a class="reference internal" href="thermo_style.html"><em>thermodynamic output</em></a>.  This is a fictitious
 quantity but is needed so that the <a class="reference internal" href="minimize.html"><em>minimize</em></a> command
 can include the forces added by this fix in a consistent manner.
 I.e. there is a decrease in potential energy when atoms move in the
 direction of the added force due to the electric field.</p>
 <p>This fix computes a global scalar and a global 3-vector of forces,
 which can be accessed by various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  The scalar is the potential
 energy discussed above.  The vector is the total force added to the
 group of atoms.  The scalar and vector values calculated by this fix
 are &#8220;extensive&#8221;.</p>
 <p>No parameter of this fix can be used with the <em>start/stop</em> keywords of
 the <a class="reference internal" href="run.html"><em>run</em></a> command.</p>
 <p>The forces due to this fix are imposed during an energy minimization,
 invoked by the <a class="reference internal" href="minimize.html"><em>minimize</em></a> command.  You should not
 specify force components with a variable that has time-dependence for
 use with a minimizer, since the minimizer increments the timestep as
 the iteration count during the minimization.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">If you want the fictitious potential energy associated
 with the added forces to be included in the total potential energy of
 the system (the quantity being minimized), you MUST enable the
 <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> <em>energy</em> option for this fix.</p>
 </div>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>This fix is part of the MISC package.  It is only enabled if LAMMPS
 was built with that package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="fix_addforce.html"><em>fix addforce</em></a></p>
 <p><strong>Default:</strong> none</p>
 </div>
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   <div class="section" id="fix-external-command">
 <span id="index-0"></span><h1>fix external command<a class="headerlink" href="#fix-external-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID external mode args
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>external = style name of this fix command</li>
 <li>mode = <em>pf/callback</em> or <em>pf/array</em></li>
 </ul>
 <pre class="literal-block">
 <em>pf/callback</em> args = Ncall Napply
-    Ncall = make callback every Ncall steps
-    Napply = apply callback forces every Napply steps
-  <em>pf/array</em> args = Napply
-    Napply = apply array forces every Napply steps
+  Ncall = make callback every Ncall steps
+  Napply = apply callback forces every Napply steps
+<em>pf/array</em> args = Napply
+  Napply = apply array forces every Napply steps
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix 1 all external pf/callback 1 1
 fix 1 all external pf/callback 100 1
 fix 1 all external pf/array 10
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>This fix allows external programs that are running LAMMPS through its
 <a class="reference internal" href="Section_howto.html#howto-19"><span>library interface</span></a> to modify certain
 LAMMPS properties on specific timesteps, similar to the way other
 fixes do.  The external driver can be a <a class="reference internal" href="Section_howto.html#howto-19"><span>C/C++ or Fortran program</span></a> or a <a class="reference internal" href="Section_python.html"><em>Python script</em></a>.</p>
 <hr class="docutils" />
 <p>If mode is <em>pf/callback</em> then the fix will make a callback every
 <em>Ncall</em> timesteps or minimization iterations to the external program.
 The external program computes forces on atoms by setting values in an
 array owned by the fix.  The fix then adds these forces to each atom
 in the group, once every <em>Napply</em> steps, similar to the way the <a class="reference internal" href="fix_addforce.html"><em>fix addforce</em></a> command works.  Note that if <em>Ncall</em> &gt;
 <em>Napply</em>, the force values produced by one callback will persist, and
 be used multiple times to update atom forces.</p>
 <p>The callback function &#8220;foo&#8221; is invoked by the fix as:</p>
 <div class="highlight-python"><div class="highlight"><pre>foo(void *ptr, bigint timestep, int nlocal, int *ids, double **x, double **fexternal);
 </pre></div>
 </div>
 <p>The arguments are as follows:</p>
 <ul class="simple">
 <li>ptr = pointer provided by and simply passed back to external driver</li>
 <li>timestep = current LAMMPS timestep</li>
 <li>nlocal = # of atoms on this processor</li>
 <li>ids = list of atom IDs on this processor</li>
 <li>x = coordinates of atoms on this processor</li>
 <li>fexternal = forces to add to atoms on this processor</li>
 </ul>
 <p>Note that timestep is a &#8220;bigint&#8221; which is defined in src/lmptype.h,
 typically as a 64-bit integer.</p>
 <p>Fexternal are the forces returned by the driver program.</p>
 <p>The fix has a set_callback() method which the external driver can call
 to pass a pointer to its foo() function.  See the
 couple/lammps_quest/lmpqst.cpp file in the LAMMPS distribution for an
 example of how this is done.  This sample application performs
 classical MD using quantum forces computed by a density functional
 code <a class="reference external" href="http://dft.sandia.gov/Quest">Quest</a>.</p>
 <hr class="docutils" />
 <p>If mode is <em>pf/array</em> then the fix simply stores force values in an
 array.  The fix adds these forces to each atom in the group, once
 every <em>Napply</em> steps, similar to the way the <a class="reference internal" href="fix_addforce.html"><em>fix addforce</em></a> command works.</p>
 <p>The name of the public force array provided by the FixExternal
 class is</p>
 <div class="highlight-python"><div class="highlight"><pre><span class="n">double</span> <span class="o">**</span><span class="n">fexternal</span><span class="p">;</span>
 </pre></div>
 </div>
 <p>It is allocated by the FixExternal class as an (N,3) array where N is
 the number of atoms owned by a processor.  The 3 corresponds to the
 fx, fy, fz components of force.</p>
 <p>It is up to the external program to set the values in this array to
 the desired quantities, as often as desired.  For example, the driver
 program might perform an MD run in stages of 1000 timesteps each.  In
 between calls to the LAMMPS <a class="reference internal" href="run.html"><em>run</em></a> command, it could retrieve
 atom coordinates from LAMMPS, compute forces, set values in fexternal,
 etc.</p>
 <hr class="docutils" />
 <p>To use this fix during energy minimization, the energy corresponding
 to the added forces must also be set so as to be consistent with the
 added forces.  Otherwise the minimization will not converge correctly.</p>
 <p>This can be done from the external driver by calling this public
 method of the FixExternal class:</p>
 <div class="highlight-python"><div class="highlight"><pre>void set_energy(double eng);
 </pre></div>
 </div>
 <p>where eng is the potential energy.  Eng is an extensive quantity,
 meaning it should be the sum over per-atom energies of all affected
 atoms.  It should also be provided in <a class="reference internal" href="units.html"><em>energy units</em></a>
 consistent with the simulation.  See the details below for how to
 insure this energy setting is used appropriately in a minimization.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.</p>
 <p>The <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> <em>energy</em> option is supported by this
 fix to add the potential &#8220;energy&#8221; set by the external driver to the
 system&#8217;s potential energy as part of <a class="reference internal" href="thermo_style.html"><em>thermodynamic output</em></a>.  This is a fictitious quantity but is
 needed so that the <a class="reference internal" href="minimize.html"><em>minimize</em></a> command can include the
 forces added by this fix in a consistent manner.  I.e. there is a
 decrease in potential energy when atoms move in the direction of the
 added force.</p>
 <p>This fix computes a global scalar which can be accessed by various
 <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  The scalar is the
 potential energy discussed above.  The scalar stored by this fix
 is &#8220;extensive&#8221;.</p>
 <p>No parameter of this fix can be used with the <em>start/stop</em> keywords of
 the <a class="reference internal" href="run.html"><em>run</em></a> command.</p>
 <p>The forces due to this fix are imposed during an energy minimization,
 invoked by the <a class="reference internal" href="minimize.html"><em>minimize</em></a> command.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">If you want the fictitious potential energy associated
 with the added forces to be included in the total potential energy of
 the system (the quantity being minimized), you MUST enable the
 <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> <em>energy</em> option for this fix.</p>
 </div>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <blockquote>
 <div>none</div></blockquote>
 <p><strong>Related commands:</strong> none</p>
 <p><strong>Default:</strong> none</p>
 </div>
 </div>
 
 
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   <div class="section" id="fix-gravity-command">
 <span id="index-0"></span><h1>fix gravity command<a class="headerlink" href="#fix-gravity-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="fix-gravity-cuda-command">
 <h1>fix gravity/cuda command<a class="headerlink" href="#fix-gravity-cuda-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="fix-gravity-omp-command">
 <h1>fix gravity/omp command<a class="headerlink" href="#fix-gravity-omp-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group gravity magnitude style args
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>gravity = style name of this fix command</li>
 <li>magnitude = size of acceleration (force/mass units)</li>
 <li>magnitude can be a variable (see below)</li>
 <li>style = <em>chute</em> or <em>spherical</em> or <em>gradient</em> or <em>vector</em></li>
 </ul>
 <pre class="literal-block">
 <em>chute</em> args = angle
-    angle = angle in +x away from -z or -y axis in 3d/2d (in degrees)
-    angle can be a variable (see below)
-  <em>spherical</em> args = phi theta
-    phi = azimuthal angle from +x axis (in degrees)
-    theta = angle from +z or +y axis in 3d/2d (in degrees)
-    phi or theta can be a variable (see below)
-  <em>vector</em> args = x y z
-    x y z = vector direction to apply the acceleration
-    x or y or z can be a variable (see below)
+  angle = angle in +x away from -z or -y axis in 3d/2d (in degrees)
+  angle can be a variable (see below)
+<em>spherical</em> args = phi theta
+  phi = azimuthal angle from +x axis (in degrees)
+  theta = angle from +z or +y axis in 3d/2d (in degrees)
+  phi or theta can be a variable (see below)
+<em>vector</em> args = x y z
+  x y z = vector direction to apply the acceleration
+  x or y or z can be a variable (see below)
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix 1 all gravity 1.0 chute 24.0
 fix 1 all gravity v_increase chute 24.0
 fix 1 all gravity 1.0 spherical 0.0 -180.0
 fix 1 all gravity 10.0 spherical v_phi v_theta
 fix 1 all gravity 100.0 vector 1 1 0
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Impose an additional acceleration on each particle in the group.  This
 fix is typically used with granular systems to include a &#8220;gravity&#8221;
 term acting on the macroscopic particles.  More generally, it can
 represent any kind of driving field, e.g. a pressure gradient inducing
 a Poiseuille flow in a fluid.  Note that this fix operates differently
 than the <a class="reference internal" href="fix_addforce.html"><em>fix addforce</em></a> command.  The addforce fix
 adds the same force to each atom, independent of its mass.  This
 command imparts the same acceleration to each atom (force/mass).</p>
 <p>The <em>magnitude</em> of the acceleration is specified in force/mass units.
 For granular systems (LJ units) this is typically 1.0.  See the
 <a class="reference internal" href="units.html"><em>units</em></a> command for details.</p>
 <p>Style <em>chute</em> is typically used for simulations of chute flow where
 the specified <em>angle</em> is the chute angle, with flow occurring in the +x
 direction.  For 3d systems, the tilt is away from the z axis; for 2d
 systems, the tilt is away from the y axis.</p>
 <p>Style <em>spherical</em> allows an arbitrary 3d direction to be specified for
 the acceleration vector.  <em>Phi</em> and <em>theta</em> are defined in the usual
 spherical coordinates.  Thus for acceleration acting in the -z
 direction, <em>theta</em> would be 180.0 (or -180.0).  <em>Theta</em> = 90.0 and
 <em>phi</em> = -90.0 would mean acceleration acts in the -y direction.  For
 2d systems, <em>phi</em> is ignored and <em>theta</em> is an angle in the xy plane
 where <em>theta</em> = 0.0 is the y-axis.</p>
 <p>Style <em>vector</em> imposes an acceleration in the vector direction given
 by (x,y,z).  Only the direction of the vector is important; it&#8217;s
 length is ignored.  For 2d systems, the <em>z</em> component is ignored.</p>
 <p>Any of the quantities <em>magnitude</em>, <em>angle</em>, <em>phi</em>, <em>theta</em>, <em>x</em>, <em>y</em>,
 <em>z</em> which define the gravitational magnitude and direction, can be
 specified as an equal-style <a class="reference internal" href="variable.html"><em>variable</em></a>.  If the value is
 a variable, it should be specified as v_name, where name is the
 variable name.  In this case, the variable will be evaluated each
 timestep, and its value used to determine the quantity.  You should
 insure that the variable calculates a result in the approriate units,
 e.g. force/mass or degrees.</p>
 <p>Equal-style variables can specify formulas with various mathematical
 functions, and include <a class="reference internal" href="thermo_style.html"><em>thermo_style</em></a> command
 keywords for the simulation box parameters and timestep and elapsed
 time.  Thus it is easy to specify a time-dependent gravitational
 field.</p>
 <hr class="docutils" />
 <p>Styles with a <em>cuda</em>, <em>gpu</em>, <em>intel</em>, <em>kk</em>, <em>omp</em>, or <em>opt</em> suffix are
 functionally the same as the corresponding style without the suffix.
 They have been optimized to run faster, depending on your available
 hardware, as discussed in <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a>
 of the manual.  The accelerated styles take the same arguments and
 should produce the same results, except for round-off and precision
 issues.</p>
 <p>These accelerated styles are part of the USER-CUDA, GPU, USER-INTEL,
 KOKKOS, USER-OMP and OPT packages, respectively.  They are only
 enabled if LAMMPS was built with those packages.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 <p>You can specify the accelerated styles explicitly in your input script
 by including their suffix, or you can use the <a class="reference internal" href="Section_start.html#start-7"><span>-suffix command-line switch</span></a> when you invoke LAMMPS, or you can
 use the <a class="reference internal" href="suffix.html"><em>suffix</em></a> command in your input script.</p>
 <p>See <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a> of the manual for
 more instructions on how to use the accelerated styles effectively.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.</p>
 <p>The <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> <em>energy</em> option is supported by this
 fix to add the gravitational potential energy of the system to the
 system&#8217;s potential energy as part of <a class="reference internal" href="thermo_style.html"><em>thermodynamic output</em></a>.</p>
 <p>This fix computes a global scalar which can be accessed by various
 <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  This scalar is the
 gravitational potential energy of the particles in the defined field,
 namely mass * (g dot x) for each particles, where x and mass are the
 particles position and mass, and g is the gravitational field.  The
 scalar value calculated by this fix is &#8220;extensive&#8221;.</p>
 <p>No parameter of this fix can be used with the <em>start/stop</em> keywords of
 the <a class="reference internal" href="run.html"><em>run</em></a> command.  This fix is not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <blockquote>
 <div>none</div></blockquote>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="atom_style.html"><em>atom_style sphere</em></a>, <a class="reference internal" href="fix_addforce.html"><em>fix addforce</em></a></p>
 <p><strong>Default:</strong> none</p>
 </div>
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   <div class="section" id="fix-heat-command">
 <span id="index-0"></span><h1>fix heat command<a class="headerlink" href="#fix-heat-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID heat N eflux
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>heat = style name of this fix command</li>
 <li>N = add/subtract heat every this many timesteps</li>
 <li>eflux = rate of heat addition or subtraction (energy/time units)</li>
 <li>eflux can be a variable (see below)</li>
 <li>zero or more keyword/value pairs may be appended to args</li>
 <li>keyword = <em>region</em></li>
 </ul>
 <pre class="literal-block">
 <em>region</em> value = region-ID
-    region-ID = ID of region atoms must be in to have added force
+  region-ID = ID of region atoms must be in to have added force
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix 3 qin heat 1 1.0
 fix 3 qin heat 10 v_flux
 fix 4 qout heat 1 -1.0 region top
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Add non-translational kinetic energy (heat) to a group of atoms in a
 manner that conserves their aggregate momentum.  Two of these fixes
 can be used to establish a temperature gradient across a simulation
 domain by adding heat (energy) to one group of atoms (hot reservoir)
 and subtracting heat from another (cold reservoir).  E.g. a simulation
 sampling from the McDLT ensemble.</p>
 <p>If the <em>region</em> keyword is used, the atom must be in both the group
 and the specified geometric <a class="reference internal" href="region.html"><em>region</em></a> in order to have
 energy added or subtracted to it.  If not specified, then the atoms in
 the group are affected wherever they may move to.</p>
 <p>Heat addition/subtraction is performed every N timesteps.  The <em>eflux</em>
 parameter can be specified as a numeric constant or as a variable (see
 below).  If it is a numeric constant or equal-style variable which
 evaluates to a scalar value, then the <em>eflux</em> determines the change in
 aggregate energy of the entire group of atoms per unit time, e.g. in
 eV/psec for <a class="reference internal" href="units.html"><em>metal units</em></a>.  In this case it is an
 &#8220;extensive&#8221; quantity, meaning its magnitude should be scaled with the
 number of atoms in the group.  Note that since <em>eflux</em> has per-time
 units (i.e. it is a flux), this means that a larger value of N will
 add/subtract a larger amount of energy each time the fix is invoked.</p>
 <p>If <em>eflux</em> is specified as an atom-style variable (see below), then
 the variable computes one value per atom.  In this case, each value is
 the energy flux for a single atom, again in units of energy per unit
 time.  In this case, each value is an &#8220;intensive&#8221; quantity, which need
 not be scaled with the number of atoms in the group.</p>
 <p>As mentioned above, the <em>eflux</em> parameter can be specified as an
 equal-style or atom_style <a class="reference internal" href="variable.html"><em>variable</em></a>.  If the value is a
 variable, it should be specified as v_name, where name is the variable
 name.  In this case, the variable will be evaluated each timestep, and
 its value(s) used to determine the flux.</p>
 <p>Equal-style variables can specify formulas with various mathematical
 functions, and include <a class="reference internal" href="thermo_style.html"><em>thermo_style</em></a> command
 keywords for the simulation box parameters and timestep and elapsed
 time.  Thus it is easy to specify a time-dependent flux.</p>
 <p>Atom-style variables can specify the same formulas as equal-style
 variables but can also include per-atom values, such as atom
 coordinates.  Thus it is easy to specify a spatially-dependent flux
 with optional time-dependence as well.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">If heat is subtracted from the system too aggressively
 so that the group&#8217;s kinetic energy would go to zero, or any individual
 atom&#8217;s kinetic energy would go to zero for the case where <em>eflux</em> is
 an atom-style variable, then LAMMPS will halt with an error message.</p>
 </div>
 <p>Fix heat is different from a thermostat such as <a class="reference internal" href="fix_nh.html"><em>fix nvt</em></a>
 or <a class="reference internal" href="fix_temp_rescale.html"><em>fix temp/rescale</em></a> in that energy is
 added/subtracted continually.  Thus if there isn&#8217;t another mechanism
 in place to counterbalance this effect, the entire system will heat or
 cool continuously.  You can use multiple heat fixes so that the net
 energy change is 0.0 or use <a class="reference internal" href="fix_viscous.html"><em>fix viscous</em></a> to drain
 energy from the system.</p>
 <p>This fix does not change the coordinates of its atoms; it only scales
 their velocities.  Thus you must still use an integration fix
 (e.g. <a class="reference internal" href="fix_nve.html"><em>fix nve</em></a>) on the affected atoms.  This fix should
 not normally be used on atoms that have their temperature controlled
 by another fix - e.g. <a class="reference internal" href="fix_nh.html"><em>fix nvt</em></a> or <a class="reference internal" href="fix_langevin.html"><em>fix langevin</em></a> fix.</p>
 </div>
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.  None of the <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> options
 are relevant to this fix.</p>
 <p>This fix computes a global scalar which can be accessed by various
 <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  This scalar is the
 most recent value by which velocites were scaled.  The scalar value
 calculated by this fix is &#8220;intensive&#8221;.  If <em>eflux</em> is specified as
 an atom-style variable, this fix computes the average value by which
 the velocities were scaled for all of the atoms that had their
 velocities scaled.</p>
 <p>No parameter of this fix can be used with the <em>start/stop</em> keywords of
 the <a class="reference internal" href="run.html"><em>run</em></a> command.  This fix is not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <blockquote>
 <div>none</div></blockquote>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="compute_temp.html"><em>compute temp</em></a>, <a class="reference internal" href="compute_temp_region.html"><em>compute temp/region</em></a></p>
 <p><strong>Default:</strong> none</p>
 </div>
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   <div class="section" id="fix-imd-command">
 <span id="index-0"></span><h1>fix imd command<a class="headerlink" href="#fix-imd-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID imd trate port keyword values ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>imd = style name of this fix command</li>
 <li>port = port number on which the fix listens for an IMD client</li>
 <li>keyword = <em>unwrap</em> or <em>fscale</em> or <em>trate</em></li>
 </ul>
 <pre class="literal-block">
 <em>unwrap</em> arg = <em>on</em> or <em>off</em>
-    off = coordinates are wrapped back into the principal unit cell (default)
-    on = &quot;unwrapped&quot; coordinates using the image flags used
-  <em>fscale</em> arg = factor
-    factor = floating point number to scale IMD forces (default: 1.0)
-  <em>trate</em> arg = transmission rate of coordinate data sets (default: 1)
-  <em>nowait</em> arg = <em>on</em> or <em>off</em>
-    off = LAMMPS waits to be connected to an IMD client before continuing (default)
-    on = LAMMPS listens for an IMD client, but continues with the run
+  off = coordinates are wrapped back into the principal unit cell (default)
+  on = &quot;unwrapped&quot; coordinates using the image flags used
+<em>fscale</em> arg = factor
+  factor = floating point number to scale IMD forces (default: 1.0)
+<em>trate</em> arg = transmission rate of coordinate data sets (default: 1)
+<em>nowait</em> arg = <em>on</em> or <em>off</em>
+  off = LAMMPS waits to be connected to an IMD client before continuing (default)
+  on = LAMMPS listens for an IMD client, but continues with the run
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix vmd all imd 5678
 fix comm all imd 8888 trate 5 unwrap on fscale 10.0
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>This fix implements the &#8220;Interactive MD&#8221; (IMD) protocol which allows
 realtime visualization and manipulation of MD simulations through the
 IMD protocol, as initially implemented in VMD and NAMD.  Specifically
 it allows LAMMPS to connect an IMD client, for example the <a class="reference external" href="http://www.ks.uiuc.edu/Research/vmd">VMD visualization program</a>, so that it can monitor the progress of the
 simulation and interactively apply forces to selected atoms.</p>
 <p>If LAMMPS is compiled with the preprocessor flag -DLAMMPS_ASYNC_IMD
 then fix imd will use POSIX threads to spawn a IMD communication
 thread on MPI rank 0 in order to offload data reading and writing
 from the main execution thread and potentially lower the inferred
 latencies for slow communication links. This feature has only been
 tested under linux.</p>
 <p>There are example scripts for using this package with LAMMPS in
 examples/USER/imd. Additional examples and a driver for use with the
 Novint Falcon game controller as haptic device can be found at:
 <a class="reference external" href="http://sites.google.com/site/akohlmey/software/vrpn-icms">http://sites.google.com/site/akohlmey/software/vrpn-icms</a>.</p>
 <p>The source code for this fix includes code developed by the
 Theoretical and Computational Biophysics Group in the Beckman
 Institute for Advanced Science and Technology at the University of
 Illinois at Urbana-Champaign.  We thank them for providing a software
 interface that allows codes like LAMMPS to hook to <a class="reference external" href="http://www.ks.uiuc.edu/Research/vmd">VMD</a>.</p>
 <p>Upon initialization of the fix, it will open a communication port on
 the node with MPI task 0 and wait for an incoming connection.  As soon
 as an IMD client is connected, the simulation will continue and the
 fix will send the current coordinates of the fix&#8217;s group to the IMD
 client at every trate MD step. When using r-RESPA, trate applies to
 the steps of the outmost RESPA level.  During a run with an active IMD
 connection also the IMD client can request to apply forces to selected
 atoms of the fix group.</p>
 <p>The port number selected must be an available network port number.  On
 many machines, port numbers &lt; 1024 are reserved for accounts with
 system manager privilege and specific applications. If multiple imd
 fixes would be active at the same time, each needs to use a different
 port number.</p>
 <p>The <em>nowait</em> keyword controls the behavior of the fix when no IMD
 client is connected. With the default setting of <em>off</em>, LAMMPS will
 wait until a connection is made before continuing with the
 execution. Setting <em>nowait</em> to <em>on</em> will have the LAMMPS code be ready
 to connect to a client, but continue with the simulation. This can for
 example be used to monitor the progress of an ongoing calculation
 without the need to be permanently connected or having to download a
 trajectory file.</p>
 <p>The <em>trate</em> keyword allows to select how often the coordinate data is
 sent to the IMD client. It can also be changed on request of the IMD
 client through an IMD protocol message.  The <em>unwrap</em> keyword allows
 to send &#8220;unwrapped&#8221; coordinates to the IMD client that undo the
 wrapping back of coordinates into the principle unit cell, as done by
 default in LAMMPS.  The <em>fscale</em> keyword allows to apply a scaling
 factor to forces transmitted by the IMD client. The IMD protocols
 stipulates that forces are transferred in kcal/mol/angstrom under the
 assumption that coordinates are given in angstrom. For LAMMPS runs
 with different units or as a measure to tweak the forces generated by
 the manipulation of the IMD client, this option allows to make
 adjustments.</p>
 <p>To connect VMD to a listening LAMMPS simulation on the same machine
 with fix imd enabled, one needs to start VMD and load a coordinate or
 topology file that matches the fix group.  When the VMD command
 prompts appears, one types the command line:</p>
 <div class="highlight-python"><div class="highlight"><pre>imd connect localhost 5678
 </pre></div>
 </div>
 <p>This assumes that <em>fix imd</em> was started with 5678 as a port
 number for the IMD protocol.</p>
 <p>The steps to do interactive manipulation of a running simulation in
 VMD are the following:</p>
 <p>In the Mouse menu of the VMD Main window, select &#8220;Mouse -&gt; Force -&gt;
 Atom&#8221;.  You may alternately select &#8220;Residue&#8221;, or &#8220;Fragment&#8221; to apply
 forces to whole residues or fragments. Your mouse can now be used to
 apply forces to your simulation. Click on an atom, residue, or
 fragment and drag to apply a force. Click quickly without moving the
 mouse to turn the force off. You can also use a variety of 3D position
 trackers to apply forces to your simulation. Game controllers or haptic
 devices with force-feedback such as the Novint Falcon or Sensable
 PHANTOM allow you to feel the resistance due to inertia or interactions
 with neighbors that the atoms experience you are trying to move, as if
 they were real objects. See the <a class="reference external" href="http://www.ks.uiuc.edu/Research/vmd/imd/">VMD IMD Homepage</a> and the
 <a class="reference external" href="http://sites.google.com/site/akohlmey/software/vrpn-icms">VRPN-ICMS Homepage</a> for more details.</p>
 <p>If IMD control messages are received, a line of text describing the
 message and its effect will be printed to the LAMMPS output screen, if
 screen output is active.</p>
 </div>
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.  None of the <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> options
 are relevant to this fix.  No global scalar or vector or per-atom
 quantities are stored by this fix for access by various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  No parameter of this fix can
 be used with the <em>start/stop</em> keywords of the <a class="reference internal" href="run.html"><em>run</em></a> command.
 This fix is not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>This fix is part of the USER-MISC package.  It is only enabled if
 LAMMPS was built with that package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 <p>When used in combination with VMD, a topology or coordinate file has
 to be loaded, which matches (in number and ordering of atoms) the
 group the fix is applied to. The fix internally sorts atom IDs by
 ascending integer value; in VMD (and thus the IMD protocol) those will
 be assigned 0-based consecutive index numbers.</p>
 <p>When using multiple active IMD connections at the same time, each
 needs to use a different port number.</p>
 <p><strong>Related commands:</strong> none</p>
 <p><strong>Default:</strong> none</p>
 </div>
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   <div class="section" id="fix-indent-command">
 <span id="index-0"></span><h1>fix indent command<a class="headerlink" href="#fix-indent-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID indent K keyword values ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>indent = style name of this fix command</li>
 <li>K = force constant for indenter surface (force/distance^2 units)</li>
 <li>one or more keyword/value pairs may be appended</li>
 <li>keyword = <em>sphere</em> or <em>cylinder</em> or <em>plane</em> or <em>side</em> or <em>units</em></li>
 </ul>
 <pre class="literal-block">
 <em>sphere</em> args = x y z R
-    x,y,z = initial position of center of indenter (distance units)
-    R = sphere radius of indenter (distance units)
-    any of x,y,z,R can be a variable (see below)
-  <em>cylinder</em> args = dim c1 c2 R
-    dim = <em>x</em> or <em>y</em> or <em>z</em> = axis of cylinder
-    c1,c2 = coords of cylinder axis in other 2 dimensions (distance units)
-    R = cylinder radius of indenter (distance units)
-    any of c1,c2,R can be a variable (see below)
-  <em>plane</em> args = dim pos side
-    dim = <em>x</em> or <em>y</em> or <em>z</em> = plane perpendicular to this dimension
-    pos = position of plane in dimension x, y, or z (distance units)
-    pos can be a variable (see below)
-    side = <em>lo</em> or <em>hi</em>
-  <em>side</em> value = <em>in</em> or <em>out</em>
-    <em>in</em> = the indenter acts on particles inside the sphere or cylinder
-    <em>out</em> = the indenter acts on particles outside the sphere or cylinder
-  <em>units</em> value = <em>lattice</em> or <em>box</em>
-    lattice = the geometry is defined in lattice units
-    box = the geometry is defined in simulation box units
+  x,y,z = initial position of center of indenter (distance units)
+  R = sphere radius of indenter (distance units)
+  any of x,y,z,R can be a variable (see below)
+<em>cylinder</em> args = dim c1 c2 R
+  dim = <em>x</em> or <em>y</em> or <em>z</em> = axis of cylinder
+  c1,c2 = coords of cylinder axis in other 2 dimensions (distance units)
+  R = cylinder radius of indenter (distance units)
+  any of c1,c2,R can be a variable (see below)
+<em>plane</em> args = dim pos side
+  dim = <em>x</em> or <em>y</em> or <em>z</em> = plane perpendicular to this dimension
+  pos = position of plane in dimension x, y, or z (distance units)
+  pos can be a variable (see below)
+  side = <em>lo</em> or <em>hi</em>
+<em>side</em> value = <em>in</em> or <em>out</em>
+  <em>in</em> = the indenter acts on particles inside the sphere or cylinder
+  <em>out</em> = the indenter acts on particles outside the sphere or cylinder
+<em>units</em> value = <em>lattice</em> or <em>box</em>
+  lattice = the geometry is defined in lattice units
+  box = the geometry is defined in simulation box units
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix 1 all indent 10.0 sphere 0.0 0.0 15.0 3.0
 fix 1 all indent 10.0 sphere v_x v_y 0.0 v_radius side in
 fix 2 flow indent 10.0 cylinder z 0.0 0.0 10.0 units box
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Insert an indenter within a simulation box.  The indenter repels all
 atoms that touch it, so it can be used to push into a material or as
 an obstacle in a flow.  Or it can be used as a constraining wall
 around a simulation; see the discussion of the <em>side</em> keyword below.</p>
 <p>The indenter can either be spherical or cylindrical or planar.  You
 must set one of those 3 keywords.</p>
 <p>A spherical indenter exerts a force of magnitude</p>
 <div class="highlight-python"><div class="highlight"><pre><span class="n">F</span><span class="p">(</span><span class="n">r</span><span class="p">)</span> <span class="o">=</span> <span class="o">-</span> <span class="n">K</span> <span class="p">(</span><span class="n">r</span> <span class="o">-</span> <span class="n">R</span><span class="p">)</span><span class="o">^</span><span class="mi">2</span>
 </pre></div>
 </div>
 <p>on each atom where <em>K</em> is the specified force constant, <em>r</em> is the
 distance from the atom to the center of the indenter, and <em>R</em> is the
 radius of the indenter.  The force is repulsive and F(r) = 0 for <em>r</em> &gt;
 <em>R</em>.</p>
 <p>A cylindrical indenter exerts the same force, except that <em>r</em> is the
 distance from the atom to the center axis of the cylinder.  The
 cylinder extends infinitely along its axis.</p>
 <p>Spherical and cylindrical indenters account for periodic boundaries in
 two ways.  First, the center point of a spherical indenter (x,y,z) or
 axis of a cylindrical indenter (c1,c2) is remapped back into the
 simulation box, if the box is periodic in a particular dimension.
 This occurs every timestep if the indenter geometry is specified with
 a variable (see below), e.g. it is moving over time.  Second, the
 calculation of distance to the indenter center or axis accounts for
 periodic boundaries.  Both of these mean that an indenter can
 effectively move through and straddle one or more periodic boundaries.</p>
 <p>A planar indenter is really an axis-aligned infinite-extent wall
 exerting the same force on atoms in the system, where <em>R</em> is the
 position of the plane and <em>r-R</em> is the distance from the plane.  If
 the <em>side</em> parameter of the plane is specified as <em>lo</em> then it will
 indent from the lo end of the simulation box, meaning that atoms with
 a coordinate less than the plane&#8217;s current position will be pushed
 towards the hi end of the box and atoms with a coordinate higher than
 the plane&#8217;s current position will feel no force.  Vice versa if <em>side</em>
 is specified as <em>hi</em>.</p>
 <p>Any of the 4 quantities defining a spherical indenter&#8217;s geometry can
 be specified as an equal-style <a class="reference internal" href="variable.html"><em>variable</em></a>, namely <em>x</em>,
 <em>y</em>, <em>z</em>, or <em>R</em>.  Similarly, for a cylindrical indenter, any of <em>c1</em>,
 <em>c2</em>, or <em>R</em>, can be a variable.  For a planar indenter, <em>pos</em> can be
 a variable.  If the value is a variable, it should be specified as
 v_name, where name is the variable name.  In this case, the variable
 will be evaluated each timestep, and its value used to define the
 indenter geometry.</p>
 <p>Note that equal-style variables can specify formulas with various
 mathematical functions, and include <a class="reference internal" href="thermo_style.html"><em>thermo_style</em></a>
 command keywords for the simulation box parameters and timestep and
 elapsed time.  Thus it is easy to specify indenter properties that
 change as a function of time or span consecutive runs in a continuous
 fashion.  For the latter, see the <em>start</em> and <em>stop</em> keywords of the
 <a class="reference internal" href="run.html"><em>run</em></a> command and the <em>elaplong</em> keyword of <a class="reference internal" href="thermo_style.html"><em>thermo_style custom</em></a> for details.</p>
 <p>For example, if a spherical indenter&#8217;s x-position is specfied as v_x,
 then this variable definition will keep it&#8217;s center at a relative
 position in the simulation box, 1/4 of the way from the left edge to
 the right edge, even if the box size changes:</p>
 <div class="highlight-python"><div class="highlight"><pre>variable x equal &quot;xlo + 0.25*lx&quot;
 </pre></div>
 </div>
 <p>Similarly, either of these variable definitions will move the indenter
 from an initial position at 2.5 at a constant velocity of 5:</p>
 <div class="highlight-python"><div class="highlight"><pre>variable x equal &quot;2.5 + 5*elaplong*dt&quot;
 variable x equal vdisplace(2.5,5)
 </pre></div>
 </div>
 <p>If a spherical indenter&#8217;s radius is specified as v_r, then these
 variable definitions will grow the size of the indenter at a specfied
 rate.</p>
 <div class="highlight-python"><div class="highlight"><pre>variable r0 equal 0.0
 variable rate equal 1.0
 variable r equal &quot;v_r0 + step*dt*v_rate&quot;
 </pre></div>
 </div>
 <p>If the <em>side</em> keyword is specified as <em>out</em>, which is the default,
 then particles outside the indenter are pushded away from its outer
 surface, as described above.  This only applies to spherical or
 cylindrical indenters.  If the <em>side</em> keyword is specified as <em>in</em>,
 the action of the indenter is reversed.  Particles inside the indenter
 are pushed away from its inner surface.  In other words, the indenter
 is now a containing wall that traps the particles inside it.  If the
 radius shrinks over time, it will squeeze the particles.</p>
 <p>The <em>units</em> keyword determines the meaning of the distance units used
 to define the indenter geometry.  A <em>box</em> value selects standard
 distance units as defined by the <a class="reference internal" href="units.html"><em>units</em></a> command,
 e.g. Angstroms for units = real or metal.  A <em>lattice</em> value means the
 distance units are in lattice spacings.  The <a class="reference internal" href="lattice.html"><em>lattice</em></a>
 command must have been previously used to define the lattice spacing.
 The (x,y,z) coords of the indenter position are scaled by the x,y,z
 lattice spacings respectively.  The radius of a spherical or
 cylindrical indenter is scaled by the x lattice spacing.</p>
 <p>Note that the units keyword only affects indenter geometry parameters
 specified directly with numbers, not those specified as variables.  In
 the latter case, you should use the <em>xlat</em>, <em>ylat</em>, <em>zlat</em> keywords of
 the <a class="reference internal" href="thermo_style.html"><em>thermo_style</em></a> command if you want to include
 lattice spacings in a variable formula.</p>
 <p>The force constant <em>K</em> is not affected by the <em>units</em> keyword.  It is
 always in force/distance^2 units where force and distance are defined
 by the <a class="reference internal" href="units.html"><em>units</em></a> command.  If you wish K to be scaled by the
 lattice spacing, you can define K with a variable whose formula
 contains <em>xlat</em>, <em>ylat</em>, <em>zlat</em> keywords of the
 <a class="reference internal" href="thermo_style.html"><em>thermo_style</em></a> command, e.g.</p>
 <div class="highlight-python"><div class="highlight"><pre>variable k equal 100.0/xlat/xlat
 fix 1 all indent $k sphere ...
 </pre></div>
 </div>
 </div>
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.</p>
 <p>The <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> <em>energy</em> option is supported by this
 fix to add the energy of interaction between atoms and the indenter to
 the system&#8217;s potential energy as part of <a class="reference internal" href="thermo_style.html"><em>thermodynamic output</em></a>.  The energy of each particle interacting
 with the indenter is K/3 (r - R)^3.</p>
 <p>This fix computes a global scalar energy and a global 3-vector of
 forces (on the indenter), which can be accessed by various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  The scalar and vector values
 calculated by this fix are &#8220;extensive&#8221;.</p>
 <p>The forces due to this fix are imposed during an energy minimization,
 invoked by the <a class="reference internal" href="minimize.html"><em>minimize</em></a> command.  Note that if you
 define the indenter geometry with a variable using a time-dependent
 formula, LAMMPS uses the iteration count in the minimizer as the
 timestep.  But it is almost certainly a bad idea to have the indenter
 change its position or size during a minimization.  LAMMPS does not
 check if you have done this.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">If you want the atom/indenter interaction energy to be
 included in the total potential energy of the system (the quantity
 being minimized), you must enable the <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a>
 <em>energy</em> option for this fix.</p>
 </div>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <blockquote>
 <div>none</div></blockquote>
 <p><strong>Related commands:</strong> none</p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The option defaults are side = out and units = lattice.</p>
 </div>
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   <div class="section" id="fix-langevin-command">
 <span id="index-0"></span><h1>fix langevin command<a class="headerlink" href="#fix-langevin-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="fix-langevin-kk-command">
 <h1>fix langevin/kk command<a class="headerlink" href="#fix-langevin-kk-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID langevin Tstart Tstop damp seed keyword values ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>langevin = style name of this fix command</li>
 <li>Tstart,Tstop = desired temperature at start/end of run (temperature units)</li>
 <li>Tstart can be a variable (see below)</li>
 <li>damp = damping parameter (time units)</li>
 <li>seed = random number seed to use for white noise (positive integer)</li>
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>angmom</em> or <em>omega</em> or <em>scale</em> or <em>tally</em> or <em>zero</em></li>
 </ul>
 <pre class="literal-block">
 <em>angmom</em> value = <em>no</em> or scale
-    <em>no</em> = do not thermostat rotational degrees of freedom via the angular momentum
-    factor = do thermostat rotational degrees of freedom via the angular momentum and apply numeric factor as discussed below
-  <em>gjf</em> value = <em>no</em> or <em>yes</em>
-    <em>no</em> = use standard formulation
-    <em>yes</em> = use Gronbech-Jensen/Farago formulation
-  <em>omega</em> value = <em>no</em> or <em>yes</em>
-    <em>no</em> = do not thermostat rotational degrees of freedom via the angular velocity
-    <em>yes</em> = do thermostat rotational degrees of freedom via the angular velocity
-  <em>scale</em> values = type ratio
-    type = atom type (1-N)
-    ratio = factor by which to scale the damping coefficient
-  <em>tally</em> value = <em>no</em> or <em>yes</em>
-    <em>no</em> = do not tally the energy added/subtracted to atoms
-    <em>yes</em> = do tally the energy added/subtracted to atoms
-  <em>zero</em> value = <em>no</em> or <em>yes</em>
-    <em>no</em> = do not set total random force to zero
-    <em>yes</em> = set total random force to zero
+  <em>no</em> = do not thermostat rotational degrees of freedom via the angular momentum
+  factor = do thermostat rotational degrees of freedom via the angular momentum and apply numeric factor as discussed below
+<em>gjf</em> value = <em>no</em> or <em>yes</em>
+  <em>no</em> = use standard formulation
+  <em>yes</em> = use Gronbech-Jensen/Farago formulation
+<em>omega</em> value = <em>no</em> or <em>yes</em>
+  <em>no</em> = do not thermostat rotational degrees of freedom via the angular velocity
+  <em>yes</em> = do thermostat rotational degrees of freedom via the angular velocity
+<em>scale</em> values = type ratio
+  type = atom type (1-N)
+  ratio = factor by which to scale the damping coefficient
+<em>tally</em> value = <em>no</em> or <em>yes</em>
+  <em>no</em> = do not tally the energy added/subtracted to atoms
+  <em>yes</em> = do tally the energy added/subtracted to atoms
+<em>zero</em> value = <em>no</em> or <em>yes</em>
+  <em>no</em> = do not set total random force to zero
+  <em>yes</em> = set total random force to zero
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix 3 boundary langevin 1.0 1.0 1000.0 699483
 fix 1 all langevin 1.0 1.1 100.0 48279 scale 3 1.5
 fix 1 all langevin 1.0 1.1 100.0 48279 angmom 3.333
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Apply a Langevin thermostat as described in <a class="reference internal" href="fix_langevin_eff.html#schneider"><span>(Schneider)</span></a>
 to a group of atoms which models an interaction with a background
 implicit solvent.  Used with <a class="reference internal" href="fix_nve.html"><em>fix nve</em></a>, this command
 performs Brownian dynamics (BD), since the total force on each atom
 will have the form:</p>
 <div class="highlight-python"><div class="highlight"><pre>F = Fc + Ff + Fr
 Ff = - (m / damp) v
 Fr is proportional to sqrt(Kb T m / (dt damp))
 </pre></div>
 </div>
 <p>Fc is the conservative force computed via the usual inter-particle
 interactions (<a class="reference internal" href="pair_style.html"><em>pair_style</em></a>,
 <a class="reference internal" href="bond_style.html"><em>bond_style</em></a>, etc).</p>
 <p>The Ff and Fr terms are added by this fix on a per-particle basis.
 See the <a class="reference internal" href="pair_dpd.html"><em>pair_style dpd/tstat</em></a> command for a
 thermostatting option that adds similar terms on a pairwise basis to
 pairs of interacting particles.</p>
 <p>Ff is a frictional drag or viscous damping term proportional to the
 particle&#8217;s velocity.  The proportionality constant for each atom is
 computed as m/damp, where m is the mass of the particle and damp is
 the damping factor specified by the user.</p>
 <p>Fr is a force due to solvent atoms at a temperature T randomly bumping
 into the particle.  As derived from the fluctuation/dissipation
 theorem, its magnitude as shown above is proportional to sqrt(Kb T m /
 dt damp), where Kb is the Boltzmann constant, T is the desired
 temperature, m is the mass of the particle, dt is the timestep size,
 and damp is the damping factor.  Random numbers are used to randomize
 the direction and magnitude of this force as described in
 <a class="reference internal" href="fix_langevin_eff.html#dunweg"><span>(Dunweg)</span></a>, where a uniform random number is used (instead of
 a Gaussian random number) for speed.</p>
 <p>Note that unless you use the <em>omega</em> or <em>angmom</em> keywords, the
 thermostat effect of this fix is applied to only the translational
 degrees of freedom for the particles, which is an important
 consideration for finite-size particles, which have rotational degrees
 of freedom, are being thermostatted.  The translational degrees of
 freedom can also have a bias velocity removed from them before
 thermostatting takes place; see the description below.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">Unlike the <a class="reference internal" href="fix_nh.html"><em>fix nvt</em></a> command which
 performs Nose/Hoover thermostatting AND time integration, this fix
 does NOT perform time integration.  It only modifies forces to effect
 thermostatting.  Thus you must use a separate time integration fix,
 like <a class="reference internal" href="fix_nve.html"><em>fix nve</em></a> to actually update the velocities and
 positions of atoms using the modified forces.  Likewise, this fix
 should not normally be used on atoms that also have their temperature
 controlled by another fix - e.g. by <a class="reference internal" href="fix_nh.html"><em>fix nvt</em></a> or <a class="reference internal" href="fix_temp_rescale.html"><em>fix temp/rescale</em></a> commands.</p>
 </div>
 <p>See <a class="reference internal" href="Section_howto.html#howto-16"><span>this howto section</span></a> of the manual for
 a discussion of different ways to compute temperature and perform
 thermostatting.</p>
 <p>The desired temperature at each timestep is a ramped value during the
 run from <em>Tstart</em> to <em>Tstop</em>.</p>
 <p><em>Tstart</em> can be specified as an equal-style or atom-style
 <a class="reference internal" href="variable.html"><em>variable</em></a>.  In this case, the <em>Tstop</em> setting is
 ignored.  If the value is a variable, it should be specified as
 v_name, where name is the variable name.  In this case, the variable
 will be evaluated each timestep, and its value used to determine the
 target temperature.</p>
 <p>Equal-style variables can specify formulas with various mathematical
 functions, and include <a class="reference internal" href="thermo_style.html"><em>thermo_style</em></a> command
 keywords for the simulation box parameters and timestep and elapsed
 time.  Thus it is easy to specify a time-dependent temperature.</p>
 <p>Atom-style variables can specify the same formulas as equal-style
 variables but can also include per-atom values, such as atom
 coordinates.  Thus it is easy to specify a spatially-dependent
 temperature with optional time-dependence as well.</p>
 <p>Like other fixes that perform thermostatting, this fix can be used
 with <a class="reference internal" href="compute.html"><em>compute commands</em></a> that remove a &#8220;bias&#8221; from the
 atom velocities.  E.g. removing the center-of-mass velocity from a
 group of atoms or removing the x-component of velocity from the
 calculation.  This is not done by default, but only if the
 <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> command is used to assign a temperature
 compute to this fix that includes such a bias term.  See the doc pages
 for individual <a class="reference internal" href="compute.html"><em>compute commands</em></a> to determine which ones
 include a bias.  In this case, the thermostat works in the following
 manner: bias is removed from each atom, thermostatting is performed on
 the remaining thermal degrees of freedom, and the bias is added back
 in.</p>
 <p>The <em>damp</em> parameter is specified in time units and determines how
 rapidly the temperature is relaxed.  For example, a value of 100.0
 means to relax the temperature in a timespan of (roughly) 100 time
 units (tau or fmsec or psec - see the <a class="reference internal" href="units.html"><em>units</em></a> command).
 The damp factor can be thought of as inversely related to the
 viscosity of the solvent.  I.e. a small relaxation time implies a
 hi-viscosity solvent and vice versa.  See the discussion about gamma
 and viscosity in the documentation for the <a class="reference internal" href="fix_viscous.html"><em>fix viscous</em></a> command for more details.</p>
 <p>The random # <em>seed</em> must be a positive integer.  A Marsaglia random
 number generator is used.  Each processor uses the input seed to
 generate its own unique seed and its own stream of random numbers.
 Thus the dynamics of the system will not be identical on two runs on
 different numbers of processors.</p>
 <hr class="docutils" />
 <p>The keyword/value option pairs are used in the following ways.</p>
 <p>The keyword <em>angmom</em> and <em>omega</em> keywords enable thermostatting of
 rotational degrees of freedom in addition to the usual translational
 degrees of freedom.  This can only be done for finite-size particles.</p>
 <p>A simulation using atom_style sphere defines an omega for finite-size
 spheres.  A simulation using atom_style ellipsoid defines a finite
 size and shape for aspherical particles and an angular momentum.
 The Langevin formulas for thermostatting the rotational degrees of
 freedom are the same as those above, where force is replaced by
 torque, m is replaced by the moment of inertia I, and v is replaced by
 omega (which is derived from the angular momentum in the case of
 aspherical particles).</p>
 <p>The rotational temperature of the particles can be monitored by the
 <a class="reference internal" href="compute_temp_sphere.html"><em>compute temp/sphere</em></a> and <a class="reference internal" href="compute_temp_asphere.html"><em>compute temp/asphere</em></a> commands with their rotate
 options.</p>
 <p>For the <em>omega</em> keyword there is also a scale factor of 10.0/3.0 that
 is applied as a multiplier on the Ff (damping) term in the equation
 above and of sqrt(10.0/3.0) as a multiplier on the Fr term.  This does
 not affect the thermostatting behaviour of the Langevin formalism but
 insures that the randomized rotational diffusivity of spherical
 particles is correct.</p>
 <p>For the <em>angmom</em> keyword a similar scale factor is needed which is
 10.0/3.0 for spherical particles, but is anisotropic for aspherical
 particles (e.g. ellipsoids).  Currently LAMMPS only applies an
 isotropic scale factor, and you can choose its magnitude as the
 specified value of the <em>angmom</em> keyword.  If your aspherical particles
 are (nearly) spherical than a value of 10.0/3.0 = 3.333 is a good
 choice.  If they are highly aspherical, a value of 1.0 is as good a
 choice as any, since the effects on rotational diffusivity of the
 particles will be incorrect regardless.  Note that for any reasonable
 scale factor, the thermostatting effect of the <em>angmom</em> keyword on the
 rotational temperature of the aspherical particles should still be
 valid.</p>
 <p>The keyword <em>scale</em> allows the damp factor to be scaled up or down by
 the specified factor for atoms of that type.  This can be useful when
 different atom types have different sizes or masses.  It can be used
 multiple times to adjust damp for several atom types.  Note that
 specifying a ratio of 2 increases the relaxation time which is
 equivalent to the solvent&#8217;s viscosity acting on particles with 1/2 the
 diameter.  This is the opposite effect of scale factors used by the
 <a class="reference internal" href="fix_viscous.html"><em>fix viscous</em></a> command, since the damp factor in fix
 <em>langevin</em> is inversely related to the gamma factor in fix <em>viscous</em>.
 Also note that the damping factor in fix <em>langevin</em> includes the
 particle mass in Ff, unlike fix <em>viscous</em>.  Thus the mass and size of
 different atom types should be accounted for in the choice of ratio
 values.</p>
 <p>The keyword <em>tally</em> enables the calculation of the cumulative energy
 added/subtracted to the atoms as they are thermostatted.  Effectively
 it is the energy exchanged between the infinite thermal reservoir and
 the particles.  As described below, this energy can then be printed
 out or added to the potential energy of the system to monitor energy
 conservation.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">this accumulated energy does NOT include kinetic
 energy removed by the <em>zero</em> flag. LAMMPS will print a warning when
 both options are active.</p>
 </div>
 <p>The keyword <em>zero</em> can be used to eliminate drift due to the
 thermostat. Because the random forces on different atoms are
 independent, they do not sum exactly to zero.  As a result, this fix
 applies a small random force to the entire system, and the
 center-of-mass of the system undergoes a slow random walk.  If the
 keyword <em>zero</em> is set to <em>yes</em>, the total random force is set exactly
 to zero by subtracting off an equal part of it from each atom in the
 group.  As a result, the center-of-mass of a system with zero initial
 momentum will not drift over time.</p>
 <p>The keyword <em>gjf</em> can be used to run the <a class="reference internal" href="#gronbech-jensen"><span>Gronbech-Jensen/Farago</span></a> time-discretization of the Langevin model.  As
 described in the papers cited below, the purpose of this method is to
 enable longer timesteps to be used (up to the numerical stability
 limit of the integrator), while still producing the correct Boltzmann
 distribution of atom positions.  It is implemented within LAMMPS, by
 changing how the the random force is applied so that it is composed of
 the average of two random forces representing half-contributions from
 the previous and current time intervals.</p>
 <p>In common with all methods based on Verlet integration, the
 discretized velocities generated by this method in conjunction with
 velocity-Verlet time integration are not exactly conjugate to the
 positions.  As a result the temperature (computed from the discretized
 velocities) will be systematically lower than the target temperature,
 by a small amount which grows with the timestep.  Nonetheless, the
 distribution of atom positions will still be consistent with the
 target temperature.</p>
 <p>As an example of using the <em>gjf</em> keyword, for molecules containing C-H
 bonds, configurational properties generated with dt = 2.5 fs and tdamp
 = 100 fs are indistinguishable from dt = 0.5 fs.  Because the velocity
 distribution systematically decreases with increasing timestep, the
 method should not be used to generate properties that depend on the
 velocity distribution, such as the velocity autocorrelation function
 (VACF). In this example, the velocity distribution at dt = 2.5fs
 generates an average temperature of 220 K, instead of 300 K.</p>
 <hr class="docutils" />
 <p>Styles with a <em>cuda</em>, <em>gpu</em>, <em>intel</em>, <em>kk</em>, <em>omp</em>, or <em>opt</em> suffix are
 functionally the same as the corresponding style without the suffix.
 They have been optimized to run faster, depending on your available
 hardware, as discussed in <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a>
 of the manual.  The accelerated styles take the same arguments and
 should produce the same results, except for round-off and precision
 issues.</p>
 <p>These accelerated styles are part of the USER-CUDA, GPU, USER-INTEL,
 KOKKOS, USER-OMP and OPT packages, respectively.  They are only
 enabled if LAMMPS was built with those packages.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 <p>You can specify the accelerated styles explicitly in your input script
 by including their suffix, or you can use the <a class="reference internal" href="Section_start.html#start-7"><span>-suffix command-line switch</span></a> when you invoke LAMMPS, or you can
 use the <a class="reference internal" href="suffix.html"><em>suffix</em></a> command in your input script.</p>
 <p>See <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a> of the manual for
 more instructions on how to use the accelerated styles effectively.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.  Because the state of the random number generator
 is not saved in restart files, this means you cannot do &#8220;exact&#8221;
 restarts with this fix, where the simulation continues on the same as
 if no restart had taken place.  However, in a statistical sense, a
 restarted simulation should produce the same behavior.</p>
 <p>The <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> <em>temp</em> option is supported by this
 fix.  You can use it to assign a temperature <a class="reference internal" href="compute.html"><em>compute</em></a>
 you have defined to this fix which will be used in its thermostatting
 procedure, as described above.  For consistency, the group used by
 this fix and by the compute should be the same.</p>
 <p>The <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> <em>energy</em> option is supported by this
 fix to add the energy change induced by Langevin thermostatting to the
 system&#8217;s potential energy as part of <a class="reference internal" href="thermo_style.html"><em>thermodynamic output</em></a>.  Note that use of this option requires
 setting the <em>tally</em> keyword to <em>yes</em>.</p>
 <p>This fix computes a global scalar which can be accessed by various
 <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  The scalar is the
 cummulative energy change due to this fix.  The scalar value
 calculated by this fix is &#8220;extensive&#8221;.  Note that calculation of this
 quantity requires setting the <em>tally</em> keyword to <em>yes</em>.</p>
 <p>This fix can ramp its target temperature over multiple runs, using the
 <em>start</em> and <em>stop</em> keywords of the <a class="reference internal" href="run.html"><em>run</em></a> command.  See the
 <a class="reference internal" href="run.html"><em>run</em></a> command for details of how to do this.</p>
 <p>This fix is not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <blockquote>
 <div>none</div></blockquote>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="fix_nh.html"><em>fix nvt</em></a>, <a class="reference internal" href="fix_temp_rescale.html"><em>fix temp/rescale</em></a>, <a class="reference internal" href="fix_viscous.html"><em>fix viscous</em></a>, <a class="reference internal" href="fix_nh.html"><em>fix nvt</em></a>, <a class="reference internal" href="pair_dpd.html"><em>pair_style dpd/tstat</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The option defaults are angmom = no, omega = no, scale = 1.0 for all
 types, tally = no, zero = no, gjf = no.</p>
 <hr class="docutils" />
 <p id="dunweg"><strong>(Dunweg)</strong> Dunweg and Paul, Int J of Modern Physics C, 2, 817-27 (1991).</p>
 <p id="schneider"><strong>(Schneider)</strong> Schneider and Stoll, Phys Rev B, 17, 1302 (1978).</p>
 <p id="gronbech-jensen"><strong>(Gronbech-Jensen)</strong> Gronbech-Jensen and Farago, Mol Phys, 111, 983
 (2013); Gronbech-Jensen, Hayre, and Farago, Comp Phys Comm,
 185, 524 (2014)</p>
 </div>
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   <div class="section" id="fix-langevin-drude-command">
 <span id="index-0"></span><h1>fix langevin/drude command<a class="headerlink" href="#fix-langevin-drude-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID langevin/drude Tcom damp_com seed_com Tdrude damp_drude seed_drude keyword values ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>langevin/drude = style name of this fix command</li>
 <li>Tcom = desired temperature of the centers of mass (temperature units)</li>
 <li>damp_com = damping parameter for the thermostat on centers of mass (time units)</li>
 <li>seed_com = random number seed to use for white noise of the thermostat on centers of mass (positive integer)</li>
 <li>Tdrude = desired temperature of the Drude oscillators (temperature units)</li>
 <li>damp_drude = damping parameter for the thermostat on Drude oscillators (time units)</li>
 <li>seed_drude = random number seed to use for white noise of the thermostat on Drude oscillators (positive integer)</li>
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>zero</em></li>
 </ul>
 <pre class="literal-block">
 <em>zero</em> value = <em>no</em> or <em>yes</em>
-    <em>no</em> = do not set total random force on centers of mass to zero
-    <em>yes</em> = set total random force on centers of mass to zero
+  <em>no</em> = do not set total random force on centers of mass to zero
+  <em>yes</em> = set total random force on centers of mass to zero
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix 3 all langevin/drude 300.0 100.0 19377 1.0 20.0 83451
 fix 1 all langevin/drude 298.15 100.0 19377 5.0 10.0 83451 zero yes
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Apply two Langevin thermostats as described in <a class="reference internal" href="tutorial_drude.html#jiang"><span>(Jiang)</span></a> for
 thermalizing the reduced degrees of freedom of Drude oscillators.
 This link describes how to use the <a class="reference internal" href="tutorial_drude.html"><em>thermalized Drude oscillator model</em></a> in LAMMPS and polarizable models in LAMMPS
 are discussed in <a class="reference internal" href="Section_howto.html#howto-25"><span>this Section</span></a>.</p>
 <p>Drude oscillators are a way to simulate polarizables atoms, by
 splitting them into a core and a Drude particle bound by a harmonic
 bond.  The thermalization works by transforming the particles degrees
 of freedom by these equations.  In these equations upper case denotes
 atomic or center of mass values and lower case denotes Drude particle
 or dipole values. Primes denote the transformed (reduced) values,
 while bare letters denote the original values.</p>
 <p>Velocities:
 begin{equation} V&#8217; = frac {M, V + m, v} {M&#8217;} end{equation}
 begin{equation} v&#8217; = v - V end{equation}
 Masses:
 begin{equation} M&#8217; = M + m end{equation}
 begin{equation} m&#8217; = frac {M, m } {M&#8217;} end{equation}
 The Langevin forces are computed as
 begin{equation} F&#8217; = - frac {M&#8217;} {mathtt{damp_com}}, V&#8217; + F_r&#8217; end{equation}
 begin{equation} f&#8217; = - frac {m&#8217;} {mathtt{damp_drude}}, v&#8217; + f_r&#8217; end{equation}
 (F_r&#8217;) is a random force proportional to
 (sqrt { frac {2, k_B mathtt{Tcom}, m&#8217;}</p>
 <blockquote>
 <div><blockquote>
 <div>{mathrm dt, mathtt{damp_com} }</div></blockquote>
 <p>} ).</p>
 </div></blockquote>
 <p>(f_r&#8217;) is a random force proportional to
 (sqrt { frac {2, k_B mathtt{Tdrude}, m&#8217;}</p>
 <blockquote>
 <div><blockquote>
 <div>{mathrm dt, mathtt{damp_drude} }</div></blockquote>
 <p>} ).</p>
 </div></blockquote>
 <p>Then the real forces acting on the particles are computed from the inverse
 transform:
 begin{equation} F = frac M {M&#8217;}, F&#8217; - f&#8217; end{equation}
 begin{equation} f = frac m {M&#8217;}, F&#8217; + f&#8217; end{equation}</p>
 <p>This fix also thermostates non-polarizable atoms in the group at
 temperature <em>Tcom</em>, as if they had a massless Drude partner.  The
 Drude particles themselves need not be in the group. The center of
 mass and the dipole are thermostated iff the core atom is in the
 group.</p>
 <p>Note that the thermostat effect of this fix is applied to only the
 translational degrees of freedom of the particles, which is an
 important consideration if finite-size particles, which have
 rotational degrees of freedom, are being thermostated. The
 translational degrees of freedom can also have a bias velocity removed
 from them before thermostating takes place; see the description below.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">Like the <a class="reference internal" href="fix_langevin.html"><em>fix langevin</em></a> command,
 this fix does NOT perform time integration. It only modifies forces to
 effect thermostating. Thus you must use a separate time integration
 fix, like <a class="reference internal" href="fix_nve.html"><em>fix nve</em></a> or <a class="reference internal" href="fix_nh.html"><em>fix nph</em></a> to actually
 update the velocities and positions of atoms using the modified
 forces.  Likewise, this fix should not normally be used on atoms that
 also have their temperature controlled by another fix - e.g. by <a class="reference internal" href="fix_nh.html"><em>fix nvt</em></a> or <a class="reference internal" href="fix_temp_rescale.html"><em>fix temp/rescale</em></a> commands.</p>
 </div>
 <p>See <a class="reference internal" href="Section_howto.html#howto-16"><span>this howto section</span></a> of the manual for
 a discussion of different ways to compute temperature and perform
 thermostating.</p>
 <hr class="docutils" />
 <p>This fix requires each atom know whether it is a Drude particle or
 not.  You must therefore use the <a class="reference internal" href="fix_drude.html"><em>fix drude</em></a> command to
 specify the Drude status of each atom type.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">only the Drude core atoms need to be in the group
 specified for this fix. A Drude electron will be transformed together
 with its cores even if it is not itself in the group.  It is safe to
 include Drude electrons or non-polarizable atoms in the group. The
 non-polarizable atoms will simply not be thermostatted as if they had
 a massless Drude partner (electron).</p>
 </div>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">Ghost atoms need to know their velocity for this fix
 to act correctly.  You must use the <a class="reference internal" href="comm_modify.html"><em>comm_modify</em></a>
 command to enable this, e.g.</p>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>comm_modify vel yes
 </pre></div>
 </div>
 <hr class="docutils" />
 <p><em>Tcom</em> is the target temperature of the centers of mass, which would
 be used to thermostate the non-polarizable atoms.  <em>Tdrude</em> is the
 (normally low) target temperature of the core-Drude particle pairs
 (dipoles).  <em>Tcom</em> and <em>Tdrude</em> can be specified as an equal-style
 <a class="reference internal" href="variable.html"><em>variable</em></a>.  If the value is a variable, it should be
 specified as v_name, where name is the variable name. In this case,
 the variable will be evaluated each timestep, and its value used to
 determine the target temperature.</p>
 <p>Equal-style variables can specify formulas with various mathematical
 functions, and include <a class="reference internal" href="thermo_style.html"><em>thermo_style</em></a> command
 keywords for the simulation box parameters and timestep and elapsed
 time.  Thus it is easy to specify a time-dependent temperature.</p>
 <p>Like other fixes that perform thermostating, this fix can be used with
 <a class="reference internal" href="compute.html"><em>compute commands</em></a> that remove a &#8220;bias&#8221; from the atom
 velocities.  E.g. removing the center-of-mass velocity from a group of
 atoms.  This is not done by default, but only if the
 <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> command is used to assign a temperature
 compute to this fix that includes such a bias term.  See the doc pages
 for individual <a class="reference internal" href="compute.html"><em>compute commands</em></a> to determine which ones
 include a bias.  In this case, the thermostat works in the following
 manner: bias is removed from each atom, thermostating is performed on
 the remaining thermal degrees of freedom, and the bias is added back
 in.  NOTE: this feature has not been tested.</p>
 <p>Note: The temperature thermostating the core-Drude particle pairs
 should be chosen low enough, so as to mimic as closely as possible the
 self-consistent minimization. It must however be high enough, so that
 the dipoles can follow the local electric field exerted by the
 neighbouring atoms. The optimal value probably depends on the
 temperature of the centers of mass and on the mass of the Drude
 particles.</p>
 <p><em>damp_com</em> is the characteristic time for reaching thermal equilibrium
 of the centers of mass.  For example, a value of 100.0 means to relax
 the temperature of the centers of mass in a timespan of (roughly) 100
 time units (tau or fmsec or psec - see the <a class="reference internal" href="units.html"><em>units</em></a>
 command).  <em>damp_drude</em> is the characteristic time for reaching
 thermal equilibrium of the dipoles. It is typically a few timesteps.</p>
 <p>The number <em>seed_com</em> and <em>seed_drude</em> are positive integers. They set
 the seeds of the Marsaglia random number generators used for
 generating the random forces on centers of mass and on the
 dipoles. Each processor uses the input seed to generate its own unique
 seed and its own stream of random numbers.  Thus the dynamics of the
 system will not be identical on two runs on different numbers of
 processors.</p>
 <p>The keyword <em>zero</em> can be used to eliminate drift due to the
 thermostat on centers of mass. Because the random forces on different
 centers of mass are independent, they do not sum exactly to zero.  As
 a result, this fix applies a small random force to the entire system,
 and the momentum of the total center of mass of the system undergoes a
 slow random walk.  If the keyword <em>zero</em> is set to <em>yes</em>, the total
 random force on the centers of mass is set exactly to zero by
 subtracting off an equal part of it from each center of mass in the
 group. As a result, the total center of mass of a system with zero
 initial momentum will not drift over time.</p>
 <p>The actual temperatures of cores and Drude particles, in
 center-of-mass and relatice coordinates, respectively, can be
 calculated using the <a class="reference internal" href="compute_temp_drude.html"><em>compute temp/drude</em></a>
 command.</p>
 <hr class="docutils" />
 <p>Usage example for rigid bodies in the NPT ensemble:</p>
 <div class="highlight-python"><div class="highlight"><pre>comm_modify vel yes
 fix TEMP all langevin/drude 300. 100. 1256 1. 20. 13977 zero yes
 fix NPH ATOMS rigid/nph/small molecule iso 1. 1. 500.
 fix NVE DRUDES nve
 thermo_style custom step cpu etotal ke pe ebond ecoul elong press vol temp c_TATOM c_TDRUDE f_TEMP[1] f_TEMP[2]
 </pre></div>
 </div>
 <p>Comments:</p>
 <ul class="simple">
 <li>Drude particles should not be in the rigid group, otherwise the Drude</li>
 <li>oscillators will be frozen and the system will lose its</li>
 <li>polarizability.  <em>zero yes</em> avoids a drift of the center of mass of</li>
 <li>the system, but is a bit slower.  use two different random seeds to</li>
 <li>avoid unphysical correlations.  temperature is controlled by the fix</li>
 <li><em>langevin/drude</em>, so the time-integration fixes do not thermostate.</li>
 <li>don&#8217;t forget to time-integrate both cores and Drude particles.</li>
 <li>pressure is time-integrated only once by using <em>nve</em> for Drude</li>
 <li>particles and <em>nph</em> for atoms/cores (or vice versa). Do not use <em>nph</em></li>
 <li>for both.  contrary to the alternative thermostating using Nose-Hoover</li>
 <li>thermostat fix <em>npt</em> and fix <em>drude/transform</em>, the <em>fix_modify</em></li>
 <li>command is not required here, because the fix <em>nph</em> computes the</li>
 <li>global pressure even if its group is <em>ATOMS</em>. This is what we want. If</li>
 <li>we thermostated <em>ATOMS</em> using <em>npt</em>, the pressure should be the global</li>
 <li>one, but the temperature should be only that of the cores. That&#8217;s why</li>
 <li>the command <em>fix_modify</em> should be called in that case.  f_TEMP[1]</li>
 <li>and f_TEMP[2] contain the reduced temperatures of the cores/atoms</li>
 <li>and of the Drude particles (see below). They should be 300. and 1. on</li>
 <li>average here.</li>
 </ul>
 </div>
 <hr class="docutils" />
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.  Because the state of the random number generator
 is not saved in restart files, this means you cannot do &#8220;exact&#8221;
 restarts with this fix, where the simulation continues on the same as
 if no restart had taken place.  However, in a statistical sense, a
 restarted simulation should produce the same behavior.</p>
 <p>The <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> <em>temp</em> option is supported by this
 fix.  You can use it to assign a temperature <a class="reference internal" href="compute.html"><em>compute</em></a>
 you have defined to this fix which will be used in its thermostating
 procedure, as described above. For consistency, the group used by the
 compute should include the group of this fix and the Drude particles.</p>
 <p>This fix is not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <blockquote>
 <div>none</div></blockquote>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="fix_langevin.html"><em>fix langevin</em></a>,
 <a class="reference internal" href="fix_drude.html"><em>fix drude</em></a>,
 <a class="reference internal" href="fix_drude_transform.html"><em>fix drude/transform</em></a>,
 <a class="reference internal" href="compute_temp_drude.html"><em>compute temp/drude</em></a>,
 <a class="reference internal" href="pair_thole.html"><em>pair_style thole</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The option defaults are zero = no.</p>
 <hr class="docutils" />
 <p id="jiang"><strong>(Jiang)</strong> Jiang, Hardy, Phillips, MacKerell, Schulten, and Roux, J
 Phys Chem Lett, 2, 87-92 (2011).</p>
 </div>
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   <div class="section" id="fix-langevin-eff-command">
 <span id="index-0"></span><h1>fix langevin/eff command<a class="headerlink" href="#fix-langevin-eff-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID langevin/eff Tstart Tstop damp seed keyword values ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>langevin/eff = style name of this fix command</li>
 <li>Tstart,Tstop = desired temperature at start/end of run (temperature units)</li>
 <li>damp = damping parameter (time units)</li>
 <li>seed = random number seed to use for white noise (positive integer)</li>
 <li>zero or more keyword/value pairs may be appended</li>
 </ul>
 <pre class="literal-block">
 keyword = <em>scale</em> or <em>tally</em> or <em>zero</em>
   <em>scale</em> values = type ratio
     type = atom type (1-N)
     ratio = factor by which to scale the damping coefficient
   <em>tally</em> values = <em>no</em> or <em>yes</em>
     <em>no</em> = do not tally the energy added/subtracted to atoms
     <em>yes</em> = do tally the energy added/subtracted to atoms
 </pre>
 <pre class="literal-block">
 <em>zero</em> value = <em>no</em> or <em>yes</em>
-    <em>no</em> = do not set total random force to zero
-    <em>yes</em> = set total random force to zero
+  <em>no</em> = do not set total random force to zero
+  <em>yes</em> = set total random force to zero
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix 3 boundary langevin/eff 1.0 1.0 10.0 699483
 fix 1 all langevin/eff 1.0 1.1 10.0 48279 scale 3 1.5
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Apply a Langevin thermostat as described in <a class="reference internal" href="#schneider"><span>(Schneider)</span></a>
 to a group of nuclei and electrons in the <a class="reference internal" href="pair_eff.html"><em>electron force field</em></a> model.  Used with <a class="reference internal" href="fix_nve_eff.html"><em>fix nve/eff</em></a>,
 this command performs Brownian dynamics (BD), since the total force on
 each atom will have the form:</p>
 <div class="highlight-python"><div class="highlight"><pre>F = Fc + Ff + Fr
 Ff = - (m / damp) v
 Fr is proportional to sqrt(Kb T m / (dt damp))
 </pre></div>
 </div>
 <p>Fc is the conservative force computed via the usual inter-particle
 interactions (<a class="reference internal" href="pair_style.html"><em>pair_style</em></a>).</p>
 <p>The Ff and Fr terms are added by this fix on a per-particle basis.</p>
 <p>The operation of this fix is exactly like that described by the <a class="reference internal" href="fix_langevin.html"><em>fix langevin</em></a> command, except that the thermostatting
 is also applied to the radial electron velocity for electron
 particles.</p>
 </div>
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.  Because the state of the random number generator
 is not saved in restart files, this means you cannot do &#8220;exact&#8221;
 restarts with this fix, where the simulation continues on the same as
 if no restart had taken place.  However, in a statistical sense, a
 restarted simulation should produce the same behavior.</p>
 <p>The <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> <em>temp</em> option is supported by this
 fix.  You can use it to assign a temperature <a class="reference internal" href="compute.html"><em>compute</em></a>
 you have defined to this fix which will be used in its thermostatting
 procedure, as described above.  For consistency, the group used by
 this fix and by the compute should be the same.</p>
 <p>The <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> <em>energy</em> option is supported by this
 fix to add the energy change induced by Langevin thermostatting to the
 system&#8217;s potential energy as part of <a class="reference internal" href="thermo_style.html"><em>thermodynamic output</em></a>.  Note that use of this option requires
 setting the <em>tally</em> keyword to <em>yes</em>.</p>
 <p>This fix computes a global scalar which can be accessed by various
 <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  The scalar is the
 cummulative energy change due to this fix.  The scalar value
 calculated by this fix is &#8220;extensive&#8221;.  Note that calculation of this
 quantity requires setting the <em>tally</em> keyword to <em>yes</em>.</p>
 <p>This fix can ramp its target temperature over multiple runs, using the
 <em>start</em> and <em>stop</em> keywords of the <a class="reference internal" href="run.html"><em>run</em></a> command.  See the
 <a class="reference internal" href="run.html"><em>run</em></a> command for details of how to do this.</p>
 <p>This fix is not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <blockquote>
 <div>none</div></blockquote>
 <p>This fix is part of the USER-EFF package.  It is only enabled if
 LAMMPS was built with that package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="fix_langevin.html"><em>fix langevin</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The option defaults are scale = 1.0 for all types and tally = no.</p>
 <hr class="docutils" />
 <p id="dunweg"><strong>(Dunweg)</strong> Dunweg and Paul, Int J of Modern Physics C, 2, 817-27 (1991).</p>
 <p id="schneider"><strong>(Schneider)</strong> Schneider and Stoll, Phys Rev B, 17, 1302 (1978).</p>
 </div>
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   <div class="section" id="fix-lb-fluid-command">
 <span id="index-0"></span><h1>fix lb/fluid command<a class="headerlink" href="#fix-lb-fluid-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID lb/fluid nevery LBtype viscosity density keyword values ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>lb/fluid = style name of this fix command</li>
 <li>nevery = update the lattice-Boltzmann fluid every this many timesteps</li>
 <li>LBtype = 1 to use the standard finite difference LB integrator,
 2 to use the LB integrator of <a class="reference internal" href="#ollila"><span>Ollila et al.</span></a></li>
 <li>viscosity = the fluid viscosity (units of mass/(time*length)).</li>
 <li>density = the fluid density.</li>
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>setArea</em> or <em>setGamma</em> or <em>scaleGamma</em> or <em>dx</em> or <em>dm</em> or <em>a0</em> or <em>noise</em> or <em>calcforce</em> or <em>trilinear</em> or <em>D3Q19</em> or <em>read_restart</em> or <em>write_restart</em> or <em>zwall_velocity</em> or <em>bodyforce</em> or <em>printfluid</em></li>
 </ul>
 <pre class="literal-block">
 <em>setArea</em> values = type node_area
-      type = atom type (1-N)
-      node_area = portion of the surface area of the composite object associated with the particular atom type (used when the force coupling constant is set by default).
-  <em>setGamma</em> values = gamma
-      gamma = user set value for the force coupling constant.
-  <em>scaleGamma</em> values = type gammaFactor
-      type = atom type (1-N)
-      gammaFactor = factor to scale the <em>setGamma</em> gamma value by, for the specified atom type.
-  <em>dx</em> values = dx_LB = the lattice spacing.
-  <em>dm</em> values = dm_LB = the lattice-Boltzmann mass unit.
-  <em>a0</em> values = a_0_real = the square of the speed of sound in the fluid.
-  <em>noise</em> values = Temperature seed
-      Temperature = fluid temperature.
-      seed = random number generator seed (positive integer)
-  <em>calcforce</em> values = N forcegroup-ID
-      N = output the force and torque every N timesteps
-      forcegroup-ID = ID of the particle group to calculate the force and torque of
-  <em>trilinear</em> values = none (used to switch from the default Peskin interpolation stencil to the trilinear stencil).
-  <em>D3Q19</em> values = none (used to switch from the default D3Q15, 15 velocity lattice, to the D3Q19, 19 velocity lattice).
-  <em>read_restart</em> values = restart file = name of the restart file to use to restart a fluid run.
-  <em>write_restart</em> values = N = write a restart file every N MD timesteps.
-  <em>zwall_velocity</em> values = velocity_bottom velocity_top = velocities along the y-direction of the bottom and top walls (located at z=zmin and z=zmax).
-  <em>bodyforce</em> values = bodyforcex bodyforcey bodyforcez = the x,y and z components of a constant body force added to the fluid.
-  <em>printfluid</em> values = N = print the fluid density and velocity at each grid point every N timesteps.
+    type = atom type (1-N)
+    node_area = portion of the surface area of the composite object associated with the particular atom type (used when the force coupling constant is set by default).
+<em>setGamma</em> values = gamma
+    gamma = user set value for the force coupling constant.
+<em>scaleGamma</em> values = type gammaFactor
+    type = atom type (1-N)
+    gammaFactor = factor to scale the <em>setGamma</em> gamma value by, for the specified atom type.
+<em>dx</em> values = dx_LB = the lattice spacing.
+<em>dm</em> values = dm_LB = the lattice-Boltzmann mass unit.
+<em>a0</em> values = a_0_real = the square of the speed of sound in the fluid.
+<em>noise</em> values = Temperature seed
+    Temperature = fluid temperature.
+    seed = random number generator seed (positive integer)
+<em>calcforce</em> values = N forcegroup-ID
+    N = output the force and torque every N timesteps
+    forcegroup-ID = ID of the particle group to calculate the force and torque of
+<em>trilinear</em> values = none (used to switch from the default Peskin interpolation stencil to the trilinear stencil).
+<em>D3Q19</em> values = none (used to switch from the default D3Q15, 15 velocity lattice, to the D3Q19, 19 velocity lattice).
+<em>read_restart</em> values = restart file = name of the restart file to use to restart a fluid run.
+<em>write_restart</em> values = N = write a restart file every N MD timesteps.
+<em>zwall_velocity</em> values = velocity_bottom velocity_top = velocities along the y-direction of the bottom and top walls (located at z=zmin and z=zmax).
+<em>bodyforce</em> values = bodyforcex bodyforcey bodyforcez = the x,y and z components of a constant body force added to the fluid.
+<em>printfluid</em> values = N = print the fluid density and velocity at each grid point every N timesteps.
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix 1 all lb/fluid 1 2 1.0 1.0 setGamma 13.0 dx 4.0 dm 10.0 calcforce sphere1
 fix 1 all lb/fluid 1 1 1.0 0.0009982071 setArea 1 1.144592082 dx 2.0 dm 0.3 trilinear noise 300.0 8979873
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Implement a lattice-Boltzmann fluid on a uniform mesh covering the LAMMPS
 simulation domain.  The MD particles described by <em>group-ID</em> apply a velocity
 dependent force to the fluid.</p>
 <p>The lattice-Boltzmann algorithm solves for the fluid motion governed by
 the Navier Stokes equations,</p>
 <img alt="_images/fix_lb_fluid_navierstokes.jpg" class="align-center" src="_images/fix_lb_fluid_navierstokes.jpg" />
 <p>with,</p>
 <img alt="_images/fix_lb_fluid_viscosity.jpg" class="align-center" src="_images/fix_lb_fluid_viscosity.jpg" />
 <p>where rho is the fluid density, u is the local fluid velocity, sigma
 is the stress tensor, F is a local external force, and eta and Lambda
 are the shear and bulk viscosities respectively.  Here, we have
 implemented</p>
 <img alt="_images/fix_lb_fluid_stress.jpg" class="align-center" src="_images/fix_lb_fluid_stress.jpg" />
 <p>with a_0 set to 1/3 (dx/dt)^2 by default.</p>
 <p>The algorithm involves tracking the time evolution of a set of partial
 distribution functions which evolve according to a velocity
 discretized version of the Boltzmann equation,</p>
 <img alt="_images/fix_lb_fluid_boltzmann.jpg" class="align-center" src="_images/fix_lb_fluid_boltzmann.jpg" />
 <p>where the first term on the right hand side represents a single time
 relaxation towards the equilibrium distribution function, and tau is a
 parameter physically related to the viscosity.  On a technical note,
 we have implemented a 15 velocity model (D3Q15) as default; however,
 the user can switch to a 19 velocity model (D3Q19) through the use of
 the <em>D3Q19</em> keyword.  This fix provides the user with the choice of
 two algorithms to solve this equation, through the specification of
 the keyword <em>LBtype</em>.  If <em>LBtype</em> is set equal to 1, the standard
 finite difference LB integrator is used.  If <em>LBtype</em> is set equal to
 2, the algorithm of <a class="reference internal" href="#ollila"><span>Ollila et al.</span></a> is used.</p>
 <p>Physical variables are then defined in terms of moments of the distribution
 functions,</p>
 <img alt="_images/fix_lb_fluid_properties.jpg" class="align-center" src="_images/fix_lb_fluid_properties.jpg" />
 <p>Full details of the lattice-Boltzmann algorithm used can be found in
 <a class="reference internal" href="fix_lb_viscous.html#mackay"><span>Mackay et al.</span></a>.</p>
 <p>The fluid is coupled to the MD particles described by <em>group-ID</em>
 through a velocity dependent force.  The contribution to the fluid
 force on a given lattice mesh site j due to MD particle alpha is
 calculated as:</p>
 <img alt="_images/fix_lb_fluid_fluidforce.jpg" class="align-center" src="_images/fix_lb_fluid_fluidforce.jpg" />
 <p>where v_n is the velocity of the MD particle, u_f is the fluid
 velocity interpolated to the particle location, and gamma is the force
 coupling constant.  Zeta is a weight assigned to the grid point,
 obtained by distributing the particle to the nearest lattice sites.
 For this, the user has the choice between a trilinear stencil, which
 provides a support of 8 lattice sites, or the immersed boundary method
 Peskin stencil, which provides a support of 64 lattice sites.  While
 the Peskin stencil is seen to provide more stable results, the
 trilinear stencil may be better suited for simulation of objects close
 to walls, due to its smaller support.  Therefore, by default, the
 Peskin stencil is used; however the user may switch to the trilinear
 stencil by specifying the keyword, <em>trilinear</em>.</p>
 <p>By default, the force coupling constant, gamma, is calculated according to</p>
 <img alt="_images/fix_lb_fluid_gammadefault.jpg" class="align-center" src="_images/fix_lb_fluid_gammadefault.jpg" />
 <p>Here, m_v is the mass of the MD particle, m_u is a representative
 fluid mass at the particle location, and dt_collision is a collision
 time, chosen such that tau/dt_collision = 1 (see <a class="reference internal" href="#mackay2"><span>Mackay and Denniston</span></a> for full details).  In order to calculate m_u, the
 fluid density is interpolated to the MD particle location, and
 multiplied by a volume, node_area*dx_lb, where node_area represents
 the portion of the surface area of the composite object associated
 with a given MD particle.  By default, node_area is set equal to
 dx_lb*dx_lb; however specific values for given atom types can be set
 using the <em>setArea</em> keyword.</p>
 <p>The user also has the option of specifying their own value for the
 force coupling constant, for all the MD particles associated with the
 fix, through the use of the <em>setGamma</em> keyword.  This may be useful
 when modelling porous particles.  See <a class="reference internal" href="fix_lb_viscous.html#mackay"><span>Mackay et al.</span></a> for a
 detailed description of the method by which the user can choose an
 appropriate gamma value.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">while this fix applies the force of the particles on
 the fluid, it does not apply the force of the fluid to the particles.
 When the force coupling constant is set using the default method,
 there is only one option to include this hydrodynamic force on the
 particles, and that is through the use of the
 <a class="reference internal" href="fix_lb_viscous.html"><em>lb/viscous</em></a> fix.  This fix adds the hydrodynamic
 force to the total force acting on the particles, after which any of
 the built-in LAMMPS integrators can be used to integrate the particle
 motion.  However, if the user specifies their own value for the force
 coupling constant, as mentioned in <a class="reference internal" href="fix_lb_viscous.html#mackay"><span>Mackay et al.</span></a>, the
 built-in LAMMPS integrators may prove to be unstable.  Therefore, we
 have included our own integrators <a class="reference internal" href="fix_lb_rigid_pc_sphere.html"><em>fix lb/rigid/pc/sphere</em></a>, and <a class="reference internal" href="fix_lb_pc.html"><em>fix lb/pc</em></a>, to solve for the particle motion in these
 cases.  These integrators should not be used with the
 <a class="reference internal" href="fix_lb_viscous.html"><em>lb/viscous</em></a> fix, as they add hydrodynamic forces
 to the particles directly.  In addition, they can not be used if the
 force coupling constant has been set the default way.</p>
 </div>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">if the force coupling constant is set using the
 default method, and the <a class="reference internal" href="fix_lb_viscous.html"><em>lb/viscous</em></a> fix is NOT
 used to add the hydrodynamic force to the total force acting on the
 particles, this physically corresponds to a situation in which an
 infinitely massive particle is moving through the fluid (since
 collisions between the particle and the fluid do not act to change the
 particle&#8217;s velocity).  Therefore, the user should set the mass of the
 particle to be significantly larger than the mass of the fluid at the
 particle location, in order to approximate an infinitely massive
 particle (see the dragforce test run for an example).</p>
 </div>
 <hr class="docutils" />
 <p>Inside the fix, parameters are scaled by the lattice-Boltzmann
 timestep, dt, grid spacing, dx, and mass unit, dm.  dt is set equal to
 (nevery*dt_MD), where dt_MD is the MD timestep.  By default, dm is set
 equal to 1.0, and dx is chosen so that tau/(dt) =
 (3*eta*dt)/(rho*dx^2) is approximately equal to 1.  However, the user
 has the option of specifying their own values for dm, and dx, by using
 the optional keywords <em>dm</em>, and <em>dx</em> respectively.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">Care must be taken when choosing both a value for dx,
 and a simulation domain size.  This fix uses the same subdivision of
 the simulation domain among processors as the main LAMMPS program.  In
 order to uniformly cover the simulation domain with lattice sites, the
 lengths of the individual LAMMPS subdomains must all be evenly
 divisible by dx.  If the simulation domain size is cubic, with equal
 lengths in all dimensions, and the default value for dx is used, this
 will automatically be satisfied.</p>
 </div>
 <p>Physical parameters describing the fluid are specified through
 <em>viscosity</em>, <em>density</em>, and <em>a0</em>. If the force coupling constant is
 set the default way, the surface area associated with the MD particles
 is specified using the <em>setArea</em> keyword.  If the user chooses to
 specify a value for the force coupling constant, this is set using the
 <em>setGamma</em> keyword.  These parameters should all be given in terms of
 the mass, distance, and time units chosen for the main LAMMPS run, as
 they are scaled by the LB timestep, lattice spacing, and mass unit,
 inside the fix.</p>
 <hr class="docutils" />
 <p>The <em>setArea</em> keyword allows the user to associate a surface area with
 a given atom type.  For example if a spherical composite object of
 radius R is represented as a spherical shell of N evenly distributed
 MD particles, all of the same type, the surface area per particle
 associated with that atom type should be set equal to 4*pi*R^2/N.
 This keyword should only be used if the force coupling constant,
 gamma, is set the default way.</p>
 <p>The <em>setGamma</em> keyword allows the user to specify their own value for
 the force coupling constant, gamma, instead of using the default
 value.</p>
 <p>The <em>scaleGamma</em> keyword should be used in conjunction with the
 <em>setGamma</em> keyword, when the user wishes to specify different gamma
 values for different atom types.  This keyword allows the user to
 scale the <em>setGamma</em> gamma value by a factor, gammaFactor, for a given
 atom type.</p>
 <p>The <em>dx</em> keyword allows the user to specify a value for the LB grid
 spacing.</p>
 <p>The <em>dm</em> keyword allows the user to specify the LB mass unit.</p>
 <p>If the <em>a0</em> keyword is used, the value specified is used for the
 square of the speed of sound in the fluid.  If this keyword is not
 present, the speed of sound squared is set equal to (1/3)*(dx/dt)^2.
 Setting a0 &gt; (dx/dt)^2 is not allowed, as this may lead to
 instabilities.</p>
 <p>If the <em>noise</em> keyword is used, followed by a a positive temperature
 value, and a positive integer random number seed, a thermal
 lattice-Boltzmann algorithm is used.  If <em>LBtype</em> is set equal to 1
 (i.e. the standard LB integrator is chosen), the thermal LB algorithm
 of <a class="reference internal" href="#adhikari"><span>Adhikari et al.</span></a> is used; however if <em>LBtype</em> is set
 equal to 2 both the LB integrator, and thermal LB algorithm described
 in <a class="reference internal" href="#ollila"><span>Ollila et al.</span></a> are used.</p>
 <p>If the <em>calcforce</em> keyword is used, both the fluid force and torque
 acting on the specified particle group are printed to the screen every
 N timesteps.</p>
 <p>If the keyword <em>trilinear</em> is used, the trilinear stencil is used to
 interpolate the particle nodes onto the fluid mesh.  By default, the
 immersed boundary method, Peskin stencil is used.  Both of these
 interpolation methods are described in <a class="reference internal" href="fix_lb_viscous.html#mackay"><span>Mackay et al.</span></a>.</p>
 <p>If the keyword <em>D3Q19</em> is used, the 19 velocity (D3Q19) lattice is
 used by the lattice-Boltzmann algorithm.  By default, the 15 velocity
 (D3Q15) lattice is used.</p>
 <p>If the keyword <em>write_restart</em> is used, followed by a positive
 integer, N, a binary restart file is printed every N LB timesteps.
 This restart file only contains information about the fluid.
 Therefore, a LAMMPS restart file should also be written in order to
 print out full details of the simulation.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">When a large number of lattice grid points are used,
 the restart files may become quite large.</p>
 </div>
 <p>In order to restart the fluid portion of the simulation, the keyword
 <em>read_restart</em> is specified, followed by the name of the binary
 lb_fluid restart file to be used.</p>
 <p>If the <em>zwall_velocity</em> keyword is used y-velocities are assigned to
 the lower and upper walls.  This keyword requires the presence of
 walls in the z-direction.  This is set by assigning fixed boundary
 conditions in the z-direction.  If fixed boundary conditions are
 present in the z-direction, and this keyword is not used, the walls
 are assumed to be stationary.</p>
 <p>If the <em>bodyforce</em> keyword is used, a constant body force is added to
 the fluid, defined by it&#8217;s x, y and z components.</p>
 <p>If the <em>printfluid</em> keyword is used, followed by a positive integer, N,
 the fluid densities and velocities at each lattice site are printed to the
 screen every N timesteps.</p>
 <hr class="docutils" />
 <p>For further details, as well as descriptions and results of several
 test runs, see <a class="reference internal" href="fix_lb_viscous.html#mackay"><span>Mackay et al.</span></a>.  Please include a citation to
 this paper if the lb_fluid fix is used in work contributing to
 published research.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>Due to the large size of the fluid data, this fix writes it&#8217;s own
 binary restart files, if requested, independent of the main LAMMPS
 <a class="reference internal" href="restart.html"><em>binary restart files</em></a>; no information about <em>lb_fluid</em>
 is written to the main LAMMPS <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.</p>
 <p>None of the <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> options are relevant to this
 fix.  No global or per-atom quantities are stored by this fix for
 access by various <span class="xref std std-ref">output commands</span>.  No
 parameter of this fix can be used with the <em>start/stop</em> keywords of
 the <a class="reference internal" href="run.html"><em>run</em></a> command.  This fix is not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>This fix is part of the USER-LB package.  It is only enabled if LAMMPS
 was built with that package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 <p>This fix can only be used with an orthogonal simulation domain.</p>
 <p>Walls have only been implemented in the z-direction.  Therefore, the
 boundary conditions, as specified via the main LAMMPS boundary command
 must be periodic for x and y, and either fixed or periodic for z.
 Shrink-wrapped boundary conditions are not permitted with this fix.</p>
 <p>This fix must be used before any of <a class="reference internal" href="fix_lb_viscous.html"><em>fix lb/viscous</em></a>, <a class="reference internal" href="fix_lb_momentum.html"><em>fix lb/momentum</em></a>, <a class="reference internal" href="fix_lb_rigid_pc_sphere.html"><em>fix lb/rigid/pc/sphere</em></a>, and/ or <a class="reference internal" href="fix_lb_pc.html"><em>fix lb/pc</em></a> , as the fluid needs to be initialized before
 any of these routines try to access its properties.  In addition, in
 order for the hydrodynamic forces to be added to the particles, this
 fix must be used in conjunction with the
 <a class="reference internal" href="fix_lb_viscous.html"><em>lb/viscous</em></a> fix if the force coupling constant is
 set by default, or either the <a class="reference internal" href="fix_lb_viscous.html"><em>lb/viscous</em></a> fix or
 one of the <a class="reference internal" href="fix_lb_rigid_pc_sphere.html"><em>lb/rigid/pc/sphere</em></a> or
 <a class="reference internal" href="fix_lb_pc.html"><em>lb/pc</em></a> integrators, if the user chooses to specifiy
 their own value for the force coupling constant.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="fix_lb_viscous.html"><em>fix lb/viscous</em></a>, <a class="reference internal" href="fix_lb_momentum.html"><em>fix lb/momentum</em></a>, <a class="reference internal" href="fix_lb_rigid_pc_sphere.html"><em>fix lb/rigid/pc/sphere</em></a>, <a class="reference internal" href="fix_lb_pc.html"><em>fix lb/pc</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>By default, the force coupling constant is set according to</p>
 <img alt="_images/fix_lb_fluid_gammadefault.jpg" class="align-center" src="_images/fix_lb_fluid_gammadefault.jpg" />
 <p>and an area of dx_lb^2 per node, used to calculate the fluid mass at
 the particle node location, is assumed.</p>
 <p>dx is chosen such that tau/(delta t_LB) =
 (3 eta dt_LB)/(rho dx_lb^2) is approximately equal to 1.
 dm is set equal to 1.0.
 a0 is set equal to (1/3)*(dx_lb/dt_lb)^2.
 The Peskin stencil is used as the default interpolation method.
 The D3Q15 lattice is used for the lattice-Boltzmann algorithm.
 If walls are present, they are assumed to be stationary.</p>
 <hr class="docutils" />
 <p id="ollila"><strong>(Ollila et al.)</strong> Ollila, S.T.T., Denniston, C., Karttunen, M., and Ala-Nissila, T., Fluctuating lattice-Boltzmann model for complex fluids, J. Chem. Phys. 134 (2011) 064902.</p>
 <p id="mackay"><strong>(Mackay et al.)</strong> Mackay, F. E., Ollila, S.T.T., and Denniston, C., Hydrodynamic Forces Implemented into LAMMPS through a lattice-Boltzmann fluid, Computer Physics Communications 184 (2013) 2021-2031.</p>
 <p id="mackay2"><strong>(Mackay and Denniston)</strong> Mackay, F. E., and Denniston, C., Coupling MD particles to a lattice-Boltzmann fluid through the use of conservative forces, J. Comput. Phys. 237 (2013) 289-298.</p>
 <p id="adhikari"><strong>(Adhikari et al.)</strong> Adhikari, R., Stratford, K.,  Cates, M. E., and Wagner, A. J., Fluctuating lattice Boltzmann, Europhys. Lett. 71 (2005) 473-479.</p>
 </div>
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diff --git a/doc/fix_lb_momentum.html b/doc/fix_lb_momentum.html
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 <li class="toctree-l1"><a class="reference internal" href="Section_intro.html">1. Introduction</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Section_start.html">2. Getting Started</a></li>
 <li class="toctree-l1"><a class="reference internal" href="Section_commands.html">3. Commands</a></li>
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   <div class="section" id="fix-lb-momentum-command">
 <span id="index-0"></span><h1>fix lb/momentum command<a class="headerlink" href="#fix-lb-momentum-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID lb/momentum nevery keyword values ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in the <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>lb/momentum = style name of this fix command</li>
 <li>nevery = adjust the momentum every this many timesteps</li>
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>linear</em></li>
 </ul>
 <pre class="literal-block">
 <em>linear</em> values = xflag yflag zflag
-    xflag,yflag,zflag = 0/1 to exclude/include each dimension.
+  xflag,yflag,zflag = 0/1 to exclude/include each dimension.
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix 1 sphere lb/momentum
 fix 1 all lb/momentum linear 1 1 0
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>This fix is based on the <a class="reference internal" href="fix_momentum.html"><em>fix momentum</em></a> command, and
 was created to be used in place of that command, when a
 lattice-Boltzmann fluid is present.</p>
 <p>Zero the total linear momentum of the system, including both the atoms
 specified by group-ID and the lattice-Boltzmann fluid every nevery
 timesteps.  This is accomplished by adjusting the particle velocities
 and the fluid velocities at each lattice site.</p>
 <div class="admonition note">
 <p class="first admonition-title">Note</p>
 <p class="last">This fix only considers the linear momentum of the system.</p>
 </div>
 <p>By default, the subtraction is performed for each dimension.  This can
 be changed by specifying the keyword <em>linear</em>, along with a set of
 three flags set to 0/1 in order to exclude/ include the corresponding
 dimension.</p>
 </div>
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.  None of the <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> options
 are relevant to this fix.  No global or per-atom quantities are stored
 by this fix for access by various <span class="xref std std-ref">output commands</span>.  No parameter of this fix can be
 used with the <em>start/stop</em> keywords of the <a class="reference internal" href="run.html"><em>run</em></a> command.
 This fix is not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>Can only be used if a lattice-Boltzmann fluid has been created via the
 <a class="reference internal" href="fix_lb_fluid.html"><em>fix lb/fluid</em></a> command, and must come after this
 command.</p>
 <p>This fix is part of the USER-LB package.  It is only enabled if LAMMPS
 was built with that package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="fix_momentum.html"><em>fix momentum</em></a>, <a class="reference internal" href="fix_lb_fluid.html"><em>fix lb/fluid</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>Zeros the total system linear momentum in each dimension.</p>
 </div>
 </div>
 
 
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diff --git a/doc/fix_lb_rigid_pc_sphere.html b/doc/fix_lb_rigid_pc_sphere.html
index 711ec2554..13848ce4d 100644
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+++ b/doc/fix_lb_rigid_pc_sphere.html
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   <div class="section" id="fix-lb-rigid-pc-sphere-command">
 <span id="index-0"></span><h1>fix lb/rigid/pc/sphere command<a class="headerlink" href="#fix-lb-rigid-pc-sphere-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID lb/rigid/pc/sphere bodystyle args keyword values ...
 </pre></div>
 </div>
 <ul>
 <li><p class="first">ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</p>
 </li>
 <li><p class="first">lb/rigid/pc/sphere = style name of this fix command</p>
 </li>
 <li><p class="first">bodystyle = <em>single</em> or <em>molecule</em> or <em>group</em></p>
 </li>
 <li><dl class="first docutils">
 <dt><em>single</em> args = none</dt>
 <dd><p class="first"><em>molecule</em> args = none
 <em>group</em> args = N groupID1 groupID2 ...</p>
 <blockquote class="last">
 <div><p>N = # of groups</p>
 </div></blockquote>
 </dd>
 </dl>
 <p>zero or more keyword/value pairs may be appended</p>
 </li>
 <li><p class="first">keyword = <em>force</em> or <em>torque</em> or <em>innerNodes</em></p>
 </li>
 </ul>
 <pre class="literal-block">
 <em>force</em> values = M xflag yflag zflag
-    M = which rigid body from 1-Nbody (see asterisk form below)
-    xflag,yflag,zflag = off/on if component of center-of-mass force is active
-  <em>torque</em> values = M xflag yflag zflag
-    M = which rigid body from 1-Nbody (see asterisk form below)
-    xflag,yflag,zflag = off/on if component of center-of-mass torque is active
-  <em>innerNodes</em> values = innergroup-ID
-    innergroup-ID = ID of the atom group which does not experience a hydrodynamic force from the lattice-Boltzmann fluid
+  M = which rigid body from 1-Nbody (see asterisk form below)
+  xflag,yflag,zflag = off/on if component of center-of-mass force is active
+<em>torque</em> values = M xflag yflag zflag
+  M = which rigid body from 1-Nbody (see asterisk form below)
+  xflag,yflag,zflag = off/on if component of center-of-mass torque is active
+<em>innerNodes</em> values = innergroup-ID
+  innergroup-ID = ID of the atom group which does not experience a hydrodynamic force from the lattice-Boltzmann fluid
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix 1 spheres lb/rigid/pc/sphere
 fix 1 all lb/rigid/pc/sphere force 1 0 0 innerNodes ForceAtoms
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>This fix is based on the <a class="reference internal" href="fix_rigid.html"><em>fix rigid</em></a> command, and was
 created to be used in place of that fix, to integrate the equations of
 motion of spherical rigid bodies when a lattice-Boltzmann fluid is
 present with a user-specified value of the force-coupling constant.
 The fix uses the integration algorithm described in <a class="reference internal" href="fix_lb_viscous.html#mackay"><span>Mackay et al.</span></a> to update the positions, velocities, and orientations of
 a set of spherical rigid bodies experiencing velocity dependent
 hydrodynamic forces.  The spherical bodies are assumed to rotate as
 solid, uniform density spheres, with moments of inertia calculated
 using the combined sum of the masses of all the constituent particles
 (which are assumed to be point particles).</p>
 <hr class="docutils" />
 <p>By default, all of the atoms that this fix acts on experience a
 hydrodynamic force due to the presence of the lattice-Boltzmann fluid.
 However, the <em>innerNodes</em> keyword allows the user to specify atoms
 belonging to a rigid object which do not interact with the
 lattice-Boltzmann fluid (i.e. these atoms do not feel a hydrodynamic
 force from the lattice-Boltzmann fluid).  This can be used to
 distinguish between atoms on the surface of a non-porous object, and
 those on the inside.</p>
 <p>This feature can be used, for example, when implementing a hard sphere
 interaction between two spherical objects.  Instead of interactions
 occurring between the particles on the surfaces of the two spheres, it
 is desirable simply to place an atom at the center of each sphere,
 which does not contribute to the hydrodynamic force, and have these
 central atoms interact with one another.</p>
 <hr class="docutils" />
 <p>Apart from the features described above, this fix is very similar to
 the rigid fix (although it includes fewer optional arguments, and
 assumes the constituent atoms are point particles); see
 <a class="reference internal" href="fix_rigid.html"><em>fix_rigid</em></a> for a complete documentation.</p>
 </div>
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about the <em>rigid</em> and <em>rigid/nve</em> fixes are written to
 <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.</p>
 <p>Similar to the <a class="reference internal" href="fix_rigid.html"><em>fix_rigid</em></a> command: &amp;quot; The rigid
 fix computes a global scalar which can be accessed by various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  The scalar value calculated by
 these fixes is &#8220;intensive&#8221;.  The scalar is the current temperature of
 the collection of rigid bodies.  This is averaged over all rigid
 bodies and their translational and rotational degrees of freedom.  The
 translational energy of a rigid body is 1/2 m v^2, where m = total
 mass of the body and v = the velocity of its center of mass.  The
 rotational energy of a rigid body is 1/2 I w^2, where I = the moment
 of inertia tensor of the body and w = its angular velocity.  Degrees
 of freedom constrained by the <em>force</em> and <em>torque</em> keywords are
 removed from this calculation.&amp;quot;</p>
 <p>&amp;quot;All of these fixes compute a global array of values which can be
 accessed by various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.
 The number of rows in the array is equal to the number of rigid
 bodies.  The number of columns is 15.  Thus for each rigid body, 15
 values are stored: the xyz coords of the center of mass (COM), the xyz
 components of the COM velocity, the xyz components of the force acting
 on the COM, the xyz components of the torque acting on the COM, and
 the xyz image flags of the COM, which have the same meaning as image
 flags for atom positions (see the &#8220;dump&#8221; command).  The force and
 torque values in the array are not affected by the <em>force</em> and
 <em>torque</em> keywords in the fix rigid command; they reflect values before
 any changes are made by those keywords.</p>
 <p>The ordering of the rigid bodies (by row in the array) is as follows.
 For the <em>single</em> keyword there is just one rigid body.  For the
 <em>molecule</em> keyword, the bodies are ordered by ascending molecule ID.
 For the <em>group</em> keyword, the list of group IDs determines the ordering
 of bodies.</p>
 <p>The array values calculated by these fixes are &#8220;intensive&#8221;, meaning
 they are independent of the number of atoms in the simulation.</p>
 <p>No parameter of these fixes can be used with the <em>start/stop</em> keywords
 of the <a class="reference internal" href="run.html"><em>run</em></a> command.  These fixes are not invoked during
 <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>. &amp;quot;</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>This fix is part of the USER-LB package.  It is only enabled if LAMMPS
 was built with that package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 <p>Can only be used if a lattice-Boltzmann fluid has been created via the
 <a class="reference internal" href="fix_lb_fluid.html"><em>fix lb/fluid</em></a> command, and must come after this
 command.  Should only be used if the force coupling constant used in
 <a class="reference internal" href="fix_lb_fluid.html"><em>fix lb/fluid</em></a> has been set by the user; this
 integration fix cannot be used if the force coupling constant is set
 by default.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="fix_lb_fluid.html"><em>fix lb/fluid</em></a>, <a class="reference internal" href="fix_lb_pc.html"><em>fix lb/pc</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The defaults are force * on on on, and torque * on on on.</p>
 <hr class="docutils" />
 <p id="mackay"><strong>(Mackay et al.)</strong> Mackay, F. E., Ollila, S.T.T., and Denniston, C., Hydrodynamic Forces Implemented into LAMMPS through a lattice-Boltzmann fluid, Computer Physics Communications 184 (2013) 2021-2031.</p>
 </div>
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   <div class="section" id="fix-modify-command">
 <span id="index-0"></span><h1>fix_modify command<a class="headerlink" href="#fix-modify-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix_modify fix-ID keyword value ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>fix-ID = ID of the fix to modify</li>
 <li>one or more keyword/value pairs may be appended</li>
 <li>keyword = <em>temp</em> or <em>press</em> or <em>energy</em></li>
 </ul>
 <pre class="literal-block">
 <em>temp</em> value = compute ID that calculates a temperature
-  <em>press</em> value = compute ID that calculates a pressure
-  <em>energy</em> value = <em>yes</em> or <em>no</em>
+<em>press</em> value = compute ID that calculates a pressure
+<em>energy</em> value = <em>yes</em> or <em>no</em>
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix_modify 3 temp myTemp press myPress
 fix_modify 1 energy yes
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Modify one or more parameters of a previously defined fix.  Only
 specific fix styles support specific parameters.  See the doc pages
 for individual fix commands for info on which ones support which
 fix_modify parameters.</p>
 <p>The <em>temp</em> keyword is used to determine how a fix computes
 temperature.  The specified compute ID must have been previously
 defined by the user via the <a class="reference internal" href="compute.html"><em>compute</em></a> command and it must
 be a style of compute that calculates a temperature.  All fixes that
 compute temperatures define their own compute by default, as described
 in their documentation.  Thus this option allows the user to override
 the default method for computing T.</p>
 <p>The <em>press</em> keyword is used to determine how a fix computes pressure.
 The specified compute ID must have been previously defined by the user
 via the <a class="reference internal" href="compute.html"><em>compute</em></a> command and it must be a style of
 compute that calculates a pressure.  All fixes that compute pressures
 define their own compute by default, as described in their
 documentation.  Thus this option allows the user to override the
 default method for computing P.</p>
 <p>For fixes that calculate a contribution to the potential energy of the
 system, the <em>energy</em> keyword will include that contribution in
 thermodynamic output of potential energy.  See the
 <a class="reference internal" href="thermo_style.html"><em>thermo_style</em></a> command for info on how potential
 energy is output.  The contribution by itself can be printed by using
 the keyword f_ID in the thermo_style custom command, where ID is the
 fix-ID of the appropriate fix.  Note that you must use this setting
 for a fix if you are using it when performing an <a class="reference internal" href="minimize.html"><em>energy minimization</em></a> and if you want the energy and forces it
 produces to be part of the optimization criteria.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <blockquote>
 <div>none</div></blockquote>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="fix.html"><em>fix</em></a>, <a class="reference internal" href="compute_temp.html"><em>compute temp</em></a>, <a class="reference internal" href="compute_pressure.html"><em>compute pressure</em></a>, <a class="reference internal" href="thermo_style.html"><em>thermo_style</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The option defaults are temp = ID defined by fix, press = ID defined
 by fix, energy = no.</p>
 </div>
 </div>
 
 
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   <div class="section" id="fix-momentum-command">
 <span id="index-0"></span><h1>fix momentum command<a class="headerlink" href="#fix-momentum-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID momentum N keyword values ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>momentum = style name of this fix command</li>
 <li>N = adjust the momentum every this many timesteps
 one or more keyword/value pairs may be appended</li>
 <li>keyword = <em>linear</em> or <em>angular</em> or <em>rescale</em></li>
 </ul>
 <pre class="literal-block">
 <em>linear</em> values = xflag yflag zflag
-    xflag,yflag,zflag = 0/1 to exclude/include each dimension
-  <em>angular</em> values = none
+  xflag,yflag,zflag = 0/1 to exclude/include each dimension
+<em>angular</em> values = none
 </pre>
 <pre class="literal-block">
 <em>rescale</em> values = none
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix 1 all momentum 1 linear 1 1 0
 fix 1 all momentum 1 linear 1 1 1 rescale
 fix 1 all momentum 100 linear 1 1 1 angular
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Zero the linear and/or angular momentum of the group of atoms every N
 timesteps by adjusting the velocities of the atoms.  One (or both) of
 the <em>linear</em> or <em>angular</em> keywords must be specified.</p>
 <p>If the <em>linear</em> keyword is used, the linear momentum is zeroed by
 subtracting the center-of-mass velocity of the group from each atom.
 This does not change the relative velocity of any pair of atoms.  One
 or more dimensions can be excluded from this operation by setting the
 corresponding flag to 0.</p>
 <p>If the <em>angular</em> keyword is used, the angular momentum is zeroed by
 subtracting a rotational component from each atom.</p>
 <p>This command can be used to insure the entire collection of atoms (or
 a subset of them) does not drift or rotate during the simulation due
 to random perturbations (e.g. <a class="reference internal" href="fix_langevin.html"><em>fix langevin</em></a>
 thermostatting).</p>
 <p>The <em>rescale</em> keyword enables conserving the kinetic energy of the group
 of atoms by rescaling the velocities after the momentum was removed.</p>
 <p>Note that the <a class="reference internal" href="velocity.html"><em>velocity</em></a> command can be used to create
 initial velocities with zero aggregate linear and/or angular momentum.</p>
 </div>
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.  None of the <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> options
 are relevant to this fix.  No global or per-atom quantities are stored
 by this fix for access by various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  No parameter of this fix can
 be used with the <em>start/stop</em> keywords of the <a class="reference internal" href="run.html"><em>run</em></a> command.
 This fix is not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <blockquote>
 <div>none</div></blockquote>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="fix_recenter.html"><em>fix recenter</em></a>, <a class="reference internal" href="velocity.html"><em>velocity</em></a></p>
 <p><strong>Default:</strong> none</p>
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   <div class="section" id="fix-move-command">
 <span id="index-0"></span><h1>fix move command<a class="headerlink" href="#fix-move-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID move style args keyword values ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>move = style name of this fix command</li>
 <li>style = <em>linear</em> or <em>wiggle</em> or <em>rotate</em> or <em>variable</em></li>
 </ul>
 <pre class="literal-block">
 <em>linear</em> args = Vx Vy Vz
-    Vx,Vy,Vz = components of velocity vector (velocity units), any component can be specified as NULL
-  <em>wiggle</em> args = Ax Ay Az period
-    Ax,Ay,Az = components of amplitude vector (distance units), any component can be specified as NULL
-    period = period of oscillation (time units)
-  <em>rotate</em> args = Px Py Pz Rx Ry Rz period
-    Px,Py,Pz = origin point of axis of rotation (distance units)
-    Rx,Ry,Rz = axis of rotation vector
-    period = period of rotation (time units)
-  <em>variable</em> args = v_dx v_dy v_dz v_vx v_vy v_vz
-    v_dx,v_dy,v_dz = 3 variable names that calculate x,y,z displacement as function of time, any component can be specified as NULL
-    v_vx,v_vy,v_vz = 3 variable names that calculate x,y,z velocity as function of time, any component can be specified as NULL
+  Vx,Vy,Vz = components of velocity vector (velocity units), any component can be specified as NULL
+<em>wiggle</em> args = Ax Ay Az period
+  Ax,Ay,Az = components of amplitude vector (distance units), any component can be specified as NULL
+  period = period of oscillation (time units)
+<em>rotate</em> args = Px Py Pz Rx Ry Rz period
+  Px,Py,Pz = origin point of axis of rotation (distance units)
+  Rx,Ry,Rz = axis of rotation vector
+  period = period of rotation (time units)
+<em>variable</em> args = v_dx v_dy v_dz v_vx v_vy v_vz
+  v_dx,v_dy,v_dz = 3 variable names that calculate x,y,z displacement as function of time, any component can be specified as NULL
+  v_vx,v_vy,v_vz = 3 variable names that calculate x,y,z velocity as function of time, any component can be specified as NULL
 </pre>
 <ul class="simple">
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>units</em></li>
 </ul>
 <pre class="literal-block">
 <em>units</em> value = <em>box</em> or <em>lattice</em>
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix 1 boundary move wiggle 3.0 0.0 0.0 1.0 units box
 fix 2 boundary move rotate 0.0 0.0 0.0 0.0 0.0 1.0 5.0
 fix 2 boundary move variable v_myx v_myy NULL v_VX v_VY NULL
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Perform updates of position and velocity for atoms in the group each
 timestep using the specified settings or formulas, without regard to
 forces on the atoms.  This can be useful for boundary or other atoms,
 whose movement can influence nearby atoms.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">The atoms affected by this fix should not normally be
 time integrated by other fixes (e.g. <a class="reference internal" href="fix_nve.html"><em>fix nve</em></a>, <a class="reference internal" href="fix_nh.html"><em>fix nvt</em></a>), since that will change their positions and
 velocities twice.</p>
 </div>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">As atoms move due to this fix, they will pass thru
 periodic boundaries and be remapped to the other side of the
 simulation box, just as they would during normal time integration
 (e.g. via the <a class="reference internal" href="fix_nve.html"><em>fix nve</em></a> command).  It is up to you to
 decide whether periodic boundaries are appropriate with the kind of
 atom motion you are prescribing with this fix.</p>
 </div>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">As dicsussed below, atoms are moved relative to their
 initial position at the time the fix is specified.  These initial
 coordinates are stored by the fix in &#8220;unwrapped&#8221; form, by using the
 image flags associated with each atom.  See the <a class="reference internal" href="dump.html"><em>dump custom</em></a> command for a discussion of &#8220;unwrapped&#8221; coordinates.
 See the Atoms section of the <a class="reference internal" href="read_data.html"><em>read_data</em></a> command for a
 discussion of image flags and how they are set for each atom.  You can
 reset the image flags (e.g. to 0) before invoking this fix by using
 the <a class="reference internal" href="set.html"><em>set image</em></a> command.</p>
 </div>
 <hr class="docutils" />
 <p>The <em>linear</em> style moves atoms at a constant velocity, so that their
 position <em>X</em> = (x,y,z) as a function of time is given in vector
 notation as</p>
 <div class="highlight-python"><div class="highlight"><pre><span class="n">X</span><span class="p">(</span><span class="n">t</span><span class="p">)</span> <span class="o">=</span> <span class="n">X0</span> <span class="o">+</span> <span class="n">V</span> <span class="o">*</span> <span class="n">delta</span>
 </pre></div>
 </div>
 <p>where <em>X0</em> = (x0,y0,z0) is their position at the time the fix is
 specified, <em>V</em> is the specified velocity vector with components
 (Vx,Vy,Vz), and <em>delta</em> is the time elapsed since the fix was
 specified.  This style also sets the velocity of each atom to V =
 (Vx,Vy,Vz).  If any of the velocity components is specified as NULL,
 then the position and velocity of that component is time integrated
 the same as the <a class="reference internal" href="fix_nve.html"><em>fix nve</em></a> command would perform, using
 the corresponding force component on the atom.</p>
 <p>Note that the <em>linear</em> style is identical to using the <em>variable</em>
 style with an <a class="reference internal" href="variable.html"><em>equal-style variable</em></a> that uses the
 vdisplace() function.  E.g.</p>
 <div class="highlight-python"><div class="highlight"><pre>variable V equal 10.0
 variable x equal vdisplace(0.0,$V)
 fix 1 boundary move variable v_x NULL NULL v_V NULL NULL
 </pre></div>
 </div>
 <p>The <em>wiggle</em> style moves atoms in an oscillatory fashion, so that
 their position <em>X</em> = (x,y,z) as a function of time is given in vector
 notation as</p>
 <div class="highlight-python"><div class="highlight"><pre>X(t) = X0 + A sin(omega*delta)
 </pre></div>
 </div>
 <p>where <em>X0</em> = (x0,y0,z0) is their position at the time the fix is
 specified, <em>A</em> is the specified amplitude vector with components
 (Ax,Ay,Az), <em>omega</em> is 2 PI / <em>period</em>, and <em>delta</em> is the time
 elapsed since the fix was specified.  This style also sets the
 velocity of each atom to the time derivative of this expression.  If
 any of the amplitude components is specified as NULL, then the
 position and velocity of that component is time integrated the same as
 the <a class="reference internal" href="fix_nve.html"><em>fix nve</em></a> command would perform, using the
 corresponding force component on the atom.</p>
 <p>Note that the <em>wiggle</em> style is identical to using the <em>variable</em>
 style with <a class="reference internal" href="variable.html"><em>equal-style variables</em></a> that use the
 swiggle() and cwiggle() functions.  E.g.</p>
 <div class="highlight-python"><div class="highlight"><pre>variable A equal 10.0
 variable T equal 5.0
 variable omega equal 2.0*PI/$T
 variable x equal swiggle(0.0,$A,$T)
 variable v equal v_omega*($A-cwiggle(0.0,$A,$T))
 fix 1 boundary move variable v_x NULL NULL v_v NULL NULL
 </pre></div>
 </div>
 <p>The <em>rotate</em> style rotates atoms around a rotation axis <em>R</em> =
 (Rx,Ry,Rz) that goes thru a point <em>P</em> = (Px,Py,Pz).  The <em>period</em> of
 the rotation is also specified.  This style also sets the velocity of
 each atom to (omega cross Rperp) where omega is its angular velocity
 around the rotation axis and Rperp is a perpendicular vector from the
 rotation axis to the atom.  If the defined
 <a class="reference internal" href="atom_style.html"><em>atom_style</em></a> assigns an angular velocity to each atom,
 then each atom&#8217;s angular velocity is also set to omega.  Note that the
 direction of rotation for the atoms around the rotation axis is
 consistent with the right-hand rule: if your right-hand&#8217;s thumb points
 along <em>R</em>, then your fingers wrap around the axis in the direction of
 rotation.</p>
 <p>The <em>variable</em> style allows the position and velocity components of
 each atom to be set by formulas specified via the
 <a class="reference internal" href="variable.html"><em>variable</em></a> command.  Each of the 6 variables is
 specified as an argument to the fix as v_name, where name is the
 variable name that is defined elsewhere in the input script.</p>
 <p>Each variable must be of either the <em>equal</em> or <em>atom</em> style.
 <em>Equal</em>-style variables compute a single numeric quantity, that can be
 a function of the timestep as well as of other simulation values.
 <em>Atom</em>-style variables compute a numeric quantity for each atom, that
 can be a function per-atom quantities, such as the atom&#8217;s position, as
 well as of the timestep and other simulation values.  Note that this
 fix stores the original coordinates of each atom (see note below) so
 that per-atom quantity can be used in an atom-style variable formula.
 See the <a class="reference internal" href="variable.html"><em>variable</em></a> command for details.</p>
 <p>The first 3 variables (v_dx,v_dy,v_dz) specified for the <em>variable</em>
 style are used to calculate a displacement from the atom&#8217;s original
 position at the time the fix was specified.  The second 3 variables
 (v_vx,v_vy,v_vz) specified are used to compute a velocity for each
 atom.</p>
 <p>Any of the 6 variables can be specified as NULL.  If both the
 displacement and velocity variables for a particular x,y,z component
 are specified as NULL, then the position and velocity of that
 component is time integrated the same as the <a class="reference internal" href="fix_nve.html"><em>fix nve</em></a>
 command would perform, using the corresponding force component on the
 atom.  If only the velocity variable for a component is specified as
 NULL, then the displacement variable will be used to set the position
 of the atom, and its velocity component will not be changed.  If only
 the displacement variable for a component is specified as NULL, then
 the velocity variable will be used to set the velocity of the atom,
 and the position of the atom will be time integrated using that
 velocity.</p>
 <p>The <em>units</em> keyword determines the meaning of the distance units used
 to define the <em>linear</em> velocity and <em>wiggle</em> amplitude and <em>rotate</em>
 origin.  This setting is ignored for the <em>variable</em> style.  A <em>box</em>
 value selects standard units as defined by the <a class="reference internal" href="units.html"><em>units</em></a>
 command, e.g. velocity in Angstroms/fmsec and amplitude and position
 in Angstroms for units = real.  A <em>lattice</em> value means the velocity
 units are in lattice spacings per time and the amplitude and position
 are in lattice spacings.  The <a class="reference internal" href="lattice.html"><em>lattice</em></a> command must have
 been previously used to define the lattice spacing.  Each of these 3
 quantities may be dependent on the x,y,z dimension, since the lattice
 spacings can be different in x,y,z.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>This fix writes the original coordinates of moving atoms to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>, as well as the initial timestep, so that
 the motion can be continuous in a restarted simulation.  See the
 <a class="reference internal" href="read_restart.html"><em>read_restart</em></a> command for info on how to re-specify
 a fix in an input script that reads a restart file, so that the
 operation of the fix continues in an uninterrupted fashion.</p>
 <p>IMPORTANNT NOTE: Because the move positions are a function of the
 current timestep and the initial timestep, you cannot reset the
 timestep to a different value after reading a restart file, if you
 expect a fix move command to work in an uninterrupted fashion.</p>
 <p>None of the <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> options are relevant to this
 fix.</p>
 <p>This fix produces a per-atom array which can be accessed by various
 <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  The number of columns
 for each atom is 3, and the columns store the original unwrapped x,y,z
 coords of each atom.  The per-atom values can be accessed on any
 timestep.</p>
 <p>No parameter of this fix can be used with the <em>start/stop</em> keywords of
 the <a class="reference internal" href="run.html"><em>run</em></a> command.  This fix is not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 <p>For <a class="reference internal" href="run_style.html"><em>rRESPA time integration</em></a>, this fix adjusts the
 position and velocity of atoms on the outermost rRESPA level.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <blockquote>
 <div>none</div></blockquote>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="fix_nve.html"><em>fix nve</em></a>, <a class="reference internal" href="displace_atoms.html"><em>displace_atoms</em></a></p>
 <p><strong>Default:</strong> none</p>
 <p>The option default is units = lattice.</p>
 </div>
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   <div class="section" id="fix-msst-command">
 <span id="index-0"></span><h1>fix msst command<a class="headerlink" href="#fix-msst-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID msst dir shockvel keyword value ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>msst = style name of this fix</li>
 <li>dir = <em>x</em> or <em>y</em> or <em>z</em></li>
 <li>shockvel = shock velocity (strictly positive, distance/time units)</li>
 <li>zero or more keyword value pairs may be appended</li>
 <li>keyword = <em>q</em> or <em>mu</em> or <em>p0</em> or <em>v0</em> or <em>e0</em> or <em>tscale</em></li>
 </ul>
 <pre class="literal-block">
 <em>q</em> value = cell mass-like parameter (mass^2/distance^4 units)
-  <em>mu</em> value = artificial viscosity (mass/length/time units)
-  <em>p0</em> value = initial pressure in the shock equations (pressure units)
-  <em>v0</em> value = initial simulation cell volume in the shock equations (distance^3 units)
-  <em>e0</em> value = initial total energy (energy units)
-  <em>tscale</em> value = reduction in initial temperature (unitless fraction between 0.0 and 1.0)
+<em>mu</em> value = artificial viscosity (mass/length/time units)
+<em>p0</em> value = initial pressure in the shock equations (pressure units)
+<em>v0</em> value = initial simulation cell volume in the shock equations (distance^3 units)
+<em>e0</em> value = initial total energy (energy units)
+<em>tscale</em> value = reduction in initial temperature (unitless fraction between 0.0 and 1.0)
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix 1 all msst y 100.0 q 1.0e5 mu 1.0e5
 fix 2 all msst z 50.0 q 1.0e4 mu 1.0e4  v0 4.3419e+03 p0 3.7797e+03 e0 -9.72360e+02 tscale 0.01
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>This command performs the Multi-Scale Shock Technique (MSST)
 integration to update positions and velocities each timestep to mimic
 a compressive shock wave passing over the system. See <a class="reference internal" href="#reed"><span>(Reed)</span></a>
 for a detailed description of this method.  The MSST varies the cell
 volume and temperature in such a way as to restrain the system to the
 shock Hugoniot and the Rayleigh line. These restraints correspond to
 the macroscopic conservation laws dictated by a shock
 front. <em>shockvel</em> determines the steady shock velocity that will be
 simulated.</p>
 <p>To perform a simulation, choose a value of <em>q</em> that provides volume
 compression on the timescale of 100 fs to 1 ps.  If the volume is not
 compressing, either the shock speed is chosen to be below the material
 sound speed or <em>p0</em> has been chosen inaccurately.  Volume compression
 at the start can be sped up by using a non-zero value of <em>tscale</em>. Use
 the smallest value of <em>tscale</em> that results in compression.</p>
 <p>Under some special high-symmetry conditions, the pressure (volume)
 and/or temperature of the system may oscillate for many cycles even
 with an appropriate choice of mass-like parameter <em>q</em>. Such
 oscillations have physical significance in some cases.  The optional
 <em>mu</em> keyword adds an artificial viscosity that helps break the system
 symmetry to equilibrate to the shock Hugoniot and Rayleigh line more
 rapidly in such cases.</p>
 <p><em>tscale</em> is a factor between 0 and 1 that determines what fraction of
 thermal kinetic energy is converted to compressive strain kinetic
 energy at the start of the simulation.  Setting this parameter to a
 non-zero value may assist in compression at the start of simulations
 where it is slow to occur.</p>
 <p>If keywords <em>e0</em>, <em>p0</em>,or <em>v0</em> are not supplied, these quantities will
 be calculated on the first step, after the energy specified by
 <em>tscale</em> is removed.  The value of <em>e0</em> is not used in the dynamical
 equations, but is used in calculating the deviation from the Hugoniot.</p>
 <p>Values of shockvel less than a critical value determined by the
 material response will not have compressive solutions. This will be
 reflected in lack of significant change of the volume in the MSST.</p>
 <p>For all pressure styles, the simulation box stays orthogonal in shape.
 Parrinello-Rahman boundary conditions (tilted box) are supported by
 LAMMPS, but are not implemented for MSST.</p>
 <p>This fix computes a temperature and pressure each timestep. To do
 this, the fix creates its own computes of style &#8220;temp&#8221; and &#8220;pressure&#8221;,
 as if these commands had been issued:</p>
 <div class="highlight-python"><div class="highlight"><pre>compute fix-ID_temp group-ID temp
 compute fix-ID_press group-ID pressure fix-ID_temp
 </pre></div>
 </div>
 <p>See the <a class="reference internal" href="compute_temp.html"><em>compute temp</em></a> and <a class="reference internal" href="compute_pressure.html"><em>compute pressure</em></a> commands for details.  Note that the
 IDs of the new computes are the fix-ID + underscore + &#8220;temp&#8221; or fix_ID
 + underscore + &#8220;press&#8221;.  The group for the new computes is &#8220;all&#8221;.</p>
 </div>
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>This fix writes the state of all internal variables to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.  See the <a class="reference internal" href="read_restart.html"><em>read_restart</em></a> command
 for info on how to re-specify a fix in an input script that reads a
 restart file, so that the operation of the fix continues in an
 uninterrupted fashion.</p>
 <p>The progress of the MSST can be monitored by printing the global
 scalar and global vector quantities computed by the fix.</p>
 <p>The scalar is the cumulative energy change due to the fix. This is
 also the energy added to the potential energy by the
 <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> <em>energy</em> command.  With this command, the
 thermo keyword <em>etotal</em> prints the conserved quantity of the MSST
 dynamic equations. This can be used to test if the MD timestep is
 sufficiently small for accurate integration of the dynamic
 equations. See also <a class="reference internal" href="thermo_style.html"><em>thermo_style</em></a> command.</p>
 <p>The global vector contains four values in this order:</p>
 <p>[<em>dhugoniot</em>, <em>drayleigh</em>, <em>lagrangian_speed</em>, <em>lagrangian_position</em>]</p>
 <ol class="arabic simple">
 <li><em>dhugoniot</em> is the departure from the Hugoniot (temperature units).</li>
 <li><em>drayleigh</em> is the departure from the Rayleigh line (pressure units).</li>
 <li><em>lagrangian_speed</em> is the laboratory-frame Lagrangian speed (particle velocity) of the computational cell (velocity units).</li>
 <li><em>lagrangian_position</em> is the computational cell position in the reference frame moving at the shock speed. This is usually a good estimate of distance of the computational cell behind the shock front.</li>
 </ol>
 <p>To print these quantities to the log file with descriptive column
 headers, the following LAMMPS commands are suggested:</p>
 <div class="highlight-python"><div class="highlight"><pre>fix           msst all msst z
 fix_modify       msst energy yes
 variable dhug    equal f_msst[1]
 variable dray    equal f_msst[2]
 variable lgr_vel equal f_msst[3]
 variable lgr_pos equal f_msst[4]
 thermo_style     custom step temp ke pe lz pzz etotal v_dhug v_dray v_lgr_vel v_lgr_pos f_msst
 </pre></div>
 </div>
 <p>These fixes compute a global scalar and a global vector of 4
 quantities, which can be accessed by various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  The scalar values calculated
 by this fix are &#8220;extensive&#8221;; the vector values are &#8220;intensive&#8221;.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>This fix style is part of the SHOCK package.  It is only enabled if
 LAMMPS was built with that package. See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 <p>All cell dimensions must be periodic. This fix can not be used with a
 triclinic cell.  The MSST fix has been tested only for the group-ID
 all.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="fix_nphug.html"><em>fix nphug</em></a>, <a class="reference internal" href="fix_deform.html"><em>fix deform</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The keyword defaults are q = 10, mu = 0, tscale = 0.01. p0, v0, and e0
 are calculated on the first step.</p>
 <hr class="docutils" />
 <p id="reed"><strong>(Reed)</strong> Reed, Fried, and Joannopoulos, Phys. Rev. Lett., 90, 235503 (2003).</p>
 </div>
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   <div class="section" id="fix-nve-sphere-command">
 <span id="index-0"></span><h1>fix nve/sphere command<a class="headerlink" href="#fix-nve-sphere-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="fix-nve-sphere-omp-command">
 <h1>fix nve/sphere/omp command<a class="headerlink" href="#fix-nve-sphere-omp-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID nve/sphere
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>nve/sphere = style name of this fix command</li>
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>update</em></li>
 </ul>
 <pre class="literal-block">
 <em>update</em> value = <em>dipole</em>
-    dipole = update orientation of dipole moment during integration
+  dipole = update orientation of dipole moment during integration
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix 1 all nve/sphere
 fix 1 all nve/sphere update dipole
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Perform constant NVE integration to update position, velocity, and
 angular velocity for finite-size spherical particles in the group each
 timestep.  V is volume; E is energy.  This creates a system trajectory
 consistent with the microcanonical ensemble.</p>
 <p>This fix differs from the <a class="reference internal" href="fix_nve.html"><em>fix nve</em></a> command, which
 assumes point particles and only updates their position and velocity.</p>
 <p>If the <em>update</em> keyword is used with the <em>dipole</em> value, then the
 orientation of the dipole moment of each particle is also updated
 during the time integration.  This option should be used for models
 where a dipole moment is assigned to particles via use of the
 <a class="reference internal" href="atom_style.html"><em>atom_style dipole</em></a> command.</p>
 <hr class="docutils" />
 <p>Styles with a <em>cuda</em>, <em>gpu</em>, <em>intel</em>, <em>kk</em>, <em>omp</em>, or <em>opt</em> suffix are
 functionally the same as the corresponding style without the suffix.
 They have been optimized to run faster, depending on your available
 hardware, as discussed in <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a>
 of the manual.  The accelerated styles take the same arguments and
 should produce the same results, except for round-off and precision
 issues.</p>
 <p>These accelerated styles are part of the USER-CUDA, GPU, USER-INTEL,
 KOKKOS, USER-OMP and OPT packages, respectively.  They are only
 enabled if LAMMPS was built with those packages.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 <p>You can specify the accelerated styles explicitly in your input script
 by including their suffix, or you can use the <a class="reference internal" href="Section_start.html#start-7"><span>-suffix command-line switch</span></a> when you invoke LAMMPS, or you can
 use the <a class="reference internal" href="suffix.html"><em>suffix</em></a> command in your input script.</p>
 <p>See <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a> of the manual for
 more instructions on how to use the accelerated styles effectively.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.  None of the <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> options
 are relevant to this fix.  No global or per-atom quantities are stored
 by this fix for access by various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  No parameter of this fix can
 be used with the <em>start/stop</em> keywords of the <a class="reference internal" href="run.html"><em>run</em></a> command.
 This fix is not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>This fix requires that atoms store torque and angular velocity (omega)
 and a radius as defined by the <a class="reference internal" href="atom_style.html"><em>atom_style sphere</em></a>
 command.  If the <em>dipole</em> keyword is used, then they must also store a
 dipole moment as defined by the <a class="reference internal" href="atom_style.html"><em>atom_style dipole</em></a>
 command.</p>
 <p>All particles in the group must be finite-size spheres.  They cannot
 be point particles.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="fix_nve.html"><em>fix nve</em></a>, <a class="reference internal" href="fix_nve_asphere.html"><em>fix nve/asphere</em></a></p>
 <p><strong>Default:</strong> none</p>
 </div>
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   <div class="section" id="fix-orient-fcc-command">
 <span id="index-0"></span><h1>fix orient/fcc command<a class="headerlink" href="#fix-orient-fcc-command" title="Permalink to this headline">¶</a></h1>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID orient/fcc nstats dir alat dE cutlo cuthi file0 file1
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>nstats = print stats every this many steps, 0 = never</li>
 <li>dir = 0/1 for which crystal is used as reference</li>
 <li>alat = fcc cubic lattice constant (distance units)</li>
 <li>dE = energy added to each atom (energy units)</li>
 <li>cutlo,cuthi = values between 0.0 and 1.0, cutlo &lt; cuthi</li>
 <li>file0,file1 = files that specify orientation of each grain</li>
 </ul>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix gb all orient/fcc 0 1 4.032008 0.001 0.25 0.75 xi.vec chi.vec
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>The fix applies an orientation-dependent force to atoms near a planar
 grain boundary which can be used to induce grain boundary migration
 (in the direction perpendicular to the grain boundary plane).  The
 motivation and explanation of this force and its application are
 described in <a class="reference internal" href="#janssens"><span>(Janssens)</span></a>.  The force is only applied to
 atoms in the fix group.</p>
 <p>The basic idea is that atoms in one grain (on one side of the
 boundary) have a potential energy dE added to them.  Atoms in the
 other grain have 0.0 potential energy added.  Atoms near the boundary
 (whose neighbor environment is intermediate between the two grain
 orientations) have an energy between 0.0 and dE added.  This creates
 an effective driving force to reduce the potential energy of atoms
 near the boundary by pushing them towards one of the grain
 orientations.  For dir = 1 and dE &gt; 0, the boundary will thus move so
 that the grain described by file0 grows and the grain described by
 file1 shrinks.  Thus this fix is designed for simulations of two-grain
 systems, either with one grain boundary and free surfaces parallel to
 the boundary, or a system with periodic boundary conditions and two
 equal and opposite grain boundaries.  In either case, the entire
 system can displace during the simulation, and such motion should be
 accounted for in measuring the grain boundary velocity.</p>
 <p>The potential energy added to atom I is given by these formulas</p>
 <img alt="_images/fix_orient_fcc.jpg" class="align-center" src="_images/fix_orient_fcc.jpg" />
 <p>which are fully explained in <a class="reference internal" href="#janssens"><span>(Janssens)</span></a>.  The order
 parameter Xi for atom I in equation (1) is a sum over the 12 nearest
 neighbors of atom I.  Rj is the vector from atom I to its neighbor J,
 and RIj is a vector in the reference (perfect) crystal.  That is, if
 dir = 0/1, then RIj is a vector to an atom coord from file 0/1.
 Equation (2) gives the expected value of the order parameter XiIJ in
 the other grain.  Hi and lo cutoffs are defined in equations (3) and
 (4), using the input parameters <em>cutlo</em> and <em>cuthi</em> as thresholds to
 avoid adding grain boundary energy when the deviation in the order
 parameter from 0 or 1 is small (e.g. due to thermal fluctuations in a
 perfect crystal).  The added potential energy Ui for atom I is given
 in equation (6) where it is interpolated between 0 and dE using the
 two threshold Xi values and the Wi value of equation (5).</p>
 <p>The derivative of this energy expression gives the force on each atom
 which thus depends on the orientation of its neighbors relative to the
 2 grain orientations.  Only atoms near the grain boundary feel a net
 force which tends to drive them to one of the two grain orientations.</p>
 <p>In equation (1), the reference vector used for each neighbor is the
 reference vector closest to the actual neighbor position.  This means
 it is possible two different neighbors will use the same reference
 vector.  In such cases, the atom in question is far from a perfect
 orientation and will likely receive the full dE addition, so the
 effect of duplicate reference vector usage is small.</p>
 <p>The <em>dir</em> parameter determines which grain wants to grow at the
 expense of the other.  A value of 0 means the first grain will shrink;
 a value of 1 means it will grow.  This assumes that <em>dE</em> is positive.
 The reverse will be true if <em>dE</em> is negative.</p>
 <p>The <em>alat</em> parameter is the cubic lattice constant for the fcc
 material and is only used to compute a cutoff distance of 1.57 * alat
 / sqrt(2) for finding the 12 nearest neighbors of each atom (which
 should be valid for an fcc crystal).  A longer/shorter cutoff can be
 imposed by adjusting <em>alat</em>.  If a particular atom has less than 12
 neighbors within the cutoff, the order parameter of equation (1) is
 effectively multiplied by 12 divided by the actual number of neighbors
 within the cutoff.</p>
 <p>The <em>dE</em> parameter is the maximum amount of additional energy added to
 each atom in the grain which wants to shrink.</p>
 <p>The <em>cutlo</em> and <em>cuthi</em> parameters are used to reduce the force added
 to bulk atoms in each grain far away from the boundary.  An atom in
 the bulk surrounded by neighbors at the ideal grain orientation would
 compute an order parameter of 0 or 1 and have no force added.
 However, thermal vibrations in the solid will cause the order
 parameters to be greater than 0 or less than 1.  The cutoff parameters
 mask this effect, allowing forces to only be added to atoms with
 order-parameters between the cutoff values.</p>
 <p><em>File0</em> and <em>file1</em> are filenames for the two grains which each
 contain 6 vectors (6 lines with 3 values per line) which specify the
 grain orientations.  Each vector is a displacement from a central atom
 (0,0,0) to a nearest neighbor atom in an fcc lattice at the proper
 orientation.  The vector lengths should all be identical since an fcc
 lattice has a coordination number of 12.  Only 6 are listed due to
 symmetry, so the list must include one from each pair of
 equal-and-opposite neighbors.  A pair of orientation files for a
 Sigma=5 tilt boundary are show below.</p>
 </div>
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.</p>
 <p>The <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> <em>energy</em> option is supported by this
 fix to add the potential energy of atom interactions with the grain
 boundary driving force to the system&#8217;s potential energy as part of
 <a class="reference internal" href="thermo_style.html"><em>thermodynamic output</em></a>.</p>
 <p>This fix calculates a global scalar which can be accessed by various
 <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  The scalar is the
 potential energy change due to this fix.  The scalar value calculated
 by this fix is &#8220;extensive&#8221;.</p>
 <p>This fix also calculates a per-atom array which can be accessed by
 various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  The array
 stores the order parameter Xi and normalized order parameter (0 to 1)
 for each atom.  The per-atom values can be accessed on any timestep.</p>
 <p>No parameter of this fix can be used with the <em>start/stop</em> keywords of
 the <a class="reference internal" href="run.html"><em>run</em></a> command.  This fix is not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>This fix is part of the MISC package.  It is only enabled if LAMMPS
 was built with that package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 <p>This fix should only be used with fcc lattices.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a></p>
 <p><strong>Default:</strong> none</p>
 <hr class="docutils" />
 <p id="janssens"><strong>(Janssens)</strong> Janssens, Olmsted, Holm, Foiles, Plimpton, Derlet, Nature
 Materials, 5, 124-127 (2006).</p>
 <hr class="docutils" />
 <p>For illustration purposes, here are example files that specify a
 Sigma=5 &lt;100&gt; tilt boundary.  This is for a lattice constant of 3.5706
 Angs.</p>
 <p>file0:</p>
-<div class="highlight-python"><div class="highlight"><pre>0.798410432046075    1.785300000000000    1.596820864092150
-    -0.798410432046075    1.785300000000000   -1.596820864092150
-     2.395231296138225    0.000000000000000    0.798410432046075
-     0.798410432046075    0.000000000000000   -2.395231296138225
-     1.596820864092150    1.785300000000000   -0.798410432046075
-     1.596820864092150   -1.785300000000000   -0.798410432046075
+<div class="highlight-python"><div class="highlight"><pre> 0.798410432046075    1.785300000000000    1.596820864092150
+-0.798410432046075    1.785300000000000   -1.596820864092150
+ 2.395231296138225    0.000000000000000    0.798410432046075
+ 0.798410432046075    0.000000000000000   -2.395231296138225
+ 1.596820864092150    1.785300000000000   -0.798410432046075
+ 1.596820864092150   -1.785300000000000   -0.798410432046075
 </pre></div>
 </div>
 <p>file1:</p>
 <div class="highlight-python"><div class="highlight"><pre>-0.798410432046075    1.785300000000000    1.596820864092150
-     0.798410432046075    1.785300000000000   -1.596820864092150
-     0.798410432046075    0.000000000000000    2.395231296138225
-     2.395231296138225    0.000000000000000   -0.798410432046075
-     1.596820864092150    1.785300000000000    0.798410432046075
-     1.596820864092150   -1.785300000000000    0.798410432046075
+ 0.798410432046075    1.785300000000000   -1.596820864092150
+ 0.798410432046075    0.000000000000000    2.395231296138225
+ 2.395231296138225    0.000000000000000   -0.798410432046075
+ 1.596820864092150    1.785300000000000    0.798410432046075
+ 1.596820864092150   -1.785300000000000    0.798410432046075
 </pre></div>
 </div>
 </div>
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diff --git a/doc/fix_phonon.html b/doc/fix_phonon.html
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   <div class="section" id="fix-phonon-command">
 <span id="index-0"></span><h1>fix phonon command<a class="headerlink" href="#fix-phonon-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID phonon N Noutput Nwait map_file prefix keyword values ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>phonon = style name of this fix command</li>
 <li>N = measure the Green&#8217;s function every this many timesteps</li>
 <li>Noutput = output the dynamical matrix every this many measurements</li>
 <li>Nwait = wait this many timesteps before measuring</li>
 <li>map_file = <em>file</em> or <em>GAMMA</em></li>
 </ul>
 <pre class="literal-block">
 <em>file</em> is the file that contains the mapping info between atom ID and the lattice indices.
 </pre>
 <pre class="literal-block">
 <em>GAMMA</em> flags to treate the whole simulation box as a unit cell, so that the mapping
-  info can be generated internally. In this case, dynamical matrix at only the gamma-point
-  will/can be evaluated.
+info can be generated internally. In this case, dynamical matrix at only the gamma-point
+will/can be evaluated.
 </pre>
 <ul class="simple">
 <li>prefix = prefix for output files</li>
 <li>one or none keyword/value pairs may be appended</li>
 <li>keyword = <em>sysdim</em> or <em>nasr</em></li>
 </ul>
 <pre class="literal-block">
 <em>sysdim</em> value = d
-    d = dimension of the system, usually the same as the MD model dimension
-  <em>nasr</em> value = n
-    n = number of iterations to enforce the acoustic sum rule
+  d = dimension of the system, usually the same as the MD model dimension
+<em>nasr</em> value = n
+  n = number of iterations to enforce the acoustic sum rule
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix 1 all phonon 20 5000 200000 map.in LJ1D sysdim 1
 fix 1 all phonon 20 5000 200000 map.in EAM3D
 fix 1 all phonon 10 5000 500000 GAMMA EAM0D nasr 100
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Calculate the dynamical matrix from molecular dynamics simulations
 based on fluctuation-dissipation theory for a group of atoms.</p>
 <p>Consider a crystal with <em>N</em> unit cells in three dimensions labelled <em>l
 = (l&lt;sub&gt;1&lt;/sub&gt;,l&lt;sub&gt;2&lt;/sub&gt;,l&lt;sub&gt;3&lt;/sub&gt;)</em> where <em>l&lt;sub&gt;i&lt;/sub&gt;</em>
 are integers.  Each unit cell is defined by three linearly independent
 vectors <a href="#id1"><span class="problematic" id="id2">**</span></a>a**&lt;sub&gt;1&lt;/sub&gt;, <a href="#id3"><span class="problematic" id="id4">**</span></a>a**&lt;sub&gt;2&lt;/sub&gt;, <a href="#id5"><span class="problematic" id="id6">**</span></a>a**&lt;sub&gt;3&lt;/sub&gt; forming a
 parallelipiped, containing <em>K</em> basis atoms labelled <em>k</em>.</p>
 <p>Based on fluctuation-dissipation theory, the force constant
 coefficients of the system in reciprocal space are given by
 (<a class="reference internal" href="#campana"><span>Campa&amp;ntilde;&amp;aacute;</span></a> , <a class="reference internal" href="#kong"><span>Kong</span></a>)
 &lt;center&gt;&lt;b&gt;&amp;Phi;&lt;/b&gt;&lt;sub&gt;k&amp;alpha;,k&#8217;&amp;beta;&lt;/sub&gt;(&lt;b&gt;q&lt;/b&gt;) =
 k&lt;sub&gt;B&lt;/sub&gt;T
 &lt;b&gt;G&lt;/b&gt;&lt;sup&gt;-1&lt;/sup&gt;&lt;sub&gt;k&amp;alpha;,k&#8217;&amp;beta;&lt;/sub&gt;(&lt;b&gt;q&lt;/b&gt;),&lt;/center&gt;</p>
 <p>where <strong>G</strong> is the Green&#8217;s functions coefficients given by</p>
 <center><b>G</b><sub>k&alpha;,k'&beta;</sub>(<b>q</b>) =
 <<b>u</b><sub>k&alpha;</sub>(<b>q</b>)&#149;<b>u</b><sub>k'&beta;</sub><sup>*</sup>(<b>q</b>)>,</center><p>where &lt;...&gt; denotes the ensemble average, and
 &lt;center&gt;**u**&lt;sub&gt;k&amp;alpha;&lt;/sub&gt;(&lt;b&gt;q&lt;/b&gt;) = &amp;sum;&lt;sub&gt;l&lt;/sub&gt;
 &lt;b&gt;u&lt;/b&gt;&lt;sub&gt;lk&amp;alpha;&lt;/sub&gt; exp(i**qr**&lt;sub&gt;l&lt;/sub&gt;)&lt;/center&gt;</p>
 <p>is the &amp;alpha; component of the atomic displacement for the <em>k*th atom
 in the unit cell in reciprocal space at **q*</em>. In practice, the Green&#8217;s
 functions coefficients can also be measured according to the following
 formula,</p>
 <center><b>G</b><sub>k&alpha;,k'&beta;</sub>(<b>q</b>) =
 <<b>R</b><sub>k&alpha;</sub>(<b>q</b>)&#149;<b>R</b><sup>*</sup><sub>k'&beta;</sub>(<b>q</b>)>
 - <<b>R</b>><sub>k&alpha;</sub>(<b>q</b>)&#149;<<b>R</b>><sup>*</sup><sub>k'&beta;</sub>(<b>q</b>),
 </center><p>where <strong>R</strong> is the instantaneous positions of atoms, and &lt;<strong>R</strong>&gt; is the
 averaged atomic positions. It gives essentially the same results as
 the displacement method and is easier to implement in an MD code.</p>
 <p>Once the force constant matrix is known, the dynamical matrix <strong>D</strong> can
 then be obtained by</p>
 <center><b>D</b><sub>k&alpha;, k'&beta;</sub>(<b>q</b>) = (m<sub>k</sub>m<sub>k'</sub>)<sup>-1/2</sup> <b>&Phi;</b><sub>k&alpha;,k'&beta;</sub>(<b>q</b>)</center><p>whose eigenvalues are exactly the phonon frequencies at <strong>q</strong>.</p>
 <p>This fix uses positions of atoms in the specified group and calculates
 two-point correlations.  To achieve this. the positions of the atoms
 are examined every <em>Nevery</em> steps and are Fourier-transformed into
 reciprocal space, where the averaging process and correlation
 computation is then done.  After every <em>Noutput</em> measurements, the
 matrix <strong>G**(**q</strong>) is calculated and inverted to obtain the elastic
 stiffness coefficients.  The dynamical matrices are then constructed
 and written to <em>prefix</em>.bin.timestep files in binary format and to the
 file <em>prefix</em>.log for each wavevector <strong>q</strong>.</p>
 <p>A detailed description of this method can be found in
 (<a class="reference internal" href="#kong2011"><span>Kong2011</span></a>).</p>
 <p>The <em>sysdim</em> keyword is optional.  If specified with a value smaller
 than the dimensionality of the LAMMPS simulation, its value is used
 for the dynamical matrix calculation.  For example, using LAMMPS ot
 model a 2D or 3D system, the phonon dispersion of a 1D atomic chain
 can be computed using <em>sysdim</em> = 1.</p>
 <p>The <em>nasr</em> keyword is optional.  An iterative procedure is employed to
 enforce the acoustic sum rule on &amp;Phi; at &amp;Gamma;, and the number
 provided by keyword <em>nasr</em> gives the total number of iterations. For a
 system whose unit cell has only one atom, <em>nasr</em> = 1 is sufficient;
 for other systems, <em>nasr</em> = 10 is typically sufficient.</p>
 <p>The <em>map_file</em> contains the mapping information between the lattice
 indices and the atom IDs, which tells the code which atom sits at
 which lattice point; the lattice indices start from 0. An auxiliary
 code, <a class="reference external" href="http://code.google.com/p/latgen">latgen</a>, can be employed to
 generate the compatible map file for various crystals.</p>
 <p>In case one simulates an aperiodic system, where the whole simulation box
 is treated as a unit cell, one can set <em>map_file</em> as <em>GAMMA</em>, so that the mapping
 info will be generated internally and a file is not needed. In this case, the
 dynamical matrix at only the gamma-point will/can be evaluated. Please keep in
 mind that fix-phonon is designed for cyrstals, it will be inefficient and
 even degrade the performance of lammps in case the unit cell is too large.</p>
 <p>The calculated dynamical matrix elements are written out in
 <a class="reference internal" href="units.html"><em>energy/distance^2/mass</em></a> units.  The coordinates for <em>q</em>
 points in the log file is in the units of the basis vectors of the
 corresponding reciprocal lattice.</p>
 </div>
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.</p>
 <p>The <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> <em>temp</em> option is supported by this
 fix. You can use it to change the temperature compute from thermo_temp
 to the one that reflects the true temperature of atoms in the group.</p>
 <p>No global scalar or vector or per-atom quantities are stored by this
 fix for access by various <span class="xref std std-ref">output commands</span>.</p>
 <p>Instead, this fix outputs its initialization information (including
 mapping information) and the calculated dynamical matrices to the file
 <em>prefix</em>.log, with the specified <em>prefix</em>.  The dynamical matrices are
 also written to files <em>prefix</em>.bin.timestep in binary format.  These
 can be read by the post-processing tool in tools/phonon to compute the
 phonon density of states and/or phonon dispersion curves.</p>
 <p>No parameter of this fix can be used with the <em>start/stop</em> keywords
 of the <a class="reference internal" href="run.html"><em>run</em></a> command.</p>
 <p>This fix is not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>This fix assumes a crystalline system with periodical lattice. The
 temperature of the system should not exceed the melting temperature to
 keep the system in its solid state.</p>
 <p>This fix is part of the USER-PHONON package.  It is only enabled if
 LAMMPS was built with that package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 <p>This fix requires LAMMPS be built with an FFT library.  See the
 <a class="reference internal" href="Section_start.html#start-2"><span>Making LAMMPS</span></a> section for more info.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="compute_msd.html"><em>compute msd</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The option defaults are sysdim = the same dimemsion as specified by
 the <a class="reference external" href="dimension">dimension</a> command, and nasr = 20.</p>
 <hr class="docutils" />
 <p id="campana"><strong>(Campa&amp;ntilde;&amp;aacute;)</strong> C. Campa&amp;ntilde;&amp;aacute; and
 M. H. M&amp;uuml;ser, <em>Practical Green&#8217;s function approach to the
 simulation of elastic semi-infinite solids</em>, <a class="reference external" href="http://dx.doi.org/10.1103/PhysRevB.74.075420">Phys. Rev. B [74], 075420 (2006)</a></p>
 <p id="kong"><strong>(Kong)</strong> L.T. Kong, G. Bartels, C. Campa&amp;ntilde;&amp;aacute;,
 C. Denniston, and Martin H. M&amp;uuml;ser, <em>Implementation of Green&#8217;s
 function molecular dynamics: An extension to LAMMPS</em>, <a class="reference external" href="http://dx.doi.org/10.1016/j.cpc.2008.12.035">Computer Physics Communications [180](6):1004-1010 (2009).</a></p>
 <p>L.T. Kong, C. Denniston, and Martin H. M&amp;uuml;ser,
 <em>An improved version of the Green&#8217;s function molecular dynamics
 method</em>, <a class="reference external" href="http://dx.doi.org/10.1016/j.cpc.2010.10.006">Computer Physics Communications [182](2):540-541 (2011).</a></p>
 <p id="kong2011"><strong>(Kong2011)</strong> L.T. Kong, <em>Phonon dispersion measured directly from
 molecular dynamics simulations</em>, <a class="reference external" href="http://dx.doi.org/10.1016/j.cpc.2011.04.019">Computer Physics Communications [182](10):2201-2207, (2011).</a></p>
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   <div class="section" id="fix-pimd-command">
 <span id="index-0"></span><h1>fix pimd command<a class="headerlink" href="#fix-pimd-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID pimd keyword value ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>pimd = style name of this fix command</li>
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>method</em> or <em>fmass</em> or <em>sp</em> or <em>temp</em> or <em>nhc</em></li>
 </ul>
 <pre class="literal-block">
 <em>method</em> value = <em>pimd</em> or <em>nmpimd</em> or <em>cmd</em>
-  <em>fmass</em> value = scaling factor on mass
-  <em>sp</em> value = scaling factor on Planck constant
-  <em>temp</em> value = temperature (temperarate units)
-  <em>nhc</em> value = Nc = number of chains in Nose-Hoover thermostat
+<em>fmass</em> value = scaling factor on mass
+<em>sp</em> value = scaling factor on Planck constant
+<em>temp</em> value = temperature (temperarate units)
+<em>nhc</em> value = Nc = number of chains in Nose-Hoover thermostat
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix 1 all pimd method nmpimd fmass 1.0 sp 2.0 temp 300.0 nhc 4
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>This command performs quantum molecular dynamics simulations based on
 the Feynman path integral to include effects of tunneling and
 zero-point motion.  In this formalism, the isomorphism of a quantum
 partition function for the original system to a classical partition
 function for a ring-polymer system is exploited, to efficiently sample
 configurations from the canonical ensemble <a class="reference internal" href="#feynman"><span>(Feynman)</span></a>.
 The classical partition function and its components are given
 by the following equations:</p>
 <img alt="_images/fix_pimd.jpg" class="align-center" src="_images/fix_pimd.jpg" />
 <p>The interested user is referred to any of the numerous references on
 this methodology, but briefly, each quantum particle in a path
 integral simulation is represented by a ring-polymer of P quasi-beads,
 labeled from 1 to P.  During the simulation, each quasi-bead interacts
 with beads on the other ring-polymers with the same imaginary time
 index (the second term in the effective potential above).  The
 quasi-beads also interact with the two neighboring quasi-beads through
 the spring potential in imaginary-time space (first term in effective
 potential).  To sample the canonical ensemble, a Nose-Hoover massive
 chain thermostat is applied <a class="reference internal" href="run_style.html#tuckerman"><span>(Tuckerman)</span></a>.  With the
 massive chain algorithm, a chain of NH thermostats is coupled to each
 degree of freedom for each quasi-bead.  The keyword <em>temp</em> sets the
 target temperature for the system and the keyword <em>nhc</em> sets the
 number <em>Nc</em> of thermostats in each chain.  For example, for a
 simulation of N particles with P beads in each ring-polymer, the total
 number of NH thermostats would be 3 x N x P x Nc.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">This fix implements a complete velocity-verlet
 integrator combined with NH massive chain thermostat, so no
 other time integration fix should be used.</p>
 </div>
 <p>The <em>method</em> keyword determines what style of PIMD is performed.  A
 value of <em>pimd</em> is standard PIMD.  A value of <em>nmpimd</em> is for
 normal-mode PIMD.  A value of <em>cmd</em> is for centroid molecular dynamics
 (CMD).  The difference between the styles is as follows.</p>
 <p>In standard PIMD, the value used for a bead&#8217;s fictitious mass is
 arbitrary.  A common choice is to use Mi = m/P, which results in the
 mass of the entire ring-polymer being equal to the real quantum
 particle.  But it can be difficult to efficiently integrate the
 equations of motion for the stiff harmonic interactions in the ring
 polymers.</p>
 <p>A useful way to resolve this issue is to integrate the equations of
 motion in a normal mode representation, using Normal Mode
 Path-Integral Molecular Dynamics (NMPIMD) <a class="reference internal" href="#cao1"><span>(Cao1)</span></a>.  In NMPIMD,
 the NH chains are attached to each normal mode of the ring-polymer and
 the fictitious mass of each mode is chosen as Mk = the eigenvalue of
 the Kth normal mode for k &gt; 0. The k = 0 mode, referred to as the
 zero-frequency mode or centroid, corresponds to overall translation of
 the ring-polymer and is assigned the mass of the real particle.</p>
 <p>Motion of the centroid can be effectively uncoupled from the other
 normal modes by scaling the fictitious masses to achieve a partial
 adiabatic separation.  This is called a Centroid Molecular Dynamics
 (CMD) approximation <a class="reference internal" href="#cao2"><span>(Cao2)</span></a>.  The time-evolution (and resulting
 dynamics) of the quantum particles can be used to obtain centroid time
 correlation functions, which can be further used to obtain the true
 quantum correlation function for the original system.  The CMD method
 also uses normal modes to evolve the system, except only the k &gt; 0
 modes are thermostatted, not the centroid degrees of freedom.</p>
 <p>The keyword <em>fmass</em> sets a further scaling factor for the fictitious
 masses of beads, which can be used for the Partial Adiabatic CMD
 <a class="reference internal" href="#hone"><span>(Hone)</span></a>, or to be set as P, which results in the fictitious
 masses to be equal to the real particle masses.</p>
 <p>The keyword <em>sp</em> is a scaling factor on Planck&#8217;s constant, which can
 be useful for debugging or other purposes.  The default value of 1.0
 is appropriate for most situations.</p>
 <p>The PIMD algorithm in LAMMPS is implemented as a hyper-parallel scheme
 as described in <a class="reference internal" href="#calhoun"><span>(Calhoun)</span></a>.  In LAMMPS this is done by using
 <a class="reference internal" href="Section_howto.html#howto-5"><span>multi-replica feature</span></a> in LAMMPS, where
 each quasi-particle system is stored and simulated on a separate
 partition of processors.  The following diagram illustrates this
 approach.  The original system with 2 ring polymers is shown in red.
 Since each ring has 4 quasi-beads (imaginary time slices), there are 4
 replicas of the system, each running on one of the 4 partitions of
 processors.  Each replica (shown in green) owns one quasi-bead in each
 ring.</p>
 <img alt="_images/pimd.jpg" class="align-center" src="_images/pimd.jpg" />
 <p>To run a PIMD simulation with M quasi-beads in each ring polymer using
 N MPI tasks for each partition&#8217;s domain-decomposition, you would use P
 = MxN processors (cores) and run the simulation as follows:</p>
 <div class="highlight-python"><div class="highlight"><pre>mpirun -np P lmp_mpi -partition MxN -in script
 </pre></div>
 </div>
 <p>Note that in the LAMMPS input script for a multi-partition simulation,
 it is often very useful to define a <a class="reference internal" href="variable.html"><em>uloop-style variable</em></a> such as</p>
 <div class="highlight-python"><div class="highlight"><pre>variable ibead uloop M pad
 </pre></div>
 </div>
 <p>where M is the number of quasi-beads (partitions) used in the
 calculation.  The uloop variable can then be used to manage I/O
 related tasks for each of the partitions, e.g.</p>
 <div class="highlight-python"><div class="highlight"><pre>dump dcd all dcd 10 system_${ibead}.dcd
 restart 1000 system_${ibead}.restart1 system_${ibead}.restart2
 read_restart system_${ibead}.restart2
 </pre></div>
 </div>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>This fix is part of the USER-MISC package.  It is only enabled if
 LAMMPS was built with that package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 <p>A PIMD simulation can be initialized with a single data file read via
 the <a class="reference internal" href="read_data.html"><em>read_data</em></a> command.  However, this means all
 quasi-beads in a ring polymer will have identical positions and
 velocities, resulting in identical trajectories for all quasi-beads.
 To avoid this, users can simply initialize velocities with different
 random number seeds assigned to each partition, as defined by the
 uloop variable, e.g.</p>
 <div class="highlight-python"><div class="highlight"><pre>velocity all create 300.0 1234${ibead} rot yes dist gaussian
 </pre></div>
 </div>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The keyword defaults are method = pimd, fmass = 1.0, sp = 1.0, temp = 300.0,
 and nhc = 2.</p>
 <hr class="docutils" />
 <p id="feynman"><strong>(Feynman)</strong> R. Feynman and A. Hibbs, Chapter 7, Quantum Mechanics and
 Path Integrals, McGraw-Hill, New York (1965).</p>
 <p id="tuckerman"><strong>(Tuckerman)</strong> M. Tuckerman and B. Berne, J Chem Phys, 99, 2796 (1993).</p>
 <p id="cao1"><strong>(Cao1)</strong> J. Cao and B. Berne, J Chem Phys, 99, 2902 (1993).</p>
 <p id="cao2"><strong>(Cao2)</strong> J. Cao and G. Voth, J Chem Phys, 100, 5093 (1994).</p>
 <p id="hone"><strong>(Hone)</strong> T. Hone, P. Rossky, G. Voth, J Chem Phys, 124,
 154103 (2006).</p>
 <p id="calhoun"><strong>(Calhoun)</strong> A. Calhoun, M. Pavese, G. Voth, Chem Phys Letters, 262,
 415 (1996).</p>
 </div>
 </div>
 
 
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   <div class="section" id="fix-poems">
 <h1>fix poems<a class="headerlink" href="#fix-poems" title="Permalink to this headline">¶</a></h1>
 <p>Syntax:</p>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID poems keyword values
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>poems = style name of this fix command</li>
 <li>keyword = <em>group</em> or <em>file</em> or <em>molecule</em></li>
 </ul>
 <pre class="literal-block">
 <em>group</em> values = list of group IDs
-  <em>molecule</em> values = none
-  <em>file</em> values = filename
+<em>molecule</em> values = none
+<em>file</em> values = filename
 </pre>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix 3 fluid poems group clump1 clump2 clump3
 fix 3 fluid poems file cluster.list
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Treats one or more sets of atoms as coupled rigid bodies.  This means
 that each timestep the total force and torque on each rigid body is
 computed and the coordinates and velocities of the atoms are updated
 so that the collection of bodies move as a coupled set.  This can be
 useful for treating a large biomolecule as a collection of connected,
 coarse-grained particles.</p>
 <p>The coupling, associated motion constraints, and time integration is
 performed by the software package <a class="reference external" href="http://www.rpi.edu/~anderk5/lab">Parallelizable Open source Efficient Multibody Software (POEMS)</a> which computes the
 constrained rigid-body motion of articulated (jointed) multibody
 systems <a class="reference internal" href="#anderson"><span>(Anderson)</span></a>.  POEMS was written and is distributed
 by Prof Kurt Anderson, his graduate student Rudranarayan Mukherjee,
 and other members of his group at Rensselaer Polytechnic Institute
 (RPI).  Rudranarayan developed the LAMMPS/POEMS interface.  For
 copyright information on POEMS and other details, please refer to the
 documents in the poems directory distributed with LAMMPS.</p>
 <p>This fix updates the positions and velocities of the rigid atoms with
 a constant-energy time integration, so you should not update the same
 atoms via other fixes (e.g. nve, nvt, npt, temp/rescale, langevin).</p>
 <p>Each body must have a non-degenerate inertia tensor, which means if
 must contain at least 3 non-collinear atoms.  Which atoms are in which
 bodies can be defined via several options.</p>
 <p>For option <em>group</em>, each of the listed groups is treated as a rigid
 body.  Note that only atoms that are also in the fix group are
 included in each rigid body.</p>
 <p>For option <em>molecule</em>, each set of atoms in the group with a different
 molecule ID is treated as a rigid body.</p>
 <p>For option <em>file</em>, sets of atoms are read from the specified file and
 each set is treated as a rigid body.  Each line of the file specifies
 a rigid body in the following format:</p>
 <p>ID type atom1-ID atom2-ID atom3-ID ...</p>
 <p>ID as an integer from 1 to M (the number of rigid bodies).  Type is
 any integer; it is not used by the fix poems command.  The remaining
 arguments are IDs of atoms in the rigid body, each typically from 1 to
 N (the number of atoms in the system).  Only atoms that are also in
 the fix group are included in each rigid body.  Blank lines and lines
 that begin with &#8216;#&#8217; are skipped.</p>
 <p>A connection between a pair of rigid bodies is inferred if one atom is
 common to both bodies.  The POEMS solver treats that atom as a
 spherical joint with 3 degrees of freedom.  Currently, a collection of
 bodies can only be connected by joints as a linear chain.  The entire
 collection of rigid bodies can represent one or more chains.  Other
 connection topologies (tree, ring) are not allowed, but will be added
 later.  Note that if no joints exist, it is more efficient to use the
 <a class="reference internal" href="fix_rigid.html"><em>fix rigid</em></a> command to simulate the system.</p>
 <p>When the poems fix is defined, it will print out statistics on the
 total # of clusters, bodies, joints, atoms involved.  A cluster in
 this context means a set of rigid bodies connected by joints.</p>
 <p>For computational efficiency, you should turn off pairwise and bond
 interactions within each rigid body, as they no longer contribute to
 the motion.  The &#8220;neigh_modify exclude&#8221; and &#8220;delete_bonds&#8221; commands
 can be used to do this if each rigid body is a group.</p>
 <p>For computational efficiency, you should only define one fix poems
 which includes all the desired rigid bodies.  LAMMPS will allow
 multiple poems fixes to be defined, but it is more expensive.</p>
 <p>The degrees-of-freedom removed by coupled rigid bodies are accounted
 for in temperature and pressure computations.  Similarly, the rigid
 body contribution to the pressure virial is also accounted for.  The
 latter is only correct if forces within the bodies have been turned
 off, and there is only a single fix poems defined.</p>
 </div>
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.  None of the <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> options
 are relevant to this fix.  No global or per-atom quantities are stored
 by this fix for access by various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  No parameter of this fix can
 be used with the <em>start/stop</em> keywords of the <a class="reference internal" href="run.html"><em>run</em></a> command.
 This fix is not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>This fix is part of the POEMS package.  It is only enabled if LAMMPS
 was built with that package, which also requires the POEMS library be
 built and linked with LAMMPS.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="fix_rigid.html"><em>fix rigid</em></a>, <a class="reference internal" href="delete_bonds.html"><em>delete_bonds</em></a>,
 <a class="reference internal" href="neigh_modify.html"><em>neigh_modify</em></a> exclude</p>
 <p><strong>Default:</strong> none</p>
 <hr class="docutils" />
 <p id="anderson"><strong>(Anderson)</strong> Anderson, Mukherjee, Critchley, Ziegler, and Lipton
 &#8220;POEMS: Parallelizable Open-source Efficient Multibody Software &#8221;,
 Engineering With Computers (2006). (<a class="reference external" href="http://dx.doi.org/10.1007/s00366-006-0026-x">link to paper</a>)</p>
 </div>
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   <div class="section" id="fix-pour-command">
 <span id="index-0"></span><h1>fix pour command<a class="headerlink" href="#fix-pour-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID pour N type seed keyword values ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>pour = style name of this fix command</li>
 <li>N = # of atoms to insert</li>
 <li>type = atom type to assign to inserted atoms (offset for molecule insertion)</li>
 <li>seed = random # seed (positive integer)</li>
 <li>one or more keyword/value pairs may be appended to args</li>
 <li>keyword = <em>region</em> or <em>diam</em> or <em>dens</em> or <em>vol</em> or <em>rate</em> or <em>vel</em> or <em>mol</em> or <em>rigid</em> or <em>shake</em></li>
 </ul>
 <pre class="literal-block">
 <em>region</em> value = region-ID
-    region-ID = ID of region to use as insertion volume
-  <em>diam</em> values = dstyle args
-    dstyle = <em>one</em> or <em>range</em> or <em>poly</em>
-      <em>one</em> args = D
-        D = single diameter for inserted particles (distance units)
-      <em>range</em> args = Dlo Dhi
-        Dlo,Dhi = range of diameters for inserted particles (distance units)
-      <em>poly</em> args = Npoly D1 P1 D2 P2 ...
-        Npoly = # of (D,P) pairs
-        D1,D2,... = diameter for subset of inserted particles (distance units)
-        P1,P2,... = percentage of inserted particles with this diameter (0-1)
-  <em>vol</em> values = fraction Nattempt
-    fraction = desired volume fraction for filling insertion volume
-    Nattempt = max # of insertion attempts per atom
-  <em>rate</em> value = V
-    V = z velocity (3d) or y velocity (2d) at which
-        insertion volume moves (velocity units)
-  <em>vel</em> values (3d) = vxlo vxhi vylo vyhi vz
-  <em>vel</em> values (2d) = vxlo vxhi vy
-    vxlo,vxhi = range of x velocities for inserted particles (velocity units)
-    vylo,vyhi = range of y velocities for inserted particles (velocity units)
-    vz = z velocity (3d) assigned to inserted particles (velocity units)
-    vy = y velocity (2d) assigned to inserted particles (velocity units)
-  <em>mol</em> value = template-ID
-    template-ID = ID of molecule template specified in a separate <a class="reference internal" href="molecule.html"><em>molecule</em></a> command
-  <em>molfrac</em> values = f1 f2 ... fN
-    f1 to fN = relative probability of creating each of N molecules in template-ID
-  <em>rigid</em> value = fix-ID
-    fix-ID = ID of <a class="reference internal" href="fix_rigid.html"><em>fix rigid/small</em></a> command
-  <em>shake</em> value = fix-ID
-    fix-ID = ID of <a class="reference internal" href="fix_shake.html"><em>fix shake</em></a> command
+  region-ID = ID of region to use as insertion volume
+<em>diam</em> values = dstyle args
+  dstyle = <em>one</em> or <em>range</em> or <em>poly</em>
+    <em>one</em> args = D
+      D = single diameter for inserted particles (distance units)
+    <em>range</em> args = Dlo Dhi
+      Dlo,Dhi = range of diameters for inserted particles (distance units)
+    <em>poly</em> args = Npoly D1 P1 D2 P2 ...
+      Npoly = # of (D,P) pairs
+      D1,D2,... = diameter for subset of inserted particles (distance units)
+      P1,P2,... = percentage of inserted particles with this diameter (0-1)
+<em>vol</em> values = fraction Nattempt
+  fraction = desired volume fraction for filling insertion volume
+  Nattempt = max # of insertion attempts per atom
+<em>rate</em> value = V
+  V = z velocity (3d) or y velocity (2d) at which
+      insertion volume moves (velocity units)
+<em>vel</em> values (3d) = vxlo vxhi vylo vyhi vz
+<em>vel</em> values (2d) = vxlo vxhi vy
+  vxlo,vxhi = range of x velocities for inserted particles (velocity units)
+  vylo,vyhi = range of y velocities for inserted particles (velocity units)
+  vz = z velocity (3d) assigned to inserted particles (velocity units)
+  vy = y velocity (2d) assigned to inserted particles (velocity units)
+<em>mol</em> value = template-ID
+  template-ID = ID of molecule template specified in a separate <a class="reference internal" href="molecule.html"><em>molecule</em></a> command
+<em>molfrac</em> values = f1 f2 ... fN
+  f1 to fN = relative probability of creating each of N molecules in template-ID
+<em>rigid</em> value = fix-ID
+  fix-ID = ID of <a class="reference internal" href="fix_rigid.html"><em>fix rigid/small</em></a> command
+<em>shake</em> value = fix-ID
+  fix-ID = ID of <a class="reference internal" href="fix_shake.html"><em>fix shake</em></a> command
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix 3 all pour 1000 2 29494 region myblock
 fix 2 all pour 10000 1 19985583 region disk vol 0.33 100 rate 1.0 diam range 0.9 1.1
 fix 2 all pour 10000 1 19985583 region disk diam poly 2 0.7 0.4 1.5 0.6
 fix ins all pour 500 1 4767548 vol 0.8 10 region slab mol object rigid myRigid
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Insert finite-size particles or molecules into the simulation box
 every few timesteps within a specified region until N particles or
 molecules have been inserted.  This is typically used to model the
 pouring of granular particles into a container under the influence of
 gravity.  For the remainder of this doc page, a single inserted atom
 or molecule is referred to as a &#8220;particle&#8221;.</p>
 <p>If inserted particles are individual atoms, they are assigned the
 specified atom type.  If they are molecules, the type of each atom in
 the inserted molecule is specified in the file read by the
 <a class="reference internal" href="molecule.html"><em>molecule</em></a> command, and those values are added to the
 specified atom type.  E.g. if the file specifies atom types 1,2,3, and
 those are the atom types you want for inserted molecules, then specify
 <em>type</em> = 0.  If you specify <em>type</em> = 2, the in the inserted molecule
 will have atom types 3,4,5.</p>
 <p>All atoms in the inserted particle are assigned to two groups: the
 default group &#8220;all&#8221; and the group specified in the fix pour command
 (which can also be &#8220;all&#8221;).</p>
 <p>This command must use the <em>region</em> keyword to define an insertion
 volume.  The specified region must have been previously defined with a
 <a class="reference internal" href="region.html"><em>region</em></a> command.  It must be of type <em>block</em> or a z-axis
 <em>cylinder</em> and must be defined with side = <em>in</em>.  The cylinder style
 of region can only be used with 3d simulations.</p>
 <p>Individual atoms are inserted, unless the <em>mol</em> keyword is used.  It
 specifies a <em>template-ID</em> previously defined using the
 <a class="reference internal" href="molecule.html"><em>molecule</em></a> command, which reads a file that defines the
 molecule.  The coordinates, atom types, center-of-mass, moments of
 inertia, etc, as well as any bond/angle/etc and special neighbor
 information for the molecule can be specified in the molecule file.
 See the <a class="reference internal" href="molecule.html"><em>molecule</em></a> command for details.  The only
 settings required to be in this file are the coordinates and types of
 atoms in the molecule.</p>
 <p>If the molecule template contains more than one molecule, the relative
 probability of depositing each molecule can be specified by the
 <em>molfrac</em> keyword.  N relative probablities, each from 0.0 to 1.0, are
 specified, where N is the number of molecules in the template.  Each
 time a molecule is inserted, a random number is used to sample from
 the list of relative probabilities.  The N values must sum to 1.0.</p>
 <p>If you wish to insert molecules via the <em>mol</em> keyword, that will be
 treated as rigid bodies, use the <em>rigid</em> keyword, specifying as its
 value the ID of a separate <code class="xref doc docutils literal"><span class="pre">fix</span> <span class="pre">rigid/small</span></code>
 command which also appears in your input script.</p>
 <p>If you wish to insert molecules via the <em>mol</em> keyword, that will have
 their bonds or angles constrained via SHAKE, use the <em>shake</em> keyword,
 specifying as its value the ID of a separate <a class="reference internal" href="fix_shake.html"><em>fix shake</em></a> command which also appears in your input script.</p>
 <p>Each timestep particles are inserted, they are placed randomly inside
 the insertion volume so as to mimic a stream of poured particles.  If
 they are molecules they are also oriented randomly.  Each atom in the
 particle is tested for overlaps with existing particles, including
 effects due to periodic boundary conditions if applicable.  If an
 overlap is detected, another random insertion attempt is made; see the
 <em>vol</em> keyword discussion below.  The larger the volume of the
 insertion region, the more particles that can be inserted at any one
 timestep.  Particles are inserted again after enough time has elapsed
 that the previously inserted particles fall out of the insertion
 volume under the influence of gravity.  Insertions continue every so
 many timesteps until the desired # of particles has been inserted.</p>
 <p>All other keywords are optional with defaults as shown below.</p>
 <p>The <em>diam</em> option is only used when inserting atoms and specifes the
 diameters of inserted particles.  There are 3 styles: <em>one</em>, <em>range</em>,
 or <em>poly</em>.  For <em>one</em>, all particles will have diameter <em>D</em>.  For
 <em>range</em>, the diameter of each particle will be chosen randomly and
 uniformly between the specified <em>Dlo</em> and <em>Dhi</em> bounds.  For <em>poly</em>, a
 series of <em>Npoly</em> diameters is specified.  For each diameter a
 percentage value from 0.0 to 1.0 is also specified.  The <em>Npoly</em>
 percentages must sum to 1.0.  For the example shown above with &#8220;diam 2
 0.7 0.4 1.5 0.6&#8221;, all inserted particles will have a diameter of 0.7
 or 1.5.  40% of the particles will be small; 60% will be large.</p>
 <p>Note that for molecule insertion, the diameters of individual atoms in
 the molecule can be specified in the file read by the
 <a class="reference internal" href="molecule.html"><em>molecule</em></a> command.  If not specified, the diameter of
 each atom in the molecule has a default diameter of 1.0.</p>
 <p>The <em>dens</em> and <em>vel</em> options enable inserted particles to have a range
 of densities or xy velocities.  The specific values for a particular
 inserted particle will be chosen randomly and uniformly between the
 specified bounds.  The <em>vz</em> or <em>vy</em> value for option <em>vel</em> assigns a
 z-velocity (3d) or y-velocity (2d) to each inserted particle.</p>
 <p>The <em>vol</em> option specifies what volume fraction of the insertion
 volume will be filled with particles.  For particles with a size
 specified by the <em>diam range</em> keyword, they are assumed to all be of
 maximum diamter <em>Dhi</em> for purposes of computing their contribution to
 the volume fraction.</p>
 <p>The higher the volume fraction value, the more particles are inserted
 each timestep.  Since inserted particles cannot overlap, the maximum
 volume fraction should be no higher than about 0.6.  Each timestep
 particles are inserted, LAMMPS will make up to a total of M tries to
 insert the new particles without overlaps, where M = # of inserted
 particles * Nattempt.  If LAMMPS is unsuccessful at completing all
 insertions, it prints a warning.</p>
 <p>The <em>rate</em> option moves the insertion volume in the z direction (3d)
 or y direction (2d).  This enables pouring particles from a
 successively higher height over time.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">If you are monitoring the temperature of a system
 where the particle count is changing due to adding particles, you
 typically should use the <a class="reference internal" href="compute_modify.html"><em>compute_modify dynamic yes</em></a> command for the temperature compute you are
 using.</p>
 </div>
 </div>
 <hr class="docutils" />
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.  This means you must be careful when restarting a
 pouring simulation, when the restart file was written in the middle of
 the pouring operation.  Specifically, you should use a new fix pour
 command in the input script for the restarted simulation that
 continues the operation.  You will need to adjust the arguments of the
 original fix pour command to do this.</p>
 <p>Also note that because the state of the random number generator is not
 saved in restart files, you cannot do &#8220;exact&#8221; restarts with this fix,
 where the simulation continues on the same as if no restart had taken
 place.  However, in a statistical sense, a restarted simulation should
 produce the same behavior if you adjust the fix pour parameters
 appropriately.</p>
 <p>None of the <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> options are relevant to this
 fix.  No global or per-atom quantities are stored by this fix for
 access by various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  No
 parameter of this fix can be used with the <em>start/stop</em> keywords of
 the <a class="reference internal" href="run.html"><em>run</em></a> command.  This fix is not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>This fix is part of the GRANULAR package.  It is only enabled if
 LAMMPS was built with that package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 <p>For 3d simulations, a gravity fix in the -z direction must be defined
 for use in conjunction with this fix.  For 2d simulations, gravity
 must be defined in the -y direction.</p>
 <p>The specified insertion region cannot be a &#8220;dynamic&#8221; region, as
 defined by the <a class="reference internal" href="region.html"><em>region</em></a> command.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="fix_deposit.html"><em>fix_deposit</em></a>, <a class="reference internal" href="fix_gravity.html"><em>fix_gravity</em></a>,
 <a class="reference internal" href="region.html"><em>region</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>Insertions are performed for individual particles, i.e. no <em>mol</em>
 setting is defined.  If the <em>mol</em> keyword is used, the default for
 <em>molfrac</em> is an equal probabilities for all molecules in the template.
 Additional option defaults are diam = one 1.0, dens = 1.0 1.0, vol =
 0.25 50, rate = 0.0, vel = 0.0 0.0 0.0 0.0 0.0.</p>
 </div>
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   <div class="section" id="fix-print-command">
 <span id="index-0"></span><h1>fix print command<a class="headerlink" href="#fix-print-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID print N string keyword value ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>print = style name of this fix command</li>
 <li>N = print every N steps</li>
 <li>string = text string to print with optional variable names</li>
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>file</em> or <em>append</em> or <em>screen</em> or <em>title</em></li>
 </ul>
 <pre class="literal-block">
 <em>file</em> value = filename
-  <em>append</em> value = filename
-  <em>screen</em> value = <em>yes</em> or <em>no</em>
-  <em>title</em> value = string
-    string =  text to print as 1st line of output file
+<em>append</em> value = filename
+<em>screen</em> value = <em>yes</em> or <em>no</em>
+<em>title</em> value = string
+  string =  text to print as 1st line of output file
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix extra all print 100 &quot;Coords of marker atom = $x $y $z&quot;
 fix extra all print 100 &quot;Coords of marker atom = $x $y $z&quot; file coord.txt
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Print a text string every N steps during a simulation run.  This can
 be used for diagnostic purposes or as a debugging tool to monitor some
 quantity during a run.  The text string must be a single argument, so
 it should be enclosed in double quotes if it is more than one word.
 If it contains variables it must be enclosed in double quotes to
 insure they are not evaluated when the input script line is read, but
 will instead be evaluated each time the string is printed.</p>
 <p>See the <a class="reference internal" href="variable.html"><em>variable</em></a> command for a description of <em>equal</em>
 style variables which are the most useful ones to use with the fix
 print command, since they are evaluated afresh each timestep that the
 fix print line is output.  Equal-style variables calculate formulas
 involving mathematical operations, atom properties, group properties,
 thermodynamic properties, global values calculated by a
 <a class="reference internal" href="compute.html"><em>compute</em></a> or <a class="reference internal" href="fix.html"><em>fix</em></a>, or references to other
 <a class="reference internal" href="variable.html"><em>variables</em></a>.</p>
 <p>If the <em>file</em> or <em>append</em> keyword is used, a filename is specified to
 which the output generated by this fix will be written.  If <em>file</em> is
 used, then the filename is overwritten if it already exists.  If
 <em>append</em> is used, then the filename is appended to if it already
 exists, or created if it does not exist.</p>
 <p>If the <em>screen</em> keyword is used, output by this fix to the screen and
 logfile can be turned on or off as desired.</p>
 <p>The <em>title</em> keyword allow specification of the string that will be
 printed as the first line of the output file, assuming the <em>file</em>
 keyword was used.  By default, the title line is as follows:</p>
 <div class="highlight-python"><div class="highlight"><pre><span class="c"># Fix print output for fix ID</span>
 </pre></div>
 </div>
 <p>where ID is replaced with the fix-ID.</p>
 </div>
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.  None of the <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> options
 are relevant to this fix.  No global or per-atom quantities are stored
 by this fix for access by various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  No parameter of this fix can
 be used with the <em>start/stop</em> keywords of the <a class="reference internal" href="run.html"><em>run</em></a> command.
 This fix is not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <blockquote>
 <div>none</div></blockquote>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="variable.html"><em>variable</em></a>, <a class="reference internal" href="print.html"><em>print</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The option defaults are no file output, screen = yes, and title string
 as described above.</p>
 </div>
 </div>
 
 
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   <div class="section" id="fix-property-atom-command">
 <span id="index-0"></span><h1>fix property/atom command<a class="headerlink" href="#fix-property-atom-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID property/atom vec1 vec2 ... keyword value ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>property/atom = style name of this fix command</li>
 <li>vec1,vec2,... = <em>mol</em> or <em>q</em> or <em>i_name</em> or <em>d_name</em></li>
 </ul>
 <pre class="literal-block">
 <em>mol</em> = molecule IDs
-  <em>q</em> = charge
-  <em>i_name</em> = new integer vector referenced by name
-  <em>d_name</em> = new floating-point vector referenced by name
+<em>q</em> = charge
+<em>i_name</em> = new integer vector referenced by name
+<em>d_name</em> = new floating-point vector referenced by name
 </pre>
 <ul class="simple">
 <li>zero of more keyword/value pairs may be appended</li>
 <li>keyword = <em>ghost</em></li>
 </ul>
 <pre class="literal-block">
 <em>ghost</em> value = <em>no</em> or <em>yes</em> for whether ghost atom info in communicated
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix 1 all property/atom mol
 fix 1 all property/atom i_myflag1 i_myflag2
 fix 1 all property/atom d_sx d_sy d_sz
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Create one or more additional per-atom vectors to store information
 about atoms and to use during a simulation.  The specified <em>group-ID</em>
 is ignored by this fix.</p>
 <p>The atom style used for a simulation defines a set of per-atom
 properties, as explained on the <a class="reference internal" href="atom_style.html"><em>atom_style</em></a> and
 <a class="reference internal" href="read_data.html"><em>read_data</em></a> doc pages.  The latter command allows these
 properties to be defined for each atom in the system when a data file
 is read.  This fix will augment the set of properties with new custom
 ones.</p>
 <p>This can be useful in at least two scenarios.</p>
 <p>If the atom style does not define molecule IDs or per-atom charge,
 they can be added using the <em>mol</em> or <em>q</em> keywords.  This can be
 useful, e.g, to define &#8220;molecules&#8221; to use as rigid bodies with the
 <a class="reference internal" href="fix_rigid.html"><em>fix rigid</em></a> command, or just to carry around an extra
 flag with the atoms (stored as a molecule ID).  An alternative is to
 use an atom style that does define molecule IDs or charge or to use a
 hybrid atom style that combines two styles to allow for molecule IDs
 or charge, but that has 2 practical drawbacks.  First it typically
 necessitates changing the format of the data file.  And it may define
 additional properties that aren&#8217;t needed such as bond lists, which has
 some overhead when there are no bonds.</p>
 <p>In the future, we may add additional per-atom properties similar to
 <em>mol</em> or <em>q</em>, which &#8220;turn-on&#8221; specific properties defined by some atom
 styles, so they can be used by atom styles that don&#8217;t define them.</p>
 <p>More generally, the <em>i_name</em> and <em>d_name</em> vectors allow one or more
 new custom per-atom properties to be defined.  Each name must be
 unique and can use alphanumeric or underscore characters.  These
 vectors can store whatever values you decide are useful in your
 simulation.  As explained below there are several ways to initialize
 and access and output these values, both via input script commands and
 in new code that you add to LAMMPS.</p>
 <p>This is effectively a simple way to add per-atom properties to a model
 without needing to write code for a new <a class="reference internal" href="atom_style.html"><em>atom style</em></a>
 that defines the properties.  Note however that implementing a new
 atom style allows new atom properties to be more tightly and
 seamlessly integrated with the rest of the code.</p>
 <p>The new atom properties encode values that migrate with atoms to new
 processors and are written to restart files.  If you want the new
 properties to also be defined for ghost atoms, then use the <em>ghost</em>
 keyword with a value of <em>yes</em>.  This will invoke extra communication
 when ghost atoms are created (at every re-neighboring) to insure the
 new properties are also defined for the ghost atoms.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">If you use this command with the <em>mol</em> or <em>charge</em>
 vectors than you most likely want to set <em>ghost</em> yes, since these
 properties are stored with ghost atoms if you use an
 <a class="reference internal" href="atom_style.html"><em>atom_style</em></a> that defines them, and many LAMMPS
 operations that use molecule IDs or charge, such as neighbor lists and
 pair styles, will expect ghost atoms to have these valuse.  LAMMPS
 will issue a warning it you define those vectors but do not set
 <em>ghost</em> yes.</p>
 </div>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">The properties for ghost atoms are not updated every
 timestep, but only once every few steps when neighbor lists are
 re-built.  Thus the <em>ghost</em> keyword is suitable for static properties,
 like molecule IDs, but not for dynamic properties that change every
 step.  For the latter, the code you add to LAMMPS to change the
 properties will also need to communicate their new values to/from
 ghost atoms, an operation that can be invoked from within a <a class="reference internal" href="pair_style.html"><em>pair style</em></a> or <a class="reference internal" href="fix.html"><em>fix</em></a> or <a class="reference internal" href="compute.html"><em>compute</em></a>
 that you write.</p>
 </div>
 <hr class="docutils" />
 <p>This fix is one of a small number that can be defined in an input
 script before the simulation box is created or atoms are defined.
 This is so it can be used with the <a class="reference internal" href="read_data.html"><em>read_data</em></a> command
 as described below.</p>
 <p>Per-atom properties that are defined by the <a class="reference internal" href="atom_style.html"><em>atom style</em></a> are initialized when atoms are created, e.g. by
 the <a class="reference internal" href="read_data.html"><em>read_data</em></a> or <a class="reference internal" href="create_atoms.html"><em>create_atoms</em></a>
 commands.  The per-atom properaties defined by this fix are not.  So
 you need to initialize them explicitly.  This can be done by the
 <a class="reference internal" href="read_data.html"><em>read_data</em></a> command, using its <em>fix</em> keyword and
 passing it the fix-ID of this fix.</p>
 <p>Thus these commands:</p>
 <div class="highlight-python"><div class="highlight"><pre>fix prop all property/atom mol d_flag
 read_data data.txt fix prop NULL Molecules
 </pre></div>
 </div>
 <p>would allow a data file to have a section like this:</p>
 <div class="highlight-python"><div class="highlight"><pre><span class="n">Molecules</span>
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>1 4 1.5
 2 4 3.0
 3 10 1.0
 4 10 1.0
 5 10 1.0
 ...
 N 763 4.5
 </pre></div>
 </div>
 <p>where N is the number of atoms, and the first field on each line is
 the atom-ID, followed by a molecule-ID and a floating point value that
 will be stored in a new property called &#8220;flag&#8221;.  Note that the list of
 per-atom properties can be in any order.</p>
 <p>Another way of initializing the new properties is via the
 <a class="reference internal" href="set.html"><em>set</em></a> command.  For example, if you wanted molecules
 defined for every set of 10 atoms, based on their atom-IDs,
 these commands could be used:</p>
 <div class="highlight-python"><div class="highlight"><pre>fix prop all property/atom mol
 variable cluster atom ((id-1)/10)+1
 set id * mol v_cluster
 </pre></div>
 </div>
 <p>The <a class="reference internal" href="variable.html"><em>atom-style variable</em></a> will create values for atoms
 with IDs 31,32,33,...40 that are 4.0,4.1,4.2,...,4.9.  When the
 <a class="reference internal" href="set.html"><em>set</em></a> commands assigns them to the molecule ID for each atom,
 they will be truncated to an integer value, so atoms 31-40 will all be
 assigned a molecule ID of 4.</p>
 <p>Note that <a class="reference internal" href="variable.html"><em>atomfile-style variables</em></a> can also be used in
 place of atom-style variables, which means in this case that the
 molecule IDs could be read-in from a separate file and assinged by the
 <a class="reference internal" href="set.html"><em>set</em></a> command.  This allows you to initialize new per-atom
 properties in a completely general fashion.</p>
 <hr class="docutils" />
 <p>For new atom properties specified as <em>i_name</em> or <em>d_name</em>, the
 <a class="reference internal" href="compute_property_atom.html"><em>compute property/atom</em></a> command can access
 their values.  This means that the values can be output via the <a class="reference internal" href="dump.html"><em>dump custom</em></a> command, accessed by fixes like <a class="reference internal" href="fix_ave_atom.html"><em>fix ave/atom</em></a>, accessed by other computes like <a class="reference internal" href="compute_reduce.html"><em>compute reduce</em></a>, or used in <a class="reference external" href="variables">atom-style variables</a>.</p>
 <p>For example, these commands will output two new properties to a custom
 dump file:</p>
 <div class="highlight-python"><div class="highlight"><pre>fix prop all property/atom i_flag1 d_flag2
 compute 1 all property/atom i_flag1 d_flag2
 dump 1 all custom 100 tmp.dump id x y z c_1[1] c_1[2]
 </pre></div>
 </div>
 <hr class="docutils" />
 <p>If you wish to add new <a class="reference internal" href="pair_style.html"><em>pair styles</em></a>,
 <a class="reference internal" href="fix.html"><em>fixes</em></a>, or <a class="reference internal" href="compute.html"><em>computes</em></a> that use the per-atom
 properties defined by this fix, see <a class="reference internal" href="Section_modify.html#mod-1"><span>Section modify</span></a> of the manual which has some details
 on how the properties can be accessed from added classes.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>This fix writes the per-atom values it stores to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>, so that the values can be restored when a
 simulation is restarted.  See the <a class="reference internal" href="read_restart.html"><em>read_restart</em></a>
 command for info on how to re-specify a fix in an input script that
 reads a restart file, so that the operation of the fix continues in an
 uninterrupted fashion.</p>
 <p>None of the <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> options
 are relevant to this fix.  No global or per-atom quantities are stored
 by this fix for access by various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  No parameter of this fix can
 be used with the <em>start/stop</em> keywords of the <a class="reference internal" href="run.html"><em>run</em></a> command.
 This fix is not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <blockquote>
 <div>none</div></blockquote>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="read_data.html"><em>read_data</em></a>, <a class="reference internal" href="set.html"><em>set</em></a>, <a class="reference internal" href="compute_property_atom.html"><em>compute property/atom</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The default keyword values are ghost = no.</p>
 </div>
 </div>
 
 
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   <div class="section" id="fix-qbmsst-command">
 <span id="index-0"></span><h1>fix qbmsst command<a class="headerlink" href="#fix-qbmsst-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID qbmsst dir shockvel keyword value ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>qbmsst = style name of this fix</li>
 <li>dir = <em>x</em> or <em>y</em> or <em>z</em></li>
 <li>shockvel = shock velocity (strictly positive, velocity units)</li>
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>q</em> or <em>mu</em> or <em>p0</em> or <em>v0</em> or <em>e0</em> or <em>tscale</em> or <em>damp</em> or <em>seed*or *f_max</em> or <em>N_f</em> or <em>eta</em> or <em>beta</em> or <em>T_init</em></li>
 </ul>
 <pre class="literal-block">
 <em>q</em> value = cell mass-like parameter (mass^2/distance^4 units)
-  <em>mu</em> value = artificial viscosity (mass/distance/time units)
-  <em>p0</em> value = initial pressure in the shock equations (pressure units)
-  <em>v0</em> value = initial simulation cell volume in the shock equations (distance^3 units)
-  <em>e0</em> value = initial total energy (energy units)
-  <em>tscale</em> value = reduction in initial temperature (unitless fraction between 0.0 and 1.0)
-  <em>damp</em> value = damping parameter (time units) inverse of friction &lt;i&gt;&amp;gamma;&lt;/i&gt;
-  <em>seed</em> value = random number seed (positive integer)
-  <em>f_max</em> value = upper cutoff frequency of the vibration spectrum (1/time units)
-  <em>N_f</em> value = number of frequency bins (positive integer)
-  <em>eta</em> value = coupling constant between the shock system and the quantum thermal bath (positive unitless)
-  <em>beta</em> value = the quantum temperature is updated every beta time steps (positive integer)
-  <em>T_init</em> value = quantum temperature for the initial state (temperature units)
+<em>mu</em> value = artificial viscosity (mass/distance/time units)
+<em>p0</em> value = initial pressure in the shock equations (pressure units)
+<em>v0</em> value = initial simulation cell volume in the shock equations (distance^3 units)
+<em>e0</em> value = initial total energy (energy units)
+<em>tscale</em> value = reduction in initial temperature (unitless fraction between 0.0 and 1.0)
+<em>damp</em> value = damping parameter (time units) inverse of friction &lt;i&gt;&amp;gamma;&lt;/i&gt;
+<em>seed</em> value = random number seed (positive integer)
+<em>f_max</em> value = upper cutoff frequency of the vibration spectrum (1/time units)
+<em>N_f</em> value = number of frequency bins (positive integer)
+<em>eta</em> value = coupling constant between the shock system and the quantum thermal bath (positive unitless)
+<em>beta</em> value = the quantum temperature is updated every beta time steps (positive integer)
+<em>T_init</em> value = quantum temperature for the initial state (temperature units)
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix 1 all qbmsst z 0.122 q 25 mu 0.9 tscale 0.01 damp 200 seed 35082 f_max 0.3 N_f 100 eta 1 beta 400 T_init 110 (liquid methane modeled with the REAX force field, real units)
 fix 2 all qbmsst z 72 q 40 tscale 0.05 damp 1 seed 47508 f_max 120.0 N_f 100 eta 1.0 beta 500 T_init 300 (quartz modeled with the BKS force field, metal units)
 </pre></div>
 </div>
 <p>Two example input scripts are given, including shocked alpha quartz
 and shocked liquid methane. The input script first equilibrate an
 initial state with the quantum thermal bath at the target temperature
 and then apply the qbmsst to simulate shock compression with quantum
 nuclear correction.  The following two figures plot related quantities
 for shocked alpha quartz.</p>
 <img alt="_images/qbmsst_init.jpg" class="align-center" src="_images/qbmsst_init.jpg" />
 <p>Figure 1. Classical temperature &lt;i&gt;T&lt;/i&gt;&lt;sup&gt;cl&lt;/sup&gt; = &amp;sum;
 &lt;i&gt;m&lt;sub&gt;i&lt;/sub&gt;v&lt;sub&gt;i&lt;/sub&gt;&lt;sup&gt;2&lt;/sup&gt;/3Nk&lt;/i&gt;&lt;sub&gt;B&lt;/sub&gt; vs. time
 for coupling the alpha quartz initial state with the quantum thermal
 bath at target quantum temperature &lt;i&gt;T&lt;/i&gt;&lt;sup&gt;qm&lt;/sup&gt; = 300 K. The
 NpH ensemble is used for time integration while QTB provides the
 colored random force. &lt;i&gt;T&lt;/i&gt;&lt;sup&gt;cl&lt;/sup&gt; converges at the timescale
 of <em>damp</em> which is set to be 1 ps.</p>
 <img alt="_images/qbmsst_shock.jpg" class="align-center" src="_images/qbmsst_shock.jpg" />
 <p>Figure 2. Quantum temperature and pressure vs. time for simulating
 shocked alpha quartz with the QBMSST. The shock propagates along the z
 direction. Restart of the QBMSST command is demonstrated in the
 example input script. Thermodynamic quantities stay continuous before
 and after the restart.</p>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>This command performs the Quantum-Bath coupled Multi-Scale Shock
 Technique (QBMSST) integration. See <a class="reference internal" href="#qi"><span>(Qi)</span></a> for a detailed
 description of this method.  The QBMSST provides description of the
 thermodynamics and kinetics of shock processes while incorporating
 quantum nuclear effects.  The <em>shockvel</em> setting determines the steady
 shock velocity that will be simulated along direction <em>dir</em>.</p>
 <p>Quantum nuclear effects <a class="reference internal" href="fix_qtb.html"><em>(fix qtb)</em></a> can be crucial
 especially when the temperature of the initial state is below the
 classical limit or there is a great change in the zero point energies
 between the initial and final states. Theoretical post processing
 quantum corrections of shock compressed water and methane have been
 reported as much as 30% of the temperatures <a class="reference internal" href="#goldman"><span>(Goldman)</span></a>.  A
 self-consistent method that couples the shock to a quantum thermal
 bath described by a colored noise Langevin thermostat has been
 developed by Qi et al <a class="reference internal" href="#qi"><span>(Qi)</span></a> and applied to shocked methane.  The
 onset of chemistry is reported to be at a pressure on the shock
 Hugoniot that is 40% lower than observed with classical molecular
 dynamics.</p>
 <p>It is highly recommended that the system be already in an equilibrium
 state with a quantum thermal bath at temperature of <em>T_init</em>.  The fix
 command <a class="reference internal" href="fix_qtb.html"><em>fix qtb</em></a> at constant temperature <em>T_init</em> could
 be used before applying this command to introduce self-consistent
 quantum nuclear effects into the initial state.</p>
 <p>The parameters <em>q</em>, <em>mu</em>, <em>e0</em>, <em>p0</em>, <em>v0</em> and <em>tscale</em> are described
 in the command <a class="reference internal" href="fix_msst.html"><em>fix msst</em></a>. The values of <em>e0</em>, <em>p0</em>, or
 <em>v0</em> will be calculated on the first step if not specified.  The
 parameter of <em>damp</em>, <em>f_max</em>, and <em>N_f</em> are described in the command
 <a class="reference internal" href="fix_qtb.html"><em>fix qtb</em></a>.</p>
 <p>The fix qbmsst command couples the shock system to a quantum thermal
 bath with a rate that is proportional to the change of the total
 energy of the shock system, &lt;i&gt;etot&lt;/i&gt; - &lt;i&gt;etot&lt;/i&gt;&lt;sub&gt;0&lt;/sub&gt;.
 Here &lt;i&gt;etot&lt;/i&gt; consists of both the system energy and a thermal
 term, see <a class="reference internal" href="#qi"><span>(Qi)</span></a>, and &lt;i&gt;etot&lt;/i&gt;&lt;sub&gt;0&lt;/sub&gt; = <em>e0</em> is the
 initial total energy.</p>
 <p>The <em>eta</em> (&lt;i&gt;&amp;eta;&lt;/i&gt;) parameter is a unitless coupling constant
 between the shock system and the quantum thermal bath. A small <em>eta</em>
 value cannot adjust the quantum temperature fast enough during the
 temperature ramping period of shock compression while large <em>eta</em>
 leads to big temperature oscillation. A value of <em>eta</em> between 0.3 and
 1 is usually appropriate for simulating most systems under shock
 compression. We observe that different values of <em>eta</em> lead to almost
 the same final thermodynamic state behind the shock, as expected.</p>
 <p>The quantum temperature is updated every <em>beta</em> (&lt;i&gt;&amp;beta;&lt;/i&gt;) steps
 with an integration time interval <em>beta</em> times longer than the
 simulation time step. In that case, &lt;i&gt;etot&lt;/i&gt; is taken as its
 average over the past <em>beta</em> steps. The temperature of the quantum
 thermal bath &lt;i&gt;T&lt;/i&gt;&lt;sup&gt;qm&lt;/sup&gt; changes dynamically according to
 the following equation where &amp;Delta;&lt;i&gt;t&lt;/i&gt; is the MD time step and
 &lt;i&gt;&amp;gamma;&lt;/i&gt; is the friction constant which is equal to the inverse
 of the <em>damp</em> parameter.</p>
 <center><font size="4"> <i>dT</i><sup>qm</sup>/<i>dt =
 &gamma;&eta;</i>&sum;<i><sup>&beta;</sup><sub>l =
 1</sub></i>[<i>etot</i>(<i>t-l</i>&Delta;<i>t</i>)-<i>etot</i><sub>0</sub>]/<i>3&beta;Nk</i><sub>B</sub>
 </font></center><p>The parameter <em>T_init</em> is the initial temperature of the quantum
 thermal bath and the system before shock loading.</p>
 <p>For all pressure styles, the simulation box stays orthorhombic in
 shape. Parrinello-Rahman boundary conditions (tilted box) are
 supported by LAMMPS, but are not implemented for QBMSST.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>Because the state of the random number generator is not written to
 <a class="reference internal" href="restart.html"><em>binary restart files</em></a>, this fix cannot be restarted
 &#8220;exactly&#8221; in an uninterrupted fashion. However, in a statistical
 sense, a restarted simulation should produce similar behaviors of the
 system as if it is not interrupted.  To achieve such a restart, one
 should write explicitly the same value for <em>q</em>, <em>mu</em>, <em>damp</em>, <em>f_max</em>,
 <em>N_f</em>, <em>eta</em>, and <em>beta</em> and set <em>tscale</em> = 0 if the system is
 compressed during the first run.</p>
 <p>The progress of the QBMSST can be monitored by printing the global
 scalar and global vector quantities computed by the fix.  The global
 vector contains five values in this order:</p>
 <p>[<em>dhugoniot</em>, <em>drayleigh</em>, <em>lagrangian_speed</em>, <em>lagrangian_position</em>,
 <em>quantum_temperature</em>]</p>
 <ol class="arabic simple">
 <li><em>dhugoniot</em> is the departure from the Hugoniot (temperature units).</li>
 <li><em>drayleigh</em> is the departure from the Rayleigh line (pressure units).</li>
 <li><em>lagrangian_speed</em> is the laboratory-frame Lagrangian speed (particle velocity) of the computational cell (velocity units).</li>
 <li><em>lagrangian_position</em> is the computational cell position in the reference frame moving at the shock speed. This is the distance of the computational cell behind the shock front.</li>
 <li><em>quantum_temperature</em> is the temperature of the quantum thermal bath &lt;i&gt;T&lt;/i&gt;&lt;sup&gt;qm&lt;/sup&gt;.</li>
 </ol>
 <p>To print these quantities to the log file with descriptive column
 headers, the following LAMMPS commands are suggested. Here the
 <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> energy command is also enabled to allow
 the thermo keyword <em>etotal</em> to print the quantity &lt;i&gt;etot&lt;/i&gt;.  See
 also the <a class="reference internal" href="thermo_style.html"><em>thermo_style</em></a> command.</p>
 <div class="highlight-python"><div class="highlight"><pre>fix          fix_id all msst z
 fix_modify   fix_id energy yes
 variable     dhug    equal f_fix_id[1]
 variable     dray    equal f_fix_id[2]
 variable     lgr_vel equal f_fix_id[3]
 variable     lgr_pos equal f_fix_id[4]
 variable     T_qm    equal f_fix_id[5]
 thermo_style custom  step temp ke pe lz pzz etotal v_dhug v_dray v_lgr_vel v_lgr_pos v_T_qm f_fix_id
 </pre></div>
 </div>
 <p>The global scalar under the entry f_fix_id is the quantity of thermo
 energy as an extra part of &lt;i&gt;etot&lt;/i&gt;. This global scalar and the
 vector of 5 quantities can be accessed by various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>. It is worth noting that the
 temp keyword under the <a class="reference internal" href="thermo_style.html"><em>thermo_style</em></a> command print
 the instantaneous classical temperature &lt;i&gt;T&lt;/i&gt;&lt;sup&gt;cl&lt;/sup&gt; as
 described in the command <a class="reference internal" href="fix_qtb.html"><em>fix qtb</em></a>.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>This fix style is part of the USER-QTB package.  It is only enabled if
 LAMMPS was built with that package. See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 <p>All cell dimensions must be periodic. This fix can not be used with a
 triclinic cell.  The QBMSST fix has been tested only for the group-ID
 all.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="fix_qtb.html"><em>fix qtb</em></a>, <a class="reference internal" href="fix_msst.html"><em>fix msst</em></a></p>
 </div>
 <hr class="docutils" />
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The keyword defaults are q = 10, mu = 0, tscale = 0.01, damp = 1, seed
 = 880302, f_max = 200.0, N_f = 100, eta = 1.0, beta = 100, and
 T_init=300.0. e0, p0, and v0 are calculated on the first step.</p>
 <hr class="docutils" />
 <p id="goldman"><strong>(Goldman)</strong> Goldman, Reed and Fried, J. Chem. Phys. 131, 204103 (2009)</p>
 <p id="qi"><strong>(Qi)</strong> Qi and Reed, J. Phys. Chem. A 116, 10451 (2012).</p>
 </div>
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diff --git a/doc/fix_qeq_comb.html b/doc/fix_qeq_comb.html
index 61f509b83..5d9005ded 100644
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   <div class="section" id="fix-qeq-comb-command">
 <span id="index-0"></span><h1>fix qeq/comb command<a class="headerlink" href="#fix-qeq-comb-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="fix-qeq-comb-omp-command">
 <h1>fix qeq/comb/omp command<a class="headerlink" href="#fix-qeq-comb-omp-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID qeq/comb Nevery precision keyword value ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>qeq/comb = style name of this fix command</li>
 <li>Nevery = perform charge equilibration every this many steps</li>
 <li>precision = convergence criterion for charge equilibration</li>
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>file</em></li>
 </ul>
 <pre class="literal-block">
 <em>file</em> value = filename
-    filename = name of file to write QEQ equilibration info to
+  filename = name of file to write QEQ equilibration info to
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix 1 surface qeq/comb 10 0.0001
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Perform charge equilibration (QeQ) in conjunction with the COMB
 (Charge-Optimized Many-Body) potential as described in
 <a class="reference internal" href="#comb-1"><span>(COMB_1)</span></a> and <a class="reference internal" href="#comb-2"><span>(COMB_2)</span></a>.  It performs the charge
 equilibration portion of the calculation using the so-called QEq
 method, whereby the charge on each atom is adjusted to minimize the
 energy of the system.  This fix can only be used with the COMB
 potential; see the <a class="reference internal" href="fix_qeq_reax.html"><em>fix qeq/reax</em></a> command for a QeQ
 calculation that can be used with any potential.</p>
 <p>Only charges on the atoms in the specified group are equilibrated.
 The fix relies on the pair style (COMB in this case) to calculate the
 per-atom electronegativity (effective force on the charges).  An
 electronegativity equalization calculation (or QEq) is performed in an
 interative fashion, which in parallel requires communication at each
 iteration for processors to exchange charge information about nearby
 atoms with each other.  See <a class="reference internal" href="#rappe-and-goddard"><span>Rappe_and_Goddard</span></a> and
 <a class="reference internal" href="#rick-and-stuart"><span>Rick_and_Stuart</span></a> for details.</p>
 <p>During a run, charge equilibration is peformed every <em>Nevery</em> time
 steps.  Charge equilibration is also always enforced on the first step
 of each run.  The <em>precision</em> argument controls the tolerance for the
 difference in electronegativity for all atoms during charge
 equilibration.  <em>Precision</em> is a trade-off between the cost of
 performing charge equilibration (more iterations) and accuracy.</p>
 <p>If the <em>file</em> keyword is used, then information about each
 equilibration calculation is written to the specifed file.</p>
 <hr class="docutils" />
 <p>Styles with a <em>cuda</em>, <em>gpu</em>, <em>intel</em>, <em>kk</em>, <em>omp</em>, or <em>opt</em> suffix are
 functionally the same as the corresponding style without the suffix.
 They have been optimized to run faster, depending on your available
 hardware, as discussed in <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a>
 of the manual.  The accelerated styles take the same arguments and
 should produce the same results, except for round-off and precision
 issues.</p>
 <p>These accelerated styles are part of the USER-CUDA, GPU, USER-INTEL,
 KOKKOS, USER-OMP and OPT packages, respectively.  They are only
 enabled if LAMMPS was built with those packages.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 <p>You can specify the accelerated styles explicitly in your input script
 by including their suffix, or you can use the <a class="reference internal" href="Section_start.html#start-7"><span>-suffix command-line switch</span></a> when you invoke LAMMPS, or you can
 use the <a class="reference internal" href="suffix.html"><em>suffix</em></a> command in your input script.</p>
 <p>See <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a> of the manual for
 more instructions on how to use the accelerated styles effectively.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.  None of the <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> options
 are relevant to this fix.</p>
 <p>This fix produces a per-atom vector which can be accessed by various
 <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  The vector stores the
 gradient of the charge on each atom.  The per-atom values be accessed
 on any timestep.</p>
 <p>No parameter of this fix can be used with the <em>start/stop</em> keywords of
 the <a class="reference internal" href="run.html"><em>run</em></a> command.</p>
 <p>This fix can be invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>This fix command currently only supports <a class="reference internal" href="pair_comb.html"><em>pair style *comb*</em></a>.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="pair_comb.html"><em>pair_style comb</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>No file output is performed.</p>
 <hr class="docutils" />
 <p id="comb-1"><strong>(COMB_1)</strong> J. Yu, S. B. Sinnott, S. R. Phillpot, Phys Rev B, 75, 085311 (2007),</p>
 <p id="comb-2"><strong>(COMB_2)</strong> T.-R. Shan, B. D. Devine, T. W. Kemper, S. B. Sinnott, S. R.
 Phillpot, Phys Rev B, 81, 125328 (2010).</p>
 <p id="rappe-and-goddard"><strong>(Rappe_and_Goddard)</strong> A. K. Rappe, W. A. Goddard, J Phys Chem 95, 3358
 (1991).</p>
 <p id="rick-and-stuart"><strong>(Rick_and_Stuart)</strong> S. W. Rick, S. J. Stuart, B. J. Berne, J Chem Phys
 101, 16141 (1994).</p>
 </div>
 </div>
 
 
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diff --git a/doc/fix_qtb.html b/doc/fix_qtb.html
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   <div class="section" id="fix-qtb-command">
 <span id="index-0"></span><h1>fix qtb command<a class="headerlink" href="#fix-qtb-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID qtb keyword value ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>qtb = style name of this fix</li>
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>temp</em> or <em>damp</em> or <em>seed</em> or <em>f_max</em> or <em>N_f</em></li>
 </ul>
 <pre class="literal-block">
 <em>temp</em> value = target quantum temperature (temperature units)
-  <em>damp</em> value = damping parameter (time units) inverse of friction &lt;i&gt;&amp;gamma&lt;/i&gt;;
-  <em>seed</em> value = random number seed (positive integer)
-  <em>f_max</em> value = upper cutoff frequency of the vibration spectrum (1/time units)
-  <em>N_f</em> value = number of frequency bins (positive integer)
+<em>damp</em> value = damping parameter (time units) inverse of friction &lt;i&gt;&amp;gamma&lt;/i&gt;;
+<em>seed</em> value = random number seed (positive integer)
+<em>f_max</em> value = upper cutoff frequency of the vibration spectrum (1/time units)
+<em>N_f</em> value = number of frequency bins (positive integer)
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix 1 all nve
 fix 1 all qtb temp 110 damp 200 seed 35082 f_max 0.3 N_f 100 (liquid methane modeled with the REAX force field, real units)
 fix 2 all nph iso 1.01325 1.01325 1
 fix 2 all qtb temp 300 damp 1 seed 47508 f_max 120.0 N_f 100 (quartz modeled with the BKS force field, metal units)
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>This command performs the quantum thermal bath scheme proposed by
 <a class="reference internal" href="#dammak"><span>(Dammak)</span></a> to include self-consistent quantum nuclear effects,
 when used in conjunction with the <a class="reference internal" href="fix_nve.html"><em>fix nve</em></a> or <a class="reference internal" href="fix_nh.html"><em>fix nph</em></a> commands.</p>
 <p>Classical molecular dynamics simulation does not include any quantum
 nuclear effect. Quantum treatment of the vibrational modes will
 introduce zero point energy into the system, alter the energy power
 spectrum and bias the heat capacity from the classical limit. Missing
 all the quantum nuclear effects, classical MD cannot model systems at
 temperatures lower than their classical limits. This effect is
 especially important for materials with a large population of hydrogen
 atoms and thus higher classical limits.</p>
 <p>The equation of motion implemented by this command follows a Langevin
 form:</p>
 <center><font size="4"><i> m<sub>i</sub>a<sub>i</sub> = f<sub>i</sub>
 + R<sub>i</sub> -
 m<sub>i</sub>&gamma;v<sub>i</sub>. </i></font></center><p>Here &lt;i&gt;m&lt;sub&gt;i&lt;/sub&gt;&lt;/i&gt;, &lt;i&gt;a&lt;sub&gt;i&lt;/sub&gt;&lt;/i&gt;, &lt;i&gt;f&lt;sub&gt;i&lt;/sub&gt;
 &lt;/i&gt;, &lt;i&gt;R&lt;sub&gt;i&lt;/sub&gt;&lt;/i&gt;, &lt;i&gt;&amp;gamma;&lt;/i&gt; and &lt;i&gt;v&lt;sub&gt;i&lt;/sub&gt; &lt;/i&gt;
 represent mass, acceleration, force exerted by all other atoms, random
 force, frictional coefficient (the inverse of damping parameter damp),
 and velocity. The random force &lt;i&gt;R&lt;sub&gt;i&lt;/sub&gt;&lt;/i&gt; is &#8220;colored&#8221; so
 that any vibrational mode with frequency &lt;i&gt;&amp;omega;&lt;/i&gt; will have a
 temperature-sensitive energy &lt;i&gt;&amp;theta;&lt;/i&gt;(&lt;i&gt;&amp;omega;,T&lt;/i&gt;) which
 resembles the energy expectation for a quantum harmonic oscillator
 with the same natural frequency:</p>
 <center><font size="4"> <i>&theta;</i>(<i>&omega;,T</i>) =
 &#8463;&omega;/2 +
 &#8463;&omega;[</i>exp(<i>&#8463;&omega;/k</i><sub>B</sub><i>T</i>)<i>-1</i>]<i><sup>-1</sup></i>
 </font></center><p>To efficiently generate the random forces, we employ the method
 of <a class="reference internal" href="#barrat"><span>(Barrat)</span></a>, that circumvents the need to generate all
 random forces for all times before the simulation. The memory
 requirement of this approach is less demanding and independent
 of the simulation duration. Since the total random force &lt;i&gt;R&lt;/i&gt;&lt;sub&gt;tot&lt;/sub&gt;
 does not necessarily vanish for a finite number of atoms,
 &lt;i&gt;R&lt;sub&gt;i&lt;/sub&gt;&lt;/i&gt; is replaced by &lt;i&gt;R&lt;sub&gt;i&lt;/sub&gt;&lt;/i&gt; - &lt;i&gt;R&lt;/i&gt;&lt;sub&gt;tot&lt;/sub&gt;/&lt;i&gt;N&lt;/i&gt;&lt;sub&gt;tot&lt;/sub&gt;
 to avoid collective motion of the system.</p>
 <p>The <em>temp</em> parameter sets the target quantum temperature. LAMMPS will
 still have an output temperature in its thermo style. That is the
 instantaneous classical temperature &lt;i&gt;T&lt;/i&gt;&lt;sup&gt;cl&lt;/sup&gt; derived from
 the atom velocities at thermal equilibrium. A non-zero
 &lt;i&gt;T&lt;/i&gt;&lt;sup&gt;cl&lt;/sup&gt; will be present even when the quantum
 temperature approaches zero. This is associated with zero-point energy
 at low temperatures.</p>
 <center><font size="4"> <i>T</i><sup>cl</sup> = &sum;
 <i>m<sub>i</sub>v<sub>i</sub><sup>2</sup>/3Nk</i><sub>B</sub>
 </font></center><p>The <em>damp</em> parameter is specified in time units, and it equals the
 inverse of the frictional coefficient &lt;i&gt;&amp;gamma;&lt;/i&gt;. &lt;i&gt;&amp;gamma;&lt;/i&gt;
 should be as small as possible but slightly larger than the timescale
 of anharmonic coupling in the system which is about 10 ps to 100
 ps. When &lt;i&gt;&amp;gamma;&lt;/i&gt; is too large, it gives an energy spectrum that
 differs from the desired Bose-Einstein spectrum. When &lt;i&gt;&amp;gamma;&lt;/i&gt;
 is too small, the quantum thermal bath coupling to the system will be
 less significant than anharmonic effects, reducing to a classical
 limit. We find that setting &lt;i&gt;&amp;gamma;&lt;/i&gt; between 5 THz and 1 THz
 could be appropriate depending on the system.</p>
 <p>The random number <em>seed</em> is a positive integer used to initiate a
 Marsaglia random number generator. Each processor uses the input seed
 to generate its own unique seed and its own stream of random
 numbers. Thus the dynamics of the system will not be identical on two
 runs on different numbers of processors.</p>
 <p>The <em>f_max</em> parameter truncate the noise frequency domain so that
 vibrational modes with frequencies higher than <em>f_max</em> will not be
 modulated. If we denote &amp;Delta;&lt;i&gt;t&lt;/i&gt; as the time interval for the
 MD integration, <em>f_max</em> is always reset by the code to make
 &lt;i&gt;&amp;alpha;&lt;/i&gt; = (int)(2*f_max*&amp;Delta;&lt;i&gt;t&lt;/i&gt;)&lt;sup&gt;&lt;i&gt;-1&lt;/i&gt;&lt;/sup&gt; a
 positive integer and print out relative information. An appropriate
 value for the cutoff frequency <em>f_max</em> would be around 2~3
 &lt;i&gt;f&lt;/i&gt;&lt;sub&gt;D&lt;/sub&gt;, where &lt;i&gt;f&lt;/i&gt;&lt;sub&gt;D&lt;/sub&gt; is the Debye
 frequency.</p>
 <p>The <em>N_f</em> parameter is the frequency grid size, the number of points
 from 0 to <em>f_max</em> in the frequency domain that will be
 sampled. &lt;i&gt;3&amp;times;2&lt;/i&gt; <em>N_f</em> per-atom random numbers are required
 in the random force generation and there could be as many atoms as in
 the whole simulation that can migrate into every individual
 processor. A larger <em>N_f</em> provides a more accurate sampling of the
 spectrum while consumes more memory.  With fixed <em>f_max</em> and
 &lt;i&gt;&amp;gamma;&lt;/i&gt;, <em>N_f</em> should be big enough to converge the classical
 temperature &lt;i&gt;T&lt;/i&gt;&lt;sup&gt;cl&lt;/sup&gt; as a function of target quantum bath
 temperature. Memory usage per processor could be from 10 to 100
 Mbytes.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">Unlike the <a class="reference internal" href="fix_nh.html"><em>fix nvt</em></a> command which
 performs Nose/Hoover thermostatting AND time integration, this fix
 does NOT perform time integration. It only modifies forces to a
 colored thermostat. Thus you must use a separate time integration fix,
 like <a class="reference internal" href="fix_nve.html"><em>fix nve</em></a> or <a class="reference internal" href="fix_nh.html"><em>fix nph</em></a> to actually
 update the velocities and positions of atoms (as shown in the
 examples). Likewise, this fix should not normally be used with other
 fixes or commands that also specify system temperatures , e.g. <a class="reference internal" href="fix_nh.html"><em>fix nvt</em></a> and <a class="reference internal" href="fix_temp_rescale.html"><em>fix temp/rescale</em></a>.</p>
 </div>
 <hr class="docutils" />
 <p><strong>Restart, fix_modify, output, run start/stop, minimizie info:</strong></p>
 <p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.  Because the state of the random number generator
 is not saved in restart files, this means you cannot do &#8220;exact&#8221;
 restarts with this fix. However, in a statistical sense, a restarted
 simulation should produce similar behaviors of the system.</p>
 <p>This fix is not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>This fix style is part of the USER-QTB package.  It is only enabled if
 LAMMPS was built with that package. See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="fix_nve.html"><em>fix nve</em></a>, <a class="reference internal" href="fix_nh.html"><em>fix nph</em></a>, <a class="reference internal" href="fix_langevin.html"><em>fix langevin</em></a>, <a class="reference internal" href="fix_qbmsst.html"><em>fix qbmsst</em></a></p>
 </div>
 <hr class="docutils" />
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The keyword defaults are temp = 300, damp = 1, seed = 880302,
 f_max=200.0 and N_f = 100.</p>
 <hr class="docutils" />
 <p id="dammak"><strong>(Dammak)</strong> Dammak, Chalopin, Laroche, Hayoun, and Greffet, Phys Rev
 Lett, 103, 190601 (2009).</p>
 <p id="barrat"><strong>(Barrat)</strong> Barrat and Rodney, J. Stat. Phys, 144, 679 (2011).</p>
 </div>
 </div>
 
 
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diff --git a/doc/fix_reaxc_species.html b/doc/fix_reaxc_species.html
index 77f008c2d..58fa7aa7a 100644
--- a/doc/fix_reaxc_species.html
+++ b/doc/fix_reaxc_species.html
@@ -1,324 +1,324 @@
 
 
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   <div class="section" id="fix-reax-c-species-command">
 <span id="index-0"></span><h1>fix reax/c/species command<a class="headerlink" href="#fix-reax-c-species-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID reax/c/species Nevery Nrepeat Nfreq filename keyword value ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>reax/c/species = style name of this command</li>
 <li>Nevery = sample bond-order every this many timesteps</li>
 <li>Nrepeat = # of bond-order samples used for calculating averages</li>
 <li>Nfreq = calculate average bond-order every this many timesteps</li>
 <li>filename = name of output file</li>
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>cutoff</em> or <em>element</em> or <em>position</em></li>
 </ul>
 <pre class="literal-block">
 <em>cutoff</em> value = I J Cutoff
-    I, J = atom types
-    Cutoff = Bond-order cutoff value for this pair of atom types
-  <em>element</em> value = Element1, Element2, ...
-  <em>position</em> value = posfreq filepos
-    posfreq = write position files every this many timestep
-    filepos = name of position output file
+  I, J = atom types
+  Cutoff = Bond-order cutoff value for this pair of atom types
+<em>element</em> value = Element1, Element2, ...
+<em>position</em> value = posfreq filepos
+  posfreq = write position files every this many timestep
+  filepos = name of position output file
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix 1 all reax/c/species 10 10 100 species.out
 fix 1 all reax/c/species 1 2 20 species.out cutoff 1 1 0.40 cutoff 1 2 0.55
 fix 1 all reax/c/species 1 100 100 species.out element Au O H position 1000 AuOH.pos
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Write out the chemical species information computed by the ReaxFF
 potential specified by <a class="reference internal" href="pair_reax_c.html"><em>pair_style reax/c</em></a>.
 Bond-order values (either averaged or instantaneous, depending on
 value of <em>Nrepeat</em>) are used to determine chemical bonds.  Every
 <em>Nfreq</em> timesteps, chemical species information is written to
 <em>filename</em> as a two line output.  The first line is a header
 containing labels. The second line consists of the following:
 timestep, total number of molecules, total number of distinct species,
 number of molecules of each species.  In this context, &#8220;species&#8221; means
 a unique molecule.  The chemical formula of each species is given in
 the first line.</p>
 <p>Optional keyword <em>cutoff</em> can be assigned to change the minimum
 bond-order values used in identifying chemical bonds between pairs of
 atoms.  Bond-order cutoffs should be carefully chosen, as bond-order
 cutoffs that are too small may include too many bonds (which will
 result in an error), while cutoffs that are too large will result in
 fragmented molecules.  The default cutoff of 0.3 usually gives good
 results.</p>
 <p>The optional keyword <em>element</em> can be used to specify the chemical
 symbol printed for each LAMMPS atom type. The number of symbols must
 match the number of LAMMPS atom types and each symbol must consist of
 1 or 2 alphanumeric characters. Normally, these symbols should be
 chosen to match the chemical identity of each LAMMPS atom type, as
 specified using the <a class="reference internal" href="pair_reax_c.html"><em>reax/c pair_coeff</em></a> command and
 the ReaxFF force field file.</p>
 <p>The optional keyword <em>position</em> writes center-of-mass positions of
 each identified molecules to file <em>filepos</em> every <em>posfreq</em> timesteps.
 The first line contains information on timestep, total number of
 molecules, total number of distinct species, and box dimensions.  The
 second line is a header containing labels.  From the third line
 downward, each molecule writes a line of output containing the
 following information: molecule ID, number of atoms in this molecule,
 chemical formula, total charge, and center-of-mass xyz positions of
 this molecule.  The xyz positions are in fractional coordinates
 relative to the box dimensions.</p>
 <p>For the keyword <em>position</em>, the <em>filepos</em> is the name of the output
 file.  It can contain the wildcard character &#8220;*&#8221;.  If the &#8220;*&#8221;
 character appears in <em>filepos</em>, then one file per snapshot is written
 at <em>posfreq</em> and the &#8220;*&#8221; character is replaced with the timestep
 value.  For example, AuO.pos.* becomes AuO.pos.0, AuO.pos.1000, etc.</p>
 <hr class="docutils" />
 <p>The <em>Nevery</em>, <em>Nrepeat</em>, and <em>Nfreq</em> arguments specify on what
 timesteps the bond-order values are sampled to get the average bond
 order.  The species analysis is performed using the average bond-order
 on timesteps that are a multiple of <em>Nfreq</em>.  The average is over
 <em>Nrepeat</em> bond-order samples, computed in the preceding portion of the
 simulation every <em>Nevery</em> timesteps.  <em>Nfreq</em> must be a multiple of
 <em>Nevery</em> and <em>Nevery</em> must be non-zero even if <em>Nrepeat</em> is 1.  Also,
 the timesteps contributing to the average bond-order cannot overlap,
 i.e. Nfreq &gt; (Nrepeat-1)*Nevery is required.</p>
 <p>For example, if Nevery=2, Nrepeat=6, and Nfreq=100, then bond-order
 values on timesteps 90,92,94,96,98,100 will be used to compute the
 average bond-order for the species analysis output on timestep 100.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.  None of the <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> options
 are relevant to this fix.</p>
 <p>This fix computes both a global vector of length 2 and a per-atom
 vector, either of which can be accessed by various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  The values in the global
 vector are &#8220;intensive&#8221;.</p>
 <p>The 2 values in the global vector are as follows:</p>
 <ul class="simple">
 <li>1 = total number of molecules</li>
 <li>2 = total number of distinct species</li>
 </ul>
 <p>The per-atom vector stores the molecule ID for each atom as identified
 by the fix.  If an atom is not in a molecule, its ID will be 0.
 For atoms in the same molecule, the molecule ID for all of them
 will be the same and will be equal to the smallest atom ID of
 any atom in the molecule.</p>
 <p>No parameter of this fix can be used with the <em>start/stop</em> keywords of
 the <a class="reference internal" href="run.html"><em>run</em></a> command.  This fix is not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>The fix species currently only works with
 <a class="reference internal" href="pair_reax_c.html"><em>pair_style reax/c</em></a> and it requires that the <a class="reference internal" href="pair_reax_c.html"><em>pair_style reax/c</em></a> be invoked.  This fix is part of the
 USER-REAXC package.  It is only enabled if LAMMPS was built with that
 package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section
 for more info.</p>
 <p>It should be possible to extend it to other reactive pair_styles (such as
 <a class="reference internal" href="pair_airebo.html"><em>rebo</em></a>, <a class="reference internal" href="pair_airebo.html"><em>airebo</em></a>,
 <a class="reference internal" href="pair_comb.html"><em>comb</em></a>, and <a class="reference internal" href="pair_bop.html"><em>bop</em></a>), but this has not yet been done.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="pair_reax_c.html"><em>pair_style reax/c</em></a>, <a class="reference internal" href="fix_reax_bonds.html"><em>fix reax/bonds</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The default values for bond-order cutoffs are 0.3 for all I-J pairs.  The
 default element symbols are C, H, O, N.  Position files are not written
 by default.</p>
 </div>
 </div>
 
 
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   <div class="section" id="fix-recenter-command">
 <span id="index-0"></span><h1>fix recenter command<a class="headerlink" href="#fix-recenter-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID recenter x y z keyword value ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>recenter = style name of this fix command</li>
 <li>x,y,z = constrain center-of-mass to these coords (distance units),         any coord can also be NULL or INIT (see below)</li>
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>shift</em> or <em>units</em></li>
 </ul>
 <pre class="literal-block">
 <em>shift</em> value = group-ID
-    group-ID = group of atoms whose coords are shifted
-  <em>units</em> value = <em>box</em> or <em>lattice</em> or <em>fraction</em>
+  group-ID = group of atoms whose coords are shifted
+<em>units</em> value = <em>box</em> or <em>lattice</em> or <em>fraction</em>
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix 1 all recenter 0.0 0.5 0.0
 fix 1 all recenter INIT INIT NULL
 fix 1 all recenter INIT 0.0 0.0 units box
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Constrain the center-of-mass position of a group of atoms by adjusting
 the coordinates of the atoms every timestep.  This is simply a small
 shift that does not alter the dynamics of the system or change the
 relative coordinates of any pair of atoms in the group.  This can be
 used to insure the entire collection of atoms (or a portion of them)
 do not drift during the simulation due to random perturbations
 (e.g. <a class="reference internal" href="fix_langevin.html"><em>fix langevin</em></a> thermostatting).</p>
 <p>Distance units for the x,y,z values are determined by the setting of
 the <em>units</em> keyword, as discussed below.  One or more x,y,z values can
 also be specified as NULL, which means exclude that dimension from
 this operation.  Or it can be specified as INIT which means to
 constrain the center-of-mass to its initial value at the beginning of
 the run.</p>
 <p>The center-of-mass (COM) is computed for the group specified by the
 fix.  If the current COM is different than the specified x,y,z, then a
 group of atoms has their coordinates shifted by the difference.  By
 default the shifted group is also the group specified by the fix.  A
 different group can be shifted by using the <em>shift</em> keyword.  For
 example, the COM could be computed on a protein to keep it in the
 center of the simulation box.  But the entire system (protein + water)
 could be shifted.</p>
 <p>If the <em>units</em> keyword is set to <em>box</em>, then the distance units of
 x,y,z are defined by the <a class="reference internal" href="units.html"><em>units</em></a> command - e.g. Angstroms
 for <em>real</em> units.  A <em>lattice</em> value means the distance units are in
 lattice spacings.  The <a class="reference internal" href="lattice.html"><em>lattice</em></a> command must have been
 previously used to define the lattice spacing.  A <em>fraction</em> value
 means a fractional distance between the lo/hi box boundaries, e.g. 0.5
 = middle of the box.  The default is to use lattice units.</p>
 <p>Note that the <a class="reference internal" href="velocity.html"><em>velocity</em></a> command can be used to create
 velocities with zero aggregate linear and/or angular momentum.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">This fix performs its operations at the same point in
 the timestep as other time integration fixes, such as <a class="reference internal" href="fix_nve.html"><em>fix nve</em></a>, <a class="reference internal" href="fix_nh.html"><em>fix nvt</em></a>, or <a class="reference internal" href="fix_nh.html"><em>fix npt</em></a>.
 Thus fix recenter should normally be the last such fix specified in
 the input script, since the adjustments it makes to atom coordinates
 should come after the changes made by time integration.  LAMMPS will
 warn you if your fixes are not ordered this way.</p>
 </div>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">If you use this fix on a small group of atoms (e.g. a
 molecule in solvent) without using the <em>shift</em> keyword to adjust the
 positions of all atoms in the system, then the results can be
 unpredictable.  For example, if the molecule is pushed in one
 direction by the solvent, its velocity will increase.  But its
 coordinates will be recentered, meaning it is pushed back towards the
 force.  Thus over time, the velocity and temperature of the molecule
 could become very large (though it won&#8217;t appear to be moving due to
 the recentering).  If you are thermostatting the entire system, then
 the solvent would be cooled to compensate.  A better solution for this
 simulation scenario is to use the <a class="reference internal" href="fix_spring.html"><em>fix spring</em></a> command
 to tether the molecule in place.</p>
 </div>
 </div>
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.  None of the <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> options
 are relevant to this fix.</p>
 <p>This fix computes a global scalar which can be accessed by various
 <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  The scalar is the
 distance the group is moved by fix recenter.</p>
 <p>This fix also computes global 3-vector which can be accessed by
 various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  The 3
 quantities in the vector are xyz components of displacement applied to
 the group of atoms by the fix.</p>
 <p>The scalar and vector values calculated by this fix are &#8220;extensive&#8221;.</p>
 <p>No parameter of this fix can be used with the <em>start/stop</em> keywords of
 the <a class="reference internal" href="run.html"><em>run</em></a> command.  This fix is not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>This fix should not be used with an x,y,z setting that causes a large
 shift in the system on the 1st timestep, due to the requested COM
 being very different from the initial COM.  This could cause atoms to
 be lost, especially in parallel.  Instead, use the
 <a class="reference internal" href="displace_atoms.html"><em>displace_atoms</em></a> command, which can be used to
 move atoms a large distance.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="fix_momentum.html"><em>fix momentum</em></a>, <a class="reference internal" href="velocity.html"><em>velocity</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The option defaults are shift = fix group-ID, and units = lattice.</p>
 </div>
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   <div class="section" id="fix-restrain-command">
 <span id="index-0"></span><h1>fix restrain command<a class="headerlink" href="#fix-restrain-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID restrain keyword args ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>restrain = style name of this fix command</li>
 <li>one or more keyword/arg pairs may be appended</li>
 <li>keyword = <em>bond</em> or <em>angle</em> or <em>dihedral</em></li>
 </ul>
 <pre class="literal-block">
 <em>bond</em> args = atom1 atom2 Kstart Kstop r0
-    atom1,atom2 = IDs of 2 atoms in bond
-    Kstart,Kstop = restraint coefficients at start/end of run (energy units)
-    r0 = equilibrium bond distance (distance units)
-  <em>angle</em> args = atom1 atom2 atom3 Kstart Kstop theta0
-    atom1,atom2,atom3 = IDs of 3 atoms in angle, atom2 = middle atom
-    Kstart,Kstop = restraint coefficients at start/end of run (energy units)
-    theta0 = equilibrium angle theta (degrees)
-  <em>dihedral</em> args = atom1 atom2 atom3 atom4 Kstart Kstop phi0
-    atom1,atom2,atom3,atom4 = IDs of 4 atoms in dihedral in linear order
-    Kstart,Kstop = restraint coefficients at start/end of run (energy units)
-    phi0 = equilibrium dihedral angle phi (degrees)
+  atom1,atom2 = IDs of 2 atoms in bond
+  Kstart,Kstop = restraint coefficients at start/end of run (energy units)
+  r0 = equilibrium bond distance (distance units)
+<em>angle</em> args = atom1 atom2 atom3 Kstart Kstop theta0
+  atom1,atom2,atom3 = IDs of 3 atoms in angle, atom2 = middle atom
+  Kstart,Kstop = restraint coefficients at start/end of run (energy units)
+  theta0 = equilibrium angle theta (degrees)
+<em>dihedral</em> args = atom1 atom2 atom3 atom4 Kstart Kstop phi0
+  atom1,atom2,atom3,atom4 = IDs of 4 atoms in dihedral in linear order
+  Kstart,Kstop = restraint coefficients at start/end of run (energy units)
+  phi0 = equilibrium dihedral angle phi (degrees)
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix holdem all restrain bond 45 48 2000.0 2000.0 2.75
 fix holdem all restrain dihedral 1 2 3 4 2000.0 2000.0 120.0
 fix holdem all restrain bond 45 48 2000.0 2000.0 2.75 dihedral 1 2 3 4 2000.0 2000.0 120.0
 fix texas_holdem all restrain dihedral 1 2 3 4 0.0 2000.0 120.0 dihedral 1 2 3 5 0.0 2000.0 -120.0 dihedral 1 2 3 6 0.0 2000.0 0.0
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Restrain the motion of the specified sets of atoms by making them part
 of a bond or angle or dihedral interaction whose strength can vary
 over time during a simulation.  This is functionally equivalent to
 creating a bond or angle or dihedral for the same atoms in a data
 file, as specified by the <a class="reference internal" href="read_data.html"><em>read_data</em></a> command, albeit
 with a time-varying pre-factor coefficient.  For the purpose of
 forcefield parameter-fitting or mapping a molecular potential energy
 surface, this fix reduces the hassle and risk associated with
 modifying data files.  In other words, use this fix to temporarily
 force a molecule to adopt a particular conformation.  To create a
 permanent bond or angle or dihedral, you should modify the data file.</p>
 <p>The group-ID specified by this fix is ignored.</p>
 <p>The second example above applies a restraint to hold the dihedral
 angle formed by atoms 1, 2, 3, and 4 near 120 degrees using a constant
 restraint coefficient.  The fourth example applies similar restraints
 to multiple dihedral angles using a restraint coefficient that
 increases from 0.0 to 2000.0 over the course of the run.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">Adding a force to atoms implies a change in their
 potential energy as they move due to the applied force field.  For
 dynamics via the <a class="reference internal" href="run.html"><em>run</em></a> command, this energy can be added to
 the system&#8217;s potential energy for thermodynamic output (see below).
 For energy minimization via the <a class="reference internal" href="minimize.html"><em>minimize</em></a> command, this
 energy must be added to the system&#8217;s potential energy to formulate a
 self-consistent minimization problem (see below).</p>
 </div>
 <p>In order for a restraint to be effective, the restraint force must
 typically be significantly larger than the forces associated with
 conventional forcefield terms.  If the restraint is applied during a
 dynamics run (as opposed to during an energy minimization), a large
 restraint coefficient can significantly reduce the stable timestep
 size, especially if the atoms are initially far from the preferred
 conformation.  You may need to experiment to determine what value of K
 works best for a given application.</p>
 <p>For the case of finding a minimum energy structure for a single
 molecule with particular restratins (e.g. for fitting forcefield
 parameters or constructing a potential energy surface), commands such
 as the following may be useful:</p>
 <div class="highlight-python"><div class="highlight"><pre># minimize molecule energy with restraints
 velocity all create 600.0 8675309 mom yes rot yes dist gaussian
 fix NVE all nve
 fix TFIX all langevin 600.0 0.0 100 24601
 fix REST all restrain dihedral 2 1 3 8 0.0 5000.0 $*angle1* dihedral 3 1 2 9 0.0 5000.0 $*angle2*
 fix_modify REST energy yes
 run 10000
 fix TFIX all langevin 0.0 0.0 100 24601
 fix REST all restrain dihedral 2 1 3 8 5000.0 5000.0 $*angle1* dihedral 3 1 2 9 5000.0 5000.0 $*angle2*
 fix_modify REST energy yes
 run 10000
 # sanity check for convergence
 minimize 1e-6 1e-9 1000 100000
 # report unrestrained energies
 unfix REST
 run 0
 </pre></div>
 </div>
 <hr class="docutils" />
 <p>The <em>bond</em> keyword applies a bond restraint to the specified atoms
 using the same functional form used by the <a class="reference internal" href="bond_harmonic.html"><em>bond_style harmonic</em></a> command.  The potential associated with
 the restraint is</p>
 <img alt="_images/bond_harmonic.jpg" class="align-center" src="_images/bond_harmonic.jpg" />
 <p>with the following coefficients:</p>
 <ul class="simple">
 <li>K (energy/distance^2)</li>
 <li>r0 (distance)</li>
 </ul>
 <p>K and r0 are specified with the fix.  Note that the usual 1/2 factor
 is included in K.</p>
 <hr class="docutils" />
 <p>The <em>angle</em> keyword applies an angle restraint to the specified atoms
 using the same functional form used by the <a class="reference internal" href="angle_harmonic.html"><em>angle_style harmonic</em></a> command.  The potential associated with
 the restraint is</p>
 <img alt="_images/angle_harmonic.jpg" class="align-center" src="_images/angle_harmonic.jpg" />
 <p>with the following coefficients:</p>
 <ul class="simple">
 <li>K (energy/radian^2)</li>
 <li>theta0 (degrees)</li>
 </ul>
 <p>K and theta0 are specified with the fix.  Note that the usual 1/2
 factor is included in K.</p>
 <hr class="docutils" />
 <p>The <em>dihedral</em> keyword applies a dihedral restraint to the specified
 atoms using a simplified form of the function used by the
 <a class="reference internal" href="dihedral_charmm.html"><em>dihedral_style charmm</em></a> command.  The potential
 associated with the restraint is</p>
 <img alt="_images/dihedral_charmm.jpg" class="align-center" src="_images/dihedral_charmm.jpg" />
 <p>with the following coefficients:</p>
 <ul class="simple">
 <li>K (energy)</li>
 <li>n = 1</li>
 <li>d (degrees) = phi0 + 180</li>
 </ul>
 <p>K and phi0 are specified with the fix.  Note that the value of n is
 hard-wired to 1.  Also note that the energy will be a minimum when the
 current dihedral angle phi is equal to phi0.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.</p>
 <p>The <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> <em>energy</em> option is supported by this
 fix to add the potential energy associated with this fix to the
 system&#8217;s potential energy as part of <a class="reference internal" href="thermo_style.html"><em>thermodynamic output</em></a>.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">If you want the fictitious potential energy associated
 with the added forces to be included in the total potential energy of
 the system (the quantity being minimized), you MUST enable the
 <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> <em>energy</em> option for this fix.</p>
 </div>
 <p>This fix computes a global scalar, which can be accessed by various
 <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  The scalar is the
 potential energy for all the restraints as discussed above. The scalar
 value calculated by this fix is &#8220;extensive&#8221;.</p>
 <p>No parameter of this fix can be used with the <em>start/stop</em> keywords of
 the <a class="reference internal" href="run.html"><em>run</em></a> command.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <blockquote>
 <div>none</div></blockquote>
 <p><strong>Related commands:</strong> none</p>
 <p><strong>Default:</strong> none</p>
 </div>
 </div>
 
 
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   <div class="section" id="fix-rigid-command">
 <span id="index-0"></span><h1>fix rigid command<a class="headerlink" href="#fix-rigid-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="fix-rigid-nve-command">
 <h1>fix rigid/nve command<a class="headerlink" href="#fix-rigid-nve-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="fix-rigid-nvt-command">
 <h1>fix rigid/nvt command<a class="headerlink" href="#fix-rigid-nvt-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="fix-rigid-npt-command">
 <h1>fix rigid/npt command<a class="headerlink" href="#fix-rigid-npt-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="fix-rigid-nph-command">
 <h1>fix rigid/nph command<a class="headerlink" href="#fix-rigid-nph-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="fix-rigid-small-command">
 <h1>fix rigid/small command<a class="headerlink" href="#fix-rigid-small-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="fix-rigid-nve-small-command">
 <h1>fix rigid/nve/small command<a class="headerlink" href="#fix-rigid-nve-small-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="fix-rigid-nvt-small-command">
 <h1>fix rigid/nvt/small command<a class="headerlink" href="#fix-rigid-nvt-small-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="fix-rigid-npt-small-command">
 <h1>fix rigid/npt/small command<a class="headerlink" href="#fix-rigid-npt-small-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="fix-rigid-nph-small-command">
 <h1>fix rigid/nph/small command<a class="headerlink" href="#fix-rigid-nph-small-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID style bodystyle args keyword values ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>style = <em>rigid</em> or <em>rigid/nve</em> or <em>rigid/nvt</em> or <em>rigid/npt</em> or <em>rigid/nph</em> or <em>rigid/small</em> or <em>rigid/nve/small</em> or <em>rigid/nvt/small</em> or <em>rigid/npt/small</em> or <em>rigid/nph/small</em></li>
 <li>bodystyle = <em>single</em> or <em>molecule</em> or <em>group</em></li>
 </ul>
 <pre class="literal-block">
 <em>single</em> args = none
-  <em>molecule</em> args = none
-  <em>group</em> args = N groupID1 groupID2 ...
-    N = # of groups
-    groupID1, groupID2, ... = list of N group IDs
+<em>molecule</em> args = none
+<em>group</em> args = N groupID1 groupID2 ...
+  N = # of groups
+  groupID1, groupID2, ... = list of N group IDs
 </pre>
 <ul class="simple">
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>langevin</em> or <em>temp</em> or <em>iso</em> or <em>aniso</em> or <em>x</em> or <em>y</em> or <em>z</em> or <em>couple</em> or <em>tparam</em> or <em>pchain</em> or <em>dilate</em> or <em>force</em> or <em>torque</em> or <em>infile</em></li>
 </ul>
 <pre class="literal-block">
 <em>langevin</em> values = Tstart Tstop Tperiod seed
-    Tstart,Tstop = desired temperature at start/stop of run (temperature units)
-    Tdamp = temperature damping parameter (time units)
-    seed = random number seed to use for white noise (positive integer)
-  <em>temp</em> values = Tstart Tstop Tdamp
-    Tstart,Tstop = desired temperature at start/stop of run (temperature units)
-    Tdamp = temperature damping parameter (time units)
-  <em>iso</em> or <em>aniso</em> values = Pstart Pstop Pdamp
-    Pstart,Pstop = scalar external pressure at start/end of run (pressure units)
-    Pdamp = pressure damping parameter (time units)
-  <em>x</em> or <em>y</em> or <em>z</em> values = Pstart Pstop Pdamp
-    Pstart,Pstop = external stress tensor component at start/end of run (pressure units)
-    Pdamp = stress damping parameter (time units)
-  <em>couple</em> = <em>none</em> or <em>xyz</em> or <em>xy</em> or <em>yz</em> or <em>xz</em>
-  <em>tparam</em> values = Tchain Titer Torder
-    Tchain = length of Nose/Hoover thermostat chain
-    Titer = number of thermostat iterations performed
-    Torder = 3 or 5 = Yoshida-Suzuki integration parameters
-  <em>pchain</em> values = Pchain
-    Pchain = length of the Nose/Hoover thermostat chain coupled with the barostat
-  <em>dilate</em> value = dilate-group-ID
-    dilate-group-ID = only dilate atoms in this group due to barostat volume changes
-  <em>force</em> values = M xflag yflag zflag
-    M = which rigid body from 1-Nbody (see asterisk form below)
-    xflag,yflag,zflag = off/on if component of center-of-mass force is active
-  <em>torque</em> values = M xflag yflag zflag
-    M = which rigid body from 1-Nbody (see asterisk form below)
-    xflag,yflag,zflag = off/on if component of center-of-mass torque is active
-  <em>infile</em> filename
-    filename = file with per-body values of mass, center-of-mass, moments of inertia
-  <em>mol</em> value = template-ID
-    template-ID = ID of molecule template specified in a separate <a class="reference internal" href="molecule.html"><em>molecule</em></a> command
+  Tstart,Tstop = desired temperature at start/stop of run (temperature units)
+  Tdamp = temperature damping parameter (time units)
+  seed = random number seed to use for white noise (positive integer)
+<em>temp</em> values = Tstart Tstop Tdamp
+  Tstart,Tstop = desired temperature at start/stop of run (temperature units)
+  Tdamp = temperature damping parameter (time units)
+<em>iso</em> or <em>aniso</em> values = Pstart Pstop Pdamp
+  Pstart,Pstop = scalar external pressure at start/end of run (pressure units)
+  Pdamp = pressure damping parameter (time units)
+<em>x</em> or <em>y</em> or <em>z</em> values = Pstart Pstop Pdamp
+  Pstart,Pstop = external stress tensor component at start/end of run (pressure units)
+  Pdamp = stress damping parameter (time units)
+<em>couple</em> = <em>none</em> or <em>xyz</em> or <em>xy</em> or <em>yz</em> or <em>xz</em>
+<em>tparam</em> values = Tchain Titer Torder
+  Tchain = length of Nose/Hoover thermostat chain
+  Titer = number of thermostat iterations performed
+  Torder = 3 or 5 = Yoshida-Suzuki integration parameters
+<em>pchain</em> values = Pchain
+  Pchain = length of the Nose/Hoover thermostat chain coupled with the barostat
+<em>dilate</em> value = dilate-group-ID
+  dilate-group-ID = only dilate atoms in this group due to barostat volume changes
+<em>force</em> values = M xflag yflag zflag
+  M = which rigid body from 1-Nbody (see asterisk form below)
+  xflag,yflag,zflag = off/on if component of center-of-mass force is active
+<em>torque</em> values = M xflag yflag zflag
+  M = which rigid body from 1-Nbody (see asterisk form below)
+  xflag,yflag,zflag = off/on if component of center-of-mass torque is active
+<em>infile</em> filename
+  filename = file with per-body values of mass, center-of-mass, moments of inertia
+<em>mol</em> value = template-ID
+  template-ID = ID of molecule template specified in a separate <a class="reference internal" href="molecule.html"><em>molecule</em></a> command
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix 1 clump rigid single
 fix 1 clump rigid/small molecule
 fix 1 clump rigid single force 1 off off on langevin 1.0 1.0 1.0 428984
 fix 1 polychains rigid/nvt molecule temp 1.0 1.0 5.0
 fix 1 polychains rigid molecule force 1*5 off off off force 6*10 off off on
 fix 1 polychains rigid/small molecule langevin 1.0 1.0 1.0 428984
 fix 2 fluid rigid group 3 clump1 clump2 clump3 torque * off off off
 fix 1 rods rigid/npt molecule temp 300.0 300.0 100.0 iso 0.5 0.5 10.0
 fix 1 particles rigid/npt molecule temp 1.0 1.0 5.0 x 0.5 0.5 1.0 z 0.5 0.5 1.0 couple xz
 fix 1 water rigid/nph molecule iso 0.5 0.5 1.0
 fix 1 particles rigid/npt/small molecule temp 1.0 1.0 1.0 iso 0.5 0.5 1.0
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Treat one or more sets of atoms as independent rigid bodies.  This
 means that each timestep the total force and torque on each rigid body
 is computed as the sum of the forces and torques on its constituent
 particles.  The coordinates, velocities, and orientations of the atoms
 in each body are then updated so that the body moves and rotates as a
 single entity.</p>
 <p>Examples of large rigid bodies are a colloidal particle, or portions
 of a biomolecule such as a protein.</p>
 <p>Example of small rigid bodies are patchy nanoparticles, such as those
 modeled in <a class="reference internal" href="pair_gran.html#zhang"><span>this paper</span></a> by Sharon Glotzer&#8217;s group, clumps of
 granular particles, lipid molecules consiting of one or more point
 dipoles connected to other spheroids or ellipsoids, irregular
 particles built from line segments (2d) or triangles (3d), and
 coarse-grain models of nano or colloidal particles consisting of a
 small number of constituent particles.  Note that the <a class="reference internal" href="fix_shake.html"><em>fix shake</em></a> command can also be used to rigidify small
 molecules of 2, 3, or 4 atoms, e.g. water molecules.  That fix treats
 the constituent atoms as point masses.</p>
 <p>These fixes also update the positions and velocities of the atoms in
 each rigid body via time integration, in the NVE, NVT, NPT, or NPH
 ensemble, as described below.</p>
 <p>There are two main variants of this fix, fix rigid and fix
 rigid/small.  The NVE/NVT/NPT/NHT versions belong to one of the two
 variants, as their style names indicate.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">Not all of the <em>bodystyle</em> options and keyword/value
 options are available for both the <em>rigid</em> and <em>rigid/small</em> variants.
 See details below.</p>
 </div>
 <p>The <em>rigid</em> variant is typically the best choice for a system with a
 small number of large rigid bodies, each of which can extend across
 the domain of many processors.  It operates by creating a single
 global list of rigid bodies, which all processors contribute to.
 MPI_Allreduce operations are performed each timestep to sum the
 contributions from each processor to the force and torque on all the
 bodies.  This operation will not scale well in parallel if large
 numbers of rigid bodies are simulated.</p>
 <p>The <em>rigid/small</em> variant is typically best for a system with a large
 number of small rigid bodies.  Each body is assigned to the atom
 closest to the geometrical center of the body.  The fix operates using
 local lists of rigid bodies owned by each processor and information is
 exchanged and summed via local communication between neighboring
 processors when ghost atom info is accumlated.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">To use <em>rigid/small</em> the ghost atom cutoff must be
 large enough to span the distance between the atom that owns the body
 and every other atom in the body.  This distance value is printed out
 when the rigid bodies are defined.  If the
 <a class="reference internal" href="pair_style.html"><em>pair_style</em></a> cutoff plus neighbor skin does not span
 this distance, then you should use the <a class="reference internal" href="comm_modify.html"><em>comm_modify cutoff</em></a> command with a setting epsilon larger than
 the distance.</p>
 </div>
 <p>Which of the two variants is faster for a particular problem is hard
 to predict.  The best way to decide is to perform a short test run.
 Both variants should give identical numerical answers for short runs.
 Long runs should give statistically similar results, but round-off
 differences may accumulate to produce divergent trajectories.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">You should not update the atoms in rigid bodies via
 other time-integration fixes (e.g. <a class="reference internal" href="fix_nve.html"><em>fix nve</em></a>, <code class="xref doc docutils literal"><span class="pre">fix</span> <span class="pre">nvt</span></code>, <code class="xref doc docutils literal"><span class="pre">fix</span> <span class="pre">npt</span></code>), or you will be integrating
 their motion more than once each timestep.  When performing a hybrid
 simulation with some atoms in rigid bodies, and some not, a separate
 time integration fix like <a class="reference internal" href="fix_nve.html"><em>fix nve</em></a> or <a class="reference internal" href="fix_nh.html"><em>fix nvt</em></a> should be used for the non-rigid particles.</p>
 </div>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">These fixes are overkill if you simply want to hold a
 collection of atoms stationary or have them move with a constant
 velocity.  A simpler way to hold atoms stationary is to not include
 those atoms in your time integration fix.  E.g. use &#8220;fix 1 mobile nve&#8221;
 instead of &#8220;fix 1 all nve&#8221;, where &#8220;mobile&#8221; is the group of atoms that
 you want to move.  You can move atoms with a constant velocity by
 assigning them an initial velocity (via the <a class="reference internal" href="velocity.html"><em>velocity</em></a>
 command), setting the force on them to 0.0 (via the <a class="reference internal" href="fix_setforce.html"><em>fix setforce</em></a> command), and integrating them as usual
 (e.g. via the <a class="reference internal" href="fix_nve.html"><em>fix nve</em></a> command).</p>
 </div>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">The aggregate properties of each rigid body are
 calculated one time at the start of the first simulation run after
 this fix is specified.  The properties include the position and
 velocity of the center-of-mass of the body, its moments of inertia,
 and its angular momentum.  This is done using the properties of the
 constituent atoms of the body at that point in time (or see the
 <em>infile</em> keyword option).  Thereafter, changing properties of
 individual atoms in the body will have no effect on a rigid body&#8217;s
 dynamics, unless they effect the <a class="reference internal" href="pair_style.html"><em>pair_style</em></a>
 interactions that individual particles are part of.  For example, you
 might think you could displace the atoms in a body or add a large
 velocity to each atom in a body to make it move in a desired direction
 before a 2nd run is performed, using the <a class="reference internal" href="set.html"><em>set</em></a> or
 <a class="reference internal" href="displace_atoms.html"><em>displace_atoms</em></a> or <a class="reference internal" href="velocity.html"><em>velocity</em></a>
 command.  But these commands will not affect the internal attributes
 of the body, and the position and velocity or individual atoms in the
 body will be reset when time integration starts.</p>
 </div>
 <hr class="docutils" />
 <p>Each rigid body must have two or more atoms.  An atom can belong to at
 most one rigid body.  Which atoms are in which bodies can be defined
 via several options.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">With fix rigid/small, which requires bodystyle
 <em>molecule</em>, you can define a system that has no rigid bodies
 initially.  This is useful when you are using the <em>mol</em> keyword in
 conjunction with another fix that is adding rigid bodies on-the-fly,
 such as <a class="reference internal" href="fix_deposit.html"><em>fix deposit</em></a> or <a class="reference internal" href="fix_pour.html"><em>fix pour</em></a>.</p>
 </div>
 <p>For bodystyle <em>single</em> the entire fix group of atoms is treated as one
 rigid body.  This option is only allowed for fix rigid and its
 sub-styles.</p>
 <p>For bodystyle <em>molecule</em>, each set of atoms in the fix group with a
 different molecule ID is treated as a rigid body.  This option is
 allowed for fix rigid and fix rigid/small, and their sub-styles.  Note
 that atoms with a molecule ID = 0 will be treated as a single rigid
 body.  For a system with atomic solvent (typically this is atoms with
 molecule ID = 0) surrounding rigid bodies, this may not be what you
 want.  Thus you should be careful to use a fix group that only
 includes atoms you want to be part of rigid bodies.</p>
 <p>For bodystyle <em>group</em>, each of the listed groups is treated as a
 separate rigid body.  Only atoms that are also in the fix group are
 included in each rigid body.  This option is only allowed for fix
 rigid and its sub-styles.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">To compute the initial center-of-mass position and
 other properties of each rigid body, the image flags for each atom in
 the body are used to &#8220;unwrap&#8221; the atom coordinates.  Thus you must
 insure that these image flags are consistent so that the unwrapping
 creates a valid rigid body (one where the atoms are close together),
 particularly if the atoms in a single rigid body straddle a periodic
 boundary.  This means the input data file or restart file must define
 the image flags for each atom consistently or that you have used the
 <a class="reference internal" href="set.html"><em>set</em></a> command to specify them correctly.  If a dimension is
 non-periodic then the image flag of each atom must be 0 in that
 dimension, else an error is generated.</p>
 </div>
 <p>The <em>force</em> and <em>torque</em> keywords discussed next are only allowed for
 fix rigid and its sub-styles.</p>
 <p>By default, each rigid body is acted on by other atoms which induce an
 external force and torque on its center of mass, causing it to
 translate and rotate.  Components of the external center-of-mass force
 and torque can be turned off by the <em>force</em> and <em>torque</em> keywords.
 This may be useful if you wish a body to rotate but not translate, or
 vice versa, or if you wish it to rotate or translate continuously
 unaffected by interactions with other particles.  Note that if you
 expect a rigid body not to move or rotate by using these keywords, you
 must insure its initial center-of-mass translational or angular
 velocity is 0.0.  Otherwise the initial translational or angular
 momentum the body has will persist.</p>
 <p>An xflag, yflag, or zflag set to <em>off</em> means turn off the component of
 force of torque in that dimension.  A setting of <em>on</em> means turn on
 the component, which is the default.  Which rigid body(s) the settings
 apply to is determined by the first argument of the <em>force</em> and
 <em>torque</em> keywords.  It can be an integer M from 1 to Nbody, where
 Nbody is the number of rigid bodies defined.  A wild-card asterisk can
 be used in place of, or in conjunction with, the M argument to set the
 flags for multiple rigid bodies.  This takes the form &#8220;*&#8221; or &#8220;<em>n&#8221; or
 &#8220;n</em>&#8221; or &#8220;m*n&#8221;.  If N = the number of rigid bodies, then an asterisk
 with no numeric values means all bodies from 1 to N.  A leading
 asterisk means all bodies from 1 to n (inclusive).  A trailing
 asterisk means all bodies from n to N (inclusive).  A middle asterisk
 means all types from m to n (inclusive).  Note that you can use the
 <em>force</em> or <em>torque</em> keywords as many times as you like.  If a
 particular rigid body has its component flags set multiple times, the
 settings from the final keyword are used.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">For computational efficiency, you may wish to turn off
 pairwise and bond interactions within each rigid body, as they no
 longer contribute to the motion.  The <a class="reference internal" href="neigh_modify.html"><em>neigh_modify exclude</em></a> and <a class="reference internal" href="delete_bonds.html"><em>delete_bonds</em></a>
 commands are used to do this.  If the rigid bodies have strongly
 overalapping atoms, you may need to turn off these interactions to
 avoid numerical problems due to large equal/opposite intra-body forces
 swamping the contribution of small inter-body forces.</p>
 </div>
 <p>For computational efficiency, you should typically define one fix
 rigid or fix rigid/small command which includes all the desired rigid
 bodies.  LAMMPS will allow multiple rigid fixes to be defined, but it
 is more expensive.</p>
 <hr class="docutils" />
 <p>The constituent particles within a rigid body can be point particles
 (the default in LAMMPS) or finite-size particles, such as spheres or
 ellipsoids or line segments or triangles.  See the <a class="reference internal" href="atom_style.html"><em>atom_style sphere and ellipsoid and line and tri</em></a> commands for more
 details on these kinds of particles.  Finite-size particles contribute
 differently to the moment of inertia of a rigid body than do point
 particles.  Finite-size particles can also experience torque (e.g. due
 to <a class="reference internal" href="pair_gran.html"><em>frictional granular interactions</em></a>) and have an
 orientation.  These contributions are accounted for by these fixes.</p>
 <p>Forces between particles within a body do not contribute to the
 external force or torque on the body.  Thus for computational
 efficiency, you may wish to turn off pairwise and bond interactions
 between particles within each rigid body.  The <a class="reference internal" href="neigh_modify.html"><em>neigh_modify exclude</em></a> and <a class="reference internal" href="delete_bonds.html"><em>delete_bonds</em></a>
 commands are used to do this.  For finite-size particles this also
 means the particles can be highly overlapped when creating the rigid
 body.</p>
 <hr class="docutils" />
 <p>The <em>rigid</em> and <em>rigid/small</em> and <em>rigid/nve</em> styles perform constant
 NVE time integration.  The only difference is that the <em>rigid</em> and
 <em>rigid/small</em> styles use an integration technique based on Richardson
 iterations.  The <em>rigid/nve</em> style uses the methods described in the
 paper by <a class="reference internal" href="#miller"><span>Miller</span></a>, which are thought to provide better energy
 conservation than an iterative approach.</p>
 <p>The <em>rigid/nvt</em> and <em>rigid/nvt/small</em> styles performs constant NVT
 integration using a Nose/Hoover thermostat with chains as described
 originally in <a class="reference internal" href="#hoover"><span>(Hoover)</span></a> and <a class="reference internal" href="#martyna"><span>(Martyna)</span></a>, which
 thermostats both the translational and rotational degrees of freedom
 of the rigid bodies.  The rigid-body algorithm used by <em>rigid/nvt</em>
 is described in the paper by <a class="reference internal" href="#kamberaj"><span>Kamberaj</span></a>.</p>
 <p>The <em>rigid/npt</em> and <em>rigid/nph</em> (and their /small counterparts) styles
 perform constant NPT or NPH integration using a Nose/Hoover barostat
 with chains.  For the NPT case, the same Nose/Hoover thermostat is also
 used as with <em>rigid/nvt</em>.</p>
 <p>The barostat parameters are specified using one or more of the <em>iso</em>,
 <em>aniso</em>, <em>x</em>, <em>y</em>, <em>z</em> and <em>couple</em> keywords.  These keywords give you
 the ability to specify 3 diagonal components of the external stress
 tensor, and to couple these components together so that the dimensions
 they represent are varied together during a constant-pressure
 simulation.  The effects of these keywords are similar to those
 defined in <a class="reference internal" href="fix_nh.html"><em>fix npt/nph</em></a></p>
 <div class="admonition note">
 <p class="first admonition-title">Note</p>
 <p class="last">Currently the <em>rigid/npt</em> and <em>rigid/nph</em> (and their /small
 counterparts) styles do not support triclinic (non-orthongonal) boxes.</p>
 </div>
 <p>The target pressures for each of the 6 components of the stress tensor
 can be specified independently via the <em>x</em>, <em>y</em>, <em>z</em> keywords, which
 correspond to the 3 simulation box dimensions.  For each component,
 the external pressure or tensor component at each timestep is a ramped
 value during the run from <em>Pstart</em> to <em>Pstop</em>. If a target pressure is
 specified for a component, then the corresponding box dimension will
 change during a simulation.  For example, if the <em>y</em> keyword is used,
 the y-box length will change.  A box dimension will not change if that
 component is not specified, although you have the option to change
 that dimension via the <a class="reference internal" href="fix_deform.html"><em>fix deform</em></a> command.</p>
 <p>For all barostat keywords, the <em>Pdamp</em> parameter operates like the
 <em>Tdamp</em> parameter, determining the time scale on which pressure is
 relaxed.  For example, a value of 10.0 means to relax the pressure in
 a timespan of (roughly) 10 time units (e.g. tau or fmsec or psec - see
 the <a class="reference internal" href="units.html"><em>units</em></a> command).</p>
 <p>Regardless of what atoms are in the fix group (the only atoms which
 are time integrated), a global pressure or stress tensor is computed
 for all atoms.  Similarly, when the size of the simulation box is
 changed, all atoms are re-scaled to new positions, unless the keyword
 <em>dilate</em> is specified with a <em>dilate-group-ID</em> for a group that
 represents a subset of the atoms.  This can be useful, for example, to
 leave the coordinates of atoms in a solid substrate unchanged and
 controlling the pressure of a surrounding fluid.  Another example is a
 system consisting of rigid bodies and point particles where the
 barostat is only coupled with the rigid bodies.  This option should be
 used with care, since it can be unphysical to dilate some atoms and
 not others, because it can introduce large, instantaneous
 displacements between a pair of atoms (one dilated, one not) that are
 far from the dilation origin.</p>
 <p>The <em>couple</em> keyword allows two or three of the diagonal components of
 the pressure tensor to be &#8220;coupled&#8221; together.  The value specified
 with the keyword determines which are coupled.  For example, <em>xz</em>
 means the <em>Pxx</em> and <em>Pzz</em> components of the stress tensor are coupled.
 <em>Xyz</em> means all 3 diagonal components are coupled.  Coupling means two
 things: the instantaneous stress will be computed as an average of the
 corresponding diagonal components, and the coupled box dimensions will
 be changed together in lockstep, meaning coupled dimensions will be
 dilated or contracted by the same percentage every timestep.  The
 <em>Pstart</em>, <em>Pstop</em>, <em>Pdamp</em> parameters for any coupled dimensions must
 be identical.  <em>Couple xyz</em> can be used for a 2d simulation; the <em>z</em>
 dimension is simply ignored.</p>
 <p>The <em>iso</em> and <em>aniso</em> keywords are simply shortcuts that are
 equivalent to specifying several other keywords together.</p>
 <p>The keyword <em>iso</em> means couple all 3 diagonal components together when
 pressure is computed (hydrostatic pressure), and dilate/contract the
 dimensions together.  Using &#8220;iso Pstart Pstop Pdamp&#8221; is the same as
 specifying these 4 keywords:</p>
 <div class="highlight-python"><div class="highlight"><pre>x Pstart Pstop Pdamp
 y Pstart Pstop Pdamp
 z Pstart Pstop Pdamp
 couple xyz
 </pre></div>
 </div>
 <p>The keyword <em>aniso</em> means <em>x</em>, <em>y</em>, and <em>z</em> dimensions are controlled
 independently using the <em>Pxx</em>, <em>Pyy</em>, and <em>Pzz</em> components of the
 stress tensor as the driving forces, and the specified scalar external
 pressure.  Using &#8220;aniso Pstart Pstop Pdamp&#8221; is the same as specifying
 these 4 keywords:</p>
 <div class="highlight-python"><div class="highlight"><pre>x Pstart Pstop Pdamp
 y Pstart Pstop Pdamp
 z Pstart Pstop Pdamp
 couple none
 </pre></div>
 </div>
 <hr class="docutils" />
 <p>The keyword/value option pairs are used in the following ways.</p>
 <p>The <em>langevin</em> and <em>temp</em> and <em>tparam</em> keywords perform thermostatting
 of the rigid bodies, altering both their translational and rotational
 degrees of freedom.  What is meant by &#8220;temperature&#8221; of a collection of
 rigid bodies and how it can be monitored via the fix output is
 discussed below.</p>
 <p>The <em>langevin</em> keyword applies a Langevin thermostat to the constant
 NVE time integration performed by either the <em>rigid</em> or <em>rigid/small</em>
 or <em>rigid/nve</em> styles.  It cannot be used with the <em>rigid/nvt</em> style.
 The desired temperature at each timestep is a ramped value during the
 run from <em>Tstart</em> to <em>Tstop</em>.  The <em>Tdamp</em> parameter is specified in
 time units and determines how rapidly the temperature is relaxed.  For
 example, a value of 100.0 means to relax the temperature in a timespan
 of (roughly) 100 time units (tau or fmsec or psec - see the
 <a class="reference internal" href="units.html"><em>units</em></a> command).  The random # <em>seed</em> must be a positive
 integer.</p>
 <p>The way that Langevin thermostatting operates is explained on the <a class="reference internal" href="fix_langevin.html"><em>fix langevin</em></a> doc page.  If you wish to simply viscously
 damp the rotational motion without thermostatting, you can set
 <em>Tstart</em> and <em>Tstop</em> to 0.0, which means only the viscous drag term in
 the Langevin thermostat will be applied.  See the discussion on the
 <code class="xref doc docutils literal"><span class="pre">fix</span> <span class="pre">viscous</span></code> doc page for details.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">When the <em>langevin</em> keyword is used with fix rigid
 versus fix rigid/small, different dynamics will result for parallel
 runs.  This is because of the way random numbers are used in the two
 cases.  The dynamics for the two cases should be statistically
 similar, but will not be identical, even for a single timestep.</p>
 </div>
 <p>The <em>temp</em> and <em>tparam</em> keywords apply a Nose/Hoover thermostat to the
 NVT time integration performed by the <em>rigid/nvt</em> style.  They cannot
 be used with the <em>rigid</em> or <em>rigid/small</em> or <em>rigid/nve</em> styles.  The
 desired temperature at each timestep is a ramped value during the run
 from <em>Tstart</em> to <em>Tstop</em>.  The <em>Tdamp</em> parameter is specified in time
 units and determines how rapidly the temperature is relaxed.  For
 example, a value of 100.0 means to relax the temperature in a timespan
 of (roughly) 100 time units (tau or fmsec or psec - see the
 <a class="reference internal" href="units.html"><em>units</em></a> command).</p>
 <p>Nose/Hoover chains are used in conjunction with this thermostat.  The
 <em>tparam</em> keyword can optionally be used to change the chain settings
 used.  <em>Tchain</em> is the number of thermostats in the Nose Hoover chain.
 This value, along with <em>Tdamp</em> can be varied to dampen undesirable
 oscillations in temperature that can occur in a simulation.  As a rule
 of thumb, increasing the chain length should lead to smaller
 oscillations. The keyword <em>pchain</em> specifies the number of
 thermostats in the chain thermostatting the barostat degrees of
 freedom.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">There are alternate ways to thermostat a system of
 rigid bodies.  You can use <a class="reference internal" href="fix_langevin.html"><em>fix langevin</em></a> to treat
 the individual particles in the rigid bodies as effectively immersed
 in an implicit solvent, e.g. a Brownian dynamics model.  For hybrid
 systems with both rigid bodies and solvent particles, you can
 thermostat only the solvent particles that surround one or more rigid
 bodies by appropriate choice of groups in the compute and fix commands
 for temperature and thermostatting.  The solvent interactions with the
 rigid bodies should then effectively thermostat the rigid body
 temperature as well without use of the Langevin or Nose/Hoover options
 associated with the fix rigid commands.</p>
 </div>
 <hr class="docutils" />
 <p>The <em>mol</em> keyword can only be used with fix rigid/small.  It must be
 used when other commands, such as <a class="reference internal" href="fix_deposit.html"><em>fix deposit</em></a> or
 <a class="reference internal" href="fix_pour.html"><em>fix pour</em></a>, add rigid bodies on-the-fly during a
 simulation.  You specify a <em>template-ID</em> previously defined using the
 <a class="reference internal" href="molecule.html"><em>molecule</em></a> command, which reads a file that defines the
 molecule.  You must use the same <em>template-ID</em> that the other fix
 which is adding rigid bodies uses.  The coordinates, atom types, atom
 diameters, center-of-mass, and moments of inertia can be specified in
 the molecule file.  See the <a class="reference internal" href="molecule.html"><em>molecule</em></a> command for
 details.  The only settings required to be in this file are the
 coordinates and types of atoms in the molecule, in which case the
 molecule command calculates the other quantities itself.</p>
 <p>Note that these other fixes create new rigid bodies, in addition to
 those defined initially by this fix via the <em>bodystyle</em> setting.</p>
 <p>Also note that when using the <em>mol</em> keyword, extra restart information
 about all rigid bodies is written out whenever a restart file is
 written out.  See the IMPORTANT NOTE in the next section for details.</p>
 <hr class="docutils" />
 <p>The <em>infile</em> keyword allows a file of rigid body attributes to be read
 in from a file, rather then having LAMMPS compute them.  There are 5
 such attributes: the total mass of the rigid body, its center-of-mass
 position, its 6 moments of inertia, its center-of-mass velocity, and
 the 3 image flags of the center-of-mass position.  For rigid bodies
 consisting of point particles or non-overlapping finite-size
 particles, LAMMPS can compute these values accurately.  However, for
 rigid bodies consisting of finite-size particles which overlap each
 other, LAMMPS will ignore the overlaps when computing these 4
 attributes.  The amount of error this induces depends on the amount of
 overlap.  To avoid this issue, the values can be pre-computed
 (e.g. using Monte Carlo integration).</p>
 <p>The format of the file is as follows.  Note that the file does not
 have to list attributes for every rigid body integrated by fix rigid.
 Only bodies which the file specifies will have their computed
 attributes overridden.  The file can contain initial blank lines or
 comment lines starting with &#8220;#&#8221; which are ignored.  The first
 non-blank, non-comment line should list N = the number of lines to
 follow.  The N successive lines contain the following information:</p>
 <div class="highlight-python"><div class="highlight"><pre>ID1 masstotal xcm ycm zcm ixx iyy izz ixy ixz iyz vxcm vycm vzcm lx ly lz ixcm iycm izcm
 ID2 masstotal xcm ycm zcm ixx iyy izz ixy ixz iyz vxcm vycm vzcm lx ly lz ixcm iycm izcm
 ...
 IDN masstotal xcm ycm zcm ixx iyy izz ixy ixz iyz vxcm vycm vzcm lx ly lz ixcm iycm izcm
 </pre></div>
 </div>
 <p>The rigid body IDs are all positive integers.  For the <em>single</em>
 bodystyle, only an ID of 1 can be used.  For the <em>group</em> bodystyle,
 IDs from 1 to Ng can be used where Ng is the number of specified
 groups.  For the <em>molecule</em> bodystyle, use the molecule ID for the
 atoms in a specific rigid body as the rigid body ID.</p>
 <p>The masstotal and center-of-mass coordinates (xcm,ycm,zcm) are
 self-explanatory.  The center-of-mass should be consistent with what
 is calculated for the position of the rigid body with all its atoms
 unwrapped by their respective image flags.  If this produces a
 center-of-mass that is outside the simulation box, LAMMPS wraps it
 back into the box.</p>
 <p>The 6 moments of inertia (ixx,iyy,izz,ixy,ixz,iyz) should be the
 values consistent with the current orientation of the rigid body
 around its center of mass.  The values are with respect to the
 simulation box XYZ axes, not with respect to the prinicpal axes of the
 rigid body itself.  LAMMPS performs the latter calculation internally.</p>
 <p>The (vxcm,vycm,vzcm) values are the velocity of the center of mass.
 The (lx,ly,lz) values are the angular momentum of the body.  The
 (vxcm,vycm,vzcm) and (lx,ly,lz) values can simply be set to 0 if you
 wish the body to have no initial motion.</p>
 <p>The (ixcm,iycm,izcm) values are the image flags of the center of mass
 of the body.  For periodic dimensions, they specify which image of the
 simulation box the body is considered to be in.  An image of 0 means
 it is inside the box as defined.  A value of 2 means add 2 box lengths
 to get the true value.  A value of -1 means subtract 1 box length to
 get the true value.  LAMMPS updates these flags as the rigid bodies
 cross periodic boundaries during the simulation.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">If you use the <em>infile</em> or <em>mol</em> keywords and write
 restart files during a simulation, then each time a restart file is
 written, the fix also write an auxiliary restart file with the name
 rfile.rigid, where &#8220;rfile&#8221; is the name of the restart file,
 e.g. tmp.restart.10000 and tmp.restart.10000.rigid.  This auxiliary
 file is in the same format described above.  Thus it can be used in a
 new input script that restarts the run and re-specifies a rigid fix
 using an <em>infile</em> keyword and the appropriate filename.  Note that the
 auxiliary file will contain one line for every rigid body, even if the
 original file only listed a subset of the rigid bodies.</p>
 </div>
 <hr class="docutils" />
 <p>If you use a <a class="reference internal" href="compute.html"><em>temperature compute</em></a> with a group that
 includes particles in rigid bodies, the degrees-of-freedom removed by
 each rigid body are accounted for in the temperature (and pressure)
 computation, but only if the temperature group includes all the
 particles in a particular rigid body.</p>
 <p>A 3d rigid body has 6 degrees of freedom (3 translational, 3
 rotational), except for a collection of point particles lying on a
 straight line, which has only 5, e.g a dimer.  A 2d rigid body has 3
 degrees of freedom (2 translational, 1 rotational).</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">You may wish to explicitly subtract additional
 degrees-of-freedom if you use the <em>force</em> and <em>torque</em> keywords to
 eliminate certain motions of one or more rigid bodies.  LAMMPS does
 not do this automatically.</p>
 </div>
 <p>The rigid body contribution to the pressure of the system (virial) is
 also accounted for by this fix.</p>
 <hr class="docutils" />
 <p>If your simlulation is a hybrid model with a mixture of rigid bodies
 and non-rigid particles (e.g. solvent) there are several ways these
 rigid fixes can be used in tandem with <a class="reference internal" href="fix_nve.html"><em>fix nve</em></a>, <a class="reference internal" href="fix_nh.html"><em>fix nvt</em></a>, <a class="reference internal" href="fix_nh.html"><em>fix npt</em></a>, and <a class="reference internal" href="fix_nh.html"><em>fix nph</em></a>.</p>
 <p>If you wish to perform NVE dynamics (no thermostatting or
 barostatting), use fix rigid or fix rigid/nve to integrate the rigid
 bodies, and <a class="reference internal" href="fix_nve.html"><em>fix nve</em></a> to integrate the non-rigid
 particles.</p>
 <p>If you wish to perform NVT dynamics (thermostatting, but no
 barostatting), you can use fix rigid/nvt for the rigid bodies, and any
 thermostatting fix for the non-rigid particles (<a class="reference internal" href="fix_nh.html"><em>fix nvt</em></a>,
 <a class="reference internal" href="fix_langevin.html"><em>fix langevin</em></a>, <a class="reference internal" href="fix_temp_berendsen.html"><em>fix temp/berendsen</em></a>).  You can also use fix rigid
 or fix rigid/nve for the rigid bodies and thermostat them using <a class="reference internal" href="fix_langevin.html"><em>fix langevin</em></a> on the group that contains all the
 particles in the rigid bodies.  The net force added by <a class="reference internal" href="fix_langevin.html"><em>fix langevin</em></a> to each rigid body effectively thermostats
 its translational center-of-mass motion.  Not sure how well it does at
 thermostatting its rotational motion.</p>
 <p>If you with to perform NPT or NPH dynamics (barostatting), you cannot
 use both <a class="reference internal" href="fix_nh.html"><em>fix npt</em></a> and fix rigid/npt (or the nph
 variants).  This is because there can only be one fix which monitors
 the global pressure and changes the simulation box dimensions.  So you
 have 3 choices:</p>
 <ul class="simple">
 <li>Use fix rigid/npt for the rigid bodies.  Use the <em>dilate</em> all option
 so that it will dilate the positions of the non-rigid particles as
 well.  Use <a class="reference internal" href="fix_nh.html"><em>fix nvt</em></a> (or any other thermostat) for the
 non-rigid particles.</li>
 <li>Use <a class="reference internal" href="fix_nh.html"><em>fix npt</em></a> for the group of non-rigid particles.  Use
 the <em>dilate</em> all option so that it will dilate the center-of-mass
 positions of the rigid bodies as well.  Use fix rigid/nvt for the
 rigid bodies.</li>
 <li>Use <a class="reference internal" href="fix_press_berendsen.html"><em>fix press/berendsen</em></a> to compute the
 pressure and change the box dimensions.  Use fix rigid/nvt for the
 rigid bodies.  Use <a class="reference external" href="fix_nh.thml">fix nvt</a> (or any other thermostat) for
 the non-rigid particles.</li>
 </ul>
 <p>In all case, the rigid bodies and non-rigid particles both contribute
 to the global pressure and the box is scaled the same by any of the
 barostatting fixes.</p>
 <p>You could even use the 2nd and 3rd options for a non-hybrid simulation
 consisting of only rigid bodies, assuming you give <a class="reference internal" href="fix_nh.html"><em>fix npt</em></a> an empty group, though it&#8217;s an odd thing to do.  The
 barostatting fixes (<a class="reference internal" href="fix_nh.html"><em>fix npt</em></a> and <a class="reference internal" href="fix_press_berendsen.html"><em>fix press/berensen</em></a>) will monitor the pressure
 and change the box dimensions, but not time integrate any particles.
 The integration of the rigid bodies will be performed by fix
 rigid/nvt.</p>
 <hr class="docutils" />
 <p>Styles with a <em>cuda</em>, <em>gpu</em>, <em>intel</em>, <em>kk</em>, <em>omp</em>, or <em>opt</em> suffix are
 functionally the same as the corresponding style without the suffix.
 They have been optimized to run faster, depending on your available
 hardware, as discussed in <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a>
 of the manual.  The accelerated styles take the same arguments and
 should produce the same results, except for round-off and precision
 issues.</p>
 <p>These accelerated styles are part of the USER-CUDA, GPU, USER-INTEL,
 KOKKOS, USER-OMP and OPT packages, respectively.  They are only
 enabled if LAMMPS was built with those packages.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 <p>You can specify the accelerated styles explicitly in your input script
 by including their suffix, or you can use the <a class="reference internal" href="Section_start.html#start-7"><span>-suffix command-line switch</span></a> when you invoke LAMMPS, or you can
 use the <a class="reference internal" href="suffix.html"><em>suffix</em></a> command in your input script.</p>
 <p>See <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a> of the manual for
 more instructions on how to use the accelerated styles effectively.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about the <em>rigid</em> and <em>rigid/small</em> and <em>rigid/nve</em>
 fixes are written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.  The
 exception is if the <em>infile</em> or <em>mol</em> keyword is used, in which case
 an auxiliary file is written out with rigid body information each time
 a restart file is written, as explained above for the <em>infile</em>
 keyword.  For style <em>rigid/nvt</em> the state of the Nose/Hoover
 thermostat is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.  See the
 <a class="reference internal" href="read_restart.html"><em>read_restart</em></a> command for info on how to re-specify
 a fix in an input script that reads a restart file, so that the
 operation of the fix continues in an uninterrupted fashion.</p>
 <p>The <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> <em>energy</em> option is supported by the
 rigid/nvt fix to add the energy change induced by the thermostatting
 to the system&#8217;s potential energy as part of <a class="reference internal" href="thermo_style.html"><em>thermodynamic output</em></a>.</p>
 <p>The <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> <em>temp</em> and <em>press</em> options are
 supported by the rigid/npt and rigid/nph fixes to change the computes used
 to calculate the instantaneous pressure tensor. Note that the rigid/nvt fix
 does not use any external compute to compute instantaneous temperature.</p>
 <p>The <em>rigid</em> and <em>rigid/small</em> and <em>rigid/nve</em> fixes compute a global
 scalar which can be accessed by various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  The scalar value calculated by
 these fixes is &#8220;intensive&#8221;.  The scalar is the current temperature of
 the collection of rigid bodies.  This is averaged over all rigid
 bodies and their translational and rotational degrees of freedom.  The
 translational energy of a rigid body is 1/2 m v^2, where m = total
 mass of the body and v = the velocity of its center of mass.  The
 rotational energy of a rigid body is 1/2 I w^2, where I = the moment
 of inertia tensor of the body and w = its angular velocity.  Degrees
 of freedom constrained by the <em>force</em> and <em>torque</em> keywords are
 removed from this calculation, but only for the <em>rigid</em> and
 <em>rigid/nve</em> fixes.</p>
 <p>The <em>rigid/nvt</em>, <em>rigid/npt</em>, and <em>rigid/nph</em> fixes compute a global
 scalar which can be accessed by various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  The scalar value calculated by
 these fixes is &#8220;extensive&#8221;.  The scalar is the cumulative energy
 change due to the thermostatting and barostatting the fix performs.</p>
 <p>All of the <em>rigid</em> fixes except <em>rigid/small</em> compute a global array
 of values which can be accessed by various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  The number of rows in the
 array is equal to the number of rigid bodies.  The number of columns
 is 15.  Thus for each rigid body, 15 values are stored: the xyz coords
 of the center of mass (COM), the xyz components of the COM velocity,
 the xyz components of the force acting on the COM, the xyz components
 of the torque acting on the COM, and the xyz image flags of the COM.</p>
 <p>The center of mass (COM) for each body is similar to unwrapped
 coordinates written to a dump file.  It will always be inside (or
 slightly outside) the simulation box.  The image flags have the same
 meaning as image flags for atom positions (see the &#8220;dump&#8221; command).
 This means you can calculate the unwrapped COM by applying the image
 flags to the COM, the same as when unwrapped coordinates are written
 to a dump file.</p>
 <p>The force and torque values in the array are not affected by the
 <em>force</em> and <em>torque</em> keywords in the fix rigid command; they reflect
 values before any changes are made by those keywords.</p>
 <p>The ordering of the rigid bodies (by row in the array) is as follows.
 For the <em>single</em> keyword there is just one rigid body.  For the
 <em>molecule</em> keyword, the bodies are ordered by ascending molecule ID.
 For the <em>group</em> keyword, the list of group IDs determines the ordering
 of bodies.</p>
 <p>The array values calculated by these fixes are &#8220;intensive&#8221;, meaning
 they are independent of the number of atoms in the simulation.</p>
 <p>No parameter of these fixes can be used with the <em>start/stop</em> keywords
 of the <a class="reference internal" href="run.html"><em>run</em></a> command.  These fixes are not invoked during
 <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>These fixes are all part of the RIGID package.  It is only enabled if
 LAMMPS was built with that package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 <p>Assigning a temperature via the <a class="reference internal" href="velocity.html"><em>velocity create</em></a>
 command to a system with <a class="reference internal" href=""><em>rigid bodies</em></a> may not have
 the desired outcome for two reasons.  First, the velocity command can
 be invoked before the rigid-body fix is invoked or initialized and the
 number of adjusted degrees of freedom (DOFs) is known.  Thus it is not
 possible to compute the target temperature correctly.  Second, the
 assigned velocities may be partially canceled when constraints are
 first enforced, leading to a different temperature than desired.  A
 workaround for this is to perform a <a class="reference internal" href="run.html"><em>run 0</em></a> command, which
 insures all DOFs are accounted for properly, and then rescale the
 temperature to the desired value before performing a simulation.  For
 example:</p>
 <div class="highlight-python"><div class="highlight"><pre>velocity all create 300.0 12345
 run 0                             # temperature may not be 300K
 velocity all scale 300.0          # now it should be
 </pre></div>
 </div>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="delete_bonds.html"><em>delete_bonds</em></a>, <a class="reference internal" href="neigh_modify.html"><em>neigh_modify</em></a>
 exclude, <a class="reference internal" href="fix_shake.html"><em>fix shake</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The option defaults are force * on on on and torque * on on on,
 meaning all rigid bodies are acted on by center-of-mass force and
 torque.  Also Tchain = Pchain = 10, Titer = 1, Torder = 3.</p>
 <hr class="docutils" />
 <p id="hoover"><strong>(Hoover)</strong> Hoover, Phys Rev A, 31, 1695 (1985).</p>
 <p id="kamberaj"><strong>(Kamberaj)</strong> Kamberaj, Low, Neal, J Chem Phys, 122, 224114 (2005).</p>
 <p id="martyna"><strong>(Martyna)</strong> Martyna, Klein, Tuckerman, J Chem Phys, 97, 2635 (1992);
 Martyna, Tuckerman, Tobias, Klein, Mol Phys, 87, 1117.</p>
 <p id="miller"><strong>(Miller)</strong> Miller, Eleftheriou, Pattnaik, Ndirango, and Newns,
 J Chem Phys, 116, 8649 (2002).</p>
 <p id="zhang"><strong>(Zhang)</strong> Zhang, Glotzer, Nanoletters, 4, 1407-1413 (2004).</p>
 </div>
 </div>
 
 
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           <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article">
            <div itemprop="articleBody">
             
   <div class="section" id="fix-setforce-command">
 <span id="index-0"></span><h1>fix setforce command<a class="headerlink" href="#fix-setforce-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="fix-setforce-cuda-command">
 <h1>fix setforce/cuda command<a class="headerlink" href="#fix-setforce-cuda-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID setforce fx fy fz keyword value ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>setforce = style name of this fix command</li>
 <li>fx,fy,fz = force component values</li>
 <li>any of fx,fy,fz can be a variable (see below)</li>
 <li>zero or more keyword/value pairs may be appended to args</li>
 <li>keyword = <em>region</em></li>
 </ul>
 <pre class="literal-block">
 <em>region</em> value = region-ID
-    region-ID = ID of region atoms must be in to have added force
+  region-ID = ID of region atoms must be in to have added force
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix freeze indenter setforce 0.0 0.0 0.0
 fix 2 edge setforce NULL 0.0 0.0
 fix 2 edge setforce NULL 0.0 v_oscillate
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Set each component of force on each atom in the group to the specified
 values fx,fy,fz.  This erases all previously computed forces on the
 atom, though additional fixes could add new forces.  This command can
 be used to freeze certain atoms in the simulation by zeroing their
 force, either for running dynamics or performing an energy
 minimization.  For dynamics, this assumes their initial velocity is
 also zero.</p>
 <p>Any of the fx,fy,fz values can be specified as NULL which means do not
 alter the force component in that dimension.</p>
 <p>Any of the 3 quantities defining the force components can be specified
 as an equal-style or atom-style <a class="reference internal" href="variable.html"><em>variable</em></a>, namely <em>fx</em>,
 <em>fy</em>, <em>fz</em>.  If the value is a variable, it should be specified as
 v_name, where name is the variable name.  In this case, the variable
 will be evaluated each timestep, and its value used to determine the
 force component.</p>
 <p>Equal-style variables can specify formulas with various mathematical
 functions, and include <a class="reference internal" href="thermo_style.html"><em>thermo_style</em></a> command
 keywords for the simulation box parameters and timestep and elapsed
 time.  Thus it is easy to specify a time-dependent force field.</p>
 <p>Atom-style variables can specify the same formulas as equal-style
 variables but can also include per-atom values, such as atom
 coordinates.  Thus it is easy to specify a spatially-dependent force
 field with optional time-dependence as well.</p>
 <p>If the <em>region</em> keyword is used, the atom must also be in the
 specified geometric <a class="reference internal" href="region.html"><em>region</em></a> in order to have force added
 to it.</p>
 <hr class="docutils" />
 <p>Styles with a <em>cuda</em> suffix are functionally the same as the
 corresponding style without the suffix.  They have been optimized to
 run faster, depending on your available hardware, as discussed in
 <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a> of the manual.  The
 accelerated styles take the same arguments and should produce the same
 results, except for round-off and precision issues.</p>
 <p>These accelerated styles are part of the USER-CUDA package.  They are
 only enabled if LAMMPS was built with that package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 <p>You can specify the accelerated styles explicitly in your input script
 by including their suffix, or you can use the <a class="reference internal" href="Section_start.html#start-7"><span>-suffix command-line switch</span></a> when you invoke LAMMPS, or you can
 use the <a class="reference internal" href="suffix.html"><em>suffix</em></a> command in your input script.</p>
 <p>See <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a> of the manual for
 more instructions on how to use the accelerated styles effectively.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.  None of the <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> options
 are relevant to this fix.</p>
 <p>This fix computes a global 3-vector of forces, which can be accessed
 by various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  This is the
 total force on the group of atoms before the forces on individual
 atoms are changed by the fix.  The vector values calculated by this
 fix are &#8220;extensive&#8221;.</p>
 <p>No parameter of this fix can be used with the <em>start/stop</em> keywords of
 the <a class="reference internal" href="run.html"><em>run</em></a> command.</p>
 <p>The forces due to this fix are imposed during an energy minimization,
 invoked by the <a class="reference internal" href="minimize.html"><em>minimize</em></a> command, but you cannot set
 forces to any value besides zero when performing a minimization.  Use
 the <a class="reference internal" href="fix_addforce.html"><em>fix addforce</em></a> command if you want to apply a
 non-zero force to atoms during a minimization.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <blockquote>
 <div>none</div></blockquote>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="fix_addforce.html"><em>fix addforce</em></a>, <a class="reference internal" href="fix_aveforce.html"><em>fix aveforce</em></a></p>
 <p><strong>Default:</strong> none</p>
 </div>
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diff --git a/doc/fix_shake.html b/doc/fix_shake.html
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   <div class="section" id="fix-shake-command">
 <span id="index-0"></span><h1>fix shake command<a class="headerlink" href="#fix-shake-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="fix-shake-cuda-command">
 <h1>fix shake/cuda command<a class="headerlink" href="#fix-shake-cuda-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="fix-rattle-command">
 <h1>fix rattle command<a class="headerlink" href="#fix-rattle-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID style tol iter N constraint values ... keyword value ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>style = shake or rattle = style name of this fix command</li>
 <li>tol = accuracy tolerance of SHAKE solution</li>
 <li>iter = max # of iterations in each SHAKE solution</li>
 <li>N = print SHAKE statistics every this many timesteps (0 = never)</li>
 <li>one or more constraint/value pairs are appended</li>
 <li>constraint = <em>b</em> or <em>a</em> or <em>t</em> or <em>m</em></li>
 </ul>
 <pre class="literal-block">
 <em>b</em> values = one or more bond types
-  <em>a</em> values = one or more angle types
-  <em>t</em> values = one or more atom types
-  <em>m</em> value = one or more mass values
+<em>a</em> values = one or more angle types
+<em>t</em> values = one or more atom types
+<em>m</em> value = one or more mass values
 </pre>
 <ul class="simple">
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>mol</em></li>
 </ul>
 <pre class="literal-block">
 <em>mol</em> value = template-ID
-    template-ID = ID of molecule template specified in a separate <a class="reference internal" href="molecule.html"><em>molecule</em></a> command
+  template-ID = ID of molecule template specified in a separate <a class="reference internal" href="molecule.html"><em>molecule</em></a> command
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix 1 sub shake 0.0001 20 10 b 4 19 a 3 5 2
 fix 1 sub shake 0.0001 20 10 t 5 6 m 1.0 a 31
 fix 1 sub shake 0.0001 20 10 t 5 6 m 1.0 a 31 mol myMol
 fix 1 sub rattle 0.0001 20 10 t 5 6 m 1.0 a 31
 fix 1 sub rattle 0.0001 20 10 t 5 6 m 1.0 a 31 mol myMol
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Apply bond and angle constraints to specified bonds and angles in the
 simulation by either the SHAKE or RATTLE algorithms.  This typically
 enables a longer timestep.</p>
 <p><strong>SHAKE vs RATTLE:</strong></p>
 <p>The SHAKE algorithm was invented for schemes such as standard Verlet
 timesteppnig, where only the coordinates are integrated and the
 velocities are approximated as finite differences to the trajectories
 (<a class="reference internal" href="#ryckaert"><span>Ryckaert et al. (1977)</span></a>).  If the velocities are
 integrated explicitly, as with velocity Verlet which is what LAMMPS
 uses as an integration method, a second set of constraining forces is
 required in order to eliminate velocity components along the bonds
 (<a class="reference internal" href="#andersen"><span>Andersen (1983)</span></a>).</p>
 <p>In order to formulate individual constraints for SHAKE and RATTLE,
 focus on a single molecule whose bonds are constrained.  Let Ri and Vi
 be the position and velocity of atom <em>i</em> at time <em>n</em>, for
 <em>i*=1,...,*N</em>, where <em>N</em> is the number of sites of our reference
 molecule. The distance vector between sites <em>i</em> and <em>j</em> is given by</p>
 <img alt="_images/fix_rattle_rij.jpg" class="align-center" src="_images/fix_rattle_rij.jpg" />
 <p>The constraints can then be formulated as</p>
 <img alt="_images/fix_rattle_constraints.jpg" class="align-center" src="_images/fix_rattle_constraints.jpg" />
 <p>The SHAKE algorithm satisfies the first condition, i.e. the sites at
 time <em>n+1</em> will have the desired separations Dij immediately after the
 coordinates are integrated.  If we also enforce the second condition,
 the velocity components along the bonds will vanish.  RATTLE satisfies
 both conditions.  As implemented in LAMMPS, fix rattle uses fix shake
 for satisfying the coordinate constraints. Therefore the settings and
 optional keywords are the same for both fixes, and all the information
 below about SHAKE is also relevant for RATTLE.</p>
 <p><strong>SHAKE:</strong></p>
 <p>Each timestep the specified bonds and angles are reset to their
 equilibrium lengths and angular values via the SHAKE algorithm
 (<a class="reference internal" href="#ryckaert"><span>Ryckaert et al. (1977)</span></a>).  This is done by applying an
 additional constraint force so that the new positions preserve the
 desired atom separations.  The equations for the additional force are
 solved via an iterative method that typically converges to an accurate
 solution in a few iterations.  The desired tolerance (e.g. 1.0e-4 = 1
 part in 10000) and maximum # of iterations are specified as arguments.
 Setting the N argument will print statistics to the screen and log
 file about regarding the lengths of bonds and angles that are being
 constrained.  Small delta values mean SHAKE is doing a good job.</p>
 <p>In LAMMPS, only small clusters of atoms can be constrained.  This is
 so the constraint calculation for a cluster can be performed by a
 single processor, to enable good parallel performance.  A cluster is
 defined as a central atom connected to others in the cluster by
 constrained bonds.  LAMMPS allows for the following kinds of clusters
 to be constrained: one central atom bonded to 1 or 2 or 3 atoms, or
 one central atom bonded to 2 others and the angle between the 3 atoms
 also constrained.  This means water molecules or CH2 or CH3 groups may
 be constrained, but not all the C-C backbone bonds of a long polymer
 chain.</p>
 <p>The <em>b</em> constraint lists bond types that will be constrained.  The <em>t</em>
 constraint lists atom types.  All bonds connected to an atom of the
 specified type will be constrained.  The <em>m</em> constraint lists atom
 masses.  All bonds connected to atoms of the specified masses will be
 constrained (within a fudge factor of MASSDELTA specified in
 fix_shake.cpp).  The <em>a</em> constraint lists angle types.  If both bonds
 in the angle are constrained then the angle will also be constrained
 if its type is in the list.</p>
 <p>For all constraints, a particular bond is only constrained if both
 atoms in the bond are in the group specified with the SHAKE fix.</p>
 <p>The degrees-of-freedom removed by SHAKE bonds and angles are accounted
 for in temperature and pressure computations.  Similarly, the SHAKE
 contribution to the pressure of the system (virial) is also accounted
 for.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">This command works by using the current forces on
 atoms to caculate an additional constraint force which when added will
 leave the atoms in positions that satisfy the SHAKE constraints
 (e.g. bond length) after the next time integration step.  If you
 define fixes (e.g. <a class="reference internal" href="fix_efield.html"><em>fix efield</em></a>) that add additional
 force to the atoms after fix shake operates, then this fix will not
 take them into account and the time integration will typically not
 satisfy the SHAKE constraints.  The solution for this is to make sure
 that fix shake is defined in your input script after any other fixes
 which add or change forces (to atoms that fix shake operates on).</p>
 </div>
 <hr class="docutils" />
 <p>The <em>mol</em> keyword should be used when other commands, such as <a class="reference internal" href="fix_deposit.html"><em>fix deposit</em></a> or <a class="reference internal" href="fix_pour.html"><em>fix pour</em></a>, add molecules
 on-the-fly during a simulation, and you wish to contrain the new
 molecules via SHAKE.  You specify a <em>template-ID</em> previously defined
 using the <a class="reference internal" href="molecule.html"><em>molecule</em></a> command, which reads a file that
 defines the molecule.  You must use the same <em>template-ID</em> that the
 command adding molecules uses.  The coordinates, atom types, special
 bond restrictions, and SHAKE info can be specified in the molecule
 file.  See the <a class="reference internal" href="molecule.html"><em>molecule</em></a> command for details.  The only
 settings required to be in this file (by this command) are the SHAKE
 info of atoms in the molecule.</p>
 <hr class="docutils" />
 <p>Styles with a <em>cuda</em> suffix are functionally the same as the
 corresponding style without the suffix.  They have been optimized to
 run faster, depending on your available hardware, as discussed in
 <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a> of the manual.  The
 accelerated styles take the same arguments and should produce the same
 results, except for round-off and precision issues.</p>
 <p>These accelerated styles are part of the USER-CUDA package.  They are
 only enabled if LAMMPS was built with that package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 <p>You can specify the accelerated styles explicitly in your input script
 by including their suffix, or you can use the <a class="reference internal" href="Section_start.html#start-7"><span>-suffix command-line switch</span></a> when you invoke LAMMPS, or you can
 use the <a class="reference internal" href="suffix.html"><em>suffix</em></a> command in your input script.</p>
 <p>See <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a> of the manual for
 more instructions on how to use the accelerated styles effectively.</p>
 <hr class="docutils" />
 <p><strong>RATTLE:</strong></p>
 <p>The velocity constraints lead to a linear system of equations which
 can be solved analytically.  The implementation of the algorithm in
 LAMMPS closely follows (<a class="reference internal" href="#andersen"><span>Andersen (1983)</span></a>).</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">The fix rattle command modifies forces and velocities
 and thus should be defined after all other integration fixes in your
 input script.  If you define other fixes that modify velocities or
 forces after fix rattle operates, then fix rattle will not take them
 into account and the overall time integration will typically not
 satisfy the RATTLE constraints.  You can check whether the constraints
 work correctly by setting the value of RATTLE_DEBUG in
 src/fix_rattle.cpp to 1 and recompiling LAMMPS.</p>
 </div>
 </div>
 <hr class="docutils" />
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about these fixes is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.  None of the <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> options
 are relevant to these fixes.  No global or per-atom quantities are
 stored by these fixes for access by various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  No parameter of these fixes
 can be used with the <em>start/stop</em> keywords of the <a class="reference internal" href="run.html"><em>run</em></a>
 command.  These fixes are not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>These fixes are part of the RIGID package.  They are only enabled if
 LAMMPS was built with that package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 <p>For computational efficiency, there can only be one shake or rattle
 fix defined in a simulation.</p>
 <p>If you use a tolerance that is too large or a max-iteration count that
 is too small, the constraints will not be enforced very strongly,
 which can lead to poor energy conservation.  You can test for this in
 your system by running a constant NVE simulation with a particular set
 of SHAKE parameters and monitoring the energy versus time.</p>
 <p>SHAKE or RATTLE should not be used to contrain an angle at 180 degrees
 (e.g. linear CO2 molecule).  This causes numeric difficulties.</p>
 <p><strong>Related commands:</strong> none</p>
 <p><strong>Default:</strong> none</p>
 <hr class="docutils" />
 <p id="ryckaert"><strong>(Ryckaert)</strong> J.-P. Ryckaert, G. Ciccotti and H. J. C. Berendsen,
 J of Comp Phys, 23, 327-341 (1977).</p>
 <p id="andersen"><strong>(Andersen)</strong> H. Andersen, J of Comp Phys, 52, 24-34 (1983).</p>
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   <div class="section" id="fix-smd-command">
 <span id="index-0"></span><h1>fix smd command<a class="headerlink" href="#fix-smd-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID smd type values keyword values
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>smd  = style name of this fix command</li>
 <li>mode = <em>cvel</em> or <em>cfor</em> to select constant velocity or constant force SMD</li>
 </ul>
 <pre class="literal-block">
 <em>cvel</em> values = K vel
-    K = spring constant (force/distance units)
-    vel = velocity of pulling (distance/time units)
-  <em>cfor</em> values = force
-    force = pulling force (force units)
+  K = spring constant (force/distance units)
+  vel = velocity of pulling (distance/time units)
+<em>cfor</em> values = force
+  force = pulling force (force units)
 </pre>
 <ul class="simple">
 <li>keyword = <em>tether</em> or <em>couple</em></li>
 </ul>
 <pre class="literal-block">
 <em>tether</em> values = x y z R0
-    x,y,z = point to which spring is tethered
-    R0 = distance of end of spring from tether point (distance units)
-  <em>couple</em> values = group-ID2 x y z R0
-    group-ID2 = 2nd group to couple to fix group with a spring
-    x,y,z = direction of spring, automatically computed with 'auto'
-    R0 = distance of end of spring (distance units)
+  x,y,z = point to which spring is tethered
+  R0 = distance of end of spring from tether point (distance units)
+<em>couple</em> values = group-ID2 x y z R0
+  group-ID2 = 2nd group to couple to fix group with a spring
+  x,y,z = direction of spring, automatically computed with 'auto'
+  R0 = distance of end of spring (distance units)
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix  pull    cterm smd cvel 20.0 -0.00005 tether NULL NULL 100.0 0.0
 fix  pull    cterm smd cvel 20.0 -0.0001 tether 25.0 25 25.0 0.0
 fix  stretch cterm smd cvel 20.0  0.0001 couple nterm auto auto auto 0.0
 fix  pull    cterm smd cfor  5.0 tether 25.0 25.0 25.0 0.0
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>This fix implements several options of steered MD (SMD) as reviewed in
 <span class="xref std std-ref">(Izrailev)</span>, which allows to induce conformational changes
 in systems and to compute the potential of mean force (PMF) along the
 assumed reaction coordinate <span class="xref std std-ref">(Park)</span> based on Jarzynski&#8217;s
 equality <span class="xref std std-ref">(Jarzynski)</span>.  This fix borrows a lot from <a class="reference internal" href="fix_spring.html"><em>fix spring</em></a> and <a class="reference internal" href="fix_setforce.html"><em>fix setforce</em></a>.</p>
 <p>You can apply a moving spring force to a group of atoms (<em>tether</em>
 style) or between two groups of atoms (<em>couple</em> style).  The spring
 can then be used in either constant velocity (<em>cvel</em>) mode or in
 constant force (<em>cfor</em>) mode to induce transitions in your systems.
 When running in <em>tether</em> style, you may need some way to fix some
 other part of the system (e.g. via <a class="reference internal" href="fix_spring_self.html"><em>fix spring/self</em></a>)</p>
 <p>The <em>tether</em> style attaches a spring between a point at a distance of
 R0 away from a fixed point <em>x,y,z</em> and the center of mass of the fix
 group of atoms.  A restoring force of magnitude K (R - R0) Mi / M is
 applied to each atom in the group where <em>K</em> is the spring constant, Mi
 is the mass of the atom, and M is the total mass of all atoms in the
 group.  Note that <em>K</em> thus represents the total force on the group of
 atoms, not a per-atom force.</p>
 <p>In <em>cvel</em> mode the distance R is incremented or decremented
 monotonously according to the pulling (or pushing) velocity.
 In <em>cfor</em> mode a constant force is added and the actual distance
 in direction of the spring is recorded.</p>
 <p>The <em>couple</em> style links two groups of atoms together.  The first
 group is the fix group; the second is specified by group-ID2.  The
 groups are coupled together by a spring that is at equilibrium when
 the two groups are displaced by a vector in direction <em>x,y,z</em> with
 respect to each other and at a distance R0 from that displacement.
 Note that <em>x,y,z</em> only provides a direction and will be internally
 normalized. But since it represents the <em>absolute</em> displacement of
 group-ID2 relative to the fix group, (1,1,0) is a different spring
 than (-1,-1,0).  For each vector component, the displacement can be
 described with the <em>auto</em> parameter. In this case the direction is
 recomputed in every step, which can be useful for steering a local
 process where the whole object undergoes some other change.  When the
 relative positions and distance between the two groups are not in
 equilibrium, the same spring force described above is applied to atoms
 in each of the two groups.</p>
 <p>For both the <em>tether</em> and <em>couple</em> styles, any of the x,y,z values can
 be specified as NULL which means do not include that dimension in the
 distance calculation or force application.</p>
 <p>For constant velocity pulling (<em>cvel</em> mode), the running integral
 over the pulling force in direction of the spring is recorded and
 can then later be used to compute the potential of mean force (PMF)
 by averaging over multiple independent trajectories along the same
 pulling path.</p>
 </div>
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>The fix stores the direction of the spring, current pulling target
 distance and the running PMF to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.
 See the <a class="reference internal" href="read_restart.html"><em>read_restart</em></a> command for info on how to
 re-specify a fix in an input script that reads a restart file, so that
 the operation of the fix continues in an uninterrupted fashion.</p>
 <p>None of the <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> options are relevant to this
 fix.</p>
 <p>This fix computes a vector list of 7 quantities, which can be accessed
 by various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  The
 quantities in the vector are in this order: the x-, y-, and
 z-component of the pulling force, the total force in direction of the
 pull, the equilibrium distance of the spring, the distance between the
 two reference points, and finally the accumulated PMF (the sum of
 pulling forces times displacement).</p>
 <p>The force is the total force on the group of atoms by the spring.  In
 the case of the <em>couple</em> style, it is the force on the fix group
 (group-ID) or the negative of the force on the 2nd group (group-ID2).
 The vector values calculated by this fix are &#8220;extensive&#8221;.</p>
 <p>No parameter of this fix can be used with the <em>start/stop</em> keywords of
 the <a class="reference internal" href="run.html"><em>run</em></a> command.  This fix is not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>This fix is part of the USER-MISC package.  It is only enabled if
 LAMMPS was built with that package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="fix_drag.html"><em>fix drag</em></a>, <a class="reference internal" href="fix_spring.html"><em>fix spring</em></a>,
 <a class="reference internal" href="fix_spring_self.html"><em>fix spring/self</em></a>,
 <a class="reference internal" href="fix_spring_rg.html"><em>fix spring/rg</em></a></p>
 <p><strong>Default:</strong> none</p>
 <hr class="docutils" />
 <p id="israilev"><strong>(Izrailev)</strong> Izrailev, Stepaniants, Isralewitz, Kosztin, Lu, Molnar,
 Wriggers, Schulten. Computational Molecular Dynamics: Challenges,
 Methods, Ideas, volume 4 of Lecture Notes in Computational Science and
 Engineering, pp. 39-65. Springer-Verlag, Berlin, 1998.</p>
 <p><strong>(Park)</strong>
 Park, Schulten, J. Chem. Phys. 120 (13), 5946 (2004)</p>
 <p><strong>(Jarzynski)</strong>
 Jarzynski, Phys. Rev. Lett. 78, 2690 (1997)</p>
 </div>
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   <div class="section" id="fix-spring-command">
 <span id="index-0"></span><h1>fix spring command<a class="headerlink" href="#fix-spring-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID spring keyword values
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>spring = style name of this fix command</li>
 <li>keyword = <em>tether</em> or <em>couple</em></li>
 </ul>
 <pre class="literal-block">
 <em>tether</em> values = K x y z R0
-    K = spring constant (force/distance units)
-    x,y,z = point to which spring is tethered
-    R0 = equilibrium distance from tether point (distance units)
-  <em>couple</em> values = group-ID2 K x y z R0
-    group-ID2 = 2nd group to couple to fix group with a spring
-    K = spring constant (force/distance units)
-    x,y,z = direction of spring
-    R0 = equilibrium distance of spring (distance units)
+  K = spring constant (force/distance units)
+  x,y,z = point to which spring is tethered
+  R0 = equilibrium distance from tether point (distance units)
+<em>couple</em> values = group-ID2 K x y z R0
+  group-ID2 = 2nd group to couple to fix group with a spring
+  K = spring constant (force/distance units)
+  x,y,z = direction of spring
+  R0 = equilibrium distance of spring (distance units)
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix pull ligand spring tether 50.0 0.0 0.0 0.0 0.0
 fix pull ligand spring tether 50.0 0.0 0.0 0.0 5.0
 fix pull ligand spring tether 50.0 NULL NULL 2.0 3.0
 fix 5 bilayer1 spring couple bilayer2 100.0 NULL NULL 10.0 0.0
 fix longitudinal pore spring couple ion 100.0 NULL NULL -20.0 0.0
 fix radial pore spring couple ion 100.0 0.0 0.0 NULL 5.0
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Apply a spring force to a group of atoms or between two groups of
 atoms.  This is useful for applying an umbrella force to a small
 molecule or lightly tethering a large group of atoms (e.g. all the
 solvent or a large molecule) to the center of the simulation box so
 that it doesn&#8217;t wander away over the course of a long simulation.  It
 can also be used to hold the centers of mass of two groups of atoms at
 a given distance or orientation with respect to each other.</p>
 <p>The <em>tether</em> style attaches a spring between a fixed point <em>x,y,z</em> and
 the center of mass of the fix group of atoms.  The equilibrium
 position of the spring is R0.  At each timestep the distance R from
 the center of mass of the group of atoms to the tethering point is
 computed, taking account of wrap-around in a periodic simulation box.
 A restoring force of magnitude K (R - R0) Mi / M is applied to each
 atom in the group where <em>K</em> is the spring constant, Mi is the mass of
 the atom, and M is the total mass of all atoms in the group.  Note
 that <em>K</em> thus represents the total force on the group of atoms, not a
 per-atom force.</p>
 <p>The <em>couple</em> style links two groups of atoms together.  The first
 group is the fix group; the second is specified by group-ID2.  The
 groups are coupled together by a spring that is at equilibrium when
 the two groups are displaced by a vector <em>x,y,z</em> with respect to each
 other and at a distance R0 from that displacement.  Note that <em>x,y,z</em>
 is the equilibrium displacement of group-ID2 relative to the fix
 group.  Thus (1,1,0) is a different spring than (-1,-1,0).  When the
 relative positions and distance between the two groups are not in
 equilibrium, the same spring force described above is applied to atoms
 in each of the two groups.</p>
 <p>For both the <em>tether</em> and <em>couple</em> styles, any of the x,y,z values can
 be specified as NULL which means do not include that dimension in the
 distance calculation or force application.</p>
 <p>The first example above pulls the ligand towards the point (0,0,0).
 The second example holds the ligand near the surface of a sphere of
 radius 5 around the point (0,0,0).  The third example holds the ligand
 a distance 3 away from the z=2 plane (on either side).</p>
 <p>The fourth example holds 2 bilayers a distance 10 apart in z.  For the
 last two examples, imagine a pore (a slab of atoms with a cylindrical
 hole cut out) oriented with the pore axis along z, and an ion moving
 within the pore.  The fifth example holds the ion a distance of -20
 below the z = 0 center plane of the pore (umbrella sampling).  The
 last example holds the ion a distance 5 away from the pore axis
 (assuming the center-of-mass of the pore in x,y is the pore axis).</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">The center of mass of a group of atoms is calculated
 in &#8220;unwrapped&#8221; coordinates using atom image flags, which means that
 the group can straddle a periodic boundary.  See the <a class="reference internal" href="dump.html"><em>dump</em></a>
 doc page for a discussion of unwrapped coordinates.  It also means
 that a spring connecting two groups or a group and the tether point
 can cross a periodic boundary and its length be calculated correctly.
 One exception is for rigid bodies, which should not be used with the
 fix spring command, if the rigid body will cross a periodic boundary.
 This is because image flags for rigid bodies are used in a different
 way, as explained on the <a class="reference internal" href="fix_rigid.html"><em>fix rigid</em></a> doc page.</p>
 </div>
 </div>
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.</p>
 <p>The <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> <em>energy</em> option is supported by this
 fix to add the energy stored in the spring to the system&#8217;s potential
 energy as part of <a class="reference internal" href="thermo_style.html"><em>thermodynamic output</em></a>.</p>
 <p>This fix computes a global scalar which can be accessed by various
 <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  The scalar is the
 spring energy = 0.5 * K * r^2.</p>
 <p>This fix also computes global 4-vector which can be accessed by
 various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  The first 3
 quantities in the vector are xyz components of the total force added
 to the group of atoms by the spring.  In the case of the <em>couple</em>
 style, it is the force on the fix group (group-ID) or the negative of
 the force on the 2nd group (group-ID2).  The 4th quantity in the
 vector is the magnitude of the force added by the spring, as a
 positive value if (r-R0) &gt; 0 and a negative value if (r-R0) &lt; 0.  This
 sign convention can be useful when using the spring force to compute a
 potential of mean force (PMF).</p>
 <p>The scalar and vector values calculated by this fix are &#8220;extensive&#8221;.</p>
 <p>No parameter of this fix can be used with the <em>start/stop</em> keywords of
 the <a class="reference internal" href="run.html"><em>run</em></a> command.</p>
 <p>The forces due to this fix are imposed during an energy minimization,
 invoked by the <a class="reference internal" href="minimize.html"><em>minimize</em></a> command.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">If you want the spring energy to be included in the
 total potential energy of the system (the quantity being minimized),
 you MUST enable the <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> <em>energy</em> option for
 this fix.</p>
 </div>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <blockquote>
 <div>none</div></blockquote>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="fix_drag.html"><em>fix drag</em></a>, <a class="reference internal" href="fix_spring_self.html"><em>fix spring/self</em></a>,
 <a class="reference internal" href="fix_spring_rg.html"><em>fix spring/rg</em></a>, <a class="reference internal" href="fix_smd.html"><em>fix smd</em></a></p>
 <p><strong>Default:</strong> none</p>
 </div>
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   <div class="section" id="fix-srd-command">
 <span id="index-0"></span><h1>fix srd command<a class="headerlink" href="#fix-srd-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID srd N groupbig-ID Tsrd hgrid seed keyword value ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>srd = style name of this fix command</li>
 <li>N = reset SRD particle velocities every this many timesteps</li>
 <li>groupbig-ID = ID of group of large particles that SRDs interact with</li>
 <li>Tsrd = temperature of SRD particles (temperature units)</li>
 <li>hgrid = grid spacing for SRD grouping (distance units)</li>
 <li>seed = random # seed (positive integer)</li>
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>lamda</em> or <em>collision</em> or <em>overlap</em> or <em>inside</em> or <em>exact</em> or <em>radius</em> or <em>bounce</em> or <em>search</em> or <em>cubic</em> or <em>shift</em> or <em>tstat</em> or <em>rescale</em></li>
 </ul>
 <pre class="literal-block">
 <em>lamda</em> value = mean free path of SRD particles (distance units)
-  <em>collision</em> value = <em>noslip</em> or <em>slip</em> = collision model
-  <em>overlap</em> value = <em>yes</em> or <em>no</em> = whether big particles may overlap
-  <em>inside</em> value = <em>error</em> or <em>warn</em> or <em>ignore</em> = how SRD particles which end up inside a big particle are treated
-  <em>exact</em> value = <em>yes</em> or <em>no</em>
-  <em>radius</em> value = rfactor = scale collision radius by this factor
-  <em>bounce</em> value = Nbounce = max # of collisions an SRD particle can undergo in one timestep
-  <em>search</em> value = sgrid = grid spacing for collision partner searching (distance units)
-  <em>cubic</em> values = style tolerance
-    style = <em>error</em> or <em>warn</em>
-    tolerance = fractional difference allowed (0 &lt;= tol &lt;= 1)
-  <em>shift</em> values = flag shiftseed
-    flag = <em>yes</em> or <em>no</em> or <em>possible</em> = SRD bin shifting for better statistics
-      <em>yes</em> = perform bin shifting each time SRD velocities are rescaled
-      <em>no</em> = no shifting
-      <em>possible</em> = shift depending on mean free path and bin size
-    shiftseed = random # seed (positive integer)
-  <em>tstat</em> value = <em>yes</em> or <em>no</em> = thermostat SRD particles or not
-  <em>rescale</em> value = <em>yes</em> or <em>no</em> or <em>rotate</em> or <em>collide</em> = rescaling of SRD velocities
-    <em>yes</em> = rescale during velocity rotation and collisions
-    <em>no</em> = no rescaling
-    <em>rotate</em> = rescale during velocity rotation, but not collisions
-    <em>collide</em> = rescale during collisions, but not velocity rotation
+<em>collision</em> value = <em>noslip</em> or <em>slip</em> = collision model
+<em>overlap</em> value = <em>yes</em> or <em>no</em> = whether big particles may overlap
+<em>inside</em> value = <em>error</em> or <em>warn</em> or <em>ignore</em> = how SRD particles which end up inside a big particle are treated
+<em>exact</em> value = <em>yes</em> or <em>no</em>
+<em>radius</em> value = rfactor = scale collision radius by this factor
+<em>bounce</em> value = Nbounce = max # of collisions an SRD particle can undergo in one timestep
+<em>search</em> value = sgrid = grid spacing for collision partner searching (distance units)
+<em>cubic</em> values = style tolerance
+  style = <em>error</em> or <em>warn</em>
+  tolerance = fractional difference allowed (0 &lt;= tol &lt;= 1)
+<em>shift</em> values = flag shiftseed
+  flag = <em>yes</em> or <em>no</em> or <em>possible</em> = SRD bin shifting for better statistics
+    <em>yes</em> = perform bin shifting each time SRD velocities are rescaled
+    <em>no</em> = no shifting
+    <em>possible</em> = shift depending on mean free path and bin size
+  shiftseed = random # seed (positive integer)
+<em>tstat</em> value = <em>yes</em> or <em>no</em> = thermostat SRD particles or not
+<em>rescale</em> value = <em>yes</em> or <em>no</em> or <em>rotate</em> or <em>collide</em> = rescaling of SRD velocities
+  <em>yes</em> = rescale during velocity rotation and collisions
+  <em>no</em> = no rescaling
+  <em>rotate</em> = rescale during velocity rotation, but not collisions
+  <em>collide</em> = rescale during collisions, but not velocity rotation
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix 1 srd srd 10 big 1.0 0.25 482984
 fix 1 srd srd 10 big 0.5 0.25 482984 collision slip search 0.5
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Treat a group of partilces as stochastic rotation dynamics (SRD)
 particles that serve as a background solvent when interacting with big
 (colloidal) particles in groupbig-ID.  The SRD formalism is described
 in <a class="reference internal" href="#hecht"><span>(Hecht)</span></a>.  The key idea behind using SRD particles as a
 cheap coarse-grained solvent is that SRD particles do not interact
 with each other, but only with the solute particles, which in LAMMPS
 can be spheroids, ellipsoids, or line segments, or triangles, or rigid
 bodies containing multiple spherioids or ellipsoids or line segments
 or triangles.  The collision and rotation properties of the model
 imbue the SRD particles with fluid-like properties, including an
 effective viscosity.  Thus simulations with large solute particles can
 be run more quickly, to measure solute propoerties like diffusivity
 and viscosity in a background fluid.  The usual LAMMPS fixes for such
 simulations, such as <a class="reference internal" href="fix_deform.html"><em>fix deform</em></a>, <a class="reference internal" href="fix_viscosity.html"><em>fix viscosity</em></a>, and <a class="reference internal" href="fix_nvt_sllod.html"><em>fix nvt/sllod</em></a>,
 can be used in conjunction with the SRD model.</p>
 <p>For more details on how the SRD model is implemented in LAMMPS, <a class="reference internal" href="kspace_style.html#petersen"><span>this paper</span></a> describes the implementation and usage of pure SRD
 fluids.  <a class="reference internal" href="#lechman"><span>This paper</span></a>, which is nearly complete, describes
 the implementation and usage of mixture systems (solute particles in
 an SRD fluid).  See the examples/srd directory for sample input
 scripts using SRD particles in both settings.</p>
 <p>This fix does 2 things:</p>
 <p>(1) It advects the SRD particles, performing collisions between SRD
 and big particles or walls every timestep, imparting force and torque
 to the big particles.  Collisions also change the position and
 velocity of SRD particles.</p>
 <p>(2) It resets the velocity distribution of SRD particles via random
 rotations every N timesteps.</p>
 <p>SRD particles have a mass, temperature, characteristic timestep
 dt_SRD, and mean free path between collisions (lamda).  The
 fundamental equation relating these 4 quantities is</p>
 <div class="highlight-python"><div class="highlight"><pre><span class="n">lamda</span> <span class="o">=</span> <span class="n">dt_SRD</span> <span class="o">*</span> <span class="n">sqrt</span><span class="p">(</span><span class="n">Kboltz</span> <span class="o">*</span> <span class="n">Tsrd</span> <span class="o">/</span> <span class="n">mass</span><span class="p">)</span>
 </pre></div>
 </div>
 <p>The mass of SRD particles is set by the <a class="reference internal" href="mass.html"><em>mass</em></a> command
 elsewhere in the input script.  The SRD timestep dt_SRD is N times the
 step dt defined by the <a class="reference internal" href="timestep.html"><em>timestep</em></a> command.  Big
 particles move in the normal way via a time integration <a class="reference internal" href="fix.html"><em>fix</em></a>
 with a short timestep dt.  SRD particles advect with a large timestep
 dt_SRD &gt;= dt.</p>
 <p>If the <em>lamda</em> keyword is not specified, the the SRD temperature
 <em>Tsrd</em> is used in the above formula to compute lamda.  If the <em>lamda</em>
 keyword is specified, then the <em>Tsrd</em> setting is ignored and the above
 equation is used to compute the SRD temperature.</p>
 <p>The characteristic length scale for the SRD fluid is set by <em>hgrid</em>
 which is used to bin SRD particles for purposes of resetting their
 velocities.  Normally hgrid is set to be 1/4 of the big particle
 diameter or smaller, to adequately resolve fluid properties around the
 big particles.</p>
 <p>Lamda cannot be smaller than 0.6 * hgrid, else an error is generated
 (unless the <em>shift</em> keyword is used, see below).  The velocities of
 SRD particles are bounded by Vmax, which is set so that an SRD
 particle will not advect further than Dmax = 4*lamda in dt_SRD.  This
 means that roughly speaking, Dmax should not be larger than a big
 particle diameter, else SRDs may pass thru big particles without
 colliding.  A warning is generated if this is the case.</p>
 <p>Collisions between SRD particles and big particles or walls are
 modeled as a lightweight SRD point particle hitting a heavy big
 particle of given diameter or a wall at a point on its surface and
 bouncing off with a new velocity.  The collision changes the momentum
 of the SRD particle.  It imparts a force and torque to the big
 particle.  It imparts a force to a wall.  Static or moving SRD walls
 are setup via the <a class="reference internal" href="fix_wall_srd.html"><em>fix wall/srd</em></a> command.  For the
 remainder of this doc page, a collision of an SRD particle with a wall
 can be viewed as a collision with a big particle of infinite radius
 and mass.</p>
 <p>The <em>collision</em> keyword sets the style of collisions.  The <em>slip</em>
 style means that the tangential component of the SRD particle momentum
 is preserved.  Thus a force is imparted to a big particle, but no
 torque.  The normal component of the new SRD velocity is sampled from
 a Gaussian distribution at temperature <em>Tsrd</em>.</p>
 <p>For the <em>noslip</em> style, both the normal and tangential components of
 the new SRD velocity are sampled from a Gaussian distribution at
 temperature <em>Tsrd</em>.  Additionally, a new tangential direction for the
 SRD velocity is chosen randomly.  This collision style imparts torque
 to a big particle.  Thus a time integrator <a class="reference internal" href="fix.html"><em>fix</em></a> that rotates
 the big particles appropriately should be used.</p>
 <hr class="docutils" />
 <p>The <em>overlap</em> keyword should be set to <em>yes</em> if two (or more) big
 particles can ever overlap.  This depends on the pair potential
 interaction used for big-big interactions, or could be the case if
 multiple big particles are held together as rigid bodies via the <a class="reference internal" href="fix_rigid.html"><em>fix rigid</em></a> command.  If the <em>overlap</em> keyword is <em>no</em> and
 big particles do in fact overlap, then SRD/big collisions can generate
 an error if an SRD ends up inside two (or more) big particles at once.
 How this error is treated is determined by the <em>inside</em> keyword.
 Running with <em>overlap</em> set to <em>no</em> allows for faster collision
 checking, so it should only be set to <em>yes</em> if needed.</p>
 <p>The <em>inside</em> keyword determines how a collision is treated if the
 computation determines that the timestep started with the SRD particle
 already inside a big particle.  If the setting is <em>error</em> then this
 generates an error message and LAMMPS stops.  If the setting is <em>warn</em>
 then this generates a warning message and the code continues.  If the
 setting is <em>ignore</em> then no message is generated.  One of the output
 quantities logged by the fix (see below) tallies the number of such
 events, so it can be monitored.  Note that once an SRD particle is
 inside a big particle, it may remain there for several steps until it
 drifts outside the big particle.</p>
 <p>The <em>exact</em> keyword determines how accurately collisions are computed.
 A setting of <em>yes</em> computes the time and position of each collision as
 SRD and big particles move together.  A setting of <em>no</em> estimates the
 position of each collision based on the end-of-timestep positions of
 the SRD and big particle.  If <em>overlap</em> is set to yes, the setting of
 the <em>exact</em> keyword is ignored since time-accurate collisions are
 needed.</p>
 <p>The <em>radius</em> keyword scales the effective size of big particles.  If
 big particles will overlap as they undergo dynamics, then this keyword
 can be used to scale down their effective collision radius by an
 amount <em>rfactor</em>, so that SRD particle will only collide with one big
 particle at a time.  For example, in a Lennard-Jones system at a
 temperature of 1.0 (in reduced LJ units), the minimum separation
 bewteen two big particles is as small as about 0.88 sigma.  Thus an
 <em>rfactor</em> value of 0.85 should prevent dual collisions.</p>
 <p>The <em>bounce</em> keyword can be used to limit the maximum number of
 collisions an SRD particle undergoes in a single timestep as it
 bounces between nearby big particles.  Note that if the limit is
 reached, the SRD can be left inside a big particle.  A setting of 0 is
 the same as no limit.</p>
 <hr class="docutils" />
 <p>There are 2 kinds of bins created and maintained when running an SRD
 simulation.  The first are &#8220;SRD bins&#8221; which are used to bin SRD
 particles and reset their velocities, as discussed above.  The second
 are &#8220;search bins&#8221; which are used to identify SRD/big particle
 collisions.</p>
 <p>The <em>search</em> keyword can be used to choose a search bin size for
 identifying SRD/big particle collisions.  The default is to use the
 <em>hgrid</em> parameter for SRD bins as the search bin size.  Choosing a
 smaller or large value may be more efficient, depending on the
 problem.  But, in a statistical sense, it should not change the
 simulation results.</p>
 <p>The <em>cubic</em> keyword can be used to generate an error or warning when
 the bin size chosen by LAMMPS creates SRD bins that are non-cubic or
 different than the requested value of <em>hgrid</em> by a specified
 <em>tolerance</em>.  Note that using non-cubic SRD bins can lead to
 undetermined behavior when rotating the velocities of SRD particles,
 hence LAMMPS tries to protect you from this problem.</p>
 <p>LAMMPS attempts to set the SRD bin size to exactly <em>hgrid</em>.  However,
 there must be an integer number of bins in each dimension of the
 simulation box.  Thus the actual bin size will depend on the size and
 shape of the overall simulation box.  The actual bin size is printed
 as part of the SRD output when a simulation begins.</p>
 <p>If the actual bin size in non-cubic by an amount exceeding the
 tolerance, an error or warning is printed, depending on the style of
 the <em>cubic</em> keyword.  Likewise, if the actual bin size differs from
 the requested <em>hgrid</em> value by an amount exceeding the tolerance, then
 an error or warning is printed.  The <em>tolerance</em> is a fractional
 difference.  E.g. a tolerance setting of 0.01 on the shape means that
 if the ratio of any 2 bin dimensions exceeds (1 +/- tolerance) then an
 error or warning is generated.  Similarly, if the ratio of any bin
 dimension with <em>hgrid</em> exceeds (1 +/- tolerance), then an error or
 warning is generated.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">The fix srd command can be used with simluations the
 size and/or shape of the simulation box changes.  This can be due to
 non-periodic boundary conditions or the use of fixes such as the <a class="reference internal" href="fix_deform.html"><em>fix deform</em></a> or <a class="reference internal" href="fix_wall_srd.html"><em>fix wall/srd</em></a> commands
 to impose a shear on an SRD fluid or an interaction with an external
 wall.  If the box size changes then the size of SRD bins must be
 recalculated every reneighboring.  This is not necessary if only the
 box shape changes.  This re-binning is always done so as to fit an
 integer number of bins in the current box dimension, whether it be a
 fixed, shrink-wrapped, or periodic boundary, as set by the
 <a class="reference internal" href="boundary.html"><em>boundary</em></a> command.  If the box size or shape changes,
 then the size of the search bins must be recalculated avery
 reneighboring.  Note that changing the SRD bin size may alter the
 properties of the SRD fluid, such as its viscosity.</p>
 </div>
 <p>The <em>shift</em> keyword determines whether the coordinates of SRD
 particles are randomly shifted when binned for purposes of rotating
 their velocities.  When no shifting is performed, SRD particles are
 binned and the velocity distribution of the set of SRD particles in
 each bin is adjusted via a rotation operator.  This is a statistically
 valid operation if SRD particles move sufficiently far between
 successive rotations.  This is determined by their mean-free path
 lamda.  If lamda is less than 0.6 of the SRD bin size, then shifting
 is required.  A shift means that all of the SRD particles are shifted
 by a vector whose coordinates are chosen randomly in the range [-1/2
 bin size, 1/2 bin size].  Note that all particles are shifted by the
 same vector.  The specified random number <em>shiftseed</em> is used to
 generate these vectors.  This operation sufficiently randomizes which
 SRD particles are in the same bin, even if lamda is small.</p>
 <p>If the <em>shift</em> flag is set to <em>no</em>, then no shifting is performed, but
 bin data will be communicated if bins overlap processor boundaries.
 An error will be generated if lamda &lt; 0.6 of the SRD bin size.  If the
 <em>shift</em> flag is set to <em>possible</em>, then shifting is performed only if
 lamda &lt; 0.6 of the SRD bin size.  A warning is generated to let you
 know this is occurring.  If the <em>shift</em> flag is set to <em>yes</em> then
 shifting is performed regardless of the magnitude of lamda.  Note that
 the <em>shiftseed</em> is not used if the <em>shift</em> flag is set to <em>no</em>, but
 must still be specified.</p>
 <p>Note that shifting of SRD coordinates requires extra communication,
 hence it should not normally be enabled unless required.</p>
 <p>The <em>tstat</em> keyword will thermostat the SRD particles to the specified
 <em>Tsrd</em>.  This is done every N timesteps, during the velocity rotation
 operation, by rescaling the thermal velocity of particles in each SRD
 bin to the desired temperature.  If there is a streaming velocity
 associated with the system, e.g. due to use of the <a class="reference internal" href="fix_deform.html"><em>fix deform</em></a> command to perform a simulation undergoing
 shear, then that is also accounted for.  The mean velocity of each bin
 of SRD particles is set to the position-dependent streaming velocity,
 based on the coordinates of the center of the SRD bin.  Note that
 collisions of SRD particles with big particles or walls has a
 thermostatting effect on the colliding particles, so it may not be
 necessary to thermostat the SRD particles on a bin by bin basis in
 that case.  Also note that for streaming simulations, if no
 thermostatting is performed (the default), then it may take a long
 time for the SRD fluid to come to equilibrium with a velocity profile
 that matches the simulation box deformation.</p>
 <p>The <em>rescale</em> keyword enables rescaling of an SRD particle&#8217;s velocity
 if it would travel more than 4 mean-free paths in an SRD timestep.  If
 an SRD particle exceeds this velocity it is possible it will be lost
 when migrating to other processors or that collisions with big
 particles will be missed, either of which will generate errors.  Thus
 the safest mode is to run with rescaling enabled.  However rescaling
 removes kinetic energy from the system (the particle&#8217;s velocity is
 reduced).  The latter will not typically be a problem if
 thermostatting is enabled via the <em>tstat</em> keyword or if SRD collisions
 with big particles or walls effectively thermostat the system.  If you
 wish to turn off rescaling (on is the default), e.g. for a pure SRD
 system with no thermostatting so that the temperature does not decline
 over time, the <em>rescale</em> keyword can be used.  The <em>no</em> value turns
 rescaling off during collisions and the per-bin velocity rotation
 operation.  The <em>collide</em> and <em>rotate</em> values turn it on for
 one of the operations and off for the other.</p>
 <hr class="docutils" />
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">This fix is normally used for simulations with a huge
 number of SRD particles relative to the number of big particles,
 e.g. 100 to 1.  In this scenario, computations that involve only big
 particles (neighbor list creation, communication, time integration)
 can slow down dramatically due to the large number of background SRD
 particles.</p>
 </div>
 <p>Three other input script commands will largely overcome this effect,
 speeding up an SRD simulation by a significant amount.  These are the
 <a class="reference internal" href="atom_modify.html"><em>atom_modify first</em></a>, <a class="reference internal" href="neigh_modify.html"><em>neigh_modify include</em></a>, and <a class="reference internal" href="comm_modify.html"><em>comm_modify group</em></a>
 commands.  Each takes a group-ID as an argument, which in this case
 should be the group-ID of the big solute particles.</p>
 <p>Additionally, when a <a class="reference internal" href="pair_style.html"><em>pair_style</em></a> for big/big particle
 interactions is specified, the <a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a> command
 should be used to turn off big/SRD interactions, e.g. by setting their
 epsilon or cutoff length to 0.0.</p>
 <p>The &#8220;delete_atoms overlap&#8221; command may be useful in setting up an SRD
 simulation to insure there are no initial overlaps between big and SRD
 particles.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.  None of the <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> options
 are relevant to this fix.</p>
 <p>This fix tabulates several SRD statistics which are stored in a vector
 of length 12, which can be accessed by various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  The vector values calculated
 by this fix are &#8220;intensive&#8221;, meaning they do not scale with the size
 of the simulation.  Technically, the first 8 do scale with the size of
 the simulation, but treating them as intensive means they are not
 scaled when printed as part of thermodyanmic output.</p>
 <p>These are the 12 quantities.  All are values for the current timestep,
 except for quantity 5 and the last three, each of which are
 cummulative quantities since the beginning of the run.</p>
 <ul class="simple">
 <li><ol class="first arabic">
 <li># of SRD/big collision checks performed</li>
 </ol>
 </li>
 <li><ol class="first arabic" start="2">
 <li># of SRDs which had a collision</li>
 </ol>
 </li>
 <li><ol class="first arabic" start="3">
 <li># of SRD/big colllisions (including multiple bounces)</li>
 </ol>
 </li>
 <li><ol class="first arabic" start="4">
 <li># of SRD particles inside a big particle</li>
 </ol>
 </li>
 <li><ol class="first arabic" start="5">
 <li># of SRD particles whose velocity was rescaled to be &lt; Vmax</li>
 </ol>
 </li>
 <li><ol class="first arabic" start="6">
 <li># of bins for collision searching</li>
 </ol>
 </li>
 <li><ol class="first arabic" start="7">
 <li># of bins for SRD velocity rotation</li>
 </ol>
 </li>
 <li><ol class="first arabic" start="8">
 <li># of bins in which SRD temperature was computed</li>
 </ol>
 </li>
 <li><ol class="first arabic" start="9">
 <li>SRD temperature</li>
 </ol>
 </li>
 <li><ol class="first arabic" start="10">
 <li># of SRD particles which have undergone max # of bounces</li>
 </ol>
 </li>
 <li><ol class="first arabic" start="11">
 <li>max # of bounces any SRD particle has had in a single step</li>
 </ol>
 </li>
 <li><ol class="first arabic" start="12">
 <li># of reneighborings due to SRD particles moving too far</li>
 </ol>
 </li>
 </ul>
 <p>No parameter of this fix can be used with the <em>start/stop</em> keywords of
 the <a class="reference internal" href="run.html"><em>run</em></a> command.  This fix is not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>This command can only be used if LAMMPS was built with the SRD
 package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section
 for more info on packages.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="fix_wall_srd.html"><em>fix wall/srd</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The option defaults are lamda inferred from Tsrd, collision = noslip,
 overlap = no, inside = error, exact = yes, radius = 1.0, bounce = 0,
 search = hgrid, cubic = error 0.01, shift = no, tstat = no, and
 rescale = yes.</p>
 <hr class="docutils" />
 <p id="hecht"><strong>(Hecht)</strong> Hecht, Harting, Ihle, Herrmann, Phys Rev E, 72, 011408 (2005).</p>
 <p id="petersen"><strong>(Petersen)</strong> Petersen, Lechman, Plimpton, Grest, in&#8217; t Veld, Schunk, J
 Chem Phys, 132, 174106 (2010).</p>
 <p id="lechman"><strong>(Lechman)</strong> Lechman, et al, in preparation (2010).</p>
 </div>
 </div>
 
 
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   <div class="section" id="fix-store-state-command">
 <span id="index-0"></span><h1>fix store/state command<a class="headerlink" href="#fix-store-state-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID store/state N input1 input2 ... keyword value ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>store/state = style name of this fix command</li>
 <li>N = store atom attributes every N steps, N = 0 for initial store only</li>
 <li>input = one or more atom attributes</li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>possible attributes = id, mol, type, mass,
-                     x, y, z, xs, ys, zs, xu, yu, zu, ix, iy, iz,
-                     vx, vy, vz, fx, fy, fz,
-                        q, mux, muy, muz,
-                        radius, omegax, omegay, omegaz,
-                        angmomx, angmomy, angmomz, tqx, tqy, tqz,
-                        c_ID, c_ID[N], f_ID, f_ID[N], v_name,
-                        d_name, i_name
+                   x, y, z, xs, ys, zs, xu, yu, zu, ix, iy, iz,
+                   vx, vy, vz, fx, fy, fz,
+                      q, mux, muy, muz,
+                      radius, omegax, omegay, omegaz,
+                      angmomx, angmomy, angmomz, tqx, tqy, tqz,
+                      c_ID, c_ID[N], f_ID, f_ID[N], v_name,
+                      d_name, i_name
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>id = atom ID
-      mol = molecule ID
-      type = atom type
-      mass = atom mass
-      x,y,z = unscaled atom coordinates
-      xs,ys,zs = scaled atom coordinates
-      xu,yu,zu = unwrapped atom coordinates
-      ix,iy,iz = box image that the atom is in
-      vx,vy,vz = atom velocities
-      fx,fy,fz = forces on atoms
-      q = atom charge
-      mux,muy,muz = orientation of dipolar atom
-      radius = radius of spherical particle
-      omegax,omegay,omegaz = angular velocity of spherical particle
-      angmomx,angmomy,angmomz = angular momentum of aspherical particle
-      tqx,tqy,tqz = torque on finite-size particles
-      c_ID = per-atom vector calculated by a compute with ID
-      c_ID[I] = Ith column of per-atom array calculated by a compute with ID
-      f_ID = per-atom vector calculated by a fix with ID
-      f_ID[I] = Ith column of per-atom array calculated by a fix with ID
-      v_name = per-atom vector calculated by an atom-style variable with name
-      d_name = per-atom floating point vector name, managed by fix property/atom
-      i_name = per-atom integer vector name, managed by fix property/atom
+mol = molecule ID
+type = atom type
+mass = atom mass
+x,y,z = unscaled atom coordinates
+xs,ys,zs = scaled atom coordinates
+xu,yu,zu = unwrapped atom coordinates
+ix,iy,iz = box image that the atom is in
+vx,vy,vz = atom velocities
+fx,fy,fz = forces on atoms
+q = atom charge
+mux,muy,muz = orientation of dipolar atom
+radius = radius of spherical particle
+omegax,omegay,omegaz = angular velocity of spherical particle
+angmomx,angmomy,angmomz = angular momentum of aspherical particle
+tqx,tqy,tqz = torque on finite-size particles
+c_ID = per-atom vector calculated by a compute with ID
+c_ID[I] = Ith column of per-atom array calculated by a compute with ID
+f_ID = per-atom vector calculated by a fix with ID
+f_ID[I] = Ith column of per-atom array calculated by a fix with ID
+v_name = per-atom vector calculated by an atom-style variable with name
+d_name = per-atom floating point vector name, managed by fix property/atom
+i_name = per-atom integer vector name, managed by fix property/atom
 </pre></div>
 </div>
 <ul class="simple">
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>com</em></li>
 </ul>
 <pre class="literal-block">
 <em>com</em> value = <em>yes</em> or <em>no</em>
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix 1 all store/state 0 x y z
 fix 1 all store/state 0 xu yu zu com yes
 fix 2 all store/state 1000 vx vy vz
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Define a fix that stores attributes for each atom in the group at the
 time the fix is defined.  If <em>N</em> is 0, then the values are never
 updated, so this is a way of archiving an atom attribute at a given
 time for future use in a calculation or output.  See the discussion of
 <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a> that take fixes as
 inputs.  And see for example, the <a class="reference internal" href="compute_reduce.html"><em>compute reduce</em></a>, <a class="reference internal" href="fix_ave_atom.html"><em>fix ave/atom</em></a>, <a class="reference internal" href="fix_ave_histo.html"><em>fix ave/histo</em></a>, <a class="reference internal" href="fix_ave_spatial.html"><em>fix ave/spatial</em></a>,
 and <a class="reference internal" href="variable.html"><em>atom-style variable</em></a> commands.</p>
 <p>If <em>N</em> is not zero, then the attributes will be updated every <em>N</em>
 steps.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">Actually, only atom attributes specified by keywords
 like <em>xu</em> or <em>vy</em> are initially stored immediately at the point in
 your input script when the fix is defined.  Attributes specified by a
 compute, fix, or variable are not initially stored until the first run
 following the fix definition begins.  This is because calculating
 those attributes may require quantities that are not defined in
 between runs.</p>
 </div>
 <p>The list of possible attributes is the same as that used by the <a class="reference internal" href="dump.html"><em>dump custom</em></a> command, which describes their meaning.</p>
 <p>If the <em>com</em> keyword is set to <em>yes</em> then the <em>xu</em>, <em>yu</em>, and <em>zu</em>
 inputs store the position of each atom relative to the center-of-mass
 of the group of atoms, instead of storing the absolute position.  This
 option is used by the <a class="reference internal" href="compute_msd.html"><em>compute msd</em></a> command.</p>
 <p>The requested values are stored in a per-atom vector or array as
 discussed below.  Zeroes are stored for atoms not in the specified
 group.</p>
 </div>
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>This fix writes the per-atom values it stores to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>, so that the values can be restored when a
 simulation is restarted.  See the <a class="reference internal" href="read_restart.html"><em>read_restart</em></a>
 command for info on how to re-specify a fix in an input script that
 reads a restart file, so that the operation of the fix continues in an
 uninterrupted fashion.</p>
 <p>None of the <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> options are relevant to this
 fix.</p>
 <p>If a single input is specified, this fix produces a per-atom vector.
 If multiple inputs are specified, a per-atom array is produced where
 the number of columns for each atom is the number of inputs.  These
 can be accessed by various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  The per-atom values be
 accessed on any timestep.</p>
 <p>No parameter of this fix can be used with the <em>start/stop</em> keywords of
 the <a class="reference internal" href="run.html"><em>run</em></a> command.  This fix is not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <blockquote>
 <div>none</div></blockquote>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="dump.html"><em>dump custom</em></a>, <a class="reference internal" href="compute_property_atom.html"><em>compute property/atom</em></a>,
 <a class="reference internal" href="fix_property_atom.html"><em>fix property/atom</em></a>, <a class="reference internal" href="variable.html"><em>variable</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The option default is com = no.</p>
 </div>
 </div>
 
 
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   <div class="section" id="fix-tfmc-command">
 <span id="index-0"></span><h1>fix tfmc command<a class="headerlink" href="#fix-tfmc-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID tfmc Delta Temp seed keyword value
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>tfmc = style name of this fix command</li>
 <li>Delta = maximal displacement length (distance units)</li>
 <li>Temp = imposed temperature of the system</li>
 <li>seed = random number seed (positive integer)</li>
 <li>zero or more keyword/arg pairs may be appended</li>
 <li>keyword = <em>com</em> or <em>rot</em></li>
 </ul>
 <pre class="literal-block">
 <em>com</em> args = xflag yflag zflag
-    xflag,yflag,zflag = 0/1 to exclude/include each dimension
-  <em>rot</em> args = none
+  xflag,yflag,zflag = 0/1 to exclude/include each dimension
+<em>rot</em> args = none
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix 1 all tfmc 0.1 1000.0 159345
 fix 1 all tfmc 0.05 600.0 658943 com 1 1 0
 fix 1 all tfmc 0.1 750.0 387068 com 1 1 1 rot
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Perform uniform-acceptance force-bias Monte Carlo (fbMC) simulations,
 using the time-stamped force-bias Monte Carlo (tfMC) algorithm
 described in <a class="reference internal" href="#mees"><span>(Mees)</span></a> and <a class="reference internal" href="#bal"><span>(Bal)</span></a>.</p>
 <p>One successful use case of force-bias Monte Carlo methods is that they
 can be used to extend the time scale of atomistic simulations, in
 particular when long time scale relaxation effects must be considered;
 some interesting examples are given in the review by <a class="reference internal" href="#neyts"><span>(Neyts)</span></a>.
 An example of a typical use case would be the modelling of chemical
 vapour deposition (CVD) processes on a surface, in which impacts by
 gas-phase species can be performed using MD, but subsequent relaxation
 of the surface is too slow to be done using MD only. Using tfMC can
 allow for a much faster relaxation of the surface, so that higher
 fluxes can be used, effectively extending the time scale of the
 simulation. (Such an alternating simulation approach could be set up
 using a <a class="reference internal" href="jump.html"><em>loop</em></a>.)</p>
 <p>The initial version of tfMC algorithm in <a class="reference internal" href="#mees"><span>(Mees)</span></a> contained an
 estimation of the effective time scale of such a simulation, but it
 was later shown that the speed-up one can gain from a tfMC simulation
 is system- and process-dependent, ranging from none to several orders
 of magnitude. In general, solid-state processes such as
 (re)crystallisation or growth can be accelerated by up to two or three
 orders of magnitude, whereas diffusion in the liquid phase is not
 accelerated at all. The observed pseudodynamics when using the tfMC
 method is not the actual dynamics one would obtain using MD, but the
 relative importance of processes can match the actual relative
 dynamics of the system quite well, provided <em>Delta</em> is chosen with
 care. Thus, the system&#8217;s equilibrium is reached faster than in MD,
 along a path that is generally roughly similar to a typical MD
 simulation (but not necessarily so). See <a class="reference internal" href="#bal"><span>(Bal)</span></a> for details.</p>
 <p>Each step, all atoms in the selected group are displaced using the
 stochastic tfMC algorithm, which is designed to sample the canonical
 (NVT) ensemble at the temperature <em>Temp</em>. Although tfMC is a Monte
 Carlo algorithm and thus strictly speaking does not perform time
 integration, it is similar in the sense that it uses the forces on all
 atoms in order to update their positions. Therefore, it is implemented
 as a time integration fix, and no other fixes of this type (such as
 <a class="reference internal" href="fix_nve.html"><em>fix nve</em></a>) should be used at the same time. Because
 velocities do not play a role in this kind of Monte Carlo simulations,
 instantaneous temperatures as calculated by <a class="reference internal" href="compute_temp.html"><em>temperature computes</em></a> or <a class="reference internal" href="thermo_style.html"><em>thermodynamic output</em></a> have no meaning: the only relevant
 temperature is the sampling temperature <em>Temp</em>.  Similarly, performing
 tfMC simulations does not require setting a <a class="reference internal" href="timestep.html"><em>timestep</em></a>
 and the <a class="reference internal" href="thermo_style.html"><em>simulated time</em></a> as calculated by LAMMPS is
 meaningless.</p>
 <p>The critical parameter determining the success of a tfMC simulation is
 <em>Delta</em>, the maximal displacement length of the lightest element in
 the system: the larger it is, the longer the effective time scale of
 the simulation will be (there is an approximately quadratic
 dependence). However, <em>Delta</em> must also be chosen sufficiently small
 in order to comply with detailed balance; in general values between 5
 and 10 % of the nearest neighbor distance are found to be a good
 choice. For a more extensive discussion with specific examples, please
 refer to <a class="reference internal" href="#bal"><span>(Bal)</span></a>, which also describes how the code calculates
 element-specific maximal displacements from <em>Delta</em>, based on the
 fourth root of their mass.</p>
 <p>Because of the uncorrelated movements of the atoms, the center-of-mass
 of the fix group will not necessarily be stationary, just like its
 orientation. When the <em>com</em> keyword is used, all atom positions will
 be shifted (after every tfMC iteration) in order to fix the position
 of the center-of-mass along the included directions, by setting the
 corresponding flag to 1. The <em>rot</em> keyword does the same for the
 rotational component of the tfMC displacements after every iteration.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">the <em>com</em> and <em>rot</em> keywords should not be used if an
 external force is acting on the specified fix group, along the
 included directions. This can be either a true external force (e.g.
 through <a class="reference internal" href="fix_wall.html"><em>fix wall</em></a>) or forces due to the interaction
 with atoms not included in the fix group. This is because in such
 cases, translations or rotations of the fix group could be induced by
 these external forces, and removing them will lead to a violation of
 detailed balance.</p>
 </div>
 </div>
 <hr class="docutils" />
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.</p>
 <p>None of the <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> options are relevant to this
 fix.</p>
 <p>This fix is not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>This fix is part of the MC package.  It is only enabled if LAMMPS was
 built with that package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 <p>This fix is not compatible with <a class="reference internal" href="fix_shake.html"><em>fix shake</em></a>.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="fix_gcmc.html"><em>fix gcmc</em></a>, <a class="reference internal" href="fix_nh.html"><em>fix nvt</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The option default is com = 0 0 0</p>
 <hr class="docutils" />
 <p id="bal"><strong>(Bal)</strong> K. M Bal and E. C. Neyts, J. Chem. Phys. 141, 204104 (2014).</p>
 <p id="mees"><strong>(Mees)</strong> M. J. Mees, G. Pourtois, E. C. Neyts, B. J. Thijsse, and
 A. Stesmans, Phys. Rev. B 85, 134301 (2012).</p>
 <p id="neyts"><strong>(Neyts)</strong> E. C. Neyts and A. Bogaerts, Theor. Chem. Acc. 132, 1320
 (2013).</p>
 </div>
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   <div class="section" id="fix-ti-rs-command">
 <span id="index-0"></span><h1>fix ti/rs command<a class="headerlink" href="#fix-ti-rs-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID ti/rs lambda_initial lambda_final t_switch t_equil keyword value ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>ti/rs = style name of this fix command</li>
 <li>lambda_initial/lambda_final = initial/final values of the coupling parameter</li>
 <li>t_switch/t_equil = number of steps of the switching/equilibration procedure</li>
 <li>keyword = <em>function</em></li>
 </ul>
 <pre class="literal-block">
 <em>function</em> value = function-ID
-    function-ID = ID of the switching function (1, 2 or 3)
+  function-ID = ID of the switching function (1, 2 or 3)
 </pre>
 <p><strong>Example:</strong></p>
 <div class="highlight-python"><div class="highlight"><pre>fix ref all ti/rs 50.0 2000 1000
 fix vf vacancy ti/rs 10.0 70000 50000 function 2
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>This fix allows you to compute the free energy temperature dependence
 by performing a thermodynamic integration procedure known as
 Reversible Scaling <a class="reference internal" href="#dekoning99"><span>(de Koning99,</span></a> <span class="xref std std-ref">de Koning00a)</span>. The thermodynamic integration is performed
 using the nonequilibrium method of Adiabatic Switching
 <a class="reference internal" href="fix_ti_spring.html#watanabe"><span>(Watanabe,</span></a> <a class="reference internal" href="fix_ti_spring.html#dekoning96"><span>de Koning96)</span></a>.</p>
 <p>The forces on the atoms are dynamically scaled during the simulation,
 the rescaling is done in the following manner:</p>
 <img alt="_images/fix_ti_rs_force.jpg" class="align-center" src="_images/fix_ti_rs_force.jpg" />
 <p>where F_int is the total force on the atoms due to the interatomic
 potential and lambda is the coupling parameter of the thermodynamic
 integration.</p>
 <p>The fix acts as follows: during the first <em>t_equil</em> steps after the
 fix is defined the value of lambda is <em>lambda_initial</em> , this is the
 period to equilibrate the system in the lambda = <em>lambda_initial</em>
 state. After this the value of lambda changes continuously from
 <em>lambda_initial</em> to <em>lambda_final</em> according to the function defined
 using the keyword <em>function</em> (described below), this is done in
 <em>t_switch</em> steps. Then comes the second equilibration period of
 <em>t_equil</em> to equilibrate the system in the lambda = <em>lambda_final</em>
 state. After that the switching back to the lambda = <em>lambda_initial</em>
 state is done using <em>t_switch</em> timesteps and following the same
 switching function. After this period the value of lambda is kept
 equal to <em>lambda_initial</em> indefinitely or until a <a class="reference internal" href="unfix.html"><em>unfix</em></a>
 erase the fix.</p>
 <p>The description of thermodynamic integration in both directions is
 done in <a class="reference internal" href="#dekoning00b"><span>de Koning00b</span></a>, the main reason is to try to
 eliminate the dissipated heat due to the nonequilibrium process.</p>
 <p>The <em>function</em> keyword allows the use of three different switching
 rates. The option <em>1</em> results in a constant rescaling where the lambda
 parameter changes at a constant rate during the switching time
 according to the switching function</p>
 <img alt="_images/fix_ti_rs_function_1.jpg" class="align-center" src="_images/fix_ti_rs_function_1.jpg" />
 <p>where tau is the scaled time variable t/t_switch. This switching
 function has the characteristic that the temperature scaling is faster
 at temperatures closer to the final temperature of the procedure. The
 option number <em>2</em> performs the switching at a rate defined by the
 following switching function</p>
 <img alt="_images/fix_ti_rs_function_2.jpg" class="align-center" src="_images/fix_ti_rs_function_2.jpg" />
 <p>This switching function has the characteristic that the temperature
 scaling occurs at a constant rate during all the procedure. The option
 number <em>3</em> performs the switching at a rate defined by the following
 switching function</p>
 <img alt="_images/fix_ti_rs_function_3.jpg" class="align-center" src="_images/fix_ti_rs_function_3.jpg" />
 <p>This switching function has the characteristic that the temperature
 scaling is faster at temperatures closer to the initial temperature of
 the procedure.</p>
 <p>An example script using this command is provided in the
 examples/USER/misc/ti directory.</p>
 </div>
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.</p>
 <p>This fix computes a global vector quantitie which can be accessed by
 various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>. The vector has
 2 positions, the first one is the coupling parameter lambda and the
 second one is the time derivative of lambda. The scalar and vector
 values calculated by this fix are &#8220;extensive&#8221;.</p>
 <p>No parameter of this fix can be used with the <em>start/stop</em> keywords of
 the <a class="reference internal" href="run.html"><em>run</em></a> command.</p>
 <p>The forces due to this fix are imposed during an energy minimization,
 invoked by the <a class="reference internal" href="minimize.html"><em>minimize</em></a> command.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="fix_ti_spring.html"><em>fix ti/spring</em></a></p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>This command is part of the USER-MISC package.  It is only enabled if
 LAMMPS was built with those packages.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The keyword default is function = 1.</p>
 <hr class="docutils" />
 <p id="dekoning99"><strong>(de Koning 99)</strong> M. de Koning, A. Antonelli and S. Yip, Phys Rev Lett, 83, 3973 (1999).</p>
 <p id="watanabe"><strong>(Watanabe)</strong> M. Watanabe and W. P. Reinhardt, Phys Rev Lett, 65, 3301 (1990).</p>
 <p id="dekoning96"><strong>(de Koning 96)</strong> M. de Koning and A. Antonelli, Phys Rev E, 53, 465 (1996).</p>
 <p id="dekoning00a"><strong>(de Koning 00a)</strong> M. de Koning, A. Antonelli and S. Yip, J Chem Phys, 115, 11025 (2000).</p>
 <p id="dekoning00b"><strong>(de Koning 00b)</strong> M. de Koning et al., Computing in Science &amp; Engineering, 2, 88 (2000).</p>
 </div>
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diff --git a/doc/fix_ti_spring.html b/doc/fix_ti_spring.html
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   <div class="section" id="fix-ti-spring-command">
 <span id="index-0"></span><h1>fix ti/spring command<a class="headerlink" href="#fix-ti-spring-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID ti/spring K t_switch t_equil keyword value ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>ti/spring = style name of this fix command</li>
 <li>K = spring constant (force/distance units)</li>
 <li>t_switch/t_equil = number of steps of the switching/equilibration procedure</li>
 <li>zero or more keyword/value pairs may be appended to args</li>
 <li>keyword = <em>function</em></li>
 </ul>
 <pre class="literal-block">
 <em>function</em> value = function-ID
-    function-ID = ID of the switching function (1 or 2)
+  function-ID = ID of the switching function (1 or 2)
 </pre>
 <p><strong>Example:</strong></p>
 <div class="highlight-python"><div class="highlight"><pre>fix ref all ti/spring 50.0 2000 1000 function 2
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>This fix allows you to compute the free energy of solids by performing
 a thermodynamic integration between the solid of interest and an
 Einstein crystal <a class="reference internal" href="#frenkel"><span>(Frenkel)</span></a>. The thermodynamic integration
 is performed using the nonequilibrium method of Adiabatic Switching
 <a class="reference internal" href="#watanabe"><span>(Watanabe,</span></a> <a class="reference internal" href="#dekoning96"><span>de Koning96)</span></a>.</p>
 <p>A spring force is applied independently to each atom in the group to
 tether it to its initial position. The initial position for each atom
 is its location at the time the fix command was issued. More details
 about the springs are available in <a class="reference internal" href="fix_spring_self.html"><em>fix spring/self</em></a>. The forces on the atoms are
 dynamically scaled during the simulation, the rescaling is done in the
 following manner:</p>
 <img alt="_images/fix_ti_spring_force.jpg" class="align-center" src="_images/fix_ti_spring_force.jpg" />
 <p>where F_harm is the force due to the springs, F_solid is the total
 force on the atoms due to the interatomic potential and lambda is the
 coupling parameter of the thermodynamic integration.</p>
 <p>The fix acts as follows: during the first <em>t_equil</em> steps after the
 fix is defined the value of lambda is zero, this is the period to
 equilibrate the system in the lambda = 0 state. After this the value
 of lambda changes continuously from 0 to 1 according to the function
 defined using the keyword <em>function</em> (described below), this is done
 in <em>t_switch</em> steps. Then comes the second equilibration period of
 <em>t_equil</em> to equilibrate the system in the lambda = 1 state. After
 that the switching back to the lambda = 0 state is made using
 <em>t_switch</em> timesteps and following the same switching function. After
 this period the value of lambda is kept equal to zero and the fix has
 no action in the dynamics of the system anymore.</p>
 <p>The description of thermodynamic integration in both directions is
 done in <a class="reference internal" href="#dekoning97"><span>de Koning97</span></a>, the main reason is to try to
 eliminate the dissipated heat due to the nonequilibrium process.</p>
 <p>The <em>function</em> keyword allows the use of two different switching
 rates, the option <em>1</em> results in a constant rescaling where the lambda
 parameter changes at a constant rate during the switching time
 according to the switching function</p>
 <img alt="_images/fix_ti_spring_function_1.jpg" class="align-center" src="_images/fix_ti_spring_function_1.jpg" />
 <p>where tau is the scaled time variable t/t_switch. The option number
 <em>2</em> performs the switching at a rate defined by the following
 switching function</p>
 <img alt="_images/fix_ti_spring_function_2.jpg" class="align-center" src="_images/fix_ti_spring_function_2.jpg" />
 <p>This function has zero slope as lambda approaches its extreme values
 (0 and 1), according to (<a class="reference internal" href="#dekoning96"><span>de Koning96)</span></a> this results in
 smaller fluctuations on the integral to be computed on the
 thermodynamic integration.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">It is importante to keep the center of mass fixed
 during the thermodynamic integration, a non-zero total velocity will
 result in divergencies during the integration due to the fact that the
 atoms are &#8216;attatched&#8217; to its equilibrium positions by the Einstein
 crystal. Check the option <em>zero</em> of <a class="reference external" href="fix_langevin_html">fix langevin</a>
 and <a class="reference internal" href="velocity.html"><em>velocity</em></a>. The use of the Nose-Hoover thermostat
 (<code class="xref doc docutils literal"><span class="pre">fix</span> <span class="pre">nvt</span></code>) is NOT recommended due to its well documented
 issues with the canonical sampling of harmonic degrees of freedom
 (notice that the <em>chain</em> option will NOT solve this problem). The
 Langevin thermostat (<a class="reference external" href="fix_langevin.html&quot;">fix langevin</a>) works fine.</p>
 </div>
 </div>
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>This fix writes the original coordinates of tethered atoms to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>, so that the spring effect will be the
 same in a restarted simulation. See the <a class="reference internal" href="read_restart.html"><em>read restart</em></a> command for info on how to re-specify a fix
 in an input script that reads a restart file, so that the operation of
 the fix continues in an uninterrupted fashion.</p>
 <p>The <a class="reference internal" href="fix_modify.html"><em>fix modify</em></a> <em>energy</em> option is supported by this
 fix to add the energy stored in the per-atom springs to the system&#8217;s
 potential energy as part of <a class="reference internal" href="thermo_style.html"><em>thermodynamic output</em></a>.</p>
 <p>This fix computes a global scalar and a global vector quantities which
 can be accessed by various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  The scalar is an energy which
 is the sum of the spring energy for each atom, where the per-atom
 energy is 0.5 * K * r^2. The vector has 2 positions, the first one is
 the coupling parameter lambda and the second one is the time
 derivative of lambda. The scalar and vector values calculated by this
 fix are &#8220;extensive&#8221;.</p>
 <p>No parameter of this fix can be used with the <em>start/stop</em> keywords of
 the <a class="reference internal" href="run.html"><em>run</em></a> command.</p>
 <p>The forces due to this fix are imposed during an energy minimization,
 invoked by the <a class="reference internal" href="minimize.html"><em>minimize</em></a> command.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">If you want the per-atom spring energy to be included
 in the total potential energy of the system (the quantity being
 minimized), you MUST enable the <a class="reference internal" href="fix_modify.html"><em>fix modify</em></a> <em>energy</em>
 option for this fix.</p>
 </div>
 <p>An example script using this command is provided in the
 examples/USER/misc/ti directory.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="fix_spring.html"><em>fix spring</em></a>, <a class="reference internal" href="fix_ti_rs.html"><em>fix ti/rs</em></a></p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>This command is part of the USER-MISC package.  It is only enabled if
 LAMMPS was built with those packages.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The keyword default is function = 1.</p>
 <hr class="docutils" />
 <p id="frenkel"><strong>(Frenkel)</strong> Daan Frenkel and Anthony J. C. Ladd, J. Chem. Phys. 81, 3188
 (1984).</p>
 <p id="watanabe"><strong>(Watanabe)</strong> M. Watanabe and W. P. Reinhardt, Phys Rev Lett, 65, 3301 (1990).</p>
 <p id="dekoning96"><strong>(de Koning 96)</strong> M. de Koning and A. Antonelli, Phys Rev E, 53, 465 (1996).</p>
 <p id="dekoning97"><strong>(de Koning 97)</strong> M. de Koning and A. Antonelli, Phys Rev B, 55, 735 (1997).</p>
 </div>
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   <div class="section" id="fix-ttm-command">
 <span id="index-0"></span><h1>fix ttm command<a class="headerlink" href="#fix-ttm-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="fix-ttm-mod-command">
 <h1>fix ttm/mod command<a class="headerlink" href="#fix-ttm-mod-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID ttm seed C_e rho_e kappa_e gamma_p gamma_s v_0 Nx Ny Nz T_infile N T_outfile
 fix ID group-ID ttm/mod seed init_file Nx Ny Nz T_infile N T_outfile
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>style = <em>ttm</em> or <em>ttm_mod</em></li>
 <li>seed = random number seed to use for white noise (positive integer)</li>
 <li>remaining arguments for fix ttm:</li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>C_e  = electronic specific heat (energy/(electron*temperature) units)
-  rho_e = electronic density (electrons/volume units)
-  kappa_e = electronic thermal conductivity (energy/(time*distance*temperature) units)
-  gamma_p = friction coefficient due to electron-ion interactions (mass/time units)
-  gamma_s = friction coefficient due to electronic stopping (mass/time units)
-  v_0 = electronic stopping critical velocity (velocity units)
-  Nx = number of thermal solve grid points in the x-direction (positive integer)
-  Ny = number of thermal solve grid points in the y-direction (positive integer)
-  Nz = number of thermal solve grid points in the z-direction (positive integer)
-  T_infile = filename to read initial electronic temperature from
-  N = dump TTM temperatures every this many timesteps, 0 = no dump
-  T_outfile = filename to write TTM temperatures to (only needed if N &gt; 0)
+rho_e = electronic density (electrons/volume units)
+kappa_e = electronic thermal conductivity (energy/(time*distance*temperature) units)
+gamma_p = friction coefficient due to electron-ion interactions (mass/time units)
+gamma_s = friction coefficient due to electronic stopping (mass/time units)
+v_0 = electronic stopping critical velocity (velocity units)
+Nx = number of thermal solve grid points in the x-direction (positive integer)
+Ny = number of thermal solve grid points in the y-direction (positive integer)
+Nz = number of thermal solve grid points in the z-direction (positive integer)
+T_infile = filename to read initial electronic temperature from
+N = dump TTM temperatures every this many timesteps, 0 = no dump
+T_outfile = filename to write TTM temperatures to (only needed if N &gt; 0)
 </pre></div>
 </div>
 <ul class="simple">
 <li>remaining arguments for fix ttm/mod:</li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>init_file = file with the parameters to TTM
-  Nx = number of thermal solve grid points in the x-direction (positive integer)
-  Ny = number of thermal solve grid points in the y-direction (positive integer)
-  Nz = number of thermal solve grid points in the z-direction (positive integer)
-  T_infile = filename to read initial electronic temperature from
-  N = dump TTM temperatures every this many timesteps, 0 = no dump
-  T_outfile = filename to write TTM temperatures to (only needed if N &gt; 0)
+Nx = number of thermal solve grid points in the x-direction (positive integer)
+Ny = number of thermal solve grid points in the y-direction (positive integer)
+Nz = number of thermal solve grid points in the z-direction (positive integer)
+T_infile = filename to read initial electronic temperature from
+N = dump TTM temperatures every this many timesteps, 0 = no dump
+T_outfile = filename to write TTM temperatures to (only needed if N &gt; 0)
 </pre></div>
 </div>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix 2 all ttm 699489 1.0 1.0 10 0.1 0.0 2.0 1 12 1 initialTs 1000 T.out
 fix 2 all ttm 123456 1.0 1.0 1.0 1.0 1.0 5.0 5 5 5 Te.in 1 Te.out
 fix 2 all ttm/mod 34277 parameters.txt 5 5 5 T_init 10 T_out
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Use a two-temperature model (TTM) to represent heat transfer through
 and between electronic and atomic subsystems.  LAMMPS models the
 atomic subsystem as usual with a molecular dynamics model and the
 classical force field specified by the user, but the electronic
 subsystem is modeled as a continuum, or a background &#8220;gas&#8221;, on a
 regular grid.  Energy can be transferred spatially within the grid
 representing the electrons.  Energy can also be transferred between
 the electronic and the atomic subsystems.  The algorithm underlying
 this fix was derived by D. M.  Duffy and A. M. Rutherford and is
 discussed in two J Physics: Condensed Matter papers: <a class="reference internal" href="#duffy"><span>(Duffy)</span></a>
 and <a class="reference internal" href="#rutherford"><span>(Rutherford)</span></a>.  They used this algorithm in cascade
 simulations where a primary knock-on atom (PKA) was initialized with a
 high velocity to simulate a radiation event.</p>
 <p>The description in this sub-section applies to both fix ttm and fix
 ttm/mod.  Fix ttm/mod adds options to account for external heat
 sources (e.g. at a surface) and for specifying parameters that allow
 the electronic heat capacity to depend strongly on electronic
 temperature.  It is more expensive computationally than fix ttm
 because it treats the thermal diffusion equation as non-linear.  More
 details on fix ttm/mod are given below.</p>
 <p>Heat transfer between the electronic and atomic subsystems is carried
 out via an inhomogeneous Langevin thermostat.  This thermostat differs
 from the regular Langevin thermostat (<a class="reference internal" href="fix_langevin.html"><em>fix langevin</em></a>) in three important ways.  First, the
 Langevin thermostat is applied uniformly to all atoms in the
 user-specified group for a single target temperature, whereas the TTM
 fix applies Langevin thermostatting locally to atoms within the
 volumes represented by the user-specified grid points with a target
 temperature specific to that grid point.  Second, the Langevin
 thermostat couples the temperature of the atoms to an infinite heat
 reservoir, whereas the heat reservoir for fix TTM is finite and
 represents the local electrons.  Third, the TTM fix allows users to
 specify not just one friction coefficient, but rather two independent
 friction coefficients: one for the electron-ion interactions
 (<em>gamma_p</em>), and one for electron stopping (<em>gamma_s</em>).</p>
 <p>When the friction coefficient due to electron stopping, <em>gamma_s</em>, is
 non-zero, electron stopping effects are included for atoms moving
 faster than the electron stopping critical velocity, <em>v_0</em>.  For
 further details about this algorithm, see <a class="reference internal" href="#duffy"><span>(Duffy)</span></a> and
 <a class="reference internal" href="#rutherford"><span>(Rutherford)</span></a>.</p>
 <p>Energy transport within the electronic subsystem is solved according
 to the heat diffusion equation with added source terms for heat
 transfer between the subsystems:</p>
 <img alt="_images/fix_ttm.jpg" class="align-center" src="_images/fix_ttm.jpg" />
 <p>where C_e is the specific heat, rho_e is the density, kappa_e is the
 thermal conductivity, T is temperature, the &#8220;e&#8221; and &#8220;a&#8221; subscripts
 represent electronic and atomic subsystems respectively, g_p is the
 coupling constant for the electron-ion interaction, and g_s is the
 electron stopping coupling parameter.  C_e, rho_e, and kappa_e are
 specified as parameters to the fix.  The other quantities are derived.
 The form of the heat diffusion equation used here is almost the same
 as that in equation 6 of <a class="reference internal" href="#duffy"><span>(Duffy)</span></a>, with the exception that the
 electronic density is explicitly reprensented, rather than being part
 of the the specific heat parameter.</p>
 <p>Currently, fix ttm assumes that none of the user-supplied parameters
 will vary with temperature. Note that <a class="reference internal" href="#duffy"><span>(Duffy)</span></a> used a tanh()
 functional form for the temperature dependence of the electronic
 specific heat, but ignored temperature dependencies of any of the
 other parameters.  See more discussion below for fix ttm/mod.</p>
 <p>These fixes require use of periodic boundary conditions and a 3D
 simulation.  Periodic boundary conditions are also used in the heat
 equation solve for the electronic subsystem.  This varies from the
 approach of <a class="reference internal" href="#rutherford"><span>(Rutherford)</span></a> where the atomic subsystem was
 embedded within a larger continuum representation of the electronic
 subsystem.</p>
 <p>The initial electronic temperature input file, <em>T_infile</em>, is a text
 file LAMMPS reads in with no header and with four numeric columns
 (ix,iy,iz,Temp) and with a number of rows equal to the number of
 user-specified grid points (Nx by Ny by Nz).  The ix,iy,iz are node
 indices from 0 to nxnodes-1, etc.  For example, the initial electronic
 temperatures on a 1 by 2 by 3 grid could be specified in a <em>T_infile</em>
 as follows:</p>
 <div class="highlight-python"><div class="highlight"><pre>0 0 0 1.0
 0 0 1 1.0
 0 0 2 1.0
 0 1 0 2.0
 0 1 1 2.0
 0 1 2 2.0
 </pre></div>
 </div>
 <p>where the electronic temperatures along the y=0 plane have been set to
 1.0, and the electronic temperatures along the y=1 plane have been set
 to 2.0.  The order of lines in this file is no important.  If all the
 nodal values are not specified, LAMMPS will generate an error.</p>
 <p>The temperature output file, <em>T_oufile</em>, is created and written by
 this fix.  Temperatures for both the electronic and atomic subsystems
 at every node and every N timesteps are output.  If N is specified as
 zero, no output is generated, and no output filename is needed.  The
 format of the output is as follows.  One long line is written every
 output timestep.  The timestep itself is given in the first column.
 The next Nx*Ny*Nz columns contain the temperatures for the atomic
 subsystem, and the final Nx*Ny*Nz columns contain the temperatures for
 the electronic subsystem.  The ordering of the Nx*Ny*Nz columns is
 with the z index varing fastest, y the next fastest, and x the
 slowest.</p>
 <p>These fixes do not change the coordinates of their atoms; they only
 scales their velocities.  Thus a time integration fix (e.g. <a class="reference internal" href="fix_nve.html"><em>fix nve</em></a>) should still be used to time integrate the affected
 atoms.  The fixes should not normally be used on atoms that have their
 temperature controlled by another fix - e.g. <a class="reference internal" href="fix_nh.html"><em>fix nvt</em></a> or
 <a class="reference internal" href="fix_langevin.html"><em>fix langevin</em></a>.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">The current implementations of these fixes create a
 copy of the electron grid that overlays the entire simulation domain,
 for each processor.  Values on the grid are summed across all
 processors.  Thus you should insure that this grid is not too large,
 else your simulation could incur high memory and communication costs.</p>
 </div>
 <hr class="docutils" />
 <p><strong>Additional details for fix ttm/mod</strong></p>
 <p>Fix ttm/mod uses the heat diffusion equation with possible external
 heat sources (e.g. laser heating in ablation simulations):</p>
 <img alt="_images/fix_ttm_mod.jpg" class="align-center" src="_images/fix_ttm_mod.jpg" />
 <p>where theta is the Heaviside step function, I_0 is the (absorbed)
 laser pulse intensity for ablation simulations, l_skin is the depth
 of skin-layer, and all other designations have the same meaning as in
 the former equation. The duration of the pulse is set by the parameter
 <em>tau</em> in the <em>init_file</em>.</p>
 <p>Fix ttm/mod also allows users to specify the dependencies of C_e and
 kappa_e on the electronic temperature. The specific heat is expressed
 as</p>
 <img alt="_images/fix_ttm_ce.jpg" class="align-center" src="_images/fix_ttm_ce.jpg" />
 <p>where <em>X</em> = T_e/1000, and the thermal conductivity is defined as
 kappa_e = D_e*rho_e*C_e, where D_e is the thermal diffusion
 coefficient.</p>
 <p>Electronic pressure effects are included in the TTM model to account
 for the blast force acting on ions because of electronic pressure
 gradient (see <a class="reference internal" href="#chen"><span>(Chen)</span></a>, <a class="reference internal" href="#norman"><span>(Norman)</span></a>).  The total force
 acting on an ion is:</p>
 <img alt="_images/fix_ttm_blast.jpg" class="align-center" src="_images/fix_ttm_blast.jpg" />
 <p>where F_langevin is a force from Langevin thermostat simulating
 electron-phonon coupling, and nabla P_e/n_ion is the electron blast
 force.</p>
 <p>The electronic pressure is taken to be P_e = B*rho_e*C_e*T_e</p>
 <p>The current fix ttm/mod implementation allows TTM simulations with a
 vacuum. The vacuum region is defined as the grid cells with zero
 electronic temperature. The numerical scheme does not allow energy
 exchange with such cells. Since the material can expand to previously
 unoccupied region in some simulations, the vacuum border can be
 allowed to move. It is controlled by the <em>surface_movement</em> parameter
 in the <em>init_file</em>. If it is set to 1, then &#8220;vacuum&#8221; cells can be
 changed to &#8220;electron-filled&#8221; cells with the temperature <em>T_e_min</em> if
 atoms move into them (currently only implemented for the case of
 1-dimensional motion of flat surface normal to the X axis). The
 initial borders of vacuum can be set in the <em>init_file</em> via <em>lsurface</em>
 and <em>rsurface</em> parameters. In this case, electronic pressure gradient
 is calculated as</p>
 <img alt="_images/fix_ttm_blast1.jpg" class="align-center" src="_images/fix_ttm_blast1.jpg" />
 <p>where lambda is the electron mean free path (see <a class="reference internal" href="#norman"><span>(Norman)</span></a>,
 <a class="reference internal" href="#pisarev"><span>(Pisarev)</span></a>)</p>
 <p>The fix ttm/mod parameter file <em>init_file</em> has the following syntax/
 Every line with the odd number is considered as a comment and
 ignored. The lines with the even numbers are treated as follows:</p>
 <div class="highlight-python"><div class="highlight"><pre>a_0, energy/(temperature*electron) units
 a_1, energy/(temperature^2*electron) units
 a_2, energy/(temperature^3*electron) units
 a_3, energy/(temperature^4*electron) units
 a_4, energy/(temperature^5*electron) units
 C_0, energy/(temperature*electron) units
 A, 1/temperature units
 rho_e, electrons/volume units
 D_e, length^2/time units
 gamma_p, mass/time units
 gamma_s, mass/time units
 v_0, length/time units
 I_0, energy/(time*length^2) units
 lsurface, electron grid units (positive integer)
 rsurface, electron grid units (positive integer)
 l_skin, length units
 tau, time units
 B, dimensionless
 lambda, length units
 n_ion, ions/volume units
 surface_movement: 0 to disable tracking of surface motion, 1 to enable
 T_e_min, temperature units
 </pre></div>
 </div>
 </div>
 <hr class="docutils" />
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>These fixes write the state of the electronic subsystem and the energy
 exchange between the subsystems to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.  See the <a class="reference internal" href="read_restart.html"><em>read_restart</em></a> command
 for info on how to re-specify a fix in an input script that reads a
 restart file, so that the operation of the fix continues in an
 uninterrupted fashion.</p>
 <p>Because the state of the random number generator is not saved in the
 restart files, this means you cannot do &#8220;exact&#8221; restarts with this
 fix, where the simulation continues on the same as if no restart had
 taken place.  However, in a statistical sense, a restarted simulation
 should produce the same behavior.</p>
 <p>None of the <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> options are relevant to these
 fixes.</p>
 <p>Both fixes compute 2 output quantities stored in a vector of length 2,
 which can be accessed by various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  The first quantity is the
 total energy of the electronic subsystem. The second quantity is the
 energy transferred from the electronic to the atomic subsystem on that
 timestep. Note that the velocity verlet integrator applies the fix ttm
 forces to the atomic subsystem as two half-step velocity updates: one
 on the current timestep and one on the subsequent timestep.
 Consequently, the change in the atomic subsystem energy is lagged by
 half a timestep relative to the change in the electronic subsystem
 energy. As a result of this, users may notice slight fluctuations in
 the sum of the atomic and electronic subsystem energies reported at
 the end of the timestep.</p>
 <p>The vector values calculated are &#8220;extensive&#8221;.</p>
 <p>No parameter of the fixes can be used with the <em>start/stop</em> keywords
 of the <a class="reference internal" href="run.html"><em>run</em></a> command.  The fixes are not invoked during
 <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>Fix <em>ttm</em> is part of the MISC package. It is only enabled if LAMMPS
 was built with that package.  Fix <em>ttm/mod</em> is part of the USER-MISC
 package. It is only enabled if LAMMPS was built with that package.
 See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more
 info.</p>
 <p>These fixes can only be used for 3d simulations and orthogonal
 simlulation boxes.  You must also use periodic
 <a class="reference internal" href="boundary.html"><em>boundary</em></a> conditions.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="fix_langevin.html"><em>fix langevin</em></a>, <a class="reference internal" href="fix_dt_reset.html"><em>fix dt/reset</em></a></p>
 <p><strong>Default:</strong> none</p>
 <hr class="docutils" />
 <p id="duffy"><strong>(Duffy)</strong> D M Duffy and A M Rutherford, J. Phys.: Condens. Matter, 19,
 016207-016218 (2007).</p>
 <p id="rutherford"><strong>(Rutherford)</strong> A M Rutherford and D M Duffy, J. Phys.:
 Condens. Matter, 19, 496201-496210 (2007).</p>
 <p id="chen"><strong>(Chen)</strong> J Chen, D Tzou and J Beraun, Int. J. Heat
 Mass Transfer, 49, 307-316 (2006).</p>
 <p id="norman"><strong>(Norman)</strong> G E Norman, S V Starikov, V V Stegailov et al., Contrib.
 Plasma Phys., 53, 129-139 (2013).</p>
 <p id="pisarev"><strong>(Pisarev)</strong> V V Pisarev and S V Starikov, J. Phys.: Condens. Matter, 26,
 475401 (2014).</p>
 </div>
 </div>
 
 
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   <div class="section" id="fix-vector-command">
 <span id="index-0"></span><h1>fix vector command<a class="headerlink" href="#fix-vector-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID vector Nevery value1 value2 ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>ave/time = style name of this fix command</li>
 <li>Nevery = use input values every this many timesteps</li>
 <li>one or more input values can be listed</li>
 <li>value = c_ID, c_ID[N], f_ID, f_ID[N], v_name</li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>c_ID = global scalar calculated by a compute with ID
-  c_ID[I] = Ith component of global vector calculated by a compute with ID
-  f_ID = global scalar calculated by a fix with ID
-  f_ID[I] = Ith component of global vector calculated by a fix with ID
-  v_name = global value calculated by an equal-style variable with name
+c_ID[I] = Ith component of global vector calculated by a compute with ID
+f_ID = global scalar calculated by a fix with ID
+f_ID[I] = Ith component of global vector calculated by a fix with ID
+v_name = global value calculated by an equal-style variable with name
 </pre></div>
 </div>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix 1 all vector 100 c_myTemp
 fix 1 all vector 5 c_myTemp v_integral
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Use one or more global values as inputs every few timesteps, and
 simply store them.  For a single specified value, the values are
 stored as a global vector of growing length.  For multiple specified
 values, they are stored as rows in a global array, whose number of
 rows is growing.  The resulting vector or array can be used by other
 <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.</p>
 <p>One way to to use this command is to accumulate a vector that is
 time-integrated using the <a class="reference internal" href="variable.html"><em>variable trap()</em></a> function.
 For example the velocity auto-correlation function (VACF) can be
 time-integrated, to yield a diffusion coefficient, as follows:</p>
 <div class="highlight-python"><div class="highlight"><pre>compute         2 all vacf
 fix             5 all vector 1 c_2[4]
 variable        diff equal dt*trap(f_5)
 thermo_style    custom step v_diff
 </pre></div>
 </div>
 <p>The group specified with this command is ignored.  However, note that
 specified values may represent calculations performed by computes and
 fixes which store their own &#8220;group&#8221; definitions.</p>
 <p>Each listed value can be the result of a <a class="reference internal" href="compute.html"><em>compute</em></a> or
 <a class="reference internal" href="fix.html"><em>fix</em></a> or the evaluation of an equal-style
 <a class="reference internal" href="variable.html"><em>variable</em></a>.  In each case, the compute, fix, or variable
 must produce a global quantity, not a per-atom or local quantity.
 And the global quantity must be a scalar, not a vector or array.</p>
 <p><a class="reference internal" href="compute.html"><em>Computes</em></a> that produce global quantities are those which
 do not have the word <em>atom</em> in their style name.  Only a few
 <a class="reference internal" href="fix.html"><em>fixes</em></a> produce global quantities.  See the doc pages for
 individual fixes for info on which ones produce such values.
 <a class="reference internal" href="variable.html"><em>Variables</em></a> of style <em>equal</em> are the only ones that can
 be used with this fix.  Variables of style <em>atom</em> cannot be used,
 since they produce per-atom values.</p>
 <p>The <em>Nevery</em> argument specifies on what timesteps the input values
 will be used in order to be stored.  Only timesteps that are a
 multiple of <em>Nevery</em>, including timestep 0, will contribute values.</p>
 <p>Note that if you perform multiple runs, using the &#8220;pre no&#8221; option of
 the <a class="reference internal" href="run.html"><em>run</em></a> command to avoid initialization on subsequent runs,
 then you need to use the <em>stop</em> keyword with the first <a class="reference internal" href="run.html"><em>run</em></a>
 command with a timestep value that encompasses all the runs.  This is
 so that the vector or array stored by this fix can be allocated to a
 sufficient size.</p>
 <hr class="docutils" />
 <p>If a value begins with &#8220;<a href="#id1"><span class="problematic" id="id2">c_</span></a>&#8221;, a compute ID must follow which has been
 previously defined in the input script.  If no bracketed term is
 appended, the global scalar calculated by the compute is used.  If a
 bracketed term is appended, the Ith element of the global vector
 calculated by the compute is used.</p>
 <p>Note that there is a <a class="reference internal" href="compute_reduce.html"><em>compute reduce</em></a> command
 which can sum per-atom quantities into a global scalar or vector which
 can thus be accessed by fix vector.  Or it can be a compute defined
 not in your input script, but by <a class="reference internal" href="thermo_style.html"><em>thermodynamic output</em></a> or other fixes such as <a class="reference internal" href="fix_nh.html"><em>fix nvt</em></a>
 or <a class="reference internal" href="fix_temp_rescale.html"><em>fix temp/rescale</em></a>.  See the doc pages for
 these commands which give the IDs of these computes.  Users can also
 write code for their own compute styles and <a class="reference internal" href="Section_modify.html"><em>add them to LAMMPS</em></a>.</p>
 <p>If a value begins with &#8220;<a href="#id3"><span class="problematic" id="id4">f_</span></a>&#8221;, a fix ID must follow which has been
 previously defined in the input script.  If no bracketed term is
 appended, the global scalar calculated by the fix is used.  If a
 bracketed term is appended, the Ith element of the global vector
 calculated by the fix is used.</p>
 <p>Note that some fixes only produce their values on certain timesteps,
 which must be compatible with <em>Nevery</em>, else an error will result.
 Users can also write code for their own fix styles and <a class="reference internal" href="Section_modify.html"><em>add them to LAMMPS</em></a>.</p>
 <p>If a value begins with &#8220;<a href="#id5"><span class="problematic" id="id6">v_</span></a>&#8221;, a variable name must follow which has
 been previously defined in the input script.  Only equal-style
 variables can be referenced.  See the <a class="reference internal" href="variable.html"><em>variable</em></a> command
 for details.  Note that variables of style <em>equal</em> define a formula
 which can reference individual atom properties or thermodynamic
 keywords, or they can invoke other computes, fixes, or variables when
 they are evaluated, so this is a very general means of specifying
 quantities to be stored by fix vector.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.  None of the <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> options
 are relevant to this fix.</p>
 <p>This fix produces a global vector or global array which can be
 accessed by various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.
 The values can only be accessed on timesteps that are multiples of
 <em>Nevery</em>.</p>
 <p>A vector is produced if only a single input value is specified.
 An array is produced if multiple input values are specified.
 The length of the vector or the number of rows in the array grows
 by 1 every <em>Nevery</em> timesteps.</p>
 <p>If the fix prouduces a vector, then the entire vector will be either
 &#8220;intensive&#8221; or &#8220;extensive&#8221;, depending on whether the values stored in
 the vector are &#8220;intensive&#8221; or &#8220;extensive&#8221;.  If the fix produces an
 array, then all elements in the array must be the same, either
 &#8220;intensive&#8221; or &#8220;extensive&#8221;.  If a compute or fix provides the value
 stored, then the compute or fix determines whether the value is
 intensive or extensive; see the doc page for that compute or fix for
 further info.  Values produced by a variable are treated as intensive.</p>
 <p>This fix can allocate storage for stored values accumulated over
 multiple runs, using the <em>start</em> and <em>stop</em> keywords of the
 <a class="reference internal" href="run.html"><em>run</em></a> command.  See the <a class="reference internal" href="run.html"><em>run</em></a> command for details of
 how to do this.  If using the <a class="reference internal" href="run.html"><em>run pre no</em></a> command option,
 this is required to allow the fix to allocate sufficient storage for
 stored values.</p>
 <p>This fix is not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <blockquote>
 <div>none</div></blockquote>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="compute.html"><em>compute</em></a>, <a class="reference internal" href="variable.html"><em>variable</em></a></p>
 <p><strong>Default:</strong> none</p>
 </div>
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   <div class="section" id="fix-viscosity-command">
 <span id="index-0"></span><h1>fix viscosity command<a class="headerlink" href="#fix-viscosity-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID viscosity N vdim pdim Nbin keyword value ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>viscosity = style name of this fix command</li>
 <li>N = perform momentum exchange every N steps</li>
 <li>vdim = <em>x</em> or <em>y</em> or <em>z</em> = which momentum component to exchange</li>
 <li>pdim = <em>x</em> or <em>y</em> or <em>z</em> = direction of momentum transfer</li>
 <li>Nbin = # of layers in pdim direction (must be even number)</li>
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>swap</em> or <em>target</em></li>
 </ul>
 <pre class="literal-block">
 <em>swap</em> value = Nswap = number of swaps to perform every N steps
-  <em>vtarget</em> value = V or INF = target velocity of swap partners (velocity units)
+<em>vtarget</em> value = V or INF = target velocity of swap partners (velocity units)
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix 1 all viscosity 100 x z 20
 fix 1 all viscosity 50 x z 20 swap 2 vtarget 1.5
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Use the Muller-Plathe algorithm described in <a class="reference internal" href="#muller-plathe"><span>this paper</span></a> to exchange momenta between two particles in
 different regions of the simulation box every N steps.  This induces a
 shear velocity profile in the system.  As described below this enables
 a viscosity of the fluid to be calculated.  This algorithm is
 sometimes called a reverse non-equilibrium MD (reverse NEMD) approach
 to computing viscosity.  This is because the usual NEMD approach is to
 impose a shear velocity profile on the system and measure the response
 via an off-diagonal component of the stress tensor, which is
 proportional to the momentum flux.  In the Muller-Plathe method, the
 momentum flux is imposed, and the shear velocity profile is the
 system&#8217;s response.</p>
 <p>The simulation box is divided into <em>Nbin</em> layers in the <em>pdim</em>
 direction, where the layer 1 is at the low end of that dimension and
 the layer <em>Nbin</em> is at the high end.  Every N steps, Nswap pairs of
 atoms are chosen in the following manner.  Only atoms in the fix group
 are considered.  Nswap atoms in layer 1 with positive velocity
 components in the <em>vdim</em> direction closest to the target value <em>V</em> are
 selected.  Similarly, Nswap atoms in the &#8220;middle&#8221; layer (see below) with
 negative velocity components in the <em>vdim</em> direction closest to the
 negative of the target value <em>V</em> are selected.  The two sets of Nswap
 atoms are paired up and their <em>vdim</em> momenta components are swapped
 within each pair.  This resets their velocities, typically in opposite
 directions.  Over time, this induces a shear velocity profile in the
 system which can be measured using commands such as the following,
 which writes the profile to the file tmp.profile:</p>
 <div class="highlight-python"><div class="highlight"><pre>fix f1 all ave/spatial 100 10 1000 z lower 0.05 vx &amp;
     file tmp.profile units reduced
 </pre></div>
 </div>
 <p>Note that by default, Nswap = 1 and vtarget = INF, though this can be
 changed by the optional <em>swap</em> and <em>vtarget</em> keywords.  When vtarget =
 INF, one or more atoms with the most positive and negative velocity
 components are selected.  Setting these parameters appropriately, in
 conjunction with the swap rate N, allows the momentum flux rate to be
 adjusted across a wide range of values, and the momenta to be
 exchanged in large chunks or more smoothly.</p>
 <p>The &#8220;middle&#8221; layer for momenta swapping is defined as the <em>Nbin</em>/2 + 1
 layer.  Thus if <em>Nbin</em> = 20, the two swapping layers are 1 and 11.
 This should lead to a symmetric velocity profile since the two layers
 are separated by the same distance in both directions in a periodic
 sense.  This is why <em>Nbin</em> is restricted to being an even number.</p>
 <p>As described below, the total momentum transferred by these velocity
 swaps is computed by the fix and can be output.  Dividing this
 quantity by time and the cross-sectional area of the simulation box
 yields a momentum flux.  The ratio of momentum flux to the slope of
 the shear velocity profile is proportional to the viscosity of the
 fluid, in appropriate units.  See the <a class="reference internal" href="#muller-plathe"><span>Muller-Plathe paper</span></a> for details.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">If your system is periodic in the direction of the
 momentum flux, then the flux is going in 2 directions.  This means the
 effective momentum flux in one direction is reduced by a factor of 2.
 You will see this in the equations for viscosity in the Muller-Plathe
 paper.  LAMMPS is simply tallying momentum which does not account for
 whether or not your system is periodic; you must use the value
 appropriately to yield a viscosity for your system.</p>
 </div>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">After equilibration, if the velocity profile you
 observe is not linear, then you are likely swapping momentum too
 frequently and are not in a regime of linear response.  In this case
 you cannot accurately infer a viscosity and should try increasing
 the Nevery parameter.</p>
 </div>
 <p>An alternative method for calculating a viscosity is to run a NEMD
 simulation, as described in <a class="reference internal" href="Section_howto.html#howto-13"><span>Section_howto 13</span></a> of the manual.  NEMD simulations
 deform the simmulation box via the <a class="reference internal" href="fix_deform.html"><em>fix deform</em></a>
 command.  Thus they cannot be run on a charged system using a <a class="reference internal" href="kspace_style.html"><em>PPPM solver</em></a> since PPPM does not currently support
 non-orthogonal boxes.  Using fix viscosity keeps the box orthogonal;
 thus it does not suffer from this limitation.</p>
 </div>
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.  None of the <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> options
 are relevant to this fix.</p>
 <p>This fix computes a global scalar which can be accessed by various
 <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  The scalar is the
 cummulative momentum transferred between the bottom and middle of the
 simulation box (in the <em>pdim</em> direction) is stored as a scalar
 quantity by this fix.  This quantity is zeroed when the fix is defined
 and accumlates thereafter, once every N steps.  The units of the
 quantity are momentum = mass*velocity.  The scalar value calculated by
 this fix is &#8220;intensive&#8221;.</p>
 <p>No parameter of this fix can be used with the <em>start/stop</em> keywords of
 the <a class="reference internal" href="run.html"><em>run</em></a> command.  This fix is not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>This fix is part of the MISC package.  It is only enabled if LAMMPS
 was built with that package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 <p>Swaps conserve both momentum and kinetic energy, even if the masses of
 the swapped atoms are not equal.  Thus you should not need to
 thermostat the system.  If you do use a thermostat, you may want to
 apply it only to the non-swapped dimensions (other than <em>vdim</em>).</p>
 <p>LAMMPS does not check, but you should not use this fix to swap
 velocities of atoms that are in constrained molecules, e.g. via <a class="reference internal" href="fix_shake.html"><em>fix shake</em></a> or <a class="reference internal" href="fix_rigid.html"><em>fix rigid</em></a>.  This is because
 application of the constraints will alter the amount of transferred
 momentum.  You should, however, be able to use flexible molecules.
 See the <a class="reference internal" href="#maginn"><span>Maginn paper</span></a> for an example of using this algorithm
 in a computation of alcohol molecule properties.</p>
 <p>When running a simulation with large, massive particles or molecules
 in a background solvent, you may want to only exchange momenta bewteen
 solvent particles.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="fix_ave_spatial.html"><em>fix ave/spatial</em></a>, <a class="reference internal" href="fix_thermal_conductivity.html"><em>fix thermal/conductivity</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The option defaults are swap = 1 and vtarget = INF.</p>
 <hr class="docutils" />
 <p id="muller-plathe"><strong>(Muller-Plathe)</strong> Muller-Plathe, Phys Rev E, 59, 4894-4898 (1999).</p>
 <p id="maginn"><strong>(Maginn)</strong> Kelkar, Rafferty, Maginn, Siepmann, Fluid Phase Equilibria,
 260, 218-231 (2007).</p>
 </div>
 </div>
 
 
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   <div class="section" id="fix-wall-lj93-command">
 <span id="index-0"></span><h1>fix wall/lj93 command<a class="headerlink" href="#fix-wall-lj93-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="fix-wall-lj126-command">
 <h1>fix wall/lj126 command<a class="headerlink" href="#fix-wall-lj126-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="fix-wall-lj1043-command">
 <h1>fix wall/lj1043 command<a class="headerlink" href="#fix-wall-lj1043-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="fix-wall-colloid-command">
 <h1>fix wall/colloid command<a class="headerlink" href="#fix-wall-colloid-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="fix-wall-harmonic-command">
 <h1>fix wall/harmonic command<a class="headerlink" href="#fix-wall-harmonic-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID style face args ... keyword value ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>style = <em>wall/lj93</em> or <em>wall/lj126</em> or <em>wall/lj1043</em> or <em>wall/colloid</em> or <em>wall/harmonic</em></li>
 <li>one or more face/arg pairs may be appended</li>
 <li>face = <em>xlo</em> or <em>xhi</em> or <em>ylo</em> or <em>yhi</em> or <em>zlo</em> or <em>zhi</em></li>
 </ul>
 <pre class="literal-block">
 args = coord epsilon sigma cutoff
-    coord = position of wall = EDGE or constant or variable
-      EDGE = current lo or hi edge of simulation box
-      constant = number like 0.0 or -30.0 (distance units)
-      variable = <a class="reference internal" href="variable.html"><em>equal-style variable</em></a> like v_x or v_wiggle
-    epsilon = strength factor for wall-particle interaction (energy or energy/distance^2 units)
-      epsilon can be a variable (see below)
-    sigma = size factor for wall-particle interaction (distance units)
-      sigma can be a variable (see below)
-    cutoff = distance from wall at which wall-particle interaction is cut off (distance units)
+  coord = position of wall = EDGE or constant or variable
+    EDGE = current lo or hi edge of simulation box
+    constant = number like 0.0 or -30.0 (distance units)
+    variable = <a class="reference internal" href="variable.html"><em>equal-style variable</em></a> like v_x or v_wiggle
+  epsilon = strength factor for wall-particle interaction (energy or energy/distance^2 units)
+    epsilon can be a variable (see below)
+  sigma = size factor for wall-particle interaction (distance units)
+    sigma can be a variable (see below)
+  cutoff = distance from wall at which wall-particle interaction is cut off (distance units)
 </pre>
 <ul class="simple">
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>units</em> or <em>fld</em></li>
 </ul>
 <pre class="literal-block">
 <em>units</em> value = <em>lattice</em> or <em>box</em>
-    <em>lattice</em> = the wall position is defined in lattice units
-    <em>box</em> = the wall position is defined in simulation box units
-  <em>fld</em> value = <em>yes</em> or <em>no</em>
-    <em>yes</em> = invoke the wall constraint to be compatible with implicit FLD
-    <em>no</em> = invoke the wall constraint in the normal way
-  <em>pbc</em> value = <em>yes</em> or <em>no</em>
-    <em>yes</em> = allow periodic boundary in a wall dimension
-    <em>no</em> = require non-perioidic boundaries in any wall dimension
+  <em>lattice</em> = the wall position is defined in lattice units
+  <em>box</em> = the wall position is defined in simulation box units
+<em>fld</em> value = <em>yes</em> or <em>no</em>
+  <em>yes</em> = invoke the wall constraint to be compatible with implicit FLD
+  <em>no</em> = invoke the wall constraint in the normal way
+<em>pbc</em> value = <em>yes</em> or <em>no</em>
+  <em>yes</em> = allow periodic boundary in a wall dimension
+  <em>no</em> = require non-perioidic boundaries in any wall dimension
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix wallhi all wall/lj93 xlo -1.0 1.0 1.0 2.5 units box
 fix wallhi all wall/lj93 xhi EDGE 1.0 1.0 2.5
 fix wallhi all wall/lj126 v_wiggle 23.2 1.0 1.0 2.5
 fix zwalls all wall/colloid zlo 0.0 1.0 1.0 0.858 zhi 40.0 1.0 1.0 0.858
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Bound the simulation domain on one or more of its faces with a flat
 wall that interacts with the atoms in the group by generating a force
 on the atom in a direction perpendicular to the wall.  The energy of
 wall-particle interactions depends on the style.</p>
 <p>For style <em>wall/lj93</em>, the energy E is given by the 9/3 potential:</p>
 <img alt="_images/fix_wall_lj93.jpg" class="align-center" src="_images/fix_wall_lj93.jpg" />
 <p>For style <em>wall/lj126</em>, the energy E is given by the 12/6 potential:</p>
 <img alt="_images/pair_lj.jpg" class="align-center" src="_images/pair_lj.jpg" />
 <p>For style <em>wall/lj1043</em>, the energy E is given by the 10/4/3 potential:</p>
 <img alt="_images/fix_wall_lj1043.jpg" class="align-center" src="_images/fix_wall_lj1043.jpg" />
 <p>For style <em>wall/colloid</em>, the energy E is given by an integrated form
 of the <a class="reference internal" href="pair_colloid.html"><em>pair_style colloid</em></a> potential:</p>
 <img alt="_images/fix_wall_colloid.jpg" class="align-center" src="_images/fix_wall_colloid.jpg" />
 <p>For style <em>wall/harmonic</em>, the energy E is given by a harmonic spring
 potential:</p>
 <img alt="_images/fix_wall_harmonic.jpg" class="align-center" src="_images/fix_wall_harmonic.jpg" />
 <p>In all cases, <em>r</em> is the distance from the particle to the wall at
 position <em>coord</em>, and Rc is the <em>cutoff</em> distance at which the
 particle and wall no longer interact.  The energy of the wall
 potential is shifted so that the wall-particle interaction energy is
 0.0 at the cutoff distance.</p>
 <p>Up to 6 walls or faces can be specified in a single command: <em>xlo</em>,
 <em>xhi</em>, <em>ylo</em>, <em>yhi</em>, <em>zlo</em>, <em>zhi</em>.  A <em>lo</em> face interacts with
 particles near the lower side of the simulation box in that dimension.
 A <em>hi</em> face interacts with particles near the upper side of the
 simulation box in that dimension.</p>
 <p>The position of each wall can be specified in one of 3 ways: as the
 EDGE of the simulation box, as a constant value, or as a variable.  If
 EDGE is used, then the corresponding boundary of the current
 simulation box is used.  If a numeric constant is specified then the
 wall is placed at that position in the appropriate dimension (x, y, or
 z).  In both the EDGE and constant cases, the wall will never move.
 If the wall position is a variable, it should be specified as v_name,
 where name is an <a class="reference internal" href="variable.html"><em>equal-style variable</em></a> name.  In this
 case the variable is evaluated each timestep and the result becomes
 the current position of the reflecting wall.  Equal-style variables
 can specify formulas with various mathematical functions, and include
 <a class="reference internal" href="thermo_style.html"><em>thermo_style</em></a> command keywords for the simulation
 box parameters and timestep and elapsed time.  Thus it is easy to
 specify a time-dependent wall position.  See examples below.</p>
 <p>For the <em>wall/lj93</em> and <em>wall/lj126</em> and <em>wall/lj1043</em> styles,
 <em>epsilon</em> and <em>sigma</em> are the usual Lennard-Jones parameters, which
 determine the strength and size of the particle as it interacts with
 the wall.  Epsilon has energy units.  Note that this <em>epsilon</em> and
 <em>sigma</em> may be different than any <em>epsilon</em> or <em>sigma</em> values defined
 for a pair style that computes particle-particle interactions.</p>
 <p>The <em>wall/lj93</em> interaction is derived by integrating over a 3d
 half-lattice of Lennard-Jones 12/6 particles.  The <em>wall/lj126</em>
 interaction is effectively a harder, more repulsive wall interaction.
 The <em>wall/lj1043</em> interaction is yet a different form of wall
 interaction, described in Magda et al in <a class="reference internal" href="#magda"><span>(Magda)</span></a>.</p>
 <p>For the <em>wall/colloid</em> style, <em>R</em> is the radius of the colloid
 particle, <em>D</em> is the distance from the surface of the colloid particle
 to the wall (r-R), and <em>sigma</em> is the size of a constituent LJ
 particle inside the colloid particle and wall.  Note that the cutoff
 distance Rc in this case is the distance from the colloid particle
 center to the wall.  The prefactor <em>epsilon</em> can be thought of as an
 effective Hamaker constant with energy units for the strength of the
 colloid-wall interaction.  More specifically, the <em>epsilon</em> pre-factor
 = 4 * pi^2 * rho_wall * rho_colloid * epsilon * sigma^6, where epsilon
 and sigma are the LJ parameters for the constituent LJ
 particles. Rho_wall and rho_colloid are the number density of the
 constituent particles, in the wall and colloid respectively, in units
 of 1/volume.</p>
 <p>The <em>wall/colloid</em> interaction is derived by integrating over
 constituent LJ particles of size <em>sigma</em> within the colloid particle
 and a 3d half-lattice of Lennard-Jones 12/6 particles of size <em>sigma</em>
 in the wall.  As mentioned in the preceeding paragraph, the density of
 particles in the wall and colloid can be different, as specified by
 the <em>epsilon</em> pre-factor.</p>
 <p>For the <em>wall/harmonic</em> style, <em>epsilon</em> is effectively the spring
 constant K, and has units (energy/distance^2).  The input parameter
 <em>sigma</em> is ignored.  The minimum energy position of the harmonic
 spring is at the <em>cutoff</em>.  This is a repulsive-only spring since the
 interaction is truncated at the <em>cutoff</em></p>
 <p>For any wall, the <em>epsilon</em> and/or <em>sigma</em> parameter can be specified
 as an <a class="reference internal" href="variable.html"><em>equal-style variable</em></a>, in which case it should be
 specified as v_name, where name is the variable name.  As with a
 variable wall position, the variable is evaluated each timestep and
 the result becomes the current epsilon or sigma of the wall.
 Equal-style variables can specify formulas with various mathematical
 functions, and include <a class="reference internal" href="thermo_style.html"><em>thermo_style</em></a> command
 keywords for the simulation box parameters and timestep and elapsed
 time.  Thus it is easy to specify a time-dependent wall interaction.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">For all of the styles, you must insure that r is
 always &gt; 0 for all particles in the group, or LAMMPS will generate an
 error.  This means you cannot start your simulation with particles at
 the wall position <em>coord</em> (r = 0) or with particles on the wrong side
 of the wall (r &lt; 0).  For the <em>wall/lj93</em> and <em>wall/lj126</em> styles, the
 energy of the wall/particle interaction (and hence the force on the
 particle) blows up as r -&gt; 0.  The <em>wall/colloid</em> style is even more
 restrictive, since the energy blows up as D = r-R -&gt; 0.  This means
 the finite-size particles of radius R must be a distance larger than R
 from the wall position <em>coord</em>.  The <em>harmonic</em> style is a softer
 potential and does not blow up as r -&gt; 0, but you must use a large
 enough <em>epsilon</em> that particles always reamin on the correct side of
 the wall (r &gt; 0).</p>
 </div>
 <p>The <em>units</em> keyword determines the meaning of the distance units used
 to define a wall position, but only when a numeric constant or
 variable is used.  It is not relevant when EDGE is used to specify a
 face position.  In the variable case, the variable is assumed to
 produce a value compatible with the <em>units</em> setting you specify.</p>
 <p>A <em>box</em> value selects standard distance units as defined by the
 <a class="reference internal" href="units.html"><em>units</em></a> command, e.g. Angstroms for units = real or metal.
 A <em>lattice</em> value means the distance units are in lattice spacings.
 The <a class="reference internal" href="lattice.html"><em>lattice</em></a> command must have been previously used to
 define the lattice spacings.</p>
 <p>The <em>fld</em> keyword can be used with a <em>yes</em> setting to invoke the wall
 constraint before pairwise interactions are computed.  This allows an
 implicit FLD model using <a class="reference internal" href="pair_lubricateU.html"><em>pair_style lubricateU</em></a>
 to include the wall force in its calculations.  If the setting is
 <em>no</em>, wall forces are imposed after pairwise interactions, in the
 usual manner.</p>
 <p>The <em>pbc</em> keyword can be used with a <em>yes</em> setting to allow walls to
 be specified in a periodic dimension.  See the
 <a class="reference internal" href="boundary.html"><em>boundary</em></a> command for options on simulation box
 boundaries.  The default for <em>pbc</em> is <em>no</em>, which means the system
 must be non-periodic when using a wall.  But you may wish to use a
 periodic box.  E.g. to allow some particles to interact with the wall
 via the fix group-ID, and others to pass through it and wrap around a
 periodic box.  In this case you should insure that the wall if
 sufficiently far enough away from the box boundary.  If you do not,
 then particles may interact with both the wall and with periodic
 images on the other side of the box, which is probably not what you
 want.</p>
 <hr class="docutils" />
 <p>Here are examples of variable definitions that move the wall position
 in a time-dependent fashion using equal-style
 <a class="reference internal" href="variable.html"><em>variables</em></a>.  The wall interaction parameters (epsilon,
 sigma) could be varied with additional variable definitions.</p>
 <div class="highlight-python"><div class="highlight"><pre>variable ramp equal ramp(0,10)
 fix 1 all wall xlo v_ramp 1.0 1.0 2.5
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>variable linear equal vdisplace(0,20)
 fix 1 all wall xlo v_linear 1.0 1.0 2.5
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>variable wiggle equal swiggle(0.0,5.0,3.0)
 fix 1 all wall xlo v_wiggle 1.0 1.0 2.5
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>variable wiggle equal cwiggle(0.0,5.0,3.0)
 fix 1 all wall xlo v_wiggle 1.0 1.0 2.5
 </pre></div>
 </div>
 <p>The ramp(lo,hi) function adjusts the wall position linearly from lo to
 hi over the course of a run.  The vdisplace(c0,velocity) function does
 something similar using the equation position = c0 + velocity*delta,
 where delta is the elapsed time.</p>
 <p>The swiggle(c0,A,period) function causes the wall position to
 oscillate sinusoidally according to this equation, where omega = 2 PI
 / period:</p>
 <div class="highlight-python"><div class="highlight"><pre>position = c0 + A sin(omega*delta)
 </pre></div>
 </div>
 <p>The cwiggle(c0,A,period) function causes the wall position to
 oscillate sinusoidally according to this equation, which will have an
 initial wall velocity of 0.0, and thus may impose a gentler
 perturbation on the particles:</p>
 <div class="highlight-python"><div class="highlight"><pre><span class="n">position</span> <span class="o">=</span> <span class="n">c0</span> <span class="o">+</span> <span class="n">A</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">cos</span><span class="p">(</span><span class="n">omega</span><span class="o">*</span><span class="n">delta</span><span class="p">))</span>
 </pre></div>
 </div>
 </div>
 <hr class="docutils" />
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.</p>
 <p>The <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> <em>energy</em> option is supported by this
 fix to add the energy of interaction between atoms and each wall to
 the system&#8217;s potential energy as part of <a class="reference internal" href="thermo_style.html"><em>thermodynamic output</em></a>.</p>
 <p>This fix computes a global scalar energy and a global vector of
 forces, which can be accessed by various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  Note that the scalar energy is
 the sum of interactions with all defined walls.  If you want the
 energy on a per-wall basis, you need to use multiple fix wall
 commands.  The length of the vector is equal to the number of walls
 defined by the fix.  Each vector value is the normal force on a
 specific wall.  Note that an outward force on a wall will be a
 negative value for <em>lo</em> walls and a positive value for <em>hi</em> walls.
 The scalar and vector values calculated by this fix are &#8220;extensive&#8221;.</p>
 <p>No parameter of this fix can be used with the <em>start/stop</em> keywords of
 the <a class="reference internal" href="run.html"><em>run</em></a> command.</p>
 <p>The forces due to this fix are imposed during an energy minimization,
 invoked by the <a class="reference internal" href="minimize.html"><em>minimize</em></a> command.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">If you want the atom/wall interaction energy to be
 included in the total potential energy of the system (the quantity
 being minimized), you MUST enable the <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a>
 <em>energy</em> option for this fix.</p>
 </div>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <blockquote>
 <div>none</div></blockquote>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="fix_wall_reflect.html"><em>fix wall/reflect</em></a>,
 <a class="reference internal" href="fix_wall_gran.html"><em>fix wall/gran</em></a>,
 <a class="reference internal" href="fix_wall_region.html"><em>fix wall/region</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The option defaults units = lattice, fld = no, and pbc = no.</p>
 <hr class="docutils" />
 <p id="magda"><strong>(Magda)</strong> Magda, Tirrell, Davis, J Chem Phys, 83, 1888-1901 (1985);
 erratum in JCP 84, 2901 (1986).</p>
 </div>
 </div>
 
 
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index 3e30a6149..1216dd14a 100644
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   <div class="section" id="fix-wall-gran-command">
 <span id="index-0"></span><h1>fix wall/gran command<a class="headerlink" href="#fix-wall-gran-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID wall/gran Kn Kt gamma_n gamma_t xmu dampflag wallstyle args keyword values ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>wall/gran = style name of this fix command</li>
 <li>Kn = elastic constant for normal particle repulsion (force/distance units or pressure units - see discussion below)</li>
 <li>Kt = elastic constant for tangential contact (force/distance units or pressure units - see discussion below)</li>
 <li>gamma_n = damping coefficient for collisions in normal direction (1/time units or 1/time-distance units - see discussion below)</li>
 <li>gamma_t = damping coefficient for collisions in tangential direction (1/time units or 1/time-distance units - see discussion below)</li>
 <li>xmu = static yield criterion (unitless value between 0.0 and 1.0e4)</li>
 <li>dampflag = 0 or 1 if tangential damping force is excluded or included</li>
 <li>wallstyle = <em>xplane</em> or <em>yplane</em> or <em>zplane</em> or <em>zcylinder</em></li>
 <li>args = list of arguments for a particular style</li>
 </ul>
 <pre class="literal-block">
 <em>xplane</em> or <em>yplane</em> or <em>zplane</em> args = lo hi
-    lo,hi = position of lower and upper plane (distance units), either can be NULL)
-  <em>zcylinder</em> args = radius
-    radius = cylinder radius (distance units)
+  lo,hi = position of lower and upper plane (distance units), either can be NULL)
+<em>zcylinder</em> args = radius
+  radius = cylinder radius (distance units)
 </pre>
 <ul class="simple">
 <li>zero or more keyword/value pairs may be appended to args</li>
 <li>keyword = <em>wiggle</em> or <em>shear</em></li>
 </ul>
 <pre class="literal-block">
 <em>wiggle</em> values = dim amplitude period
-    dim = <em>x</em> or <em>y</em> or <em>z</em>
-    amplitude = size of oscillation (distance units)
-    period = time of oscillation (time units)
-  <em>shear</em> values = dim vshear
-    dim = <em>x</em> or <em>y</em> or <em>z</em>
-    vshear = magnitude of shear velocity (velocity units)
+  dim = <em>x</em> or <em>y</em> or <em>z</em>
+  amplitude = size of oscillation (distance units)
+  period = time of oscillation (time units)
+<em>shear</em> values = dim vshear
+  dim = <em>x</em> or <em>y</em> or <em>z</em>
+  vshear = magnitude of shear velocity (velocity units)
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix 1 all wall/gran 200000.0 NULL 50.0 NULL 0.5 0 xplane -10.0 10.0
 fix 1 all wall/gran 200000.0 NULL 50.0 NULL 0.5 0 zplane 0.0 NULL
 fix 2 all wall/gran 100000.0 20000.0 50.0 30.0 0.5 1 zcylinder 15.0 wiggle z 3.0 2.0
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Bound the simulation domain of a granular system with a frictional
 wall.  All particles in the group interact with the wall when they are
 close enough to touch it.</p>
 <p>The first set of parameters (Kn, Kt, gamma_n, gamma_t, xmu, and
 dampflag) have the same meaning as those specified with the
 <a class="reference internal" href="pair_gran.html"><em>pair_style granular</em></a> force fields.  This means a NULL
 can be used for either Kt or gamma_t as described on that page.  If a
 NULL is used for Kt, then a default value is used where Kt = 2/7 Kn.
 If a NULL is used for gamma_t, then a default value is used where
 gamma_t = 1/2 gamma_n.</p>
 <p>The nature of the wall/particle interactions are determined by which
 pair_style is used in your input script: <em>hooke</em>, <em>hooke/history</em>, or
 <em>hertz/history</em>.  The equation for the force between the wall and
 particles touching it is the same as the corresponding equation on the
 <a class="reference internal" href="pair_gran.html"><em>pair_style granular</em></a> doc page, in the limit of one of
 the two particles going to infinite radius and mass (flat wall).
 I.e. delta = radius - r = overlap of particle with wall, m_eff = mass
 of particle, and sqrt(RiRj/Ri+Rj) becomes sqrt(radius of particle).
 The units for Kn, Kt, gamma_n, and gamma_t are as described on that
 doc page.  The meaning of xmu and dampflag are also as described on
 that page.  Note that you can choose different values for these 6
 wall/particle coefficients than for particle/particle interactions, if
 you wish your wall to interact differently with the particles, e.g. if
 the wall is a different material.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">As discussed on the doc page for <a class="reference internal" href="pair_gran.html"><em>pair_style granular</em></a>, versions of LAMMPS before 9Jan09 used a
 different equation for Hertzian interactions.  This means Hertizian
 wall/particle interactions have also changed.  They now include a
 sqrt(radius) term which was not present before.  Also the previous
 versions used Kn and Kt from the pairwise interaction and hardwired
 dampflag to 1, rather than letting them be specified directly.  This
 means you can set the values of the wall/particle coefficients
 appropriately in the current code to reproduce the results of a
 prevoius Hertzian monodisperse calculation.  For example, for the
 common case of a monodisperse system with particles of diameter 1, Kn,
 Kt, gamma_n, and gamma_s should be set sqrt(2.0) larger than they were
 previously.</p>
 </div>
 <p>The <em>wallstyle</em> can be planar or cylindrical.  The 3 planar options
 specify a pair of walls in a dimension.  Wall positions are given by
 <em>lo</em> and <em>hi</em>.  Either of the values can be specified as NULL if a
 single wall is desired.  For a <em>zcylinder</em> wallstyle, the cylinder&#8217;s
 axis is at x = y = 0.0, and the radius of the cylinder is specified.</p>
 <p>Optionally, the wall can be moving, if the <em>wiggle</em> or <em>shear</em>
 keywords are appended.  Both keywords cannot be used together.</p>
 <p>For the <em>wiggle</em> keyword, the wall oscillates sinusoidally, similar to
 the oscillations of particles which can be specified by the
 <a class="reference internal" href="fix_move.html"><em>fix_move</em></a> command.  This is useful in packing
 simulations of granular particles.  The arguments to the <em>wiggle</em>
 keyword specify a dimension for the motion, as well as it&#8217;s
 <em>amplitude</em> and <em>period</em>.  Note that if the dimension is in the plane
 of the wall, this is effectively a shearing motion.  If the dimension
 is perpendicular to the wall, it is more of a shaking motion.  A
 <em>zcylinder</em> wall can only be wiggled in the z dimension.</p>
 <p>Each timestep, the position of a wiggled wall in the appropriate <em>dim</em>
 is set according to this equation:</p>
 <div class="highlight-python"><div class="highlight"><pre>position = coord + A - A cos (omega * delta)
 </pre></div>
 </div>
 <p>where <em>coord</em> is the specified initial position of the wall, <em>A</em> is
 the <em>amplitude</em>, <em>omega</em> is 2 PI / <em>period</em>, and <em>delta</em> is the time
 elapsed since the fix was specified.  The velocity of the wall is set
 to the derivative of this expression.</p>
 <p>For the <em>shear</em> keyword, the wall moves continuously in the specified
 dimension with velocity <em>vshear</em>.  The dimension must be tangential to
 walls with a planar <em>wallstyle</em>, e.g. in the <em>y</em> or <em>z</em> directions for
 an <em>xplane</em> wall.  For <em>zcylinder</em> walls, a dimension of <em>z</em> means the
 cylinder is moving in the z-direction along it&#8217;s axis.  A dimension of
 <em>x</em> or <em>y</em> means the cylinder is spinning around the z-axis, either in
 the clockwise direction for <em>vshear</em> &gt; 0 or counter-clockwise for
 <em>vshear</em> &lt; 0.  In this case, <em>vshear</em> is the tangential velocity of
 the wall at whatever <em>radius</em> has been defined.</p>
 </div>
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>This fix writes the shear friction state of atoms interacting with the
 wall to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>, so that a simulation can
 continue correctly if granular potentials with shear &#8220;history&#8221; effects
 are being used.  See the <a class="reference internal" href="read_restart.html"><em>read_restart</em></a> command for
 info on how to re-specify a fix in an input script that reads a
 restart file, so that the operation of the fix continues in an
 uninterrupted fashion.</p>
 <p>None of the <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> options are relevant to this
 fix.  No global or per-atom quantities are stored by this fix for
 access by various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  No
 parameter of this fix can be used with the <em>start/stop</em> keywords of
 the <a class="reference internal" href="run.html"><em>run</em></a> command.  This fix is not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>This fix is part of the GRANULAR package.  It is only enabled if
 LAMMPS was built with that package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 <p>Any dimension (xyz) that has a granular wall must be non-periodic.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="fix_move.html"><em>fix_move</em></a>, <a class="reference internal" href="pair_gran.html"><em>pair_style granular</em></a></p>
 <p><strong>Default:</strong> none</p>
 </div>
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   <div class="section" id="fix-wall-piston-command">
 <span id="index-0"></span><h1>fix wall/piston command<a class="headerlink" href="#fix-wall-piston-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID wall/piston face ... keyword value ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>wall/piston = style name of this fix command</li>
 <li>face = <em>zlo</em></li>
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>pos</em> or <em>vel</em> or <em>ramp</em> or <em>units</em></li>
 </ul>
 <pre class="literal-block">
 <em>pos</em> args = z
-    z = z coordinate at which the piston begins (distance units)
-  <em>vel</em> args = vz
-    vz = final velocity of the piston (velocity units)
-  <em>ramp</em> = use a linear velocity ramp from 0 to vz
-  <em>temp</em> args = target damp seed extent
-    target = target velocity for region immediately ahead of the piston
-    damp = damping paramter (time units)
-    seed = random number seed for langevin kicks
-    extent = extent of thermostated region (distance units)
-  <em>units</em> value = <em>lattice</em> or <em>box</em>
-    <em>lattice</em> = the wall position is defined in lattice units
-    <em>box</em> = the wall position is defined in simulation box units
+  z = z coordinate at which the piston begins (distance units)
+<em>vel</em> args = vz
+  vz = final velocity of the piston (velocity units)
+<em>ramp</em> = use a linear velocity ramp from 0 to vz
+<em>temp</em> args = target damp seed extent
+  target = target velocity for region immediately ahead of the piston
+  damp = damping paramter (time units)
+  seed = random number seed for langevin kicks
+  extent = extent of thermostated region (distance units)
+<em>units</em> value = <em>lattice</em> or <em>box</em>
+  <em>lattice</em> = the wall position is defined in lattice units
+  <em>box</em> = the wall position is defined in simulation box units
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix xwalls all wall/piston zlo
 fix walls all wall/piston zlo pos 1.0 vel 10.0 units box
 fix top all wall/piston zlo vel 10.0 ramp
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Bound the simulation with a moving wall which reflect particles in the
 specified group and drive the system with an effective infinite-mass
 piston capable of driving shock waves.</p>
 <p>A momentum mirror technique is used, which means that if an atom (or
 the wall) moves such that an atom is outside the wall on a timestep by
 a distance delta (e.g. due to <a class="reference internal" href="fix_nve.html"><em>fix nve</em></a>), then it is put
 back inside the face by the same delta, and the velocity relative to
 the moving wall is flipped in z.  For instance, a stationary particle
 hit with a piston wall with velocity vz, will end the timestep with a
 velocity of 2*vz.</p>
 <p>Currently the <em>face</em> keyword can only be <em>zlo</em>.  This creates a piston
 moving in the positive z direction.  Particles with z coordinate less
 than the wall position are reflected to a z coordinate greater than
 the wall position.  If the piston velocity is vpz and the particle
 velocity before reflection is vzi, the particle velocity after
 reflection is -vzi + 2*vpz.</p>
 <p>The initial position of the wall can be specified by the <em>pos</em> keyword.</p>
 <p>The final velocity of the wall can be specified by the <em>vel</em> keyword</p>
 <p>The <em>ramp</em> keyword will cause the wall/piston to adjust the velocity
 linearly from zero velocity to <em>vel</em> over the course of the run. If
 the <em>ramp</em> keyword is omitted then the wall/piston moves at a constant
 velocity defined by <em>vel</em>.</p>
 <p>The <em>temp</em> keyword will cause the region immediately in front of the
 wall/piston to be thermostated with a Langevin thermostat.  This
 region moves with the piston.  The damping and kicking are measured in
 the reference frame of the piston.  So, a temperature of zero would
 mean all particles were moving at exactly the speed of the
 wall/piston.</p>
 <p>The <em>units</em> keyword determines the meaning of the distance units used
 to define a wall position, but only when a numeric constant is used.</p>
 <p>A <em>box</em> value selects standard distance units as defined by the
 <a class="reference internal" href="units.html"><em>units</em></a> command, e.g. Angstroms for units = real or metal.
 A <em>lattice</em> value means the distance units are in lattice spacings.
 The <a class="reference internal" href="lattice.html"><em>lattice</em></a> command must have been previously used to
 define the lattice spacings.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.  None of the <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> options
 are relevant to this fix.  No global or per-atom quantities are stored
 by this fix for access by various <span class="xref std std-ref">output commands</span>.  No parameter of this fix can
 be used with the <em>start/stop</em> keywords of the <a class="reference internal" href="run.html"><em>run</em></a> command.
 This fix is not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>This fix style is part of the SHOCK package.  It is only enabled if
 LAMMPS was built with that package. See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 <p>The face that has the wall/piston must be boundary type &#8216;s&#8217;
 (shrink-wrapped). The opposing face can be
 any boundary type other than periodic.</p>
 <p>A wall/piston should not be used with rigid bodies such as those
 defined by a &#8220;fix rigid&#8221; command.  This is because the wall/piston
 displaces atoms directly rather than exerting a force on them.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="fix_wall.html"><em>fix wall/reflect</em></a> command, <a class="reference internal" href="fix_append_atoms.html"><em>fix append/atoms</em></a> command</p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The keyword defaults are pos = 0, vel = 0, units = lattice.</p>
 </div>
 </div>
 
 
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   <div class="section" id="fix-wall-reflect-command">
 <span id="index-0"></span><h1>fix wall/reflect command<a class="headerlink" href="#fix-wall-reflect-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID wall/reflect face arg ... keyword value ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>wall/reflect = style name of this fix command</li>
 <li>one or more face/arg pairs may be appended</li>
 <li>face = <em>xlo</em> or <em>xhi</em> or <em>ylo</em> or <em>yhi</em> or <em>zlo</em> or <em>zhi</em></li>
 </ul>
 <pre class="literal-block">
 <em>xlo</em>,*ylo*,*zlo* arg = EDGE or constant or variable
-    EDGE = current lo edge of simulation box
-    constant = number like 0.0 or -30.0 (distance units)
-    variable = <a class="reference internal" href="variable.html"><em>equal-style variable</em></a> like v_x or v_wiggle
-  <em>xhi</em>,*yhi*,*zhi* arg = EDGE or constant or variable
-    EDGE = current hi edge of simulation box
-    constant = number like 50.0 or 100.3 (distance units)
-    variable = <a class="reference internal" href="variable.html"><em>equal-style variable</em></a> like v_x or v_wiggle
+  EDGE = current lo edge of simulation box
+  constant = number like 0.0 or -30.0 (distance units)
+  variable = <a class="reference internal" href="variable.html"><em>equal-style variable</em></a> like v_x or v_wiggle
+<em>xhi</em>,*yhi*,*zhi* arg = EDGE or constant or variable
+  EDGE = current hi edge of simulation box
+  constant = number like 50.0 or 100.3 (distance units)
+  variable = <a class="reference internal" href="variable.html"><em>equal-style variable</em></a> like v_x or v_wiggle
 </pre>
 <ul class="simple">
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>units</em></li>
 </ul>
 <pre class="literal-block">
 <em>units</em> value = <em>lattice</em> or <em>box</em>
-    <em>lattice</em> = the wall position is defined in lattice units
-    <em>box</em> = the wall position is defined in simulation box units
+  <em>lattice</em> = the wall position is defined in lattice units
+  <em>box</em> = the wall position is defined in simulation box units
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix xwalls all wall/reflect xlo EDGE xhi EDGE
 fix walls all wall/reflect xlo 0.0 ylo 10.0 units box
 fix top all wall/reflect zhi v_pressdown
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Bound the simulation with one or more walls which reflect particles
 in the specified group when they attempt to move thru them.</p>
 <p>Reflection means that if an atom moves outside the wall on a timestep
 by a distance delta (e.g. due to <a class="reference internal" href="fix_nve.html"><em>fix nve</em></a>), then it is
 put back inside the face by the same delta, and the sign of the
 corresponding component of its velocity is flipped.</p>
 <p>When used in conjunction with <a class="reference internal" href="fix_nve.html"><em>fix nve</em></a> and <a class="reference internal" href="run_style.html"><em>run_style verlet</em></a>, the resultant time-integration algorithm is
 equivalent to the primitive splitting algorithm (PSA) described by
 <a class="reference internal" href="#bond"><span>Bond</span></a>.  Because each reflection event divides
 the corresponding timestep asymmetrically, energy conservation is only
 satisfied to O(dt), rather than to O(dt^2) as it would be for
 velocity-Verlet integration without reflective walls.</p>
 <p>Up to 6 walls or faces can be specified in a single command: <em>xlo</em>,
 <em>xhi</em>, <em>ylo</em>, <em>yhi</em>, <em>zlo</em>, <em>zhi</em>.  A <em>lo</em> face reflects particles
 that move to a coordinate less than the wall position, back in the
 <em>hi</em> direction.  A <em>hi</em> face reflects particles that move to a
 coordinate higher than the wall position, back in the <em>lo</em> direction.</p>
 <p>The position of each wall can be specified in one of 3 ways: as the
 EDGE of the simulation box, as a constant value, or as a variable.  If
 EDGE is used, then the corresponding boundary of the current
 simulation box is used.  If a numeric constant is specified then the
 wall is placed at that position in the appropriate dimension (x, y, or
 z).  In both the EDGE and constant cases, the wall will never move.
 If the wall position is a variable, it should be specified as v_name,
 where name is an <a class="reference internal" href="variable.html"><em>equal-style variable</em></a> name.  In this
 case the variable is evaluated each timestep and the result becomes
 the current position of the reflecting wall.  Equal-style variables
 can specify formulas with various mathematical functions, and include
 <a class="reference internal" href="thermo_style.html"><em>thermo_style</em></a> command keywords for the simulation
 box parameters and timestep and elapsed time.  Thus it is easy to
 specify a time-dependent wall position.</p>
 <p>The <em>units</em> keyword determines the meaning of the distance units used
 to define a wall position, but only when a numeric constant or
 variable is used.  It is not relevant when EDGE is used to specify a
 face position.  In the variable case, the variable is assumed to
 produce a value compatible with the <em>units</em> setting you specify.</p>
 <p>A <em>box</em> value selects standard distance units as defined by the
 <a class="reference internal" href="units.html"><em>units</em></a> command, e.g. Angstroms for units = real or metal.
 A <em>lattice</em> value means the distance units are in lattice spacings.
 The <a class="reference internal" href="lattice.html"><em>lattice</em></a> command must have been previously used to
 define the lattice spacings.</p>
 <hr class="docutils" />
 <p>Here are examples of variable definitions that move the wall position
 in a time-dependent fashion using equal-style
 <a class="reference internal" href="variable.html"><em>variables</em></a>.</p>
 <div class="highlight-python"><div class="highlight"><pre>variable ramp equal ramp(0,10)
 fix 1 all wall/reflect xlo v_ramp
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>variable linear equal vdisplace(0,20)
 fix 1 all wall/reflect xlo v_linear
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>variable wiggle equal swiggle(0.0,5.0,3.0)
 fix 1 all wall/reflect xlo v_wiggle
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>variable wiggle equal cwiggle(0.0,5.0,3.0)
 fix 1 all wall/reflect xlo v_wiggle
 </pre></div>
 </div>
 <p>The ramp(lo,hi) function adjusts the wall position linearly from lo to
 hi over the course of a run.  The vdisplace(c0,velocity) function does
 something similar using the equation position = c0 + velocity*delta,
 where delta is the elapsed time.</p>
 <p>The swiggle(c0,A,period) function causes the wall position to
 oscillate sinusoidally according to this equation, where omega = 2 PI
 / period:</p>
 <div class="highlight-python"><div class="highlight"><pre>position = c0 + A sin(omega*delta)
 </pre></div>
 </div>
 <p>The cwiggle(c0,A,period) function causes the wall position to
 oscillate sinusoidally according to this equation, which will have an
 initial wall velocity of 0.0, and thus may impose a gentler
 perturbation on the particles:</p>
 <div class="highlight-python"><div class="highlight"><pre><span class="n">position</span> <span class="o">=</span> <span class="n">c0</span> <span class="o">+</span> <span class="n">A</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">cos</span><span class="p">(</span><span class="n">omega</span><span class="o">*</span><span class="n">delta</span><span class="p">))</span>
 </pre></div>
 </div>
 </div>
 <hr class="docutils" />
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.  None of the <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> options
 are relevant to this fix.  No global or per-atom quantities are stored
 by this fix for access by various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  No parameter of this fix can
 be used with the <em>start/stop</em> keywords of the <a class="reference internal" href="run.html"><em>run</em></a> command.
 This fix is not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>Any dimension (xyz) that has a reflecting wall must be non-periodic.</p>
 <p>A reflecting wall should not be used with rigid bodies such as those
 defined by a &#8220;fix rigid&#8221; command.  This is because the wall/reflect
 displaces atoms directly rather than exerts a force on them.  For
 rigid bodies, use a soft wall instead, such as <a class="reference internal" href="fix_wall.html"><em>fix wall/lj93</em></a>.  LAMMPS will flag the use of a rigid
 fix with fix wall/reflect with a warning, but will not generate an
 error.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="fix_wall.html"><em>fix wall/lj93</em></a>, <a class="reference internal" href="fix_oneway.html"><em>fix oneway</em></a></p>
 <p><strong>Default:</strong> none</p>
 <hr class="docutils" />
 <p id="bond"><strong>(Bond)</strong> Bond and Leimkuhler, SIAM J Sci Comput, 30, p 134 (2007).</p>
 </div>
 </div>
 
 
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diff --git a/doc/fix_wall_srd.html b/doc/fix_wall_srd.html
index a76c35a4b..5e2e9d509 100644
--- a/doc/fix_wall_srd.html
+++ b/doc/fix_wall_srd.html
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   <div class="section" id="fix-wall-srd-command">
 <span id="index-0"></span><h1>fix wall/srd command<a class="headerlink" href="#fix-wall-srd-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix ID group-ID wall/srd face arg ... keyword value ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><em>fix</em></a> command</li>
 <li>wall/srd = style name of this fix command</li>
 <li>one or more face/arg pairs may be appended</li>
 <li>face = <em>xlo</em> or <em>xhi</em> or <em>ylo</em> or <em>yhi</em> or <em>zlo</em> or <em>zhi</em></li>
 </ul>
 <pre class="literal-block">
 <em>xlo</em>,*ylo*,*zlo* arg = EDGE or constant or variable
-    EDGE = current lo edge of simulation box
-    constant = number like 0.0 or -30.0 (distance units)
-    variable = <a class="reference internal" href="variable.html"><em>equal-style variable</em></a> like v_x or v_wiggle
-  <em>xhi</em>,*yhi*,*zhi* arg = EDGE or constant or variable
-    EDGE = current hi edge of simulation box
-    constant = number like 50.0 or 100.3 (distance units)
-    variable = <a class="reference internal" href="variable.html"><em>equal-style variable</em></a> like v_x or v_wiggle
+  EDGE = current lo edge of simulation box
+  constant = number like 0.0 or -30.0 (distance units)
+  variable = <a class="reference internal" href="variable.html"><em>equal-style variable</em></a> like v_x or v_wiggle
+<em>xhi</em>,*yhi*,*zhi* arg = EDGE or constant or variable
+  EDGE = current hi edge of simulation box
+  constant = number like 50.0 or 100.3 (distance units)
+  variable = <a class="reference internal" href="variable.html"><em>equal-style variable</em></a> like v_x or v_wiggle
 </pre>
 <ul class="simple">
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>units</em></li>
 </ul>
 <pre class="literal-block">
 <em>units</em> value = <em>lattice</em> or <em>box</em>
-    <em>lattice</em> = the wall position is defined in lattice units
-    <em>box</em> = the wall position is defined in simulation box units
+  <em>lattice</em> = the wall position is defined in lattice units
+  <em>box</em> = the wall position is defined in simulation box units
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>fix xwalls all wall/srd xlo EDGE xhi EDGE
 fix walls all wall/srd xlo 0.0 ylo 10.0 units box
 fix top all wall/srd zhi v_pressdown
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Bound the simulation with one or more walls which interact with
 stochastic reaction dynamics (SRD) particles as slip (smooth) or
 no-slip (rough) flat surfaces.  The wall interaction is actually
 invoked via the <a class="reference internal" href="fix_srd.html"><em>fix srd</em></a> command, only on the group of
 SRD particles it defines, so the group setting for the fix wall/srd
 command is ignored.</p>
 <p>A particle/wall collision occurs if an SRD particle moves outside the
 wall on a timestep.  This alters the position and velocity of the SRD
 particle and imparts a force to the wall.</p>
 <p>The <em>collision</em> and <em>Tsrd</em> settings specified via the <a class="reference internal" href="fix_srd.html"><em>fix srd</em></a> command affect the SRD/wall collisions.  A <em>slip</em>
 setting for the <em>collision</em> keyword means that the tangential
 component of the SRD particle momentum is preserved.  Thus only a
 normal force is imparted to the wall.  The normal component of the new
 SRD velocity is sampled from a Gaussian distribution at temperature
 <em>Tsrd</em>.</p>
 <p>For a <em>noslip</em> setting of the <em>collision</em> keyword, both the normal and
 tangential components of the new SRD velocity are sampled from a
 Gaussian distribution at temperature <em>Tsrd</em>.  Additionally, a new
 tangential direction for the SRD velocity is chosen randomly.  This
 collision style imparts both a normal and tangential force to the
 wall.</p>
 <p>Up to 6 walls or faces can be specified in a single command: <em>xlo</em>,
 <em>xhi</em>, <em>ylo</em>, <em>yhi</em>, <em>zlo</em>, <em>zhi</em>.  A <em>lo</em> face reflects particles
 that move to a coordinate less than the wall position, back in the
 <em>hi</em> direction.  A <em>hi</em> face reflects particles that move to a
 coordinate higher than the wall position, back in the <em>lo</em> direction.</p>
 <p>The position of each wall can be specified in one of 3 ways: as the
 EDGE of the simulation box, as a constant value, or as a variable.  If
 EDGE is used, then the corresponding boundary of the current
 simulation box is used.  If a numeric constant is specified then the
 wall is placed at that position in the appropriate dimension (x, y, or
 z).  In both the EDGE and constant cases, the wall will never move.
 If the wall position is a variable, it should be specified as v_name,
 where name is an <a class="reference internal" href="variable.html"><em>equal-style variable</em></a> name.  In this
 case the variable is evaluated each timestep and the result becomes
 the current position of the reflecting wall.  Equal-style variables
 can specify formulas with various mathematical functions, and include
 <a class="reference internal" href="thermo_style.html"><em>thermo_style</em></a> command keywords for the simulation
 box parameters and timestep and elapsed time.  Thus it is easy to
 specify a time-dependent wall position.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">Because the trajectory of the SRD particle is tracked
 as it collides with the wall, you must insure that r = distance of the
 particle from the wall, is always &gt; 0 for SRD particles, or LAMMPS
 will generate an error.  This means you cannot start your simulation
 with SRD particles at the wall position <em>coord</em> (r = 0) or with
 particles on the wrong side of the wall (r &lt; 0).</p>
 </div>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">If you have 2 or more walls that come together at an
 edge or corner (e.g. walls in the x and y dimensions), then be sure to
 set the <em>overlap</em> keyword to <em>yes</em> in the <a class="reference internal" href="fix_srd.html"><em>fix srd</em></a>
 command, since the walls effectively overlap when SRD particles
 collide with them.  LAMMPS will issue a warning if you do not do this.</p>
 </div>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">The walls of this fix only interact with SRD
 particles, as defined by the <a class="reference internal" href="fix_srd.html"><em>fix srd</em></a> command.  If you
 are simulating a mixture containing other kinds of particles, then you
 should typically use <a class="reference internal" href="fix_wall.html"><em>another wall command</em></a> to act on
 the other particles.  Since SRD particles will be colliding both with
 the walls and the other particles, it is important to insure that the
 other particle&#8217;s finite extent does not overlap an SRD wall.  If you
 do not do this, you may generate errors when SRD particles end up
 &#8220;inside&#8221; another particle or a wall at the beginning of a collision
 step.</p>
 </div>
 <p>The <em>units</em> keyword determines the meaning of the distance units used
 to define a wall position, but only when a numeric constant is used.
 It is not relevant when EDGE or a variable is used to specify a face
 position.</p>
 <p>A <em>box</em> value selects standard distance units as defined by the
 <a class="reference internal" href="units.html"><em>units</em></a> command, e.g. Angstroms for units = real or metal.
 A <em>lattice</em> value means the distance units are in lattice spacings.
 The <a class="reference internal" href="lattice.html"><em>lattice</em></a> command must have been previously used to
 define the lattice spacings.</p>
 <hr class="docutils" />
 <p>Here are examples of variable definitions that move the wall position
 in a time-dependent fashion using equal-style
 <a class="reference internal" href="variable.html"><em>variables</em></a>.</p>
 <div class="highlight-python"><div class="highlight"><pre>variable ramp equal ramp(0,10)
 fix 1 all wall/srd xlo v_ramp
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>variable linear equal vdisplace(0,20)
 fix 1 all wall/srd xlo v_linear
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>variable wiggle equal swiggle(0.0,5.0,3.0)
 fix 1 all wall/srd xlo v_wiggle
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>variable wiggle equal cwiggle(0.0,5.0,3.0)
 fix 1 all wall/srd xlo v_wiggle
 </pre></div>
 </div>
 <p>The ramp(lo,hi) function adjusts the wall position linearly from lo to
 hi over the course of a run.  The displace(c0,velocity) function does
 something similar using the equation position = c0 + velocity*delta,
 where delta is the elapsed time.</p>
 <p>The swiggle(c0,A,period) function causes the wall position to
 oscillate sinusoidally according to this equation, where omega = 2 PI
 / period:</p>
 <div class="highlight-python"><div class="highlight"><pre>position = c0 + A sin(omega*delta)
 </pre></div>
 </div>
 <p>The cwiggle(c0,A,period) function causes the wall position to
 oscillate sinusoidally according to this equation, which will have an
 initial wall velocity of 0.0, and thus may impose a gentler
 perturbation on the particles:</p>
 <div class="highlight-python"><div class="highlight"><pre><span class="n">position</span> <span class="o">=</span> <span class="n">c0</span> <span class="o">+</span> <span class="n">A</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">cos</span><span class="p">(</span><span class="n">omega</span><span class="o">*</span><span class="n">delta</span><span class="p">))</span>
 </pre></div>
 </div>
 </div>
 <hr class="docutils" />
 <div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
 <h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
 <p>No information about this fix is written to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>.  None of the <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a> options
 are relevant to this fix.</p>
 <p>This fix computes a global array of values which can be accessed by
 various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>.  The number of
 rows in the array is equal to the number of walls defined by the fix.
 The number of columns is 3, for the x,y,z components of force on each
 wall.</p>
 <p>Note that an outward normal force on a wall will be a negative value
 for <em>lo</em> walls and a positive value for <em>hi</em> walls.  The array values
 calculated by this fix are &#8220;extensive&#8221;.</p>
 <p>No parameter of this fix can be used with the <em>start/stop</em> keywords of
 the <a class="reference internal" href="run.html"><em>run</em></a> command.  This fix is not invoked during <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>Any dimension (xyz) that has an SRD wall must be non-periodic.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="fix_srd.html"><em>fix srd</em></a></p>
 <p><strong>Default:</strong> none</p>
 </div>
 </div>
 
 
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   <div class="section" id="group-command">
 <span id="index-0"></span><h1>group command<a class="headerlink" href="#group-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>group ID style args
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID = user-defined name of the group</li>
 <li>style = <em>delete</em> or <em>region</em> or <em>type</em> or <em>id</em> or <em>molecule</em> or <em>variable</em> or         <em>include</em> or <em>subtract</em> or <em>union</em> or <em>intersect</em> or         <em>dynamic</em> or <em>static</em></li>
 </ul>
 <pre class="literal-block">
 <em>delete</em> = no args
-  <em>clear</em> = no args
-  <em>region</em> args = region-ID
-  <em>type</em> or <em>id</em> or <em>molecule</em>
-    args = list of one or more atom types, atom IDs, or molecule IDs
-      any entry in list can be a sequence formatted as A:B or A:B:C where
-      A = starting index, B = ending index,
-      C = increment between indices, 1 if not specified
-    args = logical value
-      logical = &quot;&lt;&quot; or &quot;&lt;=&quot; or &quot;&gt;&quot; or &quot;&gt;=&quot; or &quot;==&quot; or &quot;!=&quot;
-      value = an atom type or atom ID or molecule ID (depending on <em>style</em>)
-    args = logical value1 value2
-      logical = &quot;&lt;&gt;&quot;
-      value1,value2 = atom types or atom IDs or molecule IDs (depending on <em>style</em>)
-  <em>variable</em> args = variable-name
-  <em>include</em> args = molecule
-    molecule = add atoms to group with same molecule ID as atoms already in group
-  <em>subtract</em> args = two or more group IDs
-  <em>union</em> args = one or more group IDs
-  <em>intersect</em> args = two or more group IDs
-  <em>dynamic</em> args = parent-ID keyword value ...
-    one or more keyword/value pairs may be appended
-    keyword = <em>region</em> or <em>var</em> or <em>every</em>
-      <em>region</em> value = region-ID
-      <em>var</em> value = name of variable
-      <em>every</em> value = N = update group every this many timesteps
-  <em>static</em> = no args
+<em>clear</em> = no args
+<em>region</em> args = region-ID
+<em>type</em> or <em>id</em> or <em>molecule</em>
+  args = list of one or more atom types, atom IDs, or molecule IDs
+    any entry in list can be a sequence formatted as A:B or A:B:C where
+    A = starting index, B = ending index,
+    C = increment between indices, 1 if not specified
+  args = logical value
+    logical = &quot;&lt;&quot; or &quot;&lt;=&quot; or &quot;&gt;&quot; or &quot;&gt;=&quot; or &quot;==&quot; or &quot;!=&quot;
+    value = an atom type or atom ID or molecule ID (depending on <em>style</em>)
+  args = logical value1 value2
+    logical = &quot;&lt;&gt;&quot;
+    value1,value2 = atom types or atom IDs or molecule IDs (depending on <em>style</em>)
+<em>variable</em> args = variable-name
+<em>include</em> args = molecule
+  molecule = add atoms to group with same molecule ID as atoms already in group
+<em>subtract</em> args = two or more group IDs
+<em>union</em> args = one or more group IDs
+<em>intersect</em> args = two or more group IDs
+<em>dynamic</em> args = parent-ID keyword value ...
+  one or more keyword/value pairs may be appended
+  keyword = <em>region</em> or <em>var</em> or <em>every</em>
+    <em>region</em> value = region-ID
+    <em>var</em> value = name of variable
+    <em>every</em> value = N = update group every this many timesteps
+<em>static</em> = no args
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>group edge region regstrip
 group water type 3 4
 group sub id 10 25 50
 group sub id 10 25 50 500:1000
 group sub id 100:10000:10
 group sub id &lt;= 150
 group polyA molecule &lt;&gt; 50 250
 group hienergy variable eng
 group hienergy include molecule
 group boundary subtract all a2 a3
 group boundary union lower upper
 group boundary intersect upper flow
 group boundary delete
 group mine dynamic all region myRegion every 100
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Identify a collection of atoms as belonging to a group.  The group ID
 can then be used in other commands such as <a class="reference internal" href="fix.html"><em>fix</em></a>,
 <a class="reference internal" href="compute.html"><em>compute</em></a>, <a class="reference internal" href="dump.html"><em>dump</em></a>, or <a class="reference internal" href="velocity.html"><em>velocity</em></a>
 to act on those atoms together.</p>
 <p>If the group ID already exists, the group command adds the specified
 atoms to the group.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">By default groups are static, meaning the atoms are
 permanently assigned to the group.  For example, if the <em>region</em> style
 is used to assign atoms to a group, the atoms will remain in the group
 even if they later move out of the region.  As explained below, the
 <em>dynamic</em> style can be used to make a group dynamic so that a periodic
 determination is made as to which atoms are in the group.  Since many
 LAMMPS commands operate on groups of atoms, you should think carefully
 about whether making a group dynamic makes sense for your model.</p>
 </div>
 <p>A group with the ID <em>all</em> is predefined.  All atoms belong to this
 group.  This group cannot be deleted, or made dynamic.</p>
 <p>The <em>delete</em> style removes the named group and un-assigns all atoms
 that were assigned to that group.  Since there is a restriction (see
 below) that no more than 32 groups can be defined at any time, the
 <em>delete</em> style allows you to remove groups that are no longer needed,
 so that more can be specified.  You cannot delete a group if it has
 been used to define a current <a class="reference internal" href="fix.html"><em>fix</em></a> or <a class="reference internal" href="compute.html"><em>compute</em></a>
 or <a class="reference internal" href="dump.html"><em>dump</em></a>.</p>
 <p>The <em>clear</em> style un-assigns all atoms that were assigned to that
 group.  This may be dangerous to do during a simulation run,
 e.g. using the <a class="reference internal" href="run.html"><em>run every</em></a> command if a fix or compute or
 other operation expects the atoms in the group to remain constant, but
 LAMMPS does not check for this.</p>
 <p>The <em>region</em> style puts all atoms in the region volume into the group.
 Note that this is a static one-time assignment.  The atoms remain
 assigned (or not assigned) to the group even in they later move out of
 the region volume.</p>
 <p>The <em>type</em>, <em>id</em>, and <em>molecule</em> styles put all atoms with the
 specified atom types, atom IDs, or molecule IDs into the group.  These
 3 styles can use arguments specified in one of two formats.</p>
 <p>The first format is a list of values (types or IDs).  For example, the
 2nd command in the examples above puts all atoms of type 3 or 4 into
 the group named <em>water</em>.  Each entry in the list can be a
 colon-separated sequence A:B or A:B:C, as in two of the examples
 above.  A &#8220;sequence&#8221; generates a sequence of values (types or IDs),
 with an optional increment.  The first example with 500:1000 has the
 default increment of 1 and would add all atom IDs from 500 to 1000
 (inclusive) to the group sub, along with 10,25,50 since they also
 appear in the list of values.  The second example with 100:10000:10
 uses an increment of 10 and would thus would add atoms IDs
 100,110,120, ... 9990,10000 to the group sub.</p>
 <p>The second format is a <em>logical</em> followed by one or two values (type
 or ID).  The 7 valid logicals are listed above.  All the logicals
 except &lt;&gt; take a single argument.  The 3rd example above adds all
 atoms with IDs from 1 to 150 to the group named <em>sub</em>.  The logical &lt;&gt;
 means &#8220;between&#8221; and takes 2 arguments.  The 4th example above adds all
 atoms belonging to molecules with IDs from 50 to 250 (inclusive) to
 the group named polyA.</p>
 <p>The <em>variable</em> style evaluates a variable to determine which atoms to
 add to the group.  It must be an <a class="reference internal" href="variable.html"><em>atom-style variable</em></a>
 previously defined in the input script.  If the variable evaluates
 to a non-zero value for a particular atom, then that atom is added
 to the specified group.</p>
 <p>Atom-style variables can specify formulas that include thermodynamic
 quantities, per-atom values such as atom coordinates, or per-atom
 quantities calculated by computes, fixes, or other variables.  They
 can also include Boolean logic where 2 numeric values are compared to
 yield a 1 or 0 (effectively a true or false).  Thus using the
 <em>variable</em> style, is a general way to flag specific atoms to include
 or exclude from a group.</p>
 <p>For example, these lines define a variable &#8220;eatom&#8221; that calculates the
 potential energy of each atom and includes it in the group if its
 potential energy is above the threshhold value -3.0.</p>
 <div class="highlight-python"><div class="highlight"><pre>compute         1 all pe/atom
 compute         2 all reduce sum c_1
 thermo_style    custom step temp pe c_2
 run             0
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>variable        eatom atom &quot;c_1 &gt; -3.0&quot;
 group           hienergy variable eatom
 </pre></div>
 </div>
 <p>Note that these lines</p>
 <div class="highlight-python"><div class="highlight"><pre>compute         2 all reduce sum c_1
 thermo_style    custom step temp pe c_2
 run             0
 </pre></div>
 </div>
 <p>are necessary to insure that the &#8220;eatom&#8221; variable is current when the
 group command invokes it.  Because the eatom variable computes the
 per-atom energy via the pe/atom compute, it will only be current if a
 run has been performed which evaluated pairwise energies, and the
 pe/atom compute was actually invoked during the run.  Printing the
 thermodyanmic info for compute 2 insures that this is the case, since
 it sums the pe/atom compute values (in the reduce compute) to output
 them to the screen.  See the &#8220;Variable Accuracy&#8221; section of the
 <a class="reference internal" href="variable.html"><em>variable</em></a> doc page for more details on insuring that
 variables are current when they are evaluated between runs.</p>
 <p>The <em>include</em> style with its arg <em>molecule</em> adds atoms to a group that
 have the same molecule ID as atoms already in the group.  The molecule
 ID = 0 is ignored in this operation, since it is assumed to flag
 isolated atoms that are not part of molecules.  An example of where
 this operation is useful is if the <em>region</em> style has been used
 previously to add atoms to a group that are within a geometric region.
 If molecules straddle the region boundary, then atoms outside the
 region that are part of molecules with atoms inside the region will
 not be in the group.  Using the group command a 2nd time with <em>include
 molecule</em> will add those atoms that are outside the region to the
 group.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">The <em>include molecule</em> operation is relatively
 expensive in a parallel sense.  This is because it requires
 communication of relevant molecule IDs between all the processors and
 each processor to loop over its atoms once per processor, to compare
 its atoms to the list of molecule IDs from every other processor.
 Hence it scales as N, rather than N/P as most of the group operations
 do, where N is the number of atoms, and P is the number of processors.</p>
 </div>
 <p>The <em>subtract</em> style takes a list of two or more existing group names
 as arguments.  All atoms that belong to the 1st group, but not to any
 of the other groups are added to the specified group.</p>
 <p>The <em>union</em> style takes a list of one or more existing group names as
 arguments.  All atoms that belong to any of the listed groups are
 added to the specified group.</p>
 <p>The <em>intersect</em> style takes a list of two or more existing group names
 as arguments.  Atoms that belong to every one of the listed groups are
 added to the specified group.</p>
 <hr class="docutils" />
 <p>The <em>dynamic</em> style flags an existing or new group as dynamic.  This
 means atoms will be (re)assigned to the group periodically as a
 simulation runs.  This is in contrast to static groups where atoms are
 permanently assigned to the group.  The way the assignment occurs is
 as follows.  Only atoms in the group specified as the parent group via
 the parent-ID are assigned to the dynamic group before the following
 conditions are applied.  If the <em>region</em> keyword is used, atoms not in
 the specified region are removed from the dynamic group.  If the <em>var</em>
 keyword is used, the variable name must be an atom-style or
 atomfile-style variable.  The variable is evaluated and atoms whose
 per-atom values are 0.0, are removed from the dynamic group.</p>
 <p>The assignment of atoms to a dynamic group is done at the beginning of
 each run and on every timestep that is a multiple of <em>N</em>, which is the
 argument for the <em>every</em> keyword (N = 1 is the default).  For an
 energy minimization, via the <a class="reference internal" href="minimize.html"><em>minimize</em></a> command, an
 assignement is made at the beginning of the minimization, but not
 during the iterations of the minimizer.</p>
 <p>The point in the timestep at which atoms are assigned to a dynamic
 group is after the initial stage of velocity Verlet time integration
 has been performed, and before neighbor lists or forces are computed.
 This is the point in the timestep where atom positions have just
 changed due to the time integration, so the region criterion should be
 accurate, if applied.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">If the <em>region</em> keyword is used to determine what
 atoms are in the dynamic group, atoms can move outside of the
 simulation box between reneighboring events.  Thus if you want to
 include all atoms on the left side of the simulation box, you probably
 want to set the left boundary of the region to be outside the
 simulation box by some reasonable amount (e.g. up to the cutoff of the
 potential), else they may be excluded from the dynamic region.</p>
 </div>
 <p>Here is an example of using a dynamic group to shrink the set of atoms
 being integrated by using a spherical region with a variable radius
 (shrinking from 18 to 5 over the course of the run).  This could be
 used to model a quench of the system, freezing atoms outside the
 shrinking sphere, then converting the remaining atoms to a static
 group and running further.</p>
 <div class="highlight-python"><div class="highlight"><pre>variable        nsteps equal 5000
 variable        rad equal 18-(step/v_nsteps)*(18-5)
 region          ss sphere 20 20 0 v_rad
 group           mobile dynamic all region ss
 fix             1 mobile nve
 run             ${nsteps}
 group           mobile static
 run          ${nsteps}
 </pre></div>
 </div>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">All fixes and computes take a group ID as an argument,
 but they do not all allow for use of a dynamic group.  If you get an
 error message that this is not allowed, but feel that it should be for
 the fix or compute in question, then please post your reasoning to the
 LAMMPS mail list and we can change it.</p>
 </div>
 <p>The <em>static</em> style removes the setting for a dynamic group, converting
 it to a static group (the default).  The atoms in the static group are
 those currently in the dynamic group.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>There can be no more than 32 groups defined at one time, including
 &#8220;all&#8221;.</p>
 <p>The parent group of a dynamic group cannot itself be a dynamic group.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="dump.html"><em>dump</em></a>, <a class="reference internal" href="fix.html"><em>fix</em></a>, <a class="reference internal" href="region.html"><em>region</em></a>,
 <a class="reference internal" href="velocity.html"><em>velocity</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>All atoms belong to the &#8220;all&#8221; group.</p>
 </div>
 </div>
 
 
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   <div class="section" id="kspace-style-command">
 <span id="index-0"></span><h1>kspace_style command<a class="headerlink" href="#kspace-style-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>kspace_style style value
 </pre></div>
 </div>
 <ul class="simple">
 <li>style = <em>none</em> or <em>ewald</em> or <em>ewald/disp</em> or <em>ewald/omp</em> or <em>pppm</em> or <em>pppm/cg</em> or <em>pppm/disp</em> or <em>pppm/tip4p</em> or <em>pppm/stagger</em> or <em>pppm/disp/tip4p</em> or <em>pppm/gpu</em> or <em>pppm/omp</em> or <em>pppm/cg/omp</em> or <em>pppm/tip4p/omp</em> or <em>msm</em> or <em>msm/cg</em> or <em>msm/omp</em> or <em>msm/cg/omp</em></li>
 </ul>
 <pre class="literal-block">
 <em>none</em> value = none
-  <em>ewald</em> value = accuracy
-    accuracy = desired relative error in forces
-  <em>ewald/disp</em> value = accuracy
-    accuracy = desired relative error in forces
-  <em>ewald/omp</em> value = accuracy
-    accuracy = desired relative error in forces
-  <em>pppm</em> value = accuracy
-    accuracy = desired relative error in forces
-  <em>pppm/cg</em> value = accuracy (smallq)
-    accuracy = desired relative error in forces
-    smallq = cutoff for charges to be considered (optional) (charge units)
-  <em>pppm/disp</em> value = accuracy
-    accuracy = desired relative error in forces
-  <em>pppm/tip4p</em> value = accuracy
-    accuracy = desired relative error in forces
-  <em>pppm/disp/tip4p</em> value = accuracy
-    accuracy = desired relative error in forces
-  <em>pppm/gpu</em> value = accuracy
-    accuracy = desired relative error in forces
-  <em>pppm/omp</em> value = accuracy
-    accuracy = desired relative error in forces
-  <em>pppm/cg/omp</em> value = accuracy
-    accuracy = desired relative error in forces
-  <em>pppm/tip4p/omp</em> value = accuracy
-    accuracy = desired relative error in forces
-  <em>pppm/stagger</em> value = accuracy
-    accuracy = desired relative error in forces
-  <em>msm</em> value = accuracy
-    accuracy = desired relative error in forces
-  <em>msm/cg</em> value = accuracy (smallq)
-    accuracy = desired relative error in forces
-    smallq = cutoff for charges to be considered (optional) (charge units)
-  <em>msm/omp</em> value = accuracy
-    accuracy = desired relative error in forces
-  <em>msm/cg/omp</em> value = accuracy (smallq)
-    accuracy = desired relative error in forces
-    smallq = cutoff for charges to be considered (optional) (charge units)
+<em>ewald</em> value = accuracy
+  accuracy = desired relative error in forces
+<em>ewald/disp</em> value = accuracy
+  accuracy = desired relative error in forces
+<em>ewald/omp</em> value = accuracy
+  accuracy = desired relative error in forces
+<em>pppm</em> value = accuracy
+  accuracy = desired relative error in forces
+<em>pppm/cg</em> value = accuracy (smallq)
+  accuracy = desired relative error in forces
+  smallq = cutoff for charges to be considered (optional) (charge units)
+<em>pppm/disp</em> value = accuracy
+  accuracy = desired relative error in forces
+<em>pppm/tip4p</em> value = accuracy
+  accuracy = desired relative error in forces
+<em>pppm/disp/tip4p</em> value = accuracy
+  accuracy = desired relative error in forces
+<em>pppm/gpu</em> value = accuracy
+  accuracy = desired relative error in forces
+<em>pppm/omp</em> value = accuracy
+  accuracy = desired relative error in forces
+<em>pppm/cg/omp</em> value = accuracy
+  accuracy = desired relative error in forces
+<em>pppm/tip4p/omp</em> value = accuracy
+  accuracy = desired relative error in forces
+<em>pppm/stagger</em> value = accuracy
+  accuracy = desired relative error in forces
+<em>msm</em> value = accuracy
+  accuracy = desired relative error in forces
+<em>msm/cg</em> value = accuracy (smallq)
+  accuracy = desired relative error in forces
+  smallq = cutoff for charges to be considered (optional) (charge units)
+<em>msm/omp</em> value = accuracy
+  accuracy = desired relative error in forces
+<em>msm/cg/omp</em> value = accuracy (smallq)
+  accuracy = desired relative error in forces
+  smallq = cutoff for charges to be considered (optional) (charge units)
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>kspace_style pppm 1.0e-4
 kspace_style pppm/cg 1.0e-5 1.0e-6
 kspace style msm 1.0e-4
 kspace_style none
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Define a long-range solver for LAMMPS to use each timestep to compute
 long-range Coulombic interactions or long-range 1/r^6 interactions.
 Most of the long-range solvers perform their computation in K-space,
 hence the name of this command.</p>
 <p>When such a solver is used in conjunction with an appropriate pair
 style, the cutoff for Coulombic or 1/r^N interactions is effectively
 infinite.  If the Coulombic case, this means each charge in the system
 interacts with charges in an infinite array of periodic images of the
 simulation domain.</p>
 <p>Note that using a long-range solver requires use of a matching <code class="xref doc docutils literal"><span class="pre">pair</span> <span class="pre">style</span></code> to perform consistent short-range pairwise
 calculations.  This means that the name of the pair style contains a
 matching keyword to the name of the KSpace style, as in this table:</p>
 <table border="1" class="docutils">
 <colgroup>
 <col width="49%" />
 <col width="51%" />
 </colgroup>
 <tbody valign="top">
 <tr class="row-odd"><td>Pair style</td>
 <td>KSpace style</td>
 </tr>
 <tr class="row-even"><td>coul/long</td>
 <td>ewald or pppm</td>
 </tr>
 <tr class="row-odd"><td>coul/msm</td>
 <td>msm</td>
 </tr>
 <tr class="row-even"><td>lj/long or buck/long</td>
 <td>disp (for dispersion)</td>
 </tr>
 <tr class="row-odd"><td>tip4p/long</td>
 <td>tip4p</td>
 </tr>
 </tbody>
 </table>
 <hr class="docutils" />
 <p>The <em>ewald</em> style performs a standard Ewald summation as described in
 any solid-state physics text.</p>
 <p>The <em>ewald/disp</em> style adds a long-range dispersion sum option for
 1/r^6 potentials and is useful for simulation of interfaces
 <a class="reference internal" href="pair_lj_long.html#veld"><span>(Veld)</span></a>.  It also performs standard Coulombic Ewald summations,
 but in a more efficient manner than the <em>ewald</em> style.  The 1/r^6
 capability means that Lennard-Jones or Buckingham potentials can be
 used without a cutoff, i.e. they become full long-range potentials.
 The <em>ewald/disp</em> style can also be used with point-dipoles
 <a class="reference internal" href="pair_dipole.html#toukmaji"><span>(Toukmaji)</span></a> and is currently the only kspace solver in
 LAMMPS with this capability.</p>
 <hr class="docutils" />
 <p>The <em>pppm</em> style invokes a particle-particle particle-mesh solver
 <a class="reference internal" href="#hockney"><span>(Hockney)</span></a> which maps atom charge to a 3d mesh, uses 3d FFTs
 to solve Poisson&#8217;s equation on the mesh, then interpolates electric
 fields on the mesh points back to the atoms.  It is closely related to
 the particle-mesh Ewald technique (PME) <a class="reference internal" href="#darden"><span>(Darden)</span></a> used in
 AMBER and CHARMM.  The cost of traditional Ewald summation scales as
 N^(3/2) where N is the number of atoms in the system.  The PPPM solver
 scales as Nlog(N) due to the FFTs, so it is almost always a faster
 choice <a class="reference internal" href="#pollock"><span>(Pollock)</span></a>.</p>
 <p>The <em>pppm/cg</em> style is identical to the <em>pppm</em> style except that it
 has an optimization for systems where most particles are uncharged.
 Similarly the <em>msm/cg</em> style implements the same optimization for <em>msm</em>.
 The optional <em>smallq</em> argument defines the cutoff for the absolute
 charge value which determines whether a particle is considered charged
 or not.  Its default value is 1.0e-5.</p>
 <p>The <em>pppm/tip4p</em> style is identical to the <em>pppm</em> style except that it
 adds a charge at the massless 4th site in each TIP4P water molecule.
 It should be used with <a class="reference internal" href="pair_style.html"><em>pair styles</em></a> with a
 <em>tip4p/long</em> in their style name.</p>
 <p>The <em>pppm/stagger</em> style performs calculations using two different
 meshes, one shifted slightly with respect to the other.  This can
 reduce force aliasing errors and increase the accuracy of the method
 for a given mesh size.  Or a coarser mesh can be used for the same
 target accuracy, which saves CPU time.  However, there is a trade-off
 since FFTs on two meshes are now performed which increases the
 compuation required.  See <a class="reference internal" href="#cerutti"><span>(Cerutti)</span></a>, <a class="reference internal" href="#neelov"><span>(Neelov)</span></a>,
 and <a class="reference internal" href="#hockney"><span>(Hockney)</span></a> for details of the method.</p>
 <p>For high relative accuracy, using staggered PPPM allows the mesh size
 to be reduced by a factor of 2 in each dimension as compared to
 regular PPPM (for the same target accuracy).  This can give up to a 4x
 speedup in the KSpace time (8x less mesh points, 2x more expensive).
 However, for low relative accuracy, the staggered PPPM mesh size may
 be essentially the same as for regular PPPM, which means the method
 will be up to 2x slower in the KSpace time (simply 2x more expensive).
 For more details and timings, see
 <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a>.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">Using <em>pppm/stagger</em> may not give the same increase in
 the accuracy of energy and pressure as it does in forces, so some
 caution must be used if energy and/or pressure are quantities of
 interest, such as when using a barostat.</p>
 </div>
 <hr class="docutils" />
 <p>The <em>pppm/disp</em> and <em>pppm/disp/tip4p</em> styles add a mesh-based long-range
 dispersion sum option for 1/r^6 potentials <a class="reference internal" href="#isele-holder"><span>(Isele-Holder)</span></a>,
 similar to the <em>ewald/disp</em> style. The 1/r^6 capability means
 that Lennard-Jones or Buckingham potentials can be used without a cutoff,
 i.e. they become full long-range potentials.</p>
 <p>For these styles, you will possibly want to adjust the default choice of
 parameters by using the <a class="reference internal" href="kspace_modify.html"><em>kspace_modify</em></a> command.
 This can be done by either choosing the Ewald and grid parameters, or
 by specifying separate accuracies for the real and kspace
 calculations. When not making any settings, the simulation will stop with
 an error message. Further information on the influence of the parameters
 and how to choose them is described in <a class="reference internal" href="#isele-holder"><span>(Isele-Holder)</span></a>,
 <a class="reference internal" href="#isele-holder2"><span>(Isele-Holder2)</span></a> and the
 <a class="reference internal" href="Section_howto.html#howto-24"><span>How-To</span></a> discussion.</p>
 <hr class="docutils" />
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">All of the PPPM styles can be used with
 single-precision FFTs by using the compiler switch -DFFT_SINGLE for
 the FFT_INC setting in your lo-level Makefile.  This setting also
 changes some of the PPPM operations (e.g. mapping charge to mesh and
 interpolating electric fields to particles) to be performed in single
 precision.  This option can speed-up long-range calulations,
 particularly in parallel or on GPUs.  The use of the -DFFT_SINGLE flag
 is discussed in <a class="reference internal" href="Section_start.html#start-2-4"><span>this section</span></a> of the
 manual. MSM does not currently support the -DFFT_SINGLE compiler switch.</p>
 </div>
 <hr class="docutils" />
 <p>The <em>msm</em> style invokes a multi-level summation method MSM solver,
 <a class="reference internal" href="#hardy"><span>(Hardy)</span></a> or <a class="reference internal" href="#hardy2"><span>(Hardy2)</span></a>, which maps atom charge to a 3d
 mesh, and uses a multi-level hierarchy of coarser and coarser meshes
 on which direct coulomb solves are done.  This method does not use
 FFTs and scales as N. It may therefore be faster than the other
 K-space solvers for relatively large problems when running on large
 core counts. MSM can also be used for non-periodic boundary conditions and
 for mixed periodic and non-periodic boundaries.</p>
 <p>MSM is most competitive versus Ewald and PPPM when only relatively
 low accuracy forces, about 1e-4 relative error or less accurate,
 are needed. Note that use of a larger coulomb cutoff (i.e. 15
 angstroms instead of 10 angstroms) provides better MSM accuracy for
 both the real space and grid computed forces.</p>
 <p>Currently calculation of the full pressure tensor in MSM is expensive.
 Using the <a class="reference internal" href="kspace_modify.html"><em>kspace_modify</em></a> <em>pressure/scalar yes</em>
 command provides a less expensive way to compute the scalar pressure
 (Pxx + Pyy + Pzz)/3.0. The scalar pressure can be used, for example,
 to run an isotropic barostat. If the full pressure tensor is needed,
 then calculating the pressure at every timestep or using a fixed
 pressure simulation with MSM will cause the code to run slower.</p>
 <hr class="docutils" />
 <p>The specified <em>accuracy</em> determines the relative RMS error in per-atom
 forces calculated by the long-range solver.  It is set as a
 dimensionless number, relative to the force that two unit point
 charges (e.g. 2 monovalent ions) exert on each other at a distance of
 1 Angstrom.  This reference value was chosen as representative of the
 magnitude of electrostatic forces in atomic systems.  Thus an accuracy
 value of 1.0e-4 means that the RMS error will be a factor of 10000
 smaller than the reference force.</p>
 <p>The accuracy setting is used in conjunction with the pairwise cutoff
 to determine the number of K-space vectors for style <em>ewald</em> or the
 grid size for style <em>pppm</em> or <em>msm</em>.</p>
 <p>Note that style <em>pppm</em> only computes the grid size at the beginning of
 a simulation, so if the length or triclinic tilt of the simulation
 cell increases dramatically during the course of the simulation, the
 accuracy of the simulation may degrade.  Likewise, if the
 <a class="reference internal" href="kspace_modify.html"><em>kspace_modify slab</em></a> option is used with
 shrink-wrap boundaries in the z-dimension, and the box size changes
 dramatically in z.  For example, for a triclinic system with all three
 tilt factors set to the maximum limit, the PPPM grid should be
 increased roughly by a factor of 1.5 in the y direction and 2.0 in the
 z direction as compared to the same system using a cubic orthogonal
 simulation cell. One way to ensure the accuracy requirement is being
 met is to run a short simulation at the maximum expected tilt or
 length, note the required grid size, and then use the
 <a class="reference internal" href="kspace_modify.html"><em>kspace_modify</em></a> <em>mesh</em> command to manually set the
 PPPM grid size to this value.</p>
 <p>RMS force errors in real space for <em>ewald</em> and <em>pppm</em> are estimated
 using equation 18 of <a class="reference internal" href="#kolafa"><span>(Kolafa)</span></a>, which is also referenced as
 equation 9 of <a class="reference internal" href="#petersen"><span>(Petersen)</span></a>. RMS force errors in K-space for
 <em>ewald</em> are estimated using equation 11 of <a class="reference internal" href="#petersen"><span>(Petersen)</span></a>,
 which is similar to equation 32 of <a class="reference internal" href="#kolafa"><span>(Kolafa)</span></a>. RMS force
 errors in K-space for <em>pppm</em> are estimated using equation 38 of
 <a class="reference internal" href="#deserno"><span>(Deserno)</span></a>. RMS force errors for <em>msm</em> are estimated
 using ideas from chapter 3 of <a class="reference internal" href="#hardy"><span>(Hardy)</span></a>, with equation 3.197
 of particular note. When using <em>msm</em> with non-periodic boundary
 conditions, it is expected that the error estimation will be too
 pessimistic. RMS force errors for dipoles when using <em>ewald/disp</em>
 are estimated using equations 33 and 46 of <a class="reference internal" href="pair_polymorphic.html#wang"><span>(Wang)</span></a>.</p>
 <p>See the <a class="reference internal" href="kspace_modify.html"><em>kspace_modify</em></a> command for additional
 options of the K-space solvers that can be set, including a <em>force</em>
 option for setting an absoulte RMS error in forces, as opposed to a
 relative RMS error.</p>
 <hr class="docutils" />
 <p>Styles with a <em>cuda</em>, <em>gpu</em>, <em>intel</em>, <em>kk</em>, <em>omp</em>, or <em>opt</em> suffix are
 functionally the same as the corresponding style without the suffix.
 They have been optimized to run faster, depending on your available
 hardware, as discussed in <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a>
 of the manual.  The accelerated styles take the same arguments and
 should produce the same results, except for round-off and precision
 issues.</p>
 <p>More specifically, the <em>pppm/gpu</em> style performs charge assignment and
 force interpolation calculations on the GPU.  These processes are
 performed either in single or double precision, depending on whether
 the -DFFT_SINGLE setting was specified in your lo-level Makefile, as
 discussed above.  The FFTs themselves are still calculated on the CPU.
 If <em>pppm/gpu</em> is used with a GPU-enabled pair style, part of the PPPM
 calculation can be performed concurrently on the GPU while other
 calculations for non-bonded and bonded force calculation are performed
 on the CPU.</p>
 <p>These accelerated styles are part of the USER-CUDA, GPU, USER-INTEL,
 KOKKOS, USER-OMP, and OPT packages respectively.  They are only
 enabled if LAMMPS was built with those packages.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 <p>See <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a> of the manual for
 more instructions on how to use the accelerated styles effectively.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>Note that the long-range electrostatic solvers in LAMMPS assume conducting
 metal (tinfoil) boundary conditions for both charge and dipole
 interactions. Vacuum boundary conditions are not currently supported.</p>
 <p>The <em>ewald/disp</em>, <em>ewald</em>, <em>pppm</em>, and <em>msm</em> styles support
 non-orthogonal (triclinic symmetry) simulation boxes. However, triclinic
 simulation cells may not yet be supported by suffix versions of these
 styles (such as <em>pppm/cuda</em>).</p>
 <p>All of the kspace styles are part of the KSPACE package.  They are
 only enabled if LAMMPS was built with that package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.  Note that
 the KSPACE package is installed by default.</p>
 <p>For MSM, a simulation must be 3d and one can use any combination of
 periodic, non-periodic, or shrink-wrapped boundaries (specified using
 the <a class="reference internal" href="boundary.html"><em>boundary</em></a> command).</p>
 <p>For Ewald and PPPM, a simulation must be 3d and periodic in all dimensions.
 The only exception is if the slab option is set with <a class="reference internal" href="kspace_modify.html"><em>kspace_modify</em></a>,
 in which case the xy dimensions must be periodic and the z dimension must be
 non-periodic.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="kspace_modify.html"><em>kspace_modify</em></a>, <a class="reference internal" href="pair_lj.html"><em>pair_style lj/cut/coul/long</em></a>, <a class="reference internal" href="pair_charmm.html"><em>pair_style lj/charmm/coul/long</em></a>, <a class="reference internal" href="pair_lj_long.html"><em>pair_style lj/long/coul/long</em></a>, <a class="reference internal" href="pair_buck.html"><em>pair_style buck/coul/long</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>kspace_style none
 </pre></div>
 </div>
 <hr class="docutils" />
 <p id="darden"><strong>(Darden)</strong> Darden, York, Pedersen, J Chem Phys, 98, 10089 (1993).</p>
 <p id="deserno"><strong>(Deserno)</strong> Deserno and Holm, J Chem Phys, 109, 7694 (1998).</p>
 <p id="hockney"><strong>(Hockney)</strong> Hockney and Eastwood, Computer Simulation Using Particles,
 Adam Hilger, NY (1989).</p>
 <p id="kolafa"><strong>(Kolafa)</strong> Kolafa and Perram, Molecular Simualtion, 9, 351 (1992).</p>
 <p id="petersen"><strong>(Petersen)</strong> Petersen, J Chem Phys, 103, 3668 (1995).</p>
 <p id="wang"><strong>(Wang)</strong> Wang and Holm, J Chem Phys, 115, 6277 (2001).</p>
 <p id="pollock"><strong>(Pollock)</strong> Pollock and Glosli, Comp Phys Comm, 95, 93 (1996).</p>
 <p id="cerutti"><strong>(Cerutti)</strong> Cerutti, Duke, Darden, Lybrand, Journal of Chemical Theory
 and Computation 5, 2322 (2009)</p>
 <p id="neelov"><strong>(Neelov)</strong> Neelov, Holm, J Chem Phys 132, 234103 (2010)</p>
 <p id="veld"><strong>(Veld)</strong> In &#8216;t Veld, Ismail, Grest, J Chem Phys, 127, 144711 (2007).</p>
 <p id="toukmaji"><strong>(Toukmaji)</strong> Toukmaji, Sagui, Board, and Darden, J Chem Phys, 113,
 10913 (2000).</p>
 <p id="isele-holder"><strong>(Isele-Holder)</strong> Isele-Holder, Mitchell, Ismail, J Chem Phys, 137, 174107 (2012).</p>
 <p id="isele-holder2"><strong>(Isele-Holder2)</strong> Isele-Holder, Mitchell, Hammond, Kohlmeyer, Ismail, J Chem Theory
 Comput 9, 5412 (2013).</p>
 <p id="hardy"><strong>(Hardy)</strong> David Hardy thesis: Multilevel Summation for the Fast
 Evaluation of Forces for the Simulation of Biomolecules, University of
 Illinois at Urbana-Champaign, (2006).</p>
 <p id="hardy2"><strong>(Hardy)</strong> Hardy, Stone, Schulten, Parallel Computing 35 (2009)
 164-177.</p>
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   <div class="section" id="lattice-command">
 <span id="index-0"></span><h1>lattice command<a class="headerlink" href="#lattice-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>lattice style scale keyword values ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>style = <em>none</em> or <em>sc</em> or <em>bcc</em> or <em>fcc</em> or <em>hcp</em> or <em>diamond</em> or         <em>sq</em> or <em>sq2</em> or <em>hex</em> or <em>custom</em></li>
 <li>scale = scale factor between lattice and simulation box</li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>scale = reduced density rho* (for LJ units)
-  scale = lattice constant in distance units (for all other units)
+scale = lattice constant in distance units (for all other units)
 </pre></div>
 </div>
 <ul class="simple">
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>origin</em> or <em>orient</em> or <em>spacing</em> or <em>a1</em> or <em>a2</em> or <em>a3</em> or <em>basis</em></li>
 </ul>
 <pre class="literal-block">
 <em>origin</em> values = x y z
-    x,y,z = fractions of a unit cell (0 &lt;= x,y,z &lt; 1)
-  <em>orient</em> values = dim i j k
-    dim = <em>x</em> or <em>y</em> or <em>z</em>
-    i,j,k = integer lattice directions
-  <em>spacing</em> values = dx dy dz
-    dx,dy,dz = lattice spacings in the x,y,z box directions
-  <em>a1</em>,*a2*,*a3* values = x y z
-    x,y,z = primitive vector components that define unit cell
-  <em>basis</em> values = x y z
-    x,y,z = fractional coords of a basis atom (0 &lt;= x,y,z &lt; 1)
+  x,y,z = fractions of a unit cell (0 &lt;= x,y,z &lt; 1)
+<em>orient</em> values = dim i j k
+  dim = <em>x</em> or <em>y</em> or <em>z</em>
+  i,j,k = integer lattice directions
+<em>spacing</em> values = dx dy dz
+  dx,dy,dz = lattice spacings in the x,y,z box directions
+<em>a1</em>,*a2*,*a3* values = x y z
+  x,y,z = primitive vector components that define unit cell
+<em>basis</em> values = x y z
+  x,y,z = fractional coords of a basis atom (0 &lt;= x,y,z &lt; 1)
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>lattice fcc 3.52
 lattice hex 0.85
 lattice sq 0.8 origin 0.0 0.5 0.0 orient x 1 1 0 orient y -1 1 0
 lattice custom 3.52 a1 1.0 0.0 0.0 a2 0.5 1.0 0.0 a3 0.0 0.0 0.5 &amp;
                     basis 0.0 0.0 0.0 basis 0.5 0.5 0.5
 lattice none 2.0
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Define a lattice for use by other commands.  In LAMMPS, a lattice is
 simply a set of points in space, determined by a unit cell with basis
 atoms, that is replicated infinitely in all dimensions.  The arguments
 of the lattice command can be used to define a wide variety of
 crystallographic lattices.</p>
 <p>A lattice is used by LAMMPS in two ways.  First, the
 <a class="reference internal" href="create_atoms.html"><em>create_atoms</em></a> command creates atoms on the lattice
 points inside the simulation box.  Note that the
 <a class="reference internal" href="create_atoms.html"><em>create_atoms</em></a> command allows different atom types
 to be assigned to different basis atoms of the lattice.  Second, the
 lattice spacing in the x,y,z dimensions implied by the lattice, can be
 used by other commands as distance units
 (e.g. <a class="reference internal" href="create_box.html"><em>create_box</em></a>, <a class="reference internal" href="region.html"><em>region</em></a> and
 <a class="reference internal" href="velocity.html"><em>velocity</em></a>), which are often convenient to use when the
 underlying problem geometry is atoms on a lattice.</p>
 <p>The lattice style must be consistent with the dimension of the
 simulation - see the <a class="reference internal" href="dimension.html"><em>dimension</em></a> command.  Styles <em>sc</em>
 or <em>bcc</em> or <em>fcc</em> or <em>hcp</em> or <em>diamond</em> are for 3d problems.  Styles
 <em>sq</em> or <em>sq2</em> or <em>hex</em> are for 2d problems.  Style <em>custom</em> can be
 used for either 2d or 3d problems.</p>
 <p>A lattice consists of a unit cell, a set of basis atoms within that
 cell, and a set of transformation parameters (scale, origin, orient)
 that map the unit cell into the simulation box.  The vectors a1,a2,a3
 are the edge vectors of the unit cell.  This is the nomenclature for
 &#8220;primitive&#8221; vectors in solid-state crystallography, but in LAMMPS the
 unit cell they determine does not have to be a &#8220;primitive cell&#8221; of
 minimum volume.</p>
 <p>Note that the lattice command can be used multiple times in an input
 script.  Each time it is invoked, the lattice attributes are
 re-defined and are used for all subsequent commands (that use lattice
 attributes).  For example, a sequence of lattice,
 <a class="reference internal" href="region.html"><em>region</em></a>, and <a class="reference internal" href="create_atoms.html"><em>create_atoms</em></a> commands
 can be repeated multiple times to build a poly-crystalline model with
 different geometric regions populated with atoms in different lattice
 orientations.</p>
 <hr class="docutils" />
 <p>A lattice of style <em>none</em> does not define a unit cell and basis set,
 so it cannot be used with the <a class="reference internal" href="create_atoms.html"><em>create_atoms</em></a>
 command.  However it does define a lattice spacing via the specified
 scale parameter.  As explained above the lattice spacings in x,y,z can
 be used by other commands as distance units.  No additional
 keyword/value pairs can be specified for the <em>none</em> style.  By
 default, a &#8220;lattice none 1.0&#8221; is defined, which means the lattice
 spacing is the same as one distance unit, as defined by the
 <a class="reference internal" href="units.html"><em>units</em></a> command.</p>
 <p>Lattices of style <em>sc</em>, <em>fcc</em>, <em>bcc</em>, and <em>diamond</em> are 3d lattices
 that define a cubic unit cell with edge length = 1.0.  This means a1 =
 1 0 0, a2 = 0 1 0, and a3 = 0 0 1.  Style <em>hcp</em> has a1 = 1 0 0, a2 = 0
 sqrt(3) 0, and a3 = 0 0 sqrt(8/3).  The placement of the basis atoms
 within the unit cell are described in any solid-state physics text.  A
 <em>sc</em> lattice has 1 basis atom at the lower-left-bottom corner of the
 cube.  A <em>bcc</em> lattice has 2 basis atoms, one at the corner and one at
 the center of the cube.  A <em>fcc</em> lattice has 4 basis atoms, one at the
 corner and 3 at the cube face centers.  A <em>hcp</em> lattice has 4 basis
 atoms, two in the z = 0 plane and 2 in the z = 0.5 plane.  A <em>diamond</em>
 lattice has 8 basis atoms.</p>
 <p>Lattices of style <em>sq</em> and <em>sq2</em> are 2d lattices that define a square
 unit cell with edge length = 1.0.  This means a1 = 1 0 0 and a2 = 0 1
 0.  A <em>sq</em> lattice has 1 basis atom at the lower-left corner of the
 square.  A <em>sq2</em> lattice has 2 basis atoms, one at the corner and one
 at the center of the square.  A <em>hex</em> style is also a 2d lattice, but
 the unit cell is rectangular, with a1 = 1 0 0 and a2 = 0 sqrt(3) 0.
 It has 2 basis atoms, one at the corner and one at the center of the
 rectangle.</p>
 <p>A lattice of style <em>custom</em> allows you to specify a1, a2, a3, and a
 list of basis atoms to put in the unit cell.  By default, a1 and a2
 and a3 are 3 orthogonal unit vectors (edges of a unit cube).  But you
 can specify them to be of any length and non-orthogonal to each other,
 so that they describe a tilted parallelepiped.  Via the <em>basis</em>
 keyword you add atoms, one at a time, to the unit cell.  Its arguments
 are fractional coordinates (0.0 &lt;= x,y,z &lt; 1.0).  The position vector
 x of a basis atom within the unit cell is thus a linear combination of
 the the unit cell&#8217;s 3 edge vectors, i.e. x = bx a1 + by a2 + bz a3,
 where bx,by,bz are the 3 values specified for the <em>basis</em> keyword.</p>
 <hr class="docutils" />
 <p>This sub-section discusses the arguments that determine how the
 idealized unit cell is transformed into a lattice of points within the
 simulation box.</p>
 <p>The <em>scale</em> argument determines how the size of the unit cell will be
 scaled when mapping it into the simulation box.  I.e. it determines a
 multiplicative factor to apply to the unit cell, to convert it to a
 lattice of the desired size and distance units in the simulation box.
 The meaning of the <em>scale</em> argument depends on the <a class="reference internal" href="units.html"><em>units</em></a>
 being used in your simulation.</p>
 <p>For all unit styles except <em>lj</em>, the scale argument is specified in
 the distance units defined by the unit style.  For example, in <em>real</em>
 or <em>metal</em> units, if the unit cell is a unit cube with edge length
 1.0, specifying scale = 3.52 would create a cubic lattice with a
 spacing of 3.52 Angstroms.  In <em>cgs</em> units, the spacing would be 3.52
 cm.</p>
 <p>For unit style <em>lj</em>, the scale argument is the Lennard-Jones reduced
 density, typically written as rho*.  LAMMPS converts this value into
 the multiplicative factor via the formula &#8220;factor^dim = rho/rho*&#8221;,
 where rho = N/V with V = the volume of the lattice unit cell and N =
 the number of basis atoms in the unit cell (described below), and dim
 = 2 or 3 for the dimensionality of the simulation.  Effectively, this
 means that if LJ particles of size sigma = 1.0 are used in the
 simulation, the lattice of particles will be at the desired reduced
 density.</p>
 <p>The <em>origin</em> option specifies how the unit cell will be shifted or
 translated when mapping it into the simulation box.  The x,y,z values
 are fractional values (0.0 &lt;= x,y,z &lt; 1.0) meaning shift the lattice
 by a fraction of the lattice spacing in each dimension.  The meaning
 of &#8220;lattice spacing&#8221; is discussed below.</p>
 <p>The <em>orient</em> option specifies how the unit cell will be rotated when
 mapping it into the simulation box.  The <em>dim</em> argument is one of the
 3 coordinate axes in the simulation box.  The other 3 arguments are
 the crystallographic direction in the lattice that you want to orient
 along that axis, specified as integers.  E.g. &#8220;orient x 2 1 0&#8221; means
 the x-axis in the simulation box will be the [210] lattice
 direction, and similarly for y and z.  The 3 lattice directions you
 specify do not have to be unit vectors, but they must be mutually
 orthogonal and obey the right-hand rule, i.e. (X cross Y) points in
 the Z direction.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">The preceding paragraph describing lattice directions
 is only valid for orthogonal cubic unit cells (or square in 2d).  If
 you are using a <em>hcp</em> or <em>hex</em> lattice or the more general lattice
 style <em>custom</em> with non-orthogonal a1,a2,a3 vectors, then you should
 think of the 3 <em>orient</em> vectors as creating a 3x3 rotation matrix
 which is applied to a1,a2,a3 to rotate the original unit cell to a new
 orientation in the simulation box.</p>
 </div>
 <hr class="docutils" />
 <p>Several LAMMPS commands have the option to use distance units that are
 inferred from &#8220;lattice spacings&#8221; in the x,y,z box directions.
 E.g. the <a class="reference internal" href="region.html"><em>region</em></a> command can create a block of size
 10x20x20, where 10 means 10 lattice spacings in the x direction.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">Though they are called lattice spacings, all the
 commands that have a &#8220;units lattice&#8221; option, simply use the 3 values
 as scale factors on the distance units defined by the
 <a class="reference internal" href="units.html"><em>units</em></a> command.  Thus if you do not like the lattice
 spacings computed by LAMMPS (e.g. for a non-orthogonal or rotated unit
 cell), you can define the 3 values to be whatever you wish, via the
 <em>spacing</em> option.</p>
 </div>
 <p>If the <em>spacing</em> option is not specified, the lattice spacings are
 computed by LAMMPS in the following way.  A unit cell of the lattice
 is mapped into the simulation box (scaled and rotated), so that it now
 has (perhaps) a modified size and orientation.  The lattice spacing in
 X is defined as the difference between the min/max extent of the x
 coordinates of the 8 corner points of the modified unit cell (4 in
 2d).  Similarly, the Y and Z lattice spacings are defined as the
 difference in the min/max of the y and z coordinates.</p>
 <p>Note that if the unit cell is orthogonal with axis-aligned edges (no
 rotation via the <em>orient</em> keyword), then the lattice spacings in each
 dimension are simply the scale factor (described above) multiplied by
 the length of a1,a2,a3.  Thus a <em>hex</em> style lattice with a scale
 factor of 3.0 Angstroms, would have a lattice spacing of 3.0 in x and
 3*sqrt(3.0) in y.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">For non-orthogonal unit cells and/or when a rotation
 is applied via the <em>orient</em> keyword, then the lattice spacings
 computed by LAMMPS are typically less intuitive.  In particular, in
 these cases, there is no guarantee that a particular lattice spacing
 is an integer multiple of the periodicity of the lattice in that
 direction.  Thus, if you create an orthogonal periodic simulation box
 whose size in a dimension is a multiple of the lattice spacing, and
 then fill it with atoms via the <a class="reference internal" href="create_atoms.html"><em>create_atoms</em></a>
 command, you will NOT necessarily create a periodic system.
 I.e. atoms may overlap incorrectly at the faces of the simulation box.</p>
 </div>
 <p>The <em>spacing</em> option sets the 3 lattice spacings directly.  All must
 be non-zero (use 1.0 for dz in a 2d simulation).  The specified values
 are multiplied by the multiplicative factor described above that is
 associated with the scale factor.  Thus a spacing of 1.0 means one
 unit cell edge length independent of the scale factor.  As mentioned
 above, this option can be useful if the spacings LAMMPS computes are
 inconvenient to use in subsequent commands, which can be the case for
 non-orthogonal or rotated lattices.</p>
 <p>Note that whenever the lattice command is used, the values of the
 lattice spacings LAMMPS calculates are printed out.  Thus their effect
 in commands that use the spacings should be decipherable.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>The <em>a1,a2,a3,basis</em> keywords can only be used with style <em>custom</em>.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="dimension.html"><em>dimension</em></a>, <a class="reference internal" href="create_atoms.html"><em>create_atoms</em></a>,
 <a class="reference internal" href="region.html"><em>region</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>lattice none 1.0
 </pre></div>
 </div>
 <p>For other lattice styles, the option defaults are origin = 0.0 0.0
 0.0, orient = x 1 0 0, orient = y 0 1 0, orient = z 0 0 1, a1 = 1 0 0,
 a2 = 0 1 0, and a3 = 0 0 1.</p>
 </div>
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   <div class="section" id="molecule-command">
 <span id="index-0"></span><h1>molecule command<a class="headerlink" href="#molecule-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>molecule ID file1 file2 ... keyword values ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID = user-assigned name for the molecule template</li>
 <li>file1,file2,... = names of files containing molecule descriptions</li>
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>offset</em></li>
 </ul>
 <pre class="literal-block">
 <em>offset</em> values = toff boff aoff doff ioff
-    toff = offset to add to atom types
-    boff = offset to add to bond types
-    aoff = offset to add to angle types
-    doff = offset to add to dihedral types
-    ioff = offset to add to improper types
+  toff = offset to add to atom types
+  boff = offset to add to bond types
+  aoff = offset to add to angle types
+  doff = offset to add to dihedral types
+  ioff = offset to add to improper types
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>molecule 1 mymol
 molecule 1 co2.txt h2o.txt
 molecule CO2 co2.txt
 molecule 1 mymol offset 6 9 18 23 14
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Define a molecule template that can be used as part of other LAMMPS
 commands, typically to define a collection of particles as a bonded
 molecule or a rigid body.  Commands that currently use molecule
 templates include:</p>
 <ul class="simple">
 <li><a class="reference internal" href="fix_deposit.html"><em>fix deposit</em></a></li>
 <li><a class="reference internal" href="fix_pour.html"><em>fix pour</em></a></li>
 <li><a class="reference internal" href="fix_rigid.html"><em>fix rigid/small</em></a></li>
 <li><a class="reference internal" href="fix_shake.html"><em>fix shake</em></a></li>
 <li><a class="reference internal" href="fix_gcmc.html"><em>fix gcmc</em></a></li>
 <li><a class="reference internal" href="create_atoms.html"><em>create_atoms</em></a></li>
 <li><a class="reference internal" href="atom_style.html"><em>atom_style template</em></a></li>
 </ul>
 <p>The ID of a molecule template can only contain alphanumeric characters
 and underscores.</p>
 <p>A single template can contain multiple molecules, listed one per file.
 Many of the commands listed above currently use only the first
 molecule in the template, and will issue a warning if the template
 contains multiple molecules.  The <a class="reference internal" href="atom_style.html"><em>atom_style template</em></a> command allows multiple-molecule templates
 to define a system with more than one templated molecule.</p>
 <p>The optional <em>offset</em> keyword adds the specified offset values to the
 atom types, bond types, angle types, dihedral types, and improper
 types as they are read from the molecule file.  E.g. if <em>toff</em> = 2,
 and the file uses atom types 1,2,3, then each created molecule will
 have atom types 3,4,5.  This is to make it easy to use the same
 molecule template file in different simulations.  Note that the same
 offsets are applied to the molecules in all specified files.  All five
 offset values must be speicified, but individual values will be
 ignored if the molecule template does not use that attribute (e.g. no
 bonds).</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">This command can be used to define molecules with
 bonds, angles, dihedrals, imporopers, or special bond lists of
 neighbors within a molecular topology, so that you can later add the
 molecules to your simulation, via one or more of the commands listed
 above.  If such molecules do not already exist when LAMMPS creates the
 simulation box, via the <a class="reference internal" href="create_box.html"><em>create_box</em></a> or
 <a class="reference internal" href="read_data.html"><em>read_data</em></a> command, when you later add them you may
 overflow the pre-allocated data structures which store molecular
 topology information with each atom, and an error will be generated.
 Both the <a class="reference internal" href="create_box.html"><em>create_box</em></a> command and the data files read
 by the <a class="reference internal" href="read_data.html"><em>read_data</em></a> command have &#8220;extra&#8221; options which
 insure space is allocated for storing topology info for molecules that
 are added later.</p>
 </div>
 <p>The format of an individual molecule file is similar to the data file
 read by the <a class="reference internal" href="read_data.html"><em>read_data</em></a> commands, and is as follows.</p>
 <p>A molecule file has a header and a body.  The header appears first.
 The first line of the header is always skipped; it typically contains
 a description of the file.  Then lines are read one at a time.  Lines
 can have a trailing comment starting with &#8216;#&#8217; that is ignored.  If the
 line is blank (only whitespace after comment is deleted), it is
 skipped.  If the line contains a header keyword, the corresponding
 value(s) is read from the line.  If it doesn&#8217;t contain a header
 keyword, the line begins the body of the file.</p>
 <p>The body of the file contains zero or more sections.  The first line
 of a section has only a keyword.  The next line is skipped.  The
 remaining lines of the section contain values.  The number of lines
 depends on the section keyword as described below.  Zero or more blank
 lines can be used between sections.  Sections can appear in any order,
 with a few exceptions as noted below.</p>
 <p>These are the recognized header keywords.  Header lines can come in
 any order.  The numeric value(s) are read from the beginning of the
 line.  The keyword should appear at the end of the line.  All these
 settings have default values, as explained below.  A line need only
 appear if the value(s) are different than the default.</p>
 <ul class="simple">
 <li>N <em>atoms</em> = # of atoms N in molecule, default = 0</li>
 <li>Nb <em>bonds</em> = # of bonds Nb in molecule, default = 0</li>
 <li>Na <em>angles</em> = # of angles Na in molecule, default = 0</li>
 <li>Nd <em>dihedrals</em> = # of dihedrals Nd in molecule, default = 0</li>
 <li>Ni <em>impropers</em> = # of impropers Ni in molecule, default = 0</li>
 <li>Mtotal <em>mass</em> = total mass of molecule</li>
 <li>Xc Yc Zc <em>com</em> = coordinates of center-of-mass of molecule</li>
 <li>Ixx Iyy Izz Ixy Ixz Iyz <em>inertia</em> = 6 components of inertia tensor of molecule</li>
 </ul>
 <p>For <em>mass</em>, <em>com</em>, and <em>inertia</em>, the default is for LAMMPS to
 calculate this quantity itself if needed, assuming the molecules
 consists of a set of point particles or finite-size particles (with a
 non-zero diameter) that do not overlap.  If finite-size particles in
 the molecule do overlap, LAMMPS will not account for the overlap
 effects when calculating any of these 3 quantities, so you should
 pre-compute them yourself and list the values in the file.</p>
 <p>The mass and center-of-mass coordinates (Xc,Yc,Zc) are
 self-explanatory.  The 6 moments of inertia (ixx,iyy,izz,ixy,ixz,iyz)
 should be the values consistent with the current orientation of the
 rigid body around its center of mass.  The values are with respect to
 the simulation box XYZ axes, not with respect to the prinicpal axes of
 the rigid body itself.  LAMMPS performs the latter calculation
 internally.</p>
 <p>These are the allowed section keywords for the body of the file.</p>
 <ul class="simple">
 <li><em>Coords, Types, Charges, Diameters, Masses</em> = atom-property sections</li>
 <li><em>Bonds, Angles, Dihedrals, Impropers</em> = molecular topology sections</li>
 <li><em>Special Bond Counts, Special Bonds</em> = special neighbor info</li>
 <li><em>Shake Flags, Shake Atoms, Shake Bond Types</em> = SHAKE info</li>
 </ul>
 <p>If a Bonds section is specified then the Special Bond Counts and
 Special Bonds sections can also be used, if desired, to explicitly
 list the 1-2, 1-3, 1-4 neighbors within the molecule topology (see
 details below).  This is optional since if these sections are not
 included, LAMMPS will auto-generate this information.  Note that
 LAMMPS uses this info to properly exclude or weight bonded pairwise
 interactions between bonded atoms.  See the
 <a class="reference internal" href="special_bonds.html"><em>special_bonds</em></a> command for more details.  One
 reason to list the special bond info explicitly is for the
 <a class="reference internal" href="tutorial_drude.html"><em>thermalized Drude oscillator model</em></a> which treats
 the bonds between nuclear cores and Drude electrons in a different
 manner.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">Whether a section is required depends on how the
 molecule template is used by other LAMMPS commands.  For example, to
 add a molecule via the <a class="reference internal" href="fix_deposit.html"><em>fix deposit</em></a> command, the
 Coords and Types sections are required.  To add a rigid body via the
 <code class="xref doc docutils literal"><span class="pre">fix</span> <span class="pre">pour</span></code> command, the Bonds (Angles, etc) sections are
 not required, since the molecule will be treated as a rigid body.
 Some sections are optional.  For example, the <a class="reference internal" href="fix_pour.html"><em>fix pour</em></a>
 command can be used to add &#8220;molecules&#8221; which are clusters of
 finite-size granular particles.  If the Diameters section is not
 specified, each particle in the molecule will have a default diameter
 of 1.0.  See the doc pages for LAMMPS commands that use molecule
 templates for more details.</p>
 </div>
 <p>Each section is listed below in alphabetic order.  The format of each
 section is described including the number of lines it must contain and
 rules (if any) for whether it can appear in the data file.  In each
 case the ID is ignored; it is simply included for readability, and
 should be a number from 1 to Nlines for the section, indicating which
 atom (or bond, etc) the entry applies to.  The lines are assumed to be
 listed in order from 1 to Nlines, but LAMMPS does not check for this.</p>
 <hr class="docutils" />
 <p><em>Coords</em> section:</p>
 <ul class="simple">
 <li>one line per atom</li>
 <li>line syntax: ID x y z</li>
 <li>x,y,z = coordinate of atom</li>
 </ul>
 <hr class="docutils" />
 <p><em>Types</em> section:</p>
 <ul class="simple">
 <li>one line per atom</li>
 <li>line syntax: ID type</li>
 <li>type = atom type of atom</li>
 </ul>
 <hr class="docutils" />
 <p><em>Charges</em> section:</p>
 <ul class="simple">
 <li>one line per atom</li>
 <li>line syntax: ID q</li>
 <li>q = charge on atom</li>
 </ul>
 <p>This section is only allowed for <a class="reference internal" href="atom_style.html"><em>atom styles</em></a> that
 support charge.  If this section is not included, the default charge
 on each atom in the molecule is 0.0.</p>
 <hr class="docutils" />
 <p><em>Diameters</em> section:</p>
 <ul class="simple">
 <li>one line per atom</li>
 <li>line syntax: ID diam</li>
 <li>diam = diameter of atom</li>
 </ul>
 <p>This section is only allowed for <a class="reference internal" href="atom_style.html"><em>atom styles</em></a> that
 support finite-size spherical particles, e.g. atom_style sphere.  If
 not listed, the default diameter of each atom in the molecule is 1.0.</p>
 <hr class="docutils" />
 <p><em>Masses</em> section:</p>
 <ul class="simple">
 <li>one line per atom</li>
 <li>line syntax: ID mass</li>
 <li>mass = mass of atom</li>
 </ul>
 <p>This section is only allowed for <a class="reference internal" href="atom_style.html"><em>atom styles</em></a> that
 support per-atom mass, as opposed to per-type mass.  See the
 <a class="reference internal" href="mass.html"><em>mass</em></a> command for details.  If this section is not
 included, the default mass for each atom is derived from its volume
 (see Diameters section) and a default density of 1.0, in
 <a class="reference internal" href="units.html"><em>units</em></a> of mass/volume.</p>
 <hr class="docutils" />
 <p><em>Bonds</em> section:</p>
 <ul class="simple">
 <li>one line per bond</li>
 <li>line syntax: ID type atom1 atom2</li>
 <li>type = bond type (1-Nbondtype)</li>
 <li>atom1,atom2 = IDs of atoms in bond</li>
 </ul>
 <p>The IDs for the two atoms in each bond should be values
 from 1 to Natoms, where Natoms = # of atoms in the molecule.</p>
 <hr class="docutils" />
 <p><em>Angles</em> section:</p>
 <ul class="simple">
 <li>one line per angle</li>
 <li>line syntax: ID type atom1 atom2 atom3</li>
 <li>type = angle type (1-Nangletype)</li>
 <li>atom1,atom2,atom3 = IDs of atoms in angle</li>
 </ul>
 <p>The IDs for the three atoms in each angle should be values from 1 to
 Natoms, where Natoms = # of atoms in the molecule.  The 3 atoms are
 ordered linearly within the angle.  Thus the central atom (around
 which the angle is computed) is the atom2 in the list.</p>
 <hr class="docutils" />
 <p><em>Dihedrals</em> section:</p>
 <ul class="simple">
 <li>one line per dihedral</li>
 <li>line syntax: ID type atom1 atom2 atom3 atom4</li>
 <li>type = dihedral type (1-Ndihedraltype)</li>
 <li>atom1,atom2,atom3,atom4 = IDs of atoms in dihedral</li>
 </ul>
 <p>The IDs for the four atoms in each dihedral should be values from 1 to
 Natoms, where Natoms = # of atoms in the molecule.  The 4 atoms are
 ordered linearly within the dihedral.</p>
 <hr class="docutils" />
 <p><em>Impropers</em> section:</p>
 <ul class="simple">
 <li>one line per improper</li>
 <li>line syntax: ID type atom1 atom2 atom3 atom4</li>
 <li>type = improper type (1-Nimpropertype)</li>
 <li>atom1,atom2,atom3,atom4 = IDs of atoms in improper</li>
 </ul>
 <p>The IDs for the four atoms in each improper should be values from 1 to
 Natoms, where Natoms = # of atoms in the molecule.  The ordering of
 the 4 atoms determines the definition of the improper angle used in
 the formula for the defined <a class="reference internal" href="improper_style.html"><em>improper style</em></a>.  See
 the doc pages for individual styles for details.</p>
 <hr class="docutils" />
 <p><em>Special Bond Counts</em> section:</p>
 <ul class="simple">
 <li>one line per atom</li>
 <li>line syntax: ID N1 N2 N3</li>
 <li>N1 = # of 1-2 bonds</li>
 <li>N2 = # of 1-3 bonds</li>
 <li>N3 = # of 1-4 bonds</li>
 </ul>
 <p>N1, N2, N3 are the number of 1-2, 1-3, 1-4 neighbors respectively of
 this atom within the topology of the molecule.  See the
 <a class="reference internal" href="special_bonds.html"><em>special_bonds</em></a> doc page for more discussion of
 1-2, 1-3, 1-4 neighbors.  If this section appears, the Special Bonds
 section must also appear.  If this section is not specied, the
 atoms in the molecule will have no special bonds.</p>
 <hr class="docutils" />
 <p><em>Special Bonds</em> section:</p>
 <ul class="simple">
 <li>one line per atom</li>
 <li>line syntax: ID a b c d ...</li>
 <li>a,b,c,d,... = IDs of atoms in N1+N2+N3 special bonds</li>
 </ul>
 <p>A, b, c, d, etc are the IDs of the n1+n2+n3 atoms that are 1-2, 1-3,
 1-4 neighbors of this atom.  The IDs should be values from 1 to
 Natoms, where Natoms = # of atoms in the molecule.  The first N1
 values should be the 1-2 neighbors, the next N2 should be the 1-3
 neighbors, the last N3 should be the 1-4 neighbors.  No atom ID should
 appear more than once.  See the <a class="reference internal" href="special_bonds.html"><em>special_bonds</em></a> doc
 page for more discussion of 1-2, 1-3, 1-4 neighbors.  If this section
 appears, the Special Bond Counts section must also appear.  If this
 section is not specied, the atoms in the molecule will have no special
 bonds.</p>
 <hr class="docutils" />
 <p><em>Shake Flags</em> section:</p>
 <ul class="simple">
 <li>one line per atom</li>
 <li>line syntax: ID flag</li>
 <li>flag = 0,1,2,3,4</li>
 </ul>
 <p>This section is only needed when molecules created using the template
 will be constrained by SHAKE via the &#8220;fix shake&#8221; command.  The other
 two Shake sections must also appear in the file, following this one.</p>
 <p>The meaning of the flag for each atom is as follows.  See the <a class="reference internal" href="fix_shake.html"><em>fix shake</em></a> doc page for a further description of SHAKE
 clusters.</p>
 <ul class="simple">
 <li>0 = not part of a SHAKE cluster</li>
 <li>1 = part of a SHAKE angle cluster (two bonds and the angle they form)</li>
 <li>2 = part of a 2-atom SHAKE cluster with a single bond</li>
 <li>3 = part of a 3-atom SHAKE cluster with two bonds</li>
 <li>4 = part of a 4-atom SHAKE cluster with three bonds</li>
 </ul>
 <hr class="docutils" />
 <p><em>Shake Atoms</em> section:</p>
 <ul class="simple">
 <li>one line per atom</li>
 <li>line syntax: ID a b c d</li>
 <li>a,b,c,d = IDs of atoms in cluster</li>
 </ul>
 <p>This section is only needed when molecules created using the template
 will be constrained by SHAKE via the &#8220;fix shake&#8221; command.  The other
 two Shake sections must also appear in the file.</p>
 <p>The a,b,c,d values are atom IDs (from 1 to Natoms) for all the atoms
 in the SHAKE cluster that this atom belongs to.  The number of values
 that must appear is determined by the shake flag for the atom (see the
 Shake Flags section above).  All atoms in a particular cluster should
 list their a,b,c,d values identically.</p>
 <p>If flag = 0, no a,b,c,d values are listed on the line, just the
 (ignored) ID.</p>
 <p>If flag = 1, a,b,c are listed, where a = ID of central atom in the
 angle, and b,c the other two atoms in the angle.</p>
 <p>If flag = 2, a,b are listed, where a = ID of atom in bond with the the
 lowest ID, and b = ID of atom in bond with the highest ID.</p>
 <p>If flag = 3, a,b,c are listed, where a = ID of central atom,
 and b,c = IDs of other two atoms bonded to the central atom.</p>
 <p>If flag = 4, a,b,c,d are listed, where a = ID of central atom,
 and b,c,d = IDs of other three atoms bonded to the central atom.</p>
 <p>See the <a class="reference internal" href="fix_shake.html"><em>fix shake</em></a> doc page for a further description
 of SHAKE clusters.</p>
 <hr class="docutils" />
 <p><em>Shake Bond Types</em> section:</p>
 <ul class="simple">
 <li>one line per atom</li>
 <li>line syntax: ID a b c</li>
 <li>a,b,c = bond types (or angle type) of bonds (or angle) in cluster</li>
 </ul>
 <p>This section is only needed when molecules created using the template
 will be constrained by SHAKE via the &#8220;fix shake&#8221; command.  The other
 two Shake sections must also appear in the file.</p>
 <p>The a,b,c values are bond types (from 1 to Nbondtypes) for all bonds
 in the SHAKE cluster that this atom belongs to.  The number of values
 that must appear is determined by the shake flag for the atom (see the
 Shake Flags section above).  All atoms in a particular cluster should
 list their a,b,c values identically.</p>
 <p>If flag = 0, no a,b,c values are listed on the line, just the
 (ignored) ID.</p>
 <p>If flag = 1, a,b,c are listed, where a = bondtype of the bond between
 the central atom and the first non-central atom (value b in the Shake
 Atoms section), b = bondtype of the bond between the central atom and
 the 2nd non-central atom (value c in the Shake Atoms section), and c =
 the angle type (1 to Nangletypes) of the angle between the 3 atoms.</p>
 <p>If flag = 2, only a is listed, where a = bondtype of the bond between
 the 2 atoms in the cluster.</p>
 <p>If flag = 3, a,b are listed, where a = bondtype of the bond between
 the central atom and the first non-central atom (value b in the Shake
 Atoms section), and b = bondtype of the bond between the central atom
 and the 2nd non-central atom (value c in the Shake Atoms section).</p>
 <p>If flag = 4, a,b,c are listed, where a = bondtype of the bond between
 the central atom and the first non-central atom (value b in the Shake
 Atoms section), b = bondtype of the bond between the central atom and
 the 2nd non-central atom (value c in the Shake Atoms section), and c =
 bondtype of the bond between the central atom and the 3rd non-central
 atom (value d in the Shake Atoms section).</p>
 <p>See the <a class="reference internal" href="fix_shake.html"><em>fix shake</em></a> doc page for a further description
 of SHAKE clusters.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <blockquote>
 <div>none</div></blockquote>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="fix_deposit.html"><em>fix deposit</em></a>, <a class="reference internal" href="fix_pour.html"><em>fix pour</em></a>,
 <a class="reference internal" href="fix_gcmc.html"><em>fix_gcmc</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The default keyword value is offset 0 0 0 0 0.</p>
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   <div class="section" id="neb-command">
 <span id="index-0"></span><h1>neb command<a class="headerlink" href="#neb-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>neb etol ftol N1 N2 Nevery file-style arg
 </pre></div>
 </div>
 <ul class="simple">
 <li>etol = stopping tolerance for energy (energy units)</li>
 <li>ftol = stopping tolerance for force (force units)</li>
 <li>N1 = max # of iterations (timesteps) to run initial NEB</li>
 <li>N2 = max # of iterations (timesteps) to run barrier-climbing NEB</li>
 <li>Nevery = print replica energies and reaction coordinates every this many timesteps</li>
 <li>file-style= <em>final</em> or <em>each</em> or <em>none</em></li>
 </ul>
 <pre class="literal-block">
 <em>final</em> arg = filename
-    filename = file with initial coords for final replica
-      coords for intermediate replicas are linearly interpolated between first and last replica
-  <em>each</em> arg = filename
-    filename = unique filename for each replica (except first) with its initial coords
-  <em>none</em> arg = no argument
-    all replicas assumed to already have their initial coords
+  filename = file with initial coords for final replica
+    coords for intermediate replicas are linearly interpolated between first and last replica
+<em>each</em> arg = filename
+  filename = unique filename for each replica (except first) with its initial coords
+<em>none</em> arg = no argument
+  all replicas assumed to already have their initial coords
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>neb 0.1 0.0 1000 500 50 final coords.final
 neb 0.0 0.001 1000 500 50 each coords.initial.$i
 neb 0.0 0.001 1000 500 50 none
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Perform a nudged elastic band (NEB) calculation using multiple
 replicas of a system.  Two or more replicas must be used; the first
 and last are the end points of the transition path.</p>
 <p>NEB is a method for finding both the atomic configurations and height
 of the energy barrier associated with a transition state, e.g. for an
 atom to perform a diffusive hop from one energy basin to another in a
 coordinated fashion with its neighbors.  The implementation in LAMMPS
 follows the discussion in these 3 papers: <a class="reference internal" href="#henkelman1"><span>(Henkelman1)</span></a>,
 <a class="reference internal" href="#henkelman2"><span>(Henkelman2)</span></a>, and <a class="reference internal" href="#nakano"><span>(Nakano)</span></a>.</p>
 <p>Each replica runs on a partition of one or more processors.  Processor
 partitions are defined at run-time using the -partition command-line
 switch; see <a class="reference internal" href="Section_start.html#start-7"><span>Section_start 7</span></a> of the
 manual.  Note that if you have MPI installed, you can run a
 multi-replica simulation with more replicas (partitions) than you have
 physical processors, e.g you can run a 10-replica simulation on just
 one or two processors.  You will simply not get the performance
 speed-up you would see with one or more physical processors per
 replica.  See <a class="reference internal" href="Section_howto.html#howto-5"><span>this section</span></a> of the manual
 for further discussion.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">The current NEB implementation in LAMMPS only allows
 there to be one processor per replica.</p>
 </div>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">As explained below, a NEB calculation perfoms a damped
 dynamics minimization across all the replicas.  The mimimizer uses
 whatever timestep you have defined in your input script, via the
 <a class="reference internal" href="timestep.html"><em>timestep</em></a> command.  Often NEB will converge more
 quickly if you use a timestep about 10x larger than you would normally
 use for dynamics simulations.</p>
 </div>
 <p>When a NEB calculation is performed, it is assumed that each replica
 is running the same system, though LAMMPS does not check for this.
 I.e. the simulation domain, the number of atoms, the interaction
 potentials, and the starting configuration when the neb command is
 issued should be the same for every replica.</p>
 <p>In a NEB calculation each atom in a replica is connected to the same
 atom in adjacent replicas by springs, which induce inter-replica
 forces.  These forces are imposed by the <a class="reference internal" href="fix_neb.html"><em>fix neb</em></a>
 command, which must be used in conjunction with the neb command.  The
 group used to define the fix neb command defines the NEB atoms which
 are the only ones that inter-replica springs are applied to.  If the
 group does not include all atoms, then non-NEB atoms have no
 inter-replica springs and the forces they feel and their motion is
 computed in the usual way due only to other atoms within their
 replica.  Conceptually, the non-NEB atoms provide a background force
 field for the NEB atoms.  They can be allowed to move during the NEB
 minimiation procedure (which will typically induce different
 coordinates for non-NEB atoms in different replicas), or held fixed
 using other LAMMPS commands such as <a class="reference external" href="fix_setforce">fix setforce</a>.  Note
 that the <a class="reference internal" href="partition.html"><em>partition</em></a> command can be used to invoke a
 command on a subset of the replicas, e.g. if you wish to hold NEB or
 non-NEB atoms fixed in only the end-point replicas.</p>
 <p>The initial atomic configuration for each of the replicas can be
 specified in different manners via the <em>file-style</em> setting, as
 discussed below.  Only atoms whose initial coordinates should differ
 from the current configuration need be specified.</p>
 <p>Conceptually, the initial configuration for the first replica should
 be a state with all the atoms (NEB and non-NEB) having coordinates on
 one side of the energy barrier.  A perfect energy minimum is not
 required, since atoms in the first replica experience no spring forces
 from the 2nd replica.  Thus the damped dynamics minimizaiton will
 drive the first replica to an energy minimum if it is not already
 there.  However, you will typically get better convergence if the
 initial state is already at a minimum.  For example, for a system with
 a free surface, the surface should be fully relaxed before attempting
 a NEB calculation.</p>
 <p>Likewise, the initial configuration of the final replica should be a
 state with all the atoms (NEB and non-NEB) on the other side of the
 energy barrier.  Again, a perfect energy minimum is not required,
 since the atoms in the last replica also experience no spring forces
 from the next-to-last replica, and thus the damped dynamics
 minimization will drive it to an energy minimum.</p>
 <p>As explained below, the initial configurations of intermediate
 replicas can be atomic coordinates interpolated in a linear fashion
 between the first and last replicas.  This is often adequate state for
 simple transitions.  For more complex transitions, it may lead to slow
 convergence or even bad results if the minimum energy path (MEP, see
 below) of states over the barrier cannot be correctly converged to
 from such an initial configuration.  In this case, you will want to
 generate initial states for the intermediate replicas that are
 geometrically closer to the MEP and read them in.</p>
 <hr class="docutils" />
 <p>For a <em>file-style</em> setting of <em>final</em>, a filename is specified which
 contains atomic coordinates for zero or more atoms, in the format
 described below.  For each atom that appears in the file, the new
 coordinates are assigned to that atom in the final replica.  Each
 intermediate replica also assigns a new position to that atom in an
 interpolated manner.  This is done by using the current position of
 the atom as the starting point and the read-in position as the final
 point.  The distance between them is calculated, and the new position
 is assigned to be a fraction of the distance.  E.g. if there are 10
 replicas, the 2nd replica will assign a position that is 10% of the
 distance along a line between the starting and final point, and the
 9th replica will assign a position that is 90% of the distance along
 the line.  Note that this procedure to produce consistent coordinates
 across all the replicas, the current coordinates need to be the same
 in all replicas.  LAMMPS does not check for this, but invalid initial
 configurations will likely result if it is not the case.</p>
 <div class="admonition note">
 <p class="first admonition-title">Note</p>
 <p class="last">The &#8220;distance&#8221; between the starting and final point is
 calculated in a minimum-image sense for a periodic simulation box.
 This means that if the two positions are on opposite sides of a box
 (periodic in that dimension), the distance between them will be small,
 because the periodic image of one of the atoms is close to the other.
 Similarly, even if the assigned position resulting from the
 interpolation is outside the periodic box, the atom will be wrapped
 back into the box when the NEB calculation begins.</p>
 </div>
 <p>For a <em>file-style</em> setting of <em>each</em>, a filename is specified which is
 assumed to be unique to each replica.  This can be done by
 using a variable in the filename, e.g.</p>
 <div class="highlight-python"><div class="highlight"><pre>variable i equal part
 neb 0.0 0.001 1000 500 50 each coords.initial.$i
 </pre></div>
 </div>
 <p>which in this case will substitute the partition ID (0 to N-1) for the
 variable I, which is also effectively the replica ID.  See the
 <a class="reference internal" href="variable.html"><em>variable</em></a> command for other options, such as using
 world-, universe-, or uloop-style variables.</p>
 <p>Each replica (except the first replica) will read its file, formatted
 as described below, and for any atom that appears in the file, assign
 the specified coordinates to its atom.  The various files do not need
 to contain the same set of atoms.</p>
 <p>For a <em>file-style</em> setting of <em>none</em>, no filename is specified.  Each
 replica is assumed to already be in its initial configuration at the
 time the neb command is issued.  This allows each replica to define
 its own configuration by reading a replica-specific data or restart or
 dump file, via the <a class="reference internal" href="read_data.html"><em>read_data</em></a>,
 <a class="reference internal" href="read_restart.html"><em>read_restart</em></a>, or <a class="reference internal" href="read_dump.html"><em>read_dump</em></a>
 commands.  The replica-specific names of these files can be specified
 as in the discussion above for the <em>each</em> file-style.  Also see the
 section below for how a NEB calculation can produce restart files, so
 that a long calculation can be restarted if needed.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">None of the <em>file-style</em> settings change the initial
 configuration of any atom in the first replica.  The first replica
 must thus be in the correct initial configuration at the time the neb
 command is issued.</p>
 </div>
 <hr class="docutils" />
 <p>A NEB calculation proceeds in two stages, each of which is a
 minimization procedure, performed via damped dynamics.  To enable
 this, you must first define a damped dynamics
 <a class="reference internal" href="min_style.html"><em>min_style</em></a>, such as <em>quickmin</em> or <em>fire</em>.  The <em>cg</em>,
 <em>sd</em>, and <em>hftn</em> styles cannot be used, since they perform iterative
 line searches in their inner loop, which cannot be easily synchronized
 across multiple replicas.</p>
 <p>The minimizer tolerances for energy and force are set by <em>etol</em> and
 <em>ftol</em>, the same as for the <a class="reference internal" href="minimize.html"><em>minimize</em></a> command.</p>
 <p>A non-zero <em>etol</em> means that the NEB calculation will terminate if the
 energy criterion is met by every replica.  The energies being compared
 to <em>etol</em> do not include any contribution from the inter-replica
 forces, since these are non-conservative.  A non-zero <em>ftol</em> means
 that the NEB calculation will terminate if the force criterion is met
 by every replica.  The forces being compared to <em>ftol</em> include the
 inter-replica forces between an atom and its images in adjacent
 replicas.</p>
 <p>The maximum number of iterations in each stage is set by <em>N1</em> and
 <em>N2</em>.  These are effectively timestep counts since each iteration of
 damped dynamics is like a single timestep in a dynamics
 <a class="reference internal" href="run.html"><em>run</em></a>.  During both stages, the potential energy of each
 replica and its normalized distance along the reaction path (reaction
 coordinate RD) will be printed to the screen and log file every
 <em>Nevery</em> timesteps.  The RD is 0 and 1 for the first and last replica.
 For intermediate replicas, it is the cumulative distance (normalized
 by the total cumulative distance) between adjacent replicas, where
 &#8220;distance&#8221; is defined as the length of the 3N-vector of differences in
 atomic coordinates, where N is the number of NEB atoms involved in the
 transition.  These outputs allow you to monitor NEB&#8217;s progress in
 finding a good energy barrier.  <em>N1</em> and <em>N2</em> must both be multiples
 of <em>Nevery</em>.</p>
 <p>In the first stage of NEB, the set of replicas should converge toward
 the minimum energy path (MEP) of conformational states that transition
 over the barrier.  The MEP for a barrier is defined as a sequence of
 3N-dimensional states that cross the barrier at its saddle point, each
 of which has a potential energy gradient parallel to the MEP itself.
 The replica states will also be roughly equally spaced along the MEP
 due to the inter-replica spring force added by the <a class="reference internal" href="fix_neb.html"><em>fix neb</em></a> command.</p>
 <p>In the second stage of NEB, the replica with the highest energy
 is selected and the inter-replica forces on it are converted to a
 force that drives its atom coordinates to the top or saddle point of
 the barrier, via the barrier-climbing calculation described in
 <span class="xref std std-ref">(Henkelman2)</span>.  As before, the other replicas rearrange
 themselves along the MEP so as to be roughly equally spaced.</p>
 <p>When both stages are complete, if the NEB calculation was successful,
 one of the replicas should be an atomic configuration at the top or
 saddle point of the barrier, the potential energies for the set of
 replicas should represent the energy profile of the barrier along the
 MEP, and the configurations of the replicas should be a sequence of
 configurations along the MEP.</p>
 <hr class="docutils" />
 <p>A few other settings in your input script are required or advised to
 perform a NEB calculation.  See the IMPORTANT NOTE about the choice of
 timestep at the beginning of this doc page.</p>
 <p>An atom map must be defined which it is not by default for <a class="reference internal" href="atom_style.html"><em>atom_style atomic</em></a> problems.  The <a class="reference internal" href="atom_modify.html"><em>atom_modify map</em></a> command can be used to do this.</p>
 <p>The &#8220;atom_modify sort 0 0.0&#8221; command should be used to turn off atom
 sorting.</p>
 <div class="admonition note">
 <p class="first admonition-title">Note</p>
 <p class="last">This sorting restriction will be removed in a future version of
 NEB in LAMMPS.</p>
 </div>
 <p>The minimizers in LAMMPS operate on all atoms in your system, even
 non-NEB atoms, as defined above.  To prevent non-NEB atoms from moving
 during the minimization, you should use the <a class="reference internal" href="fix_setforce.html"><em>fix setforce</em></a> command to set the force on each of those
 atoms to 0.0.  This is not required, and may not even be desired in
 some cases, but if those atoms move too far (e.g. because the initial
 state of your system was not well-minimized), it can cause problems
 for the NEB procedure.</p>
 <p>The damped dynamics <a class="reference internal" href="min_style.html"><em>minimizers</em></a>, such as <em>quickmin</em>
 and <em>fire</em>), adjust the position and velocity of the atoms via an
 Euler integration step.  Thus you must define an appropriate
 <a class="reference internal" href="timestep.html"><em>timestep</em></a> to use with NEB.  As mentioned above, NEB
 will often converge more quickly if you use a timestep about 10x
 larger than you would normally use for dynamics simulations.</p>
 <hr class="docutils" />
 <p>Each file read by the neb command containing atomic coordinates used
 to initialize one or more replicas must be formatted as follows.</p>
 <p>The file can be ASCII text or a gzipped text file (detected by a .gz
 suffix).  The file can contain initial blank lines or comment lines
 starting with &#8220;#&#8221; which are ignored.  The first non-blank, non-comment
 line should list N = the number of lines to follow.  The N successive
 lines contain the following information:</p>
 <div class="highlight-python"><div class="highlight"><pre>ID1 x1 y1 z1
 ID2 x2 y2 z2
 ...
 IDN xN yN zN
 </pre></div>
 </div>
 <p>The fields are the the atom ID, followed by the x,y,z coordinates.
 The lines can be listed in any order.  Additional trailing information
 on the line is OK, such as a comment.</p>
 <p>Note that for a typical NEB calculation you do not need to specify
 initial coordinates for very many atoms to produce differing starting
 and final replicas whose intermediate replicas will converge to the
 energy barrier.  Typically only new coordinates for atoms
 geometrically near the barrier need be specified.</p>
 <p>Also note there is no requirement that the atoms in the file
 correspond to the NEB atoms in the group defined by the <a class="reference internal" href="fix_neb.html"><em>fix neb</em></a> command.  Not every NEB atom need be in the file,
 and non-NEB atoms can be listed in the file.</p>
 <hr class="docutils" />
 <p>Four kinds of output can be generated during a NEB calculation: energy
 barrier statistics, thermodynamic output by each replica, dump files,
 and restart files.</p>
 <p>When running with multiple partitions (each of which is a replica in
 this case), the print-out to the screen and master log.lammps file
 contains a line of output, printed once every <em>Nevery</em> timesteps.  It
 contains the timestep, the maximum force per replica, the maximum
 force per atom (in any replica), potential gradients in the initial,</p>
 <blockquote>
 <div>final, and climbing replicas,</div></blockquote>
 <p>the forward and backward energy barriers,
 the total reaction coordinate (RDT), and
 the normalized reaction coordinate and potential energy of each replica.</p>
 <p>The &#8220;maximum force per replica&#8221; is
 the two-norm of the 3N-length force vector for the atoms in each
 replica, maximized across replicas, which is what the <em>ftol</em> setting
 is checking against.  In this case, N is all the atoms in each
 replica.  The &#8220;maximum force per atom&#8221; is the maximum force component
 of any atom in any replica.  The potential gradients are the two-norm
 of the 3N-length force vector solely due to the interaction potential i.e.
 without adding in inter-replica forces. Note that inter-replica forces
 are zero in the initial and final replicas, and only affect
 the direction in the climbing replica. For this reason, the &#8220;maximum
 force per replica&#8221; is often equal to the potential gradient in the
 climbing replica. In the first stage of NEB, there is no climbing
 replica, and so the potential gradient in the highest energy replica
 is reported, since this replica will become the climbing replica
 in the second stage of NEB.</p>
 <p>The &#8220;reaction coordinate&#8221; (RD) for each
 replica is the two-norm of the 3N-length vector of distances between
 its atoms and the preceding replica&#8217;s atoms, added to the RD of the
 preceding replica. The RD of the first replica RD1 = 0.0;
 the RD of the final replica RDN = RDT, the total reaction coordinate.
 The normalized RDs are divided by RDT,
 so that they form a monotonically increasing sequence
 from zero to one. When computing RD, N only includes the atoms
 being operated on by the fix neb command.</p>
 <p>The forward (reverse) energy barrier is the potential energy of the highest
 replica minus the energy of the first (last) replica.</p>
 <p>When running on multiple partitions, LAMMPS produces additional log
 files for each partition, e.g. log.lammps.0, log.lammps.1, etc.  For a
 NEB calculation, these contain the thermodynamic output for each
 replica.</p>
 <p>If <a class="reference internal" href="dump.html"><em>dump</em></a> commands in the input script define a filename
 that includes a <em>universe</em> or <em>uloop</em> style <a class="reference internal" href="variable.html"><em>variable</em></a>,
 then one dump file (per dump command) will be created for each
 replica.  At the end of the NEB calculation, the final snapshot in
 each file will contain the sequence of snapshots that transition the
 system over the energy barrier.  Earlier snapshots will show the
 convergence of the replicas to the MEP.</p>
 <p>Likewise, <a class="reference internal" href="restart.html"><em>restart</em></a> filenames can be specified with a
 <em>universe</em> or <em>uloop</em> style <a class="reference internal" href="variable.html"><em>variable</em></a>, to generate
 restart files for each replica.  These may be useful if the NEB
 calculation fails to converge properly to the MEP, and you wish to
 restart the calculation from an intermediate point with altered
 parameters.</p>
 <p>There are 2 Python scripts provided in the tools/python directory,
 neb_combine.py and neb_final.py, which are useful in analyzing output
 from a NEB calculation.  Assume a NEB simulation with M replicas, and
 the NEB atoms labelled with a specific atom type.</p>
 <p>The neb_combine.py script extracts atom coords for the NEB atoms from
 all M dump files and creates a single dump file where each snapshot
 contains the NEB atoms from all the replicas and one copy of non-NEB
 atoms from the first replica (presumed to be identical in other
 replicas).  This can be visualized/animated to see how the NEB atoms
 relax as the NEB calculation proceeds.</p>
 <p>The neb_final.py script extracts the final snapshot from each of the M
 dump files to create a single dump file with M snapshots.  This can be
 visualized to watch the system make its transition over the energy
 barrier.</p>
 <p>To illustrate, here are images from the final snapshot produced by the
 neb_combine.py script run on the dump files produced by the two
 example input scripts in examples/neb.  Click on them to see a larger
 image.</p>
 <a data-lightbox="group-default"
                    href="_images/hop1.jpg"
                    class=""
                    title=""
                    data-title=""
                    ><img src="_images/hop1.jpg"
                     class=""
                     width="25%"
                     height="auto"
                     alt=""/>
                     </a><a data-lightbox="group-default"
                    href="_images/hop2.jpg"
                    class=""
                    title=""
                    data-title=""
                    ><img src="_images/hop2.jpg"
                     class=""
                     width="25%"
                     height="auto"
                     alt=""/>
                     </a></div>
 <hr class="docutils" />
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>This command can only be used if LAMMPS was built with the REPLICA
 package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section
 for more info on packages.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="prd.html"><em>prd</em></a>, <a class="reference internal" href="temper.html"><em>temper</em></a>, <a class="reference internal" href="fix_langevin.html"><em>fix langevin</em></a>, <a class="reference internal" href="fix_viscous.html"><em>fix viscous</em></a></p>
 <p><strong>Default:</strong> none</p>
 <hr class="docutils" />
 <p id="henkelman1"><strong>(Henkelman1)</strong> Henkelman and Jonsson, J Chem Phys, 113, 9978-9985 (2000).</p>
 <p id="henkelman2"><strong>(Henkelman2)</strong> Henkelman, Uberuaga, Jonsson, J Chem Phys, 113,
 9901-9904 (2000).</p>
 <p id="nakano"><strong>(Nakano)</strong> Nakano, Comp Phys Comm, 178, 280-289 (2008).</p>
 </div>
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   <div class="section" id="package-command">
 <span id="index-0"></span><h1>package command<a class="headerlink" href="#package-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>package style args
 </pre></div>
 </div>
 <ul class="simple">
 <li>style = <em>cuda</em> or <em>gpu</em> or <em>intel</em> or <em>kokkos</em> or <em>omp</em></li>
 <li>args = arguments specific to the style</li>
 </ul>
 <pre class="literal-block">
 <em>cuda</em> args = Ngpu keyword value ...
-    Ngpu = # of GPUs per node
-    zero or more keyword/value pairs may be appended
-    keywords = <em>newton</em> or <em>gpuID</em> or <em>timing</em> or <em>test</em> or <em>thread</em>
-      <em>newton</em> = <em>off</em> or <em>on</em>
-        off = set Newton pairwise and bonded flags off (default)
-        on = set Newton pairwise and bonded flags on
-      <em>gpuID</em> values = gpu1 .. gpuN
-        gpu1 .. gpuN = IDs of the Ngpu GPUs to use
-      <em>timing</em> values = none
-      <em>test</em> values = id
-        id = atom-ID of a test particle
-      <em>thread</em> = auto or tpa or bpa
-        auto = test whether tpa or bpa is faster
-        tpa = one thread per atom
-        bpa = one block per atom
-  <em>gpu</em> args = Ngpu keyword value ...
-    Ngpu = # of GPUs per node
-    zero or more keyword/value pairs may be appended
-    keywords = <em>neigh</em> or <em>newton</em> or <em>binsize</em> or <em>split</em> or <em>gpuID</em> or <em>tpa</em> or <em>device</em>
-      <em>neigh</em> value = <em>yes</em> or <em>no</em>
-        yes = neighbor list build on GPU (default)
-        no = neighbor list build on CPU
-      <em>newton</em> = <em>off</em> or <em>on</em>
-        off = set Newton pairwise flag off (default and required)
-        on = set Newton pairwise flag on (currently not allowed)
-      <em>binsize</em> value = size
-        size = bin size for neighbor list construction (distance units)
-      <em>split</em> = fraction
-        fraction = fraction of atoms assigned to GPU (default = 1.0)
-      <em>gpuID</em> values = first last
-        first = ID of first GPU to be used on each node
-        last = ID of last GPU to be used on each node
-      <em>tpa</em> value = Nthreads
-        Nthreads = # of GPU threads used per atom
-      <em>device</em> value = device_type
-        device_type = <em>kepler</em> or <em>fermi</em> or <em>cypress</em> or <em>generic</em>
-  <em>intel</em> args = NPhi keyword value ...
-    Nphi = # of coprocessors per node
-    zero or more keyword/value pairs may be appended
-    keywords = <em>omp</em> or <em>mode</em> or <em>balance</em> or <em>ghost</em> or <em>tpc</em> or <em>tptask</em> or <em>no_affinity</em>
-      <em>omp</em> value = Nthreads
-        Nthreads = number of OpenMP threads to use on CPU (default = 0)
-      <em>mode</em> value = <em>single</em> or <em>mixed</em> or <em>double</em>
-        single = perform force calculations in single precision
-        mixed = perform force calculations in mixed precision
-        double = perform force calculations in double precision
-      <em>balance</em> value = split
-        split = fraction of work to offload to coprocessor, -1 for dynamic
-      <em>ghost</em> value = <em>yes</em> or <em>no</em>
-        yes = include ghost atoms for offload
-        no = do not include ghost atoms for offload
-      <em>tpc</em> value = Ntpc
-        Ntpc = max number of coprocessor threads per coprocessor core (default = 4)
-      <em>tptask</em> value = Ntptask
-        Ntptask = max number of coprocessor threads per MPI task (default = 240)
-      <em>no_affinity</em> values = none
-  <em>kokkos</em> args = keyword value ...
-    zero or more keyword/value pairs may be appended
-    keywords = <em>neigh</em> or <em>newton</em> or <em>binsize</em> or <em>comm</em> or <em>comm/exchange</em> or <em>comm/forward</em>
-      <em>neigh</em> value = <em>full</em> or <em>half/thread</em> or <em>half</em> or <em>n2</em> or <em>full/cluster</em>
-        full = full neighbor list
-        half/thread = half neighbor list built in thread-safe manner
-        half = half neighbor list, not thread-safe, only use when 1 thread/MPI task
-        n2 = non-binning neighbor list build, O(N^2) algorithm
-        full/cluster = full neighbor list with clustered groups of atoms
-      <em>newton</em> = <em>off</em> or <em>on</em>
-        off = set Newton pairwise and bonded flags off (default)
-        on = set Newton pairwise and bonded flags on
-      <em>binsize</em> value = size
-        size = bin size for neighbor list construction (distance units)
-      <em>comm</em> value = <em>no</em> or <em>host</em> or <em>device</em>
-        use value for both comm/exchange and comm/forward
-      <em>comm/exchange</em> value = <em>no</em> or <em>host</em> or <em>device</em>
-      <em>comm/forward</em> value = <em>no</em> or <em>host</em> or <em>device</em>
-        no = perform communication pack/unpack in non-KOKKOS mode
-        host = perform pack/unpack on host (e.g. with OpenMP threading)
-        device = perform pack/unpack on device (e.g. on GPU)
-  <em>omp</em> args = Nthreads keyword value ...
-    Nthread = # of OpenMP threads to associate with each MPI process
-    zero or more keyword/value pairs may be appended
-    keywords = <em>neigh</em>
-      <em>neigh</em> value = <em>yes</em> or <em>no</em>
-        yes = threaded neighbor list build (default)
-        no = non-threaded neighbor list build
+  Ngpu = # of GPUs per node
+  zero or more keyword/value pairs may be appended
+  keywords = <em>newton</em> or <em>gpuID</em> or <em>timing</em> or <em>test</em> or <em>thread</em>
+    <em>newton</em> = <em>off</em> or <em>on</em>
+      off = set Newton pairwise and bonded flags off (default)
+      on = set Newton pairwise and bonded flags on
+    <em>gpuID</em> values = gpu1 .. gpuN
+      gpu1 .. gpuN = IDs of the Ngpu GPUs to use
+    <em>timing</em> values = none
+    <em>test</em> values = id
+      id = atom-ID of a test particle
+    <em>thread</em> = auto or tpa or bpa
+      auto = test whether tpa or bpa is faster
+      tpa = one thread per atom
+      bpa = one block per atom
+<em>gpu</em> args = Ngpu keyword value ...
+  Ngpu = # of GPUs per node
+  zero or more keyword/value pairs may be appended
+  keywords = <em>neigh</em> or <em>newton</em> or <em>binsize</em> or <em>split</em> or <em>gpuID</em> or <em>tpa</em> or <em>device</em>
+    <em>neigh</em> value = <em>yes</em> or <em>no</em>
+      yes = neighbor list build on GPU (default)
+      no = neighbor list build on CPU
+    <em>newton</em> = <em>off</em> or <em>on</em>
+      off = set Newton pairwise flag off (default and required)
+      on = set Newton pairwise flag on (currently not allowed)
+    <em>binsize</em> value = size
+      size = bin size for neighbor list construction (distance units)
+    <em>split</em> = fraction
+      fraction = fraction of atoms assigned to GPU (default = 1.0)
+    <em>gpuID</em> values = first last
+      first = ID of first GPU to be used on each node
+      last = ID of last GPU to be used on each node
+    <em>tpa</em> value = Nthreads
+      Nthreads = # of GPU threads used per atom
+    <em>device</em> value = device_type
+      device_type = <em>kepler</em> or <em>fermi</em> or <em>cypress</em> or <em>generic</em>
+<em>intel</em> args = NPhi keyword value ...
+  Nphi = # of coprocessors per node
+  zero or more keyword/value pairs may be appended
+  keywords = <em>omp</em> or <em>mode</em> or <em>balance</em> or <em>ghost</em> or <em>tpc</em> or <em>tptask</em> or <em>no_affinity</em>
+    <em>omp</em> value = Nthreads
+      Nthreads = number of OpenMP threads to use on CPU (default = 0)
+    <em>mode</em> value = <em>single</em> or <em>mixed</em> or <em>double</em>
+      single = perform force calculations in single precision
+      mixed = perform force calculations in mixed precision
+      double = perform force calculations in double precision
+    <em>balance</em> value = split
+      split = fraction of work to offload to coprocessor, -1 for dynamic
+    <em>ghost</em> value = <em>yes</em> or <em>no</em>
+      yes = include ghost atoms for offload
+      no = do not include ghost atoms for offload
+    <em>tpc</em> value = Ntpc
+      Ntpc = max number of coprocessor threads per coprocessor core (default = 4)
+    <em>tptask</em> value = Ntptask
+      Ntptask = max number of coprocessor threads per MPI task (default = 240)
+    <em>no_affinity</em> values = none
+<em>kokkos</em> args = keyword value ...
+  zero or more keyword/value pairs may be appended
+  keywords = <em>neigh</em> or <em>newton</em> or <em>binsize</em> or <em>comm</em> or <em>comm/exchange</em> or <em>comm/forward</em>
+    <em>neigh</em> value = <em>full</em> or <em>half/thread</em> or <em>half</em> or <em>n2</em> or <em>full/cluster</em>
+      full = full neighbor list
+      half/thread = half neighbor list built in thread-safe manner
+      half = half neighbor list, not thread-safe, only use when 1 thread/MPI task
+      n2 = non-binning neighbor list build, O(N^2) algorithm
+      full/cluster = full neighbor list with clustered groups of atoms
+    <em>newton</em> = <em>off</em> or <em>on</em>
+      off = set Newton pairwise and bonded flags off (default)
+      on = set Newton pairwise and bonded flags on
+    <em>binsize</em> value = size
+      size = bin size for neighbor list construction (distance units)
+    <em>comm</em> value = <em>no</em> or <em>host</em> or <em>device</em>
+      use value for both comm/exchange and comm/forward
+    <em>comm/exchange</em> value = <em>no</em> or <em>host</em> or <em>device</em>
+    <em>comm/forward</em> value = <em>no</em> or <em>host</em> or <em>device</em>
+      no = perform communication pack/unpack in non-KOKKOS mode
+      host = perform pack/unpack on host (e.g. with OpenMP threading)
+      device = perform pack/unpack on device (e.g. on GPU)
+<em>omp</em> args = Nthreads keyword value ...
+  Nthread = # of OpenMP threads to associate with each MPI process
+  zero or more keyword/value pairs may be appended
+  keywords = <em>neigh</em>
+    <em>neigh</em> value = <em>yes</em> or <em>no</em>
+      yes = threaded neighbor list build (default)
+      no = non-threaded neighbor list build
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>package gpu 1
 package gpu 1 split 0.75
 package gpu 2 split -1.0
 package cuda 2 gpuID 0 2
 package cuda 1 test 3948
 package kokkos neigh half/thread comm device
 package omp 0 neigh no
 package omp 4
 package intel 1
 package intel 2 omp 4 mode mixed balance 0.5
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>This command invokes package-specific settings for the various
 accelerator packages available in LAMMPS.  Currently the following
 packages use settings from this command: USER-CUDA, GPU, USER-INTEL,
 KOKKOS, and USER-OMP.</p>
 <p>If this command is specified in an input script, it must be near the
 top of the script, before the simulation box has been defined.  This
 is because it specifies settings that the accelerator packages use in
 their intialization, before a simultion is defined.</p>
 <p>This command can also be specified from the command-line when
 launching LAMMPS, using the &#8220;-pk&#8221; <a class="reference internal" href="Section_start.html#start-7"><span>command-line switch</span></a>.  The syntax is exactly the same as
 when used in an input script.</p>
 <p>Note that all of the accelerator packages require the package command
 to be specified (except the OPT package), if the package is to be used
 in a simulation (LAMMPS can be built with an accelerator package
 without using it in a particular simulation).  However, in all cases,
 a default version of the command is typically invoked by other
 accelerator settings.</p>
 <p>The USER-CUDA and KOKKOS packages require a &#8220;-c on&#8221; or &#8220;-k on&#8221;
 <a class="reference internal" href="Section_start.html#start-7"><span>command-line switch</span></a> respectively, which
 invokes a &#8220;package cuda&#8221; or &#8220;package kokkos&#8221; command with default
 settings.</p>
 <p>For the GPU, USER-INTEL, and USER-OMP packages, if a &#8220;-sf gpu&#8221; or &#8220;-sf
 intel&#8221; or &#8220;-sf omp&#8221; <a class="reference internal" href="Section_start.html#start-7"><span>command-line switch</span></a>
 is used to auto-append accelerator suffixes to various styles in the
 input script, then those switches also invoke a &#8220;package gpu&#8221;,
 &#8220;package intel&#8221;, or &#8220;package omp&#8221; command with default settings.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">A package command for a particular style can be
 invoked multiple times when a simulation is setup, e.g. by the &#8220;-c
 on&#8221;, &#8220;-k on&#8221;, &#8220;-sf&#8221;, and &#8220;-pk&#8221; <a class="reference internal" href="Section_start.html#start-7"><span>command-line switches</span></a>, and by using this command in an
 input script.  Each time it is used all of the style options are set,
 either to default values or to specified settings.  I.e. settings from
 previous invocations do not persist across multiple invocations.</p>
 </div>
 <p>See the <a class="reference internal" href="Section_accelerate.html"><em>Section Accelerate</em></a> section of the
 manual for more details about using the various accelerator packages
 for speeding up LAMMPS simulations.</p>
 <hr class="docutils" />
 <p>The <em>cuda</em> style invokes settings associated with the use of the
 USER-CUDA package.</p>
 <p>The <em>Ngpus</em> argument sets the number of GPUs per node.  There must be
 exactly one MPI task per GPU, as set by the mpirun or mpiexec command.</p>
 <p>Optional keyword/value pairs can also be specified.  Each has a
 default value as listed below.</p>
 <p>The <em>newton</em> keyword sets the Newton flags for pairwise and bonded
 interactions to <em>off</em> or <em>on</em>, the same as the <a class="reference internal" href="newton.html"><em>newton</em></a>
 command allows.  The default is <em>off</em> because this will almost always
 give better performance for the USER-CUDA package.  This means
 more computation is done, but less communication.</p>
 <p>The <em>gpuID</em> keyword allows selection of which GPUs on each node will
 be used for a simulation.  GPU IDs range from 0 to N-1 where N is the
 physical number of GPUs/node.  An ID is specified for each of the
 Ngpus being used.  For example if you have three GPUs on a machine,
 one of which is used for the X-Server (the GPU with the ID 1) while
 the others (with IDs 0 and 2) are used for computations you would
 specify:</p>
 <div class="highlight-python"><div class="highlight"><pre>package cuda 2 gpuID 0 2
 </pre></div>
 </div>
 <p>The purpose of the <em>gpuID</em> keyword is to allow two (or more)
 simulations to be run on one workstation.  In that case one could set
 the first simulation to use GPU 0 and the second to use GPU 1. This is
 not necessary however, if the GPUs are in what is called <em>compute
 exclusive</em> mode.  Using that setting, every process will get its own
 GPU automatically.  This <em>compute exclusive</em> mode can be set as root
 using the <em>nvidia-smi</em> tool which is part of the CUDA installation.</p>
 <p>Also note that if the <em>gpuID</em> keyword is not used, the USER-CUDA
 package sorts existing GPUs on each node according to their number of
 multiprocessors.  This way, compute GPUs will be priorized over
 X-Server GPUs.</p>
 <p>If the <em>timing</em> keyword is specified, detailed timing information for
 various subroutines will be output.</p>
 <p>If the <em>test</em> keyword is specified, information for the specified atom
 with atom-ID will be output at several points during each timestep.
 This is mainly usefull for debugging purposes.  Note that the
 simulation slow down dramatically if this option is used.</p>
 <p>The <em>thread</em> keyword can be used to specify how GPU threads are
 assigned work during pair style force evaluation.  If the value =
 <em>tpa</em>, one thread per atom is used.  If the value = <em>bpa</em>, one block
 per atom is used.  If the value = <em>auto</em>, a short test is performed at
 the beginning of each run to determing where <em>tpa</em> or <em>bpa</em> mode is
 faster.  The result of this test is output.  Since <em>auto</em> is the
 default value, it is usually not necessary to use this keyword.</p>
 <hr class="docutils" />
 <p>The <em>gpu</em> style invokes settings associated with the use of the GPU
 package.</p>
 <p>The <em>Ngpu</em> argument sets the number of GPUs per node.  There must be
 at least as many MPI tasks per node as GPUs, as set by the mpirun or
 mpiexec command.  If there are more MPI tasks (per node)
 than GPUs, multiple MPI tasks will share each GPU.</p>
 <p>Optional keyword/value pairs can also be specified.  Each has a
 default value as listed below.</p>
 <p>The <em>neigh</em> keyword specifies where neighbor lists for pair style
 computation will be built.  If <em>neigh</em> is <em>yes</em>, which is the default,
 neighbor list building is performed on the GPU.  If <em>neigh</em> is <em>no</em>,
 neighbor list building is performed on the CPU.  GPU neighbor list
 building currently cannot be used with a triclinic box.  GPU neighbor
 list calculation currently cannot be used with
 <a class="reference internal" href="pair_hybrid.html"><em>hybrid</em></a> pair styles.  GPU neighbor lists are not
 compatible with comannds that are not GPU-enabled.  When a non-GPU
 enabled command requires a neighbor list, it will also be built on the
 CPU.  In these cases, it will typically be more efficient to only use
 CPU neighbor list builds.</p>
 <p>The <em>newton</em> keyword sets the Newton flags for pairwise (not bonded)
 interactions to <em>off</em> or <em>on</em>, the same as the <a class="reference internal" href="newton.html"><em>newton</em></a>
 command allows.  Currently, only an <em>off</em> value is allowed, since all
 the GPU package pair styles require this setting.  This means more
 computation is done, but less communication.  In the future a value of
 <em>on</em> may be allowed, so the <em>newton</em> keyword is included as an option
 for compatibility with the package command for other accelerator
 styles.  Note that the newton setting for bonded interactions is not
 affected by this keyword.</p>
 <p>The <em>binsize</em> keyword sets the size of bins used to bin atoms in
 neighbor list builds performed on the GPU, if <em>neigh</em> = <em>yes</em> is set.
 If <em>binsize</em> is set to 0.0 (the default), then bins = the size of the
 pairwise cutoff + neighbor skin distance.  This is 2x larger than the
 LAMMPS default used for neighbor list building on the CPU.  This will
 be close to optimal for the GPU, so you do not normally need to use
 this keyword.  Note that if you use a longer-than-usual pairwise
 cutoff, e.g. to allow for a smaller fraction of KSpace work with a
 <a class="reference internal" href="kspace_style.html"><em>long-range Coulombic solver</em></a> because the GPU is
 faster at performing pairwise interactions, then it may be optimal to
 make the <em>binsize</em> smaller than the default.  For example, with a
 cutoff of 20*sigma in LJ <a class="reference internal" href="units.html"><em>units</em></a> and a neighbor skin
 distance of sigma, a <em>binsize</em> = 5.25*sigma can be more efficient than
 the default.</p>
 <p>The <em>split</em> keyword can be used for load balancing force calculations
 between CPU and GPU cores in GPU-enabled pair styles. If 0 &lt; <em>split</em> &lt;
 1.0, a fixed fraction of particles is offloaded to the GPU while force
 calculation for the other particles occurs simulataneously on the CPU.
 If <em>split</em> &lt; 0.0, the optimal fraction (based on CPU and GPU timings)
 is calculated every 25 timesteps, i.e. dynamic load-balancing across
 the CPU and GPU is performed.  If <em>split</em> = 1.0, all force
 calculations for GPU accelerated pair styles are performed on the GPU.
 In this case, other <a class="reference internal" href="pair_hybrid.html"><em>hybrid</em></a> pair interactions,
 <a class="reference internal" href="bond_style.html"><em>bond</em></a>, <a class="reference internal" href="angle_style.html"><em>angle</em></a>,
 <a class="reference internal" href="dihedral_style.html"><em>dihedral</em></a>, <a class="reference internal" href="improper_style.html"><em>improper</em></a>, and
 <a class="reference internal" href="kspace_style.html"><em>long-range</em></a> calculations can be performed on the
 CPU while the GPU is performing force calculations for the GPU-enabled
 pair style.  If all CPU force computations complete before the GPU
 completes, LAMMPS will block until the GPU has finished before
 continuing the timestep.</p>
 <p>As an example, if you have two GPUs per node and 8 CPU cores per node,
 and would like to run on 4 nodes (32 cores) with dynamic balancing of
 force calculation across CPU and GPU cores, you could specify</p>
 <div class="highlight-python"><div class="highlight"><pre>mpirun -np 32 -sf gpu -in in.script    # launch command
 package gpu 2 split -1                 # input script command
 </pre></div>
 </div>
 <p>In this case, all CPU cores and GPU devices on the nodes would be
 utilized.  Each GPU device would be shared by 4 CPU cores. The CPU
 cores would perform force calculations for some fraction of the
 particles at the same time the GPUs performed force calculation for
 the other particles.</p>
 <p>The <em>gpuID</em> keyword allows selection of which GPUs on each node will
 be used for a simulation.  The <em>first</em> and <em>last</em> values specify the
 GPU IDs to use (from 0 to Ngpu-1).  By default, first = 0 and last =
 Ngpu-1, so that all GPUs are used, assuming Ngpu is set to the number
 of physical GPUs.  If you only wish to use a subset, set Ngpu to a
 smaller number and first/last to a sub-range of the available GPUs.</p>
 <p>The <em>tpa</em> keyword sets the number of GPU thread per atom used to
 perform force calculations.  With a default value of 1, the number of
 threads will be chosen based on the pair style, however, the value can
 be set explicitly with this keyword to fine-tune performance.  For
 large cutoffs or with a small number of particles per GPU, increasing
 the value can improve performance. The number of threads per atom must
 be a power of 2 and currently cannot be greater than 32.</p>
 <p>The <em>device</em> keyword can be used to tune parameters optimized for a
 specific accelerator, when using OpenCL.  For CUDA, the <em>device</em>
 keyword is ignored.  Currently, the device type is limited to NVIDIA
 Kepler, NVIDIA Fermi, AMD Cypress, or a generic device.  More devices
 may be added later.  The default device type can be specified when
 building LAMMPS with the GPU library, via settings in the
 lib/gpu/Makefile that is used.</p>
 <hr class="docutils" />
 <p>The <em>intel</em> style invokes settings associated with the use of the
 USER-INTEL package.  All of its settings, except the <em>omp</em> and <em>mode</em>
 keywords, are ignored if LAMMPS was not built with Xeon Phi
 coprocessor support.  All of its settings, including the <em>omp</em> and
 <em>mode</em> keyword are applicable if LAMMPS was built with coprocessor
 support.</p>
 <p>The <em>Nphi</em> argument sets the number of coprocessors per node.
 This can be set to any value, including 0, if LAMMPS was not
 built with coprocessor support.</p>
 <p>Optional keyword/value pairs can also be specified.  Each has a
 default value as listed below.</p>
 <p>The <em>omp</em> keyword determines the number of OpenMP threads allocated
 for each MPI task when any portion of the interactions computed by a
 USER-INTEL pair style are run on the CPU.  This can be the case even
 if LAMMPS was built with coprocessor support; see the <em>balance</em>
 keyword discussion below.  If you are running with less MPI tasks/node
 than there are CPUs, it can be advantageous to use OpenMP threading on
 the CPUs.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">The <em>omp</em> keyword has nothing to do with coprocessor
 threads on the Xeon Phi; see the <em>tpc</em> and <em>tptask</em> keywords below for
 a discussion of coprocessor threads.</p>
 </div>
 <p>The <em>Nthread</em> value for the <em>omp</em> keyword sets the number of OpenMP
 threads allocated for each MPI task.  Setting <em>Nthread</em> = 0 (the
 default) instructs LAMMPS to use whatever value is the default for the
 given OpenMP environment. This is usually determined via the
 <em>OMP_NUM_THREADS</em> environment variable or the compiler runtime, which
 is usually a value of 1.</p>
 <p>For more details, including examples of how to set the OMP_NUM_THREADS
 environment variable, see the discussion of the <em>Nthreads</em> setting on
 this doc page for the &#8220;package omp&#8221; command.  Nthreads is a required
 argument for the USER-OMP package.  Its meaning is exactly the same
 for the USER-INTEL pacakge.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">If you build LAMMPS with both the USER-INTEL and
 USER-OMP packages, be aware that both packages allow setting of the
 <em>Nthreads</em> value via their package commands, but there is only a
 single global <em>Nthreads</em> value used by OpenMP.  Thus if both package
 commands are invoked, you should insure the two values are consistent.
 If they are not, the last one invoked will take precedence, for both
 packages.  Also note that if the &#8220;-sf intel&#8221; <a class="reference internal" href="Section_start.html#start-7"><span>command-line switch</span></a> is used, it invokes a &#8220;package
 intel&#8221; command, followed by a &#8220;package omp&#8221; command, both with a
 setting of <em>Nthreads</em> = 0.</p>
 </div>
 <p>The <em>mode</em> keyword determines the precision mode to use for
 computing pair style forces, either on the CPU or on the coprocessor,
 when using a USER-INTEL supported <a class="reference internal" href="pair_style.html"><em>pair style</em></a>.  It
 can take a value of <em>single</em>, <em>mixed</em> which is the default, or
 <em>double</em>.  <em>Single</em> means single precision is used for the entire
 force calculation.  <em>Mixed</em> means forces between a pair of atoms are
 computed in single precision, but accumulated and stored in double
 precision, including storage of forces, torques, energies, and virial
 quantities.  <em>Double</em> means double precision is used for the entire
 force calculation.</p>
 <p>The <em>balance</em> keyword sets the fraction of <a class="reference internal" href="pair_style.html"><em>pair style</em></a> work offloaded to the coprocessor for split
 values between 0.0 and 1.0 inclusive.  While this fraction of work is
 running on the coprocessor, other calculations will run on the host,
 including neighbor and pair calculations that are not offloaded, as
 well as angle, bond, dihedral, kspace, and some MPI communications.
 If <em>split</em> is set to -1, the fraction of work is dynamically adjusted
 automatically throughout the run.  This typically give performance
 within 5 to 10 percent of the optimal fixed fraction.</p>
 <p>The <em>ghost</em> keyword determines whether or not ghost atoms, i.e. atoms
 at the boundaries of proessor sub-domains, are offloaded for neighbor
 and force calculations.  When the value = &#8220;no&#8221;, ghost atoms are not
 offloaded.  This option can reduce the amount of data transfer with
 the coprocessor and can also overlap MPI communication of forces with
 computation on the coprocessor when the <a class="reference internal" href="newton.html"><em>newton pair</em></a>
 setting is &#8220;on&#8221;.  When the value = &#8220;yes&#8221;, ghost atoms are offloaded.
 In some cases this can provide better performance, especially if the
 <em>balance</em> fraction is high.</p>
 <p>The <em>tpc</em> keyword sets the max # of coprocessor threads <em>Ntpc</em> that
 will run on each core of the coprocessor.  The default value = 4,
 which is the number of hardware threads per core supported by the
 current generation Xeon Phi chips.</p>
 <p>The <em>tptask</em> keyword sets the max # of coprocessor threads (Ntptask*
 assigned to each MPI task.  The default value = 240, which is the
 total # of threads an entire current generation Xeon Phi chip can run
 (240 = 60 cores * 4 threads/core).  This means each MPI task assigned
 to the Phi will enough threads for the chip to run the max allowed,
 even if only 1 MPI task is assigned.  If 8 MPI tasks are assigned to
 the Phi, each will run with 30 threads.  If you wish to limit the
 number of threads per MPI task, set <em>tptask</em> to a smaller value.
 E.g. for <em>tptask</em> = 16, if 8 MPI tasks are assigned, each will run
 with 16 threads, for a total of 128.</p>
 <p>Note that the default settings for <em>tpc</em> and <em>tptask</em> are fine for
 most problems, regardless of how many MPI tasks you assign to a Phi.</p>
 <p>The <em>no_affinity</em> keyword will turn off automatic setting of core
 affinity for MPI tasks and OpenMP threads on the host when using
 offload to a coprocessor. Affinity settings are used when possible
 to prevent MPI tasks and OpenMP threads from being on separate NUMA
 domains and to prevent offload threads from interfering with other
 processes/threads used for LAMMPS.</p>
 <hr class="docutils" />
 <p>The <em>kokkos</em> style invokes settings associated with the use of the
 KOKKOS package.</p>
 <p>All of the settings are optional keyword/value pairs.  Each has a
 default value as listed below.</p>
 <p>The <em>neigh</em> keyword determines how neighbor lists are built.  A value
 of <em>half</em> uses half-neighbor lists, the same as used by most pair
 styles in LAMMPS.  A value of <em>half/thread</em> uses a thread-safe variant
 of the half-neighbor list.  It should be used instead of <em>half</em> when
 running with more than 1 threads per MPI task on a CPU.  A value of
 <em>n2</em> uses an O(N^2) algorithm to build the neighbor list without
 binning, where N = # of atoms on a processor.  It is typically slower
 than the other methods, which use binning.</p>
 <p>A value of <em>full</em> uses a full neighbor lists and is the default.  This
 performs twice as much computation as the <em>half</em> option, however that
 is often a win because it is thread-safe and doesn&#8217;t require atomic
 operations in the calculation of pair forces.  For that reason, <em>full</em>
 is the default setting.  However, when running in MPI-only mode with 1
 thread per MPI task, <em>half</em> neighbor lists will typically be faster,
 just as it is for non-accelerated pair styles.</p>
 <p>A value of <em>full/cluster</em> is an experimental neighbor style, where
 particles interact with all particles within a small cluster, if at
 least one of the clusters particles is within the neighbor cutoff
 range.  This potentially allows for better vectorization on
 architectures such as the Intel Phi.  If also reduces the size of the
 neighbor list by roughly a factor of the cluster size, thus reducing
 the total memory footprint considerably.</p>
 <p>The <em>newton</em> keyword sets the Newton flags for pairwise and bonded
 interactions to <em>off</em> or <em>on</em>, the same as the <a class="reference internal" href="newton.html"><em>newton</em></a>
 command allows.  The default is <em>off</em> because this will almost always
 give better performance for the KOKKOS package.  This means more
 computation is done, but less communication.  However, when running in
 MPI-only mode with 1 thread per MPI task, a value of <em>on</em> will
 typically be faster, just as it is for non-accelerated pair styles.</p>
 <p>The <em>binsize</em> keyword sets the size of bins used to bin atoms in
 neighbor list builds.  The same value can be set by the <a class="reference internal" href="neigh_modify.html"><em>neigh_modify binsize</em></a> command.  Making it an option in the
 package kokkos command allows it to be set from the command line.  The
 default value is 0.0, which means the LAMMPS default will be used,
 which is bins = 1/2 the size of the pairwise cutoff + neighbor skin
 distance.  This is fine when neighbor lists are built on the CPU.  For
 GPU builds, a 2x larger binsize equal to the pairwise cutoff +
 neighbor skin, is often faster, which can be set by this keyword.
 Note that if you use a longer-than-usual pairwise cutoff, e.g. to
 allow for a smaller fraction of KSpace work with a <a class="reference internal" href="kspace_style.html"><em>long-range Coulombic solver</em></a> because the GPU is faster at
 performing pairwise interactions, then this rule of thumb may give too
 large a binsize.</p>
 <p>The <em>comm</em> and <em>comm/exchange</em> and <em>comm/forward</em> keywords determine
 whether the host or device performs the packing and unpacking of data
 when communicating per-atom data between processors.  &#8220;Exchange&#8221;
 communication happens only on timesteps that neighbor lists are
 rebuilt.  The data is only for atoms that migrate to new processors.
 &#8220;Forward&#8221; communication happens every timestep.  The data is for atom
 coordinates and any other atom properties that needs to be updated for
 ghost atoms owned by each processor.</p>
 <p>The <em>comm</em> keyword is simply a short-cut to set the same value
 for both the <em>comm/exchange</em> and <em>comm/forward</em> keywords.</p>
 <p>The value options for all 3 keywords are <em>no</em> or <em>host</em> or <em>device</em>.
 A value of <em>no</em> means to use the standard non-KOKKOS method of
 packing/unpacking data for the communication.  A value of <em>host</em> means
 to use the host, typically a multi-core CPU, and perform the
 packing/unpacking in parallel with threads.  A value of <em>device</em> means
 to use the device, typically a GPU, to perform the packing/unpacking
 operation.</p>
 <p>The optimal choice for these keywords depends on the input script and
 the hardware used.  The <em>no</em> value is useful for verifying that the
 Kokkos-based <em>host</em> and <em>device</em> values are working correctly.  It may
 also be the fastest choice when using Kokkos styles in MPI-only mode
 (i.e. with a thread count of 1).</p>
 <p>When running on CPUs or Xeon Phi, the <em>host</em> and <em>device</em> values work
 identically.  When using GPUs, the <em>device</em> value will typically be
 optimal if all of your styles used in your input script are supported
 by the KOKKOS package.  In this case data can stay on the GPU for many
 timesteps without being moved between the host and GPU, if you use the
 <em>device</em> value.  This requires that your MPI is able to access GPU
 memory directly.  Currently that is true for OpenMPI 1.8 (or later
 versions), Mvapich2 1.9 (or later), and CrayMPI.  If your script uses
 styles (e.g. fixes) which are not yet supported by the KOKKOS package,
 then data has to be move between the host and device anyway, so it is
 typically faster to let the host handle communication, by using the
 <em>host</em> value.  Using <em>host</em> instead of <em>no</em> will enable use of
 multiple threads to pack/unpack communicated data.</p>
 <hr class="docutils" />
 <p>The <em>omp</em> style invokes settings associated with the use of the
 USER-OMP package.</p>
 <p>The <em>Nthread</em> argument sets the number of OpenMP threads allocated for
 each MPI task.  For example, if your system has nodes with dual
 quad-core processors, it has a total of 8 cores per node.  You could
 use two MPI tasks per node (e.g. using the -ppn option of the mpirun
 command in MPICH or -npernode in OpenMPI), and set <em>Nthreads</em> = 4.
 This would use all 8 cores on each node.  Note that the product of MPI
 tasks * threads/task should not exceed the physical number of cores
 (on a node), otherwise performance will suffer.</p>
 <p>Setting <em>Nthread</em> = 0 instructs LAMMPS to use whatever value is the
 default for the given OpenMP environment. This is usually determined
 via the <em>OMP_NUM_THREADS</em> environment variable or the compiler
 runtime.  Note that in most cases the default for OpenMP capable
 compilers is to use one thread for each available CPU core when
 <em>OMP_NUM_THREADS</em> is not explicitly set, which can lead to poor
 performance.</p>
 <p>Here are examples of how to set the environment variable when
 launching LAMMPS:</p>
 <div class="highlight-python"><div class="highlight"><pre>env OMP_NUM_THREADS=4 lmp_machine -sf omp -in in.script
 env OMP_NUM_THREADS=2 mpirun -np 2 lmp_machine -sf omp -in in.script
 mpirun -x OMP_NUM_THREADS=2 -np 2 lmp_machine -sf omp -in in.script
 </pre></div>
 </div>
 <p>or you can set it permanently in your shell&#8217;s start-up script.
 All three of these examples use a total of 4 CPU cores.</p>
 <p>Note that different MPI implementations have different ways of passing
 the OMP_NUM_THREADS environment variable to all MPI processes.  The
 2nd example line above is for MPICH; the 3rd example line with -x is
 for OpenMPI.  Check your MPI documentation for additional details.</p>
 <p>What combination of threads and MPI tasks gives the best performance
 is difficult to predict and can depend on many components of your
 input.  Not all features of LAMMPS support OpenMP threading via the
 USER-OMP packaage and the parallel efficiency can be very different,
 too.</p>
 <p>Optional keyword/value pairs can also be specified.  Each has a
 default value as listed below.</p>
 <p>The <em>neigh</em> keyword specifies whether neighbor list building will be
 multi-threaded in addition to force calculations.  If <em>neigh</em> is set
 to <em>no</em> then neighbor list calculation is performed only by MPI tasks
 with no OpenMP threading.  If <em>mode</em> is <em>yes</em> (the default), a
 multi-threaded neighbor list build is used.  Using <em>neigh</em> = <em>yes</em> is
 almost always faster and should produce idential neighbor lists at the
 expense of using more memory.  Specifically, neighbor list pages are
 allocated for all threads at the same time and each thread works
 within its own pages.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>This command cannot be used after the simulation box is defined by a
 <a class="reference internal" href="read_data.html"><em>read_data</em></a> or <a class="reference internal" href="create_box.html"><em>create_box</em></a> command.</p>
 <p>The cuda style of this command can only be invoked if LAMMPS was built
 with the USER-CUDA package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 <p>The gpu style of this command can only be invoked if LAMMPS was built
 with the GPU package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 <p>The intel style of this command can only be invoked if LAMMPS was
 built with the USER-INTEL package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 <p>The kk style of this command can only be invoked if LAMMPS was built
 with the KOKKOS package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 <p>The omp style of this command can only be invoked if LAMMPS was built
 with the USER-OMP package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="suffix.html"><em>suffix</em></a>, &#8220;-pk&#8221; <a class="reference internal" href="Section_start.html#start-7"><span>command-line setting</span></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>For the USER-CUDA package, the default is Ngpu = 1 and the option
 defaults are newton = off, gpuID = 0 to Ngpu-1, timing = not enabled,
 test = not enabled, and thread = auto.  These settings are made
 automatically by the required &#8220;-c on&#8221; <a class="reference internal" href="Section_start.html#start-7"><span>command-line switch</span></a>.  You can change them bu using the
 package cuda command in your input script or via the &#8220;-pk cuda&#8221;
 <a class="reference internal" href="Section_start.html#start-7"><span>command-line switch</span></a>.</p>
 <p>For the GPU package, the default is Ngpu = 1 and the option defaults
 are neigh = yes, newton = off, binsize = 0.0, split = 1.0, gpuID = 0
 to Ngpu-1, tpa = 1, and device = not used.  These settings are made
 automatically if the &#8220;-sf gpu&#8221; <a class="reference internal" href="Section_start.html#start-7"><span>command-line switch</span></a> is used.  If it is not used, you
 must invoke the package gpu command in your input script or via the
 &#8220;-pk gpu&#8221; <a class="reference internal" href="Section_start.html#start-7"><span>command-line switch</span></a>.</p>
 <p>For the USER-INTEL package, the default is Nphi = 1 and the option
 defaults are omp = 0, mode = mixed, balance = -1, tpc = 4, tptask =
 240.  The default ghost option is determined by the pair style being
 used.  This value is output to the screen in the offload report at the
 end of each run.  Note that all of these settings, except &#8220;omp&#8221; and
 &#8220;mode&#8221;, are ignored if LAMMPS was not built with Xeon Phi coprocessor
 support.  These settings are made automatically if the &#8220;-sf intel&#8221;
 <a class="reference internal" href="Section_start.html#start-7"><span>command-line switch</span></a> is used.  If it is
 not used, you must invoke the package intel command in your input
 script or or via the &#8220;-pk intel&#8221; <a class="reference internal" href="Section_start.html#start-7"><span>command-line switch</span></a>.</p>
 <p>For the KOKKOS package, the option defaults neigh = full, newton =
 off, binsize = 0.0, and comm = host.  These settings are made
 automatically by the required &#8220;-k on&#8221; <a class="reference internal" href="Section_start.html#start-7"><span>command-line switch</span></a>.  You can change them bu using the
 package kokkos command in your input script or via the &#8220;-pk kokkos&#8221;
 <a class="reference internal" href="Section_start.html#start-7"><span>command-line switch</span></a>.</p>
 <p>For the OMP package, the default is Nthreads = 0 and the option
 defaults are neigh = yes.  These settings are made automatically if
 the &#8220;-sf omp&#8221; <a class="reference internal" href="Section_start.html#start-7"><span>command-line switch</span></a> is
 used.  If it is not used, you must invoke the package omp command in
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   <div class="section" id="pair-style-awpmd-cut-command">
 <span id="index-0"></span><h1>pair_style awpmd/cut command<a class="headerlink" href="#pair-style-awpmd-cut-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>pair_style awpmd/cut Rc keyword value ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>Rc = global cutoff, -1 means cutoff of half the shortest box length</li>
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>hartree</em> or <em>dproduct</em> or <em>uhf</em> or <em>free</em> or <em>pbc</em> or <em>fix</em> or <em>harm</em> or <em>ermscale</em> or <em>flex_press</em></li>
 </ul>
 <pre class="literal-block">
 <em>hartree</em> value = none
-  <em>dproduct</em> value = none
-  <em>uhf</em> value = none
-  <em>free</em> value = none
-  <em>pbc</em> value = Plen
-    Plen = periodic width of electron = -1 or positive value (distance units)
-  <em>fix</em> value = Flen
-    Flen = fixed width of electron = -1 or positive value (distance units)
-  <em>harm</em> value = width
-    width = harmonic width constraint
-  <em>ermscale</em> value = factor
-    factor = scaling between electron mass and width variable mass
-  <em>flex_press</em> value = none
+<em>dproduct</em> value = none
+<em>uhf</em> value = none
+<em>free</em> value = none
+<em>pbc</em> value = Plen
+  Plen = periodic width of electron = -1 or positive value (distance units)
+<em>fix</em> value = Flen
+  Flen = fixed width of electron = -1 or positive value (distance units)
+<em>harm</em> value = width
+  width = harmonic width constraint
+<em>ermscale</em> value = factor
+  factor = scaling between electron mass and width variable mass
+<em>flex_press</em> value = none
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>pair_style awpmd/cut -1
 pair_style awpmd/cut 40.0 uhf free
 pair_coeff * *
 pair_coeff 2 2 20.0
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>This pair style contains an implementation of the Antisymmetrized Wave
 Packet Molecular Dynamics (AWPMD) method.  Need citation here.  Need
 basic formulas here.  Could be links to other documents.</p>
 <p>Rc is the cutoff.</p>
 <p>The pair_style command allows for several optional keywords
 to be specified.</p>
 <p>The <em>hartree</em>, <em>dproduct</em>, and <em>uhf</em> keywords specify the form of the
 initial trial wave function for the system.  If the <em>hartree</em> keyword
 is used, then a Hartree multielectron trial wave function is used.  If
 the <em>dproduct</em> keyword is used, then a trial function which is a
 product of two determinants for each spin type is used.  If the <em>uhf</em>
 keyword is used, then an unrestricted Hartree-Fock trial wave function
 is used.</p>
 <p>The <em>free</em>, <em>pbc</em>, and <em>fix</em> keywords specify a width constraint on
 the electron wavepackets.  If the <em>free</em> keyword is specified, then there is no
 constraint.  If the <em>pbc</em> keyword is used and <em>Plen</em> is specified as
 -1, then the maximum width is half the shortest box length.  If <em>Plen</em>
 is a positive value, then the value is the maximum width.  If the
 <em>fix</em> keyword is used and <em>Flen</em> is specified as -1, then electrons
 have a constant width that is read from the data file.  If <em>Flen</em> is a
 positive value, then the constant width for all electrons is set to
 <em>Flen</em>.</p>
 <p>The <em>harm</em> keyword allow oscillations in the width of the
 electron wavepackets.  More details are needed.</p>
 <p>The <em>ermscale</em> keyword specifies a unitless scaling factor
 between the electron masses and the width variable mass.  More
 details needed.</p>
 <p>If the <em>flex_press</em> keyword is used, then a contribution from the
 electrons is added to the total virial and pressure of the system.</p>
 <p>This potential is designed to be used with <a class="reference internal" href="atom_style.html"><em>atom_style wavepacket</em></a> definitions, in order to handle the
 description of systems with interacting nuclei and explicit electrons.</p>
 <p>The following coefficients must be defined for each pair of atoms
 types via the <a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a> command as in the examples
 above, or in the data file or restart files read by the
 <a class="reference internal" href="read_data.html"><em>read_data</em></a> or <a class="reference internal" href="read_restart.html"><em>read_restart</em></a>
 commands, or by mixing as described below:</p>
 <ul class="simple">
 <li>cutoff (distance units)</li>
 </ul>
 <p>For <em>awpmd/cut</em>, the cutoff coefficient is optional.  If it is not
 used (as in some of the examples above), the default global value
 specified in the pair_style command is used.</p>
 <hr class="docutils" />
 <p><strong>Mixing, shift, table, tail correction, restart, rRESPA info</strong>:</p>
 <p>The <a class="reference internal" href="pair_modify.html"><em>pair_modify</em></a> mix, shift, table, and tail options
 are not relevant for this pair style.</p>
 <p>This pair style writes its information to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>, so pair_style and pair_coeff commands do not need
 to be specified in an input script that reads a restart file.</p>
 <p>This pair style can only be used via the <em>pair</em> keyword of the
 <a class="reference internal" href="run_style.html"><em>run_style respa</em></a> command.  It does not support the
 <em>inner</em>, <em>middle</em>, <em>outer</em> keywords.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <blockquote>
 <div>none</div></blockquote>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>These are the defaults for the pair_style keywords: <em>hartree</em> for the
 initial wavefunction, <em>free</em> for the wavepacket width.</p>
 </div>
 </div>
 
 
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   <div class="section" id="pair-style-born-command">
 <span id="index-0"></span><h1>pair_style born command<a class="headerlink" href="#pair-style-born-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-born-omp-command">
 <h1>pair_style born/omp command<a class="headerlink" href="#pair-style-born-omp-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-born-gpu-command">
 <h1>pair_style born/gpu command<a class="headerlink" href="#pair-style-born-gpu-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-born-coul-long-command">
 <h1>pair_style born/coul/long command<a class="headerlink" href="#pair-style-born-coul-long-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-born-coul-long-cs-command">
 <h1>pair_style born/coul/long/cs command<a class="headerlink" href="#pair-style-born-coul-long-cs-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-born-coul-long-cuda-command">
 <h1>pair_style born/coul/long/cuda command<a class="headerlink" href="#pair-style-born-coul-long-cuda-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-born-coul-long-gpu-command">
 <h1>pair_style born/coul/long/gpu command<a class="headerlink" href="#pair-style-born-coul-long-gpu-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-born-coul-long-omp-command">
 <h1>pair_style born/coul/long/omp command<a class="headerlink" href="#pair-style-born-coul-long-omp-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-born-coul-msm-command">
 <h1>pair_style born/coul/msm command<a class="headerlink" href="#pair-style-born-coul-msm-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-born-coul-msm-omp-command">
 <h1>pair_style born/coul/msm/omp command<a class="headerlink" href="#pair-style-born-coul-msm-omp-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-born-coul-wolf-command">
 <h1>pair_style born/coul/wolf command<a class="headerlink" href="#pair-style-born-coul-wolf-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-born-coul-wolf-gpu-command">
 <h1>pair_style born/coul/wolf/gpu command<a class="headerlink" href="#pair-style-born-coul-wolf-gpu-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-born-coul-wolf-omp-command">
 <h1>pair_style born/coul/wolf/omp command<a class="headerlink" href="#pair-style-born-coul-wolf-omp-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>pair_style style args
 </pre></div>
 </div>
 <ul class="simple">
 <li>style = <em>born</em> or <em>born/coul/long</em> or <em>born/coul/long/cs</em> or <em>born/coul/msm</em> or <em>born/coul/wolf</em></li>
 <li>args = list of arguments for a particular style</li>
 </ul>
 <pre class="literal-block">
 <em>born</em> args = cutoff
-    cutoff = global cutoff for non-Coulombic interactions (distance units)
-  <em>born/coul/long</em> or <em>born/coul/long/cs</em> args = cutoff (cutoff2)
-    cutoff = global cutoff for non-Coulombic (and Coulombic if only 1 arg) (distance units)
-    cutoff2 = global cutoff for Coulombic (optional) (distance units)
-  <em>born/coul/msm</em> args = cutoff (cutoff2)
-    cutoff = global cutoff for non-Coulombic (and Coulombic if only 1 arg) (distance units)
-    cutoff2 = global cutoff for Coulombic (optional) (distance units)
-  <em>born/coul/wolf</em> args = alpha cutoff (cutoff2)
-    alpha = damping parameter (inverse distance units)
-    cutoff = global cutoff for non-Coulombic (and Coulombic if only 1 arg) (distance units)
-    cutoff2 = global cutoff for Coulombic (optional) (distance units)
+  cutoff = global cutoff for non-Coulombic interactions (distance units)
+<em>born/coul/long</em> or <em>born/coul/long/cs</em> args = cutoff (cutoff2)
+  cutoff = global cutoff for non-Coulombic (and Coulombic if only 1 arg) (distance units)
+  cutoff2 = global cutoff for Coulombic (optional) (distance units)
+<em>born/coul/msm</em> args = cutoff (cutoff2)
+  cutoff = global cutoff for non-Coulombic (and Coulombic if only 1 arg) (distance units)
+  cutoff2 = global cutoff for Coulombic (optional) (distance units)
+<em>born/coul/wolf</em> args = alpha cutoff (cutoff2)
+  alpha = damping parameter (inverse distance units)
+  cutoff = global cutoff for non-Coulombic (and Coulombic if only 1 arg) (distance units)
+  cutoff2 = global cutoff for Coulombic (optional) (distance units)
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>pair_style born 10.0
 pair_coeff * * 6.08 0.317 2.340 24.18 11.51
 pair_coeff 1 1 6.08 0.317 2.340 24.18 11.51
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>pair_style born/coul/long 10.0
 pair_style born/coul/long/cs 10.0
 pair_style born/coul/long 10.0 8.0
 pair_style born/coul/long/cs 10.0 8.0
 pair_coeff * * 6.08 0.317 2.340 24.18 11.51
 pair_coeff 1 1 6.08 0.317 2.340 24.18 11.51
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>pair_style born/coul/msm 10.0
 pair_style born/coul/msm 10.0 8.0
 pair_coeff * * 6.08 0.317 2.340 24.18 11.51
 pair_coeff 1 1 6.08 0.317 2.340 24.18 11.51
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>pair_style born/coul/wolf 0.25 10.0
 pair_style born/coul/wolf 0.25 10.0 9.0
 pair_coeff * * 6.08 0.317 2.340 24.18 11.51
 pair_coeff 1 1 6.08 0.317 2.340 24.18 11.51
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>The <em>born</em> style computes the Born-Mayer-Huggins or Tosi/Fumi
 potential described in <a class="reference internal" href="#fumitosi"><span>(Fumi and Tosi)</span></a>, given by</p>
 <img alt="_images/pair_born.jpg" class="align-center" src="_images/pair_born.jpg" />
 <p>where sigma is an interaction-dependent length parameter, rho is an
 ionic-pair dependent length parameter, and Rc is the cutoff.</p>
 <p>The styles with <em>coul/long</em> or <em>coul/msm</em> add a Coulombic term as
 described for the <a class="reference internal" href="pair_lj.html"><em>lj/cut</em></a> pair styles.  An additional
 damping factor is applied to the Coulombic term so it can be used in
 conjunction with the <a class="reference internal" href="kspace_style.html"><em>kspace_style</em></a> command and its
 <em>ewald</em> or <em>pppm</em> of <em>msm</em> option.  The Coulombic cutoff specified for
 this style means that pairwise interactions within this distance are
 computed directly; interactions outside that distance are computed in
 reciprocal space.</p>
 <p>If one cutoff is specified for the <em>born/coul/long</em> and
 <em>born/coul/msm</em> style, it is used for both the A,C,D and Coulombic
 terms.  If two cutoffs are specified, the first is used as the cutoff
 for the A,C,D terms, and the second is the cutoff for the Coulombic
 term.</p>
 <p>The <em>born/coul/wolf</em> style adds a Coulombic term as described for the
 Wolf potential in the <a class="reference internal" href="pair_coul.html"><em>coul/wolf</em></a> pair style.</p>
 <p>Style <em>born/coul/long/cs</em> is identical to <em>born/coul/long</em> except that
 a term is added for the <a class="reference internal" href="Section_howto.html#howto-25"><span>core/shell model</span></a>
 to allow charges on core and shell particles to be separated by r =
 0.0.</p>
 <p>Note that these potentials are related to the <a class="reference internal" href="pair_buck.html"><em>Buckingham potential</em></a>.</p>
 <p>The following coefficients must be defined for each pair of atoms
 types via the <a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a> command as in the examples
 above, or in the data file or restart files read by the
 <a class="reference internal" href="read_data.html"><em>read_data</em></a> or <a class="reference internal" href="read_restart.html"><em>read_restart</em></a>
 commands, or by mixing as described below:</p>
 <ul class="simple">
 <li>A (energy units)</li>
 <li>rho (distance units)</li>
 <li>sigma (distance units)</li>
 <li>C (energy units * distance units^6)</li>
 <li>D (energy units * distance units^8)</li>
 <li>cutoff (distance units)</li>
 </ul>
 <p>The second coefficient, rho, must be greater than zero.</p>
 <p>The last coefficient is optional.  If not specified, the global A,C,D
 cutoff specified in the pair_style command is used.</p>
 <p>For <em>born/coul/long</em> and <em>born/coul/wolf</em> no Coulombic cutoff can be
 specified for an individual I,J type pair.  All type pairs use the
 same global Coulombic cutoff specified in the pair_style command.</p>
 <hr class="docutils" />
 <p>Styles with a <em>cuda</em>, <em>gpu</em>, <em>intel</em>, <em>kk</em>, <em>omp</em>, or <em>opt</em> suffix are
 functionally the same as the corresponding style without the suffix.
 They have been optimized to run faster, depending on your available
 hardware, as discussed in <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a>
 of the manual.  The accelerated styles take the same arguments and
 should produce the same results, except for round-off and precision
 issues.</p>
 <p>These accelerated styles are part of the USER-CUDA, GPU, USER-INTEL,
 KOKKOS, USER-OMP and OPT packages, respectively.  They are only
 enabled if LAMMPS was built with those packages.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 <p>You can specify the accelerated styles explicitly in your input script
 by including their suffix, or you can use the <a class="reference internal" href="Section_start.html#start-7"><span>-suffix command-line switch</span></a> when you invoke LAMMPS, or you can
 use the <a class="reference internal" href="suffix.html"><em>suffix</em></a> command in your input script.</p>
 <p>See <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a> of the manual for
 more instructions on how to use the accelerated styles effectively.</p>
 <hr class="docutils" />
 <p><strong>Mixing, shift, table, tail correction, restart, rRESPA info</strong>:</p>
 <p>These pair styles do not support mixing.  Thus, coefficients for all
 I,J pairs must be specified explicitly.</p>
 <p>These styles support the <a class="reference internal" href="pair_modify.html"><em>pair_modify</em></a> shift option
 for the energy of the exp(), 1/r^6, and 1/r^8 portion of the pair
 interaction.</p>
 <p>The <em>born/coul/long</em> pair style supports the
 <a class="reference internal" href="pair_modify.html"><em>pair_modify</em></a> table option ti tabulate the
 short-range portion of the long-range Coulombic interaction.</p>
 <p>These styles support the pair_modify tail option for adding long-range
 tail corrections to energy and pressure.</p>
 <p>Thess styles writes thei information to binary <a class="reference internal" href="restart.html"><em>restart</em></a>
 files, so pair_style and pair_coeff commands do not need to be
 specified in an input script that reads a restart file.</p>
 <p>These styles can only be used via the <em>pair</em> keyword of the <a class="reference internal" href="run_style.html"><em>run_style respa</em></a> command.  They do not support the <em>inner</em>,
 <em>middle</em>, <em>outer</em> keywords.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>The <em>born/coul/long</em> style is part of the KSPACE package.  It is only
 enabled if LAMMPS was built with that package (which it is by
 default).  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section
 for more info.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a>, <a class="reference internal" href="pair_buck.html"><em>pair_style buck</em></a></p>
 <p><strong>Default:</strong> none</p>
 <hr class="docutils" />
 <p id="fumitosi">Fumi and Tosi, J Phys Chem Solids, 25, 31 (1964),
 Fumi and Tosi, J Phys Chem Solids, 25, 45 (1964).</p>
 </div>
 </div>
 
 
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   <div class="section" id="pair-style-buck-command">
 <span id="index-0"></span><h1>pair_style buck command<a class="headerlink" href="#pair-style-buck-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-buck-cuda-command">
 <h1>pair_style buck/cuda command<a class="headerlink" href="#pair-style-buck-cuda-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-buck-gpu-command">
 <h1>pair_style buck/gpu command<a class="headerlink" href="#pair-style-buck-gpu-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-buck-kk-command">
 <h1>pair_style buck/kk command<a class="headerlink" href="#pair-style-buck-kk-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-buck-omp-command">
 <h1>pair_style buck/omp command<a class="headerlink" href="#pair-style-buck-omp-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-buck-coul-cut-command">
 <h1>pair_style buck/coul/cut command<a class="headerlink" href="#pair-style-buck-coul-cut-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-buck-coul-cut-cuda-command">
 <h1>pair_style buck/coul/cut/cuda command<a class="headerlink" href="#pair-style-buck-coul-cut-cuda-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-buck-coul-cut-gpu-command">
 <h1>pair_style buck/coul/cut/gpu command<a class="headerlink" href="#pair-style-buck-coul-cut-gpu-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-buck-coul-cut-kk-command">
 <h1>pair_style buck/coul/cut/kk command<a class="headerlink" href="#pair-style-buck-coul-cut-kk-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-buck-coul-cut-omp-command">
 <h1>pair_style buck/coul/cut/omp command<a class="headerlink" href="#pair-style-buck-coul-cut-omp-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-buck-coul-long-command">
 <h1>pair_style buck/coul/long command<a class="headerlink" href="#pair-style-buck-coul-long-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-buck-coul-long-cs-command">
 <h1>pair_style buck/coul/long/cs command<a class="headerlink" href="#pair-style-buck-coul-long-cs-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-buck-coul-long-cuda-command">
 <h1>pair_style buck/coul/long/cuda command<a class="headerlink" href="#pair-style-buck-coul-long-cuda-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-buck-coul-long-gpu-command">
 <h1>pair_style buck/coul/long/gpu command<a class="headerlink" href="#pair-style-buck-coul-long-gpu-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-buck-coul-long-kk-command">
 <h1>pair_style buck/coul/long/kk command<a class="headerlink" href="#pair-style-buck-coul-long-kk-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-buck-coul-long-omp-command">
 <h1>pair_style buck/coul/long/omp command<a class="headerlink" href="#pair-style-buck-coul-long-omp-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-buck-coul-msm-command">
 <h1>pair_style buck/coul/msm command<a class="headerlink" href="#pair-style-buck-coul-msm-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-buck-coul-msm-omp-command">
 <h1>pair_style buck/coul/msm/omp command<a class="headerlink" href="#pair-style-buck-coul-msm-omp-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>pair_style style args
 </pre></div>
 </div>
 <ul class="simple">
 <li>style = <em>buck</em> or <em>buck/coul/cut</em> or <em>buck/coul/long</em> or <em>buck/coul/long/cs</em> or <em>buck/coul/msm</em></li>
 <li>args = list of arguments for a particular style</li>
 </ul>
 <pre class="literal-block">
 <em>buck</em> args = cutoff
-    cutoff = global cutoff for Buckingham interactions (distance units)
-  <em>buck/coul/cut</em> args = cutoff (cutoff2)
-    cutoff = global cutoff for Buckingham (and Coulombic if only 1 arg) (distance units)
-    cutoff2 = global cutoff for Coulombic (optional) (distance units)
-  <em>buck/coul/long</em> or <em>buck/coul/long/cs</em> args = cutoff (cutoff2)
-    cutoff = global cutoff for Buckingham (and Coulombic if only 1 arg) (distance units)
-    cutoff2 = global cutoff for Coulombic (optional) (distance units)
-  <em>buck/coul/msm</em> args = cutoff (cutoff2)
-    cutoff = global cutoff for Buckingham (and Coulombic if only 1 arg) (distance units)
-    cutoff2 = global cutoff for Coulombic (optional) (distance units)
+  cutoff = global cutoff for Buckingham interactions (distance units)
+<em>buck/coul/cut</em> args = cutoff (cutoff2)
+  cutoff = global cutoff for Buckingham (and Coulombic if only 1 arg) (distance units)
+  cutoff2 = global cutoff for Coulombic (optional) (distance units)
+<em>buck/coul/long</em> or <em>buck/coul/long/cs</em> args = cutoff (cutoff2)
+  cutoff = global cutoff for Buckingham (and Coulombic if only 1 arg) (distance units)
+  cutoff2 = global cutoff for Coulombic (optional) (distance units)
+<em>buck/coul/msm</em> args = cutoff (cutoff2)
+  cutoff = global cutoff for Buckingham (and Coulombic if only 1 arg) (distance units)
+  cutoff2 = global cutoff for Coulombic (optional) (distance units)
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>pair_style buck 2.5
 pair_coeff * * 100.0 1.5 200.0
 pair_coeff * * 100.0 1.5 200.0 3.0
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>pair_style buck/coul/cut 10.0
 pair_style buck/coul/cut 10.0 8.0
 pair_coeff * * 100.0 1.5 200.0
 pair_coeff 1 1 100.0 1.5 200.0 9.0
 pair_coeff 1 1 100.0 1.5 200.0 9.0 8.0
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>pair_style buck/coul/long 10.0
 pair_style buck/coul/long/cs 10.0
 pair_style buck/coul/long 10.0 8.0
 pair_style buck/coul/long/cs 10.0 8.0
 pair_coeff * * 100.0 1.5 200.0
 pair_coeff 1 1 100.0 1.5 200.0 9.0
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>pair_style buck/coul/msm 10.0
 pair_style buck/coul/msm 10.0 8.0
 pair_coeff * * 100.0 1.5 200.0
 pair_coeff 1 1 100.0 1.5 200.0 9.0
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>The <em>buck</em> style computes a Buckingham potential (exp/6 instead of
 Lennard-Jones 12/6) given by</p>
 <img alt="_images/pair_buck.jpg" class="align-center" src="_images/pair_buck.jpg" />
 <p>where rho is an ionic-pair dependent length parameter, and Rc is the
 cutoff on both terms.</p>
 <p>The styles with <em>coul/cut</em> or <em>coul/long</em> or <em>coul/msm</em> add a
 Coulombic term as described for the <a class="reference internal" href="pair_lj.html"><em>lj/cut</em></a> pair styles.
 For <em>buck/coul/long</em> and <em>buc/coul/msm</em>, an additional damping factor
 is applied to the Coulombic term so it can be used in conjunction with
 the <a class="reference internal" href="kspace_style.html"><em>kspace_style</em></a> command and its <em>ewald</em> or <em>pppm</em>
 or <em>msm</em> option.  The Coulombic cutoff specified for this style means
 that pairwise interactions within this distance are computed directly;
 interactions outside that distance are computed in reciprocal space.</p>
 <p>If one cutoff is specified for the <em>born/coul/cut</em> and
 <em>born/coul/long</em> and <em>born/coul/msm</em> styles, it is used for both the
 A,C and Coulombic terms.  If two cutoffs are specified, the first is
 used as the cutoff for the A,C terms, and the second is the cutoff for
 the Coulombic term.</p>
 <p>Style <em>buck/coul/long/cs</em> is identical to <em>buck/coul/long</em> except that
 a term is added for the <a class="reference internal" href="Section_howto.html#howto-25"><span>core/shell model</span></a>
 to allow charges on core and shell particles to be separated by r =
 0.0.</p>
 <p>Note that these potentials are related to the <a class="reference internal" href="pair_born.html"><em>Born-Mayer-Huggins potential</em></a>.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">For all these pair styles, the terms with A and C are
 always cutoff.  The additional Coulombic term can be cutoff or
 long-range (no cutoff) depending on whether the style name includes
 coul/cut or coul/long or coul/msm.  If you wish the C/r^6 term to be
 long-range (no cutoff), then see the <a class="reference internal" href="pair_buck_long.html"><em>pair_style buck/long/coul/long</em></a> command.</p>
 </div>
 <p>The following coefficients must be defined for each pair of atoms
 types via the <a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a> command as in the examples
 above, or in the data file or restart files read by the
 <a class="reference internal" href="read_data.html"><em>read_data</em></a> or <a class="reference internal" href="read_restart.html"><em>read_restart</em></a>
 commands:</p>
 <ul class="simple">
 <li>A (energy units)</li>
 <li>rho (distance units)</li>
 <li>C (energy-distance^6 units)</li>
 <li>cutoff (distance units)</li>
 <li>cutoff2 (distance units)</li>
 </ul>
 <p>The second coefficient, rho, must be greater than zero.</p>
 <p>The latter 2 coefficients are optional.  If not specified, the global
 A,C and Coulombic cutoffs are used.  If only one cutoff is specified,
 it is used as the cutoff for both A,C and Coulombic interactions for
 this type pair.  If both coefficients are specified, they are used as
 the A,C and Coulombic cutoffs for this type pair.  You cannot specify
 2 cutoffs for style <em>buck</em>, since it has no Coulombic terms.</p>
 <p>For <em>buck/coul/long</em> only the LJ cutoff can be specified since a
 Coulombic cutoff cannot be specified for an individual I,J type pair.
 All type pairs use the same global Coulombic cutoff specified in the
 pair_style command.</p>
 <hr class="docutils" />
 <p>Styles with a <em>cuda</em>, <em>gpu</em>, <em>intel</em>, <em>kk</em>, <em>omp</em>, or <em>opt</em> suffix are
 functionally the same as the corresponding style without the suffix.
 They have been optimized to run faster, depending on your available
 hardware, as discussed in <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a>
 of the manual.  The accelerated styles take the same arguments and
 should produce the same results, except for round-off and precision
 issues.</p>
 <p>These accelerated styles are part of the USER-CUDA, GPU, USER-INTEL,
 KOKKOS, USER-OMP and OPT packages, respectively.  They are only
 enabled if LAMMPS was built with those packages.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 <p>You can specify the accelerated styles explicitly in your input script
 by including their suffix, or you can use the <a class="reference internal" href="Section_start.html#start-7"><span>-suffix command-line switch</span></a> when you invoke LAMMPS, or you can
 use the <a class="reference internal" href="suffix.html"><em>suffix</em></a> command in your input script.</p>
 <p>See <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a> of the manual for
 more instructions on how to use the accelerated styles effectively.</p>
 <hr class="docutils" />
 <p><strong>Mixing, shift, table, tail correction, restart, rRESPA info</strong>:</p>
 <p>These pair styles do not support mixing.  Thus, coefficients for all
 I,J pairs must be specified explicitly.</p>
 <p>These styles support the <a class="reference internal" href="pair_modify.html"><em>pair_modify</em></a> shift option
 for the energy of the exp() and 1/r^6 portion of the pair interaction.</p>
 <p>The <em>buck/coul/long</em> pair style supports the
 <a class="reference internal" href="pair_modify.html"><em>pair_modify</em></a> table option to tabulate the
 short-range portion of the long-range Coulombic interaction.</p>
 <p>These styles support the pair_modify tail option for adding long-range
 tail corrections to energy and pressure for the A,C terms in the
 pair interaction.</p>
 <p>These styles write their information to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>, so pair_style and pair_coeff commands do not need
 to be specified in an input script that reads a restart file.</p>
 <p>These styles can only be used via the <em>pair</em> keyword of the <a class="reference internal" href="run_style.html"><em>run_style respa</em></a> command.  They do not support the <em>inner</em>,
 <em>middle</em>, <em>outer</em> keywords.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>The <em>buck/coul/long</em> style is part of the KSPACE package.  The
 <em>buck/coul/long/cs</em> style is part of the CORESHELL package.  They are
 only enabled if LAMMPS was built with that package (which it is by
 default).  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section
 for more info.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a>, <a class="reference internal" href="pair_born.html"><em>pair_style born</em></a></p>
 <p><strong>Default:</strong> none</p>
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diff --git a/doc/pair_buck_long.html b/doc/pair_buck_long.html
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   <div class="section" id="pair-style-buck-long-coul-long-command">
 <span id="index-0"></span><h1>pair_style buck/long/coul/long command<a class="headerlink" href="#pair-style-buck-long-coul-long-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-buck-long-coul-long-omp-command">
 <h1>pair_style buck/long/coul/long/omp command<a class="headerlink" href="#pair-style-buck-long-coul-long-omp-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>pair_style buck/long/coul/long flag_buck flag_coul cutoff (cutoff2)
 </pre></div>
 </div>
 <ul class="simple">
 <li>flag_buck = <em>long</em> or <em>cut</em></li>
 </ul>
 <pre class="literal-block">
 <em>long</em> = use Kspace long-range summation for the dispersion term 1/r^6
-  <em>cut</em> = use a cutoff
+<em>cut</em> = use a cutoff
 </pre>
 <ul class="simple">
 <li>flag_coul = <em>long</em> or <em>off</em></li>
 </ul>
 <pre class="literal-block">
 <em>long</em> = use Kspace long-range summation for the Coulombic term 1/r
-  <em>off</em> = omit the Coulombic term
+<em>off</em> = omit the Coulombic term
 </pre>
 <ul class="simple">
 <li>cutoff = global cutoff for Buckingham (and Coulombic if only 1 cutoff) (distance units)</li>
 <li>cutoff2 = global cutoff for Coulombic (optional) (distance units)</li>
 </ul>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>pair_style buck/long/coul/long cut off 2.5
 pair_style buck/long/coul/long cut long 2.5 4.0
 pair_style buck/long/coul/long long long 4.0
 pair_coeff * * 1 1
 pair_coeff 1 1 1 3 4
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>The <em>buck/long/coul/long</em> style computes a Buckingham potential (exp/6
 instead of Lennard-Jones 12/6) and Coulombic potential, given by</p>
 <img alt="_images/pair_buck.jpg" class="align-center" src="_images/pair_buck.jpg" />
 <img alt="_images/pair_coulomb.jpg" class="align-center" src="_images/pair_coulomb.jpg" />
 <p>Rc is the cutoff.  If one cutoff is specified in the pair_style
 command, it is used for both the Buckingham and Coulombic terms.  If
 two cutoffs are specified, they are used as cutoffs for the Buckingham
 and Coulombic terms respectively.</p>
 <p>The purpose of this pair style is to capture long-range interactions
 resulting from both attractive 1/r^6 Buckingham and Coulombic 1/r
 interactions.  This is done by use of the <em>flag_buck</em> and <em>flag_coul</em>
 settings.  The &#8220;<a class="reference internal" href="#ismail"><span>Ismail</span></a> paper has more details on when it is
 appropriate to include long-range 1/r^6 interactions, using this
 potential.</p>
 <p>If <em>flag_buck</em> is set to <em>long</em>, no cutoff is used on the Buckingham
 1/r^6 dispersion term.  The long-range portion can be calculated by
 using the <a class="reference internal" href="kspace_style.html"><em>kspace_style ewald/disp or pppm/disp</em></a>
 commands.  The specified Buckingham cutoff then determines which
 portion of the Buckingham interactions are computed directly by the
 pair potential versus which part is computed in reciprocal space via
 the Kspace style.  If <em>flag_buck</em> is set to <em>cut</em>, the Buckingham
 interactions are simply cutoff, as with <a class="reference internal" href="pair_buck.html"><em>pair_style buck</em></a>.</p>
 <p>If <em>flag_coul</em> is set to <em>long</em>, no cutoff is used on the Coulombic
 interactions.  The long-range portion can calculated by using any of
 several <a class="reference internal" href="kspace_style.html"><em>kspace_style</em></a> command options such as
 <em>pppm</em> or <em>ewald</em>.  Note that if <em>flag_buck</em> is also set to long, then
 the <em>ewald/disp</em> or <em>pppm/disp</em> Kspace style needs to be used to
 perform the long-range calculations for both the Buckingham and
 Coulombic interactions.  If <em>flag_coul</em> is set to <em>off</em>, Coulombic
 interactions are not computed.</p>
 <p>The following coefficients must be defined for each pair of atoms
 types via the <a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a> command as in the examples
 above, or in the data file or restart files read by the
 <a class="reference internal" href="read_data.html"><em>read_data</em></a> or <a class="reference internal" href="read_restart.html"><em>read_restart</em></a>
 commands:</p>
 <ul class="simple">
 <li>A (energy units)</li>
 <li>rho (distance units)</li>
 <li>C (energy-distance^6 units)</li>
 <li>cutoff (distance units)</li>
 <li>cutoff2 (distance units)</li>
 </ul>
 <p>The second coefficient, rho, must be greater than zero.</p>
 <p>The latter 2 coefficients are optional.  If not specified, the global
 Buckingham and Coulombic cutoffs specified in the pair_style command
 are used.  If only one cutoff is specified, it is used as the cutoff
 for both Buckingham and Coulombic interactions for this type pair.  If
 both coefficients are specified, they are used as the Buckingham and
 Coulombic cutoffs for this type pair.  Note that if you are using
 <em>flag_buck</em> set to <em>long</em>, you cannot specify a Buckingham cutoff for
 an atom type pair, since only one global Buckingham cutoff is allowed.
 Similarly, if you are using <em>flag_coul</em> set to <em>long</em>, you cannot
 specify a Coulombic cutoff for an atom type pair, since only one
 global Coulombic cutoff is allowed.</p>
 <hr class="docutils" />
 <p>Styles with a <em>cuda</em>, <em>gpu</em>, <em>intel</em>, <em>kk</em>, <em>omp</em>, or <em>opt</em> suffix are
 functionally the same as the corresponding style without the suffix.
 They have been optimized to run faster, depending on your available
 hardware, as discussed in <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a>
 of the manual.  The accelerated styles take the same arguments and
 should produce the same results, except for round-off and precision
 issues.</p>
 <p>These accelerated styles are part of the USER-CUDA, GPU, USER-INTEL,
 KOKKOS, USER-OMP and OPT packages, respectively.  They are only
 enabled if LAMMPS was built with those packages.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 <p>You can specify the accelerated styles explicitly in your input script
 by including their suffix, or you can use the <a class="reference internal" href="Section_start.html#start-7"><span>-suffix command-line switch</span></a> when you invoke LAMMPS, or you can
 use the <a class="reference internal" href="suffix.html"><em>suffix</em></a> command in your input script.</p>
 <p>See <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a> of the manual for
 more instructions on how to use the accelerated styles effectively.</p>
 <hr class="docutils" />
 <p><strong>Mixing, shift, table, tail correction, restart, rRESPA info</strong>:</p>
 <p>This pair styles does not support mixing.  Thus, coefficients for all
 I,J pairs must be specified explicitly.</p>
 <p>This pair style supports the <a class="reference internal" href="pair_modify.html"><em>pair_modify</em></a> shift
 option for the energy of the exp() and 1/r^6 portion of the pair
 interaction, assuming <em>flag_buck</em> is <em>cut</em>.</p>
 <p>This pair style does not support the <a class="reference internal" href="pair_modify.html"><em>pair_modify</em></a>
 shift option for the energy of the Buckingham portion of the pair
 interaction.</p>
 <p>This pair style supports the <a class="reference internal" href="pair_modify.html"><em>pair_modify</em></a> table and
 table/disp options since they can tabulate the short-range portion of
 the long-range Coulombic and dispersion interactions.</p>
 <p>This pair style write its information to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>, so pair_style and pair_coeff commands do not need
 to be specified in an input script that reads a restart file.</p>
 <p>This pair style supports the use of the <em>inner</em>, <em>middle</em>, and <em>outer</em>
 keywords of the <a class="reference internal" href="run_style.html"><em>run_style respa</em></a> command, meaning the
 pairwise forces can be partitioned by distance at different levels of
 the rRESPA hierarchy.  See the <a class="reference internal" href="run_style.html"><em>run_style</em></a> command for
 details.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>This style is part of the KSPACE package.  It is only enabled if
 LAMMPS was built with that package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.  Note that
 the KSPACE package is installed by default.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a></p>
 <p><strong>Default:</strong> none</p>
 <hr class="docutils" />
 <p id="ismail"><strong>(Ismail)</strong> Ismail, Tsige, In &#8216;t Veld, Grest, Molecular Physics
 (accepted) (2007).</p>
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   <div class="section" id="pair-style-lj-charmm-coul-charmm-command">
 <span id="index-0"></span><h1>pair_style lj/charmm/coul/charmm command<a class="headerlink" href="#pair-style-lj-charmm-coul-charmm-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-charmm-coul-charmm-cuda-command">
 <h1>pair_style lj/charmm/coul/charmm/cuda command<a class="headerlink" href="#pair-style-lj-charmm-coul-charmm-cuda-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-charmm-coul-charmm-omp-command">
 <h1>pair_style lj/charmm/coul/charmm/omp command<a class="headerlink" href="#pair-style-lj-charmm-coul-charmm-omp-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-charmm-coul-charmm-implicit-command">
 <h1>pair_style lj/charmm/coul/charmm/implicit command<a class="headerlink" href="#pair-style-lj-charmm-coul-charmm-implicit-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-charmm-coul-charmm-implicit-cuda-command">
 <h1>pair_style lj/charmm/coul/charmm/implicit/cuda command<a class="headerlink" href="#pair-style-lj-charmm-coul-charmm-implicit-cuda-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-charmm-coul-charmm-implicit-omp-command">
 <h1>pair_style lj/charmm/coul/charmm/implicit/omp command<a class="headerlink" href="#pair-style-lj-charmm-coul-charmm-implicit-omp-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-charmm-coul-long-command">
 <h1>pair_style lj/charmm/coul/long command<a class="headerlink" href="#pair-style-lj-charmm-coul-long-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-charmm-coul-long-cuda-command">
 <h1>pair_style lj/charmm/coul/long/cuda command<a class="headerlink" href="#pair-style-lj-charmm-coul-long-cuda-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-charmm-coul-long-gpu-command">
 <h1>pair_style lj/charmm/coul/long/gpu command<a class="headerlink" href="#pair-style-lj-charmm-coul-long-gpu-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-charmm-coul-long-intel-command">
 <h1>pair_style lj/charmm/coul/long/intel command<a class="headerlink" href="#pair-style-lj-charmm-coul-long-intel-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-charmm-coul-long-opt-command">
 <h1>pair_style lj/charmm/coul/long/opt command<a class="headerlink" href="#pair-style-lj-charmm-coul-long-opt-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-charmm-coul-long-omp-command">
 <h1>pair_style lj/charmm/coul/long/omp command<a class="headerlink" href="#pair-style-lj-charmm-coul-long-omp-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-charmm-coul-msm-command">
 <h1>pair_style lj/charmm/coul/msm command<a class="headerlink" href="#pair-style-lj-charmm-coul-msm-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-charmm-coul-msm-omp-command">
 <h1>pair_style lj/charmm/coul/msm/omp command<a class="headerlink" href="#pair-style-lj-charmm-coul-msm-omp-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>pair_style style args
 </pre></div>
 </div>
 <ul class="simple">
 <li>style = <em>lj/charmm/coul/charmm</em> or <em>lj/charmm/coul/charmm/implicit</em> or <em>lj/charmm/coul/long</em> or <em>lj/charmm/coul/msm</em></li>
 <li>args = list of arguments for a particular style</li>
 </ul>
 <pre class="literal-block">
 <em>lj/charmm/coul/charmm</em> args = inner outer (inner2) (outer2)
-    inner, outer = global switching cutoffs for Lennard Jones (and Coulombic if only 2 args)
-    inner2, outer2 = global switching cutoffs for Coulombic (optional)
-  <em>lj/charmm/coul/charmm/implicit</em> args = inner outer (inner2) (outer2)
-    inner, outer = global switching cutoffs for LJ (and Coulombic if only 2 args)
-    inner2, outer2 = global switching cutoffs for Coulombic (optional)
-  <em>lj/charmm/coul/long</em> args = inner outer (cutoff)
-    inner, outer = global switching cutoffs for LJ (and Coulombic if only 2 args)
-    cutoff = global cutoff for Coulombic (optional, outer is Coulombic cutoff if only 2 args)
-  <em>lj/charmm/coul/msm</em> args = inner outer (cutoff)
-    inner, outer = global switching cutoffs for LJ (and Coulombic if only 2 args)
-    cutoff = global cutoff for Coulombic (optional, outer is Coulombic cutoff if only 2 args)
+  inner, outer = global switching cutoffs for Lennard Jones (and Coulombic if only 2 args)
+  inner2, outer2 = global switching cutoffs for Coulombic (optional)
+<em>lj/charmm/coul/charmm/implicit</em> args = inner outer (inner2) (outer2)
+  inner, outer = global switching cutoffs for LJ (and Coulombic if only 2 args)
+  inner2, outer2 = global switching cutoffs for Coulombic (optional)
+<em>lj/charmm/coul/long</em> args = inner outer (cutoff)
+  inner, outer = global switching cutoffs for LJ (and Coulombic if only 2 args)
+  cutoff = global cutoff for Coulombic (optional, outer is Coulombic cutoff if only 2 args)
+<em>lj/charmm/coul/msm</em> args = inner outer (cutoff)
+  inner, outer = global switching cutoffs for LJ (and Coulombic if only 2 args)
+  cutoff = global cutoff for Coulombic (optional, outer is Coulombic cutoff if only 2 args)
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>pair_style lj/charmm/coul/charmm 8.0 10.0
 pair_style lj/charmm/coul/charmm 8.0 10.0 7.0 9.0
 pair_coeff * * 100.0 2.0
 pair_coeff 1 1 100.0 2.0 150.0 3.5
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>pair_style lj/charmm/coul/charmm/implicit 8.0 10.0
 pair_style lj/charmm/coul/charmm/implicit 8.0 10.0 7.0 9.0
 pair_coeff * * 100.0 2.0
 pair_coeff 1 1 100.0 2.0 150.0 3.5
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>pair_style lj/charmm/coul/long 8.0 10.0
 pair_style lj/charmm/coul/long 8.0 10.0 9.0
 pair_coeff * * 100.0 2.0
 pair_coeff 1 1 100.0 2.0 150.0 3.5
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>pair_style lj/charmm/coul/msm 8.0 10.0
 pair_style lj/charmm/coul/msm 8.0 10.0 9.0
 pair_coeff * * 100.0 2.0
 pair_coeff 1 1 100.0 2.0 150.0 3.5
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>The <em>lj/charmm</em> styles compute LJ and Coulombic interactions with an
 additional switching function S(r) that ramps the energy and force
 smoothly to zero between an inner and outer cutoff.  It is a widely
 used potential in the <a class="reference external" href="http://www.scripps.edu/brooks">CHARMM</a> MD code.
 See <a class="reference internal" href="special_bonds.html#mackerell"><span>(MacKerell)</span></a> for a description of the CHARMM force
 field.</p>
 <img alt="_images/pair_charmm.jpg" class="align-center" src="_images/pair_charmm.jpg" />
 <p>Both the LJ and Coulombic terms require an inner and outer cutoff.
 They can be the same for both formulas or different depending on
 whether 2 or 4 arguments are used in the pair_style command.  In each
 case, the inner cutoff distance must be less than the outer cutoff.
 It it typical to make the difference between the 2 cutoffs about 1.0
 Angstrom.</p>
 <p>Style <em>lj/charmm/coul/charmm/implicit</em> computes the same formulas as
 style <em>lj/charmm/coul/charmm</em> except that an additional 1/r term is
 included in the Coulombic formula.  The Coulombic energy thus varies
 as 1/r^2.  This is effectively a distance-dependent dielectric term
 which is a simple model for an implicit solvent with additional
 screening.  It is designed for use in a simulation of an unsolvated
 biomolecule (no explicit water molecules).</p>
 <p>Styles <em>lj/charmm/coul/long</em> and <em>lj/charmm/coul/msm</em> compute the same
 formulas as style <em>lj/charmm/coul/charmm</em> except that an additional
 damping factor is applied to the Coulombic term, as described for the
 <a class="reference internal" href="pair_lj.html"><em>lj/cut</em></a> pair styles.  Only one Coulombic cutoff is
 specified for <em>lj/charmm/coul/long</em> and <em>lj/charmm/coul/msm</em>; if only
 2 arguments are used in the pair_style command, then the outer LJ
 cutoff is used as the single Coulombic cutoff.</p>
 <p>The following coefficients must be defined for each pair of atoms
 types via the <a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a> command as in the examples
 above, or in the data file or restart files read by the
 <a class="reference internal" href="read_data.html"><em>read_data</em></a> or <a class="reference internal" href="read_restart.html"><em>read_restart</em></a>
 commands, or by mixing as described below:</p>
 <ul class="simple">
 <li>epsilon (energy units)</li>
 <li>sigma (distance units)</li>
 <li>epsilon_14 (energy units)</li>
 <li>sigma_14 (distance units)</li>
 </ul>
 <p>Note that sigma is defined in the LJ formula as the zero-crossing
 distance for the potential, not as the energy minimum at 2^(1/6)
 sigma.</p>
 <p>The latter 2 coefficients are optional.  If they are specified, they
 are used in the LJ formula between 2 atoms of these types which are
 also first and fourth atoms in any dihedral.  No cutoffs are specified
 because this CHARMM force field does not allow varying cutoffs for
 individual atom pairs; all pairs use the global cutoff(s) specified in
 the pair_style command.</p>
 <hr class="docutils" />
 <p>Styles with a <em>cuda</em>, <em>gpu</em>, <em>intel</em>, <em>kk</em>, <em>omp</em>, or <em>opt</em> suffix are
 functionally the same as the corresponding style without the suffix.
 They have been optimized to run faster, depending on your available
 hardware, as discussed in <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a>
 of the manual.  The accelerated styles take the same arguments and
 should produce the same results, except for round-off and precision
 issues.</p>
 <p>These accelerated styles are part of the USER-CUDA, GPU, USER-INTEL,
 KOKKOS, USER-OMP and OPT packages, respectively.  They are only
 enabled if LAMMPS was built with those packages.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 <p>You can specify the accelerated styles explicitly in your input script
 by including their suffix, or you can use the <a class="reference internal" href="Section_start.html#start-7"><span>-suffix command-line switch</span></a> when you invoke LAMMPS, or you can
 use the <a class="reference internal" href="suffix.html"><em>suffix</em></a> command in your input script.</p>
 <p>See <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a> of the manual for
 more instructions on how to use the accelerated styles effectively.</p>
 <hr class="docutils" />
 <p><strong>Mixing, shift, table, tail correction, restart, rRESPA info</strong>:</p>
 <p>For atom type pairs I,J and I != J, the epsilon, sigma, epsilon_14,
 and sigma_14 coefficients for all of the lj/charmm pair styles can be
 mixed.  The default mix value is <em>arithmetic</em> to coincide with the
 usual settings for the CHARMM force field.  See the &#8220;pair_modify&#8221;
 command for details.</p>
 <p>None of the lj/charmm pair styles support the
 <a class="reference internal" href="pair_modify.html"><em>pair_modify</em></a> shift option, since the Lennard-Jones
 portion of the pair interaction is smoothed to 0.0 at the cutoff.</p>
 <p>The <em>lj/charmm/coul/long</em> style supports the
 <a class="reference internal" href="pair_modify.html"><em>pair_modify</em></a> table option since it can tabulate the
 short-range portion of the long-range Coulombic interaction.</p>
 <p>None of the lj/charmm pair styles support the
 <a class="reference internal" href="pair_modify.html"><em>pair_modify</em></a> tail option for adding long-range tail
 corrections to energy and pressure, since the Lennard-Jones portion of
 the pair interaction is smoothed to 0.0 at the cutoff.</p>
 <p>All of the lj/charmm pair styles write their information to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>, so pair_style and pair_coeff commands do
 not need to be specified in an input script that reads a restart file.</p>
 <p>The lj/charmm/coul/long pair style supports the use of the <em>inner</em>,
 <em>middle</em>, and <em>outer</em> keywords of the <a class="reference internal" href="run_style.html"><em>run_style respa</em></a>
 command, meaning the pairwise forces can be partitioned by distance at
 different levels of the rRESPA hierarchy.  The other styles only
 support the <em>pair</em> keyword of run_style respa.  See the
 <a class="reference internal" href="run_style.html"><em>run_style</em></a> command for details.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>The <em>lj/charmm/coul/charmm</em> and <em>lj/charmm/coul/charmm/implicit</em>
 styles are part of the MOLECULE package.  The <em>lj/charmm/coul/long</em>
 style is part of the KSPACE package.  They are only enabled if LAMMPS
 was built with those packages.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.  Note that
 the MOLECULE and KSPACE packages are installed by default.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a></p>
 <p><strong>Default:</strong> none</p>
 <hr class="docutils" />
 <p id="mackerell"><strong>(MacKerell)</strong> MacKerell, Bashford, Bellott, Dunbrack, Evanseck, Field,
 Fischer, Gao, Guo, Ha, et al, J Phys Chem, 102, 3586 (1998).</p>
 </div>
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   <div class="section" id="pair-style-lj-class2-command">
 <span id="index-0"></span><h1>pair_style lj/class2 command<a class="headerlink" href="#pair-style-lj-class2-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-class2-cuda-command">
 <h1>pair_style lj/class2/cuda command<a class="headerlink" href="#pair-style-lj-class2-cuda-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-class2-gpu-command">
 <h1>pair_style lj/class2/gpu command<a class="headerlink" href="#pair-style-lj-class2-gpu-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-class2-kk-command">
 <h1>pair_style lj/class2/kk command<a class="headerlink" href="#pair-style-lj-class2-kk-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-class2-omp-command">
 <h1>pair_style lj/class2/omp command<a class="headerlink" href="#pair-style-lj-class2-omp-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-class2-coul-cut-command">
 <h1>pair_style lj/class2/coul/cut command<a class="headerlink" href="#pair-style-lj-class2-coul-cut-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-class2-coul-cut-cuda-command">
 <h1>pair_style lj/class2/coul/cut/cuda command<a class="headerlink" href="#pair-style-lj-class2-coul-cut-cuda-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-class2-coul-cut-kk-command">
 <h1>pair_style lj/class2/coul/cut/kk command<a class="headerlink" href="#pair-style-lj-class2-coul-cut-kk-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-class2-coul-cut-omp-command">
 <h1>pair_style lj/class2/coul/cut/omp command<a class="headerlink" href="#pair-style-lj-class2-coul-cut-omp-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-class2-coul-long-command">
 <h1>pair_style lj/class2/coul/long command<a class="headerlink" href="#pair-style-lj-class2-coul-long-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-class2-coul-long-cuda-command">
 <h1>pair_style lj/class2/coul/long/cuda command<a class="headerlink" href="#pair-style-lj-class2-coul-long-cuda-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-class2-coul-long-gpu-command">
 <h1>pair_style lj/class2/coul/long/gpu command<a class="headerlink" href="#pair-style-lj-class2-coul-long-gpu-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-class2-coul-long-kk-command">
 <h1>pair_style lj/class2/coul/long/kk command<a class="headerlink" href="#pair-style-lj-class2-coul-long-kk-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-class2-coul-long-omp-command">
 <h1>pair_style lj/class2/coul/long/omp command<a class="headerlink" href="#pair-style-lj-class2-coul-long-omp-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>pair_style style args
 </pre></div>
 </div>
 <ul class="simple">
 <li>style = <em>lj/class2</em> or <em>lj/class2/coul/cut</em> or <em>lj/class2/coul/long</em></li>
 <li>args = list of arguments for a particular style</li>
 </ul>
 <pre class="literal-block">
 <em>lj/class2</em> args = cutoff
-    cutoff = global cutoff for class 2 interactions (distance units)
-  <em>lj/class2/coul/cut</em> args = cutoff (cutoff2)
-    cutoff = global cutoff for class 2 (and Coulombic if only 1 arg) (distance units)
-    cutoff2 = global cutoff for Coulombic (optional) (distance units)
-  <em>lj/class2/coul/long</em> args = cutoff (cutoff2)
-    cutoff = global cutoff for class 2 (and Coulombic if only 1 arg) (distance units)
-    cutoff2 = global cutoff for Coulombic (optional) (distance units)
+  cutoff = global cutoff for class 2 interactions (distance units)
+<em>lj/class2/coul/cut</em> args = cutoff (cutoff2)
+  cutoff = global cutoff for class 2 (and Coulombic if only 1 arg) (distance units)
+  cutoff2 = global cutoff for Coulombic (optional) (distance units)
+<em>lj/class2/coul/long</em> args = cutoff (cutoff2)
+  cutoff = global cutoff for class 2 (and Coulombic if only 1 arg) (distance units)
+  cutoff2 = global cutoff for Coulombic (optional) (distance units)
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>pair_style lj/class2 10.0
 pair_coeff * * 100.0 2.5
 pair_coeff 1 2* 100.0 2.5 9.0
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>pair_style lj/class2/coul/cut 10.0
 pair_style lj/class2/coul/cut 10.0 8.0
 pair_coeff * * 100.0 3.0
 pair_coeff 1 1 100.0 3.5 9.0
 pair_coeff 1 1 100.0 3.5 9.0 9.0
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>pair_style lj/class2/coul/long 10.0
 pair_style lj/class2/coul/long 10.0 8.0
 pair_coeff * * 100.0 3.0
 pair_coeff 1 1 100.0 3.5 9.0
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>The <em>lj/class2</em> styles compute a 6/9 Lennard-Jones potential given by</p>
 <img alt="_images/pair_class2.jpg" class="align-center" src="_images/pair_class2.jpg" />
 <p>Rc is the cutoff.</p>
 <p>The <em>lj/class2/coul/cut</em> and <em>lj/class2/coul/long</em> styles add a
 Coulombic term as described for the <a class="reference internal" href="pair_lj.html"><em>lj/cut</em></a> pair styles.</p>
 <p>See <a class="reference internal" href="pair_modify.html#sun"><span>(Sun)</span></a> for a description of the COMPASS class2 force field.</p>
 <p>The following coefficients must be defined for each pair of atoms
 types via the <a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a> command as in the examples
 above, or in the data file or restart files read by the
 <a class="reference internal" href="read_data.html"><em>read_data</em></a> or <a class="reference internal" href="read_restart.html"><em>read_restart</em></a>
 commands, or by mixing as described below:</p>
 <ul class="simple">
 <li>epsilon (energy units)</li>
 <li>sigma (distance units)</li>
 <li>cutoff1 (distance units)</li>
 <li>cutoff2 (distance units)</li>
 </ul>
 <p>The latter 2 coefficients are optional.  If not specified, the global
 class 2 and Coulombic cutoffs are used.  If only one cutoff is
 specified, it is used as the cutoff for both class 2 and Coulombic
 interactions for this type pair.  If both coefficients are specified,
 they are used as the class 2 and Coulombic cutoffs for this type pair.
 You cannot specify 2 cutoffs for style <em>lj/class2</em>, since it has no
 Coulombic terms.</p>
 <p>For <em>lj/class2/coul/long</em> only the class 2 cutoff can be specified
 since a Coulombic cutoff cannot be specified for an individual I,J
 type pair.  All type pairs use the same global Coulombic cutoff
 specified in the pair_style command.</p>
 <hr class="docutils" />
 <p>If the pair_coeff command is not used to define coefficients for a
 particular I != J type pair, the mixing rule for epsilon and sigma for
 all class2 potentials is to use the <em>sixthpower</em> formulas documented
 by the <a class="reference internal" href="pair_modify.html"><em>pair_modify</em></a> command.  The <a class="reference internal" href="pair_modify.html"><em>pair_modify mix</em></a> setting is thus ignored for class2 potentials
 for epsilon and sigma.  However it is still followed for mixing the
 cutoff distance.</p>
 <hr class="docutils" />
 <p>Styles with a <em>cuda</em>, <em>gpu</em>, <em>intel</em>, <em>kk</em>, <em>omp</em>, or <em>opt</em> suffix are
 functionally the same as the corresponding style without the suffix.
 They have been optimized to run faster, depending on your available
 hardware, as discussed in <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a>
 of the manual.  The accelerated styles take the same arguments and
 should produce the same results, except for round-off and precision
 issues.</p>
 <p>These accelerated styles are part of the USER-CUDA, GPU, USER-INTEL,
 KOKKOS, USER-OMP and OPT packages, respectively.  They are only
 enabled if LAMMPS was built with those packages.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 <p>You can specify the accelerated styles explicitly in your input script
 by including their suffix, or you can use the <a class="reference internal" href="Section_start.html#start-7"><span>-suffix command-line switch</span></a> when you invoke LAMMPS, or you can
 use the <a class="reference internal" href="suffix.html"><em>suffix</em></a> command in your input script.</p>
 <p>See <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a> of the manual for
 more instructions on how to use the accelerated styles effectively.</p>
 <hr class="docutils" />
 <p><strong>Mixing, shift, table, tail correction, restart, rRESPA info</strong>:</p>
 <p>For atom type pairs I,J and I != J, the epsilon and sigma coefficients
 and cutoff distance for all of the lj/class2 pair styles can be mixed.
 Epsilon and sigma are always mixed with the value <em>sixthpower</em>.  The
 cutoff distance is mixed by whatever option is set by the pair_modify
 command (default = geometric).  See the &#8220;pair_modify&#8221; command for
 details.</p>
 <p>All of the lj/class2 pair styles support the
 <a class="reference internal" href="pair_modify.html"><em>pair_modify</em></a> shift option for the energy of the
 Lennard-Jones portion of the pair interaction.</p>
 <p>The <em>lj/class2/coul/long</em> pair style does not support the
 <a class="reference internal" href="pair_modify.html"><em>pair_modify</em></a> table option since a tabulation
 capability has not yet been added to this potential.</p>
 <p>All of the lj/class2 pair styles support the
 <a class="reference internal" href="pair_modify.html"><em>pair_modify</em></a> tail option for adding a long-range
 tail correction to the energy and pressure of the Lennard-Jones
 portion of the pair interaction.</p>
 <p>All of the lj/class2 pair styles write their information to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>, so pair_style and pair_coeff commands do
 not need to be specified in an input script that reads a restart file.</p>
 <p>All of the lj/class2 pair styles can only be used via the <em>pair</em>
 keyword of the <a class="reference internal" href="run_style.html"><em>run_style respa</em></a> command.  They do not
 support the <em>inner</em>, <em>middle</em>, <em>outer</em> keywords.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>These styles are part of the CLASS2 package.  They are only enabled if
 LAMMPS was built with that package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a></p>
 <p><strong>Default:</strong> none</p>
 <hr class="docutils" />
 <p id="sun"><strong>(Sun)</strong> Sun, J Phys Chem B 102, 7338-7364 (1998).</p>
 </div>
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   <div class="section" id="pair-style-born-coul-long-cs-command">
 <span id="index-0"></span><h1>pair_style born/coul/long/cs command<a class="headerlink" href="#pair-style-born-coul-long-cs-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-buck-coul-long-cs-command">
 <h1>pair_style buck/coul/long/cs command<a class="headerlink" href="#pair-style-buck-coul-long-cs-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>pair_style style args
 </pre></div>
 </div>
 <ul class="simple">
 <li>style = <em>born/coul/long/cs</em> or <em>buck/coul/long/cs</em></li>
 <li>args = list of arguments for a particular style</li>
 </ul>
 <pre class="literal-block">
 <em>born/coul/long/cs</em> args = cutoff (cutoff2)
-    cutoff = global cutoff for non-Coulombic (and Coulombic if only 1 arg) (distance units)
-    cutoff2 = global cutoff for Coulombic (optional) (distance units)
-  <em>buck/coul/long/cs</em> args = cutoff (cutoff2)
-    cutoff = global cutoff for Buckingham (and Coulombic if only 1 arg) (distance units)
-    cutoff2 = global cutoff for Coulombic (optional) (distance units)
+  cutoff = global cutoff for non-Coulombic (and Coulombic if only 1 arg) (distance units)
+  cutoff2 = global cutoff for Coulombic (optional) (distance units)
+<em>buck/coul/long/cs</em> args = cutoff (cutoff2)
+  cutoff = global cutoff for Buckingham (and Coulombic if only 1 arg) (distance units)
+  cutoff2 = global cutoff for Coulombic (optional) (distance units)
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>pair_style born/coul/long/cs 10.0 8.0
 pair_coeff 1 1 6.08 0.317 2.340 24.18 11.51
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>pair_style buck/coul/long/cs 10.0
 pair_style buck/coul/long/cs 10.0 8.0
 pair_coeff * * 100.0 1.5 200.0
 pair_coeff 1 1 100.0 1.5 200.0 9.0
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>These pair styles are designed to be used with the adiabatic
 core/shell model of <a class="reference internal" href="#mitchellfinchham"><span>(Mitchell and Finchham)</span></a>.  See
 <a class="reference internal" href="Section_howto.html#howto-25"><span>Section_howto 25</span></a> of the manual for an
 overview of the model as implemented in LAMMPS.</p>
 <p>These pair styles are identical to the <a class="reference internal" href="pair_born.html"><em>pair_style born/coul/long</em></a> and <a class="reference internal" href="pair_buck.html"><em>pair_style buck/coul/long</em></a> styles, except they correctly treat the
 special case where the distance between two charged core and shell
 atoms in the same core/shell pair approach r = 0.0.  This needs
 special treatment when a long-range solver for Coulombic interactions
 is also used, i.e. via the <a class="reference internal" href="kspace_style.html"><em>kspace_style</em></a> command.</p>
 <p>More specifically, the short-range Coulomb interaction between a core
 and its shell should be turned off using the
 <a class="reference internal" href="special_bonds.html"><em>special_bonds</em></a> command by setting the 1-2 weight
 to 0.0, which works because the core and shell atoms are bonded to
 each other.  This induces a long-range correction approximation which
 fails at small distances (~&lt; 10e-8). Therefore, the Coulomb term which
 is used to calculate the correction factor is extended by a minimal
 distance (r_min = 1.0-6) when the interaction between a core/shell
 pair is treated, as follows</p>
 <img alt="_images/pair_cs.jpg" class="align-center" src="_images/pair_cs.jpg" />
 <p>where C is an energy-conversion constant, Qi and Qj are the charges on
 the core and shell, epsilon is the dielectric constant and r_min is the
 minimal distance.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>These pair styles are part of the CORESHELL package.  They are only
 enabled if LAMMPS was built with that package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a>, <a class="reference internal" href="pair_born.html"><em>pair_style born</em></a>,
 <a class="reference internal" href="pair_buck.html"><em>pair_style buck</em></a></p>
 <p><strong>Default:</strong> none</p>
 <hr class="docutils" />
 <p id="mitchellfinchham"><strong>(Mitchell and Finchham)</strong> Mitchell, Finchham, J Phys Condensed Matter,
 5, 1031-1038 (1993).</p>
 </div>
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   <div class="section" id="pair-style-lj-cut-dipole-cut-command">
 <span id="index-0"></span><h1>pair_style lj/cut/dipole/cut command<a class="headerlink" href="#pair-style-lj-cut-dipole-cut-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-cut-dipole-cut-gpu-command">
 <h1>pair_style lj/cut/dipole/cut/gpu command<a class="headerlink" href="#pair-style-lj-cut-dipole-cut-gpu-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-cut-dipole-cut-omp-command">
 <h1>pair_style lj/cut/dipole/cut/omp command<a class="headerlink" href="#pair-style-lj-cut-dipole-cut-omp-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-sf-dipole-sf-command">
 <h1>pair_style lj/sf/dipole/sf command<a class="headerlink" href="#pair-style-lj-sf-dipole-sf-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-sf-dipole-sf-gpu-command">
 <h1>pair_style lj/sf/dipole/sf/gpu command<a class="headerlink" href="#pair-style-lj-sf-dipole-sf-gpu-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-sf-dipole-sf-omp-command">
 <h1>pair_style lj/sf/dipole/sf/omp command<a class="headerlink" href="#pair-style-lj-sf-dipole-sf-omp-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-cut-dipole-long-command">
 <h1>pair_style lj/cut/dipole/long command<a class="headerlink" href="#pair-style-lj-cut-dipole-long-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-long-dipole-long-command">
 <h1>pair_style lj/long/dipole/long command<a class="headerlink" href="#pair-style-lj-long-dipole-long-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>pair_style lj/cut/dipole/cut cutoff (cutoff2)
 pair_style lj/sf/dipole/sf cutoff (cutoff2)
 pair_style lj/cut/dipole/long cutoff (cutoff2)
 pair_style lj/long/dipole/long flag_lj flag_coul cutoff (cutoff2)
 </pre></div>
 </div>
 <ul class="simple">
 <li>cutoff = global cutoff LJ (and Coulombic if only 1 arg) (distance units)</li>
 <li>cutoff2 = global cutoff for Coulombic and dipole (optional) (distance units)</li>
 <li>flag_lj = <em>long</em> or <em>cut</em> or <em>off</em></li>
 </ul>
 <pre class="literal-block">
 <em>long</em> = use long-range damping on dispersion 1/r^6 term
-  <em>cut</em> = use a cutoff on dispersion 1/r^6 term
-  <em>off</em> = omit disperion 1/r^6 term entirely
+<em>cut</em> = use a cutoff on dispersion 1/r^6 term
+<em>off</em> = omit disperion 1/r^6 term entirely
 </pre>
 <ul class="simple">
 <li>flag_coul = <em>long</em> or <em>off</em></li>
 </ul>
 <pre class="literal-block">
 <em>long</em> = use long-range damping on Coulombic 1/r and point-dipole terms
-  <em>off</em> = omit Coulombic and point-dipole terms entirely
+<em>off</em> = omit Coulombic and point-dipole terms entirely
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>pair_style lj/cut/dipole/cut 10.0
 pair_coeff * * 1.0 1.0
 pair_coeff 2 3 1.0 1.0 2.5 4.0
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>pair_style lj/sf/dipole/sf 9.0
 pair_coeff * * 1.0 1.0
 pair_coeff 2 3 1.0 1.0 2.5 4.0
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>pair_style lj/cut/dipole/long 10.0
 pair_coeff * * 1.0 1.0
 pair_coeff 2 3 1.0 1.0 2.5 4.0
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>pair_style lj/long/dipole/long long long 3.5 10.0
 pair_coeff * * 1.0 1.0
 pair_coeff 2 3 1.0 1.0 2.5 4.0
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Style <em>lj/cut/dipole/cut</em> computes interactions between pairs of particles
 that each have a charge and/or a point dipole moment.  In addition to
 the usual Lennard-Jones interaction between the particles (Elj) the
 charge-charge (Eqq), charge-dipole (Eqp), and dipole-dipole (Epp)
 interactions are computed by these formulas for the energy (E), force
 (F), and torque (T) between particles I and J.</p>
 <img alt="_images/pair_dipole.jpg" class="align-center" src="_images/pair_dipole.jpg" />
 <p>where qi and qj are the charges on the two particles, pi and pj are
 the dipole moment vectors of the two particles, r is their separation
 distance, and the vector r = Ri - Rj is the separation vector between
 the two particles.  Note that Eqq and Fqq are simply Coulombic energy
 and force, Fij = -Fji as symmetric forces, and Tij != -Tji since the
 torques do not act symmetrically.  These formulas are discussed in
 <a class="reference internal" href="pair_gayberne.html#allen"><span>(Allen)</span></a> and in <a class="reference internal" href="#toukmaji"><span>(Toukmaji)</span></a>.</p>
 <p>Style <em>lj/sf/dipole/sf</em> computes &#8220;shifted-force&#8221; interactions between
 pairs of particles that each have a charge and/or a point dipole
 moment. In general, a shifted-force potential is a (sligthly) modified
 potential containing extra terms that make both the energy and its
 derivative go to zero at the cutoff distance; this removes
 (cutoff-related) problems in energy conservation and any numerical
 instability in the equations of motion <a class="reference internal" href="pair_gayberne.html#allen"><span>(Allen)</span></a>. Shifted-force
 interactions for the Lennard-Jones (E_LJ), charge-charge (Eqq),
 charge-dipole (Eqp), dipole-charge (Epq) and dipole-dipole (Epp)
 potentials are computed by these formulas for the energy (E), force
 (F), and torque (T) between particles I and J:</p>
 <img alt="_images/pair_dipole_sf.jpg" class="align-center" src="_images/pair_dipole_sf.jpg" />
 <img alt="_images/pair_dipole_sf2.jpg" class="align-center" src="_images/pair_dipole_sf2.jpg" />
 <p>where epsilon and sigma are the standard LJ parameters, r_c is the
 cutoff, qi and qj are the charges on the two particles, pi and pj are
 the dipole moment vectors of the two particles, r is their separation
 distance, and the vector r = Ri - Rj is the separation vector between
 the two particles.  Note that Eqq and Fqq are simply Coulombic energy
 and force, Fij = -Fji as symmetric forces, and Tij != -Tji since the
 torques do not act symmetrically.  The shifted-force formula for the
 Lennard-Jones potential is reported in <a class="reference internal" href="#stoddard"><span>(Stoddard)</span></a>.  The
 original (unshifted) formulas for the electrostatic potentials, forces
 and torques can be found in <a class="reference internal" href="#price"><span>(Price)</span></a>.  The shifted-force
 electrostatic potentials have been obtained by applying equation 5.13
 of <a class="reference internal" href="pair_gayberne.html#allen"><span>(Allen)</span></a>. The formulas for the corresponding forces and
 torques have been obtained by applying the &#8216;chain rule&#8217; as in appendix
 C.3 of <a class="reference internal" href="pair_gayberne.html#allen"><span>(Allen)</span></a>.</p>
 <p>If one cutoff is specified in the pair_style command, it is used for
 both the LJ and Coulombic (q,p) terms.  If two cutoffs are specified,
 they are used as cutoffs for the LJ and Coulombic (q,p) terms
 respectively.</p>
 <p>Style <em>lj/cut/dipole/long</em> computes long-range point-dipole
 interactions as discussed in <a class="reference internal" href="#toukmaji"><span>(Toukmaji)</span></a>. Dipole-dipole,
 dipole-charge, and charge-charge interactions are all supported, along
 with the standard 12/6 Lennard-Jones interactions, which are computed
 with a cutoff.  A <a class="reference internal" href="kspace_style.html"><em>kspace_style</em></a> must be defined to
 use this pair style.  Currently, only <a class="reference internal" href="kspace_style.html"><em>kspace_style ewald/disp</em></a> support long-range point-dipole
 interactions.</p>
 <p>Style <em>lj/long/dipole/long</em> also computes point-dipole interactions as
 discussed in <a class="reference internal" href="#toukmaji"><span>(Toukmaji)</span></a>. Long-range dipole-dipole,
 dipole-charge, and charge-charge interactions are all supported, along
 with the standard 12/6 Lennard-Jones interactions.  LJ interactions
 can be cutoff or long-ranged.</p>
 <p>For style <em>lj/long/dipole/long</em>, if <em>flag_lj</em> is set to <em>long</em>, no
 cutoff is used on the LJ 1/r^6 dispersion term.  The long-range
 portion is calculated by using the <a class="reference internal" href="kspace_style.html"><em>kspace_style ewald_disp</em></a> command.  The specified LJ cutoff then
 determines which portion of the LJ interactions are computed directly
 by the pair potential versus which part is computed in reciprocal
 space via the Kspace style.  If <em>flag_lj</em> is set to <em>cut</em>, the LJ
 interactions are simply cutoff, as with <a class="reference internal" href="pair_lj.html"><em>pair_style lj/cut</em></a>.  If <em>flag_lj</em> is set to <em>off</em>, LJ interactions
 are not computed at all.</p>
 <p>If <em>flag_coul</em> is set to <em>long</em>, no cutoff is used on the Coulombic or
 dipole interactions.  The long-range portion is calculated by using
 <em>ewald_disp</em> of the <a class="reference internal" href="kspace_style.html"><em>kspace_style</em></a> command. If
 <em>flag_coul</em> is set to <em>off</em>, Coulombic and dipole interactions are not
 computed at all.</p>
 <p>Atoms with dipole moments should be integrated using the <a class="reference internal" href="fix_nve_sphere.html"><em>fix nve/sphere update dipole</em></a> command to rotate the
 dipole moments.  The <em>omega</em> option on the <a class="reference internal" href="fix_langevin.html"><em>fix langevin</em></a> command can be used to thermostat the
 rotational motion.  The <a class="reference internal" href="compute_temp_sphere.html"><em>compute temp/sphere</em></a>
 command can be used to monitor the temperature, since it includes
 rotational degrees of freedom.  The <a class="reference internal" href="atom_style.html"><em>atom_style dipole</em></a> command should be used since it defines the
 point dipoles and their rotational state.  The magnitude of the dipole
 moment for each type of particle can be defined by the
 <code class="xref doc docutils literal"><span class="pre">dipole</span></code> command or in the &#8220;Dipoles&#8221; section of the data
 file read in by the <a class="reference internal" href="read_data.html"><em>read_data</em></a> command.  Their initial
 orientation can be defined by the <a class="reference internal" href="set.html"><em>set dipole</em></a> command or in
 the &#8220;Atoms&#8221; section of the data file.</p>
 <p>The following coefficients must be defined for each pair of atoms
 types via the <a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a> command as in the examples
 above, or in the data file or restart files read by the
 <a class="reference internal" href="read_data.html"><em>read_data</em></a> or <a class="reference internal" href="read_restart.html"><em>read_restart</em></a>
 commands, or by mixing as described below:</p>
 <ul class="simple">
 <li>epsilon (energy units)</li>
 <li>sigma (distance units)</li>
 <li>cutoff1 (distance units)</li>
 <li>cutoff2 (distance units)</li>
 </ul>
 <p>The latter 2 coefficients are optional.  If not specified, the global
 LJ and Coulombic cutoffs specified in the pair_style command are used.
 If only one cutoff is specified, it is used as the cutoff for both LJ
 and Coulombic interactions for this type pair.  If both coefficients
 are specified, they are used as the LJ and Coulombic cutoffs for this
 type pair.</p>
 <hr class="docutils" />
 <p>Styles with a <em>cuda</em>, <em>gpu</em>, <em>intel</em>, <em>kk</em>, <em>omp</em>, or <em>opt</em> suffix are
 functionally the same as the corresponding style without the suffix.
 They have been optimized to run faster, depending on your available
 hardware, as discussed in <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a>
 of the manual.  The accelerated styles take the same arguments and
 should produce the same results, except for round-off and precision
 issues.</p>
 <p>These accelerated styles are part of the USER-CUDA, GPU, USER-INTEL,
 KOKKOS, USER-OMP and OPT packages, respectively.  They are only
 enabled if LAMMPS was built with those packages.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 <p>You can specify the accelerated styles explicitly in your input script
 by including their suffix, or you can use the <a class="reference internal" href="Section_start.html#start-7"><span>-suffix command-line switch</span></a> when you invoke LAMMPS, or you can
 use the <a class="reference internal" href="suffix.html"><em>suffix</em></a> command in your input script.</p>
 <p>See <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a> of the manual for
 more instructions on how to use the accelerated styles effectively.</p>
 <hr class="docutils" />
 <p><strong>Mixing, shift, table, tail correction, restart, rRESPA info</strong>:</p>
 <p>For atom type pairs I,J and I != J, the epsilon and sigma coefficients
 and cutoff distances for this pair style can be mixed.  The default
 mix value is <em>geometric</em>.  See the &#8220;pair_modify&#8221; command for details.</p>
 <p>For atom type pairs I,J and I != J, the A, sigma, d1, and d2
 coefficients and cutoff distance for this pair style can be mixed.  A
 is an energy value mixed like a LJ epsilon.  D1 and d2 are distance
 values and are mixed like sigma.  The default mix value is
 <em>geometric</em>.  See the &#8220;pair_modify&#8221; command for details.</p>
 <p>This pair style does not support the <a class="reference internal" href="pair_modify.html"><em>pair_modify</em></a>
 shift option for the energy of the Lennard-Jones portion of the pair
 interaction; such energy goes to zero at the cutoff by construction.</p>
 <p>The <a class="reference internal" href="pair_modify.html"><em>pair_modify</em></a> table option is not relevant
 for this pair style.</p>
 <p>This pair style does not support the <a class="reference internal" href="pair_modify.html"><em>pair_modify</em></a>
 tail option for adding long-range tail corrections to energy and
 pressure.</p>
 <p>This pair style writes its information to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>, so pair_style and pair_coeff commands do not need
 to be specified in an input script that reads a restart file.</p>
 <p>This pair style can only be used via the <em>pair</em> keyword of the
 <a class="reference internal" href="run_style.html"><em>run_style respa</em></a> command.  It does not support the
 <em>inner</em>, <em>middle</em>, <em>outer</em> keywords.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>The <em>lj/cut/dipole/cut</em>, <em>lj/cut/dipole/long</em>, and
 <em>lj/long/dipole/long</em> styles are part of the DIPOLE package.  They are
 only enabled if LAMMPS was built with that package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 <p>The <em>lj/sf/dipole/sf</em> style is part of the USER-MISC package.  It is
 only enabled if LAMMPS was built with that package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 <p>Using dipole pair styles with <em>electron</em> <a class="reference internal" href="units.html"><em>units</em></a> is not
 currently supported.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a></p>
 <p><strong>Default:</strong> none</p>
 <hr class="docutils" />
 <p id="allen"><strong>(Allen)</strong> Allen and Tildesley, Computer Simulation of Liquids,
 Clarendon Press, Oxford, 1987.</p>
 <p id="toukmaji"><strong>(Toukmaji)</strong> Toukmaji, Sagui, Board, and Darden, J Chem Phys, 113,
 10913 (2000).</p>
 <p id="stoddard"><strong>(Stoddard)</strong> Stoddard and Ford, Phys Rev A, 8, 1504 (1973).</p>
 <p id="price"><strong>(Price)</strong> Price, Stone and Alderton, Mol Phys, 52, 987 (1984).</p>
 </div>
 </div>
 
 
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   <div class="section" id="pair-style-lj-gromacs-command">
 <span id="index-0"></span><h1>pair_style lj/gromacs command<a class="headerlink" href="#pair-style-lj-gromacs-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-gromacs-cuda-command">
 <h1>pair_style lj/gromacs/cuda command<a class="headerlink" href="#pair-style-lj-gromacs-cuda-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-gromacs-gpu-command">
 <h1>pair_style lj/gromacs/gpu command<a class="headerlink" href="#pair-style-lj-gromacs-gpu-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-gromacs-omp-command">
 <h1>pair_style lj/gromacs/omp command<a class="headerlink" href="#pair-style-lj-gromacs-omp-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-gromacs-coul-gromacs-command">
 <h1>pair_style lj/gromacs/coul/gromacs command<a class="headerlink" href="#pair-style-lj-gromacs-coul-gromacs-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-gromacs-coul-gromacs-cuda-command">
 <h1>pair_style lj/gromacs/coul/gromacs/cuda command<a class="headerlink" href="#pair-style-lj-gromacs-coul-gromacs-cuda-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-gromacs-coul-gromacs-omp-command">
 <h1>pair_style lj/gromacs/coul/gromacs/omp command<a class="headerlink" href="#pair-style-lj-gromacs-coul-gromacs-omp-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>pair_style style args
 </pre></div>
 </div>
 <ul class="simple">
 <li>style = <em>lj/gromacs</em> or <em>lj/gromacs/coul/gromacs</em></li>
 <li>args = list of arguments for a particular style</li>
 </ul>
 <pre class="literal-block">
 <em>lj/gromacs</em> args = inner outer
-    inner, outer = global switching cutoffs for Lennard Jones
-  <em>lj/gromacs/coul/gromacs</em> args = inner outer (inner2) (outer2)
-    inner, outer = global switching cutoffs for Lennard Jones (and Coulombic if only 2 args)
-    inner2, outer2 = global switching cutoffs for Coulombic (optional)
+  inner, outer = global switching cutoffs for Lennard Jones
+<em>lj/gromacs/coul/gromacs</em> args = inner outer (inner2) (outer2)
+  inner, outer = global switching cutoffs for Lennard Jones (and Coulombic if only 2 args)
+  inner2, outer2 = global switching cutoffs for Coulombic (optional)
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>pair_style lj/gromacs 9.0 12.0
 pair_coeff * * 100.0 2.0
 pair_coeff 2 2 100.0 2.0 8.0 10.0
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>pair_style lj/gromacs/coul/gromacs 9.0 12.0
 pair_style lj/gromacs/coul/gromacs 8.0 10.0 7.0 9.0
 pair_coeff * * 100.0 2.0
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>The <em>lj/gromacs</em> styles compute shifted LJ and Coulombic interactions
 with an additional switching function S(r) that ramps the energy and force
 smoothly to zero between an inner and outer cutoff.  It is a commonly
 used potential in the <a class="reference external" href="http://www.gromacs.org">GROMACS</a> MD code and for
 the coarse-grained models of <a class="reference internal" href="#marrink"><span>(Marrink)</span></a>.</p>
 <img alt="_images/pair_gromacs.jpg" class="align-center" src="_images/pair_gromacs.jpg" />
 <p>r1 is the inner cutoff; rc is the outer cutoff.  The coefficients A, B,
 and C are computed by LAMMPS to perform the shifting and smoothing.
 The function
 S(r) is actually applied once to each term of the LJ formula and once
 to the Coulombic formula, so there are 2 or 3 sets of A,B,C coefficients
 depending on which pair_style is used.  The boundary conditions
 applied to the smoothing function are as follows: S&#8217;(r1) = S&#8217;&#8216;(r1) = 0,
 S(rc) = -E(rc), S&#8217;(rc) = -E&#8217;(rc), and S&#8217;&#8216;(rc) = -E&#8217;&#8216;(rc),
 where E(r) is the corresponding term
 in the LJ or Coulombic potential energy function.
 Single and double primes denote first and second
 derivatives with respect to r, respectively.</p>
 <p>The inner and outer cutoff for the LJ and Coulombic terms can be the
 same or different depending on whether 2 or 4 arguments are used in
 the pair_style command.  The inner LJ cutoff must be &gt; 0, but the
 inner Coulombic cutoff can be &gt;= 0.</p>
 <p>The following coefficients must be defined for each pair of atoms
 types via the <a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a> command as in the examples
 above, or in the data file or restart files read by the
 <a class="reference internal" href="read_data.html"><em>read_data</em></a> or <a class="reference internal" href="read_restart.html"><em>read_restart</em></a>
 commands, or by mixing as described below:</p>
 <ul class="simple">
 <li>epsilon (energy units)</li>
 <li>sigma (distance units)</li>
 <li>inner (distance units)</li>
 <li>outer (distance units)</li>
 </ul>
 <p>Note that sigma is defined in the LJ formula as the zero-crossing
 distance for the potential, not as the energy minimum at 2^(1/6)
 sigma.</p>
 <p>The last 2 coefficients are optional inner and outer cutoffs for style
 <em>lj/gromacs</em>.  If not specified, the global <em>inner</em> and <em>outer</em> values
 are used.</p>
 <p>The last 2 coefficients cannot be used with style
 <em>lj/gromacs/coul/gromacs</em> because this force field does not allow
 varying cutoffs for individual atom pairs; all pairs use the global
 cutoff(s) specified in the pair_style command.</p>
 <hr class="docutils" />
 <p>Styles <em>intel</em>, <em>kk</em>, with a <em>cuda</em>, <em>gpu</em>, <em>omp</em>, or <em>opt</em> suffix are
 functionally the same as the corresponding style without the suffix.
 They have been optimized to run faster, depending on your available
 hardware, as discussed in <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a>
 of the manual.  The accelerated styles take the same arguments and
 should produce the same results, except for round-off and precision
 issues.</p>
 <p>These accelerated styles are part of the USER-CUDA, GPU, USER-INTEL,
 KOKKOS, USER-OMP and OPT packages, respectively.  They are only
 enabled if LAMMPS was built with those packages.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 <p>You can specify the accelerated styles explicitly in your input script
 by including their suffix, or you can use the <a class="reference internal" href="Section_start.html#start-7"><span>-suffix command-line switch</span></a> when you invoke LAMMPS, or you can
 use the <a class="reference internal" href="suffix.html"><em>suffix</em></a> command in your input script.</p>
 <p>See <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a> of the manual for
 more instructions on how to use the accelerated styles effectively.</p>
 <hr class="docutils" />
 <p><strong>Mixing, shift, table, tail correction, restart, rRESPA info</strong>:</p>
 <p>For atom type pairs I,J and I != J, the epsilon and sigma coefficients
 and cutoff distance for all of the lj/cut pair styles can be mixed.
 The default mix value is <em>geometric</em>.  See the &#8220;pair_modify&#8221; command
 for details.</p>
 <p>None of the GROMACS pair styles support the
 <a class="reference internal" href="pair_modify.html"><em>pair_modify</em></a> shift option, since the Lennard-Jones
 portion of the pair interaction is already smoothed to 0.0 at the
 cutoff.</p>
 <p>The <a class="reference internal" href="pair_modify.html"><em>pair_modify</em></a> table option is not relevant
 for this pair style.</p>
 <p>None of the GROMACS pair styles support the
 <a class="reference internal" href="pair_modify.html"><em>pair_modify</em></a> tail option for adding long-range tail
 corrections to energy and pressure, since there are no corrections for
 a potential that goes to 0.0 at the cutoff.</p>
 <p>All of the GROMACS pair styles write their information to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>, so pair_style and pair_coeff commands do
 not need to be specified in an input script that reads a restart file.</p>
 <p>All of the GROMACS pair styles can only be used via the <em>pair</em>
 keyword of the <a class="reference internal" href="run_style.html"><em>run_style respa</em></a> command.  They do not
 support the <em>inner</em>, <em>middle</em>, <em>outer</em> keywords.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <blockquote>
 <div>none</div></blockquote>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a></p>
 <p><strong>Default:</strong> none</p>
 <hr class="docutils" />
 <p id="marrink"><strong>(Marrink)</strong> Marrink, de Vries, Mark, J Phys Chem B, 108, 750-760 (2004).</p>
 </div>
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   <div class="section" id="pair-style-list-command">
 <span id="index-0"></span><h1>pair_style list command<a class="headerlink" href="#pair-style-list-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>pair_style list listfile cutoff keyword
 </pre></div>
 </div>
 <ul class="simple">
 <li>listfile = name of file with list of pairwise interactions</li>
 <li>cutoff = global cutoff (distance units)</li>
 <li>keyword = optional flag <em>nocheck</em> or <em>check</em> (default is <em>check</em>)</li>
 </ul>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>pair_style list restraints.txt 200.0
 pair_coeff * *
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>pair_style hybrid/overlay lj/cut 1.1225 list pair_list.txt 300.0
 pair_coeff * * lj/cut 1.0 1.0
 pair_coeff 3* 3* list
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Style <em>list</em> computes interactions between explicitly listed pairs of
 atoms with the option to select functional form and parameters for
 each individual pair.  Because the parameters are set in the list
 file, the pair_coeff command has no parameters (but still needs to be
 provided).  The <em>check</em> and <em>nocheck</em> keywords enable/disable a test
 that checks whether all listed bonds were present and computed.</p>
 <p>This pair style can be thought of as a hybrid between bonded,
 non-bonded, and restraint interactions.  It will typically be used as
 an additional interaction within the <em>hybrid/overlay</em> pair style.  It
 currently supports three interaction styles: a 12-6 Lennard-Jones, a
 Morse and a harmonic potential.</p>
 <p>The format of the list file is as follows:</p>
 <ul class="simple">
 <li>one line per pair of atoms</li>
 <li>empty lines will be ignored</li>
 <li>comment text starts with a &#8216;#&#8217; character</li>
 <li>line syntax: <em>ID1 ID2 style coeffs cutoff</em></li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>ID1 = atom ID of first atom
-  ID2 = atom ID of second atom
-  style = style of interaction
-  coeffs = list of coeffs
-  cutoff = cutoff for interaction (optional)
+ID2 = atom ID of second atom
+style = style of interaction
+coeffs = list of coeffs
+cutoff = cutoff for interaction (optional)
 </pre></div>
 </div>
 <p>The cutoff parameter is optional. If not specified, the global cutoff
 is used.</p>
 <p>Here is an example file:</p>
 <div class="highlight-python"><div class="highlight"><pre><span class="c"># this is a comment</span>
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>15 259 lj126     1.0 1.0      50.0
 15 603 morse    10.0 1.2 2.0  10.0 # and another comment
 18 470 harmonic 50.0 1.2       5.0
 </pre></div>
 </div>
 <p>The style <em>lj126</em> computes pairwise interactions with the formula</p>
 <img alt="_images/pair_lj.jpg" class="align-center" src="_images/pair_lj.jpg" />
 <p>and the coefficients:</p>
 <ul class="simple">
 <li>epsilon (energy units)</li>
 <li>sigma (distance units)</li>
 </ul>
 <p>The style <em>morse</em> computes pairwise interactions with the formula</p>
 <img alt="_images/pair_morse.jpg" class="align-center" src="_images/pair_morse.jpg" />
 <p>and the coefficients:</p>
 <ul class="simple">
 <li>D0 (energy units)</li>
 <li>alpha (1/distance units)</li>
 <li>r0 (distance units)</li>
 </ul>
 <p>The style <em>harmonic</em> computes pairwise interactions with the formula</p>
 <img alt="_images/bond_harmonic.jpg" class="align-center" src="_images/bond_harmonic.jpg" />
 <p>and the coefficients:</p>
 <ul class="simple">
 <li>K (energy units)</li>
 <li>r0 (distance units)</li>
 </ul>
 <p>Note that the usual 1/2 factor is included in K.</p>
 <hr class="docutils" />
 <p><strong>Mixing, shift, table, tail correction, restart, rRESPA info</strong>:</p>
 <p>This pair style does not support mixing since all parameters are
 explicit for each pair.</p>
 <p>The <a class="reference internal" href="pair_modify.html"><em>pair_modify</em></a> shift option is supported by this
 pair style.</p>
 <p>The <a class="reference internal" href="pair_modify.html"><em>pair_modify</em></a> table and tail options are not
 relevant for this pair style.</p>
 <p>This pair style does not write its information to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>, so pair_style and pair_coeff commands need
 to be specified in an input script that reads a restart file.</p>
 <p>This pair style can only be used via the <em>pair</em> keyword of the
 <a class="reference internal" href="run_style.html"><em>run_style respa</em></a> command.  It does not support the
 <em>inner</em>, <em>middle</em>, <em>outer</em> keywords.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>This pair style does not use a neighbor list and instead identifies
 atoms by their IDs. This has two consequences: 1) The cutoff has to be
 chosen sufficiently large, so that the second atom of a pair has to be
 a ghost atom on the same node on which the first atom is local;
 otherwise the interaction will be skipped. You can use the <em>check</em>
 option to detect, if interactions are missing. 2) Unlike other pair
 styles in LAMMPS, an atom I will not interact with multiple images of
 atom J (assuming the images are within the cutoff distance), but only
 with the nearest image.</p>
 <p>This style is part of the USER-MISC package. It is only enabled if
 LAMMPS is build with that package. See the <span class="xref std std-ref">Making of LAMMPS</span> section for more info.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a>,
 <a class="reference internal" href="pair_hybrid.html"><em>pair_style hybrid/overlay</em></a>,
 <a class="reference internal" href="pair_lj.html"><em>pair_style lj/cut</em></a>,
 <a class="reference internal" href="pair_morse.html"><em>pair_style morse</em></a>,
 <a class="reference internal" href="bond_harmonic.html"><em>bond_style harmonic</em></a></p>
 <p><strong>Default:</strong> none</p>
 </div>
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   <div class="section" id="pair-style-lj-cut-command">
 <span id="index-0"></span><h1>pair_style lj/cut command<a class="headerlink" href="#pair-style-lj-cut-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-cut-cuda-command">
 <h1>pair_style lj/cut/cuda command<a class="headerlink" href="#pair-style-lj-cut-cuda-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-cut-gpu-command">
 <h1>pair_style lj/cut/gpu command<a class="headerlink" href="#pair-style-lj-cut-gpu-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-cut-intel-command">
 <h1>pair_style lj/cut/intel command<a class="headerlink" href="#pair-style-lj-cut-intel-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-cut-kk-command">
 <h1>pair_style lj/cut/kk command<a class="headerlink" href="#pair-style-lj-cut-kk-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-cut-opt-command">
 <h1>pair_style lj/cut/opt command<a class="headerlink" href="#pair-style-lj-cut-opt-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-cut-omp-command">
 <h1>pair_style lj/cut/omp command<a class="headerlink" href="#pair-style-lj-cut-omp-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-cut-coul-cut-command">
 <h1>pair_style lj/cut/coul/cut command<a class="headerlink" href="#pair-style-lj-cut-coul-cut-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-cut-coul-cut-cuda-command">
 <h1>pair_style lj/cut/coul/cut/cuda command<a class="headerlink" href="#pair-style-lj-cut-coul-cut-cuda-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-cut-coul-cut-gpu-command">
 <h1>pair_style lj/cut/coul/cut/gpu command<a class="headerlink" href="#pair-style-lj-cut-coul-cut-gpu-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-cut-coul-cut-omp-command">
 <h1>pair_style lj/cut/coul/cut/omp command<a class="headerlink" href="#pair-style-lj-cut-coul-cut-omp-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-cut-coul-debye-command">
 <h1>pair_style lj/cut/coul/debye command<a class="headerlink" href="#pair-style-lj-cut-coul-debye-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-cut-coul-debye-cuda-command">
 <h1>pair_style lj/cut/coul/debye/cuda command<a class="headerlink" href="#pair-style-lj-cut-coul-debye-cuda-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-cut-coul-debye-gpu-command">
 <h1>pair_style lj/cut/coul/debye/gpu command<a class="headerlink" href="#pair-style-lj-cut-coul-debye-gpu-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-cut-coul-debye-kk-command">
 <h1>pair_style lj/cut/coul/debye/kk command<a class="headerlink" href="#pair-style-lj-cut-coul-debye-kk-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-cut-coul-debye-omp-command">
 <h1>pair_style lj/cut/coul/debye/omp command<a class="headerlink" href="#pair-style-lj-cut-coul-debye-omp-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-cut-coul-dsf-command">
 <h1>pair_style lj/cut/coul/dsf command<a class="headerlink" href="#pair-style-lj-cut-coul-dsf-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-cut-coul-dsf-gpu-command">
 <h1>pair_style lj/cut/coul/dsf/gpu command<a class="headerlink" href="#pair-style-lj-cut-coul-dsf-gpu-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-cut-coul-dsf-kk-command">
 <h1>pair_style lj/cut/coul/dsf/kk command<a class="headerlink" href="#pair-style-lj-cut-coul-dsf-kk-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-cut-coul-dsf-omp-command">
 <h1>pair_style lj/cut/coul/dsf/omp command<a class="headerlink" href="#pair-style-lj-cut-coul-dsf-omp-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-cut-coul-long-command">
 <h1>pair_style lj/cut/coul/long command<a class="headerlink" href="#pair-style-lj-cut-coul-long-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-cut-coul-long-cuda-command">
 <h1>pair_style lj/cut/coul/long/cuda command<a class="headerlink" href="#pair-style-lj-cut-coul-long-cuda-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-cut-coul-long-gpu-command">
 <h1>pair_style lj/cut/coul/long/gpu command<a class="headerlink" href="#pair-style-lj-cut-coul-long-gpu-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-cut-coul-long-intel-command">
 <h1>pair_style lj/cut/coul/long/intel command<a class="headerlink" href="#pair-style-lj-cut-coul-long-intel-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-cut-coul-long-opt-command">
 <h1>pair_style lj/cut/coul/long/opt command<a class="headerlink" href="#pair-style-lj-cut-coul-long-opt-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-cut-coul-long-omp-command">
 <h1>pair_style lj/cut/coul/long/omp command<a class="headerlink" href="#pair-style-lj-cut-coul-long-omp-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-cut-coul-msm-command">
 <h1>pair_style lj/cut/coul/msm command<a class="headerlink" href="#pair-style-lj-cut-coul-msm-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-cut-coul-msm-gpu-command">
 <h1>pair_style lj/cut/coul/msm/gpu command<a class="headerlink" href="#pair-style-lj-cut-coul-msm-gpu-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-cut-coul-msm-omp-command">
 <h1>pair_style lj/cut/coul/msm/omp command<a class="headerlink" href="#pair-style-lj-cut-coul-msm-omp-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-cut-tip4p-cut-command">
 <h1>pair_style lj/cut/tip4p/cut command<a class="headerlink" href="#pair-style-lj-cut-tip4p-cut-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-cut-tip4p-cut-omp-command">
 <h1>pair_style lj/cut/tip4p/cut/omp command<a class="headerlink" href="#pair-style-lj-cut-tip4p-cut-omp-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-cut-tip4p-long-command">
 <h1>pair_style lj/cut/tip4p/long command<a class="headerlink" href="#pair-style-lj-cut-tip4p-long-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-cut-tip4p-long-omp-command">
 <h1>pair_style lj/cut/tip4p/long/omp command<a class="headerlink" href="#pair-style-lj-cut-tip4p-long-omp-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-cut-tip4p-long-opt-command">
 <h1>pair_style lj/cut/tip4p/long/opt command<a class="headerlink" href="#pair-style-lj-cut-tip4p-long-opt-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>pair_style style args
 </pre></div>
 </div>
 <ul class="simple">
 <li>style = <em>lj/cut</em> or <em>lj/cut/coul/cut</em> or <em>lj/cut/coul/debye</em> or <em>lj/cut/coul/dsf</em> or <em>lj/cut/coul/long</em> or <em>lj/cut/coul/msm</em> or <em>lj/cut/tip4p/long</em></li>
 <li>args = list of arguments for a particular style</li>
 </ul>
 <pre class="literal-block">
 <em>lj/cut</em> args = cutoff
-    cutoff = global cutoff for Lennard Jones interactions (distance units)
-  <em>lj/cut/coul/cut</em> args = cutoff (cutoff2)
-    cutoff = global cutoff for LJ (and Coulombic if only 1 arg) (distance units)
-    cutoff2 = global cutoff for Coulombic (optional) (distance units)
-  <em>lj/cut/coul/debye</em> args = kappa cutoff (cutoff2)
-    kappa = inverse of the Debye length (inverse distance units)
-    cutoff = global cutoff for LJ (and Coulombic if only 1 arg) (distance units)
-    cutoff2 = global cutoff for Coulombic (optional) (distance units)
-  <em>lj/cut/coul/dsf</em> args = alpha cutoff (cutoff2)
-    alpha = damping parameter (inverse distance units)
-    cutoff = global cutoff for LJ (and Coulombic if only 1 arg) (distance units)
-    cutoff2 = global cutoff for Coulombic (distance units)
-  <em>lj/cut/coul/long</em> args = cutoff (cutoff2)
-    cutoff = global cutoff for LJ (and Coulombic if only 1 arg) (distance units)
-    cutoff2 = global cutoff for Coulombic (optional) (distance units)
-  <em>lj/cut/coul/msm</em> args = cutoff (cutoff2)
-    cutoff = global cutoff for LJ (and Coulombic if only 1 arg) (distance units)
-    cutoff2 = global cutoff for Coulombic (optional) (distance units)
-  <em>lj/cut/tip4p/cut</em> args = otype htype btype atype qdist cutoff (cutoff2)
-    otype,htype = atom types for TIP4P O and H
-    btype,atype = bond and angle types for TIP4P waters
-    qdist = distance from O atom to massless charge (distance units)
-    cutoff = global cutoff for LJ (and Coulombic if only 1 arg) (distance units)
-    cutoff2 = global cutoff for Coulombic (optional) (distance units)
-  <em>lj/cut/tip4p/long</em> args = otype htype btype atype qdist cutoff (cutoff2)
-    otype,htype = atom types for TIP4P O and H
-    btype,atype = bond and angle types for TIP4P waters
-    qdist = distance from O atom to massless charge (distance units)
-    cutoff = global cutoff for LJ (and Coulombic if only 1 arg) (distance units)
-    cutoff2 = global cutoff for Coulombic (optional) (distance units)
+  cutoff = global cutoff for Lennard Jones interactions (distance units)
+<em>lj/cut/coul/cut</em> args = cutoff (cutoff2)
+  cutoff = global cutoff for LJ (and Coulombic if only 1 arg) (distance units)
+  cutoff2 = global cutoff for Coulombic (optional) (distance units)
+<em>lj/cut/coul/debye</em> args = kappa cutoff (cutoff2)
+  kappa = inverse of the Debye length (inverse distance units)
+  cutoff = global cutoff for LJ (and Coulombic if only 1 arg) (distance units)
+  cutoff2 = global cutoff for Coulombic (optional) (distance units)
+<em>lj/cut/coul/dsf</em> args = alpha cutoff (cutoff2)
+  alpha = damping parameter (inverse distance units)
+  cutoff = global cutoff for LJ (and Coulombic if only 1 arg) (distance units)
+  cutoff2 = global cutoff for Coulombic (distance units)
+<em>lj/cut/coul/long</em> args = cutoff (cutoff2)
+  cutoff = global cutoff for LJ (and Coulombic if only 1 arg) (distance units)
+  cutoff2 = global cutoff for Coulombic (optional) (distance units)
+<em>lj/cut/coul/msm</em> args = cutoff (cutoff2)
+  cutoff = global cutoff for LJ (and Coulombic if only 1 arg) (distance units)
+  cutoff2 = global cutoff for Coulombic (optional) (distance units)
+<em>lj/cut/tip4p/cut</em> args = otype htype btype atype qdist cutoff (cutoff2)
+  otype,htype = atom types for TIP4P O and H
+  btype,atype = bond and angle types for TIP4P waters
+  qdist = distance from O atom to massless charge (distance units)
+  cutoff = global cutoff for LJ (and Coulombic if only 1 arg) (distance units)
+  cutoff2 = global cutoff for Coulombic (optional) (distance units)
+<em>lj/cut/tip4p/long</em> args = otype htype btype atype qdist cutoff (cutoff2)
+  otype,htype = atom types for TIP4P O and H
+  btype,atype = bond and angle types for TIP4P waters
+  qdist = distance from O atom to massless charge (distance units)
+  cutoff = global cutoff for LJ (and Coulombic if only 1 arg) (distance units)
+  cutoff2 = global cutoff for Coulombic (optional) (distance units)
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>pair_style lj/cut 2.5
 pair_coeff * * 1 1
 pair_coeff 1 1 1 1.1 2.8
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>pair_style lj/cut/coul/cut 10.0
 pair_style lj/cut/coul/cut 10.0 8.0
 pair_coeff * * 100.0 3.0
 pair_coeff 1 1 100.0 3.5 9.0
 pair_coeff 1 1 100.0 3.5 9.0 9.0
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>pair_style lj/cut/coul/debye 1.5 3.0
 pair_style lj/cut/coul/debye 1.5 2.5 5.0
 pair_coeff * * 1.0 1.0
 pair_coeff 1 1 1.0 1.5 2.5
 pair_coeff 1 1 1.0 1.5 2.5 5.0
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>pair_style lj/cut/coul/dsf 0.05 2.5 10.0
 pair_coeff * * 1.0 1.0
 pair_coeff 1 1 1.0 1.0 2.5
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>pair_style lj/cut/coul/long 10.0
 pair_style lj/cut/coul/long 10.0 8.0
 pair_coeff * * 100.0 3.0
 pair_coeff 1 1 100.0 3.5 9.0
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>pair_style lj/cut/coul/msm 10.0
 pair_style lj/cut/coul/msm 10.0 8.0
 pair_coeff * * 100.0 3.0
 pair_coeff 1 1 100.0 3.5 9.0
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>pair_style lj/cut/tip4p/cut 1 2 7 8 0.15 12.0
 pair_style lj/cut/tip4p/cut 1 2 7 8 0.15 12.0 10.0
 pair_coeff * * 100.0 3.0
 pair_coeff 1 1 100.0 3.5 9.0
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>pair_style lj/cut/tip4p/long 1 2 7 8 0.15 12.0
 pair_style lj/cut/tip4p/long 1 2 7 8 0.15 12.0 10.0
 pair_coeff * * 100.0 3.0
 pair_coeff 1 1 100.0 3.5 9.0
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>The <em>lj/cut</em> styles compute the standard 12/6 Lennard-Jones potential,
 given by</p>
 <img alt="_images/pair_lj.jpg" class="align-center" src="_images/pair_lj.jpg" />
 <p>Rc is the cutoff.</p>
 <p>Style <em>lj/cut/coul/cut</em> adds a Coulombic pairwise interaction given by</p>
 <img alt="_images/pair_coulomb.jpg" class="align-center" src="_images/pair_coulomb.jpg" />
 <p>where C is an energy-conversion constant, Qi and Qj are the charges on
 the 2 atoms, and epsilon is the dielectric constant which can be set
 by the <a class="reference internal" href="dielectric.html"><em>dielectric</em></a> command.  If one cutoff is
 specified in the pair_style command, it is used for both the LJ and
 Coulombic terms.  If two cutoffs are specified, they are used as
 cutoffs for the LJ and Coulombic terms respectively.</p>
 <p>Style <em>lj/cut/coul/debye</em> adds an additional exp() damping factor
 to the Coulombic term, given by</p>
 <img alt="_images/pair_debye.jpg" class="align-center" src="_images/pair_debye.jpg" />
 <p>where kappa is the inverse of the Debye length.  This potential is
 another way to mimic the screening effect of a polar solvent.</p>
 <p>Style <em>lj/cut/coul/dsf</em> computes the Coulombic term via the damped
 shifted force model described in <a class="reference internal" href="#fennell"><span>Fennell</span></a>, given by:</p>
 <img alt="_images/pair_coul_dsf.jpg" class="align-center" src="_images/pair_coul_dsf.jpg" />
 <p>where <em>alpha</em> is the damping parameter and erfc() is the complementary
 error-function. This potential is essentially a short-range,
 spherically-truncated, charge-neutralized, shifted, pairwise <em>1/r</em>
 summation.  The potential is based on Wolf summation, proposed as an
 alternative to Ewald summation for condensed phase systems where
 charge screening causes electrostatic interactions to become
 effectively short-ranged. In order for the electrostatic sum to be
 absolutely convergent, charge neutralization within the cutoff radius
 is enforced by shifting the potential through placement of image
 charges on the cutoff sphere. Convergence can often be improved by
 setting <em>alpha</em> to a small non-zero value.</p>
 <p>Styles <em>lj/cut/coul/long</em> and <em>lj/cut/coul/msm</em> compute the same
 Coulombic interactions as style <em>lj/cut/coul/cut</em> except that an
 additional damping factor is applied to the Coulombic term so it can
 be used in conjunction with the <a class="reference internal" href="kspace_style.html"><em>kspace_style</em></a>
 command and its <em>ewald</em> or <em>pppm</em> option.  The Coulombic cutoff
 specified for this style means that pairwise interactions within this
 distance are computed directly; interactions outside that distance are
 computed in reciprocal space.</p>
 <p>Styles <em>lj/cut/tip4p/cut</em> and <em>lj/cut/tip4p/long</em> implement the TIP4P
 water model of <a class="reference internal" href="#jorgensen"><span>(Jorgensen)</span></a>, which introduces a massless
 site located a short distance away from the oxygen atom along the
 bisector of the HOH angle.  The atomic types of the oxygen and
 hydrogen atoms, the bond and angle types for OH and HOH interactions,
 and the distance to the massless charge site are specified as
 pair_style arguments.  Style <em>lj/cut/tip4p/cut</em> uses a cutoff for
 Coulomb interactions; style <em>lj/cut/tip4p/long</em> is for use with a
 long-range Coulombic solver (Ewald or PPPM).</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">For each TIP4P water molecule in your system, the atom
 IDs for the O and 2 H atoms must be consecutive, with the O atom
 first.  This is to enable LAMMPS to &#8220;find&#8221; the 2 H atoms associated
 with each O atom.  For example, if the atom ID of an O atom in a TIP4P
 water molecule is 500, then its 2 H atoms must have IDs 501 and 502.</p>
 </div>
 <p>See the <a class="reference internal" href="Section_howto.html#howto-8"><span>howto section</span></a> for more
 information on how to use the TIP4P pair styles and lists of
 parameters to set.  Note that the neighobr list cutoff for Coulomb
 interactions is effectively extended by a distance 2*qdist when using
 the TIP4P pair style, to account for the offset distance of the
 fictitious charges on O atoms in water molecules.  Thus it is
 typically best in an efficiency sense to use a LJ cutoff &gt;= Coulomb
 cutoff + 2*qdist, to shrink the size of the neighbor list.  This leads
 to slightly larger cost for the long-range calculation, so you can
 test the trade-off for your model.</p>
 <p>For all of the <em>lj/cut</em> pair styles, the following coefficients must
 be defined for each pair of atoms types via the
 <a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a> command as in the examples above, or in
 the data file or restart files read by the <a class="reference internal" href="read_data.html"><em>read_data</em></a>
 or <a class="reference internal" href="read_restart.html"><em>read_restart</em></a> commands, or by mixing as
 described below:</p>
 <ul class="simple">
 <li>epsilon (energy units)</li>
 <li>sigma (distance units)</li>
 <li>cutoff1 (distance units)</li>
 <li>cutoff2 (distance units)</li>
 </ul>
 <p>Note that sigma is defined in the LJ formula as the zero-crossing
 distance for the potential, not as the energy minimum at 2^(1/6)
 sigma.</p>
 <p>The latter 2 coefficients are optional.  If not specified, the global
 LJ and Coulombic cutoffs specified in the pair_style command are used.
 If only one cutoff is specified, it is used as the cutoff for both LJ
 and Coulombic interactions for this type pair.  If both coefficients
 are specified, they are used as the LJ and Coulombic cutoffs for this
 type pair.  You cannot specify 2 cutoffs for style <em>lj/cut</em>, since it
 has no Coulombic terms.</p>
 <p>For <em>lj/cut/coul/long</em> and <em>lj/cut/coul/msm</em> and <em>lj/cut/tip4p/cut</em>
 and <em>lj/cut/tip4p/long</em> only the LJ cutoff can be specified since a
 Coulombic cutoff cannot be specified for an individual I,J type pair.
 All type pairs use the same global Coulombic cutoff specified in the
 pair_style command.</p>
 <hr class="docutils" />
 <p>Styles with a <em>cuda</em>, <em>gpu</em>, <em>intel</em>, <em>kk</em>, <em>omp</em>, or <em>opt</em> suffix are
 functionally the same as the corresponding style without the suffix.
 They have been optimized to run faster, depending on your available
 hardware, as discussed in <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a>
 of the manual.  The accelerated styles take the same arguments and
 should produce the same results, except for round-off and precision
 issues.</p>
 <p>These accelerated styles are part of the USER-CUDA, GPU, USER-INTEL,
 KOKKOS, USER-OMP and OPT packages, respectively.  They are only
 enabled if LAMMPS was built with those packages.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 <p>You can specify the accelerated styles explicitly in your input script
 by including their suffix, or you can use the <a class="reference internal" href="Section_start.html#start-7"><span>-suffix command-line switch</span></a> when you invoke LAMMPS, or you can
 use the <a class="reference internal" href="suffix.html"><em>suffix</em></a> command in your input script.</p>
 <p>See <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a> of the manual for
 more instructions on how to use the accelerated styles effectively.</p>
 <hr class="docutils" />
 <p><strong>Mixing, shift, table, tail correction, restart, rRESPA info</strong>:</p>
 <p>For atom type pairs I,J and I != J, the epsilon and sigma coefficients
 and cutoff distance for all of the lj/cut pair styles can be mixed.
 The default mix value is <em>geometric</em>.  See the &#8220;pair_modify&#8221; command
 for details.</p>
 <p>All of the <em>lj/cut</em> pair styles support the
 <a class="reference internal" href="pair_modify.html"><em>pair_modify</em></a> shift option for the energy of the
 Lennard-Jones portion of the pair interaction.</p>
 <p>The <em>lj/cut/coul/long</em> and <em>lj/cut/tip4p/long</em> pair styles support the
 <a class="reference internal" href="pair_modify.html"><em>pair_modify</em></a> table option since they can tabulate
 the short-range portion of the long-range Coulombic interaction.</p>
 <p>All of the <em>lj/cut</em> pair styles support the
 <a class="reference internal" href="pair_modify.html"><em>pair_modify</em></a> tail option for adding a long-range
 tail correction to the energy and pressure for the Lennard-Jones
 portion of the pair interaction.</p>
 <p>All of the <em>lj/cut</em> pair styles write their information to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>, so pair_style and pair_coeff commands do
 not need to be specified in an input script that reads a restart file.</p>
 <p>The <em>lj/cut</em> and <em>lj/cut/coul/long</em> pair styles support the use of the
 <em>inner</em>, <em>middle</em>, and <em>outer</em> keywords of the <a class="reference internal" href="run_style.html"><em>run_style respa</em></a> command, meaning the pairwise forces can be
 partitioned by distance at different levels of the rRESPA hierarchy.
 The other styles only support the <em>pair</em> keyword of run_style respa.
 See the <a class="reference internal" href="run_style.html"><em>run_style</em></a> command for details.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>The <em>lj/cut/coul/long</em> and <em>lj/cut/tip4p/long</em> styles are part of the
 KSPACE package. The <em>lj/cut/tip4p/cut</em> style is part of the MOLECULE
 package. These styles are only enabled if LAMMPS was built with those
 packages.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section
 for more info.  Note that the KSPACE and MOLECULE packages are
 installed by default.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a></p>
 <p><strong>Default:</strong> none</p>
 <hr class="docutils" />
 <p id="jorgensen"><strong>(Jorgensen)</strong> Jorgensen, Chandrasekhar, Madura, Impey, Klein, J Chem
 Phys, 79, 926 (1983).</p>
 <p id="fennell"><strong>(Fennell)</strong> C. J. Fennell, J. D. Gezelter, J Chem Phys, 124,
 234104 (2006).</p>
 </div>
 </div>
 
 
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   <div class="section" id="pair-style-lj-long-coul-long-command">
 <span id="index-0"></span><h1>pair_style lj/long/coul/long command<a class="headerlink" href="#pair-style-lj-long-coul-long-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-long-coul-long-omp-command">
 <h1>pair_style lj/long/coul/long/omp command<a class="headerlink" href="#pair-style-lj-long-coul-long-omp-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-long-coul-long-opt-command">
 <h1>pair_style lj/long/coul/long/opt command<a class="headerlink" href="#pair-style-lj-long-coul-long-opt-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-long-tip4p-long-command">
 <h1>pair_style lj/long/tip4p/long command<a class="headerlink" href="#pair-style-lj-long-tip4p-long-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>pair_style style args
 </pre></div>
 </div>
 <ul class="simple">
 <li>style = <em>lj/long/coul/long</em> or <em>lj/long/tip4p/long</em></li>
 <li>args = list of arguments for a particular style</li>
 </ul>
 <pre class="literal-block">
 <em>lj/long/coul/long</em> args = flag_lj flag_coul cutoff (cutoff2)
-    flag_lj = <em>long</em> or <em>cut</em> or <em>off</em>
-      <em>long</em> = use Kspace long-range summation for dispersion 1/r^6 term
-      <em>cut</em> = use a cutoff on dispersion 1/r^6 term
-      <em>off</em> = omit disperion 1/r^6 term entirely
-    flag_coul = <em>long</em> or <em>off</em>
-      <em>long</em> = use Kspace long-range summation for Coulombic 1/r term
-      <em>off</em> = omit Coulombic term
-    cutoff = global cutoff for LJ (and Coulombic if only 1 arg) (distance units)
-    cutoff2 = global cutoff for Coulombic (optional) (distance units)
-  <em>lj/long/tip4p/long</em> args = flag_lj flag_coul otype htype btype atype qdist cutoff (cutoff2)
-    flag_lj = <em>long</em> or <em>cut</em>
-      <em>long</em> = use Kspace long-range summation for dispersion 1/r^6 term
-      <em>cut</em> = use a cutoff
-    flag_coul = <em>long</em> or <em>off</em>
-      <em>long</em> = use Kspace long-range summation for Coulombic 1/r term
-      <em>off</em> = omit Coulombic term
-    otype,htype = atom types for TIP4P O and H
-    btype,atype = bond and angle types for TIP4P waters
-    qdist = distance from O atom to massless charge (distance units)
-    cutoff = global cutoff for LJ (and Coulombic if only 1 arg) (distance units)
-    cutoff2 = global cutoff for Coulombic (optional) (distance units)
+  flag_lj = <em>long</em> or <em>cut</em> or <em>off</em>
+    <em>long</em> = use Kspace long-range summation for dispersion 1/r^6 term
+    <em>cut</em> = use a cutoff on dispersion 1/r^6 term
+    <em>off</em> = omit disperion 1/r^6 term entirely
+  flag_coul = <em>long</em> or <em>off</em>
+    <em>long</em> = use Kspace long-range summation for Coulombic 1/r term
+    <em>off</em> = omit Coulombic term
+  cutoff = global cutoff for LJ (and Coulombic if only 1 arg) (distance units)
+  cutoff2 = global cutoff for Coulombic (optional) (distance units)
+<em>lj/long/tip4p/long</em> args = flag_lj flag_coul otype htype btype atype qdist cutoff (cutoff2)
+  flag_lj = <em>long</em> or <em>cut</em>
+    <em>long</em> = use Kspace long-range summation for dispersion 1/r^6 term
+    <em>cut</em> = use a cutoff
+  flag_coul = <em>long</em> or <em>off</em>
+    <em>long</em> = use Kspace long-range summation for Coulombic 1/r term
+    <em>off</em> = omit Coulombic term
+  otype,htype = atom types for TIP4P O and H
+  btype,atype = bond and angle types for TIP4P waters
+  qdist = distance from O atom to massless charge (distance units)
+  cutoff = global cutoff for LJ (and Coulombic if only 1 arg) (distance units)
+  cutoff2 = global cutoff for Coulombic (optional) (distance units)
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>pair_style lj/long/coul/long cut off 2.5
 pair_style lj/long/coul/long cut long 2.5 4.0
 pair_style lj/long/coul/long long long 2.5 4.0
 pair_coeff * * 1 1
 pair_coeff 1 1 1 3 4
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>pair_style lj/long/tip4p/long long long 1 2 7 8 0.15 12.0
 pair_style lj/long/tip4p/long long long 1 2 7 8 0.15 12.0 10.0
 pair_coeff * * 100.0 3.0
 pair_coeff 1 1 100.0 3.5 9.0
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Style <em>lj/long/coul/long</em> computes the standard 12/6 Lennard-Jones and
 Coulombic potentials, given by</p>
 <img alt="_images/pair_lj.jpg" class="align-center" src="_images/pair_lj.jpg" />
 <img alt="_images/pair_coulomb.jpg" class="align-center" src="_images/pair_coulomb.jpg" />
 <p>where C is an energy-conversion constant, Qi and Qj are the charges on
 the 2 atoms, epsilon is the dielectric constant which can be set by
 the <a class="reference internal" href="dielectric.html"><em>dielectric</em></a> command, and Rc is the cutoff.  If
 one cutoff is specified in the pair_style command, it is used for both
 the LJ and Coulombic terms.  If two cutoffs are specified, they are
 used as cutoffs for the LJ and Coulombic terms respectively.</p>
 <p>The purpose of this pair style is to capture long-range interactions
 resulting from both attractive 1/r^6 Lennard-Jones and Coulombic 1/r
 interactions.  This is done by use of the <em>flag_lj</em> and <em>flag_coul</em>
 settings.  The <a class="reference internal" href="#veld"><span>In &#8216;t Veld</span></a> paper has more details on when it is
 appropriate to include long-range 1/r^6 interactions, using this
 potential.</p>
 <p>Style <em>lj/long/tip4p/long</em> implements the TIP4P water model of
 <a class="reference internal" href="pair_lj.html#jorgensen"><span>(Jorgensen)</span></a>, which introduces a massless site located a
 short distance away from the oxygen atom along the bisector of the HOH
 angle.  The atomic types of the oxygen and hydrogen atoms, the bond
 and angle types for OH and HOH interactions, and the distance to the
 massless charge site are specified as pair_style arguments.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">For each TIP4P water molecule in your system, the atom
 IDs for the O and 2 H atoms must be consecutive, with the O atom
 first.  This is to enable LAMMPS to &#8220;find&#8221; the 2 H atoms associated
 with each O atom.  For example, if the atom ID of an O atom in a TIP4P
 water molecule is 500, then its 2 H atoms must have IDs 501 and 502.</p>
 </div>
 <p>See the <a class="reference internal" href="Section_howto.html#howto-8"><span>howto section</span></a> for more
 information on how to use the TIP4P pair style.  Note that the
 neighobr list cutoff for Coulomb interactions is effectively extended
 by a distance 2*qdist when using the TIP4P pair style, to account for
 the offset distance of the fictitious charges on O atoms in water
 molecules.  Thus it is typically best in an efficiency sense to use a
 LJ cutoff &gt;= Coulomb cutoff + 2*qdist, to shrink the size of the
 neighbor list.  This leads to slightly larger cost for the long-range
 calculation, so you can test the trade-off for your model.</p>
 <p>If <em>flag_lj</em> is set to <em>long</em>, no cutoff is used on the LJ 1/r^6
 dispersion term.  The long-range portion can be calculated by using
 the <a class="reference internal" href="kspace_style.html"><em>kspace_style ewald/disp or pppm/disp</em></a> commands.
 The specified LJ cutoff then determines which portion of the LJ
 interactions are computed directly by the pair potential versus which
 part is computed in reciprocal space via the Kspace style.  If
 <em>flag_lj</em> is set to <em>cut</em>, the LJ interactions are simply cutoff, as
 with <a class="reference internal" href="pair_lj.html"><em>pair_style lj/cut</em></a>.</p>
 <p>If <em>flag_coul</em> is set to <em>long</em>, no cutoff is used on the Coulombic
 interactions.  The long-range portion can calculated by using any of
 several <a class="reference internal" href="kspace_style.html"><em>kspace_style</em></a> command options such as
 <em>pppm</em> or <em>ewald</em>.  Note that if <em>flag_lj</em> is also set to long, then
 the <em>ewald/disp</em> or <em>pppm/disp</em> Kspace style needs to be used to
 perform the long-range calculations for both the LJ and Coulombic
 interactions.  If <em>flag_coul</em> is set to <em>off</em>, Coulombic interactions
 are not computed.</p>
 <p>The following coefficients must be defined for each pair of atoms
 types via the <a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a> command as in the examples
 above, or in the data file or restart files read by the
 <a class="reference internal" href="read_data.html"><em>read_data</em></a> or <a class="reference internal" href="read_restart.html"><em>read_restart</em></a>
 commands, or by mixing as described below:</p>
 <ul class="simple">
 <li>epsilon (energy units)</li>
 <li>sigma (distance units)</li>
 <li>cutoff1 (distance units)</li>
 <li>cutoff2 (distance units)</li>
 </ul>
 <p>Note that sigma is defined in the LJ formula as the zero-crossing
 distance for the potential, not as the energy minimum at 2^(1/6)
 sigma.</p>
 <p>The latter 2 coefficients are optional.  If not specified, the global
 LJ and Coulombic cutoffs specified in the pair_style command are used.
 If only one cutoff is specified, it is used as the cutoff for both LJ
 and Coulombic interactions for this type pair.  If both coefficients
 are specified, they are used as the LJ and Coulombic cutoffs for this
 type pair.</p>
 <p>Note that if you are using <em>flag_lj</em> set to <em>long</em>, you
 cannot specify a LJ cutoff for an atom type pair, since only one
 global LJ cutoff is allowed.  Similarly, if you are using <em>flag_coul</em>
 set to <em>long</em>, you cannot specify a Coulombic cutoff for an atom type
 pair, since only one global Coulombic cutoff is allowed.</p>
 <p>For <em>lj/long/tip4p/long</em> only the LJ cutoff can be specified
 since a Coulombic cutoff cannot be specified for an individual I,J
 type pair.  All type pairs use the same global Coulombic cutoff
 specified in the pair_style command.</p>
 <hr class="docutils" />
 <p>Styles with a <em>cuda</em>, <em>gpu</em>, <em>intel</em>, <em>kk</em>, <em>omp</em>, or <em>opt</em> suffix are
 functionally the same as the corresponding style without the suffix.
 They have been optimized to run faster, depending on your available
 hardware, as discussed in <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a>
 of the manual.  The accelerated styles take the same arguments and
 should produce the same results, except for round-off and precision
 issues.</p>
 <p>These accelerated styles are part of the USER-CUDA, GPU, USER-INTEL,
 KOKKOS, USER-OMP and OPT packages, respectively.  They are only
 enabled if LAMMPS was built with those packages.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 <p>You can specify the accelerated styles explicitly in your input script
 by including their suffix, or you can use the <a class="reference internal" href="Section_start.html#start-7"><span>-suffix command-line switch</span></a> when you invoke LAMMPS, or you can
 use the <a class="reference internal" href="suffix.html"><em>suffix</em></a> command in your input script.</p>
 <p>See <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a> of the manual for
 more instructions on how to use the accelerated styles effectively.</p>
 <hr class="docutils" />
 <p><strong>Mixing, shift, table, tail correction, restart, rRESPA info</strong>:</p>
 <p>For atom type pairs I,J and I != J, the epsilon and sigma coefficients
 and cutoff distance for all of the lj/long pair styles can be mixed.
 The default mix value is <em>geometric</em>.  See the &#8220;pair_modify&#8221; command
 for details.</p>
 <p>These pair styles support the <a class="reference internal" href="pair_modify.html"><em>pair_modify</em></a> shift
 option for the energy of the Lennard-Jones portion of the pair
 interaction, assuming <em>flag_lj</em> is <em>cut</em>.</p>
 <p>These pair styles support the <a class="reference internal" href="pair_modify.html"><em>pair_modify</em></a> table and
 table/disp options since they can tabulate the short-range portion of
 the long-range Coulombic and dispersion interactions.</p>
 <p>Thes pair styles do not support the <a class="reference internal" href="pair_modify.html"><em>pair_modify</em></a>
 tail option for adding a long-range tail correction to the
 Lennard-Jones portion of the energy and pressure.</p>
 <p>These pair styles write their information to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>, so pair_style and pair_coeff commands do not need
 to be specified in an input script that reads a restart file.</p>
 <p>The pair lj/long/coul/long styles support the use of the <em>inner</em>,
 <em>middle</em>, and <em>outer</em> keywords of the <a class="reference internal" href="run_style.html"><em>run_style respa</em></a>
 command, meaning the pairwise forces can be partitioned by distance at
 different levels of the rRESPA hierarchy.  See the
 <a class="reference internal" href="run_style.html"><em>run_style</em></a> command for details.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>These styles are part of the KSPACE package.  They are only enabled if
 LAMMPS was built with that package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.  Note that
 the KSPACE package is installed by default.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a></p>
 <p><strong>Default:</strong> none</p>
 <hr class="docutils" />
 <p id="veld"><strong>(In &#8216;t Veld)</strong> In &#8216;t Veld, Ismail, Grest, J Chem Phys (accepted) (2007).</p>
 </div>
 </div>
 
 
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   <div class="section" id="pair-style-lj-cut-soft-command">
 <span id="index-0"></span><h1>pair_style lj/cut/soft command<a class="headerlink" href="#pair-style-lj-cut-soft-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-cut-soft-omp-command">
 <h1>pair_style lj/cut/soft/omp command<a class="headerlink" href="#pair-style-lj-cut-soft-omp-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-cut-coul-cut-soft-command">
 <h1>pair_style lj/cut/coul/cut/soft command<a class="headerlink" href="#pair-style-lj-cut-coul-cut-soft-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-cut-coul-cut-soft-omp-command">
 <h1>pair_style lj/cut/coul/cut/soft/omp command<a class="headerlink" href="#pair-style-lj-cut-coul-cut-soft-omp-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-cut-coul-long-soft-command">
 <h1>pair_style lj/cut/coul/long/soft command<a class="headerlink" href="#pair-style-lj-cut-coul-long-soft-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-cut-coul-long-soft-omp-command">
 <h1>pair_style lj/cut/coul/long/soft/omp command<a class="headerlink" href="#pair-style-lj-cut-coul-long-soft-omp-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-cut-tip4p-long-soft-command">
 <h1>pair_style lj/cut/tip4p/long/soft command<a class="headerlink" href="#pair-style-lj-cut-tip4p-long-soft-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-cut-tip4p-long-soft-omp-command">
 <h1>pair_style lj/cut/tip4p/long/soft/omp command<a class="headerlink" href="#pair-style-lj-cut-tip4p-long-soft-omp-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-charmm-coul-long-soft-command">
 <h1>pair_style lj/charmm/coul/long/soft command<a class="headerlink" href="#pair-style-lj-charmm-coul-long-soft-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-charmm-coul-long-soft-omp-command">
 <h1>pair_style lj/charmm/coul/long/soft/omp command<a class="headerlink" href="#pair-style-lj-charmm-coul-long-soft-omp-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-coul-cut-soft-command">
 <h1>pair_style coul/cut/soft command<a class="headerlink" href="#pair-style-coul-cut-soft-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-coul-cut-soft-omp-command">
 <h1>pair_style coul/cut/soft/omp command<a class="headerlink" href="#pair-style-coul-cut-soft-omp-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-coul-long-soft-command">
 <h1>pair_style coul/long/soft command<a class="headerlink" href="#pair-style-coul-long-soft-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-coul-long-soft-omp-command">
 <h1>pair_style coul/long/soft/omp command<a class="headerlink" href="#pair-style-coul-long-soft-omp-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-tip4p-long-soft-command">
 <h1>pair_style tip4p/long/soft command<a class="headerlink" href="#pair-style-tip4p-long-soft-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-tip4p-long-soft-omp-command">
 <h1>pair_style tip4p/long/soft/omp command<a class="headerlink" href="#pair-style-tip4p-long-soft-omp-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>pair_style style args
 </pre></div>
 </div>
 <ul class="simple">
 <li>style = <em>lj/cut/soft</em> or <em>lj/cut/coul/cut/soft</em> or <em>lj/cut/coul/long/soft</em> or <em>lj/cut/tip4p/long/soft</em> or <em>lj/charmm/coul/long/soft</em> or <em>coul/cut/soft</em> or <em>coul/long/soft</em> or <em>tip4p/long/soft</em></li>
 <li>args = list of arguments for a particular style</li>
 </ul>
 <pre class="literal-block">
 <em>lj/cut/soft</em> args = n alpha_lj cutoff
-    n, alpha_LJ = parameters of soft-core potential
-    cutoff = global cutoff for Lennard-Jones interactions (distance units)
-  <em>lj/cut/coul/cut/soft</em> args = n alpha_LJ alpha_C cutoff (cutoff2)
-    n, alpha_LJ, alpha_C = parameters of soft-core potential
-    cutoff = global cutoff for LJ (and Coulombic if only 1 arg) (distance units)
-    cutoff2 = global cutoff for Coulombic (optional) (distance units)
-  <em>lj/cut/coul/long/soft</em> args = n alpha_LJ alpha_C cutoff
-    n, alpha_LJ, alpha_C = parameters of the soft-core potential
-    cutoff = global cutoff for LJ (and Coulombic if only 1 arg) (distance units)
-    cutoff2 = global cutoff for Coulombic (optional) (distance units)
-  <em>lj/cut/tip4p/long/soft</em> args = otype htype btype atype qdist n alpha_LJ alpha_C cutoff (cutoff2)
-    otype,htype = atom types for TIP4P O and H
-    btype,atype = bond and angle types for TIP4P waters
-    qdist = distance from O atom to massless charge (distance units)
-    n, alpha_LJ, alpha_C = parameters of the soft-core potential
-    cutoff = global cutoff for LJ (and Coulombic if only 1 arg) (distance units)
-    cutoff2 = global cutoff for Coulombic (optional) (distance units)
-  <em>lj/charmm/coul/long/soft</em> args = n alpha_LJ alpha_C inner outer (cutoff)
-    n, alpha_LJ, alpha_C = parameters of the soft-core potential
-    inner, outer = global switching cutoffs for LJ (and Coulombic if only 5 args)
-    cutoff = global cutoff for Coulombic (optional, outer is Coulombic cutoff if only 5 args)
-  <em>coul/cut/soft</em> args = n alpha_C cutoff
-    n, alpha_C = parameters of the soft-core potential
-    cutoff = global cutoff for Coulomb interactions (distance units)
-  <em>coul/long/soft</em> args = n alpha_C cutoff
-    n, alpha_C = parameters of the soft-core potential
-    cutoff = global cutoff for Coulomb interactions (distance units)
-  <em>tip4p/long/soft</em> args = otype htype btype atype qdist n alpha_C cutoff
-    otype,htype = atom types for TIP4P O and H
-    btype,atype = bond and angle types for TIP4P waters
-    qdist = distance from O atom to massless charge (distance units)
-    n, alpha_C = parameters of the soft-core potential
-    cutoff = global cutoff for Coulomb interactions (distance units)
+  n, alpha_LJ = parameters of soft-core potential
+  cutoff = global cutoff for Lennard-Jones interactions (distance units)
+<em>lj/cut/coul/cut/soft</em> args = n alpha_LJ alpha_C cutoff (cutoff2)
+  n, alpha_LJ, alpha_C = parameters of soft-core potential
+  cutoff = global cutoff for LJ (and Coulombic if only 1 arg) (distance units)
+  cutoff2 = global cutoff for Coulombic (optional) (distance units)
+<em>lj/cut/coul/long/soft</em> args = n alpha_LJ alpha_C cutoff
+  n, alpha_LJ, alpha_C = parameters of the soft-core potential
+  cutoff = global cutoff for LJ (and Coulombic if only 1 arg) (distance units)
+  cutoff2 = global cutoff for Coulombic (optional) (distance units)
+<em>lj/cut/tip4p/long/soft</em> args = otype htype btype atype qdist n alpha_LJ alpha_C cutoff (cutoff2)
+  otype,htype = atom types for TIP4P O and H
+  btype,atype = bond and angle types for TIP4P waters
+  qdist = distance from O atom to massless charge (distance units)
+  n, alpha_LJ, alpha_C = parameters of the soft-core potential
+  cutoff = global cutoff for LJ (and Coulombic if only 1 arg) (distance units)
+  cutoff2 = global cutoff for Coulombic (optional) (distance units)
+<em>lj/charmm/coul/long/soft</em> args = n alpha_LJ alpha_C inner outer (cutoff)
+  n, alpha_LJ, alpha_C = parameters of the soft-core potential
+  inner, outer = global switching cutoffs for LJ (and Coulombic if only 5 args)
+  cutoff = global cutoff for Coulombic (optional, outer is Coulombic cutoff if only 5 args)
+<em>coul/cut/soft</em> args = n alpha_C cutoff
+  n, alpha_C = parameters of the soft-core potential
+  cutoff = global cutoff for Coulomb interactions (distance units)
+<em>coul/long/soft</em> args = n alpha_C cutoff
+  n, alpha_C = parameters of the soft-core potential
+  cutoff = global cutoff for Coulomb interactions (distance units)
+<em>tip4p/long/soft</em> args = otype htype btype atype qdist n alpha_C cutoff
+  otype,htype = atom types for TIP4P O and H
+  btype,atype = bond and angle types for TIP4P waters
+  qdist = distance from O atom to massless charge (distance units)
+  n, alpha_C = parameters of the soft-core potential
+  cutoff = global cutoff for Coulomb interactions (distance units)
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>pair_style lj/cut/soft 2.0 0.5 9.5
 pair_coeff * * 0.28 3.1 1.0
 pair_coeff 1 1 0.28 3.1 1.0 9.5
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>pair_style lj/cut/coul/cut/soft 2.0 0.5 10.0 9.5
 pair_style lj/cut/coul/cut/soft 2.0 0.5 10.0 9.5 9.5
 pair_coeff * * 0.28 3.1 1.0
 pair_coeff 1 1 0.28 3.1 0.5 10.0
 pair_coeff 1 1 0.28 3.1 0.5 10.0 9.5
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>pair_style lj/cut/coul/long/soft 2.0 0.5 10.0 9.5
 pair_style lj/cut/coul/long/soft 2.0 0.5 10.0 9.5 9.5
 pair_coeff * * 0.28 3.1 1.0
 pair_coeff 1 1 0.28 3.1 0.0 10.0
 pair_coeff 1 1 0.28 3.1 0.0 10.0 9.5
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>pair_style lj/cut/tip4p/long/soft 1 2 7 8 0.15 2.0 0.5 10.0 9.8
 pair_style lj/cut/tip4p/long/soft 1 2 7 8 0.15 2.0 0.5 10.0 9.8 9.5
 pair_coeff * * 0.155 3.1536 1.0
 pair_coeff 1 1 0.155 3.1536 1.0 9.5
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>pair_style lj/charmm/coul/long 2.0 0.5 10.0 8.0 10.0
 pair_style lj/charmm/coul/long 2.0 0.5 10.0 8.0 10.0 9.0
 pair_coeff * * 0.28 3.1 1.0
 pair_coeff 1 1 0.28 3.1 1.0 0.14 3.1
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>pair_style coul/long/soft 1.0 10.0 9.5
 pair_coeff * * 1.0
 pair_coeff 1 1 1.0 9.5
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>pair_style tip4p/long/soft 1 2 7 8 0.15 2.0 0.5 10.0 9.8
 pair_coeff * * 1.0
 pair_coeff 1 1 1.0 9.5
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>The <em>lj/cut/soft</em> style and substyles compute the 12/6 Lennard-Jones
 and Coulomb potential modified by a soft core, in order to avoid
 singularities during free energy calculations when sites are created
 or anihilated <a class="reference internal" href="#beutler"><span>(Beutler)</span></a>,</p>
 <img alt="_images/pair_lj_soft.jpg" class="align-center" src="_images/pair_lj_soft.jpg" />
 <p>Coulomb interactions are also damped with a soft core at short
 distance,</p>
 <img alt="_images/pair_coul_soft.jpg" class="align-center" src="_images/pair_coul_soft.jpg" />
 <p>In the Coulomb part C is an energy-conversion constant, q_i and q_j
 are the charges on the 2 atoms, and epsilon is the dielectric constant
 which can be set by the <a class="reference internal" href="dielectric.html"><em>dielectric</em></a> command.</p>
 <p>The coefficient lambda is an activation parameter. When lambda = 1 the
 pair potentiel is identical to a Lennard-Jones term or a Coulomb term
 or a combination of both. When lambda = 0 the interactions are
 deactivated. The transition between these two extrema is smoothed by a
 soft repulsive core in order to avoid singularities in potential
 energy and forces when sites are created or anihilated and can overlap
 <a class="reference internal" href="#beutler"><span>(Beutler)</span></a>.</p>
 <p>The paratemers n, alpha_LJ and alpha_C are set in the
 <a class="reference internal" href="pair_style.html"><em>pair_style</em></a> command, before the cutoffs.  Usual
 choices for the exponent are n = 2 or n = 1. For the remaining
 coefficients alpha_LJ = 0.5 and alpha_C = 10 Angstrom^2 are
 appropriate choices. Plots of the LJ and Coulomb terms are shown
 below, for lambda ranging from 1 to 0 every 0.1.</p>
 <img alt="_images/lj_soft.jpg" class="align-center" src="_images/lj_soft.jpg" />
 <img alt="_images/coul_soft.jpg" class="align-center" src="_images/coul_soft.jpg" />
 <p>For the <em>lj/cut/coul/cut/soft</em> or <em>lj/cut/coul/long/soft</em> pair styles,
 the following coefficients must be defined for each pair of atoms
 types via the <a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a> command as in the examples
 above, or in the data file or restart files read by the
 <a class="reference internal" href="read_data.html"><em>read_data</em></a> or <a class="reference internal" href="read_restart.html"><em>read_restart</em></a>
 commands, or by mixing as described below:</p>
 <ul class="simple">
 <li>epsilon (energy units)</li>
 <li>sigma (distance units)</li>
 <li>lambda (activation parameter between 0 and 1)</li>
 <li>cutoff1 (distance units)</li>
 <li>cutoff2 (distance units)</li>
 </ul>
 <p>The latter two coefficients are optional.  If not specified, the global
 LJ and Coulombic cutoffs specified in the pair_style command are used.
 If only one cutoff is specified, it is used as the cutoff for both LJ
 and Coulombic interactions for this type pair.  If both coefficients
 are specified, they are used as the LJ and Coulombic cutoffs for this
 type pair.  You cannot specify 2 cutoffs for style <em>lj/cut/soft</em>,
 since it has no Coulombic terms. For the <em>coul/cut/soft</em> and
 <em>coul/long/soft</em> only lambda and the optional cutoff2 are to be
 specified.</p>
 <p>Style <em>lj/cut/tip4p/long/soft</em> implements a soft-core version of the
 TIP4P water model. The usage of this pair style is documented in the
 <a class="reference internal" href="pair_lj.html"><em>pair_lj</em></a> styles. The soft-core version introduces the
 lambda parameter to the list of arguments, after epsilon and sigma in
 the <a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a> command. The paratemers n, alpha_LJ
 and alpha_C are set in the <a class="reference internal" href="pair_style.html"><em>pair_style</em></a> command,
 before the cutoffs.</p>
 <p>Style <em>lj/charmm/coul/long/soft</em> implements a soft-core version of the
 CHARMM version of LJ interactions with an additional switching
 function S(r) that ramps the energy and force smoothly to zero between
 an inner and outer cutoff. The usage of this pair style is documented
 in the <a class="reference internal" href="pair_charmm.html"><em>pair_charmm</em></a> styles. The soft-core version
 introduces the lambda parameter to the list of arguments, after
 epsilon and sigma in the <a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a> command (and
 before the optional eps14 and sigma14). The paratemers n,
 alpha_LJ and alpha_C are set in the <a class="reference internal" href="pair_style.html"><em>pair_style</em></a>
 command, before the cutoffs.</p>
 <p>The <em>coul/cut/soft</em>, <em>coul/long/soft</em> and <em>tip4p/long/soft</em> substyles
 are designed to be combined with other pair potentials via the
 <a class="reference internal" href="pair_hybrid.html"><em>pair_style hybrid/overlay</em></a> command.  This is because
 they have no repulsive core.  Hence, if used by themselves, there will
 be no repulsion to keep two oppositely charged particles from
 overlapping each other. In this case, if lambda = 1, a singularity may
 occur.  These substyles are suitable to represent charges embedded in
 the Lennard-Jones radius of another site (for example hydrogen atoms
 in several water models).</p>
 <p>IMPORTANT NOTES: When using the core-softed Coulomb potentials with
 long-range solvers (<em>coul/long/soft</em>, <em>lj/cut/coul/long/soft</em>, etc.)
 in a free energy calculation in which sites holding electrostatic
 charges are being created or anihilated (using
 <a class="reference internal" href="fix_adapt_fep.html"><em>fix_adapt/fep</em></a> and <a class="reference internal" href="compute_fep.html"><em>compute_fep</em></a>)
 it is important to adapt both the lambda activation parameter (from 0
 to 1, or the reverse) and the value of the charge (from 0 to its final
 value, or the reverse). This ensures that long-range electrostatic
 terms (kspace) are correct. It is not necessary to use core-softed
 Coulomb potentials if the van der Waals site is present during the
 free-energy route, thus avoiding overlap of the charges. Examples are
 provided in the LAMMPS source directory tree, under examples/USER/fep.</p>
 <hr class="docutils" />
 <p>Styles with a <em>cuda</em>, <em>gpu</em>, <em>intel</em>, <em>kk</em>, <em>omp</em>, or <em>opt</em> suffix are
 functionally the same as the corresponding style without the suffix.
 They have been optimized to run faster, depending on your available
 hardware, as discussed in <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a>
 of the manual.  The accelerated styles take the same arguments and
 should produce the same results, except for round-off and precision
 issues.</p>
 <p>These accelerated styles are part of the USER-CUDA, GPU, USER-INTEL,
 KOKKOS, USER-OMP and OPT packages, respectively.  They are only
 enabled if LAMMPS was built with those packages.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 <p>You can specify the accelerated styles explicitly in your input script
 by including their suffix, or you can use the <a class="reference internal" href="Section_start.html#start-7"><span>-suffix command-line switch</span></a> when you invoke LAMMPS, or you can
 use the <a class="reference internal" href="suffix.html"><em>suffix</em></a> command in your input script.</p>
 <p>See <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a> of the manual for
 more instructions on how to use the accelerated styles effectively.</p>
 <hr class="docutils" />
 <p><strong>Mixing, shift, tail correction, restart info</strong>:</p>
 <p>For atom type pairs I,J and I != J, the epsilon and sigma coefficients
 and cutoff distance for this pair style can be mixed.
 The default mix value is <em>geometric</em>.  See the &#8220;pair_modify&#8221; command
 for details.</p>
 <p>These pair styles support the <a class="reference internal" href="pair_modify.html"><em>pair_modify</em></a> shift
 option for the energy of the Lennard-Jones portion of the pair
 interaction.</p>
 <p>These pair styles support the <a class="reference internal" href="pair_modify.html"><em>pair_modify</em></a> tail
 option for adding a long-range tail correction to the energy and
 pressure for the Lennard-Jones portion of the pair interaction.</p>
 <p>These pair styles write information to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>, so pair_style and pair_coeff commands do not need
 to be specified in an input script that reads a restart file.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>To avoid division by zero do not set sigma = 0; use the lambda
 parameter instead to activate/deactivate interactions, or use
 epsilon = 0 and sigma = 1. Alternatively, when sites do not
 interact though the Lennard-Jones term the <em>coul/long/soft</em> or
 similar substyle can be used via the
 <a class="reference internal" href="pair_hybrid.html"><em>pair_style hybrid/overlay</em></a> command.</p>
 <hr class="docutils" />
 <p>All of the plain <em>soft</em> pair styles are part of the USER-FEP package.
 The <em>long</em> styles also requires the KSPACE package to be installed.
 They are only enabled if LAMMPS was built with those packages.  See
 the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a>, <a class="reference internal" href="fix_adapt.html"><em>fix_adapt</em></a>,
 <a class="reference internal" href="fix_adapt_fep.html"><em>fix_adapt/fep</em></a>, <a class="reference internal" href="compute_fep.html"><em>compute_fep</em></a></p>
 <p><strong>Default:</strong> none</p>
 <hr class="docutils" />
 <p id="beutler"><strong>(Beutler)</strong> Beutler, Mark, van Schaik, Gerber, van Gunsteren, Chem
 Phys Lett, 222, 529 (1994).</p>
 </div>
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   <div class="section" id="pair-style-meam-command">
 <span id="index-0"></span><h1>pair_style meam command<a class="headerlink" href="#pair-style-meam-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>pair_style meam
 </pre></div>
 </div>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>pair_style meam
 pair_coeff * * ../potentials/library.meam Si ../potentials/si.meam Si
 pair_coeff * * ../potentials/library.meam Ni Al NULL Ni Al Ni Ni
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <div class="admonition note">
 <p class="first admonition-title">Note</p>
 <p class="last">The behavior of the MEAM potential for alloy systems has changed
 as of November 2010; see description below of the mixture_ref_t
 parameter</p>
 </div>
 <p>Style <em>meam</em> computes pairwise interactions for a variety of materials
 using modified embedded-atom method (MEAM) potentials
 <a class="reference internal" href="#baskes"><span>(Baskes)</span></a>.  Conceptually, it is an extension to the original
 <a class="reference internal" href="pair_eam.html"><em>EAM potentials</em></a> which adds angular forces.  It is
 thus suitable for modeling metals and alloys with fcc, bcc, hcp and
 diamond cubic structures, as well as covalently bonded materials like
 silicon and carbon.</p>
 <p>In the MEAM formulation, the total energy E of a system of atoms is
 given by:</p>
 <img alt="_images/pair_meam.jpg" class="align-center" src="_images/pair_meam.jpg" />
 <p>where F is the embedding energy which is a function of the atomic
 electron density rho, and phi is a pair potential interaction.  The
 pair interaction is summed over all neighbors J of atom I within the
 cutoff distance.  As with EAM, the multi-body nature of the MEAM
 potential is a result of the embedding energy term.  Details of the
 computation of the embedding and pair energies, as implemented in
 LAMMPS, are given in <a class="reference internal" href="#gullet"><span>(Gullet)</span></a> and references therein.</p>
 <p>The various parameters in the MEAM formulas are listed in two files
 which are specified by the <a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a> command.
 These are ASCII text files in a format consistent with other MD codes
 that implement MEAM potentials, such as the serial DYNAMO code and
 Warp.  Several MEAM potential files with parameters for different
 materials are included in the &#8220;potentials&#8221; directory of the LAMMPS
 distribution with a &#8221;.meam&#8221; suffix.  All of these are parameterized in
 terms of LAMMPS <a class="reference internal" href="units.html"><em>metal units</em></a>.</p>
 <p>Note that unlike for other potentials, cutoffs for MEAM potentials are
 not set in the pair_style or pair_coeff command; they are specified in
 the MEAM potential files themselves.</p>
 <p>Only a single pair_coeff command is used with the <em>meam</em> style which
 specifies two MEAM files and the element(s) to extract information
 for.  The MEAM elements are mapped to LAMMPS atom types by specifying
 N additional arguments after the 2nd filename in the pair_coeff
 command, where N is the number of LAMMPS atom types:</p>
 <ul class="simple">
 <li>MEAM library file</li>
 <li>Elem1, Elem2, ...</li>
 <li>MEAM parameter file</li>
 <li>N element names = mapping of MEAM elements to atom types</li>
 </ul>
 <p>See the <a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a> doc page for alternate ways
 to specify the path for the potential files.</p>
 <p>As an example, the potentials/library.meam file has generic MEAM
 settings for a variety of elements.  The potentials/sic.meam file has
 specific parameter settings for a Si and C alloy system.  If your
 LAMMPS simulation has 4 atoms types and you want the 1st 3 to be Si,
 and the 4th to be C, you would use the following pair_coeff command:</p>
 <div class="highlight-python"><div class="highlight"><pre>pair_coeff * * library.meam Si C sic.meam Si Si Si C
 </pre></div>
 </div>
 <p>The 1st 2 arguments must be * * so as to span all LAMMPS atom types.
 The two filenames are for the library and parameter file respectively.
 The Si and C arguments (between the file names) are the two elements
 for which info will be extracted from the library file.  The first
 three trailing Si arguments map LAMMPS atom types 1,2,3 to the MEAM Si
 element.  The final C argument maps LAMMPS atom type 4 to the MEAM C
 element.</p>
 <p>If the 2nd filename is specified as NULL, no parameter file is read,
 which simply means the generic parameters in the library file are
 used.  Use of the NULL specification for the parameter file is
 discouraged for systems with more than a single element type
 (e.g. alloys), since the parameter file is expected to set element
 interaction terms that are not captured by the information in the
 library file.</p>
 <p>If a mapping value is specified as NULL, the mapping is not performed.
 This can be used when a <em>meam</em> potential is used as part of the
 <em>hybrid</em> pair style.  The NULL values are placeholders for atom types
 that will be used with other potentials.</p>
 <p>The MEAM library file provided with LAMMPS has the name
 potentials/library.meam.  It is the &#8220;meamf&#8221; file used by other MD
 codes.  Aside from blank and comment lines (start with #) which can
 appear anywhere, it is formatted as a series of entries, each of which
 has 19 parameters and can span multiple lines:</p>
 <p>elt, lat, z, ielement, atwt, alpha, b0, b1, b2, b3, alat, esub, asub,
 t0, t1, t2, t3, rozero, ibar</p>
 <p>The &#8220;elt&#8221; and &#8220;lat&#8221; parameters are text strings, such as elt = Si or
 Cu and lat = dia or fcc.  Because the library file is used by Fortran
 MD codes, these strings may be enclosed in single quotes, but this is
 not required.  The other numeric parameters match values in the
 formulas above.  The value of the &#8220;elt&#8221; string is what is used in the
 pair_coeff command to identify which settings from the library file
 you wish to read in.  There can be multiple entries in the library
 file with the same &#8220;elt&#8221; value; LAMMPS reads the 1st matching entry it
 finds and ignores the rest.</p>
 <p>Other parameters in the MEAM library file correspond to single-element
 potential parameters:</p>
 <pre class="literal-block">
 lat      = lattice structure of reference configuration
 z        = number of nearest neighbors in the reference structure
 ielement = atomic number
 atwt     = atomic weight
 alat     = lattice constant of reference structure
 esub     = energy per atom (eV) in the reference structure at equilibrium
 asub     = &quot;A&quot; parameter for MEAM (see e.g. <a class="reference internal" href="#baskes"><span>(Baskes)</span></a>)
 </pre>
 <p>The alpha, b0, b1, b2, b3, t0, t1, t2, t3 parameters correspond to the
 standard MEAM parameters in the literature <a class="reference internal" href="#baskes"><span>(Baskes)</span></a> (the b
 parameters are the standard beta parameters).  The rozero parameter is
 an element-dependent density scaling that weights the reference
 background density (see e.g. equation 4.5 in <a class="reference internal" href="#gullet"><span>(Gullet)</span></a>) and
 is typically 1.0 for single-element systems.  The ibar parameter
 selects the form of the function G(Gamma) used to compute the electron
 density; options are</p>
-<div class="highlight-python"><div class="highlight"><pre>0 =&gt; G = sqrt(1+Gamma)
-   1 =&gt; G = exp(Gamma/2)
-   2 =&gt; not implemented
-   3 =&gt; G = 2/(1+exp(-Gamma))
-   4 =&gt; G = sqrt(1+Gamma)
-  -5 =&gt; G = +-sqrt(abs(1+Gamma))
+<div class="highlight-python"><div class="highlight"><pre> 0 =&gt; G = sqrt(1+Gamma)
+ 1 =&gt; G = exp(Gamma/2)
+ 2 =&gt; not implemented
+ 3 =&gt; G = 2/(1+exp(-Gamma))
+ 4 =&gt; G = sqrt(1+Gamma)
+-5 =&gt; G = +-sqrt(abs(1+Gamma))
 </pre></div>
 </div>
 <p>If used, the MEAM parameter file contains settings that override or
 complement the library file settings.  Examples of such parameter
 files are in the potentials directory with a &#8221;.meam&#8221; suffix.  Their
 format is the same as is read by other Fortran MD codes.  Aside from
 blank and comment lines (start with #) which can appear anywhere, each
 line has one of the following forms.  Each line can also have a
 trailing comment (starting with #) which is ignored.</p>
 <div class="highlight-python"><div class="highlight"><pre><span class="n">keyword</span> <span class="o">=</span> <span class="n">value</span>
 <span class="n">keyword</span><span class="p">(</span><span class="n">I</span><span class="p">)</span> <span class="o">=</span> <span class="n">value</span>
 <span class="n">keyword</span><span class="p">(</span><span class="n">I</span><span class="p">,</span><span class="n">J</span><span class="p">)</span> <span class="o">=</span> <span class="n">value</span>
 <span class="n">keyword</span><span class="p">(</span><span class="n">I</span><span class="p">,</span><span class="n">J</span><span class="p">,</span><span class="n">K</span><span class="p">)</span> <span class="o">=</span> <span class="n">value</span>
 </pre></div>
 </div>
 <p>The recognized keywords are as follows:</p>
 <p>Ec, alpha, rho0, delta, lattce, attrac, repuls, nn2, Cmin, Cmax, rc, delr,
 augt1, gsmooth_factor, re</p>
 <p>where</p>
 <pre class="literal-block">
 rc          = cutoff radius for cutoff function; default = 4.0
 delr        = length of smoothing distance for cutoff function; default = 0.1
 rho0(I)     = relative density for element I (overwrites value
               read from meamf file)
 Ec(I,J)     = cohesive energy of reference structure for I-J mixture
 delta(I,J)  = heat of formation for I-J alloy; if Ec_IJ is input as
               zero, then LAMMPS sets Ec_IJ = (Ec_II + Ec_JJ)/2 - delta_IJ
 alpha(I,J)  = alpha parameter for pair potential between I and J (can
               be computed from bulk modulus of reference structure
 re(I,J)     = equilibrium distance between I and J in the reference
               structure
 Cmax(I,J,K) = Cmax screening parameter when I-J pair is screened
               by K (I&lt;=J); default = 2.8
 Cmin(I,J,K) = Cmin screening parameter when I-J pair is screened
               by K (I&lt;=J); default = 2.0
 lattce(I,J) = lattice structure of I-J reference structure:
                 dia = diamond (interlaced fcc for alloy)
                 fcc = face centered cubic
                 bcc = body centered cubic
                 dim = dimer
                 b1  = rock salt (NaCl structure)
              hcp = hexagonal close-packed
              c11 = MoSi2 structure
              l12 = Cu3Au structure (lower case L, followed by 12)
                 b2  = CsCl structure (interpenetrating simple cubic)
 nn2(I,J)    = turn on second-nearest neighbor MEAM formulation for
               I-J pair (see for example <a class="reference internal" href="#lee"><span>(Lee)</span></a>).
                 0 = second-nearest neighbor formulation off
                 1 = second-nearest neighbor formulation on
                 default = 0
 attrac(I,J) = additional cubic attraction term in Rose energy I-J pair potential
                 default = 0
 repuls(I,J) = additional cubic repulsive term in Rose energy I-J pair potential
                 default = 0
 zbl(I,J)    = blend the MEAM I-J pair potential with the ZBL potential for small
               atom separations <a class="reference internal" href="pair_tersoff_zbl.html#zbl"><span>(ZBL)</span></a>
                 default = 1
 gsmooth_factor  = factor determining the length of the G-function smoothing
                   region; only significant for ibar=0 or ibar=4.
                       99.0 = short smoothing region, sharp step
                       0.5  = long smoothing region, smooth step
                       default = 99.0
 augt1           = integer flag for whether to augment t1 parameter by
                   3/5*t3 to account for old vs. new meam formulations;
                     0 = don't augment t1
                     1 = augment t1
                     default = 1
 ialloy          = integer flag to use alternative averaging rule for t parameters,
                   for comparison with the DYNAMO MEAM code
                     0 = standard averaging (matches ialloy=0 in DYNAMO)
                     1 = alternative averaging (matches ialloy=1 in DYNAMO)
                     2 = no averaging of t (use single-element values)
                     default = 0
 mixture_ref_t   = integer flag to use mixture average of t to compute the background
                   reference density for alloys, instead of the single-element values
                   (see description and warning elsewhere in this doc page)
                     0 = do not use mixture averaging for t in the reference density
                     1 = use mixture averaging for t in the reference density
                     default = 0
 erose_form      = integer value to select the form of the Rose energy function
                   (see description below).
                     default = 0
 emb_lin_neg     = integer value to select embedding function for negative densities
                     0 = F(rho)=0
                     1 = F(rho) = -asub*esub*rho (linear in rho, matches DYNAMO)
                     default = 0
 bkgd_dyn        = integer value to select background density formula
                     0 = rho_bkgd = rho_ref_meam(a) (as in the reference structure)
                     1 = rho_bkgd = rho0_meam(a)*Z_meam(a) (matches DYNAMO)
                     default = 0
 </pre>
 <p>Rc, delr, re are in distance units (Angstroms in the case of metal
 units).  Ec and delta are in energy units (eV in the case of metal
 units).</p>
 <p>Each keyword represents a quantity which is either a scalar, vector,
 2d array, or 3d array and must be specified with the correct
 corresponding array syntax.  The indices I,J,K each run from 1 to N
 where N is the number of MEAM elements being used.</p>
 <p>Thus these lines</p>
 <div class="highlight-python"><div class="highlight"><pre><span class="n">rho0</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span> <span class="o">=</span> <span class="mf">2.25</span>
 <span class="n">alpha</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">)</span> <span class="o">=</span> <span class="mf">4.37</span>
 </pre></div>
 </div>
 <p>set rho0 for the 2nd element to the value 2.25 and set alpha for the
 alloy interaction between elements 1 and 2 to 4.37.</p>
 <p>The augt1 parameter is related to modifications in the MEAM
 formulation of the partial electron density function.  In recent
 literature, an extra term is included in the expression for the
 third-order density in order to make the densities orthogonal (see for
 example <a class="reference internal" href="pair_polymorphic.html#wang"><span>(Wang)</span></a>, equation 3d); this term is included in the
 MEAM implementation in lammps.  However, in earlier published work
 this term was not included when deriving parameters, including most of
 those provided in the library.meam file included with lammps, and to
 account for this difference the parameter t1 must be augmented by
 3/5*t3.  If augt1=1, the default, this augmentation is done
 automatically.  When parameter values are fit using the modified
 density function, as in more recent literature, augt1 should be set to
 0.</p>
 <p>The mixture_ref_t parameter is available to match results with those
 of previous versions of lammps (before January 2011).  Newer versions
 of lammps, by default, use the single-element values of the t
 parameters to compute the background reference density.  This is the
 proper way to compute these parameters.  Earlier versions of lammps
 used an alloy mixture averaged value of t to compute the background
 reference density.  Setting mixture_ref_t=1 gives the old behavior.
 WARNING: using mixture_ref_t=1 will give results that are demonstrably
 incorrect for second-neighbor MEAM, and non-standard for
 first-neighbor MEAM; this option is included only for matching with
 previous versions of lammps and should be avoided if possible.</p>
 <p>The parameters attrac and repuls, along with the integer selection
 parameter erose_form, can be used to modify the Rose energy function
 used to compute the pair potential.  This function gives the energy of
 the reference state as a function of interatomic spacing.  The form of
 this function is:</p>
 <div class="highlight-python"><div class="highlight"><pre>astar = alpha * (r/re - 1.d0)
 if erose_form = 0: erose = -Ec*(1+astar+a3*(astar**3)/(r/re))*exp(-astar)
 if erose_form = 1: erose = -Ec*(1+astar+(-attrac+repuls/r)*(astar**3))*exp(-astar)
 if erose_form = 2: erose = -Ec*(1 +astar + a3*(astar**3))*exp(-astar)
 a3 = repuls, astar &lt; 0
 a3 = attrac, astar &gt;= 0
 </pre></div>
 </div>
 <p>Most published MEAM parameter sets use the default values attrac=repulse=0.
 Setting repuls=attrac=delta corresponds to the form used in several
 recent published MEAM parameter sets, such as <span class="xref std std-ref">(Vallone)</span></p>
 <div class="admonition note">
 <p class="first admonition-title">Note</p>
 <p class="last">The default form of the erose expression in LAMMPS was corrected
 in March 2009.  The current version is correct, but may show different
 behavior compared with earlier versions of lammps with the attrac
 and/or repuls parameters are non-zero.  To obtain the previous default
 form, use erose_form = 1 (this form does not seem to appear in the
 literature).  An alternative form (see e.g. <a class="reference internal" href="#lee2"><span>(Lee2)</span></a>) is
 available using erose_form = 2.</p>
 </div>
 <hr class="docutils" />
 <p><strong>Mixing, shift, table, tail correction, restart, rRESPA info</strong>:</p>
 <p>For atom type pairs I,J and I != J, where types I and J correspond to
 two different element types, mixing is performed by LAMMPS with
 user-specifiable parameters as described above.  You never need to
 specify a pair_coeff command with I != J arguments for this style.</p>
 <p>This pair style does not support the <a class="reference internal" href="pair_modify.html"><em>pair_modify</em></a>
 shift, table, and tail options.</p>
 <p>This pair style does not write its information to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>, since it is stored in potential files.  Thus, you
 need to re-specify the pair_style and pair_coeff commands in an input
 script that reads a restart file.</p>
 <p>This pair style can only be used via the <em>pair</em> keyword of the
 <a class="reference internal" href="run_style.html"><em>run_style respa</em></a> command.  It does not support the
 <em>inner</em>, <em>middle</em>, <em>outer</em> keywords.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>This style is part of the MEAM package.  It is only enabled if LAMMPS
 was built with that package, which also requires the MEAM library be
 built and linked with LAMMPS.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a>, <a class="reference internal" href="pair_eam.html"><em>pair_style eam</em></a>,
 <a class="reference internal" href="pair_meam_spline.html"><em>pair_style meam/spline</em></a></p>
 <p><strong>Default:</strong> none</p>
 <hr class="docutils" />
 <p id="baskes"><strong>(Baskes)</strong> Baskes, Phys Rev B, 46, 2727-2742 (1992).</p>
 <p id="gullet"><strong>(Gullet)</strong> Gullet, Wagner, Slepoy, SANDIA Report 2003-8782 (2003).
 This report may be accessed on-line via <a class="reference external" href="http://infoserve.sandia.gov/sand_doc/2003/038782.pdf">this link</a>.</p>
 <p id="lee"><strong>(Lee)</strong> Lee, Baskes, Phys. Rev. B, 62, 8564-8567 (2000).</p>
 <p id="lee2"><strong>(Lee2)</strong> Lee, Baskes, Kim, Cho.  Phys. Rev. B, 64, 184102 (2001).</p>
 <p id="valone"><strong>(Valone)</strong> Valone, Baskes, Martin, Phys. Rev. B, 73, 214209 (2006).</p>
 <p id="wang"><strong>(Wang)</strong> Wang, Van Hove, Ross, Baskes, J. Chem. Phys., 121, 5410 (2004).</p>
 <p id="zbl"><strong>(ZBL)</strong> J.F. Ziegler, J.P. Biersack, U. Littmark, &#8220;Stopping and Ranges
 of Ions in Matter&#8221;, Vol 1, 1985, Pergamon Press.</p>
 </div>
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 <li class="toctree-l1"><a class="reference internal" href="Section_modify.html">10. Modifying &amp; extending LAMMPS</a></li>
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   <div class="section" id="pair-modify-command">
 <span id="index-0"></span><h1>pair_modify command<a class="headerlink" href="#pair-modify-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>pair_modify keyword values ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>one or more keyword/value pairs may be listed</li>
 <li>keyword = <em>pair</em> or <em>special</em> or <em>shift</em> or <em>mix</em> or <em>table</em> or <em>table/disp</em> or <em>tabinner</em> or <em>tabinner/disp</em> or <em>tail</em> or <em>compute</em></li>
 </ul>
 <pre class="literal-block">
 <em>pair</em> values = sub-style N special which w1 wt2 wt3
-    sub-style = sub-style of <a class="reference internal" href="pair_hybrid.html"><em>pair hybrid</em></a>
-    N = which instance of sub-style (only if sub-style is used multiple times)
-  <em>special</em> values = flavor w1 w2 w3
-    flavor = <em>lj/coul</em> or <em>lj</em> or <em>coul</em>
-    w1,w2,w3 = weights from 0.0 to 1.0 inclusive
-  <em>mix</em> value = <em>geometric</em> or <em>arithmetic</em> or <em>sixthpower</em>
-  <em>shift</em> value = <em>yes</em> or <em>no</em>
-  <em>table</em> value = N
-    2^N = # of values in table
-  <em>table/disp</em> value = N
-    2^N = # of values in table
-  <em>tabinner</em> value = cutoff
-    cutoff = inner cutoff at which to begin table (distance units)
-  <em>tabinner/disp</em> value = cutoff
-    cutoff = inner cutoff at which to begin table (distance units)
-  <em>tail</em> value = <em>yes</em> or <em>no</em>
-  <em>compute</em> value = <em>yes</em> or <em>no</em>
+  sub-style = sub-style of <a class="reference internal" href="pair_hybrid.html"><em>pair hybrid</em></a>
+  N = which instance of sub-style (only if sub-style is used multiple times)
+<em>special</em> values = flavor w1 w2 w3
+  flavor = <em>lj/coul</em> or <em>lj</em> or <em>coul</em>
+  w1,w2,w3 = weights from 0.0 to 1.0 inclusive
+<em>mix</em> value = <em>geometric</em> or <em>arithmetic</em> or <em>sixthpower</em>
+<em>shift</em> value = <em>yes</em> or <em>no</em>
+<em>table</em> value = N
+  2^N = # of values in table
+<em>table/disp</em> value = N
+  2^N = # of values in table
+<em>tabinner</em> value = cutoff
+  cutoff = inner cutoff at which to begin table (distance units)
+<em>tabinner/disp</em> value = cutoff
+  cutoff = inner cutoff at which to begin table (distance units)
+<em>tail</em> value = <em>yes</em> or <em>no</em>
+<em>compute</em> value = <em>yes</em> or <em>no</em>
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>pair_modify shift yes mix geometric
 pair_modify tail yes
 pair_modify table 12
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Modify the parameters of the currently defined pair style.  Not all
 parameters are relevant to all pair styles.</p>
 <p>If used, the <em>pair</em> keyword must appear first in the list of keywords.
 It can only be used with the <a class="reference internal" href="pair_hybrid.html"><em>hybrid and hybrid/overlay</em></a> pair styles.  It means that all the
 following parameters will only be modified for the specified
 sub-style.  If the sub-style is defined multiple times, then an
 additional numeric argument <em>N</em> must also be specified, which is a
 number from 1 to M where M is the number of times the sub-style was
 listed in the <a class="reference internal" href="pair_hybrid.html"><em>pair_style hybrid</em></a> command.  The extra
 number indicates which instance of the sub-style the remaining
 keywords will be applied to.  Note that if the <em>pair</em> keyword is not
 used, and the pair style is <em>hybrid</em> or <em>hybrid/overlay</em>, then all the
 specified keywords will be applied to all sub-styles.</p>
 <p>If used, the <em>special</em> keyword must appear second in the list of
 keywords, and must follow the <em>pair</em> keyword.  Like the <em>pair</em>
 keyword, it also can only be used with the <a class="reference internal" href="pair_hybrid.html"><em>hybrid and hybrid/overlay</em></a> pair styles.  Its parameters are
 similar to the <a class="reference internal" href="special_bonds.html"><em>special_bonds</em></a> command, and it
 overrides the special_bond settings for the specified sub-style.  More
 details are given below.</p>
 <p>The <em>mix</em> keyword affects pair coefficients for interactions between
 atoms of type I and J, when I != J and the coefficients are not
 explicitly set in the input script.  Note that coefficients for I = J
 must be set explicitly, either in the input script via the
 &#8220;pair_coeff&#8221; command or in the &#8220;Pair Coeffs&#8221; section of the <a class="reference internal" href="read_data.html"><em>data file</em></a>.  For some pair styles it is not necessary to
 specify coefficients when I != J, since a &#8220;mixing&#8221; rule will create
 them from the I,I and J,J settings.  The pair_modify <em>mix</em> value
 determines what formulas are used to compute the mixed coefficients.
 In each case, the cutoff distance is mixed the same way as sigma.</p>
 <p>Note that not all pair styles support mixing.  Also, some mix options
 are not available for certain pair styles.  See the doc page for
 individual pair styles for those restrictions.  Note also that the
 <a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a> command also can be to directly set
 coefficients for a specific I != J pairing, in which case no mixing is
 performed.</p>
 <p>mix <em>geometric</em></p>
 <div class="highlight-python"><div class="highlight"><pre><span class="n">epsilon_ij</span> <span class="o">=</span> <span class="n">sqrt</span><span class="p">(</span><span class="n">epsilon_i</span> <span class="o">*</span> <span class="n">epsilon_j</span><span class="p">)</span>
 <span class="n">sigma_ij</span> <span class="o">=</span> <span class="n">sqrt</span><span class="p">(</span><span class="n">sigma_i</span> <span class="o">*</span> <span class="n">sigma_j</span><span class="p">)</span>
 </pre></div>
 </div>
 <p>mix <em>arithmetic</em></p>
 <div class="highlight-python"><div class="highlight"><pre><span class="n">epsilon_ij</span> <span class="o">=</span> <span class="n">sqrt</span><span class="p">(</span><span class="n">epsilon_i</span> <span class="o">*</span> <span class="n">epsilon_j</span><span class="p">)</span>
 <span class="n">sigma_ij</span> <span class="o">=</span> <span class="p">(</span><span class="n">sigma_i</span> <span class="o">+</span> <span class="n">sigma_j</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</span>
 </pre></div>
 </div>
 <p>mix <em>sixthpower</em></p>
 <div class="highlight-python"><div class="highlight"><pre>epsilon_ij = (2 * sqrt(epsilon_i*epsilon_j) * sigma_i^3 * sigma_j^3) /
              (sigma_i^6 + sigma_j^6)
 sigma_ij = ((sigma_i**6 + sigma_j**6) / 2) ^ (1/6)
 </pre></div>
 </div>
 <p>The <em>shift</em> keyword determines whether a Lennard-Jones potential is
 shifted at its cutoff to 0.0.  If so, this adds an energy term to each
 pairwise interaction which will be included in the thermodynamic
 output, but does not affect pair forces or atom trajectories.  See the
 doc page for individual pair styles to see which ones support this
 option.</p>
 <p>The <em>table</em> and <em>table/disp</em> keywords apply to pair styles with a
 long-range Coulombic term or long-range dispersion term respectively;
 see the doc page for individual styles to see which potentials support
 these options.  If N is non-zero, a table of length 2^N is
 pre-computed for forces and energies, which can shrink their
 computational cost by up to a factor of 2.  The table is indexed via a
 bit-mapping technique <a class="reference internal" href="pair_table.html#wolff"><span>(Wolff)</span></a> and a linear interpolation is
 performed between adjacent table values.  In our experiments with
 different table styles (lookup, linear, spline), this method typically
 gave the best performance in terms of speed and accuracy.</p>
 <p>The choice of table length is a tradeoff in accuracy versus speed.  A
 larger N yields more accurate force computations, but requires more
 memory which can slow down the computation due to cache misses.  A
 reasonable value of N is between 8 and 16.  The default value of 12
 (table of length 4096) gives approximately the same accuracy as the
 no-table (N = 0) option.  For N = 0, forces and energies are computed
 directly, using a polynomial fit for the needed erfc() function
 evaluation, which is what earlier versions of LAMMPS did.  Values
 greater than 16 typically slow down the simulation and will not
 improve accuracy; values from 1 to 8 give unreliable results.</p>
 <p>The <em>tabinner</em> and <em>tabinner/disp</em> keywords set an inner cutoff above
 which the pairwise computation is done by table lookup (if tables are
 invoked), for the corresponding Coulombic and dispersion tables
 discussed with the <em>table</em> and <em>table/disp</em> keywords.  The smaller the
 cutoff is set, the less accurate the table becomes (for a given number
 of table values), which can require use of larger tables.  The default
 cutoff value is sqrt(2.0) distance units which means nearly all
 pairwise interactions are computed via table lookup for simulations
 with &#8220;real&#8221; units, but some close pairs may be computed directly
 (non-table) for simulations with &#8220;lj&#8221; units.</p>
 <p>When the <em>tail</em> keyword is set to <em>yes</em>, certain pair styles will add
 a long-range VanderWaals tail &#8220;correction&#8221; to the energy and pressure.
 These corrections are bookkeeping terms which do not affect dynamics,
 unless a constant-pressure simulation is being performed.  See the doc
 page for individual styles to see which support this option.  These
 corrections are included in the calculation and printing of
 thermodynamic quantities (see the <a class="reference internal" href="thermo_style.html"><em>thermo_style</em></a>
 command).  Their effect will also be included in constant NPT or NPH
 simulations where the pressure influences the simulation box
 dimensions (e.g. the <a class="reference internal" href="fix_nh.html"><em>fix npt</em></a> and <a class="reference internal" href="fix_nh.html"><em>fix nph</em></a>
 commands).  The formulas used for the long-range corrections come from
 equation 5 of <a class="reference internal" href="#sun"><span>(Sun)</span></a>.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">The tail correction terms are computed at the
 beginning of each run, using the current atom counts of each atom
 type.  If atoms are deleted (or lost) or created during a simulation,
 e.g. via the <a class="reference internal" href="fix_gcmc.html"><em>fix gcmc</em></a> command, the correction factors
 are not re-computed.  If you expect the counts to change dramatically,
 you can break a run into a series of shorter runs so that the
 correction factors are re-computed more frequently.</p>
 </div>
 <p>Several additional assumptions are inherent in using tail corrections,
 including the following:</p>
 <ul class="simple">
 <li>The simulated system is a 3d bulk homogeneous liquid. This option
 should not be used for systems that are non-liquid, 2d, have a slab
 geometry (only 2d periodic), or inhomogeneous.</li>
 <li>G(r), the radial distribution function (rdf), is unity beyond the
 cutoff, so a fairly large cutoff should be used (i.e. 2.5 sigma for an
 LJ fluid), and it is probably a good idea to verify this assumption by
 checking the rdf.  The rdf is not exactly unity beyond the cutoff for
 each pair of interaction types, so the tail correction is necessarily
 an approximation.</li>
 </ul>
 <p>The tail corrections are computed at the beginning of each simulation
 run.  If the number of atoms changes during the run, e.g. due to atoms
 leaving the simulation domain, or use of the <a class="reference internal" href="fix_gcmc.html"><em>fix gcmc</em></a>
 command, then the corrections are not updates to relect the changed
 atom count.  If this is a large effect in your simulation, you should
 break the long run into several short runs, so that the correction
 factors are re-computed multiple times.</p>
 <ul class="simple">
 <li>Thermophysical properties obtained from calculations with this option
 enabled will not be thermodynamically consistent with the truncated
 force-field that was used.  In other words, atoms do not feel any LJ
 pair interactions beyond the cutoff, but the energy and pressure
 reported by the simulation include an estimated contribution from
 those interactions.</li>
 </ul>
 <p>The <em>compute</em> keyword allows pairwise computations to be turned off,
 even though a <a class="reference internal" href="pair_style.html"><em>pair_style</em></a> is defined.  This is not
 useful for running a real simulation, but can be useful for debugging
 purposes or for performing a <a class="reference internal" href="rerun.html"><em>rerun</em></a> simulation, when you
 only wish to compute partial forces that do not include the pairwise
 contribution.</p>
 <p>Two examples are as follows.  First, this option allows you to perform
 a simulation with <a class="reference internal" href="pair_hybrid.html"><em>pair_style hybrid</em></a> with only a
 subset of the hybrid sub-styles enabled.  Second, this option allows
 you to perform a simulation with only long-range interactions but no
 short-range pairwise interactions.  Doing this by simply not defining
 a pair style will not work, because the
 <a class="reference internal" href="kspace_style.html"><em>kspace_style</em></a> command requires a Kspace-compatible
 pair style be defined.</p>
 <hr class="docutils" />
 <div class="section" id="use-of-special-keyword">
 <h3>Use of <em>special</em> keyword<a class="headerlink" href="#use-of-special-keyword" title="Permalink to this headline">¶</a></h3>
 <p>The <em>special</em> keyword requires 4 values similar to those specified
 with the <a class="reference internal" href="special_bonds.html"><em>special_bonds</em></a> command, <em>flavor</em> and
 w1,w2,w3.  The <em>flavor</em> argument can be <em>lj</em> to change the
 Lennard-Jones settings, <em>coul</em> to change the Coulombic settings, or
 <em>lj/coul</em> to change both to the same set of 3 values.  The w1,w2,w3
 values are numeric weights from 0.0 to 1.0 inclusive, for the 1-2,
 1-3, and 1-4 bond topology neighbors.  For example, these commands</p>
 <div class="highlight-python"><div class="highlight"><pre>special_bonds lj/coul 0.0 0.0 0.1
 pair_hybrid lj/charmm/coul/long 8.0 10.0 lj/cut/coul/long 10.0
 pair_modify pair lj/charmm/coul/long special lj/coul 0.0 0.0 0.0
 pair_modify pair lj/cut/coul/long special lj 0.0 0.0 0.5
 pair_modify pair lj/cut/coul/long special coul 0.0 0.0 0.8333
 </pre></div>
 </div>
 <p>show how to use both the CHARMM and AMBER force fields in a single
 simulation.  The first pair modify command sets the special bonds to
 CHARMM values (all 0.0).  The last 2 pair modify commands set the
 standard AMBER values for LJ and Coulombic weights.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">The global settings specified by the
 <a class="reference internal" href="special_bonds.html"><em>special_bonds</em></a> command affect the construction of
 neighbor lists.  Weights of 0.0 (for 1-2, 1-3, or 1-4 neighbors)
 exclude those pairs from the neighbor list entirely.  Weights of 1.0
 store the neighbor with no weighting applied.  The format of the
 neighbor list cannot be changed by setting a sub-style weight to a
 non-zero or non-one value.  Thus an error is generated if the new
 sub-style value is not 0.0 (or 1.0) when the global setting is 0.0 (or
 1.0).  Note that as in the example above, the global factor can simply
 be set a value other than 0.0 or 1.0, then overridden by any of the
 sub-styles with a value that is 0.0 or 1.0.</p>
 </div>
 </div>
 </div>
 <hr class="docutils" />
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <blockquote>
 <div>none</div></blockquote>
 <p>You cannot use <em>shift</em> yes with <em>tail</em> yes, since those are
 conflicting options.  You cannot use <em>tail</em> yes with 2d simulations.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="pair_style.html"><em>pair_style</em></a>, <a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a>,
 <a class="reference internal" href="thermo_style.html"><em>thermo_style</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The option defaults are mix = geometric, shift = no, table = 12,
 tabinner = sqrt(2.0), tail = no, and compute = yes.</p>
 <p>Note that some pair styles perform mixing, but only a certain style of
 mixing.  See the doc pages for individual pair styles for details.</p>
 <hr class="docutils" />
 <p id="wolff"><strong>(Wolff)</strong> Wolff and Rudd, Comp Phys Comm, 120, 200-32 (1999).</p>
 <p id="sun"><strong>(Sun)</strong> Sun, J Phys Chem B, 102, 7338-7364 (1998).</p>
 </div>
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   <div class="section" id="pair-style-nm-cut-command">
 <span id="index-0"></span><h1>pair_style nm/cut command<a class="headerlink" href="#pair-style-nm-cut-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-nm-cut-coul-cut-command">
 <h1>pair_style nm/cut/coul/cut command<a class="headerlink" href="#pair-style-nm-cut-coul-cut-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-nm-cut-coul-long-command">
 <h1>pair_style nm/cut/coul/long command<a class="headerlink" href="#pair-style-nm-cut-coul-long-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-nm-cut-omp-command">
 <h1>pair_style nm/cut/omp command<a class="headerlink" href="#pair-style-nm-cut-omp-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-nm-cut-coul-cut-omp-command">
 <h1>pair_style nm/cut/coul/cut/omp command<a class="headerlink" href="#pair-style-nm-cut-coul-cut-omp-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-nm-cut-coul-long-omp-command">
 <h1>pair_style nm/cut/coul/long/omp command<a class="headerlink" href="#pair-style-nm-cut-coul-long-omp-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>pair_style style args
 </pre></div>
 </div>
 <ul class="simple">
 <li>style = <em>nm/cut</em> or <em>nm/cut/coul/cut</em> or <em>nm/cut/coul/long</em></li>
 <li>args = list of arguments for a particular style</li>
 </ul>
 <pre class="literal-block">
 <em>nm/cut</em> args = cutoff
-    cutoff = global cutoff for Pair interactions (distance units)
-  <em>nm/cut/coul/cut</em> args = cutoff (cutoff2)
-    cutoff = global cutoff for Pair (and Coulombic if only 1 arg) (distance units)
-    cutoff2 = global cutoff for Coulombic (optional) (distance units)
-  <em>nm/cut/coul/long</em> args = cutoff (cutoff2)
-    cutoff = global cutoff for Pair (and Coulombic if only 1 arg) (distance units)
-    cutoff2 = global cutoff for Coulombic (optional) (distance units)
+  cutoff = global cutoff for Pair interactions (distance units)
+<em>nm/cut/coul/cut</em> args = cutoff (cutoff2)
+  cutoff = global cutoff for Pair (and Coulombic if only 1 arg) (distance units)
+  cutoff2 = global cutoff for Coulombic (optional) (distance units)
+<em>nm/cut/coul/long</em> args = cutoff (cutoff2)
+  cutoff = global cutoff for Pair (and Coulombic if only 1 arg) (distance units)
+  cutoff2 = global cutoff for Coulombic (optional) (distance units)
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>pair_style nm/cut 12.0
 pair_coeff * * 0.01 5.4 8.0 7.0
 pair_coeff 1 1 0.01 4.4 7.0 6.0
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>pair_style nm/cut/coul/cut 12.0 15.0
 pair_coeff * * 0.01 5.4 8.0 7.0
 pair_coeff 1 1 0.01 4.4 7.0 6.0
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>pair_style nm/cut/coul/long 12.0 15.0
 pair_coeff * * 0.01 5.4 8.0 7.0
 pair_coeff 1 1 0.01 4.4 7.0 6.0
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Style <em>nm</em> computes site-site interactions based on the N-M potential
 by <a class="reference internal" href="#clarke"><span>Clarke</span></a>, mainly used for ionic liquids.  A site can
 represent a single atom or a united-atom site.  The energy of an
 interaction has the following form:</p>
 <img alt="_images/pair_nm.jpg" class="align-center" src="_images/pair_nm.jpg" />
 <p>Rc is the cutoff.</p>
 <p>Style <em>nm/cut/coul/cut</em> adds a Coulombic pairwise interaction given by</p>
 <img alt="_images/pair_coulomb.jpg" class="align-center" src="_images/pair_coulomb.jpg" />
 <p>where C is an energy-conversion constant, Qi and Qj are the charges on
 the 2 atoms, and epsilon is the dielectric constant which can be set
 by the <a class="reference internal" href="dielectric.html"><em>dielectric</em></a> command.  If one cutoff is
 specified in the pair_style command, it is used for both the NM and
 Coulombic terms.  If two cutoffs are specified, they are used as
 cutoffs for the NM and Coulombic terms respectively.</p>
 <p>Styles <em>nm/cut/coul/long</em> compute the same
 Coulombic interactions as style <em>nm/cut/coul/cut</em> except that an
 additional damping factor is applied to the Coulombic term so it can
 be used in conjunction with the <a class="reference internal" href="kspace_style.html"><em>kspace_style</em></a>
 command and its <em>ewald</em> or <em>pppm</em> option.  The Coulombic cutoff
 specified for this style means that pairwise interactions within this
 distance are computed directly; interactions outside that distance are
 computed in reciprocal space.</p>
 <p>For all of the <em>nm</em> pair styles, the following coefficients must
 be defined for each pair of atoms types
 via the <a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a> command as in the
 examples above, or in the data file or restart files read by the
 <a class="reference internal" href="read_data.html"><em>read_data</em></a> or <a class="reference internal" href="read_restart.html"><em>read_restart</em></a>
 commands.</p>
 <ul class="simple">
 <li>E0 (energy units)</li>
 <li>r0 (distance units)</li>
 <li>n (unitless)</li>
 <li>m (unitless)</li>
 <li>cutoff1 (distance units)</li>
 <li>cutoff2 (distance units)</li>
 </ul>
 <p>The latter 2 coefficients are optional.  If not specified, the global
 NM and Coulombic cutoffs specified in the pair_style command are used.
 If only one cutoff is specified, it is used as the cutoff for both NM
 and Coulombic interactions for this type pair.  If both coefficients
 are specified, they are used as the NM and Coulombic cutoffs for this
 type pair.  You cannot specify 2 cutoffs for style <em>nm</em>, since it
 has no Coulombic terms.</p>
 <p>For <em>nm/cut/coul/long</em> only the NM cutoff can be specified since a
 Coulombic cutoff cannot be specified for an individual I,J type pair.
 All type pairs use the same global Coulombic cutoff specified in the
 pair_style command.</p>
 <hr class="docutils" />
 <p><strong>Mixing, shift, table, tail correction, restart, rRESPA info</strong>:</p>
 <p>These pair styles do not support mixing. Thus, coefficients for all
 I,J pairs must be specified explicitly.</p>
 <p>All of the <em>nm</em> pair styles supports the
 <a class="reference internal" href="pair_modify.html"><em>pair_modify</em></a> shift option for the energy of the pair
 interaction.</p>
 <p>The <em>nm/cut/coul/long</em> pair styles support the
 <a class="reference internal" href="pair_modify.html"><em>pair_modify</em></a> table option since they can tabulate
 the short-range portion of the long-range Coulombic interaction.</p>
 <p>All of the <em>nm</em> pair styles support the <a class="reference internal" href="pair_modify.html"><em>pair_modify</em></a>
 tail option for adding a long-range tail correction to the energy and
 pressure for the NM portion of the pair interaction.</p>
 <p>All of the <em>nm</em> pair styles write their information to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>, so pair_style and pair_coeff commands do not need
 to be specified in an input script that reads a restart file.</p>
 <p>All of the <em>nm</em> pair styles can only be used via the <em>pair</em> keyword of
 the <a class="reference internal" href="run_style.html"><em>run_style respa</em></a> command.  They do not support the
 <em>inner</em>, <em>middle</em>, <em>outer</em> keywords.</p>
 <hr class="docutils" />
 <p>Styles with a <em>cuda</em>, <em>gpu</em>, <em>intel</em>, <em>kk</em>, <em>omp</em>, or <em>opt</em> suffix are
 functionally the same as the corresponding style without the suffix.
 They have been optimized to run faster, depending on your available
 hardware, as discussed in <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a>
 of the manual.  The accelerated styles take the same arguments and
 should produce the same results, except for round-off and precision
 issues.</p>
 <p>These accelerated styles are part of the USER-CUDA, GPU, USER-INTEL,
 KOKKOS, USER-OMP and OPT packages, respectively.  They are only
 enabled if LAMMPS was built with those packages.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 <p>You can specify the accelerated styles explicitly in your input script
 by including their suffix, or you can use the <a class="reference internal" href="Section_start.html#start-7"><span>-suffix command-line switch</span></a> when you invoke LAMMPS, or you can
 use the <a class="reference internal" href="suffix.html"><em>suffix</em></a> command in your input script.</p>
 <p>See <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a> of the manual for
 more instructions on how to use the accelerated styles effectively.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>These pair styles are part of the MISC package.  It is only enabled if
 LAMMPS was built with that package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a></p>
 <p><strong>Default:</strong> none</p>
 <hr class="docutils" />
 <p id="clarke"><strong>(Clarke)</strong> Clarke and Smith, J Chem Phys, 84, 2290 (1986).</p>
 </div>
 </div>
 
 
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   <div class="section" id="pair-style-lj-sdk-command">
 <span id="index-0"></span><h1>pair_style lj/sdk command<a class="headerlink" href="#pair-style-lj-sdk-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-sdk-gpu-command">
 <h1>pair_style lj/sdk/gpu command<a class="headerlink" href="#pair-style-lj-sdk-gpu-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-sdk-kk-command">
 <h1>pair_style lj/sdk/kk command<a class="headerlink" href="#pair-style-lj-sdk-kk-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-sdk-omp-command">
 <h1>pair_style lj/sdk/omp command<a class="headerlink" href="#pair-style-lj-sdk-omp-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-sdk-coul-long-command">
 <h1>pair_style lj/sdk/coul/long command<a class="headerlink" href="#pair-style-lj-sdk-coul-long-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-sdk-coul-long-gpu-command">
 <h1>pair_style lj/sdk/coul/long/gpu command<a class="headerlink" href="#pair-style-lj-sdk-coul-long-gpu-command" title="Permalink to this headline">¶</a></h1>
 </div>
 <div class="section" id="pair-style-lj-sdk-coul-long-omp-command">
 <h1>pair_style lj/sdk/coul/long/omp command<a class="headerlink" href="#pair-style-lj-sdk-coul-long-omp-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>pair_style style args
 </pre></div>
 </div>
 <ul class="simple">
 <li>style = <em>lj/sdk</em> or <em>lj/sdk/coul/long</em></li>
 <li>args = list of arguments for a particular style</li>
 </ul>
 <pre class="literal-block">
 <em>lj/sdk</em> args = cutoff
-    cutoff = global cutoff for Lennard Jones interactions (distance units)
-  <em>lj/sdk/coul/long</em> args = cutoff (cutoff2)
-    cutoff = global cutoff for LJ (and Coulombic if only 1 arg) (distance units)
-    cutoff2 = global cutoff for Coulombic (optional) (distance units)
+  cutoff = global cutoff for Lennard Jones interactions (distance units)
+<em>lj/sdk/coul/long</em> args = cutoff (cutoff2)
+  cutoff = global cutoff for LJ (and Coulombic if only 1 arg) (distance units)
+  cutoff2 = global cutoff for Coulombic (optional) (distance units)
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>pair_style lj/sdk 2.5
 pair_coeff 1 1 lj12_6 1 1.1 2.8
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>pair_style lj/sdk/coul/long 10.0
 pair_style lj/sdk/coul/long 10.0 12.0
 pair_coeff 1 1 lj9_6 100.0 3.5 12.0
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>The <em>lj/sdk</em> styles compute a 9/6, 12/4, or 12/6 Lennard-Jones potential,
 given by</p>
 <img alt="_images/pair_cmm.jpg" class="align-center" src="_images/pair_cmm.jpg" />
 <p>as required for the SDK Coarse-grained MD parametrization discussed in
 <a class="reference internal" href="#shinoda"><span>(Shinoda)</span></a> and <a class="reference internal" href="#devane"><span>(DeVane)</span></a>.  Rc is the cutoff.</p>
 <p>Style <em>lj/sdk/coul/long</em> computes the adds Coulombic interactions
 with an additional damping factor applied so it can be used in
 conjunction with the <a class="reference internal" href="kspace_style.html"><em>kspace_style</em></a> command and
 its <em>ewald</em> or <em>pppm</em> or <em>pppm/cg</em> option.  The Coulombic cutoff
 specified for this style means that pairwise interactions within
 this distance are computed directly; interactions outside that
 distance are computed in reciprocal space.</p>
 <p>The following coefficients must be defined for each pair of atoms
 types via the <a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a> command as in the examples
 above, or in the data file or restart files read by the
 <a class="reference internal" href="read_data.html"><em>read_data</em></a> or <a class="reference internal" href="read_restart.html"><em>read_restart</em></a>
 commands, or by mixing as described below:</p>
 <ul class="simple">
 <li>cg_type (lj9_6, lj12_4, or lj12_6)</li>
 <li>epsilon (energy units)</li>
 <li>sigma (distance units)</li>
 <li>cutoff1 (distance units)</li>
 </ul>
 <p>Note that sigma is defined in the LJ formula as the zero-crossing
 distance for the potential, not as the energy minimum. The prefactors
 are chosen so that the potential minimum is at -epsilon.</p>
 <p>The latter 2 coefficients are optional.  If not specified, the global
 LJ and Coulombic cutoffs specified in the pair_style command are used.
 If only one cutoff is specified, it is used as the cutoff for both LJ
 and Coulombic interactions for this type pair.  If both coefficients
 are specified, they are used as the LJ and Coulombic cutoffs for this
 type pair.</p>
 <p>For <em>lj/sdk/coul/long</em> only the LJ cutoff can be specified since a
 Coulombic cutoff cannot be specified for an individual I,J type pair.
 All type pairs use the same global Coulombic cutoff specified in the
 pair_style command.</p>
 <hr class="docutils" />
 <p>Styles with a <em>cuda</em>, <em>gpu</em>, <em>intel</em>, <em>kk</em>, <em>omp</em> or <em>opt</em> suffix are
 functionally the same as the corresponding style without the suffix.
 They have been optimized to run faster, depending on your available
 hardware, as discussed in <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a>
 of the manual.  The accelerated styles take the same arguments and
 should produce the same results, except for round-off and precision
 issues.</p>
 <p>These accelerated styles are part of the USER-CUDA, GPU, USER-INTEL,
 KOKKOS, USER-OMP, and OPT packages respectively.  They are only
 enabled if LAMMPS was built with those packages.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 <p>You can specify the accelerated styles explicitly in your input script
 by including their suffix, or you can use the <a class="reference internal" href="Section_start.html#start-7"><span>-suffix command-line switch</span></a> when you invoke LAMMPS, or you can
 use the <a class="reference internal" href="suffix.html"><em>suffix</em></a> command in your input script.</p>
 <p>See <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a> of the manual for
 more instructions on how to use the accelerated styles effectively.</p>
 <hr class="docutils" />
 <p><strong>Mixing, shift, table, tail correction, restart, and rRESPA info</strong>:</p>
 <p>For atom type pairs I,J and I != J, the epsilon and sigma coefficients
 and cutoff distance for all of the lj/sdk pair styles <em>cannot</em> be mixed,
 since different pairs may have different exponents. So all parameters
 for all pairs have to be specified explicitly through the &#8220;pair_coeff&#8221;
 command. Defining then in a data file is also not supported, due to
 limitations of that file format.</p>
 <p>All of the lj/sdk pair styles support the
 <a class="reference internal" href="pair_modify.html"><em>pair_modify</em></a> shift option for the energy of the
 Lennard-Jones portion of the pair interaction.</p>
 <p>The <em>lj/sdk/coul/long</em> pair styles support the
 <a class="reference internal" href="pair_modify.html"><em>pair_modify</em></a> table option since they can tabulate
 the short-range portion of the long-range Coulombic interaction.</p>
 <p>All of the lj/sdk pair styles write their information to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>, so pair_style and pair_coeff commands do
 not need to be specified in an input script that reads a restart file.</p>
 <p>The lj/sdk and lj/cut/coul/long pair styles do not support
 the use of the <em>inner</em>, <em>middle</em>, and <em>outer</em> keywords of the <a class="reference internal" href="run_style.html"><em>run_style respa</em></a> command.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>All of the lj/sdk pair styles are part of the USER-CG-CMM package.
 The <em>lj/sdk/coul/long</em> style also requires the KSPACE package to be
 built (which is enabled by default).  They are only enabled if LAMMPS
 was built with that package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a>, <a class="reference internal" href="angle_sdk.html"><em>angle_style sdk</em></a></p>
 <p><strong>Default:</strong> none</p>
 <hr class="docutils" />
 <p id="shinoda"><strong>(Shinoda)</strong> Shinoda, DeVane, Klein, Mol Sim, 33, 27 (2007).</p>
 <p id="devane"><strong>(DeVane)</strong>  Shinoda, DeVane, Klein, Soft Matter, 4, 2453-2462 (2008).</p>
 </div>
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   <div class="section" id="pair-style-snap-command">
 <span id="index-0"></span><h1>pair_style snap command<a class="headerlink" href="#pair-style-snap-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>pair_style snap
 </pre></div>
 </div>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>pair_style snap
 pair_coeff * * snap InP.snapcoeff In P InP.snapparam In In P P
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Style <em>snap</em> computes interactions
 using the spectral neighbor analysis potential (SNAP)
 <a class="reference internal" href="#thompson2014"><span>(Thompson)</span></a>. Like the GAP framework of Bartok et al.
 <a class="reference internal" href="#bartok2010"><span>(Bartok2010)</span></a>, <a class="reference internal" href="#bartok2013"><span>(Bartok2013)</span></a>
 it uses bispectrum components
 to characterize the local neighborhood of each atom
 in a very general way. The mathematical definition of the
 bispectrum calculation used by SNAP is identical
 to that used of <a class="reference internal" href="compute_sna_atom.html"><em>compute sna/atom</em></a>.
 In SNAP, the total energy is decomposed into a sum over
 atom energies. The energy of atom <em>i</em> is
 expressed as a weighted sum over bispectrum components.</p>
 <img alt="_images/pair_snap.jpg" class="align-center" src="_images/pair_snap.jpg" />
 <p>where <em>B_k^i</em> is the <em>k</em>-th bispectrum component of atom <em>i</em>,
 and <em>beta_k^alpha_i</em> is the corresponding linear coefficient
 that depends on <em>alpha_i</em>, the SNAP element of atom <em>i</em>. The
 number of bispectrum components used and their definitions
 depend on the values of <em>twojmax</em> and <em>diagonalstyle</em>
 defined in the SNAP parameter file described below.
 The bispectrum calculation is described in more detail
 in <a class="reference internal" href="compute_sna_atom.html"><em>compute sna/atom</em></a>.</p>
 <p>Note that unlike for other potentials, cutoffs for SNAP potentials are
 not set in the pair_style or pair_coeff command; they are specified in
 the SNAP potential files themselves.</p>
 <p>Only a single pair_coeff command is used with the <em>snap</em> style which
 specifies two SNAP files and the list SNAP element(s) to be
 extracted.
 The SNAP elements are mapped to LAMMPS atom types by specifying
 N additional arguments after the 2nd filename in the pair_coeff
 command, where N is the number of LAMMPS atom types:</p>
 <ul class="simple">
 <li>SNAP element file</li>
 <li>Elem1, Elem2, ...</li>
 <li>SNAP parameter file</li>
 <li>N element names = mapping of SNAP elements to atom types</li>
 </ul>
 <p>As an example, if a LAMMPS indium phosphide simulation has 4 atoms
 types, with the first two being indium and the 3rd and 4th being
 phophorous, the pair_coeff command would look like this:</p>
 <div class="highlight-python"><div class="highlight"><pre>pair_coeff * * snap InP.snapcoeff In P InP.snapparam In In P P
 </pre></div>
 </div>
 <p>The 1st 2 arguments must be * * so as to span all LAMMPS atom types.
 The two filenames are for the element and parameter files, respectively.
 The &#8216;In&#8217; and &#8216;P&#8217; arguments (between the file names) are the two elements
 which will be extracted from the element file. The
 two trailing &#8216;In&#8217; arguments map LAMMPS atom types 1 and 2 to the
 SNAP &#8216;In&#8217; element. The two trailing &#8216;P&#8217; arguments map LAMMPS atom types
 3 and 4 to the SNAP &#8216;P&#8217; element.</p>
 <p>If a SNAP mapping value is
 specified as NULL, the mapping is not performed.
 This can be used when a <em>snap</em> potential is used as part of the
 <em>hybrid</em> pair style.  The NULL values are placeholders for atom types
 that will be used with other potentials.</p>
 <p>The name of the SNAP element file usually ends in the
 &#8221;.snapcoeff&#8221; extension. It may contain coefficients
 for many SNAP elements.
 Only those elements listed in the pair_coeff command are extracted.
 The name of the SNAP parameter file usually ends in the &#8221;.snapparam&#8221;
 extension. It contains a small number
 of parameters that define the overall form of the SNAP potential.
 See the <a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a> doc page for alternate ways
 to specify the path for these files.</p>
 <p>Quite commonly,
 SNAP potentials are combined with one or more other LAMMPS pair styles
 using the <em>hybrid/overlay</em> pair style. As an example, the SNAP
 tantalum potential provided in the LAMMPS potentials directory
 combines the <em>snap</em> and <em>zbl</em> pair styles. It is invoked
 by the following commands:</p>
 <div class="highlight-python"><div class="highlight"><pre>variable zblcutinner equal 4
-     variable zblcutouter equal 4.8
-     variable zblz equal 73
-     pair_style hybrid/overlay &amp;
-     zbl ${zblcutinner} ${zblcutouter} snap
-     pair_coeff * * zbl 0.0
-     pair_coeff 1 1 zbl ${zblz}
-     pair_coeff * * snap ../potentials/Ta06A.snapcoeff Ta &amp;
-     ../potentials/Ta06A.snapparam Ta
+variable zblcutouter equal 4.8
+variable zblz equal 73
+pair_style hybrid/overlay &amp;
+zbl ${zblcutinner} ${zblcutouter} snap
+pair_coeff * * zbl 0.0
+pair_coeff 1 1 zbl ${zblz}
+pair_coeff * * snap ../potentials/Ta06A.snapcoeff Ta &amp;
+../potentials/Ta06A.snapparam Ta
 </pre></div>
 </div>
 <p>It is convenient to keep these commands in a separate file that can
 be inserted in any LAMMPS input script using the <a class="reference internal" href="include.html"><em>include</em></a>
 command.</p>
 <p>The top of the SNAP element file can contain any number of blank and comment
 lines (start with #), but follows a strict
 format after that. The first non-blank non-comment
 line must contain two integers:</p>
 <ul class="simple">
 <li>nelem  = Number of elements</li>
 <li>ncoeff = Number of coefficients</li>
 </ul>
 <p>This is followed by one block for each of the <em>nelem</em> elements.
 The first line of each block contains three entries:</p>
 <ul class="simple">
 <li>Element symbol (text string)</li>
 <li>R = Element radius (distance units)</li>
 <li>w = Element weight (dimensionless)</li>
 </ul>
 <p>This line is followed by <em>ncoeff</em> coefficients, one per line.</p>
 <p>The SNAP parameter file can contain blank and comment lines (start
 with #) anywhere. Each non-blank non-comment line must contain one
 keyword/value pair. The required keywords are <em>rcutfac</em> and
 <em>twojmax</em>. Optional keywords are <em>rfac0</em>, <em>rmin0</em>, <em>diagonalstyle</em>,
 and <em>switchflag</em>.</p>
 <p>The default values for these keywords are</p>
 <ul class="simple">
 <li><em>rfac0</em> = 0.99363</li>
 <li><em>rmin0</em> = 0.0</li>
 <li><em>diagonalstyle</em> = 3</li>
 <li><em>switchflag</em> = 0</li>
 </ul>
 <p>Detailed definitions of these keywords are given on the <a class="reference internal" href="compute_sna_atom.html"><em>compute sna/atom</em></a> doc page.</p>
 <hr class="docutils" />
 <p><strong>Mixing, shift, table, tail correction, restart, rRESPA info</strong>:</p>
 <p>For atom type pairs I,J and I != J, where types I and J correspond to
 two different element types, mixing is performed by LAMMPS with
 user-specifiable parameters as described above.  You never need to
 specify a pair_coeff command with I != J arguments for this style.</p>
 <p>This pair style does not support the <a class="reference internal" href="pair_modify.html"><em>pair_modify</em></a>
 shift, table, and tail options.</p>
 <p>This pair style does not write its information to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>, since it is stored in potential files.  Thus, you
 need to re-specify the pair_style and pair_coeff commands in an input
 script that reads a restart file.</p>
 <p>This pair style can only be used via the <em>pair</em> keyword of the
 <a class="reference internal" href="run_style.html"><em>run_style respa</em></a> command.  It does not support the
 <em>inner</em>, <em>middle</em>, <em>outer</em> keywords.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>This style is part of the SNAP package.  It is only enabled if
 LAMMPS was built with that package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="compute_sna_atom.html"><em>compute sna/atom</em></a>,
 <a class="reference internal" href="compute_sna_atom.html"><em>compute snad/atom</em></a>,
 <a class="reference internal" href="compute_sna_atom.html"><em>compute snav/atom</em></a></p>
 <p><strong>Default:</strong> none</p>
 <hr class="docutils" />
 <p id="thompson2014"><strong>(Thompson)</strong> Thompson, Swiler, Trott, Foiles, Tucker, under review, preprint
 available at <a class="reference external" href="http://arxiv.org/abs/1409.3880">arXiv:1409.3880</a></p>
 <p id="bartok2010"><strong>(Bartok2010)</strong> Bartok, Payne, Risi, Csanyi, Phys Rev Lett, 104, 136403 (2010).</p>
 <p id="bartok2013"><strong>(Bartok2013)</strong> Bartok, Gillan, Manby, Csanyi, Phys Rev B 87, 184115 (2013).</p>
 </div>
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   <div class="section" id="prd-command">
 <span id="index-0"></span><h1>prd command<a class="headerlink" href="#prd-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>prd N t_event n_dephase t_dephase t_correlate compute-ID seed keyword value ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>N = # of timesteps to run (not including dephasing/quenching)</li>
 <li>t_event = timestep interval between event checks</li>
 <li>n_dephase = number of velocity randomizations to perform in each dephase run</li>
 <li>t_dephase = number of timesteps to run dynamics after each velocity randomization during dephase</li>
 <li>t_correlate = number of timesteps within which 2 consecutive events are considered to be correlated</li>
 <li>compute-ID = ID of the compute used for event detection</li>
 <li>random_seed = random # seed (positive integer)</li>
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>min</em> or <em>temp</em> or <em>vel</em></li>
 </ul>
 <pre class="literal-block">
 <em>min</em> values = etol ftol maxiter maxeval
-    etol = stopping tolerance for energy, used in quenching
-    ftol = stopping tolerance for force, used in quenching
-    maxiter = max iterations of minimize, used in quenching
-    maxeval = max number of force/energy evaluations, used in quenching
-  <em>temp</em> value = Tdephase
-    Tdephase = target temperature for velocity randomization, used in dephasing
-  <em>vel</em> values = loop dist
-    loop = <em>all</em> or <em>local</em> or <em>geom</em>, used in dephasing
-    dist = <em>uniform</em> or <em>gaussian</em>, used in dephasing
-  <em>time</em> value = <em>step</em> or <em>clock</em>
-    <em>step</em> = simulation runs for N timesteps on each replica (default)
-    <em>clock</em> = simulation runs for N timesteps across all replicas
+  etol = stopping tolerance for energy, used in quenching
+  ftol = stopping tolerance for force, used in quenching
+  maxiter = max iterations of minimize, used in quenching
+  maxeval = max number of force/energy evaluations, used in quenching
+<em>temp</em> value = Tdephase
+  Tdephase = target temperature for velocity randomization, used in dephasing
+<em>vel</em> values = loop dist
+  loop = <em>all</em> or <em>local</em> or <em>geom</em>, used in dephasing
+  dist = <em>uniform</em> or <em>gaussian</em>, used in dephasing
+<em>time</em> value = <em>step</em> or <em>clock</em>
+  <em>step</em> = simulation runs for N timesteps on each replica (default)
+  <em>clock</em> = simulation runs for N timesteps across all replicas
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>prd 5000 100 10 10 100 1 54982
 prd 5000 100 10 10 100 1 54982 min 0.1 0.1 100 200
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Run a parallel replica dynamics (PRD) simulation using multiple
 replicas of a system.  One or more replicas can be used.  The total
 number of steps <em>N</em> to run can be interpreted in one of two ways; see
 discussion of the <em>time</em> keyword below.</p>
 <p>PRD is described in <a class="reference internal" href="tad.html#voter"><span>this paper</span></a> by Art Voter.  It is a method
 for performing accelerated dynamics that is suitable for
 infrequent-event systems that obey first-order kinetics.  A good
 overview of accelerated dynamics methods for such systems in given in
 <a class="reference internal" href="tad.html#voter2"><span>this review paper</span></a> from the same group.  To quote from the
 paper: &#8220;The dynamical evolution is characterized by vibrational
 excursions within a potential basin, punctuated by occasional
 transitions between basins.&#8221;  The transition probability is
 characterized by p(t) = k*exp(-kt) where k is the rate constant.
 Running multiple replicas gives an effective enhancement in the
 timescale spanned by the multiple simulations, while waiting for an
 event to occur.</p>
 <p>Each replica runs on a partition of one or more processors.  Processor
 partitions are defined at run-time using the -partition command-line
 switch; see <a class="reference internal" href="Section_start.html#start-7"><span>Section_start 6</span></a> of the
 manual.  Note that if you have MPI installed, you can run a
 multi-replica simulation with more replicas (partitions) than you have
 physical processors, e.g you can run a 10-replica simulation on one or
 two processors.  For PRD, this makes little sense, since this offers
 no effective parallel speed-up in searching for infrequent events. See
 <a class="reference internal" href="Section_howto.html#howto-5"><span>Section_howto 5</span></a> of the manual for further
 discussion.</p>
 <p>When a PRD simulation is performed, it is assumed that each replica is
 running the same model, though LAMMPS does not check for this.
 I.e. the simulation domain, the number of atoms, the interaction
 potentials, etc should be the same for every replica.</p>
 <p>A PRD run has several stages, which are repeated each time an &#8220;event&#8221;
 occurs in one of the replicas, as defined below.  The logic for a PRD
 run is as follows:</p>
 <div class="highlight-python"><div class="highlight"><pre>while (time remains):
   dephase for n_dephase*t_dephase steps
   until (event occurs on some replica):
     run dynamics for t_event steps
     quench
     check for uncorrelated event on any replica
   until (no correlated event occurs):
     run dynamics for t_correlate steps
     quench
     check for correlated event on this replica
   event replica shares state with all replicas
 </pre></div>
 </div>
 <p>Before this loop begins, the state of the system on replica 0 is
 shared with all replicas, so that all replicas begin from the same
 initial state. The first potential energy basin is identified by
 quenching (an energy minimization, see below) the initial state and
 storing the resulting coordinates for reference.</p>
 <p>In the first stage, dephasing is performed by each replica
 independently to eliminate correlations between replicas.  This is
 done by choosing a random set of velocities, based on the
 <em>random_seed</em> that is specified, and running <em>t_dephase</em> timesteps of
 dynamics.  This is repeated <em>n_dephase</em> times.  At each of the
 <em>n_dephase</em> stages, if an event occurs during the <em>t_dephase</em> steps of
 dynamics for a particular replica, the replica repeats the stage until
 no event occurs.</p>
 <p>If the <em>temp</em> keyword is not specified, the target temperature for
 velocity randomization for each replica is the current temperature of
 that replica.  Otherwise, it is the specified <em>Tdephase</em> temperature.
 The style of velocity randomization is controlled using the keyword
 <em>vel</em> with arguments that have the same meaning as their counterparts
 in the <a class="reference internal" href="velocity.html"><em>velocity</em></a> command.</p>
 <p>In the second stage, each replica runs dynamics continuously, stopping
 every <em>t_event</em> steps to check if a transition event has occurred.
 This check is performed by quenching the system and comparing the
 resulting atom coordinates to the coordinates from the previous basin.
 The first time through the PRD loop, the &#8220;previous basin&#8221; is the set
 of quenched coordinates from the initial state of the system.</p>
 <p>A quench is an energy minimization and is performed by whichever
 algorithm has been defined by the <a class="reference internal" href="min_style.html"><em>min_style</em></a> command.
 Minimization parameters may be set via the
 <a class="reference internal" href="min_modify.html"><em>min_modify</em></a> command and by the <em>min</em> keyword of the
 PRD command.  The latter are the settings that would be used with the
 <a class="reference internal" href="minimize.html"><em>minimize</em></a> command.  Note that typically, you do not
 need to perform a highly-converged minimization to detect a transition
 event.</p>
 <p>The event check is performed by a compute with the specified
 <em>compute-ID</em>.  Currently there is only one compute that works with the
 PRD commmand, which is the <a class="reference internal" href="compute_event_displace.html"><em>compute event/displace</em></a> command.  Other
 event-checking computes may be added.  <a class="reference internal" href="compute_event_displace.html"><em>Compute event/displace</em></a> checks whether any atom in
 the compute group has moved further than a specified threshold
 distance.  If so, an &#8220;event&#8221; has occurred.</p>
 <p>In the third stage, the replica on which the event occurred (event
 replica) continues to run dynamics to search for correlated events.
 This is done by running dynamics for <em>t_correlate</em> steps, quenching
 every <em>t_event</em> steps, and checking if another event has occurred.</p>
 <p>The first time no correlated event occurs, the final state of the
 event replica is shared with all replicas, the new basin reference
 coordinates are updated with the quenched state, and the outer loop
 begins again. While the replica event is searching for correlated
 events, all the other replicas also run dynamics and event checking
 with the same schedule, but the final states are always overwritten by
 the state of the event replica.</p>
 <p>The outer loop of the pseudo-code above continues until <em>N</em> steps of
 dynamics have been performed.  Note that <em>N</em> only includes the
 dynamics of stages 2 and 3, not the steps taken during dephasing or
 the minimization iterations of quenching.  The specified <em>N</em> is
 interpreted in one of two ways, depending on the <em>time</em> keyword.  If
 the <em>time</em> value is <em>step</em>, which is the default, then each replica
 runs for <em>N</em> timesteps.  If the <em>time</em> value is <em>clock</em>, then the
 simulation runs until <em>N</em> aggregate timesteps across all replicas have
 elapsed.  This aggregate time is the &#8220;clock&#8221; time defined below, which
 typically advances nearly M times faster than the timestepping on a
 single replica.</p>
 <hr class="docutils" />
 <p>Four kinds of output can be generated during a PRD run: event
 statistics, thermodynamic output by each replica, dump files, and
 restart files.</p>
 <p>When running with multiple partitions (each of which is a replica in
 this case), the print-out to the screen and master log.lammps file is
 limited to event statistics.  Note that if a PRD run is performed on
 only a single replica then the event statistics will be intermixed
 with the usual thermodynamic output discussed below.</p>
 <p>The quantities printed each time an event occurs are the timestep, CPU
 time, clock, event number, a correlation flag, the number of
 coincident events, and the replica number of the chosen event.</p>
 <p>The timestep is the usual LAMMPS timestep, except that time does not
 advance during dephasing or quenches, but only during dynamics.  Note
 that are two kinds of dynamics in the PRD loop listed above.  The
 first is when all replicas are performing independent dynamics,
 waiting for an event to occur.  The second is when correlated events
 are being searched for and only one replica is running dynamics.</p>
 <p>The CPU time is the total processor time since the start of the PRD
 run.</p>
 <p>The clock is the same as the timestep except that it advances by M
 steps every timestep during the first kind of dynamics when the M
 replicas are running independently.  The clock advances by only 1 step
 per timestep during the second kind of dynamics, since only a single
 replica is checking for a correlated event.  Thus &#8220;clock&#8221; time
 represents the aggregate time (in steps) that effectively elapses
 during a PRD simulation on M replicas.  If most of the PRD run is
 spent in the second stage of the loop above, searching for infrequent
 events, then the clock will advance nearly M times faster than it
 would if a single replica was running.  Note the clock time between
 events will be drawn from p(t).</p>
 <p>The event number is a counter that increments with each event, whether
 it is uncorrelated or correlated.</p>
 <p>The correlation flag will be 0 when an uncorrelated event occurs
 during the second stage of the loop listed above, i.e. when all
 replicas are running independently.  The correlation flag will be 1
 when a correlated event occurs during the third stage of the loop
 listed above, i.e. when only one replica is running dynamics.</p>
 <p>When more than one replica detects an event at the end of the second
 stage, then one of them is chosen at random. The number of coincident
 events is the number of replicas that detected an event. Normally, we
 expect this value to be 1. If it is often greater than 1, then either
 the number of replicas is too large, or <em>t_event</em> is too large.</p>
 <p>The replica number is the ID of the replica (from 0 to M-1) that
 found the event.</p>
 <hr class="docutils" />
 <p>When running on multiple partitions, LAMMPS produces additional log
 files for each partition, e.g. log.lammps.0, log.lammps.1, etc.  For
 the PRD command, these contain the thermodynamic output for each
 replica.  You will see short runs and minimizations corresponding to
 the dynamics and quench operations of the loop listed above.  The
 timestep will be reset aprpopriately depending on whether the
 operation advances time or not.</p>
 <p>After the PRD command completes, timing statistics for the PRD run are
 printed in each replica&#8217;s log file, giving a breakdown of how much CPU
 time was spent in each stage (dephasing, dynamics, quenching, etc).</p>
 <hr class="docutils" />
 <p>Any <a class="reference internal" href="dump.html"><em>dump files</em></a> defined in the input script, will be
 written to during a PRD run at timesteps corresponding to both
 uncorrelated and correlated events.  This means the the requested dump
 frequency in the <a class="reference internal" href="dump.html"><em>dump</em></a> command is ignored.  There will be
 one dump file (per dump command) created for all partitions.</p>
 <p>The atom coordinates of the dump snapshot are those of the minimum
 energy configuration resulting from quenching following a transition
 event.  The timesteps written into the dump files correspond to the
 timestep at which the event occurred and NOT the clock.  A dump
 snapshot corresponding to the initial minimum state used for event
 detection is written to the dump file at the beginning of each PRD
 run.</p>
 <hr class="docutils" />
 <p>If the <a class="reference internal" href="restart.html"><em>restart</em></a> command is used, a single restart file
 for all the partitions is generated, which allows a PRD run to be
 continued by a new input script in the usual manner.</p>
 <p>The restart file is generated at the end of the loop listed above.  If
 no correlated events are found, this means it contains a snapshot of
 the system at time T + <em>t_correlate</em>, where T is the time at which the
 uncorrelated event occurred.  If correlated events were found, then it
 contains a snapshot of the system at time T + <em>t_correlate</em>, where T
 is the time of the last correlated event.</p>
 <p>The restart frequency specified in the <a class="reference internal" href="restart.html"><em>restart</em></a> command
 is interpreted differently when performing a PRD run.  It does not
 mean the timestep interval between restart files.  Instead it means an
 event interval for uncorrelated events.  Thus a frequency of 1 means
 write a restart file every time an uncorrelated event occurs.  A
 frequency of 10 means write a restart file every 10th uncorrelated
 event.</p>
 <p>When an input script reads a restart file from a previous PRD run, the
 new script can be run on a different number of replicas or processors.
 However, it is assumed that <em>t_correlate</em> in the new PRD command is
 the same as it was previously.  If not, the calculation of the &#8220;clock&#8221;
 value for the first event in the new run will be slightly off.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>This command can only be used if LAMMPS was built with the REPLICA
 package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section
 for more info on packages.</p>
 <p><em>N</em> and <em>t_correlate</em> settings must be integer multiples of
 <em>t_event</em>.</p>
 <p>Runs restarted from restart file written during a PRD run will not
 produce identical results due to changes in the random numbers used
 for dephasing.</p>
 <p>This command cannot be used when any fixes are defined that keep track
 of elapsed time to perform time-dependent operations.  Examples
 include the &#8220;ave&#8221; fixes such as <a class="reference internal" href="fix_ave_spatial.html"><em>fix ave/spatial</em></a>.  Also <a class="reference internal" href="fix_dt_reset.html"><em>fix dt/reset</em></a> and <a class="reference internal" href="fix_deposit.html"><em>fix deposit</em></a>.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="compute_event_displace.html"><em>compute event/displace</em></a>,
 <a class="reference internal" href="min_modify.html"><em>min_modify</em></a>, <a class="reference internal" href="min_style.html"><em>min_style</em></a>,
 <a class="reference internal" href="run_style.html"><em>run_style</em></a>, <a class="reference internal" href="minimize.html"><em>minimize</em></a>,
 <a class="reference internal" href="velocity.html"><em>velocity</em></a>, <a class="reference internal" href="temper.html"><em>temper</em></a>, <a class="reference internal" href="neb.html"><em>neb</em></a>,
 <a class="reference internal" href="tad.html"><em>tad</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The option defaults are min = 0.1 0.1 40 50, no temp setting, vel =
 geom gaussian, and time = step.</p>
 <hr class="docutils" />
 <p id="voter"><strong>(Voter)</strong> Voter, Phys Rev B, 57, 13985 (1998).</p>
 <p id="voter2"><strong>(Voter2)</strong> Voter, Montalenti, Germann, Annual Review of Materials
 Research 32, 321 (2002).</p>
 </div>
 </div>
 
 
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   <div class="section" id="print-command">
 <span id="index-0"></span><h1>print command<a class="headerlink" href="#print-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>print string keyword value
 </pre></div>
 </div>
 <ul class="simple">
 <li>string = text string to print, which may contain variables</li>
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>file</em> or <em>append</em> or <em>screen</em></li>
 </ul>
 <pre class="literal-block">
 <em>file</em> value = filename
-  <em>append</em> value = filename
-  <em>screen</em> value = <em>yes</em> or <em>no</em>
+<em>append</em> value = filename
+<em>screen</em> value = <em>yes</em> or <em>no</em>
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>print &quot;Done with equilibration&quot; file info.dat
 print Vol=$v append info.dat screen no
 print &quot;The system volume is now $v&quot;
 print &#39;The system volume is now $v&#39;
 print &quot;&quot;&quot;
 System volume = $v
 System temperature = $t
 &quot;&quot;&quot;
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Print a text string to the screen and logfile.  The text string must
 be a single argument, so if it is one line but more than one word, it
 should be enclosed in single or double quotes.  To generate multiple
 lines of output, the string can be enclosed in triple quotes, as in
 the last example above.  If the text string contains variables, they
 will be evaluated and their current values printed.</p>
 <p>If the <em>file</em> or <em>append</em> keyword is used, a filename is specified to
 which the output will be written.  If <em>file</em> is used, then the
 filename is overwritten if it already exists.  If <em>append</em> is used,
 then the filename is appended to if it already exists, or created if
 it does not exist.</p>
 <p>If the <em>screen</em> keyword is used, output to the screen and logfile can
 be turned on or off as desired.</p>
 <p>If you want the print command to be executed multiple times (with
 changing variable values), there are 3 options.  First, consider using
 the <a class="reference internal" href="fix_print.html"><em>fix print</em></a> command, which will print a string
 periodically during a simulation.  Second, the print command can be
 used as an argument to the <em>every</em> option of the <a class="reference internal" href="run.html"><em>run</em></a>
 command.  Third, the print command could appear in a section of the
 input script that is looped over (see the <a class="reference internal" href="jump.html"><em>jump</em></a> and
 <a class="reference internal" href="next.html"><em>next</em></a> commands).</p>
 <p>See the <a class="reference internal" href="variable.html"><em>variable</em></a> command for a description of <em>equal</em>
 style variables which are typically the most useful ones to use with
 the print command.  Equal-style variables can calculate formulas
 involving mathematical operations, atom properties, group properties,
 thermodynamic properties, global values calculated by a
 <a class="reference internal" href="compute.html"><em>compute</em></a> or <a class="reference internal" href="fix.html"><em>fix</em></a>, or references to other
 <a class="reference internal" href="variable.html"><em>variables</em></a>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <blockquote>
 <div>none</div></blockquote>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="fix_print.html"><em>fix print</em></a>, <a class="reference internal" href="variable.html"><em>variable</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The option defaults are no file output and screen = yes.</p>
 </div>
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   <div class="section" id="processors-command">
 <span id="index-0"></span><h1>processors command<a class="headerlink" href="#processors-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>processors Px Py Pz keyword args ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>Px,Py,Pz = # of processors in each dimension of 3d grid overlaying the simulation domain</li>
 <li>zero or more keyword/arg pairs may be appended</li>
 <li>keyword = <em>grid</em> or <em>map</em> or <em>part</em> or <em>file</em></li>
 </ul>
 <pre class="literal-block">
 <em>grid</em> arg = gstyle params ...
-    gstyle = <em>onelevel</em> or <em>twolevel</em> or <em>numa</em> or <em>custom</em>
-      onelevel params = none
-      twolevel params = Nc Cx Cy Cz
-        Nc = number of cores per node
-        Cx,Cy,Cz = # of cores in each dimension of 3d sub-grid assigned to each node
-      numa params = none
-      custom params = infile
-        infile = file containing grid layout
-  <em>map</em> arg = <em>cart</em> or <em>cart/reorder</em> or <em>xyz</em> or <em>xzy</em> or <em>yxz</em> or <em>yzx</em> or <em>zxy</em> or <em>zyx</em>
-     cart = use MPI_Cart() methods to map processors to 3d grid with reorder = 0
-     cart/reorder = use MPI_Cart() methods to map processors to 3d grid with reorder = 1
-     xyz,xzy,yxz,yzx,zxy,zyx = map procesors to 3d grid in IJK ordering
-  <em>numa</em> arg = none
-  <em>part</em> args = Psend Precv cstyle
-    Psend = partition # (1 to Np) which will send its processor layout
-    Precv = partition # (1 to Np) which will recv the processor layout
-    cstyle = <em>multiple</em>
-      <em>multiple</em> = Psend grid will be multiple of Precv grid in each dimension
-  <em>file</em> arg = outfile
-    outfile = name of file to write 3d grid of processors to
+  gstyle = <em>onelevel</em> or <em>twolevel</em> or <em>numa</em> or <em>custom</em>
+    onelevel params = none
+    twolevel params = Nc Cx Cy Cz
+      Nc = number of cores per node
+      Cx,Cy,Cz = # of cores in each dimension of 3d sub-grid assigned to each node
+    numa params = none
+    custom params = infile
+      infile = file containing grid layout
+<em>map</em> arg = <em>cart</em> or <em>cart/reorder</em> or <em>xyz</em> or <em>xzy</em> or <em>yxz</em> or <em>yzx</em> or <em>zxy</em> or <em>zyx</em>
+   cart = use MPI_Cart() methods to map processors to 3d grid with reorder = 0
+   cart/reorder = use MPI_Cart() methods to map processors to 3d grid with reorder = 1
+   xyz,xzy,yxz,yzx,zxy,zyx = map procesors to 3d grid in IJK ordering
+<em>numa</em> arg = none
+<em>part</em> args = Psend Precv cstyle
+  Psend = partition # (1 to Np) which will send its processor layout
+  Precv = partition # (1 to Np) which will recv the processor layout
+  cstyle = <em>multiple</em>
+    <em>multiple</em> = Psend grid will be multiple of Precv grid in each dimension
+<em>file</em> arg = outfile
+  outfile = name of file to write 3d grid of processors to
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>processors * * 5
 processors 2 4 4
 processors * * 8 map xyz
 processors * * * grid numa
 processors * * * grid twolevel 4 * * 1
 processors 4 8 16 grid custom myfile
 processors * * * part 1 2 multiple
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Specify how processors are mapped as a regular 3d grid to the global
 simulation box.  The mapping involves 2 steps.  First if there are P
 processors it means choosing a factorization P = Px by Py by Pz so
 that there are Px processors in the x dimension, and similarly for the
 y and z dimensions.  Second, the P processors are mapped to the
 regular 3d grid.  The arguments to this command control each of these
 2 steps.</p>
 <p>The Px, Py, Pz parameters affect the factorization.  Any of the 3
 parameters can be specified with an asterisk &#8220;*&#8221;, which means LAMMPS
 will choose the number of processors in that dimension of the grid.
 It will do this based on the size and shape of the global simulation
 box so as to minimize the surface-to-volume ratio of each processor&#8217;s
 sub-domain.</p>
 <p>Choosing explicit values for Px or Py or Pz can be used to override
 the default manner in which LAMMPS will create the regular 3d grid of
 processors, if it is known to be sub-optimal for a particular problem.
 E.g. a problem where the extent of atoms will change dramatically in a
 particular dimension over the course of the simulation.</p>
 <p>The product of Px, Py, Pz must equal P, the total # of processors
 LAMMPS is running on.  For a <a class="reference internal" href="dimension.html"><em>2d simulation</em></a>, Pz must
 equal 1.</p>
 <p>Note that if you run on a prime number of processors P, then a grid
 such as 1 x P x 1 will be required, which may incur extra
 communication costs due to the high surface area of each processor&#8217;s
 sub-domain.</p>
 <p>Also note that if multiple partitions are being used then P is the
 number of processors in this partition; see <a class="reference internal" href="Section_start.html#start-7"><span>this section</span></a> for an explanation of the
 -partition command-line switch.  Also note that you can prefix the
 processors command with the <a class="reference internal" href="partition.html"><em>partition</em></a> command to
 easily specify different Px,Py,Pz values for different partitions.</p>
 <p>You can use the <a class="reference internal" href="partition.html"><em>partition</em></a> command to specify
 different processor grids for different partitions, e.g.</p>
 <div class="highlight-python"><div class="highlight"><pre>partition yes 1 processors 4 4 4
 partition yes 2 processors 2 3 2
 </pre></div>
 </div>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">This command only affects the initial regular 3d grid
 created when the simulation box is first specified via a
 <a class="reference internal" href="create_box.html"><em>create_box</em></a> or <a class="reference internal" href="read_data.html"><em>read_data</em></a> or
 <a class="reference internal" href="read_restart.html"><em>read_restart</em></a> command.  Or if the simulation box is
 re-created via the <a class="reference internal" href="replicate.html"><em>replicate</em></a> command.  The same
 regular grid is initially created, regardless of which
 <a class="reference internal" href="comm_style.html"><em>comm_style</em></a> command is in effect.</p>
 </div>
 <p>If load-balancing is never invoked via the <a class="reference internal" href="balance.html"><em>balance</em></a> or
 <a class="reference internal" href="fix_balance.html"><em>fix balance</em></a> commands, then the initial regular grid
 will persist for all simulations.  If balancing is performed, some of
 the methods invoked by those commands retain the logical toplogy of
 the initial 3d grid, and the mapping of processors to the grid
 specified by the processors command.  However the grid spacings in
 different dimensions may change, so that processors own sub-domains of
 different sizes.  If the <a class="reference internal" href="comm_style.html"><em>comm_style tiled</em></a> command is
 used, methods invoked by the balancing commands may discard the 3d
 grid of processors and tile the simulation domain with sub-domains of
 different sizes and shapes which no longer have a logical 3d
 connectivity.  If that occurs, all the information specified by the
 processors command is ignored.</p>
 <hr class="docutils" />
 <p>The <em>grid</em> keyword affects the factorization of P into Px,Py,Pz and it
 can also affect how the P processor IDs are mapped to the 3d grid of
 processors.</p>
 <p>The <em>onelevel</em> style creates a 3d grid that is compatible with the
 Px,Py,Pz settings, and which minimizes the surface-to-volume ratio of
 each processor&#8217;s sub-domain, as described above.  The mapping of
 processors to the grid is determined by the <em>map</em> keyword setting.</p>
 <p>The <em>twolevel</em> style can be used on machines with multicore nodes to
 minimize off-node communication.  It insures that contiguous
 sub-sections of the 3d grid are assigned to all the cores of a node.
 For example if <em>Nc</em> is 4, then 2x2x1 or 2x1x2 or 1x2x2 sub-sections of
 the 3d grid will correspond to the cores of each node.  This affects
 both the factorization and mapping steps.</p>
 <p>The <em>Cx</em>, <em>Cy</em>, <em>Cz</em> settings are similar to the <em>Px</em>, <em>Py</em>, <em>Pz</em>
 settings, only their product should equal <em>Nc</em>.  Any of the 3
 parameters can be specified with an asterisk &#8220;*&#8221;, which means LAMMPS
 will choose the number of cores in that dimension of the node&#8217;s
 sub-grid.  As with Px,Py,Pz, it will do this based on the size and
 shape of the global simulation box so as to minimize the
 surface-to-volume ratio of each processor&#8217;s sub-domain.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">For the <em>twolevel</em> style to work correctly, it
 assumes the MPI ranks of processors LAMMPS is running on are ordered
 by core and then by node.  E.g. if you are running on 2 quad-core
 nodes, for a total of 8 processors, then it assumes processors 0,1,2,3
 are on node 1, and processors 4,5,6,7 are on node 2.  This is the
 default rank ordering for most MPI implementations, but some MPIs
 provide options for this ordering, e.g. via environment variable
 settings.</p>
 </div>
 <p>The <em>numa</em> style operates similar to the <em>twolevel</em> keyword except
 that it auto-detects which cores are running on which nodes.
 Currently, it does this in only 2 levels, but it may be extended in
 the future to account for socket topology and other non-uniform memory
 access (NUMA) costs.  It also uses a different algorithm than the
 <em>twolevel</em> keyword for doing the two-level factorization of the
 simulation box into a 3d processor grid to minimize off-node
 communication, and it does its own MPI-based mapping of nodes and
 cores to the regular 3d grid.  Thus it may produce a different layout
 of the processors than the <em>twolevel</em> options.</p>
 <p>The <em>numa</em> style will give an error if the number of MPI processes is
 not divisible by the number of cores used per node, or any of the Px
 or Py of Pz values is greater than 1.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">Unlike the <em>twolevel</em> style, the <em>numa</em> style does not
 require any particular ordering of MPI ranks i norder to work
 correctly.  This is because it auto-detects which processes are
 running on which nodes.</p>
 </div>
 <p>The <em>custom</em> style uses the file <em>infile</em> to define both the 3d
 factorization and the mapping of processors to the grid.</p>
 <p>The file should have the following format.  Any number of initial
 blank or comment lines (starting with a &#8220;#&#8221; character) can be present.
 The first non-blank, non-comment line should have
 3 values:</p>
 <div class="highlight-python"><div class="highlight"><pre>Px Py Py
 </pre></div>
 </div>
 <p>These must be compatible with the total number of processors
 and the Px, Py, Pz settings of the processors commmand.</p>
 <p>This line should be immediately followed by
 P = Px*Py*Pz lines of the form:</p>
 <div class="highlight-python"><div class="highlight"><pre>ID I J K
 </pre></div>
 </div>
 <p>where ID is a processor ID (from 0 to P-1) and I,J,K are the
 processors location in the 3d grid.  I must be a number from 1 to Px
 (inclusive) and similarly for J and K.  The P lines can be listed in
 any order, but no processor ID should appear more than once.</p>
 <hr class="docutils" />
 <p>The <em>map</em> keyword affects how the P processor IDs (from 0 to P-1) are
 mapped to the 3d grid of processors.  It is only used by the
 <em>onelevel</em> and <em>twolevel</em> grid settings.</p>
 <p>The <em>cart</em> style uses the family of MPI Cartesian functions to perform
 the mapping, namely MPI_Cart_create(), MPI_Cart_get(),
 MPI_Cart_shift(), and MPI_Cart_rank().  It invokes the
 MPI_Cart_create() function with its reorder flag = 0, so that MPI is
 not free to reorder the processors.</p>
 <p>The <em>cart/reorder</em> style does the same thing as the <em>cart</em> style
 except it sets the reorder flag to 1, so that MPI can reorder
 processors if it desires.</p>
 <p>The <em>xyz</em>, <em>xzy</em>, <em>yxz</em>, <em>yzx</em>, <em>zxy</em>, and <em>zyx</em> styles are all
 similar.  If the style is IJK, then it maps the P processors to the
 grid so that the processor ID in the I direction varies fastest, the
 processor ID in the J direction varies next fastest, and the processor
 ID in the K direction varies slowest.  For example, if you select
 style <em>xyz</em> and you have a 2x2x2 grid of 8 processors, the assignments
 of the 8 octants of the simulation domain will be:</p>
 <div class="highlight-python"><div class="highlight"><pre>proc 0 = lo x, lo y, lo z octant
 proc 1 = hi x, lo y, lo z octant
 proc 2 = lo x, hi y, lo z octant
 proc 3 = hi x, hi y, lo z octant
 proc 4 = lo x, lo y, hi z octant
 proc 5 = hi x, lo y, hi z octant
 proc 6 = lo x, hi y, hi z octant
 proc 7 = hi x, hi y, hi z octant
 </pre></div>
 </div>
 <p>Note that, in principle, an MPI implementation on a particular machine
 should be aware of both the machine&#8217;s network topology and the
 specific subset of processors and nodes that were assigned to your
 simulation.  Thus its MPI_Cart calls can optimize the assignment of
 MPI processes to the 3d grid to minimize communication costs.  In
 practice, however, few if any MPI implementations actually do this.
 So it is likely that the <em>cart</em> and <em>cart/reorder</em> styles simply give
 the same result as one of the IJK styles.</p>
 <p>Also note, that for the <em>twolevel</em> grid style, the <em>map</em> setting is
 used to first map the nodes to the 3d grid, then again to the cores
 within each node.  For the latter step, the <em>cart</em> and <em>cart/reorder</em>
 styles are not supported, so an <em>xyz</em> style is used in their place.</p>
 <hr class="docutils" />
 <p>The <em>part</em> keyword affects the factorization of P into Px,Py,Pz.</p>
 <p>It can be useful when running in multi-partition mode, e.g. with the
 <a class="reference internal" href="run_style.html"><em>run_style verlet/split</em></a> command.  It specifies a
 dependency bewteen a sending partition <em>Psend</em> and a receiving
 partition <em>Precv</em> which is enforced when each is setting up their own
 mapping of their processors to the simulation box.  Each of <em>Psend</em>
 and <em>Precv</em> must be integers from 1 to Np, where Np is the number of
 partitions you have defined via the <a class="reference internal" href="Section_start.html#start-7"><span>-partition command-line switch</span></a>.</p>
 <p>A &#8220;dependency&#8221; means that the sending partition will create its
 regular 3d grid as Px by Py by Pz and after it has done this, it will
 send the Px,Py,Pz values to the receiving partition.  The receiving
 partition will wait to receive these values before creating its own
 regular 3d grid and will use the sender&#8217;s Px,Py,Pz values as a
 constraint.  The nature of the constraint is determined by the
 <em>cstyle</em> argument.</p>
 <p>For a <em>cstyle</em> of <em>multiple</em>, each dimension of the sender&#8217;s processor
 grid is required to be an integer multiple of the corresponding
 dimension in the receiver&#8217;s processor grid.  This is a requirement of
 the <a class="reference internal" href="run_style.html"><em>run_style verlet/split</em></a> command.</p>
 <p>For example, assume the sending partition creates a 4x6x10 grid = 240
 processor grid.  If the receiving partition is running on 80
 processors, it could create a 4x2x10 grid, but it will not create a
 2x4x10 grid, since in the y-dimension, 6 is not an integer multiple of
 4.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">If you use the <a class="reference internal" href="partition.html"><em>partition</em></a> command to
 invoke different &#8220;processsors&#8221; commands on different partitions, and
 you also use the <em>part</em> keyword, then you must insure that both the
 sending and receiving partitions invoke the &#8220;processors&#8221; command that
 connects the 2 partitions via the <em>part</em> keyword.  LAMMPS cannot
 easily check for this, but your simulation will likely hang in its
 setup phase if this error has been made.</p>
 </div>
 <hr class="docutils" />
 <p>The <em>file</em> keyword writes the mapping of the factorization of P
 processors and their mapping to the 3d grid to the specified file
 <em>outfile</em>.  This is useful to check that you assigned physical
 processors in the manner you desired, which can be tricky to figure
 out, especially when running on multiple partitions or on, a multicore
 machine or when the processor ranks were reordered by use of the
 <a class="reference internal" href="Section_start.html#start-7"><span>-reorder command-line switch</span></a> or due to
 use of MPI-specific launch options such as a config file.</p>
 <p>If you have multiple partitions you should insure that each one writes
 to a different file, e.g. using a <a class="reference internal" href="variable.html"><em>world-style variable</em></a>
 for the filename.  The file has a self-explanatory header, followed by
 one-line per processor in this format:</p>
 <p>world-ID universe-ID original-ID: I J K: name</p>
 <p>The IDs are the processor&#8217;s rank in this simulation (the world), the
 universe (of multiple simulations), and the original MPI communicator
 used to instantiate LAMMPS, respectively.  The world and universe IDs
 will only be different if you are running on more than one partition;
 see the <a class="reference internal" href="Section_start.html#start-7"><span>-partition command-line switch</span></a>.
 The universe and original IDs will only be different if you used the
 <a class="reference internal" href="Section_start.html#start-7"><span>-reorder command-line switch</span></a> to reorder
 the processors differently than their rank in the original
 communicator LAMMPS was instantiated with.</p>
 <p>I,J,K are the indices of the processor in the regular 3d grid, each
 from 1 to Nd, where Nd is the number of processors in that dimension
 of the grid.</p>
 <p>The <em>name</em> is what is returned by a call to MPI_Get_processor_name()
 and should represent an identifier relevant to the physical processors
 in your machine.  Note that depending on the MPI implementation,
 multiple cores can have the same <em>name</em>.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>This command cannot be used after the simulation box is defined by a
 <a class="reference internal" href="read_data.html"><em>read_data</em></a> or <a class="reference internal" href="create_box.html"><em>create_box</em></a> command.
 It can be used before a restart file is read to change the 3d
 processor grid from what is specified in the restart file.</p>
 <p>The <em>grid numa</em> keyword only currently works with the <em>map cart</em>
 option.</p>
 <p>The <em>part</em> keyword (for the receiving partition) only works with the
 <em>grid onelevel</em> or <em>grid twolevel</em> options.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="partition.html"><em>partition</em></a>, <a class="reference internal" href="Section_start.html#start-7"><span>-reorder command-line switch</span></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The option defaults are Px Py Pz = * * <a href="#id1"><span class="problematic" id="id2">*</span></a>, grid = onelevel, and map =
 cart.</p>
 </div>
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   <div class="section" id="python-command">
 <span id="index-0"></span><h1>python command<a class="headerlink" href="#python-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>python func keyword args ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>func = name of Python function</li>
 <li>one or more keyword/args pairs must be appended</li>
 </ul>
 <pre class="literal-block">
 keyword = <em>invoke</em> or <em>input</em> or <em>return</em> or <em>format</em> or <em>file</em> or <em>here</em> or <em>exists</em>
   <em>invoke</em> arg = none = invoke the previously defined Python function
   <em>input</em> args = N i1 i2 ... iN
     N = # of inputs to function
     i1,...,iN = value, SELF, or LAMMPS variable name
       value = integer number, floating point number, or string
       SELF = reference to LAMMPS itself which can be accessed by Python function
       variable = v_name, where name = name of LAMMPS variable, e.g. v_abc
   <em>return</em> arg = varReturn
     varReturn = v_name  = LAMMPS variable name which return value of function will be assigned to
   <em>format</em> arg = fstring with M characters
     M = N if no return value, where N = # of inputs
     M = N+1 if there is a return value
     fstring = each character (i,f,s,p) corresponds in order to an input or return value
     'i' = integer, 'f' = floating point, 's' = string, 'p' = SELF
   <em>file</em> arg = filename
     filename = file of Python code, which defines func
   <em>here</em> arg = inline
     inline = one or more lines of Python code which defines func
              must be a single argument, typically enclosed between triple quotes
   <em>exists</em> arg = none = Python code has been loaded by previous python command
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>python pForce input 2 v_x 20.0 return v_f format fff file force.py
 python pForce invoke
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>python factorial input 1 myN return v_fac format ii here &quot;&quot;&quot;
 def factorial(n):
   if n == 1: return n
   return n * factorial(n-1)
  &quot;&quot;&quot;
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>python loop input 1 SELF return v_value format -f here &quot;&quot;&quot;
 def loop(lmpptr,N,cut0):
   from lammps import lammps
   lmp = lammps(ptr=lmpptr)
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre><span class="c"># loop N times, increasing cutoff each time</span>
 </pre></div>
 </div>
-<div class="highlight-python"><div class="highlight"><pre>for i in range(N):
-    cut = cut0 + i*0.1
-    lmp.set_variable(&quot;cut&quot;,cut)               # set a variable in LAMMPS
-    lmp.command(&quot;pair_style lj/cut $*cut*&quot;)   # LAMMPS commands
-    lmp.command(&quot;pair_coeff * * 1.0 1.0&quot;)
-    lmp.command(&quot;run 100&quot;)
- &quot;&quot;&quot;
+<div class="highlight-python"><div class="highlight"><pre> for i in range(N):
+   cut = cut0 + i*0.1
+   lmp.set_variable(&quot;cut&quot;,cut)               # set a variable in LAMMPS
+   lmp.command(&quot;pair_style lj/cut $*cut*&quot;)   # LAMMPS commands
+   lmp.command(&quot;pair_coeff * * 1.0 1.0&quot;)
+   lmp.command(&quot;run 100&quot;)
+&quot;&quot;&quot;
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">It is not currently possible to use the
 <a class="reference internal" href=""><em>python</em></a> command described in this section with Python 3,
 only with Python 2.  The C API changed from Python 2 to 3 and the
 LAMMPS code is not compatible with both.</p>
 </div>
 <p>Define a Python function or execute a previously defined function.
 Arguments, including LAMMPS variables, can be passed to the function
 from the LAMMPS input script and a value returned by the Python
 function to a LAMMPS variable.  The Python code for the function can
 be included directly in the input script or in a separate Python file.
 The function can be standard Python code or it can make &#8220;callbacks&#8221; to
 LAMMPS through its library interface to query or set internal values
 within LAMMPS.  This is a powerful mechanism for performing complex
 operations in a LAMMPS input script that are not possible with the
 simple input script and variable syntax which LAMMPS defines.  Thus
 your input script can operate more like a true programming language.</p>
 <p>Use of this command requires building LAMMPS with the PYTHON package
 which links to the Python library so that the Python interpreter is
 embedded in LAMMPS.  More details about this process are given below.</p>
 <p>There are two ways to invoke a Python function once it has been
 defined.  One is using the <em>invoke</em> keyword.  The other is to assign
 the function to a <a class="reference internal" href="variable.html"><em>python-style variable</em></a> defined in
 your input script.  Whenever the variable is evaluated, it will
 execute the Python function to assign a value to the variable.  Note
 that variables can be evaluated in many different ways within LAMMPS.
 They can be substituted for directly in an input script.  Or they can
 be passed to various commands as arguments, so that the variable is
 evaluated during a simulation run.</p>
 <p>A broader overview of how Python can be used with LAMMPS is
 given in <a class="reference internal" href="Section_python.html"><em>Section python</em></a>.  There is an
 examples/python directory which illustrates use of the python
 command.</p>
 <hr class="docutils" />
 <p>The <em>func</em> setting specifies the name of the Python function.  The
 code for the function is defined using the <em>file</em> or <em>here</em> keywords
 as explained below.</p>
 <p>If the <em>invoke</em> keyword is used, no other keywords can be used, and a
 previous python command must have defined the Python function
 referenced by this command.  This invokes the Python function with the
 previously defined arguments and return value processed as explained
 below.  You can invoke the function as many times as you wish in your
 input script.</p>
 <p>The <em>input</em> keyword defines how many arguments <em>N</em> the Python function
 expects.  If it takes no arguments, then the <em>input</em> keyword should
 not be used.  Each argument can be specified directly as a value,
 e.g. 6 or 3.14159 or abc (a string of characters).  The type of each
 argument is specified by the <em>format</em> keyword as explained below, so
 that Python will know how to interpret the value.  If the word SELF is
 used for an argument it has a special meaning.  A pointer is passed to
 the Python function which it converts into a reference to LAMMPS
 itself.  This enables the function to call back to LAMMPS through its
 library interface as explained below.  This allows the Python function
 to query or set values internal to LAMMPS which can affect the
 subsequent execution of the input script.  A LAMMPS variable can also
 be used as an argument, specified as v_name, where &#8220;name&#8221; is the name
 of the variable.  Any style of LAMMPS variable can be used, as defined
 by the <a class="reference internal" href="variable.html"><em>variable</em></a> command.  Each time the Python
 function is invoked, the LAMMPS variable is evaluated and its value is
 passed to the Python function.</p>
 <p>The <em>return</em> keyword is only needed if the Python function returns a
 value.  The specified <em>varReturn</em> must be of the form v_name, where
 &#8220;name&#8221; is the name of a python-style LAMMPS variable, defined by the
 <a class="reference internal" href="variable.html"><em>variable</em></a> command.  The Python function can return a
 numeric or string value, as specified by the <em>format</em> keyword.</p>
 <p>As explained on the <a class="reference internal" href="variable.html"><em>variable</em></a> doc page, the definition
 of a python-style variable associates a Python function name with the
 variable.  This must match the <em>func</em> setting for this command.  For
 exampe these two commands would be self-consistent:</p>
 <div class="highlight-python"><div class="highlight"><pre>variable foo python myMultiply
 python myMultiply return v_foo format f file funcs.py
 </pre></div>
 </div>
 <p>The two commands can appear in either order in the input script so
 long as both are specified before the Python function is invoked for
 the first time.</p>
 <p>The <em>format</em> keyword must be used if the <em>input</em> or <em>return</em> keyword
 is used.  It defines an <em>fstring</em> with M characters, where M = sum of
 number of inputs and outputs.  The order of characters corresponds to
 the N inputs, followed by the return value (if it exists).  Each
 character must be one of the following: &#8220;i&#8221; for integer, &#8220;f&#8221; for
 floating point, &#8220;s&#8221; for string, or &#8220;p&#8221; for SELF.  Each character
 defines the type of the corresponding input or output value of the
 Python function and affects the type conversion that is performed
 internally as data is passed back and forth between LAMMPS and Python.
 Note that it is permissible to use a <a class="reference internal" href="variable.html"><em>python-style variable</em></a> in a LAMMPS command that allows for an
 equal-style variable as an argument, but only if the output of the
 Python function is flagged as a numeric value (&#8220;i&#8221; or &#8220;f&#8221;) via the
 <em>format</em> keyword.</p>
 <p>Either the <em>file</em>, <em>here</em>, or <em>exists</em> keyword must be used, but only
 one of them.  These keywords specify what Python code to load into the
 Python interpreter.  The <em>file</em> keyword gives the name of a file,
 which should end with a &#8221;.py&#8221; suffix, which contains Python code.  The
 code will be immediately loaded into and run in the &#8220;main&#8221; module of
 the Python interpreter.  Note that Python code which contains a
 function definition does not &#8220;execute&#8221; the function when it is run; it
 simply defines the function so that it can be invoked later.</p>
 <p>The <em>here</em> keyword does the same thing, except that the Python code
 follows as a single argument to the <em>here</em> keyword.  This can be done
 using triple quotes as delimiters, as in the examples above.  This
 allows Python code to be listed verbatim in your input script, with
 proper indentation, blank lines, and comments, as desired.  See
 <a class="reference internal" href="Section_commands.html#cmd-2"><span>Section 3.2</span></a>, for an explanation of how
 triple quotes can be used as part of input script syntax.</p>
 <p>The <em>exists</em> keyword takes no argument.  It means that Python code
 containing the required Python function defined by the <em>func</em> setting,
 is assumed to have been previously loaded by another python command.</p>
 <p>Note that the Python code that is loaded and run must contain a
 function with the specified <em>func</em> name.  To operate properly when
 later invoked, the the function code must match the <em>input</em> and
 <em>return</em> and <em>format</em> keywords specified by the python command.
 Otherwise Python will generate an error.</p>
 <hr class="docutils" />
 <p>This section describes how Python code can be written to work with
 LAMMPS.</p>
 <p>Whether you load Python code from a file or directly from your input
 script, via the <em>file</em> and <em>here</em> keywords, the code can be identical.
 It must be indented properly as Python requires.  It can contain
 comments or blank lines.  If the code is in your input script, it
 cannot however contain triple-quoted Python strings, since that will
 conflict with the triple-quote parsing that the LAMMPS input script
 performs.</p>
 <p>All the Python code you specify via one or more python commands is
 loaded into the Python &#8220;main&#8221; module, i.e. __main__.  The code can
 define global variables or statements that are outside of function
 definitions.  It can contain multiple functions, only one of which
 matches the <em>func</em> setting in the python command.  This means you can
 use the <em>file</em> keyword once to load several functions, and the
 <em>exists</em> keyword thereafter in subsequent python commands to access
 the other functions previously loaded.</p>
 <p>A Python function you define (or more generally, the code you load)
 can import other Python modules or classes, it can make calls to other
 system functions or functions you define, and it can access or modify
 global variables (in the &#8220;main&#8221; module) which will persist between
 successive function calls.  The latter can be useful, for example, to
 prevent a function from being invoke multiple times per timestep by
 different commands in a LAMMPS input script that access the returned
 python-style variable associated with the function.  For example,
 consider this function loaded with two global variables defined
 outside the function:</p>
 <div class="highlight-python"><div class="highlight"><pre><span class="n">nsteplast</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span>
 <span class="n">nvaluelast</span> <span class="o">=</span> <span class="mi">0</span>
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre><span class="k">def</span> <span class="nf">expensive</span><span class="p">(</span><span class="n">nstep</span><span class="p">):</span>
   <span class="k">global</span> <span class="n">nsteplast</span><span class="p">,</span><span class="n">nvaluelast</span>
   <span class="k">if</span> <span class="n">nstep</span> <span class="o">==</span> <span class="n">nsteplast</span><span class="p">:</span> <span class="k">return</span> <span class="n">nvaluelast</span>
   <span class="n">nsteplast</span> <span class="o">=</span> <span class="n">nstep</span>
   <span class="c"># perform complicated calculation</span>
   <span class="n">nvalue</span> <span class="o">=</span> <span class="o">...</span>
   <span class="n">nvaluelast</span> <span class="o">=</span> <span class="n">nvalue</span>
   <span class="k">return</span> <span class="n">nvalue</span>
 </pre></div>
 </div>
 <p>Nsteplast stores the previous timestep the function was invoked
 (passed as an argument to the function).  Nvaluelast stores the return
 value computed on the last function invocation.  If the function is
 invoked again on the same timestep, the previous value is simply
 returned, without re-computing it.  The &#8220;global&#8221; statement inside the
 Python function allows it to overwrite the global variables.</p>
 <p>Note that if you load Python code multiple times (via multiple python
 commands), you can overwrite previously loaded variables and functions
 if you are not careful.  E.g. if the code above were loaded twice, the
 global variables would be re-initialized, which might not be what you
 want.  Likewise, if a function with the same name exists in two chunks
 of Python code you load, the function loaded second will override the
 function loaded first.</p>
 <p>It&#8217;s important to realize that if you are running LAMMPS in parallel,
 each MPI task will load the Python interpreter and execute a local
 copy of the Python function(s) you define.  There is no connection
 between the Python interpreters running on different processors.
 This implies three important things.</p>
 <p>First, if you put a print statement in your Python function, you will
 see P copies of the output, when running on P processors.  If the
 prints occur at (nearly) the same time, the P copies of the output may
 be mixed together.  Welcome to the world of parallel programming and
 debugging.</p>
 <p>Second, if your Python code loads modules that are not pre-loaded by
 the Python library, then it will load the module from disk.  This may
 be a bottleneck if 1000s of processors try to load a module at the
 same time.  On some large supercomputers, loading of modules from disk
 by Python may be disabled.  In this case you would need to pre-build a
 Python library that has the required modules pre-loaded and link
 LAMMPS with that library.</p>
 <p>Third, if your Python code calls back to LAMMPS (discussed in the
 next section) and causes LAMMPS to perform an MPI operation requires
 global communication (e.g. via MPI_Allreduce), such as computing the
 global temperature of the system, then you must insure all your Python
 functions (running independently on different processors) call back to
 LAMMPS.  Otherwise the code may hang.</p>
 <hr class="docutils" />
 <p>Your Python function can &#8220;call back&#8221; to LAMMPS through its
 library interface, if you use the SELF input to pass Python
 a pointer to LAMMPS.  The mechanism for doing this in your
 Python function is as follows:</p>
 <div class="highlight-python"><div class="highlight"><pre><span class="k">def</span> <span class="nf">foo</span><span class="p">(</span><span class="n">lmpptr</span><span class="p">,</span><span class="o">...</span><span class="p">):</span>
   <span class="kn">from</span> <span class="nn">lammps</span> <span class="kn">import</span> <span class="n">lammps</span>
   <span class="n">lmp</span> <span class="o">=</span> <span class="n">lammps</span><span class="p">(</span><span class="n">ptr</span><span class="o">=</span><span class="n">lmpptr</span><span class="p">)</span>
   <span class="n">lmp</span><span class="o">.</span><span class="n">command</span><span class="p">(</span><span class="s">&#39;print &quot;Hello from inside Python&quot;&#39;</span><span class="p">)</span>
   <span class="o">...</span>
 </pre></div>
 </div>
 <p>The function definition must include a variable (lmpptr in this case)
 which corresponds to SELF in the python command.  The first line of
 the function imports the Python module lammps.py in the python dir of
 the distribution.  The second line creates a Python object &#8220;lmp&#8221; which
 wraps the instance of LAMMPS that called the function.  The
 &#8220;ptr=lmpptr&#8221; argument is what makes that happen.  The thrid line
 invokes the command() function in the LAMMPS library interface.  It
 takes a single string argument which is a LAMMPS input script command
 for LAMMPS to execute, the same as if it appeared in your input
 script.  In this case, LAMMPS should output</p>
 <div class="highlight-python"><div class="highlight"><pre>Hello from inside Python
 </pre></div>
 </div>
 <p>to the screen and log file.  Note that since the LAMMPS print command
 itself takes a string in quotes as its argument, the Python string
 must be delimited with a different style of quotes.</p>
 <p><a class="reference internal" href="Section_python.html#py-7"><span>Section 11.7</span></a> describes the syntax for how
 Python wraps the various functions included in the LAMMPS library
 interface.</p>
 <p>A more interesting example is in the examples/python/in.python script
 which loads and runs the following function from examples/python/funcs.py:</p>
 <div class="highlight-python"><div class="highlight"><pre>def loop(N,cut0,thresh,lmpptr):
   print &quot;LOOP ARGS&quot;,N,cut0,thresh,lmpptr
   from lammps import lammps
   lmp = lammps(ptr=lmpptr)
   natoms = lmp.get_natoms()
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre><span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">N</span><span class="p">):</span>
-    <span class="n">cut</span> <span class="o">=</span> <span class="n">cut0</span> <span class="o">+</span> <span class="n">i</span><span class="o">*</span><span class="mf">0.1</span>
+  <span class="n">cut</span> <span class="o">=</span> <span class="n">cut0</span> <span class="o">+</span> <span class="n">i</span><span class="o">*</span><span class="mf">0.1</span>
 </pre></div>
 </div>
-<div class="highlight-python"><div class="highlight"><pre>lmp.set_variable(&quot;cut&quot;,cut)                 # set a variable in LAMMPS
-    lmp.command(&quot;pair_style lj/cut $*cut*&quot;)     # LAMMPS command
-    #lmp.command(&quot;pair_style lj/cut %d&quot; % cut)  # LAMMPS command option
+<div class="highlight-python"><div class="highlight"><pre><span class="n">lmp</span><span class="o">.</span><span class="n">set_variable</span><span class="p">(</span><span class="s">&quot;cut&quot;</span><span class="p">,</span><span class="n">cut</span><span class="p">)</span>                 <span class="c"># set a variable in LAMMPS</span>
+<span class="n">lmp</span><span class="o">.</span><span class="n">command</span><span class="p">(</span><span class="s">&quot;pair_style lj/cut $*cut*&quot;</span><span class="p">)</span>     <span class="c"># LAMMPS command</span>
+<span class="c">#lmp.command(&quot;pair_style lj/cut %d&quot; % cut)  # LAMMPS command option</span>
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>lmp.command(&quot;pair_coeff * * 1.0 1.0&quot;)       # ditto
-    lmp.command(&quot;run 10&quot;)                       # ditto
-    pe = lmp.extract_compute(&quot;thermo_pe&quot;,0,0)   # extract total PE from LAMMPS
-    print &quot;PE&quot;,pe/natoms,thresh
-    if pe/natoms &lt; thresh: return
+lmp.command(&quot;run 10&quot;)                       # ditto
+pe = lmp.extract_compute(&quot;thermo_pe&quot;,0,0)   # extract total PE from LAMMPS
+print &quot;PE&quot;,pe/natoms,thresh
+if pe/natoms &lt; thresh: return
 </pre></div>
 </div>
 <p>with these input script commands:</p>
 <div class="highlight-python"><div class="highlight"><pre>python          loop input 4 10 1.0 -4.0 SELF format iffp file funcs.py
 python          loop invoke
 </pre></div>
 </div>
 <p>This has the effect of looping over a series of 10 short runs (10
 timesteps each) where the pair style cutoff is increased from a value
 of 1.0 in distance units, in increments of 0.1.  The looping stops
 when the per-atom potential energy falls below a threshhold of -4.0 in
 energy units.  More generally, Python can be used to implement a loop
 with complex logic, much more so than can be created using the LAMMPS
 <a class="reference internal" href="jump.html"><em>jump</em></a> and <a class="reference internal" href="if.html"><em>if</em></a> commands.</p>
 <p>Several LAMMPS library functions are called from the loop function.
 Get_natoms() returns the number of atoms in the simulation, so that it
 can be used to normalize the potential energy that is returned by
 extract_compute() for the &#8220;thermo_pe&#8221; compute that is defined by
 default for LAMMPS thermodynamic output.  Set_variable() sets the
 value of a string variable defined in LAMMPS.  This library function
 is a useful way for a Python function to return multiple values to
 LAMMPS, more than the single value that can be passed back via a
 return statement.  This cutoff value in the &#8220;cut&#8221; variable is then
 substituted (by LAMMPS) in the pair_style command that is executed
 next.  Alternatively, the &#8220;LAMMPS command option&#8221; line could be used
 in place of the 2 preceeding lines, to have Python insert the value
 into the LAMMPS command string.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">When using the callback mechanism just described,
 recognize that there are some operations you should not attempt
 because LAMMPS cannot execute them correctly.  If the Python function
 is invoked between runs in the LAMMPS input script, then it should be
 OK to invoke any LAMMPS input script command via the library interface
 command() or file() functions, so long as the command would work if it
 were executed in the LAMMPS input script directly at the same point.</p>
 </div>
 <p>However, a Python function can also be invoked during a run, whenever
 an associated LAMMPS variable it is assigned to is evaluted.  If the
 variable is an input argument to another LAMMPS command (e.g. <a class="reference internal" href="fix_setforce.html"><em>fix setforce</em></a>), then the Python function will be invoked
 inside the class for that command, in one of its methods that is
 invoked in the middle of a timestep.  You cannot execute arbitrary
 input script commands from the Python function (again, via the
 command() or file() functions) at that point in the run and expect it
 to work.  Other library functions such as those that invoke computes
 or other variables may have hidden side effects as well.  In these
 cases, LAMMPS has no simple way to check that something illogical is
 being attempted.</p>
 <hr class="docutils" />
 <p>If you run Python code directly on your workstation, either
 interactively or by using Python to launch a Python script stored in a
 file, and your code has an error, you will typically see informative
 error messages.  That is not the case when you run Python code from
 LAMMPS using an embedded Python interpreter.  The code will typically
 fail silently.  LAMMPS will catch some errors but cannot tell you
 where in the Python code the problem occurred.  For example, if the
 Python code cannot be loaded and run because it has syntax or other
 logic errors, you may get an error from Python pointing to the
 offending line, or you may get one of these generic errors from
 LAMMPS:</p>
 <div class="highlight-python"><div class="highlight"><pre>Could not process Python file
 Could not process Python string
 </pre></div>
 </div>
 <p>When the Python function is invoked, if it does not return properly,
 you will typically get this generic error from LAMMPS:</p>
 <div class="highlight-python"><div class="highlight"><pre>Python function evaluation failed
 </pre></div>
 </div>
 <p>Here are three suggestions for debugging your Python code while
 running it under LAMMPS.</p>
 <p>First, don&#8217;t run it under LAMMPS, at least to start with!  Debug it
 using plain Python.  Load and invoke your function, pass it arguments,
 check return values, etc.</p>
 <p>Second, add Python print statements to the function to check how far
 it gets and intermediate values it calculates.  See the discussion
 above about printing from Python when running in parallel.</p>
 <p>Third, use Python exception handling.  For example, say this statement
 in your Python function is failing, because you have not initialized the
 variable foo:</p>
 <div class="highlight-python"><div class="highlight"><pre><span class="n">foo</span> <span class="o">+=</span> <span class="mi">1</span>
 </pre></div>
 </div>
 <p>If you put one (or more) statements inside a &#8220;try&#8221; statement,
 like this:</p>
 <div class="highlight-python"><div class="highlight"><pre>import exceptions
 print &quot;Inside simple function&quot;
 try:
   foo += 1      # one or more statements here
 except Exception, e:
   print &quot;FOO error:&quot;,e
 </pre></div>
 </div>
 <p>then you will get this message printed to the screen:</p>
 <div class="highlight-python"><div class="highlight"><pre>FOO error: local variable &#39;foo&#39; referenced before assignment
 </pre></div>
 </div>
 <p>If there is no error in the try statements, then nothing is printed.
 Either way the function continues on (unless you put a return or
 sys.exit() in the except clause).</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>This command is part of the PYTHON package.  It is only enabled if
 LAMMPS was built with that package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 <p>Building LAMMPS with the PYTHON package will link LAMMPS with the
 Python library on your system.  Settings to enable this are in the
 lib/python/Makefile.lammps file.  See the lib/python/README file for
 information on those settings.</p>
 <p>If you use Python code which calls back to LAMMPS, via the SELF input
 argument explained above, there is an extra step required when
 building LAMMPS.  LAMMPS must also be built as a shared library and
 your Python function must be able to to load the Python module in
 python/lammps.py that wraps the LAMMPS library interface.  These are
 the same steps required to use Python by itself to wrap LAMMPS.
 Details on these steps are explained in <code class="xref doc docutils literal"><span class="pre">Section</span> <span class="pre">python</span></code>.  Note that it is important that the
 stand-alone LAMMPS executable and the LAMMPS shared library be
 consistent (built from the same source code files) in order for this
 to work.  If the two have been built at different times using
 different source files, problems may occur.</p>
 <p>As described above, you can use the python command to invoke a Python
 function which calls back to LAMMPS through its Python-wrapped library
 interface.  However you cannot do the opposite.  I.e. you cannot call
 LAMMPS from Python and invoke the python command to &#8220;callback&#8221; to
 Python and execute a Python function.  LAMMPS will generate an error
 if you try to do that.  Note that we think there actually should be a
 way to do that, but haven&#8217;t yet been able to figure out how to do it
 successfully.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="shell.html"><em>shell</em></a>, <a class="reference internal" href="variable.html"><em>variable</em></a></p>
 <p><strong>Default:</strong> none</p>
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   <div class="section" id="read-data-command">
 <span id="index-0"></span><h1>read_data command<a class="headerlink" href="#read-data-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>read_data file keyword args ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>file = name of data file to read in</li>
 <li>zero or more keyword/arg pairs may be appended</li>
 <li>keyword = <em>add</em> or <em>offset</em> or <em>shift</em> or <em>extra/atom/types</em> or <em>extra/bond/types</em> or <em>extra/angle/types</em> or <em>extra/dihedral/types</em> or <em>extra/improper/types</em> or <em>group</em> or <em>fix</em></li>
 </ul>
 <pre class="literal-block">
 <em>add</em> arg = <em>append</em> or <em>Nstart</em> or <em>merge</em>
-    append = add new atoms with IDs appended to current IDs
-    Nstart = add new atoms with IDs starting with Nstart
-    merge = add new atoms with their IDs unchanged
-  <em>offset</em> args = toff boff aoff doff ioff
-    toff = offset to add to atom types
-    boff = offset to add to bond types
-    aoff = offset to add to angle types
-    doff = offset to add to dihedral types
-    ioff = offset to add to improper types
-  <em>shift</em> args = Sx Sy Sz
-    Sx,Sy,Sz = distance to shift atoms when adding to system (distance units)
-  <em>extra/atom/types</em> arg = # of extra atom types
-  <em>extra/bond/types</em> arg = # of extra bond types
-  <em>extra/angle/types</em> arg = # of extra angle types
-  <em>extra/dihedral/types</em> arg = # of extra dihedral types
-  <em>extra/improper/types</em> arg = # of extra improper types
-  <em>group</em> args = groupID
-    groupID = add atoms in data file to this group
-  <em>fix</em> args = fix-ID header-string section-string
-    fix-ID = ID of fix to process header lines and sections of data file
-    header-string = header lines containing this string will be passed to fix
-    section-string = section names with this string will be passed to fix
+  append = add new atoms with IDs appended to current IDs
+  Nstart = add new atoms with IDs starting with Nstart
+  merge = add new atoms with their IDs unchanged
+<em>offset</em> args = toff boff aoff doff ioff
+  toff = offset to add to atom types
+  boff = offset to add to bond types
+  aoff = offset to add to angle types
+  doff = offset to add to dihedral types
+  ioff = offset to add to improper types
+<em>shift</em> args = Sx Sy Sz
+  Sx,Sy,Sz = distance to shift atoms when adding to system (distance units)
+<em>extra/atom/types</em> arg = # of extra atom types
+<em>extra/bond/types</em> arg = # of extra bond types
+<em>extra/angle/types</em> arg = # of extra angle types
+<em>extra/dihedral/types</em> arg = # of extra dihedral types
+<em>extra/improper/types</em> arg = # of extra improper types
+<em>group</em> args = groupID
+  groupID = add atoms in data file to this group
+<em>fix</em> args = fix-ID header-string section-string
+  fix-ID = ID of fix to process header lines and sections of data file
+  header-string = header lines containing this string will be passed to fix
+  section-string = section names with this string will be passed to fix
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>read_data data.lj
 read_data ../run7/data.polymer.gz
 read_data data.protein fix mycmap crossterm CMAP
 read_data data.water add append offset 3 1 1 1 1 shift 0.0 0.0 50.0
 read_data data.water add merge 1 group solvent
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Read in a data file containing information LAMMPS needs to run a
 simulation.  The file can be ASCII text or a gzipped text file
 (detected by a .gz suffix).  This is one of 3 ways to specify initial
 atom coordinates; see the <a class="reference internal" href="read_restart.html"><em>read_restart</em></a> and
 <a class="reference internal" href="create_atoms.html"><em>create_atoms</em></a> commands for alternative methods.
 Also see the explanation of the <a class="reference internal" href="Section_start.html#start-7"><span>-restart command-line switch</span></a> which can convert a restart file to
 a data file.</p>
 <p>This command can be used multiple times to add new atoms and their
 properties to an existing system by using the <em>add</em>, <em>offset</em>, and
 <em>shift</em> keywords.  See more details below, which includes the use case
 for the <em>extra</em> keywords.</p>
 <p>The <em>group</em> keyword adds all the atoms in the data file to the
 specified group-ID.  The group will be created if it does not already
 exist.  This is useful if you are reading multiple data files and wish
 to put sets of atoms into different groups so they can be operated on
 later.  E.g. a group of added atoms can be moved to new positions via
 the <a class="reference internal" href="displace_atoms.html"><em>displace_atoms</em></a> command.  Note that atoms
 read from the data file are also always added to the &#8220;all&#8221; group.  The
 <a class="reference internal" href="group.html"><em>group</em></a> command discusses atom groups, as used in LAMMPS.</p>
 <p>The use of the <em>fix</em> keyword is discussed below.</p>
 <hr class="docutils" />
 <p><strong>Reading multiple data files</strong></p>
 <p>The read_data command can be used multiple times with the same or
 different data files to build up a complex system from components
 contained in individual data files.  For example one data file could
 contain fluid in a confined domain; a second could contain wall atoms,
 and the second file could be read a third time to create a wall on the
 other side of the fluid.  The third set of atoms could be rotated to
 an opposing direction using the <a class="reference internal" href="displace_atoms.html"><em>displace_atoms</em></a>
 command, after the third read_data command is used.</p>
 <p>The <em>add</em>, <em>offset</em>, <em>shift</em>, <em>extra</em>, and <em>group</em> keywords are
 useful in this context.</p>
 <p>If a simulation box does not yet exist, the <em>add</em> keyword
 cannot be used; the read_data command is being used for the first
 time.  If a simulation box does exist, due to using the
 <a class="reference internal" href="create_box.html"><em>create_box</em></a> command, or a previous read_data command,
 then the <em>add</em> keyword must be used.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">The simulation box size (xlo to xhi, ylo to yhi, zlo
 to zhi) in the new data file will be merged with the existing
 simulation box to create a large enough box in each dimension to
 contain both the existing and new atoms.  Each box dimension never
 shrinks due to this merge operation, it only stays the same or
 grows. Care must be used if you are growing the existing simulation
 box in a periodic dimension.  If there are existing atoms with bonds
 that straddle that periodic boundary, then the atoms may become far
 apart if the box size grows.  This will separate the atoms in the
 bond, which can lead to &#8220;lost&#8221; bond atoms or bad dynamics.</p>
 </div>
 <p>The three choices for the <em>add</em> argument affect how the IDs of atoms
 in the data file are treated.  If <em>append</em> is specified, atoms in the
 data file are added to the current system, with their atom IDs reset
 so that an atomID = M in the data file becomes atomID = N+M, where N
 is the largest atom ID in the current system.  This rule is applied to
 all occurrences of atom IDs in the data file, e.g. in the Velocity or
 Bonds section.  If <em>Nstart</em> is specified, then <em>Nstart</em> is a numeric
 value is given, e.g. 1000, so that an atomID = M in the data file
 becomes atomID = 1000+M.  If <em>merge</em> is specified, the data file atoms
 are added to the current system without changing their IDs.  They are
 assumed to merge (without duplication) with the currently defined
 atoms.  It is up to you to insure there are no multiply defined atom
 IDs, as LAMMPS only performs an incomplete check that this is the case
 by insuring the resulting max atomID &gt;= the number of atoms.</p>
 <p>The <em>offset</em> and <em>shift</em> keywords can only be used if the <em>add</em>
 keyword is also specified.</p>
 <p>The <em>offset</em> keyword adds the specified offset values to the atom
 types, bond types, angle types, dihedral types, and improper types as
 they are read from the data file.  E.g. if <em>toff</em> = 2, and the file
 uses atom types 1,2,3, then the added atoms will have atom types
 3,4,5.  These offsets apply to all occurrences of types in the data
 file, e.g. for the Atoms or Masses or Pair Coeffs or Bond Coeffs
 sections.  This makes it easy to use atoms and molecules and their
 attributes from a data file in different simulations, where you want
 their types (atom, bond, angle, etc) to be different depending on what
 other types already exist.  All five offset values must be specified,
 but individual values will be ignored if the data file does not use
 that attribute (e.g. no bonds).</p>
 <p>The <em>shift</em> keyword can be used to specify an (Sx, Sy, Sz)
 displacement applied to the coordinates of each atom.  Sz must be 0.0
 for a 2d simulation.  This is a mechanism for adding structured
 collections of atoms at different locations within the simulation box,
 to build up a complex geometry.  It is up to you to insure atoms do
 not end up overlapping unphysically which would lead to bad dynamics.
 Note that the <a class="reference internal" href="displace_atoms.html"><em>displace_atoms</em></a> command can be used
 to move a subset of atoms after they have been read from a data file.
 Likewise, the <a class="reference internal" href="delete_atoms.html"><em>delete_atoms</em></a> command can be used to
 remove overlapping atoms.  Note that the shift values (Sx, Sy, Sz) are
 also added to the simulation box information (xlo, xhi, ylo, yhi, zlo,
 zhi) in the data file to shift its boundaries.  E.g. xlo_new = xlo +
 Sx, xhi_new = xhi + Sx.</p>
 <p>The <em>extra</em> keywords can only be used the first time the read_data
 command is used.  They are useful if you intend to add new atom, bond,
 angle, etc types later with additional read_data commands.  This is
 because the maximum number of allowed atom, bond, angle, etc types is
 set by LAMMPS when the system is first initialized.  If you do not use
 the <em>extra</em> keywords, then the number of these types will be limited
 to what appears in the first data file you read.  For example, if the
 first data file is a solid substrate of Si, it will likely specify a
 single atom type.  If you read a second data file with a different
 material (water molecules) that sit on top of the substrate, you will
 want to use different atom types for those atoms.  You can only do
 this if you set the <em>extra/atom/types</em> keyword to a sufficiently large
 value when reading the substrate data file.  Note that use of the
 <em>extra</em> keywords also allows each data file to contain sections like
 Masses or Pair Coeffs or Bond Coeffs which are sized appropriately for
 the number of types in that data file.  If the <em>offset</em> keyword is
 used appropriately when each data file is read, the values in those
 sections will be stored correctly in the larger data structures
 allocated by the use of the <em>extra</em> keywords.  E.g. the substrate file
 can list mass and pair coefficients for type 1 silicon atoms.  The
 water file can list mass and pair coeffcients for type 1 and type 2
 hydrogen and oxygen atoms.  Use of the <em>extra</em> and <em>offset</em> keywords
 will store those mass and pair coefficient values appropriately in
 data structures that allow for 3 atom types (Si, H, O).  Of course,
 you would still need to specify coefficients for H/Si and O/Si
 interactions in your input script to have a complete pairwise
 interaction model.</p>
 <p>An alternative to using the <em>extra</em> keywords with the read_data
 command, is to use the <a class="reference internal" href="create_box.html"><em>create_box</em></a> command to
 initialize the simulation box and all the various type limits you need
 via its <em>extra</em> keywords.  Then use the read_data command one or more
 times to populate the system with atoms, bonds, angles, etc, using the
 <em>offset</em> keyword if desired to alter types used in the various data
 files you read.</p>
 <hr class="docutils" />
 <p><strong>Format of a data file</strong></p>
 <p>The structure of the data file is important, though many settings and
 sections are optional or can come in any order.  See the examples
 directory for sample data files for different problems.</p>
 <p>A data file has a header and a body.  The header appears first.  The
 first line of the header is always skipped; it typically contains a
 description of the file.  Then lines are read one at a time.  Lines
 can have a trailing comment starting with &#8216;#&#8217; that is ignored.  If the
 line is blank (only whitespace after comment is deleted), it is
 skipped.  If the line contains a header keyword, the corresponding
 value(s) is read from the line.  If it doesn&#8217;t contain a header
 keyword, the line begins the body of the file.</p>
 <p>The body of the file contains zero or more sections.  The first line
 of a section has only a keyword.  This line can have a trailing
 comment starting with &#8216;#&#8217; that is either ignored or can be used to
 check for a style match, as described below.  The next line is
 skipped.  The remaining lines of the section contain values.  The
 number of lines depends on the section keyword as described below.
 Zero or more blank lines can be used between sections.  Sections can
 appear in any order, with a few exceptions as noted below.</p>
 <p>The keyword <em>fix</em> can be used one or more times.  Each usage specifies
 a fix that will be used to process a specific portion of the data
 file.  Any header line containing <em>header-string</em> and any section with
 a name containing <em>section-string</em> will be passed to the specified
 fix.  See the <a class="reference internal" href="fix_property_atom.html"><em>fix property/atom</em></a> command for
 an example of a fix that operates in this manner.  The doc page for
 the fix defines the syntax of the header line(s) and section(s) that
 it reads from the data file.  Note that the <em>header-string</em> can be
 specified as NULL, in which case no header lines are passed to the
 fix.  This means that it can infer the length of its Section from
 standard header settings, such as the number of atoms.</p>
 <p>The formatting of individual lines in the data file (indentation,
 spacing between words and numbers) is not important except that header
 and section keywords (e.g. atoms, xlo xhi, Masses, Bond Coeffs) must
 be capitalized as shown and can&#8217;t have extra white space between their
 words - e.g. two spaces or a tab between the 2 words in &#8220;xlo xhi&#8221; or
 the 2 words in &#8220;Bond Coeffs&#8221;, is not valid.</p>
 <hr class="docutils" />
 <p><strong>Format of the header of a data file</strong></p>
 <p>These are the recognized header keywords.  Header lines can come in
 any order.  The value(s) are read from the beginning of the line.
 Thus the keyword <em>atoms</em> should be in a line like &#8220;1000 atoms&#8221;; the
 keyword <em>ylo yhi</em> should be in a line like &#8220;-10.0 10.0 ylo yhi&#8221;; the
 keyword <em>xy xz yz</em> should be in a line like &#8220;0.0 5.0 6.0 xy xz yz&#8221;.
 All these settings have a default value of 0, except the lo/hi box
 size defaults are -0.5 and 0.5.  A line need only appear if the value
 is different than the default.</p>
 <ul class="simple">
 <li><em>atoms</em> = # of atoms in system</li>
 <li><em>bonds</em> = # of bonds in system</li>
 <li><em>angles</em> = # of angles in system</li>
 <li><em>dihedrals</em> = # of dihedrals in system</li>
 <li><em>impropers</em> = # of impropers in system</li>
 <li><em>atom types</em> = # of atom types in system</li>
 <li><em>bond types</em> = # of bond types in system</li>
 <li><em>angle types</em> = # of angle types in system</li>
 <li><em>dihedral types</em> = # of dihedral types in system</li>
 <li><em>improper types</em> = # of improper types in system</li>
 <li><em>extra bond per atom</em> = leave space for this many new bonds per atom</li>
 <li><em>extra angle per atom</em> = leave space for this many new angles per atom</li>
 <li><em>extra dihedral per atom</em> = leave space for this many new dihedrals per atom</li>
 <li><em>extra improper per atom</em> = leave space for this many new impropers per atom</li>
 <li><em>extra special per atom</em> = leave space for this many new special bonds per atom</li>
 <li><em>ellipsoids</em> = # of ellipsoids in system</li>
 <li><em>lines</em> = # of line segments in system</li>
 <li><em>triangles</em> = # of triangles in system</li>
 <li><em>bodies</em> = # of bodies in system</li>
 <li><em>xlo xhi</em> = simulation box boundaries in x dimension</li>
 <li><em>ylo yhi</em> = simulation box boundaries in y dimension</li>
 <li><em>zlo zhi</em> = simulation box boundaries in z dimension</li>
 <li><em>xy xz yz</em> = simulation box tilt factors for triclinic system</li>
 </ul>
 <p>The initial simulation box size is determined by the lo/hi settings.
 In any dimension, the system may be periodic or non-periodic; see the
 <a class="reference internal" href="boundary.html"><em>boundary</em></a> command.  When the simulation box is created
 it is also partitioned into a regular 3d grid of rectangular bricks,
 one per processor, based on the number of processors being used and
 the settings of the <a class="reference internal" href="processors.html"><em>processors</em></a> command.  The
 partitioning can later be changed by the <a class="reference internal" href="balance.html"><em>balance</em></a> or
 <a class="reference internal" href="fix_balance.html"><em>fix balance</em></a> commands.</p>
 <p>If the <em>xy xz yz</em> line does not appear, LAMMPS will set up an
 axis-aligned (orthogonal) simulation box.  If the line does appear,
 LAMMPS creates a non-orthogonal simulation domain shaped as a
 parallelepiped with triclinic symmetry.  The parallelepiped has its
 &#8220;origin&#8221; at (xlo,ylo,zlo) and is defined by 3 edge vectors starting
 from the origin given by A = (xhi-xlo,0,0); B = (xy,yhi-ylo,0); C =
 (xz,yz,zhi-zlo).  <em>Xy,xz,yz</em> can be 0.0 or positive or negative values
 and are called &#8220;tilt factors&#8221; because they are the amount of
 displacement applied to faces of an originally orthogonal box to
 transform it into the parallelepiped.</p>
 <p>By default, the tilt factors (xy,xz,yz) can not skew the box more than
 half the distance of the corresponding parallel box length.  For
 example, if xlo = 2 and xhi = 12, then the x box length is 10 and the
 xy tilt factor must be between -5 and 5.  Similarly, both xz and yz
 must be between -(xhi-xlo)/2 and +(yhi-ylo)/2.  Note that this is not
 a limitation, since if the maximum tilt factor is 5 (as in this
 example), then configurations with tilt = ..., -15, -5, 5, 15, 25,
 ... are all geometrically equivalent.  If you wish to define a box
 with tilt factors that exceed these limits, you can use the <a class="reference internal" href="box.html"><em>box tilt</em></a> command, with a setting of <em>large</em>; a setting of
 <em>small</em> is the default.</p>
 <p>See <a class="reference internal" href="Section_howto.html#howto-12"><span>Section_howto 12</span></a> of the doc pages
 for a geometric description of triclinic boxes, as defined by LAMMPS,
 and how to transform these parameters to and from other commonly used
 triclinic representations.</p>
 <p>When a triclinic system is used, the simulation domain should normally
 be periodic in the dimension that the tilt is applied to, which is
 given by the second dimension of the tilt factor (e.g. y for xy tilt).
 This is so that pairs of atoms interacting across that boundary will
 have one of them shifted by the tilt factor.  Periodicity is set by
 the <a class="reference internal" href="boundary.html"><em>boundary</em></a> command.  For example, if the xy tilt
 factor is non-zero, then the y dimension should be periodic.
 Similarly, the z dimension should be periodic if xz or yz is non-zero.
 LAMMPS does not require this periodicity, but you may lose atoms if
 this is not the case.</p>
 <p>Also note that if your simulation will tilt the box, e.g. via the <a class="reference internal" href="fix_deform.html"><em>fix deform</em></a> command, the simulation box must be setup to
 be triclinic, even if the tilt factors are initially 0.0.  You can
 also change an orthogonal box to a triclinic box or vice versa by
 using the <a class="reference internal" href="change_box.html"><em>change box</em></a> command with its <em>ortho</em> and
 <em>triclinic</em> options.</p>
 <p>For 2d simulations, the <em>zlo zhi</em> values should be set to bound the z
 coords for atoms that appear in the file; the default of -0.5 0.5 is
 valid if all z coords are 0.0.  For 2d triclinic simulations, the xz
 and yz tilt factors must be 0.0.</p>
 <p>If the system is periodic (in a dimension), then atom coordinates can
 be outside the bounds (in that dimension); they will be remapped (in a
 periodic sense) back inside the box.  Note that if the <em>add</em> option is
 being used to add atoms to a simulation box that already exists, this
 periodic remapping will be performed using simulation box bounds that
 are the union of the existing box and the box boundaries in the new
 data file.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">If the system is non-periodic (in a dimension), then
 all atoms in the data file must have coordinates (in that dimension)
 that are &#8220;greater than or equal to&#8221; the lo value and &#8220;less than or
 equal to&#8221; the hi value.  If the non-periodic dimension is of style
 &#8220;fixed&#8221; (see the <a class="reference internal" href="boundary.html"><em>boundary</em></a> command), then the atom
 coords must be strictly &#8220;less than&#8221; the hi value, due to the way
 LAMMPS assign atoms to processors.  Note that you should not make the
 lo/hi values radically smaller/larger than the extent of the atoms.
 For example, if your atoms extend from 0 to 50, you should not specify
 the box bounds as -10000 and 10000.  This is because LAMMPS uses the
 specified box size to layout the 3d grid of processors.  A huge
 (mostly empty) box will be sub-optimal for performance when using
 &#8220;fixed&#8221; boundary conditions (see the <a class="reference internal" href="boundary.html"><em>boundary</em></a>
 command).  When using &#8220;shrink-wrap&#8221; boundary conditions (see the
 <a class="reference internal" href="boundary.html"><em>boundary</em></a> command), a huge (mostly empty) box may cause
 a parallel simulation to lose atoms when LAMMPS shrink-wraps the box
 around the atoms.  The read_data command will generate an error
 in this case.</p>
 </div>
 <p>The &#8220;extra bond per atom&#8221; setting (angle, dihedral, improper) is only
 needed if new bonds (angles, dihedrals, impropers) will be added to
 the system when a simulation runs, e.g. by using the <a class="reference internal" href="fix_bond_create.html"><em>fix bond/create</em></a> command.  This will pre-allocate
 space in LAMMPS data structures for storing the new bonds (angles,
 dihedrals, impropers).</p>
 <p>The &#8220;extra special per atom&#8221; setting is typically only needed if new
 bonds/angles/etc will be added to the system, e.g. by using the <a class="reference internal" href="fix_bond_create.html"><em>fix bond/create</em></a> command.  Or if entire new molecules
 will be added to the system, e.g. by using the <a class="reference internal" href="fix_deposit.html"><em>fix deposit</em></a> or <a class="reference internal" href="fix_pour.html"><em>fix pour</em></a> commands, which
 will have more special 1-2,1-3,1-4 neighbors than any other molecules
 defined in the data file.  Using this setting will pre-allocate space
 in the LAMMPS data structures for storing these neighbors.  See the
 <a class="reference internal" href="special_bonds.html"><em>special_bonds</em></a> and <a class="reference internal" href="molecule.html"><em>molecule</em></a> doc
 pages for more discussion of 1-2,1-3,1-4 neighbors.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">All of the &#8220;extra&#8221; settings are only used if they
 appear in the first data file read; see the description of the <em>add</em>
 keyword above for reading multiple data files.  If they appear in
 later data files, they are ignored.</p>
 </div>
 <p>The &#8220;ellipsoids&#8221; and &#8220;lines&#8221; and &#8220;triangles&#8221; and &#8220;bodies&#8221; settings are
 only used with <a class="reference internal" href="atom_style.html"><em>atom_style ellipsoid or line or tri or body</em></a> and specify how many of the atoms are
 finite-size ellipsoids or lines or triangles or bodies; the remainder
 are point particles.  See the discussion of ellipsoidflag and the
 <em>Ellipsoids</em> section below.  See the discussion of lineflag and the
 <em>Lines</em> section below.  See the discussion of triangleflag and the
 <em>Triangles</em> section below.  See the discussion of bodyflag and the
 <em>Bodies</em> section below.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">For <a class="reference internal" href="atom_style.html"><em>atom_style template</em></a>, the
 molecular topology (bonds,angles,etc) is contained in the molecule
 templates read-in by the <a class="reference internal" href="molecule.html"><em>molecule</em></a> command.  This means
 you cannot set the <em>bonds</em>, <em>angles</em>, etc header keywords in the data
 file, nor can you define <em>Bonds</em>, <em>Angles</em>, etc sections as discussed
 below.  You can set the <em>bond types</em>, <em>angle types</em>, etc header
 keywords, though it is not necessary.  If specified, they must match
 the maximum values defined in any of the template molecules.</p>
 </div>
 <hr class="docutils" />
 <p><strong>Format of the body of a data file</strong></p>
 <p>These are the section keywords for the body of the file.</p>
 <ul class="simple">
 <li><em>Atoms, Velocities, Masses, Ellipsoids, Lines, Triangles, Bodies</em> = atom-property sections</li>
 <li><em>Bonds, Angles, Dihedrals, Impropers</em> = molecular topology sections</li>
 <li><em>Pair Coeffs, PairIJ Coeffs, Bond Coeffs, Angle Coeffs, Dihedral Coeffs,    Improper Coeffs</em> = force field sections</li>
 <li><em>BondBond Coeffs, BondAngle Coeffs, MiddleBondTorsion Coeffs,    EndBondTorsion Coeffs, AngleTorsion Coeffs, AngleAngleTorsion Coeffs,    BondBond13 Coeffs, AngleAngle Coeffs</em> = class 2 force field sections</li>
 </ul>
 <p>These keywords will check an appended comment for a match with the
 currently defined style:</p>
 <ul class="simple">
 <li><em>Atoms, Pair Coeffs, PairIJ Coeffs, Bond Coeffs, Angle Coeffs, Dihedral Coeffs, Improper Coeffs</em></li>
 </ul>
 <p>For example, these lines:</p>
 <div class="highlight-python"><div class="highlight"><pre>Atoms # sphere
 Pair Coeffs # lj/cut
 </pre></div>
 </div>
 <p>will check if the currently-defined <a class="reference internal" href="atom_style.html"><em>atom_style</em></a> is
 <em>sphere</em>, and the current <a class="reference external" href="pair_style">pair_style</a> is <em>lj/cut</em>.  If
 not, LAMMPS will issue a warning to indicate that the data file
 section likely does not contain the correct number or type of
 parameters expected for the currently-defined style.</p>
 <p>Each section is listed below in alphabetic order.  The format of each
 section is described including the number of lines it must contain and
 rules (if any) for where it can appear in the data file.</p>
 <p>Any individual line in the various sections can have a trailing
 comment starting with &#8220;#&#8221; for annotation purposes.  E.g. in the
 Atoms section:</p>
 <div class="highlight-python"><div class="highlight"><pre>10 1 17 -1.0 10.0 5.0 6.0   # salt ion
 </pre></div>
 </div>
 <hr class="docutils" />
 <p><em>Angle Coeffs</em> section:</p>
 <ul class="simple">
 <li>one line per angle type</li>
 <li>line syntax: ID coeffs</li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>ID = angle type (1-N)
-  coeffs = list of coeffs
+coeffs = list of coeffs
 </pre></div>
 </div>
 <ul class="simple">
 <li>example:</li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>6 70 108.5 0 0
 </pre></div>
 </div>
 <p>The number and meaning of the coefficients are specific to the defined
 angle style.  See the <a class="reference internal" href="angle_style.html"><em>angle_style</em></a> and
 <a class="reference internal" href="angle_coeff.html"><em>angle_coeff</em></a> commands for details.  Coefficients can
 also be set via the <a class="reference internal" href="angle_coeff.html"><em>angle_coeff</em></a> command in the
 input script.</p>
 <hr class="docutils" />
 <p><em>AngleAngle Coeffs</em> section:</p>
 <ul class="simple">
 <li>one line per improper type</li>
 <li>line syntax: ID coeffs</li>
 </ul>
 <pre class="literal-block">
 ID = improper type (1-N)
-  coeffs = list of coeffs (see <a class="reference internal" href="improper_coeff.html"><em>improper_coeff</em></a>)
+coeffs = list of coeffs (see <a class="reference internal" href="improper_coeff.html"><em>improper_coeff</em></a>)
 </pre>
 <hr class="docutils" />
 <p><em>AngleAngleTorsion Coeffs</em> section:</p>
 <ul class="simple">
 <li>one line per dihedral type</li>
 <li>line syntax: ID coeffs</li>
 </ul>
 <pre class="literal-block">
 ID = dihedral type (1-N)
-  coeffs = list of coeffs (see <a class="reference internal" href="dihedral_coeff.html"><em>dihedral_coeff</em></a>)
+coeffs = list of coeffs (see <a class="reference internal" href="dihedral_coeff.html"><em>dihedral_coeff</em></a>)
 </pre>
 <hr class="docutils" />
 <p><em>Angles</em> section:</p>
 <ul class="simple">
 <li>one line per angle</li>
 <li>line syntax: ID type atom1 atom2 atom3</li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>ID = number of angle (1-Nangles)
-  type = angle type (1-Nangletype)
-  atom1,atom2,atom3 = IDs of 1st,2nd,3rd atoms in angle
+type = angle type (1-Nangletype)
+atom1,atom2,atom3 = IDs of 1st,2nd,3rd atoms in angle
 </pre></div>
 </div>
 <p>example:
 .. parsed-literal:</p>
 <div class="highlight-python"><div class="highlight"><pre>2 2 17 29 430
 </pre></div>
 </div>
 <p>The 3 atoms are ordered linearly within the angle.  Thus the central
 atom (around which the angle is computed) is the atom2 in the list.
 E.g. H,O,H for a water molecule.  The <em>Angles</em> section must appear
 after the <em>Atoms</em> section.  All values in this section must be
 integers (1, not 1.0).</p>
 <hr class="docutils" />
 <p><em>AngleTorsion Coeffs</em> section:</p>
 <ul class="simple">
 <li>one line per dihedral type</li>
 <li>line syntax: ID coeffs</li>
 </ul>
 <pre class="literal-block">
 ID = dihedral type (1-N)
-  coeffs = list of coeffs (see <a class="reference internal" href="dihedral_coeff.html"><em>dihedral_coeff</em></a>)
+coeffs = list of coeffs (see <a class="reference internal" href="dihedral_coeff.html"><em>dihedral_coeff</em></a>)
 </pre>
 <hr class="docutils" />
 <p><em>Atoms</em> section:</p>
 <ul class="simple">
 <li>one line per atom</li>
 <li>line syntax: depends on atom style</li>
 </ul>
 <p>An <em>Atoms</em> section must appear in the data file if natoms &gt; 0 in the
 header section.  The atoms can be listed in any order.  These are the
 line formats for each <a class="reference internal" href="atom_style.html"><em>atom style</em></a> in LAMMPS.  As
 discussed below, each line can optionally have 3 flags (nx,ny,nz)
 appended to it, which indicate which image of a periodic simulation
 box the atom is in.  These may be important to include for some kinds
 of analysis.</p>
 <table border="1" class="docutils">
 <colgroup>
 <col width="15%" />
 <col width="85%" />
 </colgroup>
 <tbody valign="top">
 <tr class="row-odd"><td>angle</td>
 <td>atom-ID molecule-ID atom-type x y z</td>
 </tr>
 <tr class="row-even"><td>atomic</td>
 <td>atom-ID atom-type x y z</td>
 </tr>
 <tr class="row-odd"><td>body</td>
 <td>atom-ID atom-type bodyflag mass x y z</td>
 </tr>
 <tr class="row-even"><td>bond</td>
 <td>atom-ID molecule-ID atom-type x y z</td>
 </tr>
 <tr class="row-odd"><td>charge</td>
 <td>atom-ID atom-type q x y z</td>
 </tr>
 <tr class="row-even"><td>dipole</td>
 <td>atom-ID atom-type q x y z mux muy muz</td>
 </tr>
 <tr class="row-odd"><td>electron</td>
 <td>atom-ID atom-type q spin eradius x y z</td>
 </tr>
 <tr class="row-even"><td>ellipsoid</td>
 <td>atom-ID atom-type ellipsoidflag density x y z</td>
 </tr>
 <tr class="row-odd"><td>full</td>
 <td>atom-ID molecule-ID atom-type q x y z</td>
 </tr>
 <tr class="row-even"><td>line</td>
 <td>atom-ID molecule-ID atom-type lineflag density x y z</td>
 </tr>
 <tr class="row-odd"><td>meso</td>
 <td>atom-ID atom-type rho e cv x y z</td>
 </tr>
 <tr class="row-even"><td>molecular</td>
 <td>atom-ID molecule-ID atom-type x y z</td>
 </tr>
 <tr class="row-odd"><td>peri</td>
 <td>atom-ID atom-type volume density x y z</td>
 </tr>
 <tr class="row-even"><td>sphere</td>
 <td>atom-ID atom-type diameter density x y z</td>
 </tr>
 <tr class="row-odd"><td>template</td>
 <td>atom-ID molecule-ID template-index template-atom atom-type x y z</td>
 </tr>
 <tr class="row-even"><td>tri</td>
 <td>atom-ID molecule-ID atom-type triangleflag density x y z</td>
 </tr>
 <tr class="row-odd"><td>wavepacket</td>
 <td>atom-ID atom-type charge spin eradius etag cs_re cs_im x y z</td>
 </tr>
 <tr class="row-even"><td>hybrid</td>
 <td>atom-ID atom-type x y z sub-style1 sub-style2 ...</td>
 </tr>
 </tbody>
 </table>
 <p>The keywords have these meanings:</p>
 <ul class="simple">
 <li>atom-ID = integer ID of atom</li>
 <li>molecule-ID = integer ID of molecule the atom belongs to</li>
 <li>atom-type = type of atom (1-Ntype)</li>
 <li>q = charge on atom (charge units)</li>
 <li>diameter = diameter of spherical atom (distance units)</li>
 <li>ellipsoidflag = 1 for ellipsoidal particles, 0 for point particles</li>
 <li>lineflag = 1 for line segment particles, 0 for point particles</li>
 <li>triangleflag = 1 for triangular particles, 0 for point particles</li>
 <li>bodyflag = 1 for body particles, 0 for point particles</li>
 <li>template-index = which molecule within the molecule template the atom is part of</li>
 <li>template-atom = which atom within a template molecule the atom is</li>
 <li>density = density of particle (mass/distance^3 or mass/distance^2 or mass/distance units, depending on dimensionality of particle)</li>
 <li>mass = mass of particle (mass units)</li>
 <li>volume = volume of particle (distance^3 units)</li>
 <li>x,y,z = coordinates of atom</li>
 <li>mux,muy,muz = components of dipole moment of atom (dipole units)</li>
 <li>rho = density (need units) for SPH particles</li>
 <li>e = energy (need units) for SPH particles</li>
 <li>cv = heat capacity (need units) for SPH particles</li>
 <li>spin = electron spin (+1/-1), 0 = nuclei, 2 = fixed-core, 3 = pseudo-cores (i.e. ECP)</li>
 <li>eradius = electron radius (or fixed-core radius)</li>
 <li>etag = integer ID of electron that each wavepacket belongs to</li>
 <li>cs_re,cs_im = real/imaginary parts of wavepacket coefficients</li>
 </ul>
 <p>The units for these quantities depend on the unit style; see the
 <a class="reference internal" href="units.html"><em>units</em></a> command for details.</p>
 <p>For 2d simulations specify z as 0.0, or a value within the <em>zlo zhi</em>
 setting in the data file header.</p>
 <p>The atom-ID is used to identify the atom throughout the simulation and
 in dump files.  Normally, it is a unique value from 1 to Natoms for
 each atom.  Unique values larger than Natoms can be used, but they
 will cause extra memory to be allocated on each processor, if an atom
 map array is used, but not if an atom map hash is used; see the
 <a class="reference internal" href="atom_modify.html"><em>atom_modify</em></a> command for details.  If an atom map is
 not used (e.g. an atomic system with no bonds), and you don&#8217;t care if
 unique atom IDs appear in dump files, then the atom-IDs can all be set
 to 0.</p>
 <p>The molecule ID is a 2nd identifier attached to an atom.  Normally, it
 is a number from 1 to N, identifying which molecule the atom belongs
 to.  It can be 0 if it is an unbonded atom or if you don&#8217;t care to
 keep track of molecule assignments.</p>
 <p>The diameter specifies the size of a finite-size spherical particle.
 It can be set to 0.0, which means that atom is a point particle.</p>
 <p>The ellipsoidflag, lineflag, triangleflag, and bodyflag determine
 whether the particle is a finite-size ellipsoid or line or triangle or
 body of finite size, or whether the particle is a point particle.
 Additional attributes must be defined for each ellipsoid, line,
 triangle, or body in the corresponding <em>Ellipsoids</em>, <em>Lines</em>,
 <em>Triangles</em>, or <em>Bodies</em> section.</p>
 <p>The <em>template-index</em> and <em>template-atom</em> are only defined used by
 <a class="reference internal" href="atom_style.html"><em>atom_style template</em></a>.  In this case the
 <a class="reference internal" href="molecule.html"><em>molecule</em></a> command is used to define a molecule template
 which contains one or more molecules.  If an atom belongs to one of
 those molecules, its <em>template-index</em> and <em>template-atom</em> are both set
 to positive integers; if not the values are both 0.  The
 <em>template-index</em> is which molecule (1 to Nmols) the atom belongs to.
 The <em>template-atom</em> is which atom (1 to Natoms) within the molecule
 the atom is.</p>
 <p>Some pair styles and fixes and computes that operate on finite-size
 particles allow for a mixture of finite-size and point particles.  See
 the doc pages of individual commands for details.</p>
 <p>For finite-size particles, the density is used in conjunction with the
 particle volume to set the mass of each particle as mass = density *
 volume.  In this context, volume can be a 3d quantity (for spheres or
 ellipsoids), a 2d quantity (for triangles), or a 1d quantity (for line
 segments).  If the volume is 0.0, meaning a point particle, then the
 density value is used as the mass.  One exception is for the body atom
 style, in which case the mass of each particle (body or point
 particle) is specified explicitly.  This is because the volume of the
 body is unknown.</p>
 <p>For atom_style hybrid, following the 5 initial values (ID,type,x,y,z),
 specific values for each sub-style must be listed.  The order of the
 sub-styles is the same as they were listed in the
 <a class="reference internal" href="atom_style.html"><em>atom_style</em></a> command.  The sub-style specific values
 are those that are not the 5 standard ones (ID,type,x,y,z).  For
 example, for the &#8220;charge&#8221; sub-style, a &#8220;q&#8221; value would appear.  For
 the &#8220;full&#8221; sub-style, a &#8220;molecule-ID&#8221; and &#8220;q&#8221; would appear.  These are
 listed in the same order they appear as listed above.  Thus if</p>
 <div class="highlight-python"><div class="highlight"><pre>atom_style hybrid charge sphere
 </pre></div>
 </div>
 <p>were used in the input script, each atom line would have these fields:</p>
 <div class="highlight-python"><div class="highlight"><pre>atom-ID atom-type x y z q diameter density
 </pre></div>
 </div>
 <p>Note that if a non-standard value is defined by multiple sub-styles,
 it must appear mutliple times in the atom line.  E.g. the atom line
 for atom_style hybrid dipole full would list &#8220;q&#8221; twice:</p>
 <div class="highlight-python"><div class="highlight"><pre>atom-ID atom-type x y z q mux muy myz molecule-ID q
 </pre></div>
 </div>
 <p>Atom lines specify the (x,y,z) coordinates of atoms.  These can be
 inside or outside the simulation box.  When the data file is read,
 LAMMPS wraps coordinates outside the box back into the box for
 dimensions that are periodic.  As discussed above, if an atom is
 outside the box in a non-periodic dimension, it will be lost.</p>
 <p>LAMMPS always stores atom coordinates as values which are inside the
 simulation box.  It also stores 3 flags which indicate which image of
 the simulation box (in each dimension) the atom would be in if its
 coordinates were unwrapped across periodic boundaries.  An image flag
 of 0 means the atom is still inside the box when unwrapped.  A value
 of 2 means add 2 box lengths to get the unwrapped coordinate.  A value
 of -1 means subtract 1 box length to get the unwrapped coordinate.
 LAMMPS updates these flags as atoms cross periodic boundaries during
 the simulation.  The <a class="reference internal" href="dump.html"><em>dump</em></a> command can output atom atom
 coordinates in wrapped or unwrapped form, as well as the 3 image
 flags.</p>
 <p>In the data file, atom lines (all lines or none of them) can
 optionally list 3 trailing integer values (nx,ny,nz), which are used
 to initialize the atom&#8217;s image flags.  If nx,ny,nz values are not
 listed in the data file, LAMMPS initializes them to 0.  Note that the
 image flags are immediately updated if an atom&#8217;s coordinates need to
 wrapped back into the simulation box.</p>
 <p>It is only important to set image flags correctly in a data file if a
 simulation model relies on unwrapped coordinates for some calculation;
 otherwise they can be left unspecified.  Examples of LAMMPS commands
 that use unwrapped coordinates internally are as follows:</p>
 <ul class="simple">
 <li>Atoms in a rigid body (see <a class="reference internal" href="fix_rigid.html"><em>fix rigid</em></a>, <a class="reference internal" href="fix_rigid.html"><em>fix rigid/small</em></a>) must have consistent image flags, so that
 when the atoms are unwrapped, they are near each other, i.e. as a
 single body.</li>
 <li>If the <a class="reference internal" href="replicate.html"><em>replicate</em></a> command is used to generate a larger
 system, image flags must be consistent for bonded atoms when the bond
 crosses a periodic boundary.  I.e. the values of the image flags
 should be different by 1 (in the appropriate dimension) for the two
 atoms in such a bond.</li>
 <li>If you plan to <a class="reference internal" href="dump.html"><em>dump</em></a> image flags and perform post-analysis
 that will unwrap atom coordinates, it may be important that a
 continued run (restarted from a data file) begins with image flags
 that are consistent with the previous run.</li>
 </ul>
 <p>Atom velocities and other atom quantities not defined above are set to
 0.0 when the <em>Atoms</em> section is read.  Velocities can be set later by
 a <em>Velocities</em> section in the data file or by a
 <a class="reference internal" href="velocity.html"><em>velocity</em></a> or <a class="reference internal" href="set.html"><em>set</em></a> command in the input
 script.</p>
 <hr class="docutils" />
 <p><em>Bodies</em> section:</p>
 <ul class="simple">
 <li>one or more lines per body</li>
 <li>first line syntax: atom-ID ninteger ndouble</li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>ninteger = # of integer quantities for this particle
-  ndouble = # of floating-point quantities for this particle
+ndouble = # of floating-point quantities for this particle
 </pre></div>
 </div>
 <ul class="simple">
 <li>0 or more integer lines: one line for every 10 integer quantities</li>
 <li>0 or more double lines: one line for every 10 double quantities</li>
 <li>example:</li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>12 3 6
-  2 3 2
-  1.0 2.0 3.0 1.0 2.0 4.0
+2 3 2
+1.0 2.0 3.0 1.0 2.0 4.0
 </pre></div>
 </div>
 <ul class="simple">
 <li>example:</li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>12 0 14
-  1.0 2.0 3.0 1.0 2.0 4.0 1.0 2.0 3.0 1.0
-  2.0 4.0 4.0 2.0
+1.0 2.0 3.0 1.0 2.0 4.0 1.0 2.0 3.0 1.0
+2.0 4.0 4.0 2.0
 </pre></div>
 </div>
 <p>The <em>Bodies</em> section must appear if <a class="reference internal" href="atom_style.html"><em>atom_style body</em></a>
 is used and any atoms listed in the <em>Atoms</em> section have a bodyflag =
 1.  The number of bodies should be specified in the header section via
 the &#8220;bodies&#8221; keyword.</p>
 <p>Each body can have a variable number of integer and/or floating-point
 values.  The number and meaning of the values is defined by the body
 style, as described in the <a class="reference internal" href="body.html"><em>body</em></a> doc page.  The body style
 is given as an argument to the <a class="reference internal" href="atom_style.html"><em>atom_style body</em></a>
 command.</p>
 <p>The ninteger and ndouble values determine how many integer and
 floating-point values are specified for this particle.  Ninteger and
 ndouble can be as large as needed and can be different for every body.
 Integer values are then listed on subsequent lines, 10 values per
 line.  Floating-point values follow on subsequent lines, again 10 per
 line.  If the number of lines is not evenly divisible by 10, the last
 line in that group contains the remaining values, e.g. 4 values out of
 14 in the last example above, for floating-point values.  If there are
 no values of a particular type, no lines appear for that type,
 e.g. there are no integer lines in the last example above.</p>
 <p>The <em>Bodies</em> section must appear after the <em>Atoms</em> section.</p>
 <hr class="docutils" />
 <p><em>Bond Coeffs</em> section:</p>
 <ul class="simple">
 <li>one line per bond type</li>
 <li>line syntax: ID coeffs</li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>ID = bond type (1-N)
-  coeffs = list of coeffs
+coeffs = list of coeffs
 </pre></div>
 </div>
 <ul class="simple">
 <li>example:</li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>4 250 1.49
 </pre></div>
 </div>
 <p>The number and meaning of the coefficients are specific to the defined
 bond style.  See the <a class="reference internal" href="bond_style.html"><em>bond_style</em></a> and
 <a class="reference internal" href="bond_coeff.html"><em>bond_coeff</em></a> commands for details.  Coefficients can
 also be set via the <a class="reference internal" href="bond_coeff.html"><em>bond_coeff</em></a> command in the input
 script.</p>
 <hr class="docutils" />
 <p><em>BondAngle Coeffs</em> section:</p>
 <ul class="simple">
 <li>one line per angle type</li>
 <li>line syntax: ID coeffs</li>
 </ul>
 <pre class="literal-block">
 ID = angle type (1-N)
-  coeffs = list of coeffs (see class 2 section of <a class="reference internal" href="angle_coeff.html"><em>angle_coeff</em></a>)
+coeffs = list of coeffs (see class 2 section of <a class="reference internal" href="angle_coeff.html"><em>angle_coeff</em></a>)
 </pre>
 <hr class="docutils" />
 <p><em>BondBond Coeffs</em> section:</p>
 <ul class="simple">
 <li>one line per angle type</li>
 <li>line syntax: ID coeffs</li>
 </ul>
 <pre class="literal-block">
 ID = angle type (1-N)
-  coeffs = list of coeffs (see class 2 section of <a class="reference internal" href="angle_coeff.html"><em>angle_coeff</em></a>)
+coeffs = list of coeffs (see class 2 section of <a class="reference internal" href="angle_coeff.html"><em>angle_coeff</em></a>)
 </pre>
 <hr class="docutils" />
 <p><em>BondBond13 Coeffs</em> section:</p>
 <ul class="simple">
 <li>one line per dihedral type</li>
 <li>line syntax: ID coeffs</li>
 </ul>
 <pre class="literal-block">
 ID = dihedral type (1-N)
-  coeffs = list of coeffs (see class 2 section of <a class="reference internal" href="dihedral_coeff.html"><em>dihedral_coeff</em></a>)
+coeffs = list of coeffs (see class 2 section of <a class="reference internal" href="dihedral_coeff.html"><em>dihedral_coeff</em></a>)
 </pre>
 <hr class="docutils" />
 <p><em>Bonds</em> section:</p>
 <ul class="simple">
 <li>one line per bond</li>
 <li>line syntax: ID type atom1 atom2</li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>ID = bond number (1-Nbonds)
-  type = bond type (1-Nbondtype)
-  atom1,atom2 = IDs of 1st,2nd atoms in bond
+type = bond type (1-Nbondtype)
+atom1,atom2 = IDs of 1st,2nd atoms in bond
 </pre></div>
 </div>
 <ul class="simple">
 <li>example:</li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>12 3 17 29
 </pre></div>
 </div>
 <p>The <em>Bonds</em> section must appear after the <em>Atoms</em> section.  All values
 in this section must be integers (1, not 1.0).</p>
 <hr class="docutils" />
 <p><em>Dihedral Coeffs</em> section:</p>
 <ul class="simple">
 <li>one line per dihedral type</li>
 <li>line syntax: ID coeffs</li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>ID = dihedral type (1-N)
-  coeffs = list of coeffs
+coeffs = list of coeffs
 </pre></div>
 </div>
 <ul class="simple">
 <li>example:</li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>3 0.6 1 0 1
 </pre></div>
 </div>
 <p>The number and meaning of the coefficients are specific to the defined
 dihedral style.  See the <a class="reference internal" href="dihedral_style.html"><em>dihedral_style</em></a> and
 <a class="reference internal" href="dihedral_coeff.html"><em>dihedral_coeff</em></a> commands for details.
 Coefficients can also be set via the
 <a class="reference internal" href="dihedral_coeff.html"><em>dihedral_coeff</em></a> command in the input script.</p>
 <hr class="docutils" />
 <p><em>Dihedrals</em> section:</p>
 <ul class="simple">
 <li>one line per dihedral</li>
 <li>line syntax: ID type atom1 atom2 atom3 atom4</li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>ID = number of dihedral (1-Ndihedrals)
-  type = dihedral type (1-Ndihedraltype)
-  atom1,atom2,atom3,atom4 = IDs of 1st,2nd,3rd,4th atoms in dihedral
+type = dihedral type (1-Ndihedraltype)
+atom1,atom2,atom3,atom4 = IDs of 1st,2nd,3rd,4th atoms in dihedral
 </pre></div>
 </div>
 <ul class="simple">
 <li>example:</li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>12 4 17 29 30 21
 </pre></div>
 </div>
 <p>The 4 atoms are ordered linearly within the dihedral.  The <em>Dihedrals</em>
 section must appear after the <em>Atoms</em> section.  All values in this
 section must be integers (1, not 1.0).</p>
 <hr class="docutils" />
 <p><em>Ellipsoids</em> section:</p>
 <ul class="simple">
 <li>one line per ellipsoid</li>
 <li>line syntax: atom-ID shapex shapey shapez quatw quati quatj quatk</li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>atom-ID = ID of atom which is an ellipsoid
-  shapex,shapey,shapez = 3 diameters of ellipsoid (distance units)
-  quatw,quati,quatj,quatk = quaternion components for orientation of atom
+shapex,shapey,shapez = 3 diameters of ellipsoid (distance units)
+quatw,quati,quatj,quatk = quaternion components for orientation of atom
 </pre></div>
 </div>
 <ul class="simple">
 <li>example:</li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>12 1 2 1 1 0 0 0
 </pre></div>
 </div>
 <p>The <em>Ellipsoids</em> section must appear if <a class="reference internal" href="atom_style.html"><em>atom_style ellipsoid</em></a> is used and any atoms are listed in the
 <em>Atoms</em> section with an ellipsoidflag = 1.  The number of ellipsoids
 should be specified in the header section via the &#8220;ellipsoids&#8221;
 keyword.</p>
 <p>The 3 shape values specify the 3 diameters or aspect ratios of a
 finite-size ellipsoidal particle, when it is oriented along the 3
 coordinate axes.  They must all be non-zero values.</p>
 <p>The values <em>quatw</em>, <em>quati</em>, <em>quatj</em>, and <em>quatk</em> set the orientation
 of the atom as a quaternion (4-vector).  Note that the shape
 attributes specify the aspect ratios of an ellipsoidal particle, which
 is oriented by default with its x-axis along the simulation box&#8217;s
 x-axis, and similarly for y and z.  If this body is rotated (via the
 right-hand rule) by an angle theta around a unit vector (a,b,c), then
 the quaternion that represents its new orientation is given by
 (cos(theta/2), a*sin(theta/2), b*sin(theta/2), c*sin(theta/2)).  These
 4 components are quatw, quati, quatj, and quatk as specified above.
 LAMMPS normalizes each atom&#8217;s quaternion in case (a,b,c) is not
 specified as a unit vector.</p>
 <p>The <em>Ellipsoids</em> section must appear after the <em>Atoms</em> section.</p>
 <hr class="docutils" />
 <p><em>EndBondTorsion Coeffs</em> section:</p>
 <ul class="simple">
 <li>one line per dihedral type</li>
 <li>line syntax: ID coeffs</li>
 </ul>
 <pre class="literal-block">
 ID = dihedral type (1-N)
-  coeffs = list of coeffs (see class 2 section of <a class="reference internal" href="dihedral_coeff.html"><em>dihedral_coeff</em></a>)
+coeffs = list of coeffs (see class 2 section of <a class="reference internal" href="dihedral_coeff.html"><em>dihedral_coeff</em></a>)
 </pre>
 <hr class="docutils" />
 <p><em>Improper Coeffs</em> section:</p>
 <ul class="simple">
 <li>one line per improper type</li>
 <li>line syntax: ID coeffs</li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>ID = improper type (1-N)
-  coeffs = list of coeffs
+coeffs = list of coeffs
 </pre></div>
 </div>
 <ul class="simple">
 <li>example:</li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>2 20 0.0548311
 </pre></div>
 </div>
 <p>The number and meaning of the coefficients are specific to the defined
 improper style.  See the <a class="reference internal" href="improper_style.html"><em>improper_style</em></a> and
 <a class="reference internal" href="improper_coeff.html"><em>improper_coeff</em></a> commands for details.
 Coefficients can also be set via the
 <a class="reference internal" href="improper_coeff.html"><em>improper_coeff</em></a> command in the input script.</p>
 <hr class="docutils" />
 <p><em>Impropers</em> section:</p>
 <ul class="simple">
 <li>one line per improper</li>
 <li>line syntax: ID type atom1 atom2 atom3 atom4</li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>ID = number of improper (1-Nimpropers)
-  type = improper type (1-Nimpropertype)
-  atom1,atom2,atom3,atom4 = IDs of 1st,2nd,3rd,4th atoms in improper
+type = improper type (1-Nimpropertype)
+atom1,atom2,atom3,atom4 = IDs of 1st,2nd,3rd,4th atoms in improper
 </pre></div>
 </div>
 <ul class="simple">
 <li>example:</li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>12 3 17 29 13 100
 </pre></div>
 </div>
 <p>The ordering of the 4 atoms determines the definition of the improper
 angle used in the formula for each <a class="reference internal" href="improper_style.html"><em>improper style</em></a>.  See the doc pages for individual styles
 for details.</p>
 <p>The <em>Impropers</em> section must appear after the <em>Atoms</em> section.  All
 values in this section must be integers (1, not 1.0).</p>
 <hr class="docutils" />
 <p><em>Lines</em> section:</p>
 <ul class="simple">
 <li>one line per line segment</li>
 <li>line syntax: atom-ID x1 y1 x2 y2</li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>atom-ID = ID of atom which is a line segment
-  x1,y1 = 1st end point
-  x2,y2 = 2nd end point
+x1,y1 = 1st end point
+x2,y2 = 2nd end point
 </pre></div>
 </div>
 <ul class="simple">
 <li>example:</li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>12 1.0 0.0 2.0 0.0
 </pre></div>
 </div>
 <p>The <em>Lines</em> section must appear if <a class="reference internal" href="atom_style.html"><em>atom_style line</em></a>
 is used and any atoms are listed in the <em>Atoms</em> section with a
 lineflag = 1.  The number of lines should be specified in the header
 section via the &#8220;lines&#8221; keyword.</p>
 <p>The 2 end points are the end points of the line segment.  The ordering
 of the 2 points should be such that using a right-hand rule to cross
 the line segment with a unit vector in the +z direction, gives an
 &#8220;outward&#8221; normal vector perpendicular to the line segment.
 I.e. normal = (c2-c1) x (0,0,1).  This orientation may be important
 for defining some interactions.</p>
 <p>The <em>Lines</em> section must appear after the <em>Atoms</em> section.</p>
 <hr class="docutils" />
 <p><em>Masses</em> section:</p>
 <ul class="simple">
 <li>one line per atom type</li>
 <li>line syntax: ID mass</li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>ID = atom type (1-N)
-  mass = mass value
+mass = mass value
 </pre></div>
 </div>
 <ul class="simple">
 <li>example:</li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>3 1.01
 </pre></div>
 </div>
 <p>This defines the mass of each atom type.  This can also be set via the
 <a class="reference internal" href="mass.html"><em>mass</em></a> command in the input script.  This section cannot be
 used for atom styles that define a mass for individual atoms -
 e.g. <a class="reference internal" href="atom_style.html"><em>atom_style sphere</em></a>.</p>
 <hr class="docutils" />
 <p><em>MiddleBondTorsion Coeffs</em> section:</p>
 <ul class="simple">
 <li>one line per dihedral type</li>
 <li>line syntax: ID coeffs</li>
 </ul>
 <pre class="literal-block">
 ID = dihedral type (1-N)
-  coeffs = list of coeffs (see class 2 section of <a class="reference internal" href="dihedral_coeff.html"><em>dihedral_coeff</em></a>)
+coeffs = list of coeffs (see class 2 section of <a class="reference internal" href="dihedral_coeff.html"><em>dihedral_coeff</em></a>)
 </pre>
 <hr class="docutils" />
 <p><em>Pair Coeffs</em> section:</p>
 <ul class="simple">
 <li>one line per atom type</li>
 <li>line syntax: ID coeffs</li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>ID = atom type (1-N)
-  coeffs = list of coeffs
+coeffs = list of coeffs
 </pre></div>
 </div>
 <ul class="simple">
 <li>example:</li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>3 0.022 2.35197 0.022 2.35197
 </pre></div>
 </div>
 <p>The number and meaning of the coefficients are specific to the defined
 pair style.  See the <a class="reference internal" href="pair_style.html"><em>pair_style</em></a> and
 <a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a> commands for details.  Since pair
 coefficients for types I != J are not specified, these will be
 generated automatically by the pair style&#8217;s mixing rule.  See the
 individual pair_style doc pages and the <a class="reference internal" href="pair_modify.html"><em>pair_modify mix</em></a> command for details.  Pair coefficients can also
 be set via the <a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a> command in the input
 script.</p>
 <hr class="docutils" />
 <p><em>PairIJ Coeffs</em> section:</p>
 <ul class="simple">
 <li>one line per pair of atom types for all I,J with I &lt;= J</li>
 <li>line syntax: ID1 ID2 coeffs</li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>ID1 = atom type I = 1-N
-  ID2 = atom type J = I-N, with I &lt;= J
-  coeffs = list of coeffs
+ID2 = atom type J = I-N, with I &lt;= J
+coeffs = list of coeffs
 </pre></div>
 </div>
 <ul class="simple">
 <li>examples:</li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>3 3 0.022 2.35197 0.022 2.35197
-  3 5 0.022 2.35197 0.022 2.35197
+3 5 0.022 2.35197 0.022 2.35197
 </pre></div>
 </div>
 <p>This section must have N*(N+1)/2 lines where N = # of atom types.  The
 number and meaning of the coefficients are specific to the defined
 pair style.  See the <a class="reference internal" href="pair_style.html"><em>pair_style</em></a> and
 <a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a> commands for details.  Since pair
 coefficients for types I != J are all specified, these values will
 turn off the default mixing rule defined by the pair style.  See the
 individual pair_style doc pages and the <a class="reference internal" href="pair_modify.html"><em>pair_modify mix</em></a> command for details.  Pair coefficients can also
 be set via the <a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a> command in the input
 script.</p>
 <hr class="docutils" />
 <p><em>Triangles</em> section:</p>
 <ul class="simple">
 <li>one line per triangle</li>
 <li>line syntax: atom-ID x1 y1 x2 y2</li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>atom-ID = ID of atom which is a line segment
-  x1,y1,z1 = 1st corner point
-  x2,y2,z2 = 2nd corner point
-  x3,y3,z3 = 3rd corner point
+x1,y1,z1 = 1st corner point
+x2,y2,z2 = 2nd corner point
+x3,y3,z3 = 3rd corner point
 </pre></div>
 </div>
 <ul class="simple">
 <li>example:</li>
 </ul>
 <div class="highlight-python"><div class="highlight"><pre>12 0.0 0.0 0.0 2.0 0.0 1.0 0.0 2.0 1.0
 </pre></div>
 </div>
 <p>The <em>Triangles</em> section must appear if <a class="reference internal" href="atom_style.html"><em>atom_style tri</em></a> is used and any atoms are listed in the <em>Atoms</em>
 section with a triangleflag = 1.  The number of lines should be
 specified in the header section via the &#8220;triangles&#8221; keyword.</p>
 <p>The 3 corner points are the corner points of the triangle.  The
 ordering of the 3 points should be such that using a right-hand rule
 to go from point1 to point2 to point3 gives an &#8220;outward&#8221; normal vector
 to the face of the triangle.  I.e. normal = (c2-c1) x (c3-c1).  This
 orientation may be important for defining some interactions.</p>
 <p>The <em>Triangles</em> section must appear after the <em>Atoms</em> section.</p>
 <hr class="docutils" />
 <p><em>Velocities</em> section:</p>
 <ul class="simple">
 <li>one line per atom</li>
 <li>line syntax: depends on atom style</li>
 </ul>
 <table border="1" class="docutils">
 <colgroup>
 <col width="42%" />
 <col width="58%" />
 </colgroup>
 <tbody valign="top">
 <tr class="row-odd"><td>all styles except those listed</td>
 <td>atom-ID vx vy vz</td>
 </tr>
 <tr class="row-even"><td>electron</td>
 <td>atom-ID vx vy vz ervel</td>
 </tr>
 <tr class="row-odd"><td>ellipsoid</td>
 <td>atom-ID vx vy vz lx ly lz</td>
 </tr>
 <tr class="row-even"><td>sphere</td>
 <td>atom-ID vx vy vz wx wy wz</td>
 </tr>
 <tr class="row-odd"><td>hybrid</td>
 <td>atom-ID vx vy vz sub-style1 sub-style2 ...</td>
 </tr>
 </tbody>
 </table>
 <p>where the keywords have these meanings:</p>
 <p>vx,vy,vz = translational velocity of atom
 lx,ly,lz = angular momentum of aspherical atom
 wx,wy,wz = angular velocity of spherical atom
 ervel = electron radial velocity (0 for fixed-core):ul</p>
 <p>The velocity lines can appear in any order.  This section can only be
 used after an <em>Atoms</em> section.  This is because the <em>Atoms</em> section
 must have assigned a unique atom ID to each atom so that velocities
 can be assigned to them.</p>
 <p>Vx, vy, vz, and ervel are in <a class="reference internal" href="units.html"><em>units</em></a> of velocity.  Lx, ly,
 lz are in units of angular momentum (distance-velocity-mass).  Wx, Wy,
 Wz are in units of angular velocity (radians/time).</p>
 <p>For atom_style hybrid, following the 4 initial values (ID,vx,vy,vz),
 specific values for each sub-style must be listed.  The order of the
 sub-styles is the same as they were listed in the
 <a class="reference internal" href="atom_style.html"><em>atom_style</em></a> command.  The sub-style specific values
 are those that are not the 5 standard ones (ID,vx,vy,vz).  For
 example, for the &#8220;sphere&#8221; sub-style, &#8220;wx&#8221;, &#8220;wy&#8221;, &#8220;wz&#8221; values would
 appear.  These are listed in the same order they appear as listed
 above.  Thus if</p>
 <div class="highlight-python"><div class="highlight"><pre>atom_style hybrid electron sphere
 </pre></div>
 </div>
 <p>were used in the input script, each velocity line would have these
 fields:</p>
 <div class="highlight-python"><div class="highlight"><pre>atom-ID vx vy vz ervel wx wy wz
 </pre></div>
 </div>
 <p>Translational velocities can also be set by the
 <a class="reference internal" href="velocity.html"><em>velocity</em></a> command in the input script.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>To read gzipped data files, you must compile LAMMPS with the
 -DLAMMPS_GZIP option - see the <a class="reference internal" href="Section_start.html#start-2"><span>Making LAMMPS</span></a> section of the documentation.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="read_dump.html"><em>read_dump</em></a>, <a class="reference internal" href="read_restart.html"><em>read_restart</em></a>,
 <a class="reference internal" href="create_atoms.html"><em>create_atoms</em></a>, <a class="reference internal" href="write_data.html"><em>write_data</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The default for all the <em>extra</em> keywords is 0.</p>
 </div>
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   <div class="section" id="read-dump-command">
 <span id="index-0"></span><h1>read_dump command<a class="headerlink" href="#read-dump-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>read_dump file Nstep field1 field2 ... keyword values ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>file = name of dump file to read</li>
 <li>Nstep = snapshot timestep to read from file</li>
 <li>one or more fields may be appended</li>
 </ul>
 <pre class="literal-block">
 field = <em>x</em> or <em>y</em> or <em>z</em> or <em>vx</em> or <em>vy</em> or <em>vz</em> or <em>q</em> or <em>ix</em> or <em>iy</em> or <em>iz</em>
   <em>x</em>,*y*,*z* = atom coordinates
   <em>vx</em>,*vy*,*vz* = velocity components
   <em>q</em> = charge
   <em>ix</em>,*iy*,*iz* = image flags in each dimension
 </pre>
 <ul class="simple">
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>box</em> or <em>replace</em> or <em>purge</em> or <em>trim</em> or <em>add</em> or <em>label</em> or <em>scaled</em> or <em>wrapped</em> or <em>format</em></li>
 </ul>
 <pre class="literal-block">
 <em>box</em> value = <em>yes</em> or <em>no</em> = replace simulation box with dump box
-  <em>replace</em> value = <em>yes</em> or <em>no</em> = overwrite atoms with dump atoms
-  <em>purge</em> value = <em>yes</em> or <em>no</em> = delete all atoms before adding dump atoms
-  <em>trim</em> value = <em>yes</em> or <em>no</em> = trim atoms not in dump snapshot
-  <em>add</em> value = <em>yes</em> or <em>no</em> = add new dump atoms to system
-  <em>label</em> value = field column
-    field = one of the listed fields or <em>id</em> or <em>type</em>
-    column = label on corresponding column in dump file
-  <em>scaled</em> value = <em>yes</em> or <em>no</em> = coords in dump file are scaled/unscaled
-  <em>wrapped</em> value = <em>yes</em> or <em>no</em> = coords in dump file are wrapped/unwrapped
-  <em>format</em> values = format of dump file, must be last keyword if used
-    <em>native</em> = native LAMMPS dump file
-    <em>xyz</em> = XYZ file
-    <em>molfile</em> style path = VMD molfile plugin interface
-      style = <em>dcd</em> or <em>xyz</em> or others supported by molfile plugins
-      path = optional path for location of molfile plugins
+<em>replace</em> value = <em>yes</em> or <em>no</em> = overwrite atoms with dump atoms
+<em>purge</em> value = <em>yes</em> or <em>no</em> = delete all atoms before adding dump atoms
+<em>trim</em> value = <em>yes</em> or <em>no</em> = trim atoms not in dump snapshot
+<em>add</em> value = <em>yes</em> or <em>no</em> = add new dump atoms to system
+<em>label</em> value = field column
+  field = one of the listed fields or <em>id</em> or <em>type</em>
+  column = label on corresponding column in dump file
+<em>scaled</em> value = <em>yes</em> or <em>no</em> = coords in dump file are scaled/unscaled
+<em>wrapped</em> value = <em>yes</em> or <em>no</em> = coords in dump file are wrapped/unwrapped
+<em>format</em> values = format of dump file, must be last keyword if used
+  <em>native</em> = native LAMMPS dump file
+  <em>xyz</em> = XYZ file
+  <em>molfile</em> style path = VMD molfile plugin interface
+    style = <em>dcd</em> or <em>xyz</em> or others supported by molfile plugins
+    path = optional path for location of molfile plugins
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>read_dump dump.file 5000 x y z
 read_dump dump.xyz 5 x y z box no format xyz
 read_dump dump.xyz 10 x y z box no format molfile xyz &quot;../plugins&quot;
 read_dump dump.dcd 0 x y z box yes format molfile dcd
 read_dump dump.file 1000 x y z vx vy vz box yes format molfile lammpstrj /usr/local/lib/vmd/plugins/LINUXAMD64/plugins/molfile
 read_dump dump.file 5000 x y vx vy trim yes
 read_dump ../run7/dump.file.gz 10000 x y z box yes
 read_dump dump.xyz 10 x y z box no format molfile xyz ../plugins
 read_dump dump.dcd 0 x y z format molfile dcd
 read_dump dump.file 1000 x y z vx vy vz format molfile lammpstrj /usr/local/lib/vmd/plugins/LINUXAMD64/plugins/molfile
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Read atom information from a dump file to overwrite the current atom
 coordinates, and optionally the atom velocities and image flags and
 the simluation box dimensions.  This is useful for restarting a run
 from a particular snapshot in a dump file.  See the
 <a class="reference internal" href="read_restart.html"><em>read_restart</em></a> and <a class="reference internal" href="read_data.html"><em>read_data</em></a>
 commands for alternative methods to do this.  Also see the
 <a class="reference internal" href="rerun.html"><em>rerun</em></a> command for a means of reading multiple snapshots
 from a dump file.</p>
 <p>Note that a simulation box must already be defined before using the
 read_dump command.  This can be done by the
 <a class="reference internal" href="create_box.html"><em>create_box</em></a>, <a class="reference internal" href="read_data.html"><em>read_data</em></a>, or
 <a class="reference internal" href="read_restart.html"><em>read_restart</em></a> commands.  The read_dump command can
 reset the simulation box dimensions, as explained below.</p>
 <p>Also note that reading per-atom information from a dump snapshot is
 limited to the atom coordinates, velocities and image flags, as
 explained below.  Other atom properties, which may be necessary to run
 a valid simulation, such as atom charge, or bond topology information
 for a molecular system, are not read from (or even contained in) dump
 files.  Thus this auxiliary information should be defined in the usual
 way, e.g. in a data file read in by a <a class="reference internal" href="read_data.html"><em>read_data</em></a>
 command, before using the read_dump command, or by the <a class="reference internal" href="set.html"><em>set</em></a>
 command, after the dump snapshot is read.</p>
 <hr class="docutils" />
 <p>If the dump filename specified as <em>file</em> ends with &#8221;.gz&#8221;, the dump
 file is read in gzipped format.  You cannot (yet) read a dump file
 that was written in binary format with a &#8221;.bin&#8221; suffix, or to multiple
 files via the &#8220;%&#8221; option in the dump file name.  See the
 <a class="reference internal" href="dump.html"><em>dump</em></a> command for details.</p>
 <p>The format of the dump file is selected through the <em>format</em> keyword.
 If specified, it must be the last keyword used, since all remaining
 arguments are passed on to the dump reader.  The <em>native</em> format is
 for native LAMMPS dump files, written with a <a class="reference internal" href="dump.html"><em>dump atom</em></a> or
 <a class="reference internal" href="dump.html"><em>dump custom</em></a> command.  The <em>xyz</em> format is for generic XYZ
 formatted dump files.  These formats take no additional values.</p>
 <p>The <em>molfile</em> format supports reading data through using the <a class="reference external" href="vmd">VMD</a>
 molfile plugin interface. This dump reader format is only available,
 if the USER-MOLFILE package has been installed when compiling
 LAMMPS.</p>
 <p>The <em>molfile</em> format takes one or two additional values.  The <em>style</em>
 value determines the file format to be used and can be any format that
 the molfile plugins support, such as DCD or XYZ.  Note that DCD dump
 files can be written by LAMMPS via the <a class="reference internal" href="dump.html"><em>dump dcd</em></a> command.
 The <em>path</em> value specifies a list of directories which LAMMPS will
 search for the molfile plugins appropriate to the specified <em>style</em>.
 The syntax of the <em>path</em> value is like other search paths: it can
 contain multiple directories separated by a colon (or semi-colon on
 windows).  The <em>path</em> keyword is optional and defaults to &#8221;.&#8221;,
 i.e. the current directory.</p>
 <p>Support for other dump format readers may be added in the future.</p>
 <hr class="docutils" />
 <p>Global information is first read from the dump file, namely timestep
 and box information.</p>
 <p>The dump file is scanned for a snapshot with a time stamp that matches
 the specified <em>Nstep</em>.  This means the LAMMPS timestep the dump file
 snapshot was written on for the <em>native</em> format.  Note that the <em>xyz</em>
 and <em>molfile</em> formats do not store the timestep.  For these formats,
 timesteps are numbered logically, in a sequential manner, starting
 from 0.  Thus to access the 10th snapshot in an <em>xyz</em> or <em>mofile</em>
 formatted dump file, use <em>Nstep</em> = 9.</p>
 <p>The dimensions of the simulation box for the selected snapshot are
 also read; see the <em>box</em> keyword discussion below.  For the <em>native</em>
 format, an error is generated if the snapshot is for a triclinic box
 and the current simulation box is orthogonal or vice versa.  A warning
 will be generated if the snapshot box boundary conditions (periodic,
 shrink-wrapped, etc) do not match the current simulation boundary
 conditions, but the boundary condition information in the snapshot is
 otherwise ignored.  See the &#8220;boundary&#8221; command for more details.</p>
 <p>For the <em>xyz</em> format, no information about the box is available, so
 you must set the <em>box</em> flag to <em>no</em>.  See details below.</p>
 <p>For the <em>molfile</em> format, reading simulation box information is
 typically supported, but the location of the simulation box origin is
 lost and no explicit information about periodicity or
 orthogonal/triclinic box shape is available.  The USER-MOLFILE package
 makes a best effort to guess based on heuristics, but this may not
 always work perfectly.</p>
 <hr class="docutils" />
 <p>Per-atom information from the dump file snapshot is then read from the
 dump file snapshot.  This corresponds to the specified <em>fields</em> listed
 in the read_dump command.  It is an error to specify a z-dimension
 field, namely <em>z</em>, <em>vz</em>, or <em>iz</em>, for a 2d simulation.</p>
 <p>For dump files in <em>native</em> format, each column of per-atom data has a
 text label listed in the file.  A matching label for each field must
 appear, e.g. the label &#8220;vy&#8221; for the field <em>vy</em>.  For the <em>x</em>, <em>y</em>, <em>z</em>
 fields any of the following labels are considered a match:</p>
 <pre class="literal-block">
 x, xs, xu, xsu for field <em>x</em>
 y, ys, yu, ysu for field <em>y</em>
 z, zs, zu, zsu for field <em>z</em>
 </pre>
 <p>The meaning of xs (scaled), xu (unwrapped), and xsu (scaled and
 unwrapped) is explained on the <a class="reference internal" href="dump.html"><em>dump</em></a> command doc page.
 These labels are searched for in the list of column labels in the dump
 file, in order, until a match is found.</p>
 <p>The dump file must also contain atom IDs, with a column label of &#8220;id&#8221;.</p>
 <p>If the <em>add</em> keyword is specified with a value of <em>yes</em>, as discussed
 below, the dump file must contain atom types, with a column label of
 &#8220;type&#8221;.</p>
 <p>If a column label you want to read from the dump file is not a match
 to a specified field, the <em>label</em> keyword can be used to specify the
 specific column label from the dump file to associate with that field.
 An example is if a time-averaged coordinate is written to the dump
 file via the <a class="reference internal" href="fix_ave_atom.html"><em>fix ave/atom</em></a> command.  The column
 will then have a label corresponding to the fix-ID rather than &#8220;x&#8221; or
 &#8220;xs&#8221;.  The <em>label</em> keyword can also be used to specify new column
 labels for fields <em>id</em> and <em>type</em>.</p>
 <p>For dump files in <em>xyz</em> format, only the <em>x</em>, <em>y</em>, and <em>z</em> fields are
 supported.  The dump file does not store atom IDs, so these are
 assigned consecutively to the atoms as they appear in the dump file,
 starting from 1.  Thus you should insure that order of atoms is
 consistent from snapshot to snapshot in the the XYZ dump file.  See
 the <a class="reference internal" href="dump_modify.html"><em>dump_modify sort</em></a> command if the XYZ dump file
 was written by LAMMPS.</p>
 <p>For dump files in <em>molfile</em> format, the <em>x</em>, <em>y</em>, <em>z</em>, <em>vx</em>, <em>vy</em>, and
 <em>vz</em> fields can be specified.  However, not all molfile formats store
 velocities, or their respective plugins may not support reading of
 velocities.  The molfile dump files do not store atom IDs, so these
 are assigned consecutively to the atoms as they appear in the dump
 file, starting from 1.  Thus you should insure that order of atoms are
 consistent from snapshot to snapshot in the the molfile dump file.
 See the <a class="reference internal" href="dump_modify.html"><em>dump_modify sort</em></a> command if the dump file
 was written by LAMMPS.</p>
 <hr class="docutils" />
 <p>Information from the dump file snapshot is used to overwrite or
 replace properties of the current system.  There are various options
 for how this is done, determined by the specified fields and optional
 keywords.</p>
 <p>The timestep of the snapshot becomes the current timestep for the
 simulation.  See the <a class="reference internal" href="reset_timestep.html"><em>reset_timestep</em></a> command if
 you wish to change this after the dump snapshot is read.</p>
 <p>If the <em>box</em> keyword is specified with a <em>yes</em> value, then the current
 simulation box dimensions are replaced by the dump snapshot box
 dimensions.  If the <em>box</em> keyword is specified with a <em>no</em> value, the
 current simulatoin box is unchanged.</p>
 <p>If the <em>purge</em> keyword is specified with a <em>yes</em> value, then all
 current atoms in the system are deleted before any of the operations
 invoked by the <em>replace</em>, <em>trim</em>, or <em>add</em> keywords take place.</p>
 <p>If the <em>replace</em> keyword is specified with a <em>yes</em> value, then atoms
 with IDs that are in both the current system and the dump snapshot
 have their properties overwritten by field values.  If the <em>replace</em>
 keyword is specified with a <em>no</em> value, atoms with IDs that are in
 both the current system and the dump snapshot are not modified.</p>
 <p>If the <em>trim</em> keyword is specified with a <em>yes</em> value, then atoms with
 IDs that are in the current system but not in the dump snapshot are
 deleted.  These atoms are unaffected if the <em>trim</em> keyword is
 specified with a <em>no</em> value.</p>
 <p>If the <em>add</em> keyword is specified with a <em>yes</em> value, then atoms with
 IDs that are in the dump snapshot, but not in the current system are
 added to the system.  These dump atoms are ignored if the <em>add</em>
 keyword is specified with a <em>no</em> value.</p>
 <p>Note that atoms added via the <em>add</em> keyword will have only the
 attributes read from the dump file due to the <em>field</em> arguments.  If
 <em>x</em> or <em>y</em> or <em>z</em> is not specified as a field, a value of 0.0 is used
 for added atoms.  Added atoms must have an atom type, so this value
 must appear in the dump file.</p>
 <p>Any other attributes (e.g. charge or particle diameter for spherical
 particles) will be set to default values, the same as if the
 <a class="reference internal" href="create_atoms.html"><em>create_atoms</em></a> command were used.</p>
 <p>Note that atom IDs are not preserved for new dump snapshot atoms added
 via the <em>add</em> keyword.  The procedure for assigning new atom IDS to
 added atoms is the same as is described for the
 <a class="reference internal" href="create_atoms.html"><em>create_atoms</em></a> command.</p>
 <hr class="docutils" />
 <p>Atom coordinates read from the dump file are first converted into
 unscaled coordinates, relative to the box dimensions of the snapshot.
 These coordinates are then be assigned to an existing or new atom in
 the current simulation.  The coordinates will then be remapped to the
 simulation box, whether it is the original box or the dump snapshot
 box.  If periodic boundary conditions apply, this means the atom will
 be remapped back into the simulation box if necessary.  If shrink-wrap
 boundary conditions apply, the new coordinates may change the
 simulation box dimensions.  If fixed boundary conditions apply, the
 atom will be lost if it is outside the simulation box.</p>
 <p>For <em>native</em> format dump files, the 3 xyz image flags for an atom in
 the dump file are set to the corresponding values appearing in the
 dump file if the <em>ix</em>, <em>iy</em>, <em>iz</em> fields are specified.  If not
 specified, the image flags for replaced atoms are not changed and
 image flags for new atoms are set to default values.  If coordinates
 read from the dump file are in unwrapped format (e.g. <em>xu</em>) then the
 image flags for read-in atoms are also set to default values.  The
 remapping procedure described in the previous paragraph will then
 change images flags for all atoms (old and new) if periodic boundary
 conditions are applied to remap an atom back into the simulation box.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">If you get a warning about inconsistent image flags
 after reading in a dump snapshot, it means one or more pairs of bonded
 atoms now have inconsistent image flags.  As discussed in <a class="reference internal" href="Section_errors.html"><em>Section errors</em></a> this may or may not cause problems for
 subsequent simulations, One way this can happen is if you read image
 flag fields from the dump file but do not also use the dump file box
 parameters.</p>
 </div>
 <p>LAMMPS knows how to compute unscaled and remapped coordinates for the
 snapshot column labels discussed above, e.g. <em>x</em>, <em>xs</em>, <em>xu</em>, <em>xsu</em>.
 If another column label is assigned to the <em>x</em> or <em>y</em> or <em>z</em> field via
 the <em>label</em> keyword, e.g. for coordinates output by the <a class="reference internal" href="fix_ave_atom.html"><em>fix ave/atom</em></a> command, then LAMMPS needs to know whether
 the coordinate information in the dump file is scaled and/or wrapped.
 This can be set via the <em>scaled</em> and <em>wrapped</em> keywords.  Note that
 the value of the <em>scaled</em> and <em>wrapped</em> keywords is ignored for fields
 <em>x</em> or <em>y</em> or <em>z</em> if the <em>label</em> keyword is not used to assign a
 column label to that field.</p>
 <p>The scaled/unscaled and wrapped/unwrapped setting must be identical
 for any of the <em>x</em>, <em>y</em>, <em>z</em> fields that are specified.  Thus you
 cannot read <em>xs</em> and <em>yu</em> from the dump file.  Also, if the dump file
 coordinates are scaled and the simulation box is triclinic, then all 3
 of the <em>x</em>, <em>y</em>, <em>z</em> fields must be specified, since they are all
 needed to generate absolute, unscaled coordinates.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>To read gzipped dump files, you must compile LAMMPS with the
 -DLAMMPS_GZIP option - see the <a class="reference internal" href="Section_start.html#start-2"><span>Making LAMMPS</span></a> section of the documentation.</p>
 <p>The <em>molfile</em> dump file formats are part of the USER-MOLFILE package.
 They are only enabled if LAMMPS was built with that packages.  See the
 <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="dump.html"><em>dump</em></a>, <a class="reference internal" href="dump_molfile.html"><em>dump molfile</em></a>,
 <a class="reference internal" href="read_data.html"><em>read_data</em></a>, <a class="reference internal" href="read_restart.html"><em>read_restart</em></a>,
 <a class="reference internal" href="rerun.html"><em>rerun</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The option defaults are box = yes, replace = yes, purge = no, trim =
 no, add = no, scaled = no, wrapped = yes, and format = native.</p>
 </div>
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   <div class="section" id="region-command">
 <span id="index-0"></span><h1>region command<a class="headerlink" href="#region-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>region ID style args keyword arg ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>ID = user-assigned name for the region</li>
 <li>style = <em>delete</em> or <em>block</em> or <em>cone</em> or <em>cylinder</em> or <em>plane</em> or <em>prism</em> or <em>sphere</em> or <em>union</em> or <em>intersect</em></li>
 </ul>
 <pre class="literal-block">
 <em>delete</em> = no args
-  <em>block</em> args = xlo xhi ylo yhi zlo zhi
-    xlo,xhi,ylo,yhi,zlo,zhi = bounds of block in all dimensions (distance units)
-  <em>cone</em> args = dim c1 c2 radlo radhi lo hi
-    dim = <em>x</em> or <em>y</em> or <em>z</em> = axis of cone
-    c1,c2 = coords of cone axis in other 2 dimensions (distance units)
-    radlo,radhi = cone radii at lo and hi end (distance units)
-    lo,hi = bounds of cone in dim (distance units)
-  <em>cylinder</em> args = dim c1 c2 radius lo hi
-    dim = <em>x</em> or <em>y</em> or <em>z</em> = axis of cylinder
-    c1,c2 = coords of cylinder axis in other 2 dimensions (distance units)
-    radius = cylinder radius (distance units)
-      radius can be a variable (see below)
-    lo,hi = bounds of cylinder in dim (distance units)
-  <em>plane</em> args = px py pz nx ny nz
-    px,py,pz = point on the plane (distance units)
-    nx,ny,nz = direction normal to plane (distance units)
-  <em>prism</em> args = xlo xhi ylo yhi zlo zhi xy xz yz
-    xlo,xhi,ylo,yhi,zlo,zhi = bounds of untilted prism (distance units)
-    xy = distance to tilt y in x direction (distance units)
-    xz = distance to tilt z in x direction (distance units)
-    yz = distance to tilt z in y direction (distance units)
-  <em>sphere</em> args = x y z radius
-    x,y,z = center of sphere (distance units)
-    radius = radius of sphere (distance units)
-      radius can be a variable (see below)
-  <em>union</em> args = N reg-ID1 reg-ID2 ...
-    N = # of regions to follow, must be 2 or greater
-    reg-ID1,reg-ID2, ... = IDs of regions to join together
-  <em>intersect</em> args = N reg-ID1 reg-ID2 ...
-    N = # of regions to follow, must be 2 or greater
-    reg-ID1,reg-ID2, ... = IDs of regions to intersect
+<em>block</em> args = xlo xhi ylo yhi zlo zhi
+  xlo,xhi,ylo,yhi,zlo,zhi = bounds of block in all dimensions (distance units)
+<em>cone</em> args = dim c1 c2 radlo radhi lo hi
+  dim = <em>x</em> or <em>y</em> or <em>z</em> = axis of cone
+  c1,c2 = coords of cone axis in other 2 dimensions (distance units)
+  radlo,radhi = cone radii at lo and hi end (distance units)
+  lo,hi = bounds of cone in dim (distance units)
+<em>cylinder</em> args = dim c1 c2 radius lo hi
+  dim = <em>x</em> or <em>y</em> or <em>z</em> = axis of cylinder
+  c1,c2 = coords of cylinder axis in other 2 dimensions (distance units)
+  radius = cylinder radius (distance units)
+    radius can be a variable (see below)
+  lo,hi = bounds of cylinder in dim (distance units)
+<em>plane</em> args = px py pz nx ny nz
+  px,py,pz = point on the plane (distance units)
+  nx,ny,nz = direction normal to plane (distance units)
+<em>prism</em> args = xlo xhi ylo yhi zlo zhi xy xz yz
+  xlo,xhi,ylo,yhi,zlo,zhi = bounds of untilted prism (distance units)
+  xy = distance to tilt y in x direction (distance units)
+  xz = distance to tilt z in x direction (distance units)
+  yz = distance to tilt z in y direction (distance units)
+<em>sphere</em> args = x y z radius
+  x,y,z = center of sphere (distance units)
+  radius = radius of sphere (distance units)
+    radius can be a variable (see below)
+<em>union</em> args = N reg-ID1 reg-ID2 ...
+  N = # of regions to follow, must be 2 or greater
+  reg-ID1,reg-ID2, ... = IDs of regions to join together
+<em>intersect</em> args = N reg-ID1 reg-ID2 ...
+  N = # of regions to follow, must be 2 or greater
+  reg-ID1,reg-ID2, ... = IDs of regions to intersect
 </pre>
 <ul class="simple">
 <li>zero or more keyword/arg pairs may be appended</li>
 <li>keyword = <em>side</em> or <em>units</em> or <em>move</em> or <em>rotate</em></li>
 </ul>
 <pre class="literal-block">
 <em>side</em> value = <em>in</em> or <em>out</em>
-    <em>in</em> = the region is inside the specified geometry
-    <em>out</em> = the region is outside the specified geometry
-  <em>units</em> value = <em>lattice</em> or <em>box</em>
-    <em>lattice</em> = the geometry is defined in lattice units
-    <em>box</em> = the geometry is defined in simulation box units
-  <em>move</em> args = v_x v_y v_z
-    v_x,v_y,v_z = equal-style variables for x,y,z displacement of region over time
-  <em>rotate</em> args = v_theta Px Py Pz Rx Ry Rz
-    v_theta = equal-style variable for rotaton of region over time (in radians)
-    Px,Py,Pz = origin for axis of rotation (distance units)
-    Rx,Ry,Rz = axis of rotation vector
+  <em>in</em> = the region is inside the specified geometry
+  <em>out</em> = the region is outside the specified geometry
+<em>units</em> value = <em>lattice</em> or <em>box</em>
+  <em>lattice</em> = the geometry is defined in lattice units
+  <em>box</em> = the geometry is defined in simulation box units
+<em>move</em> args = v_x v_y v_z
+  v_x,v_y,v_z = equal-style variables for x,y,z displacement of region over time
+<em>rotate</em> args = v_theta Px Py Pz Rx Ry Rz
+  v_theta = equal-style variable for rotaton of region over time (in radians)
+  Px,Py,Pz = origin for axis of rotation (distance units)
+  Rx,Ry,Rz = axis of rotation vector
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>region 1 block -3.0 5.0 INF 10.0 INF INF
 region 2 sphere 0.0 0.0 0.0 5 side out
 region void cylinder y 2 3 5 -5.0 EDGE units box
 region 1 prism 0 10 0 10 0 10 2 0 0
 region outside union 4 side1 side2 side3 side4
 region 2 sphere 0.0 0.0 0.0 5 side out move v_left v_up NULL
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>This command defines a geometric region of space.  Various other
 commands use regions.  For example, the region can be filled with
 atoms via the <a class="reference internal" href="create_atoms.html"><em>create_atoms</em></a> command.  Or a bounding
 box around the region, can be used to define the simulation box via
 the <a class="reference internal" href="create_box.html"><em>create_box</em></a> command.  Or the atoms in the region
 can be identified as a group via the <a class="reference internal" href="group.html"><em>group</em></a> command, or
 deleted via the <a class="reference internal" href="delete_atoms.html"><em>delete_atoms</em></a> command.  Or the
 surface of the region can be used as a boundary wall via the <a class="reference internal" href="fix_wall_region.html"><em>fix wall/region</em></a> command.</p>
 <p>Commands which use regions typically test whether an atom&#8217;s position
 is contained in the region or not.  For this purpose, coordinates
 exactly on the region boundary are considered to be interior to the
 region.  This means, for example, for a spherical region, an atom on
 the sphere surface would be part of the region if the sphere were
 defined with the <em>side in</em> keyword, but would not be part of the
 region if it were defined using the <em>side out</em> keyword.  See more
 details on the <em>side</em> keyword below.</p>
 <p>Normally, regions in LAMMPS are &#8220;static&#8221;, meaning their geometric
 extent does not change with time.  If the <em>move</em> or <em>rotate</em> keyword
 is used, as described below, the region becomes &#8220;dynamic&#8221;, meaning
 it&#8217;s location or orientation changes with time.  This may be useful,
 for example, when thermostatting a region, via the compute temp/region
 command, or when the fix wall/region command uses a region surface as
 a bounding wall on particle motion, i.e. a rotating container.</p>
 <p>The <em>delete</em> style removes the named region.  Since there is little
 overhead to defining extra regions, there is normally no need to do
 this, unless you are defining and discarding large numbers of regions
 in your input script.</p>
 <p>The lo/hi values for <em>block</em> or <em>cone</em> or <em>cylinder</em> or <em>prism</em> styles
 can be specified as EDGE or INF.  EDGE means they extend all the way
 to the global simulation box boundary.  Note that this is the current
 box boundary; if the box changes size during a simulation, the region
 does not.  INF means a large negative or positive number (1.0e20), so
 it should encompass the simulation box even if it changes size.  If a
 region is defined before the simulation box has been created (via
 <a class="reference internal" href="create_box.html"><em>create_box</em></a> or <a class="reference internal" href="read_data.html"><em>read_data</em></a> or
 <a class="reference internal" href="read_restart.html"><em>read_restart</em></a> commands), then an EDGE or INF
 parameter cannot be used.  For a <em>prism</em> region, a non-zero tilt
 factor in any pair of dimensions cannot be used if both the lo/hi
 values in either of those dimensions are INF.  E.g. if the xy tilt is
 non-zero, then xlo and xhi cannot both be INF, nor can ylo and yhi.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">Regions in LAMMPS do not get wrapped across periodic
 boundaries, as specified by the <a class="reference internal" href="boundary.html"><em>boundary</em></a> command.  For
 example, a spherical region that is defined so that it overlaps a
 periodic boundary is not treated as 2 half-spheres, one on either side
 of the simulation box.</p>
 </div>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">Regions in LAMMPS are always 3d geometric objects,
 regardless of whether the <a class="reference internal" href="dimension.html"><em>dimension</em></a> of a simulation
 is 2d or 3d.  Thus when using regions in a 2d simulation, you should
 be careful to define the region so that its intersection with the 2d
 x-y plane of the simulation has the 2d geometric extent you want.</p>
 </div>
 <p>For style <em>cone</em>, an axis-aligned cone is defined which is like a
 <em>cylinder</em> except that two different radii (one at each end) can be
 defined.  Either of the radii (but not both) can be 0.0.</p>
 <p>For style <em>cone</em> and <em>cylinder</em>, the c1,c2 params are coordinates in
 the 2 other dimensions besides the cylinder axis dimension.  For dim =
 x, c1/c2 = y/z; for dim = y, c1/c2 = x/z; for dim = z, c1/c2 = x/y.
 Thus the third example above specifies a cylinder with its axis in the
 y-direction located at x = 2.0 and z = 3.0, with a radius of 5.0, and
 extending in the y-direction from -5.0 to the upper box boundary.</p>
 <p>For style <em>plane</em>, a plane is defined which contain the point
 (px,py,pz) and has a normal vector (nx,ny,nz).  The normal vector does
 not have to be of unit length.  The &#8220;inside&#8221; of the plane is the
 half-space in the direction of the normal vector; see the discussion
 of the <em>side</em> option below.</p>
 <p>For style <em>prism</em>, a parallelepiped is defined (it&#8217;s too hard to spell
 parallelepiped in an input script!).  The parallelepiped has its
 &#8220;origin&#8221; at (xlo,ylo,zlo) and is defined by 3 edge vectors starting
 from the origin given by A = (xhi-xlo,0,0); B = (xy,yhi-ylo,0); C =
 (xz,yz,zhi-zlo).  <em>Xy,xz,yz</em> can be 0.0 or positive or negative values
 and are called &#8220;tilt factors&#8221; because they are the amount of
 displacement applied to faces of an originally orthogonal box to
 transform it into the parallelepiped.</p>
 <p>A prism region that will be used with the <a class="reference internal" href="create_box.html"><em>create_box</em></a>
 command to define a triclinic simulation box must have tilt factors
 (xy,xz,yz) that do not skew the box more than half the distance of
 corresponding the parallel box length.  For example, if xlo = 2 and
 xhi = 12, then the x box length is 10 and the xy tilt factor must be
 between -5 and 5.  Similarly, both xz and yz must be between
 -(xhi-xlo)/2 and +(yhi-ylo)/2.  Note that this is not a limitation,
 since if the maximum tilt factor is 5 (as in this example), then
 configurations with tilt = ..., -15, -5, 5, 15, 25, ... are all
 geometrically equivalent.</p>
 <p>The <em>radius</em> value for style <em>sphere</em> and <em>cylinder</em> can be specified
 as an equal-style <a class="reference internal" href="variable.html"><em>variable</em></a>.  If the value is a
 variable, it should be specified as v_name, where name is the variable
 name.  In this case, the variable will be evaluated each timestep, and
 its value used to determine the radius of the region.</p>
 <p>Equal-style variables can specify formulas with various mathematical
 functions, and include <a class="reference internal" href="thermo_style.html"><em>thermo_style</em></a> command
 keywords for the simulation box parameters and timestep and elapsed
 time.  Thus it is easy to specify a time-dependent radius.</p>
 <p>See <a class="reference internal" href="Section_howto.html#howto-12"><span>Section_howto 12</span></a> of the doc pages
 for a geometric description of triclinic boxes, as defined by LAMMPS,
 and how to transform these parameters to and from other commonly used
 triclinic representations.</p>
 <p>The <em>union</em> style creates a region consisting of the volume of all the
 listed regions combined.  The <em>intersect</em> style creates a region
 consisting of the volume that is common to all the listed regions.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">The <em>union</em> and <em>intersect</em> regions operate by
 invoking methods from their list of sub-regions.  Thus you cannot
 delete the sub-regions after defining the <em>union</em> or <em>intersection</em>
 region.</p>
 </div>
 <hr class="docutils" />
 <p>The <em>side</em> keyword determines whether the region is considered to be
 inside or outside of the specified geometry.  Using this keyword in
 conjunction with <em>union</em> and <em>intersect</em> regions, complex geometries
 can be built up.  For example, if the interior of two spheres were
 each defined as regions, and a <em>union</em> style with <em>side</em> = out was
 constructed listing the region-IDs of the 2 spheres, the resulting
 region would be all the volume in the simulation box that was outside
 both of the spheres.</p>
 <p>The <em>units</em> keyword determines the meaning of the distance units used
 to define the region for any argument above listed as having distance
 units.  It also affects the scaling of the velocity vector specfied
 with the <em>vel</em> keyword, the amplitude vector specified with the
 <em>wiggle</em> keyword, and the rotation point specified with the <em>rotate</em>
 keyword, since they each involve a distance metric.</p>
 <p>A <em>box</em> value selects standard distance units as defined by the
 <a class="reference internal" href="units.html"><em>units</em></a> command, e.g. Angstroms for units = real or metal.
 A <em>lattice</em> value means the distance units are in lattice spacings.
 The <a class="reference internal" href="lattice.html"><em>lattice</em></a> command must have been previously used to
 define the lattice spacings which are used as follows:</p>
 <ul class="simple">
 <li>For style <em>block</em>, the lattice spacing in dimension x is applied to
 xlo and xhi, similarly the spacings in dimensions y,z are applied to
 ylo/yhi and zlo/zhi.</li>
 <li>For style <em>cone</em>, the lattice spacing in argument <em>dim</em> is applied to
 lo and hi.  The spacings in the two radial dimensions are applied to
 c1 and c2.  The two cone radii are scaled by the lattice
 spacing in the dimension corresponding to c1.</li>
 <li>For style <em>cylinder</em>, the lattice spacing in argument <em>dim</em> is applied
 to lo and hi.  The spacings in the two radial dimensions are applied
 to c1 and c2.  The cylinder radius is scaled by the lattice
 spacing in the dimension corresponding to c1.</li>
 <li>For style <em>plane</em>, the lattice spacing in dimension x is applied to
 px and nx, similarly the spacings in dimensions y,z are applied to
 py/ny and pz/nz.</li>
 <li>For style <em>prism</em>, the lattice spacing in dimension x is applied to
 xlo and xhi, similarly for ylo/yhi and zlo/zhi.  The lattice spacing
 in dimension x is applied to xy and xz, and the spacing in dimension y
 to yz.</li>
 <li>For style <em>sphere</em>, the lattice spacing in dimensions x,y,z are
 applied to the sphere center x,y,z.  The spacing in dimension x is
 applied to the sphere radius.</li>
 </ul>
 <hr class="docutils" />
 <p>If the <em>move</em> or <em>rotate</em> keywords are used, the region is &#8220;dynamic&#8221;,
 meaning its location or orientation changes with time.  These keywords
 cannot be used with a <em>union</em> or <em>intersect</em> style region.  Instead,
 the keywords should be used to make the individual sub-regions of the
 <em>union</em> or <em>intersect</em> region dynamic.  Normally, each sub-region
 should be &#8220;dynamic&#8221; in the same manner (e.g. rotate around the same
 point), though this is not a requirement.</p>
 <p>The <em>move</em> keyword allows one or more <a class="reference internal" href="variable.html"><em>equal-style variables</em></a> to be used to specify the x,y,z displacement
 of the region, typically as a function of time.  A variable is
 specified as v_name, where name is the variable name.  Any of the
 three variables can be specified as NULL, in which case no
 displacement is calculated in that dimension.</p>
 <p>Note that equal-style variables can specify formulas with various
 mathematical functions, and include <a class="reference internal" href="thermo_style.html"><em>thermo_style</em></a>
 command keywords for the simulation box parameters and timestep and
 elapsed time.  Thus it is easy to specify a region displacement that
 change as a function of time or spans consecutive runs in a continuous
 fashion.  For the latter, see the <em>start</em> and <em>stop</em> keywords of the
 <a class="reference internal" href="run.html"><em>run</em></a> command and the <em>elaplong</em> keyword of <a class="reference internal" href="thermo_style.html"><em>thermo_style custom</em></a> for details.</p>
 <p>For example, these commands would displace a region from its initial
 position, in the positive x direction, effectively at a constant
 velocity:</p>
 <div class="highlight-python"><div class="highlight"><pre>variable dx equal ramp(0,10)
 region 2 sphere 10.0 10.0 0.0 5 move v_dx NULL NULL
 </pre></div>
 </div>
 <p>Note that the initial displacemet is 0.0, though that is not required.</p>
 <p>Either of these varaibles would &#8220;wiggle&#8221; the region back and forth in
 the y direction:</p>
 <div class="highlight-python"><div class="highlight"><pre>variable dy equal swiggle(0,5,100)
 variable dysame equal 5*sin(2*PI*elaplong*dt/100)
 region 2 sphere 10.0 10.0 0.0 5 move NULL v_dy NULL
 </pre></div>
 </div>
 <p>The <em>rotate</em> keyword rotates the region around a rotation axis <em>R</em> =
 (Rx,Ry,Rz) that goes thru a point <em>P</em> = (Px,Py,Pz).  The rotation
 angle is calculated, presumably as a function of time, by a variable
 specified as v_theta, where theta is the variable name.  The variable
 should generate its result in radians.  The direction of rotation for
 the region around the rotation axis is consistent with the right-hand
 rule: if your right-hand thumb points along <em>R</em>, then your fingers
 wrap around the axis in the direction of rotation.</p>
 <p>The <em>move</em> and <em>rotate</em> keywords can be used together.  In this case,
 the displacement specified by the <em>move</em> keyword is applied to the <em>P</em>
 point of the <em>rotate</em> keyword.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>A prism cannot be of 0.0 thickness in any dimension; use a small z
 thickness for 2d simulations.  For 2d simulations, the xz and yz
 parameters must be 0.0.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="lattice.html"><em>lattice</em></a>, <a class="reference internal" href="create_atoms.html"><em>create_atoms</em></a>,
 <a class="reference internal" href="delete_atoms.html"><em>delete_atoms</em></a>, <a class="reference internal" href="group.html"><em>group</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The option defaults are side = in, units = lattice, and no move or
 rotation.</p>
 </div>
 </div>
 
 
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   <div class="section" id="restart-command">
 <span id="index-0"></span><h1>restart command<a class="headerlink" href="#restart-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>restart 0
 restart N root keyword value ...
 restart N file1 file2 keyword value ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>N = write a restart file every this many timesteps</li>
 <li>N can be a variable (see below)</li>
 <li>root = filename to which timestep # is appended</li>
 <li>file1,file2 = two full filenames, toggle between them when writing file</li>
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>fileper</em> or <em>nfile</em></li>
 </ul>
 <pre class="literal-block">
 <em>fileper</em> arg = Np
-    Np = write one file for every this many processors
-  <em>nfile</em> arg = Nf
-    Nf = write this many files, one from each of Nf processors
+  Np = write one file for every this many processors
+<em>nfile</em> arg = Nf
+  Nf = write this many files, one from each of Nf processors
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>restart 0
 restart 1000 poly.restart
 restart 1000 poly.restart.mpiio
 restart 1000 restart.*.equil
 restart 10000 poly.%.1 poly.%.2 nfile 10
 restart v_mystep poly.restart
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Write out a binary restart file with the current state of the
 simulation every so many timesteps, in either or both of two modes, as
 a run proceeds.  A value of 0 means do not write out any restart
 files.  The two modes are as follows.  If one filename is specified, a
 series of filenames will be created which include the timestep in the
 filename.  If two filenames are specified, only 2 restart files will
 be created, with those names.  LAMMPS will toggle between the 2 names
 as it writes successive restart files.</p>
 <p>Note that you can specify the restart command twice, once with a
 single filename and once with two filenames.  This would allow you,
 for example, to write out archival restart files every 100000 steps
 using a single filenname, and more frequent temporary restart files
 every 1000 steps, using two filenames.  Using restart 0 will turn off
 both modes of output.</p>
 <p>Similar to <a class="reference internal" href="dump.html"><em>dump</em></a> files, the restart filename(s) can contain
 two wild-card characters.</p>
 <p>If a &#8220;*&#8221; appears in the single filename, it is replaced with the
 current timestep value.  This is only recognized when a single
 filename is used (not when toggling back and forth).  Thus, the 3rd
 example above creates restart files as follows: restart.1000.equil,
 restart.2000.equil, etc.  If a single filename is used with no &#8220;*&#8221;,
 then the timestep value is appended.  E.g. the 2nd example above
 creates restart files as follows: poly.restart.1000,
 poly.restart.2000, etc.</p>
 <p>If a &#8220;%&#8221; character appears in the restart filename(s), then one file
 is written for each processor and the &#8220;%&#8221; character is replaced with
 the processor ID from 0 to P-1.  An additional file with the &#8220;%&#8221;
 replaced by &#8220;base&#8221; is also written, which contains global information.
 For example, the files written on step 1000 for filename restart.%
 would be restart.base.1000, restart.0.1000, restart.1.1000, ...,
 restart.P-1.1000.  This creates smaller files and can be a fast mode
 of output and subsequent input on parallel machines that support
 parallel I/O.  The optional <em>fileper</em> and <em>nfile</em> keywords discussed
 below can alter the number of files written.</p>
 <p>The restart file can also be written in parallel as one large binary
 file via the MPI-IO library, which is part of the MPI standard for
 versions 2.0 and above.  Using MPI-IO requires two steps.  First,
 build LAMMPS with its MPIIO package installed, e.g.</p>
 <div class="highlight-python"><div class="highlight"><pre>make yes-mpiio    # installs the MPIIO package
 make g++          # build LAMMPS for your platform
 </pre></div>
 </div>
 <p>Second, use a restart filename which contains &#8221;.mpiio&#8221;.  Note that it
 does not have to end in &#8221;.mpiio&#8221;, just contain those characters.
 Unlike MPI-IO dump files, a particular restart file must be both
 written and read using MPI-IO.</p>
 <p>Restart files are written on timesteps that are a multiple of N but
 not on the first timestep of a run or minimization.  You can use the
 <a class="reference internal" href="write_restart.html"><em>write_restart</em></a> command to write a restart file
 before a run begins.  A restart file is not written on the last
 timestep of a run unless it is a multiple of N.  A restart file is
 written on the last timestep of a minimization if N &gt; 0 and the
 minimization converges.</p>
 <p>Instead of a numeric value, N can be specifed as an <a class="reference internal" href="variable.html"><em>equal-style variable</em></a>, which should be specified as v_name, where
 name is the variable name.  In this case, the variable is evaluated at
 the beginning of a run to determine the next timestep at which a
 restart file will be written out.  On that timestep, the variable will
 be evaluated again to determine the next timestep, etc.  Thus the
 variable should return timestep values.  See the stagger() and
 logfreq() and stride() math functions for <a class="reference internal" href="variable.html"><em>equal-style variables</em></a>, as examples of useful functions to use in
 this context.  Other similar math functions could easily be added as
 options for <a class="reference internal" href="variable.html"><em>equal-style variables</em></a>.</p>
 <p>For example, the following commands will write restart files
 every step from 1100 to 1200, and could be useful for debugging
 a simulation where something goes wrong at step 1163:</p>
 <div class="highlight-python"><div class="highlight"><pre>variable     s equal stride(1100,1200,1)
 restart              v_s tmp.restart
 </pre></div>
 </div>
 <hr class="docutils" />
 <p>See the <a class="reference internal" href="read_restart.html"><em>read_restart</em></a> command for information about
 what is stored in a restart file.</p>
 <p>Restart files can be read by a <a class="reference internal" href="read_restart.html"><em>read_restart</em></a>
 command to restart a simulation from a particular state.  Because the
 file is binary (to enable exact restarts), it may not be readable on
 another machine.  In this case, you can use the <a class="reference internal" href="Section_start.html#start-7"><span>-r command-line switch</span></a> to convert a restart file to a data
 file.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">Although the purpose of restart files is to enable
 restarting a simulation from where it left off, not all information
 about a simulation is stored in the file.  For example, the list of
 fixes that were specified during the initial run is not stored, which
 means the new input script must specify any fixes you want to use.
 Even when restart information is stored in the file, as it is for some
 fixes, commands may need to be re-specified in the new input script,
 in order to re-use that information.  See the
 <a class="reference internal" href="read_restart.html"><em>read_restart</em></a> command for information about what is
 stored in a restart file.</p>
 </div>
 <hr class="docutils" />
 <p>The optional <em>nfile</em> or <em>fileper</em> keywords can be used in conjunction
 with the &#8220;%&#8221; wildcard character in the specified restart file name(s).
 As explained above, the &#8220;%&#8221; character causes the restart file to be
 written in pieces, one piece for each of P processors.  By default P =
 the number of processors the simulation is running on.  The <em>nfile</em> or
 <em>fileper</em> keyword can be used to set P to a smaller value, which can
 be more efficient when running on a large number of processors.</p>
 <p>The <em>nfile</em> keyword sets P to the specified Nf value.  For example, if
 Nf = 4, and the simulation is running on 100 processors, 4 files will
 be written, by processors 0,25,50,75.  Each will collect information
 from itself and the next 24 processors and write it to a restart file.</p>
 <p>For the <em>fileper</em> keyword, the specified value of Np means write one
 file for every Np processors.  For example, if Np = 4, every 4th
 processor (0,4,8,12,etc) will collect information from itself and the
 next 3 processors and write it to a restart file.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>To write and read restart files in parallel with MPI-IO, the MPIIO
 package must be installed.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="write_restart.html"><em>write_restart</em></a>, <a class="reference internal" href="read_restart.html"><em>read_restart</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>restart 0
 </pre></div>
 </div>
 </div>
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   <div class="section" id="run-command">
 <span id="index-0"></span><h1>run command<a class="headerlink" href="#run-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>run N keyword values ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>N = # of timesteps</li>
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>upto</em> or <em>start</em> or <em>stop</em> or <em>pre</em> or <em>post</em> or <em>every</em></li>
 </ul>
 <pre class="literal-block">
 <em>upto</em> value = none
-  <em>start</em> value = N1
-    N1 = timestep at which 1st run started
-  <em>stop</em> value = N2
-    N2 = timestep at which last run will end
-  <em>pre</em> value = <em>no</em> or <em>yes</em>
-  <em>post</em> value = <em>no</em> or <em>yes</em>
-  <em>every</em> values = M c1 c2 ...
-    M = break the run into M-timestep segments and invoke one or more commands between each segment
-    c1,c2,...,cN = one or more LAMMPS commands, each enclosed in quotes
-    c1 = NULL means no command will be invoked
+<em>start</em> value = N1
+  N1 = timestep at which 1st run started
+<em>stop</em> value = N2
+  N2 = timestep at which last run will end
+<em>pre</em> value = <em>no</em> or <em>yes</em>
+<em>post</em> value = <em>no</em> or <em>yes</em>
+<em>every</em> values = M c1 c2 ...
+  M = break the run into M-timestep segments and invoke one or more commands between each segment
+  c1,c2,...,cN = one or more LAMMPS commands, each enclosed in quotes
+  c1 = NULL means no command will be invoked
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>run 10000
 run 1000000 upto
 run 100 start 0 stop 1000
 run 1000 pre no post yes
 run 100000 start 0 stop 1000000 every 1000 &quot;print &#39;Protein Rg = $r&#39;&quot;
 run 100000 every 1000 NULL
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Run or continue dynamics for a specified number of timesteps.</p>
 <p>When the <a class="reference internal" href="run_style.html"><em>run style</em></a> is <em>respa</em>, N refers to outer
 loop (largest) timesteps.</p>
 <p>A value of N = 0 is acceptable; only the thermodynamics of the system
 are computed and printed without taking a timestep.</p>
 <p>The <em>upto</em> keyword means to perform a run starting at the current
 timestep up to the specified timestep.  E.g. if the current timestep
 is 10,000 and &#8220;run 100000 upto&#8221; is used, then an additional 90,000
 timesteps will be run.  This can be useful for very long runs on a
 machine that allocates chunks of time and terminate your job when time
 is exceeded.  If you need to restart your script multiple times
 (reading in the last restart file), you can keep restarting your
 script with the same run command until the simulation finally
 completes.</p>
 <p>The <em>start</em> or <em>stop</em> keywords can be used if multiple runs are being
 performed and you want a <a class="reference internal" href="fix.html"><em>fix</em></a> command that changes some
 value over time (e.g. temperature) to make the change across the
 entire set of runs and not just a single run.  See the doc page for
 individual fixes to see which ones can be used with the <em>start/stop</em>
 keywords.</p>
 <p>For example, consider this fix followed by 10 run commands:</p>
 <div class="highlight-python"><div class="highlight"><pre>fix       1 all nvt 200.0 300.0 1.0
 run       1000 start 0 stop 10000
 run       1000 start 0 stop 10000
 ...
 run       1000 start 0 stop 10000
 </pre></div>
 </div>
 <p>The NVT fix ramps the target temperature from 200.0 to 300.0 during a
 run.  If the run commands did not have the start/stop keywords (just
 &#8220;run 1000&#8221;), then the temperature would ramp from 200.0 to 300.0
 during the 1000 steps of each run.  With the start/stop keywords, the
 ramping takes place over the 10000 steps of all runs together.</p>
 <p>The <em>pre</em> and <em>post</em> keywords can be used to streamline the setup,
 clean-up, and associated output to the screen that happens before and
 after a run.  This can be useful if you wish to do many short runs in
 succession (e.g. LAMMPS is being called as a library which is doing
 other computations between successive short LAMMPS runs).</p>
 <p>By default (pre and post = yes), LAMMPS creates neighbor lists,
 computes forces, and imposes fix constraints before every run.  And
 after every run it gathers and prints timings statistics.  If a run is
 just a continuation of a previous run (i.e. no settings are changed),
 the initial computation is not necessary; the old neighbor list is
 still valid as are the forces.  So if <em>pre</em> is specified as &#8220;no&#8221; then
 the initial setup is skipped, except for printing thermodynamic info.
 Note that if <em>pre</em> is set to &#8220;no&#8221; for the very 1st run LAMMPS
 performs, then it is overridden, since the initial setup computations
 must be done.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">If your input script changes the system between 2
 runs, then the initial setup must be performed to insure the change is
 recognized by all parts of the code that are affected.  Examples are
 adding a <a class="reference internal" href="fix.html"><em>fix</em></a> or <a class="reference internal" href="dump.html"><em>dump</em></a> or <a class="reference internal" href="compute.html"><em>compute</em></a>,
 changing a <a class="reference internal" href="neigh_modify.html"><em>neighbor</em></a> list parameter, or writing
 restart file which can migrate atoms between processors.  LAMMPS has
 no easy way to check if this has happened, but it is an error to use
 the <em>pre no</em> option in this case.</p>
 </div>
 <p>If <em>post</em> is specified as &#8220;no&#8221;, the full timing summary is skipped;
 only a one-line summary timing is printed.</p>
 <p>The <em>every</em> keyword provides a means of breaking a LAMMPS run into a
 series of shorter runs.  Optionally, one or more LAMMPS commands (c1,
 c2, ..., cN) will be executed in between the short runs.  If used, the
 <em>every</em> keyword must be the last keyword, since it has a variable
 number of arguments.  Each of the trailing arguments is a single
 LAMMPS command, and each command should be enclosed in quotes, so that
 the entire command will be treated as a single argument.  This will
 also prevent any variables in the command from being evaluated until
 it is executed multiple times during the run.  Note that if a command
 itself needs one of its arguments quoted (e.g. the <a class="reference internal" href="print.html"><em>print</em></a>
 command), then you can use a combination of single and double quotes,
 as in the example above or below.</p>
 <p>The <em>every</em> keyword is a means to avoid listing a long series of runs
 and interleaving commands in your input script.  For example, a
 <a class="reference internal" href="print.html"><em>print</em></a> command could be invoked or a <a class="reference internal" href="fix.html"><em>fix</em></a> could
 be redefined, e.g. to reset a thermostat temperature.  Or this could
 be useful for invoking a command you have added to LAMMPS that wraps
 some other code (e.g. as a library) to perform a computation
 periodically during a long LAMMPS run.  See <a class="reference internal" href="Section_modify.html"><em>this section</em></a> of the documentation for info about how
 to add new commands to LAMMPS.  See <a class="reference internal" href="Section_howto.html#howto-10"><span>this section</span></a> of the documentation for ideas
 about how to couple LAMMPS to other codes.</p>
 <p>With the <em>every</em> option, N total steps are simulated, in shorter runs
 of M steps each.  After each M-length run, the specified commands are
 invoked.  If only a single command is specified as NULL, then no
 command is invoked.  Thus these lines:</p>
 <div class="highlight-python"><div class="highlight"><pre>variable q equal x[100]
 run 6000 every 2000 &quot;print &#39;Coord = $q&#39;&quot;
 </pre></div>
 </div>
 <p>are the equivalent of:</p>
 <div class="highlight-python"><div class="highlight"><pre>variable q equal x[100]
 run 2000
 print &quot;Coord = $q&quot;
 run 2000
 print &quot;Coord = $q&quot;
 run 2000
 print &quot;Coord = $q&quot;
 </pre></div>
 </div>
 <p>which does 3 runs of 2000 steps and prints the x-coordinate of a
 particular atom between runs.  Note that the variable &#8220;$q&#8221; will
 be evaluated afresh each time the print command is executed.</p>
 <p>Note that by using the line continuation character &#8220;&amp;&#8221;, the run every
 command can be spread across many lines, though it is still a single
 command:</p>
 <div class="highlight-python"><div class="highlight"><pre>run 100000 every 1000 &amp;
   &quot;print &#39;Minimum value = $a&#39;&quot; &amp;
   &quot;print &#39;Maximum value = $b&#39;&quot; &amp;
   &quot;print &#39;Temp = $c&#39;&quot; &amp;
   &quot;print &#39;Press = $d&#39;&quot;
 </pre></div>
 </div>
 <p>If the <em>pre</em> and <em>post</em> options are set to &#8220;no&#8221; when used with the
 <em>every</em> keyword, then the 1st run will do the full setup and the last
 run will print the full timing summary, but these operations will be
 skipped for intermediate runs.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">You might hope to specify a command that exits the run
 by jumping out of the loop, e.g.</p>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>variable t equal temp
 run 10000 every 100 &quot;if &#39;$t &lt; 300.0&#39; then &#39;jump SELF afterrun&#39;&quot;
 </pre></div>
 </div>
 <p>Unfortunately this will not currently work.  The run command simply
 executes each command one at a time each time it pauses, then
 continues the run.  You can replace the jump command with a simple
 <a class="reference internal" href="quit.html"><em>quit</em></a> command and cause LAMMPS to exit during the
 middle of a run when the condition is met.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>When not using the <em>upto</em> keyword, the number of specified timesteps N
 must fit in a signed 32-bit integer, so you are limited to slightly
 more than 2 billion steps (2^31) in a single run.  When using <em>upto</em>,
 N can be larger than a signed 32-bit integer, however the difference
 between N and the current timestep must still be no larger than
 2^31 steps.</p>
 <p>However, with or without the <em>upto</em> keyword, you can perform
 successive runs to run a simulation for any number of steps (ok, up to
 2^63 total steps).  I.e. the timestep counter within LAMMPS is a
 64-bit signed integer.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="minimize.html"><em>minimize</em></a>, <a class="reference internal" href="run_style.html"><em>run_style</em></a>,
 <a class="reference internal" href="temper.html"><em>temper</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The option defaults are start = the current timestep, stop = current
 timestep + N, pre = yes, and post = yes.</p>
 </div>
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   <div class="section" id="run-style-command">
 <span id="index-0"></span><h1>run_style command<a class="headerlink" href="#run-style-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>run_style style args
 </pre></div>
 </div>
 <ul class="simple">
 <li>style = <em>verlet</em> or <em>verlet/split</em> or <em>respa</em> or <em>respa/omp</em></li>
 </ul>
 <pre class="literal-block">
 <em>verlet</em> args = none
-  <em>verlet/split</em> args = none
-  <em>respa</em> args = N n1 n2 ... keyword values ...
-    N = # of levels of rRESPA
-    n1, n2, ... = loop factor between rRESPA levels (N-1 values)
-    zero or more keyword/value pairings may be appended to the loop factors
-    keyword = <em>bond</em> or <em>angle</em> or <em>dihedral</em> or <em>improper</em> or
-           <em>pair</em> or <em>inner</em> or <em>middle</em> or <em>outer</em> or <em>hybrid</em> or <em>kspace</em>
-      <em>bond</em> value = M
-        M = which level (1-N) to compute bond forces in
-      <em>angle</em> value = M
-        M = which level (1-N) to compute angle forces in
-      <em>dihedral</em> value = M
-        M = which level (1-N) to compute dihedral forces in
-      <em>improper</em> value = M
-        M = which level (1-N) to compute improper forces in
-      <em>pair</em> value = M
-        M = which level (1-N) to compute pair forces in
-      <em>inner</em> values = M cut1 cut2
-        M = which level (1-N) to compute pair inner forces in
-     cut1 = inner cutoff between pair inner and
-            pair middle or outer  (distance units)
-     cut2 = outer cutoff between pair inner and
-            pair middle or outer  (distance units)
-      <em>middle</em> values = M cut1 cut2
-        M = which level (1-N) to compute pair middle forces in
-     cut1 = inner cutoff between pair middle and pair outer (distance units)
-     cut2 = outer cutoff between pair middle and pair outer (distance units)
-      <em>outer</em> value = M
-        M = which level (1-N) to compute pair outer forces in
-      <em>hybrid</em> values = M1 [M2 ...] (as many values as there are hybrid sub-styles
-        M1 = which level (1-N) to compute the first pair_style hybrid sub-style in
-        M2 = which level (1-N) to compute the second pair_style hybrid sub-style in
-        ...
-      <em>kspace</em> value = M
-        M = which level (1-N) to compute kspace forces in
+<em>verlet/split</em> args = none
+<em>respa</em> args = N n1 n2 ... keyword values ...
+  N = # of levels of rRESPA
+  n1, n2, ... = loop factor between rRESPA levels (N-1 values)
+  zero or more keyword/value pairings may be appended to the loop factors
+  keyword = <em>bond</em> or <em>angle</em> or <em>dihedral</em> or <em>improper</em> or
+         <em>pair</em> or <em>inner</em> or <em>middle</em> or <em>outer</em> or <em>hybrid</em> or <em>kspace</em>
+    <em>bond</em> value = M
+      M = which level (1-N) to compute bond forces in
+    <em>angle</em> value = M
+      M = which level (1-N) to compute angle forces in
+    <em>dihedral</em> value = M
+      M = which level (1-N) to compute dihedral forces in
+    <em>improper</em> value = M
+      M = which level (1-N) to compute improper forces in
+    <em>pair</em> value = M
+      M = which level (1-N) to compute pair forces in
+    <em>inner</em> values = M cut1 cut2
+      M = which level (1-N) to compute pair inner forces in
+   cut1 = inner cutoff between pair inner and
+          pair middle or outer  (distance units)
+   cut2 = outer cutoff between pair inner and
+          pair middle or outer  (distance units)
+    <em>middle</em> values = M cut1 cut2
+      M = which level (1-N) to compute pair middle forces in
+   cut1 = inner cutoff between pair middle and pair outer (distance units)
+   cut2 = outer cutoff between pair middle and pair outer (distance units)
+    <em>outer</em> value = M
+      M = which level (1-N) to compute pair outer forces in
+    <em>hybrid</em> values = M1 [M2 ...] (as many values as there are hybrid sub-styles
+      M1 = which level (1-N) to compute the first pair_style hybrid sub-style in
+      M2 = which level (1-N) to compute the second pair_style hybrid sub-style in
+      ...
+    <em>kspace</em> value = M
+      M = which level (1-N) to compute kspace forces in
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>run_style verlet
 run_style respa 4 2 2 2 bond 1 dihedral 2 pair 3 kspace 4
 run_style respa 4 2 2 2 bond 1 dihedral 2 inner 3 5.0 6.0 outer 4 kspace 4
 </pre></div>
 </div>
 <div class="highlight-python"><div class="highlight"><pre>run_style respa 3 4 2 bond 1 hybrid 2 2 1 kspace 3
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Choose the style of time integrator used for molecular dynamics
 simulations performed by LAMMPS.</p>
 <p>The <em>verlet</em> style is a standard velocity-Verlet integrator.</p>
 <hr class="docutils" />
 <p>The <em>verlet/split</em> style is also a velocity-Verlet integrator, but it
 splits the force calculation within each timestep over 2 partitions of
 processors.  See <a class="reference internal" href="Section_start.html#start-7"><span>Section_start 6</span></a> for an
 explanation of the -partition command-line switch.</p>
 <p>Specifically, this style performs all computation except the
 <a class="reference internal" href="kspace_style.html"><em>kspace_style</em></a> portion of the force field on the 1st
 partition.  This include the <a class="reference internal" href="pair_style.html"><em>pair style</em></a>, <a class="reference internal" href="bond_style.html"><em>bond style</em></a>, <a class="reference internal" href="neighbor.html"><em>neighbor list building</em></a>,
 <a class="reference internal" href="fix.html"><em>fixes</em></a> including time intergration, and output.  The
 <a class="reference internal" href="kspace_style.html"><em>kspace_style</em></a> portion of the calculation is
 performed on the 2nd partition.</p>
 <p>This is most useful for the PPPM kspace_style when its performance on
 a large number of processors degrades due to the cost of communication
 in its 3d FFTs.  In this scenario, splitting your P total processors
 into 2 subsets of processors, P1 in the 1st partition and P2 in the
 2nd partition, can enable your simulation to run faster.  This is
 because the long-range forces in PPPM can be calculated at the same
 time as pair-wise and bonded forces are being calculated, and the FFTs
 can actually speed up when running on fewer processors.</p>
 <p>To use this style, you must define 2 partitions where P1 is a multiple
 of P2.  Typically having P1 be 3x larger than P2 is a good choice.
 The 3d processor layouts in each partition must overlay in the
 following sense.  If P1 is a Px1 by Py1 by Pz1 grid, and P2 = Px2 by
 Py2 by Pz2, then Px1 must be an integer multiple of Px2, and similarly
 for Py1 a multiple of Py2, and Pz1 a multiple of Pz2.</p>
 <p>Typically the best way to do this is to let the 1st partition choose
 its onn optimal layout, then require the 2nd partition&#8217;s layout to
 match the integer multiple constraint.  See the
 <a class="reference internal" href="processors.html"><em>processors</em></a> command with its <em>part</em> keyword for a way
 to control this, e.g.</p>
 <div class="highlight-python"><div class="highlight"><pre>procssors * * * part 1 2 multiple
 </pre></div>
 </div>
 <p>You can also use the <a class="reference internal" href="partition.html"><em>partition</em></a> command to explicitly
 specity the processor layout on each partition.  E.g. for 2 partitions
 of 60 and 15 processors each:</p>
 <div class="highlight-python"><div class="highlight"><pre>partition yes 1 processors 3 4 5
 partition yes 2 processors 3 1 5
 </pre></div>
 </div>
 <p>When you run in 2-partition mode with the <em>verlet/split</em> style, the
 thermodyanmic data for the entire simulation will be output to the log
 and screen file of the 1st partition, which are log.lammps.0 and
 screen.0 by default; see the &#8220;-plog and -pscreen command-line
 switches&#8221;Section_start.html#start_7 to change this.  The log and
 screen file for the 2nd partition will not contain thermodynamic
 output beyone the 1st timestep of the run.</p>
 <p>See <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a> of the manual for
 performance details of the speed-up offered by the <em>verlet/split</em>
 style.  One important performance consideration is the assignemnt of
 logical processors in the 2 partitions to the physical cores of a
 parallel machine.  The <a class="reference internal" href="processors.html"><em>processors</em></a> command has
 options to support this, and strategies are discussed in
 <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a> of the manual.</p>
 <hr class="docutils" />
 <p>The <em>respa</em> style implements the rRESPA multi-timescale integrator
 <a class="reference internal" href="#tuckerman"><span>(Tuckerman)</span></a> with N hierarchical levels, where level 1 is
 the innermost loop (shortest timestep) and level N is the outermost
 loop (largest timestep).  The loop factor arguments specify what the
 looping factor is between levels.  N1 specifies the number of
 iterations of level 1 for a single iteration of level 2, N2 is the
 iterations of level 2 per iteration of level 3, etc.  N-1 looping
 parameters must be specified.</p>
 <p>The <a class="reference internal" href="timestep.html"><em>timestep</em></a> command sets the timestep for the
 outermost rRESPA level.  Thus if the example command above for a
 4-level rRESPA had an outer timestep of 4.0 fmsec, the inner timestep
 would be 8x smaller or 0.5 fmsec.  All other LAMMPS commands that
 specify number of timesteps (e.g. <a class="reference internal" href="neigh_modify.html"><em>neigh_modify</em></a>
 parameters, <a class="reference internal" href="dump.html"><em>dump</em></a> every N timesteps, etc) refer to the
 outermost timesteps.</p>
 <p>The rRESPA keywords enable you to specify at what level of the
 hierarchy various forces will be computed.  If not specified, the
 defaults are that bond forces are computed at level 1 (innermost
 loop), angle forces are computed where bond forces are, dihedral
 forces are computed where angle forces are, improper forces are
 computed where dihedral forces are, pair forces are computed at the
 outermost level, and kspace forces are computed where pair forces are.
 The inner, middle, outer forces have no defaults.</p>
 <p>The <em>inner</em> and <em>middle</em> keywords take additional arguments for
 cutoffs that are used by the pairwise force computations.  If the 2
 cutoffs for <em>inner</em> are 5.0 and 6.0, this means that all pairs up to
 6.0 apart are computed by the inner force.  Those between 5.0 and 6.0
 have their force go ramped to 0.0 so the overlap with the next regime
 (middle or outer) is smooth.  The next regime (middle or outer) will
 compute forces for all pairs from 5.0 outward, with those from 5.0 to
 6.0 having their value ramped in an inverse manner.</p>
 <p>Only some pair potentials support the use of the <em>inner</em> and <em>middle</em>
 and <em>outer</em> keywords.  If not, only the <em>pair</em> keyword can be used
 with that pair style, meaning all pairwise forces are computed at the
 same rRESPA level.  See the doc pages for individual pair styles for
 details.i</p>
 <p>Another variant to use pair potentials in rRESPA is with the <em>hybrid</em>
 keyword, which requires the use of a <a class="reference internal" href="pair_hybrid.html"><em>hybrid pair_style</em></a>
 In this scenario, different sub-styles of the hybrid pair style are
 evaluated at different rRESPA levels. Thus the hybrid keyword requires
 as many level assignments as there are hybrid substyles which designate
 the respective sub-styles to the rRESPA level according to their order
 of definition in the pair_style command. Since the <em>hybrid</em> designates
 pair force computations, it is mututally exclusive with either the <em>pair</em>
 or the <em>inner</em>/<em>middle</em>/<em>outer</em> keywords.</p>
 <p>When using rRESPA (or for any MD simulation) care must be taken to
 choose a timestep size(s) that insures the Hamiltonian for the chosen
 ensemble is conserved.  For the constant NVE ensemble, total energy
 must be conserved.  Unfortunately, it is difficult to know <em>a priori</em>
 how well energy will be conserved, and a fairly long test simulation
 (~10 ps) is usually necessary in order to verify that no long-term
 drift in energy occurs with the trial set of parameters.</p>
 <p>With that caveat, a few rules-of-thumb may be useful in selecting
 <em>respa</em> settings.  The following applies mostly to biomolecular
 simulations using the CHARMM or a similar all-atom force field, but
 the concepts are adaptable to other problems.  Without SHAKE, bonds
 involving hydrogen atoms exhibit high-frequency vibrations and require
 a timestep on the order of 0.5 fmsec in order to conserve energy.  The
 relatively inexpensive force computations for the bonds, angles,
 impropers, and dihedrals can be computed on this innermost 0.5 fmsec
 step.  The outermost timestep cannot be greater than 4.0 fmsec without
 risking energy drift.  Smooth switching of forces between the levels
 of the rRESPA hierarchy is also necessary to avoid drift, and a 1-2
 angstrom &#8220;healing distance&#8221; (the distance between the outer and inner
 cutoffs) works reasonably well.  We thus recommend the following
 settings for use of the <em>respa</em> style without SHAKE in biomolecular
 simulations:</p>
 <div class="highlight-python"><div class="highlight"><pre>timestep  4.0
 run_style respa 4 2 2 2 inner 2 4.5 6.0 middle 3 8.0 10.0 outer 4
 </pre></div>
 </div>
 <p>With these settings, users can expect good energy conservation and
 roughly a 2.5 fold speedup over the <em>verlet</em> style with a 0.5 fmsec
 timestep.</p>
 <p>If SHAKE is used with the <em>respa</em> style, time reversibility is lost,
 but substantially longer time steps can be achieved.  For biomolecular
 simulations using the CHARMM or similar all-atom force field, bonds
 involving hydrogen atoms exhibit high frequency vibrations and require
 a time step on the order of 0.5 fmsec in order to conserve energy.
 These high frequency modes also limit the outer time step sizes since
 the modes are coupled.  It is therefore desirable to use SHAKE with
 respa in order to freeze out these high frequency motions and increase
 the size of the time steps in the respa hierarchy.  The following
 settings can be used for biomolecular simulations with SHAKE and
 rRESPA:</p>
 <div class="highlight-python"><div class="highlight"><pre>fix             2 all shake 0.000001 500 0 m 1.0 a 1
 timestep        4.0
 run_style    respa 2 2 inner 1 4.0 5.0 outer 2
 </pre></div>
 </div>
 <p>With these settings, users can expect good energy conservation and
 roughly a 1.5 fold speedup over the <em>verlet</em> style with SHAKE and a
 2.0 fmsec timestep.</p>
 <p>For non-biomolecular simulations, the <em>respa</em> style can be
 advantageous if there is a clear separation of time scales - fast and
 slow modes in the simulation.  Even a LJ system can benefit from
 rRESPA if the interactions are divided by the inner, middle and outer
 keywords.  A 2-fold or more speedup can be obtained while maintaining
 good energy conservation.  In real units, for a pure LJ fluid at
 liquid density, with a sigma of 3.0 angstroms, and epsilon of 0.1
 Kcal/mol, the following settings seem to work well:</p>
 <div class="highlight-python"><div class="highlight"><pre>timestep  36.0
 run_style respa 3 3 4 inner 1 3.0 4.0 middle 2 6.0 7.0 outer 3
 </pre></div>
 </div>
 <hr class="docutils" />
 <p>The <em>respa/omp</em> styles is a variant of <em>respa</em> adapted for use with
 pair, bond, angle, dihedral, improper, or kspace styles with an <em>omp</em>
 suffix. It is functionally equivalent to <em>respa</em> but performs additional
 operations required for managing <em>omp</em> styles. For more on <em>omp</em> styles
 see the <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a> of the manual.
 Accelerated styles take the same arguments and should produce the same
 results, except for round-off and precision issues.</p>
 <p>You can specify <em>respa/omp</em> explicitly in your input script, or
 you can use the <a class="reference internal" href="Section_start.html#start-7"><span>-suffix command-line switch</span></a>
 when you invoke LAMMPS, or you can use the <a class="reference internal" href="suffix.html"><em>suffix</em></a>
 command in your input script.</p>
 <p>See <a class="reference internal" href="Section_accelerate.html"><em>Section_accelerate</em></a> of the manual for
 more instructions on how to use the accelerated styles effectively.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>The <em>verlet/split</em> style can only be used if LAMMPS was built with the
 REPLICA package. Correspondingly the <em>respa/omp</em> style is available only
 if the USER-OMP package was included. See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a>
 section for more info on packages.</p>
 <p>Whenever using rRESPA, the user should experiment with trade-offs in
 speed and accuracy for their system, and verify that they are
 conserving energy to adequate precision.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="timestep.html"><em>timestep</em></a>, <a class="reference internal" href="run.html"><em>run</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>run_style verlet
 </pre></div>
 </div>
 <hr class="docutils" />
 <p id="tuckerman"><strong>(Tuckerman)</strong> Tuckerman, Berne and Martyna, J Chem Phys, 97, p 1990
 (1992).</p>
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   <div class="section" id="set-command">
 <span id="index-0"></span><h1>set command<a class="headerlink" href="#set-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>set style ID keyword values ...
 </pre></div>
 </div>
 <ul>
 <li><p class="first">style = <em>atom</em> or <em>type</em> or <em>mol</em> or <em>group</em> or <em>region</em></p>
 </li>
 <li><p class="first">ID = atom ID range or type range or mol ID range or group ID or region ID</p>
 </li>
 <li><p class="first">one or more keyword/value pairs may be appended</p>
 </li>
 <li><dl class="first docutils">
 <dt>keyword = <em>type</em> or <em>type/fraction</em> or <em>mol</em> or <em>x</em> or <em>y</em> or <em>z</em> or           <em>charge</em> or <em>dipole</em> or <em>dipole/random</em> or <em>quat</em> or     <em>quat/random</em> or <em>diameter</em> or <em>shape</em> or       <em>length</em> or <em>tri</em> or <em>theta</em> or <em>angmom</em> or     <em>mass</em> or <em>density</em> or <em>volume</em> or <em>image</em> or</dt>
 <dd><p class="first last"><em>bond</em> or <em>angle</em> or <em>dihedral</em> or <em>improper</em> or
 <em>meso_e</em> or <em>meso_cv</em> or <em>meso_rho</em> or <em>i_name</em> or <em>d_name</em></p>
 </dd>
 </dl>
 </li>
 </ul>
 <pre class="literal-block">
 <em>type</em> value = atom type
-    value can be an atom-style variable (see below)
-  <em>type/fraction</em> values = type fraction seed
-    type = new atom type
-    fraction = fraction of selected atoms to set to new atom type
-    seed = random # seed (positive integer)
-  <em>mol</em> value = molecule ID
-    value can be an atom-style variable (see below)
-  <em>x</em>,*y*,*z* value = atom coordinate (distance units)
-    value can be an atom-style variable (see below)
-  <em>charge</em> value = atomic charge (charge units)
-    value can be an atom-style variable (see below)
-  <em>dipole</em> values = x y z
-    x,y,z = orientation of dipole moment vector
-    any of x,y,z can be an atom-style variable (see below)
-  <em>dipole/random</em> value = seed Dlen
-    seed = random # seed (positive integer) for dipole moment orientations
-    Dlen = magnitude of dipole moment (dipole units)
-  <em>quat</em> values = a b c theta
-    a,b,c = unit vector to rotate particle around via right-hand rule
-    theta = rotation angle (degrees)
-    any of a,b,c,theta can be an atom-style variable (see below)
-  <em>quat/random</em> value = seed
-    seed = random # seed (positive integer) for quaternion orientations
-  <em>diameter</em> value = diameter of spherical particle (distance units)
-    value can be an atom-style variable (see below)
-  <em>shape</em> value = Sx Sy Sz
-    Sx,Sy,Sz = 3 diameters of ellipsoid (distance units)
-  <em>length</em> value = len
-    len = length of line segment (distance units)
-    len can be an atom-style variable (see below)
-  <em>tri</em> value = side
-    side = side length of equilateral triangle (distance units)
-    side can be an atom-style variable (see below)
-  <em>theta</em> value = angle (degrees)
-    angle = orientation of line segment with respect to x-axis
-    angle can be an atom-style variable (see below)
-  <em>angmom</em> values = Lx Ly Lz
-    Lx,Ly,Lz = components of angular momentum vector (distance-mass-velocity units)
-    any of Lx,Ly,Lz can be an atom-style variable (see below)
-  <em>mass</em> value = per-atom mass (mass units)
-    value can be an atom-style variable (see below)
-  <em>density</em> value = particle density for sphere or ellipsoid (mass/distance^3 or mass/distance^2 or mass/distance units, depending on dimensionality of particle)
-    value can be an atom-style variable (see below)
-  <em>volume</em> value = particle volume for Peridynamic particle (distance^3 units)
-    value can be an atom-style variable (see below)
-  <em>image</em> nx ny nz
-    nx,ny,nz = which periodic image of the simulation box the atom is in
-  <em>bond</em> value = bond type for all bonds between selected atoms
-  <em>angle</em> value = angle type for all angles between selected atoms
-  <em>dihedral</em> value = dihedral type for all dihedrals between selected atoms
-  <em>improper</em> value = improper type for all impropers between selected atoms
-  <em>meso_e</em> value = energy of SPH particles (need units)
-    value can be an atom-style variable (see below)
-  <em>meso_cv</em> value = heat capacity of SPH particles (need units)
-    value can be an atom-style variable (see below)
-  <em>meso_rho</em> value = density of SPH particles (need units)
-    value can be an atom-style variable (see below)
-  <em>i_name</em> value = value for custom integer vector with name
-    value can be an atom-style variable (see below)
-  <em>d_name</em> value = value for custom floating-point vector with name
-    value can be an atom-style variable (see below)
+  value can be an atom-style variable (see below)
+<em>type/fraction</em> values = type fraction seed
+  type = new atom type
+  fraction = fraction of selected atoms to set to new atom type
+  seed = random # seed (positive integer)
+<em>mol</em> value = molecule ID
+  value can be an atom-style variable (see below)
+<em>x</em>,*y*,*z* value = atom coordinate (distance units)
+  value can be an atom-style variable (see below)
+<em>charge</em> value = atomic charge (charge units)
+  value can be an atom-style variable (see below)
+<em>dipole</em> values = x y z
+  x,y,z = orientation of dipole moment vector
+  any of x,y,z can be an atom-style variable (see below)
+<em>dipole/random</em> value = seed Dlen
+  seed = random # seed (positive integer) for dipole moment orientations
+  Dlen = magnitude of dipole moment (dipole units)
+<em>quat</em> values = a b c theta
+  a,b,c = unit vector to rotate particle around via right-hand rule
+  theta = rotation angle (degrees)
+  any of a,b,c,theta can be an atom-style variable (see below)
+<em>quat/random</em> value = seed
+  seed = random # seed (positive integer) for quaternion orientations
+<em>diameter</em> value = diameter of spherical particle (distance units)
+  value can be an atom-style variable (see below)
+<em>shape</em> value = Sx Sy Sz
+  Sx,Sy,Sz = 3 diameters of ellipsoid (distance units)
+<em>length</em> value = len
+  len = length of line segment (distance units)
+  len can be an atom-style variable (see below)
+<em>tri</em> value = side
+  side = side length of equilateral triangle (distance units)
+  side can be an atom-style variable (see below)
+<em>theta</em> value = angle (degrees)
+  angle = orientation of line segment with respect to x-axis
+  angle can be an atom-style variable (see below)
+<em>angmom</em> values = Lx Ly Lz
+  Lx,Ly,Lz = components of angular momentum vector (distance-mass-velocity units)
+  any of Lx,Ly,Lz can be an atom-style variable (see below)
+<em>mass</em> value = per-atom mass (mass units)
+  value can be an atom-style variable (see below)
+<em>density</em> value = particle density for sphere or ellipsoid (mass/distance^3 or mass/distance^2 or mass/distance units, depending on dimensionality of particle)
+  value can be an atom-style variable (see below)
+<em>volume</em> value = particle volume for Peridynamic particle (distance^3 units)
+  value can be an atom-style variable (see below)
+<em>image</em> nx ny nz
+  nx,ny,nz = which periodic image of the simulation box the atom is in
+<em>bond</em> value = bond type for all bonds between selected atoms
+<em>angle</em> value = angle type for all angles between selected atoms
+<em>dihedral</em> value = dihedral type for all dihedrals between selected atoms
+<em>improper</em> value = improper type for all impropers between selected atoms
+<em>meso_e</em> value = energy of SPH particles (need units)
+  value can be an atom-style variable (see below)
+<em>meso_cv</em> value = heat capacity of SPH particles (need units)
+  value can be an atom-style variable (see below)
+<em>meso_rho</em> value = density of SPH particles (need units)
+  value can be an atom-style variable (see below)
+<em>i_name</em> value = value for custom integer vector with name
+  value can be an atom-style variable (see below)
+<em>d_name</em> value = value for custom floating-point vector with name
+  value can be an atom-style variable (see below)
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>set group solvent type 2
 set group solvent type/fraction 2 0.5 12393
 set group edge bond 4
 set region half charge 0.5
 set type 3 charge 0.5
 set type 1*3 charge 0.5
 set atom * charge v_atomfile
 set atom 100*200 x 0.5 y 1.0
 set atom 1492 type 3
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Set one or more properties of one or more atoms.  Since atom
 properties are initially assigned by the <a class="reference internal" href="read_data.html"><em>read_data</em></a>,
 <a class="reference internal" href="read_restart.html"><em>read_restart</em></a> or <a class="reference internal" href="create_atoms.html"><em>create_atoms</em></a>
 commands, this command changes those assignments.  This can be useful
 for overriding the default values assigned by the
 <a class="reference internal" href="create_atoms.html"><em>create_atoms</em></a> command (e.g. charge = 0.0).  It can
 be useful for altering pairwise and molecular force interactions,
 since force-field coefficients are defined in terms of types.  It can
 be used to change the labeling of atoms by atom type or molecule ID
 when they are output in <a class="reference internal" href="dump.html"><em>dump</em></a> files.  It can also be useful
 for debugging purposes; i.e. positioning an atom at a precise location
 to compute subsequent forces or energy.</p>
 <p>Note that the <em>style</em> and <em>ID</em> arguments determine which atoms have
 their properties reset.  The remaining keywords specify which
 properties to reset and what the new values are.  Some strings like
 <em>type</em> or <em>mol</em> can be used as a style and/or a keyword.</p>
 <hr class="docutils" />
 <p>This section describes how to select which atoms to change
 the properties of, via the <em>style</em> and <em>ID</em> arguments.</p>
 <p>The style <em>atom</em> selects all the atoms in a range of atom IDs.  The
 style <em>type</em> selects all the atoms in a range of types.  The style
 <em>mol</em> selects all the atoms in a range of molecule IDs.</p>
 <p>In each of the range cases, the range can be specified as a single
 numeric value, or a wildcard asterisk can be used to specify a range
 of values.  This takes the form &#8220;*&#8221; or &#8220;<em>n&#8221; or &#8220;n</em>&#8221; or &#8220;m*n&#8221;.  For
 example, for the style <em>type</em>, if N = the number of atom types, then
 an asterisk with no numeric values means all types from 1 to N.  A
 leading asterisk means all types from 1 to n (inclusive).  A trailing
 asterisk means all types from n to N (inclusive).  A middle asterisk
 means all types from m to n (inclusive).  For all the styles except
 <em>mol</em>, the lowest value for the wildcard is 1; for <em>mol</em> it is 0.</p>
 <p>The style <em>group</em> selects all the atoms in the specified group.  The
 style <em>region</em> selects all the atoms in the specified geometric
 region.  See the <a class="reference internal" href="group.html"><em>group</em></a> and <a class="reference internal" href="region.html"><em>region</em></a> commands
 for details of how to specify a group or region.</p>
 <hr class="docutils" />
 <p>This section describes the keyword options for which properties to
 change, for the selected atoms.</p>
 <p>Note that except where explicitly prohibited below, all of the
 keywords allow an <a class="reference internal" href="variable.html"><em>atom-style or atomfile-style variable</em></a> to be used as the specified value(s).  If the
 value is a variable, it should be specified as v_name, where name is
 the variable name.  In this case, the variable will be evaluated, and
 its resulting per-atom value used to determine the value assigned to
 each selected atom.  Note that the per-atom value from the variable
 will be ignored for atoms that are not selected via the <em>style</em> and
 <em>ID</em> settings explained above.  A simple way to use per-atom values
 from the variable to reset a property for all atoms is to use style
 <em>atom</em> with <em>ID</em> = &#8220;*&#8221;; this selects all atom IDs.</p>
 <p>Atom-style variables can specify formulas with various mathematical
 functions, and include <a class="reference internal" href="thermo_style.html"><em>thermo_style</em></a> command
 keywords for the simulation box parameters and timestep and elapsed
 time.  They can also include per-atom values, such as atom
 coordinates.  Thus it is easy to specify a time-dependent or
 spatially-dependent set of per-atom values.  As explained on the
 <a class="reference internal" href="variable.html"><em>variable</em></a> doc page, atomfile-style variables can be
 used in place of atom-style variables, and thus as arguments to the
 set command.  Atomfile-style variables read their per-atoms values
 from a file.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">Atom-style and atomfile-style variables return
 floating point per-atom values.  If the values are assigned to an
 integer variable, such as the molecule ID, then the floating point
 value is truncated to its integer portion, e.g. a value of 2.6 would
 become 2.</p>
 </div>
 <p>Keyword <em>type</em> sets the atom type for all selected atoms.  The
 specified value must be from 1 to ntypes, where ntypes was set by the
 <a class="reference internal" href="create_box.html"><em>create_box</em></a> command or the <em>atom types</em> field in the
 header of the data file read by the <a class="reference internal" href="read_data.html"><em>read_data</em></a>
 command.</p>
 <p>Keyword <em>type/fraction</em> sets the atom type for a fraction of the
 selected atoms.  The actual number of atoms changed is not guaranteed
 to be exactly the requested fraction, but should be statistically
 close.  Random numbers are used in such a way that a particular atom
 is changed or not changed, regardless of how many processors are being
 used.  This keyword does not allow use of an atom-style variable.</p>
 <p>Keyword <em>mol</em> sets the molecule ID for all selected atoms.  The <a class="reference internal" href="atom_style.html"><em>atom style</em></a> being used must support the use of molecule
 IDs.</p>
 <p>Keywords <em>x</em>, <em>y</em>, <em>z</em>, and <em>charge</em> set the coordinates or charge of
 all selected atoms.  For <em>charge</em>, the <a class="reference internal" href="atom_style.html"><em>atom style</em></a>
 being used must support the use of atomic charge.</p>
 <p>Keyword <em>dipole</em> uses the specified x,y,z values as components of a
 vector to set as the orientation of the dipole moment vectors of the
 selected atoms.  The magnitude of the dipole moment is set
 by the length of this orientation vector.</p>
 <p>Keyword <em>dipole/random</em> randomizes the orientation of the dipole
 moment vectors of the selected atoms and sets the magnitude of each to
 the specified <em>Dlen</em> value.  For 2d systems, the z component of the
 orientation is set to 0.0.  Random numbers are used in such a way that
 the orientation of a particular atom is the same, regardless of how
 many processors are being used.  This keyword does not allow use of an
 atom-style variable.</p>
 <p>Keyword <em>quat</em> uses the specified values to create a quaternion
 (4-vector) that represents the orientation of the selected atoms.  The
 particles must be ellipsoids as defined by the <a class="reference internal" href="atom_style.html"><em>atom_style ellipsoid</em></a> command or triangles as defined by the
 <a class="reference internal" href="atom_style.html"><em>atom_style tri</em></a> command.  Note that particles defined
 by <a class="reference internal" href="atom_style.html"><em>atom_style ellipsoid</em></a> have 3 shape parameters.
 The 3 values must be non-zero for each particle set by this command.
 They are used to specify the aspect ratios of an ellipsoidal particle,
 which is oriented by default with its x-axis along the simulation
 box&#8217;s x-axis, and similarly for y and z.  If this body is rotated (via
 the right-hand rule) by an angle theta around a unit rotation vector
 (a,b,c), then the quaternion that represents its new orientation is
 given by (cos(theta/2), a*sin(theta/2), b*sin(theta/2),
 c*sin(theta/2)).  The theta and a,b,c values are the arguments to the
 <em>quat</em> keyword.  LAMMPS normalizes the quaternion in case (a,b,c) was
 not specified as a unit vector.  For 2d systems, the a,b,c values are
 ignored, since a rotation vector of (0,0,1) is the only valid choice.</p>
 <p>Keyword <em>quat/random</em> randomizes the orientation of the quaternion of
 the selected atoms.  The particles must be ellipsoids as defined by
 the <a class="reference internal" href="atom_style.html"><em>atom_style ellipsoid</em></a> command or triangles as
 defined by the <a class="reference internal" href="atom_style.html"><em>atom_style tri</em></a> command.  Random
 numbers are used in such a way that the orientation of a particular
 atom is the same, regardless of how many processors are being used.
 For 2d systems, only orientations in the xy plane are generated.  As
 with keyword <em>quat</em>, for ellipsoidal particles, the 3 shape values
 must be non-zero for each particle set by this command.  This keyword
 does not allow use of an atom-style variable.</p>
 <p>Keyword <em>diameter</em> sets the size of the selected atoms.  The particles
 must be finite-size spheres as defined by the <a class="reference internal" href="atom_style.html"><em>atom_style sphere</em></a> command.  The diameter of a particle can be
 set to 0.0, which means they will be treated as point particles.  Note
 that this command does not adjust the particle mass, even if it was
 defined with a density, e.g. via the <a class="reference internal" href="read_data.html"><em>read_data</em></a>
 command.</p>
 <p>Keyword <em>shape</em> sets the size and shape of the selected atoms.  The
 particles must be ellipsoids as defined by the <a class="reference internal" href="atom_style.html"><em>atom_style ellipsoid</em></a> command.  The <em>Sx</em>, <em>Sy</em>, <em>Sz</em> settings are
 the 3 diameters of the ellipsoid in each direction.  All 3 can be set
 to the same value, which means the ellipsoid is effectively a sphere.
 They can also all be set to 0.0 which means the particle will be
 treated as a point particle.  Note that this command does not adjust
 the particle mass, even if it was defined with a density, e.g. via the
 <a class="reference internal" href="read_data.html"><em>read_data</em></a> command.</p>
 <p>Keyword <em>length</em> sets the length of selected atoms.  The particles
 must be line segments as defined by the <a class="reference internal" href="atom_style.html"><em>atom_style line</em></a> command.  If the specified value is non-zero the
 line segment is (re)set to a length = the specified value, centered
 around the particle position, with an orientation along the x-axis.
 If the specified value is 0.0, the particle will become a point
 particle.  Note that this command does not adjust the particle mass,
 even if it was defined with a density, e.g. via the
 <a class="reference internal" href="read_data.html"><em>read_data</em></a> command.</p>
 <p>Keyword <em>tri</em> sets the size of selected atoms.  The particles must be
 triangles as defined by the <a class="reference internal" href="atom_style.html"><em>atom_style tri</em></a> command.
 If the specified value is non-zero the triangle is (re)set to be an
 equilateral triangle in the xy plane with side length = the specified
 value, with a centroid at the particle position, with its base
 parallel to the x axis, and the y-axis running from the center of the
 base to the top point of the triangle.  If the specified value is 0.0,
 the particle will become a point particle.  Note that this command
 does not adjust the particle mass, even if it was defined with a
 density, e.g. via the <a class="reference internal" href="read_data.html"><em>read_data</em></a> command.</p>
 <p>Keyword <em>theta</em> sets the orientation of selected atoms.  The particles
 must be line segments as defined by the <a class="reference internal" href="atom_style.html"><em>atom_style line</em></a> command.  The specified value is used to set the
 orientation angle of the line segments with respect to the x axis.</p>
 <p>Keyword <em>angmom</em> sets the angular momentum of selected atoms.  The
 particles must be ellipsoids as defined by the <a class="reference internal" href="atom_style.html"><em>atom_style ellipsoid</em></a> command or triangles as defined by the
 <a class="reference internal" href="atom_style.html"><em>atom_style tri</em></a> command.  The angular momentum vector
 of the particles is set to the 3 specified components.</p>
 <p>Keyword <em>mass</em> sets the mass of all selected particles.  The particles
 must have a per-atom mass attribute, as defined by the
 <a class="reference internal" href="atom_style.html"><em>atom_style</em></a> command.  See the &#8220;mass&#8221; command for how
 to set mass values on a per-type basis.</p>
 <p>Keyword <em>density</em> also sets the mass of all selected particles, but in
 a different way.  The particles must have a per-atom mass attribute,
 as defined by the <a class="reference internal" href="atom_style.html"><em>atom_style</em></a> command.  If the atom
 has a radius attribute (see <a class="reference internal" href="atom_style.html"><em>atom_style sphere</em></a>) and
 its radius is non-zero, its mass is set from the density and particle
 volume.  If the atom has a shape attribute (see <a class="reference internal" href="atom_style.html"><em>atom_style ellipsoid</em></a>) and its 3 shape parameters are non-zero,
 then its mass is set from the density and particle volume.  If the
 atom has a length attribute (see <a class="reference internal" href="atom_style.html"><em>atom_style line</em></a>)
 and its length is non-zero, then its mass is set from the density and
 line segment length (the input density is assumed to be in
 mass/distance units).  If the atom has an area attribute (see
 <a class="reference internal" href="atom_style.html"><em>atom_style tri</em></a>) and its area is non-zero, then its
 mass is set from the density and triangle area (the input density is
 assumed to be in mass/distance^2 units).  If none of these cases are
 valid, then the mass is set to the density value directly (the input
 density is assumed to be in mass units).</p>
 <p>Keyword <em>volume</em> sets the volume of all selected particles.
 Currently, only the <a class="reference internal" href="atom_style.html"><em>atom_style peri</em></a> command defines
 particles with a volume attribute.  Note that this command does not
 adjust the particle mass.</p>
 <p>Keyword <em>image</em> sets which image of the simulation box the atom is
 considered to be in.  An image of 0 means it is inside the box as
 defined.  A value of 2 means add 2 box lengths to get the true value.
 A value of -1 means subtract 1 box length to get the true value.
 LAMMPS updates these flags as atoms cross periodic boundaries during
 the simulation.  The flags can be output with atom snapshots via the
 <a class="reference internal" href="dump.html"><em>dump</em></a> command.  If a value of NULL is specified for any of
 nx,ny,nz, then the current image value for that dimension is
 unchanged.  For non-periodic dimensions only a value of 0 can be
 specified.  This keyword does not allow use of atom-style variables.</p>
 <p>This command can be useful after a system has been equilibrated and
 atoms have diffused one or more box lengths in various directions.
 This command can then reset the image values for atoms so that they
 are effectively inside the simulation box, e.g if a diffusion
 coefficient is about to be measured via the <a class="reference internal" href="compute_msd.html"><em>compute msd</em></a> command.  Care should be taken not to reset the
 image flags of two atoms in a bond to the same value if the bond
 straddles a periodic boundary (rather they should be different by +/-
 1).  This will not affect the dynamics of a simulation, but may mess
 up analysis of the trajectories if a LAMMPS diagnostic or your own
 analysis relies on the image flags to unwrap a molecule which
 straddles the periodic box.</p>
 <p>Keywords <em>bond</em>, <em>angle</em>, <em>dihedral</em>, and <em>improper</em>, set the bond
 type (angle type, etc) of all bonds (angles, etc) of selected atoms to
 the specified value from 1 to nbondtypes (nangletypes, etc).  All
 atoms in a particular bond (angle, etc) must be selected atoms in
 order for the change to be made.  The value of nbondtype (nangletypes,
 etc) was set by the <em>bond types</em> (<em>angle types</em>, etc) field in the
 header of the data file read by the <a class="reference internal" href="read_data.html"><em>read_data</em></a>
 command.  These keywords do not allow use of an atom-style variable.</p>
 <p>Keywords <em>meso_e</em>, <em>meso_cv</em>, and <em>meso_rho</em> set the energy, heat
 capacity, and density of smmothed particle hydrodynamics (SPH)
 particles.  See <a class="reference external" href="USER/sph/SPH_LAMMPS_userguide.pdf">this PDF guide</a> to
 using SPH in LAMMPS.</p>
 <p>Keywords <em>i_name</em> and <em>d_name</em> refer to custom integer and
 floating-point properties that have been added to each atom via the
 <a class="reference internal" href="fix_property_atom.html"><em>fix property/atom</em></a> command.  When that command
 is used specific names are given to each attribute which are what is
 specified as the &#8220;name&#8221; portion of <em>i_name</em> or <em>d_name</em>.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>You cannot set an atom attribute (e.g. <em>mol</em> or <em>q</em> or <em>volume</em>) if
 the <a class="reference internal" href="atom_style.html"><em>atom_style</em></a> does not have that attribute.</p>
 <p>This command requires inter-processor communication to coordinate the
 setting of bond types (angle types, etc).  This means that your system
 must be ready to perform a simulation before using one of these
 keywords (force fields set, atom mass set, etc).  This is not
 necessary for other keywords.</p>
 <p>Using the <em>region</em> style with the bond (angle, etc) keywords can give
 unpredictable results if there are bonds (angles, etc) that straddle
 periodic boundaries.  This is because the region may only extend up to
 the boundary and partner atoms in the bond (angle, etc) may have
 coordinates outside the simulation box if they are ghost atoms.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="create_box.html"><em>create_box</em></a>, <a class="reference internal" href="create_atoms.html"><em>create_atoms</em></a>,
 <a class="reference internal" href="read_data.html"><em>read_data</em></a></p>
 <p><strong>Default:</strong> none</p>
 </div>
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   <div class="section" id="shell-command">
 <span id="index-0"></span><h1>shell command<a class="headerlink" href="#shell-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>shell cmd args
 </pre></div>
 </div>
 <ul class="simple">
 <li>cmd = <em>cd</em> or <em>mkdir</em> or <em>mv</em> or <em>rm</em> or <em>rmdir</em> or <em>putenv</em> or arbitrary command</li>
 </ul>
 <pre class="literal-block">
 <em>cd</em> arg = dir
-    dir = directory to change to
-  <em>mkdir</em> args = dir1 dir2 ...
-    dir1,dir2 = one or more directories to create
-  <em>mv</em> args = old new
-    old = old filename
-    new = new filename
-  <em>rm</em> args = file1 file2 ...
-    file1,file2 = one or more filenames to delete
-  <em>rmdir</em> args = dir1 dir2 ...
-    dir1,dir2 = one or more directories to delete
-  <em>putenv</em> args = var1=value1 var2=value2
-    var=value = one of more definitions of environment variables
-  anything else is passed as a command to the shell for direct execution
+  dir = directory to change to
+<em>mkdir</em> args = dir1 dir2 ...
+  dir1,dir2 = one or more directories to create
+<em>mv</em> args = old new
+  old = old filename
+  new = new filename
+<em>rm</em> args = file1 file2 ...
+  file1,file2 = one or more filenames to delete
+<em>rmdir</em> args = dir1 dir2 ...
+  dir1,dir2 = one or more directories to delete
+<em>putenv</em> args = var1=value1 var2=value2
+  var=value = one of more definitions of environment variables
+anything else is passed as a command to the shell for direct execution
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>shell cd sub1
 shell cd ..
 shell mkdir tmp1 tmp2 tmp3
 shell rmdir tmp1
 shell mv log.lammps hold/log.1
 shell rm TMP/file1 TMP/file2
 shell putenv LAMMPS_POTENTIALS=../../potentials
 shell my_setup file1 10 file2
 shell my_post_process 100 dump.out
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Execute a shell command.  A few simple file-based shell commands are
 supported directly, in Unix-style syntax.  Any command not listed
 above is passed as-is to the C-library system() call, which invokes
 the command in a shell.</p>
 <p>This is means to invoke other commands from your input script.  For
 example, you can move files around in preparation for the next section
 of the input script.  Or you can run a program that pre-processes data
 for input into LAMMPS.  Or you can run a program that post-processes
 LAMMPS output data.</p>
 <p>With the exception of <em>cd</em>, all commands, including ones invoked via a
 system() call, are executed by only a single processor, so that
 files/directories are not being manipulated by multiple processors.</p>
 <p>The <em>cd</em> cmd executes the Unix &#8220;cd&#8221; command to change the working
 directory.  All subsequent LAMMPS commands that read/write files will
 use the new directory.  All processors execute this command.</p>
 <p>The <em>mkdir</em> cmd executes the Unix &#8220;mkdir&#8221; command to create one or
 more directories.</p>
 <p>The <em>mv</em> cmd executes the Unix &#8220;mv&#8221; command to rename a file and/or
 move it to a new directory.</p>
 <p>The <em>rm</em> cmd executes the Unix &#8220;rm&#8221; command to remove one or more
 files.</p>
 <p>The <em>rmdir</em> cmd executes the Unix &#8220;rmdir&#8221; command to remove one or
 more directories.  A directory must be empty to be successfully
 removed.</p>
 <p>The <em>putenv</em> cmd defines or updates an environment variable directly.
 Since this command does not pass through the shell, no shell variable
 expansion or globbing is performed, only the usual substitution for
 LAMMPS variables defined with the <a class="reference internal" href="variable.html"><em>variable</em></a> command is
 performed.  The resulting string is then used literally.</p>
 <p>Any other cmd is passed as-is to the shell along with its arguments as
 one string, invoked by the C-library system() call.  For example,
 these lines in your input script:</p>
 <div class="highlight-python"><div class="highlight"><pre>variable n equal 10
 variable foo string file2
 shell my_setup file1 $n ${foo}
 </pre></div>
 </div>
 <p>would be the same as invoking</p>
 <div class="highlight-python"><div class="highlight"><pre>% my_setup file1 10 file2
 </pre></div>
 </div>
 <p>from a command-line prompt.  The executable program &#8220;my_setup&#8221; is run
 with 3 arguments: file1 10 file2.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>LAMMPS does not detect errors or print warnings when any of these
 commands execute.  E.g. if the specified directory does not exist,
 executing the <em>cd</em> command will silently do nothing.</p>
 <p><strong>Related commands:</strong> none</p>
 <p><strong>Default:</strong> none</p>
 </div>
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   <div class="section" id="special-bonds-command">
 <span id="index-0"></span><h1>special_bonds command<a class="headerlink" href="#special-bonds-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>special_bonds keyword values ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>one or more keyword/value pairs may be appended</li>
 <li>keyword = <em>amber</em> or <em>charmm</em> or <em>dreiding</em> or <em>fene</em> or <em>lj/coul</em> or <em>lj</em> or <em>coul</em> or <em>angle</em> or <em>dihedral</em> or <em>extra</em></li>
 </ul>
 <pre class="literal-block">
 <em>amber</em> values = none
-  <em>charmm</em> values = none
-  <em>dreiding</em> values = none
-  <em>fene</em> values = none
-  <em>lj/coul</em> values = w1,w2,w3
-    w1,w2,w3 = weights (0.0 to 1.0) on pairwise Lennard-Jones and Coulombic interactions
-  <em>lj</em> values = w1,w2,w3
-    w1,w2,w3 = weights (0.0 to 1.0) on pairwise Lennard-Jones interactions
-  <em>coul</em> values = w1,w2,w3
-    w1,w2,w3 = weights (0.0 to 1.0) on pairwise Coulombic interactions
-  <em>angle</em> value = <em>yes</em> or <em>no</em>
-  <em>dihedral</em> value = <em>yes</em> or <em>no</em>
-  <em>extra</em> value = N
-    N = number of extra 1-2,1-3,1-4 interactions to save space for
+<em>charmm</em> values = none
+<em>dreiding</em> values = none
+<em>fene</em> values = none
+<em>lj/coul</em> values = w1,w2,w3
+  w1,w2,w3 = weights (0.0 to 1.0) on pairwise Lennard-Jones and Coulombic interactions
+<em>lj</em> values = w1,w2,w3
+  w1,w2,w3 = weights (0.0 to 1.0) on pairwise Lennard-Jones interactions
+<em>coul</em> values = w1,w2,w3
+  w1,w2,w3 = weights (0.0 to 1.0) on pairwise Coulombic interactions
+<em>angle</em> value = <em>yes</em> or <em>no</em>
+<em>dihedral</em> value = <em>yes</em> or <em>no</em>
+<em>extra</em> value = N
+  N = number of extra 1-2,1-3,1-4 interactions to save space for
 </pre>
 <p>Examples:</p>
 <div class="highlight-python"><div class="highlight"><pre>special_bonds amber
 special_bonds charmm
 special_bonds fene dihedral no
 special_bonds lj/coul 0.0 0.0 0.5 angle yes dihedral yes
 special_bonds lj 0.0 0.0 0.5 coul 0.0 0.0 0.0 dihedral yes
 special_bonds lj/coul 0 1 1 extra 2
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Set weighting coefficients for pairwise energy and force contributions
 between pairs of atoms that are also permanently bonded to each other,
 either directly or via one or two intermediate bonds.  These weighting
 factors are used by nearly all <a class="reference internal" href="pair_style.html"><em>pair styles</em></a> in LAMMPS
 that compute simple pairwise interactions.  Permanent bonds between
 atoms are specified by defining the bond topology in the data file
 read by the <a class="reference internal" href="read_data.html"><em>read_data</em></a> command.  Typically a
 <a class="reference internal" href="bond_style.html"><em>bond_style</em></a> command is also used to define a bond
 potential.  The rationale for using these weighting factors is that
 the interaction between a pair of bonded atoms is all (or mostly)
 specified by the bond, angle, dihedral potentials, and thus the
 non-bonded Lennard-Jones or Coulombic interaction between the pair of
 atoms should be excluded (or reduced by a weighting factor).</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">These weighting factors are NOT used by <a class="reference internal" href="pair_style.html"><em>pair styles</em></a> that compute many-body interactions, since the
 &#8220;bonds&#8221; that result from such interactions are not permanent, but are
 created and broken dynamically as atom conformations change.  Examples
 of pair styles in this category are EAM, MEAM, Stillinger-Weber,
 Tersoff, COMB, AIREBO, and ReaxFF.  In fact, it generally makes no
 sense to define permanent bonds between atoms that interact via these
 potentials, though such bonds may exist elsewhere in your system,
 e.g. when using the <a class="reference internal" href="pair_hybrid.html"><em>pair_style hybrid</em></a> command.
 Thus LAMMPS ignores special_bonds settings when manybody potentials
 are calculated.</p>
 </div>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">Unlike some commands in LAMMPS, you cannot use this
 command multiple times in an incremental fashion: e.g. to first set
 the LJ settings and then the Coulombic ones.  Each time you use this
 command it sets all the coefficients to default values and only
 overrides the one you specify, so you should set all the options you
 need each time you use it.  See more details at the bottom of this
 page.</p>
 </div>
 <p>The Coulomb factors are applied to any Coulomb (charge interaction)
 term that the potential calculates.  The LJ factors are applied to the
 remaining terms that the potential calculates, whether they represent
 LJ interactions or not.  The weighting factors are a scaling
 pre-factor on the energy and force between the pair of atoms.  A value
 of 1.0 means include the full interaction; a value of 0.0 means
 exclude it completely.</p>
 <p>The 1st of the 3 coefficients (LJ or Coulombic) is the weighting
 factor on 1-2 atom pairs, which are pairs of atoms directly bonded to
 each other.  The 2nd coefficient is the weighting factor on 1-3 atom
 pairs which are those separated by 2 bonds (e.g. the two H atoms in a
 water molecule).  The 3rd coefficient is the weighting factor on 1-4
 atom pairs which are those separated by 3 bonds (e.g. the 1st and 4th
 atoms in a dihedral interaction).  Thus if the 1-2 coefficient is set
 to 0.0, then the pairwise interaction is effectively turned off for
 all pairs of atoms bonded to each other.  If it is set to 1.0, then
 that interaction will be at full strength.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">For purposes of computing weighted pairwise
 interactions, 1-3 and 1-4 interactions are not defined from the list
 of angles or dihedrals used by the simulation.  Rather, they are
 inferred topologically from the set of bonds specified when the
 simulation is defined from a data or restart file (see
 <a class="reference internal" href="read_data.html"><em>read_data</em></a> or <a class="reference internal" href="read_restart.html"><em>read_restart</em></a>
 commands).  Thus the set of 1-2,1-3,1-4 interactions that the weights
 apply to is the same whether angle and dihedral potentials are
 computed or not, and remains the same even if bonds are constrained,
 or turned off, or removed during a simulation.</p>
 </div>
 <p>The two exceptions to this rule are (a) if the <em>angle</em> or <em>dihedral</em>
 keywords are set to <em>yes</em> (see below), or (b) if the
 <a class="reference internal" href="delete_bonds.html"><em>delete_bonds</em></a> command is used with the <em>special</em>
 option that recomputes the 1-2,1-3,1-4 topologies after bonds are
 deleted; see the <a class="reference internal" href="delete_bonds.html"><em>delete_bonds</em></a> command for more
 details.</p>
 <p>The <em>amber</em> keyword sets the 3 coefficients to 0.0, 0.0, 0.5 for LJ
 interactions and to 0.0, 0.0, 0.8333 for Coulombic interactions, which
 is the default for a commonly used version of the AMBER force field,
 where the last value is really 5/6.  See <a class="reference internal" href="#cornell"><span>(Cornell)</span></a> for a
 description of the AMBER force field.</p>
 <p>The <em>charmm</em> keyword sets the 3 coefficients to 0.0, 0.0, 0.0 for both
 LJ and Coulombic interactions, which is the default for a commonly
 used version of the CHARMM force field.  Note that in pair styles
 <em>lj/charmm/coul/charmm</em> and <em>lj/charmm/coul/long</em> the 1-4 coefficients
 are defined explicitly, and these pairwise contributions are computed
 as part of the charmm dihedral style - see the
 <a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a> and <a class="reference internal" href="dihedral_style.html"><em>dihedral_style</em></a>
 commands for more information.  See <a class="reference internal" href="#mackerell"><span>(MacKerell)</span></a> for a
 description of the CHARMM force field.</p>
 <p>The <em>dreiding</em> keyword sets the 3 coefficients to 0.0, 0.0, 1.0 for both
 LJ and Coulombic interactions, which is the default for the Dreiding
 force field, as discussed in <a class="reference internal" href="#mayo"><span>(Mayo)</span></a>.</p>
 <p>The <em>fene</em> keyword sets the 3 coefficients to 0.0, 1.0, 1.0 for both
 LJ and Coulombic interactions, which is consistent with a
 coarse-grained polymer model with <a class="reference internal" href="bond_fene.html"><em>FENE bonds</em></a>.  See
 <a class="reference internal" href="#kremer"><span>(Kremer)</span></a> for a description of FENE bonds.</p>
 <p>The <em>lj/coul</em>, <em>lj</em>, and <em>coul</em> keywords allow the 3 coefficients to
 be set explicitly.  The <em>lj/coul</em> keyword sets both the LJ and
 Coulombic coefficients to the same 3 values.  The <em>lj</em> and <em>coul</em>
 keywords only set either the LJ or Coulombic coefficients.  Use both
 of them if you wish to set the LJ coefficients to different values
 than the Coulombic coefficients.</p>
 <p>The <em>angle</em> keyword allows the 1-3 weighting factor to be ignored for
 individual atom pairs if they are not listed as the first and last
 atoms in any angle defined in the simulation or as 1,3 or 2,4 atoms in
 any dihedral defined in the simulation.  For example, imagine the 1-3
 weighting factor is set to 0.5 and you have a linear molecule with 4
 atoms and bonds as follows: 1-2-3-4.  If your data file defines 1-2-3
 as an angle, but does not define 2-3-4 as an angle or 1-2-3-4 as a
 dihedral, then the pairwise interaction between atoms 1 and 3 will
 always be weighted by 0.5, but different force fields use different
 rules for weighting the pairwise interaction between atoms 2 and 4.
 If the <em>angle</em> keyword is specified as <em>yes</em>, then the pairwise
 interaction between atoms 2 and 4 will be unaffected (full weighting
 of 1.0).  If the <em>angle</em> keyword is specified as <em>no</em> which is the
 default, then the 2,4 interaction will also be weighted by 0.5.</p>
 <p>The <em>dihedral</em> keyword allows the 1-4 weighting factor to be ignored
 for individual atom pairs if they are not listed as the first and last
 atoms in any dihedral defined in the simulation.  For example, imagine
 the 1-4 weighting factor is set to 0.5 and you have a linear molecule
 with 5 atoms and bonds as follows: 1-2-3-4-5.  If your data file
 defines 1-2-3-4 as a dihedral, but does not define 2-3-4-5 as a
 dihedral, then the pairwise interaction between atoms 1 and 4 will
 always be weighted by 0.5, but different force fields use different
 rules for weighting the pairwise interaction between atoms 2 and 5.
 If the <em>dihedral</em> keyword is specified as <em>yes</em>, then the pairwise
 interaction between atoms 2 and 5 will be unaffected (full weighting
 of 1.0).  If the <em>dihedral</em> keyword is specified as <em>no</em> which is the
 default, then the 2,5 interaction will also be weighted by 0.5.</p>
 <p>The <em>extra</em> keyword can be used when additional bonds will be created
 during a simulation run, e.g. by the <a class="reference internal" href="fix_bond_create.html"><em>fix bond/create</em></a> command.  It can also be used if
 molecules will be added to the system, e.g. via the <a class="reference internal" href="fix_deposit.html"><em>fix deposit</em></a>, or <a class="reference internal" href="fix_pour.html"><em>fix pour</em></a> commands, which
 will have atoms with more special neighbors than any atom in the
 current system has.</p>
 <hr class="docutils" />
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">LAMMPS stores and maintains a data structure with a
 list of the 1st, 2nd, and 3rd neighbors of each atom (within the bond
 topology of the system).  If new bonds are created (or molecules added
 containing atoms with more special neighbors), the size of this list
 needs to grow.  Note that adding a single bond always adds a new 1st
 neighbor but may also induce <em>many</em> new 2nd and 3rd neighbors,
 depending on the molecular topology of your system.  Using the <em>extra</em>
 keyword leaves empty space in the list for this N additional 1st, 2nd,
 or 3rd neighbors to be added.  If you do not do this, you may get an
 error when bonds (or molecules) are added.</p>
 </div>
 <hr class="docutils" />
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">If you reuse this command in an input script, you
 should set all the options you need each time.  This command cannot be
 used a 2nd time incrementally, e.g. to add some extra storage
 locations via the <em>extra</em> keyword.  E.g. these two commands:</p>
 </div>
 <p>special_bonds lj 0.0 1.0 1.0
 special_bonds coul 0.0 0.0 1.0</p>
 <p>are not the same as</p>
 <p>special_bonds lj 0.0 1.0 1.0 coul 0.0 0.0 1.0</p>
 <p>In the first case you end up with (after the 2nd command):</p>
 <p>LJ: 0.0 0.0 0.0
 Coul: coul 0.0 0.0 1.0</p>
 <p>because the LJ settings are reset to their default values
 each time the command is issued.</p>
 <p>Likewise</p>
 <div class="highlight-python"><div class="highlight"><pre>special_bonds amber
 special_bonds extra 2
 </pre></div>
 </div>
 <p>is not the same as this single command:</p>
 <div class="highlight-python"><div class="highlight"><pre>special_bonds amber extra 2
 </pre></div>
 </div>
 <p>since in the former case, the 2nd command will reset all the LJ and
 Coulombic weights to 0.0 (the default).</p>
 <p>One exception to this rule is the <em>extra</em> option itself.  It is not
 reset to its default value of 0 each time the special_bonds command is
 invoked.  This is because it can also be set by the
 <a class="reference internal" href="read_data.html"><em>read_data</em></a> and <a class="reference internal" href="create_box.html"><em>create_box</em></a> commands,
 so this command will not override those settings unless you explicitly
 use <em>extra</em> as an option.</p>
 </div>
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <blockquote>
 <div>none</div></blockquote>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="delete_bonds.html"><em>delete_bonds</em></a>, <a class="reference internal" href="fix_bond_create.html"><em>fix bond/create</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>All 3 Lennard-Jones and 3 Coulombic weighting coefficients = 0.0,
 angle = no, dihedral = no, and extra = 0.</p>
 <hr class="docutils" />
 <p id="cornell"><strong>(Cornell)</strong> Cornell, Cieplak, Bayly, Gould, Merz, Ferguson,
 Spellmeyer, Fox, Caldwell, Kollman, JACS 117, 5179-5197 (1995).</p>
 <p id="kremer"><strong>(Kremer)</strong> Kremer, Grest, J Chem Phys, 92, 5057 (1990).</p>
 <p id="mackerell"><strong>(MacKerell)</strong> MacKerell, Bashford, Bellott, Dunbrack, Evanseck, Field,
 Fischer, Gao, Guo, Ha, et al, J Phys Chem, 102, 3586 (1998).</p>
 <p id="mayo"><strong>(Mayo)</strong> Mayo, Olfason, Goddard III, J Phys Chem, 94, 8897-8909
 (1990).</p>
 </div>
 </div>
 
 
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   <div class="section" id="tad-command">
 <span id="index-0"></span><h1>tad command<a class="headerlink" href="#tad-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>tad N t_event T_lo T_hi delta tmax compute-ID keyword value ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>N = # of timesteps to run (not including dephasing/quenching)</li>
 <li>t_event = timestep interval between event checks</li>
 <li>T_lo = temperature at which event times are desired</li>
 <li>T_hi = temperature at which MD simulation is performed</li>
 <li>delta = desired confidence level for stopping criterion</li>
 <li>tmax = reciprocal of lowest expected preexponential factor (time units)</li>
 <li>compute-ID = ID of the compute used for event detection</li>
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>min</em> or <em>neb</em> or <em>min_style</em> or <em>neb_style</em> or <em>neb_log</em></li>
 </ul>
 <pre class="literal-block">
 <em>min</em> values = etol ftol maxiter maxeval
-    etol = stopping tolerance for energy (energy units)
-    ftol = stopping tolerance for force (force units)
-    maxiter = max iterations of minimize
-    maxeval = max number of force/energy evaluations
-  <em>neb</em> values = ftol N1 N2 Nevery
-    etol = stopping tolerance for energy (energy units)
-    ftol = stopping tolerance for force (force units)
-    N1 = max # of iterations (timesteps) to run initial NEB
-    N2 = max # of iterations (timesteps) to run barrier-climbing NEB
-    Nevery = print NEB statistics every this many timesteps
-  <em>neb_style</em> value = <em>quickmin</em> or <em>fire</em>
-  <em>neb_step</em> value = dtneb
-    dtneb = timestep for NEB damped dynamics minimization
-  <em>neb_log</em> value = file where NEB statistics are printed
+  etol = stopping tolerance for energy (energy units)
+  ftol = stopping tolerance for force (force units)
+  maxiter = max iterations of minimize
+  maxeval = max number of force/energy evaluations
+<em>neb</em> values = ftol N1 N2 Nevery
+  etol = stopping tolerance for energy (energy units)
+  ftol = stopping tolerance for force (force units)
+  N1 = max # of iterations (timesteps) to run initial NEB
+  N2 = max # of iterations (timesteps) to run barrier-climbing NEB
+  Nevery = print NEB statistics every this many timesteps
+<em>neb_style</em> value = <em>quickmin</em> or <em>fire</em>
+<em>neb_step</em> value = dtneb
+  dtneb = timestep for NEB damped dynamics minimization
+<em>neb_log</em> value = file where NEB statistics are printed
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>tad 2000 50 1800 2300 0.01 0.01 event
 tad 2000 50 1800 2300 0.01 0.01 event &amp;
     min 1e-05 1e-05 100 100 &amp;
     neb 0.0 0.01 200 200 20 &amp;
     min_style cg &amp;
     neb_style fire &amp;
     neb_log log.neb
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Run a temperature accelerated dynamics (TAD) simulation. This method
 requires two or more partitions to perform NEB transition state
 searches.</p>
 <p>TAD is described in <a class="reference internal" href="#voter"><span>this paper</span></a> by Art Voter.  It is a method
 that uses accelerated dynamics at an elevated temperature to generate
 results at a specified lower temperature.  A good overview of
 accelerated dynamics methods for such systems is given in <a class="reference internal" href="#voter2"><span>this review paper</span></a> from the same group. In general, these methods assume
 that the long-time dynamics is dominated by infrequent events i.e. the
 system is is confined to low energy basins for long periods,
 punctuated by brief, randomly-occurring transitions to adjacent
 basins.  TAD is suitable for infrequent-event systems, where in
 addition, the transition kinetics are well-approximated by harmonic
 transition state theory (hTST). In hTST, the temperature dependence of
 transition rates follows the Arrhenius relation.  As a consequence a
 set of event times generated in a high-temperature simulation can be
 mapped to a set of much longer estimated times in the low-temperature
 system. However, because this mapping involves the energy barrier of
 the transition event, which is different for each event, the first
 event at the high temperature may not be the earliest event at the low
 temperature. TAD handles this by first generating a set of possible
 events from the current basin. After each event, the simulation is
 reflected backwards into the current basin.  This is repeated until
 the stopping criterion is satisfied, at which point the event with the
 earliest low-temperature occurrence time is selected.  The stopping
 criterion is that the confidence measure be greater than
 1-<em>delta</em>. The confidence measure is the probability that no earlier
 low-temperature event will occur at some later time in the
 high-temperature simulation.  hTST provides an lower bound for this
 probability, based on the user-specified minimum pre-exponential
 factor (reciprocal of <em>tmax</em>).</p>
 <p>In order to estimate the energy barrier for each event, the TAD method
 invokes the <a class="reference internal" href="neb.html"><em>NEB</em></a> method. Each NEB replica runs on a
 partition of processors. The current NEB implementation in LAMMPS
 restricts you to having exactly one processor per replica. For more
 information, see the documentation for the <a class="reference internal" href="neb.html"><em>neb</em></a> command.  In
 the current LAMMPS implementation of TAD, all the non-NEB TAD
 operations are performed on the first partition, while the other
 partitions remain idle. See <a class="reference internal" href="Section_howto.html#howto-5"><span>Section_howto 5</span></a> of the manual for further discussion of
 multi-replica simulations.</p>
 <p>A TAD run has several stages, which are repeated each time an event is
 performed.  The logic for a TAD run is as follows:</p>
 <div class="highlight-python"><div class="highlight"><pre>while (time remains):
   while (time &lt; tstop):
     until (event occurs):
       run dynamics for t_event steps
       quench
     run neb calculation using all replicas
     compute tlo from energy barrier
     update earliest event
     update tstop
     reflect back into current basin
   execute earliest event
 </pre></div>
 </div>
 <p>Before this outer loop begins, the initial potential energy basin is
 identified by quenching (an energy minimization, see below) the
 initial state and storing the resulting coordinates for reference.</p>
 <p>Inside the inner loop, dynamics is run continuously according to
 whatever integrator has been specified by the user, stopping every
 <em>t_event</em> steps to check if a transition event has occurred.  This
 check is performed by quenching the system and comparing the resulting
 atom coordinates to the coordinates from the previous basin.</p>
 <p>A quench is an energy minimization and is performed by whichever
 algorithm has been defined by the <a class="reference internal" href="min_style.html"><em>min_style</em></a> command;
 its default is the CG minimizer.  The tolerances and limits for each
 quench can be set by the <em>min</em> keyword.  Note that typically, you do
 not need to perform a highly-converged minimization to detect a
 transition event.</p>
 <p>The event check is performed by a compute with the specified
 <em>compute-ID</em>.  Currently there is only one compute that works with the
 TAD commmand, which is the <a class="reference internal" href="compute_event_displace.html"><em>compute event/displace</em></a> command.  Other
 event-checking computes may be added.  <a class="reference internal" href="compute_event_displace.html"><em>Compute event/displace</em></a> checks whether any atom in
 the compute group has moved further than a specified threshold
 distance.  If so, an &#8220;event&#8221; has occurred.</p>
 <p>The NEB calculation is similar to that invoked by the <a class="reference internal" href="neb.html"><em>neb</em></a>
 command, except that the final state is generated internally, instead
 of being read in from a file.  The style of minimization performed by
 NEB is determined by the <em>neb_style</em> keyword and must be a damped
 dynamics minimizer.  The tolerances and limits for each NEB
 calculation can be set by the <em>neb</em> keyword.  As discussed on the
 <a class="reference internal" href="neb.html"><em>neb</em></a>, it is often advantageous to use a larger timestep for
 NEB than for normal dyanmics.  Since the size of the timestep set by
 the <a class="reference internal" href="timestep.html"><em>timestep</em></a> command is used by TAD for performing
 dynamics, there is a <em>neb_step</em> keyword which can be used to set a
 larger timestep for each NEB calculation if desired.</p>
 <hr class="docutils" />
 <p>A key aspect of the TAD method is setting the stopping criterion
 appropriately.  If this criterion is too conservative, then many
 events must be generated before one is finally executed.  Conversely,
 if this criterion is too aggressive, high-entropy high-barrier events
 will be over-sampled, while low-entropy low-barrier events will be
 under-sampled. If the lowest pre-exponential factor is known fairly
 accurately, then it can be used to estimate <em>tmax</em>, and the value of
 <em>delta</em> can be set to the desired confidence level e.g. <em>delta</em> = 0.05
 corresponds to 95% confidence. However, for systems where the dynamics
 are not well characterized (the most common case), it will be
 necessary to experiment with the values of <em>delta</em> and <em>tmax</em> to get a
 good trade-off between accuracy and performance.</p>
 <p>A second key aspect is the choice of <em>t_hi</em>. A larger value greatly
 increases the rate at which new events are generated.  However, too
 large a value introduces errors due to anharmonicity (not accounted
 for within hTST). Once again, for any given system, experimentation is
 necessary to determine the best value of <em>t_hi</em>.</p>
 <hr class="docutils" />
 <p>Five kinds of output can be generated during a TAD run: event
 statistics, NEB statistics, thermodynamic output by each replica, dump
 files, and restart files.</p>
 <p>Event statistics are printed to the screen and master log.lammps file
 each time an event is executed. The quantities are the timestep, CPU
 time, global event number <em>N</em>, local event number <em>M</em>, event status,
 energy barrier, time margin, <em>t_lo</em> and <em>delt_lo</em>.  The timestep is
 the usual LAMMPS timestep, which corresponds to the high-temperature
 time at which the event was detected, in units of timestep.  The CPU
 time is the total processor time since the start of the TAD run.  The
 global event number <em>N</em> is a counter that increments with each
 executed event. The local event number <em>M</em> is a counter that resets to
 zero upon entering each new basin.  The event status is <em>E</em> when an
 event is executed, and is <em>D</em> for an event that is detected, while
 <em>DF</em> is for a detected event that is also the earliest (first) event
 at the low temperature.</p>
 <p>The time margin is the ratio of the high temperature time in the
 current basin to the stopping time. This last number can be used to
 judge whether the stopping time is too short or too long (see above).</p>
 <p><em>t_lo</em> is the low-temperature event time when the current basin was
 entered, in units of timestep.  del*t_lo* is the time of each detected
 event, measured relative to <em>t_lo</em>.  <em>delt_lo</em> is equal to the
 high-temperature time since entering the current basin, scaled by an
 exponential factor that depends on the hi/lo temperature ratio and the
 energy barrier for that event.</p>
 <p>On lines for executed events, with status <em>E</em>, the global event number
 is incremented by one,
 the local event number and time margin are reset to zero,
 while the global event number, energy barrier, and
 <em>delt_lo</em> match the last event with status <em>DF</em>
 in the immediately preceding block of detected events.
 The low-temperature event time <em>t_lo</em> is incremented by <em>delt_lo</em>.</p>
 <p>NEB statistics are written to the file specified by the <em>neb_log</em>
 keyword. If the keyword value is &#8220;none&#8221;, then no NEB statistics are
 printed out. The statistics are written every <em>Nevery</em> timesteps.  See
 the <a class="reference internal" href="neb.html"><em>neb</em></a> command for a full description of the NEB
 statistics. When invoked from TAD, NEB statistics are never printed to
 the screen.</p>
 <p>Because the NEB calculation must run on multiple partitions, LAMMPS
 produces additional screen and log files for each partition,
 e.g. log.lammps.0, log.lammps.1, etc. For the TAD command, these
 contain the thermodynamic output of each NEB replica. In addition, the
 log file for the first partition, log.lammps.0, will contain
 thermodynamic output from short runs and minimizations corresponding
 to the dynamics and quench operations, as well as a line for each new
 detected event, as described above.</p>
 <p>After the TAD command completes, timing statistics for the TAD run are
 printed in each replica&#8217;s log file, giving a breakdown of how much CPU
 time was spent in each stage (NEB, dynamics, quenching, etc).</p>
 <p>Any <a class="reference internal" href="dump.html"><em>dump files</em></a> defined in the input script will be written
 to during a TAD run at timesteps when an event is executed.  This
 means the the requested dump frequency in the <a class="reference internal" href="dump.html"><em>dump</em></a> command
 is ignored.  There will be one dump file (per dump command) created
 for all partitions.  The atom coordinates of the dump snapshot are
 those of the minimum energy configuration resulting from quenching
 following the executed event.  The timesteps written into the dump
 files correspond to the timestep at which the event occurred and NOT
 the clock.  A dump snapshot corresponding to the initial minimum state
 used for event detection is written to the dump file at the beginning
 of each TAD run.</p>
 <p>If the <a class="reference internal" href="restart.html"><em>restart</em></a> command is used, a single restart file
 for all the partitions is generated, which allows a TAD run to be
 continued by a new input script in the usual manner.  The restart file
 is generated after an event is executed. The restart file contains a
 snapshot of the system in the new quenched state, including the event
 number and the low-temperature time.  The restart frequency specified
 in the <a class="reference internal" href="restart.html"><em>restart</em></a> command is interpreted differently when
 performing a TAD run.  It does not mean the timestep interval between
 restart files.  Instead it means an event interval for executed
 events.  Thus a frequency of 1 means write a restart file every time
 an event is executed.  A frequency of 10 means write a restart file
 every 10th executed event.  When an input script reads a restart file
 from a previous TAD run, the new script can be run on a different
 number of replicas or processors.</p>
 <p>Note that within a single state, the dynamics will typically
 temporarily continue beyond the event that is ultimately chosen, until
 the stopping criterionis satisfied.  When the event is eventually
 executed, the timestep counter is reset to the value when the event
 was detected. Similarly, after each quench and NEB minimization, the
 timestep counter is reset to the value at the start of the
 minimization. This means that the timesteps listed in the replica log
 files do not always increase monotonically. However, the timestep
 values printed to the master log file, dump files, and restart files
 are always monotonically increasing.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>This command can only be used if LAMMPS was built with the REPLICA
 package.  See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section
 for more info on packages.</p>
 <p><em>N</em> setting must be integer multiple of <em>t_event</em>.</p>
 <p>Runs restarted from restart files written during a TAD run will only
 produce identical results if the user-specified integrator supports
 exact restarts. So <a class="reference internal" href="fix_nh.html"><em>fix nvt</em></a> will produce an exact
 restart, but <a class="reference internal" href="fix_langevin.html"><em>fix langevin</em></a> will not.</p>
 <p>This command cannot be used when any fixes are defined that keep track
 of elapsed time to perform time-dependent operations.  Examples
 include the &#8220;ave&#8221; fixes such as <a class="reference internal" href="fix_ave_spatial.html"><em>fix ave/spatial</em></a>.  Also <a class="reference internal" href="fix_dt_reset.html"><em>fix dt/reset</em></a> and <a class="reference internal" href="fix_deposit.html"><em>fix deposit</em></a>.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="compute_event_displace.html"><em>compute event/displace</em></a>,
 <a class="reference internal" href="min_modify.html"><em>min_modify</em></a>, <a class="reference internal" href="min_style.html"><em>min_style</em></a>,
 <a class="reference internal" href="run_style.html"><em>run_style</em></a>, <a class="reference internal" href="minimize.html"><em>minimize</em></a>,
 <a class="reference internal" href="temper.html"><em>temper</em></a>, <a class="reference internal" href="neb.html"><em>neb</em></a>,
 <a class="reference internal" href="prd.html"><em>prd</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The option defaults are <em>min</em> = 0.1 0.1 40 50, <em>neb</em> = 0.01 100 100
 10, <em>neb_style</em> = <em>quickmin</em>, <em>neb_step</em> = the same timestep set by
 the <a class="reference internal" href="timestep.html"><em>timestep</em></a> command, and <em>neb_log</em> = &#8220;none&#8221;.</p>
 <hr class="docutils" />
 <p id="voter"><strong>(Voter)</strong> Sorensen and Voter, J Chem Phys, 112, 9599 (2000)</p>
 <p id="voter2"><strong>(Voter2)</strong> Voter, Montalenti, Germann, Annual Review of Materials
 Research 32, 321 (2002).</p>
 </div>
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   <div class="section" id="thermo-style-command">
 <span id="index-0"></span><h1>thermo_style command<a class="headerlink" href="#thermo-style-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>thermo_style style args
 </pre></div>
 </div>
 <ul class="simple">
 <li>style = <em>one</em> or <em>multi</em> or <em>custom</em></li>
 <li>args = list of arguments for a particular style</li>
 </ul>
 <pre class="literal-block">
 <em>one</em> args = none
-  <em>multi</em> args = none
-  <em>custom</em> args = list of keywords
-    possible keywords = step, elapsed, elaplong, dt, time,
-                        cpu, tpcpu, spcpu, cpuremain, part,
-                        atoms, temp, press, pe, ke, etotal, enthalpy,
-                        evdwl, ecoul, epair, ebond, eangle, edihed, eimp,
-                        emol, elong, etail,
-                        vol, density, lx, ly, lz, xlo, xhi, ylo, yhi, zlo, zhi,
-                     xy, xz, yz, xlat, ylat, zlat,
-                        bonds, angles, dihedrals, impropers,
-                     pxx, pyy, pzz, pxy, pxz, pyz,
-                     fmax, fnorm, nbuild, ndanger,
-                     cella, cellb, cellc, cellalpha, cellbeta, cellgamma,
-                     c_ID, c_ID[I], c_ID[I][J],
-                        f_ID, f_ID[I], f_ID[I][J],
-                        v_name
-      step = timestep
-      elapsed = timesteps since start of this run
-      elaplong = timesteps since start of initial run in a series of runs
-      dt = timestep size
-      time = simulation time
-      cpu = elapsed CPU time in seconds
-      tpcpu = time per CPU second
-      spcpu = timesteps per CPU second
-      cpuremain = estimated CPU time remaining in run
-      part = which partition (0 to Npartition-1) this is
-      atoms = # of atoms
-      temp = temperature
-      press = pressure
-      pe = total potential energy
-      ke = kinetic energy
-      etotal = total energy (pe + ke)
-      enthalpy = enthalpy (etotal + press*vol)
-      evdwl = VanderWaal pairwise energy
-      ecoul = Coulombic pairwise energy
-      epair = pairwise energy (evdwl + ecoul + elong + etail)
-      ebond = bond energy
-      eangle = angle energy
-      edihed = dihedral energy
-      eimp = improper energy
-      emol = molecular energy (ebond + eangle + edihed + eimp)
-      elong = long-range kspace energy
-      etail = VanderWaal energy long-range tail correction
-      vol = volume
-      density = mass density of system
-      lx,ly,lz = box lengths in x,y,z
-      xlo,xhi,ylo,yhi,zlo,zhi = box boundaries
-      xy,xz,yz = box tilt for triclinic (non-orthogonal) simulation boxes
-      xlat,ylat,zlat = lattice spacings as calculated by <a class="reference internal" href="lattice.html"><em>lattice</em></a> command
-      bonds,angles,dihedrals,impropers = # of these interactions defined
-      pxx,pyy,pzz,pxy,pxz,pyz = 6 components of pressure tensor
-      fmax = max component of force on any atom in any dimension
-      fnorm = length of force vector for all atoms
-      nbuild = # of neighbor list builds
-      ndanger = # of dangerous neighbor list builds
-      cella,cellb,cellc = periodic cell lattice constants a,b,c
-      cellalpha, cellbeta, cellgamma = periodic cell angles alpha,beta,gamma
-      c_ID = global scalar value calculated by a compute with ID
-      c_ID[I] = Ith component of global vector calculated by a compute with ID
-      c_ID[I][J] = I,J component of global array calculated by a compute with ID
-      f_ID = global scalar value calculated by a fix with ID
-      f_ID[I] = Ith component of global vector calculated by a fix with ID
-      f_ID[I][J] = I,J component of global array calculated by a fix with ID
-      v_name = scalar value calculated by an equal-style variable with name
+<em>multi</em> args = none
+<em>custom</em> args = list of keywords
+  possible keywords = step, elapsed, elaplong, dt, time,
+                      cpu, tpcpu, spcpu, cpuremain, part,
+                      atoms, temp, press, pe, ke, etotal, enthalpy,
+                      evdwl, ecoul, epair, ebond, eangle, edihed, eimp,
+                      emol, elong, etail,
+                      vol, density, lx, ly, lz, xlo, xhi, ylo, yhi, zlo, zhi,
+                   xy, xz, yz, xlat, ylat, zlat,
+                      bonds, angles, dihedrals, impropers,
+                   pxx, pyy, pzz, pxy, pxz, pyz,
+                   fmax, fnorm, nbuild, ndanger,
+                   cella, cellb, cellc, cellalpha, cellbeta, cellgamma,
+                   c_ID, c_ID[I], c_ID[I][J],
+                      f_ID, f_ID[I], f_ID[I][J],
+                      v_name
+    step = timestep
+    elapsed = timesteps since start of this run
+    elaplong = timesteps since start of initial run in a series of runs
+    dt = timestep size
+    time = simulation time
+    cpu = elapsed CPU time in seconds
+    tpcpu = time per CPU second
+    spcpu = timesteps per CPU second
+    cpuremain = estimated CPU time remaining in run
+    part = which partition (0 to Npartition-1) this is
+    atoms = # of atoms
+    temp = temperature
+    press = pressure
+    pe = total potential energy
+    ke = kinetic energy
+    etotal = total energy (pe + ke)
+    enthalpy = enthalpy (etotal + press*vol)
+    evdwl = VanderWaal pairwise energy
+    ecoul = Coulombic pairwise energy
+    epair = pairwise energy (evdwl + ecoul + elong + etail)
+    ebond = bond energy
+    eangle = angle energy
+    edihed = dihedral energy
+    eimp = improper energy
+    emol = molecular energy (ebond + eangle + edihed + eimp)
+    elong = long-range kspace energy
+    etail = VanderWaal energy long-range tail correction
+    vol = volume
+    density = mass density of system
+    lx,ly,lz = box lengths in x,y,z
+    xlo,xhi,ylo,yhi,zlo,zhi = box boundaries
+    xy,xz,yz = box tilt for triclinic (non-orthogonal) simulation boxes
+    xlat,ylat,zlat = lattice spacings as calculated by <a class="reference internal" href="lattice.html"><em>lattice</em></a> command
+    bonds,angles,dihedrals,impropers = # of these interactions defined
+    pxx,pyy,pzz,pxy,pxz,pyz = 6 components of pressure tensor
+    fmax = max component of force on any atom in any dimension
+    fnorm = length of force vector for all atoms
+    nbuild = # of neighbor list builds
+    ndanger = # of dangerous neighbor list builds
+    cella,cellb,cellc = periodic cell lattice constants a,b,c
+    cellalpha, cellbeta, cellgamma = periodic cell angles alpha,beta,gamma
+    c_ID = global scalar value calculated by a compute with ID
+    c_ID[I] = Ith component of global vector calculated by a compute with ID
+    c_ID[I][J] = I,J component of global array calculated by a compute with ID
+    f_ID = global scalar value calculated by a fix with ID
+    f_ID[I] = Ith component of global vector calculated by a fix with ID
+    f_ID[I][J] = I,J component of global array calculated by a fix with ID
+    v_name = scalar value calculated by an equal-style variable with name
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>thermo_style multi
 thermo_style custom step temp pe etotal press vol
 thermo_style custom step temp etotal c_myTemp v_abc
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Set the style and content for printing thermodynamic data to the
 screen and log file.</p>
 <p>Style <em>one</em> prints a one-line summary of thermodynamic info that is
 the equivalent of &#8220;thermo_style custom step temp epair emol etotal
 press&#8221;.  The line contains only numeric values.</p>
 <p>Style <em>multi</em> prints a multiple-line listing of thermodynamic info
 that is the equivalent of &#8220;thermo_style custom etotal ke temp pe ebond
 eangle edihed eimp evdwl ecoul elong press&#8221;.  The listing contains
 numeric values and a string ID for each quantity.</p>
 <p>Style <em>custom</em> is the most general setting and allows you to specify
 which of the keywords listed above you want printed on each
 thermodynamic timestep.  Note that the keywords c_ID, f_ID, v_name are
 references to <a class="reference internal" href="compute.html"><em>computes</em></a>, <a class="reference internal" href="fix.html"><em>fixes</em></a>, and
 equal-style <a class="reference external" href="variable.html&quot;">variables</a> that have been defined
 elsewhere in the input script or can even be new styles which users
 have added to LAMMPS (see the <a class="reference internal" href="Section_modify.html"><em>Section_modify</em></a>
 section of the documentation).  Thus the <em>custom</em> style provides a
 flexible means of outputting essentially any desired quantity as a
 simulation proceeds.</p>
 <p>All styles except <em>custom</em> have <em>vol</em> appended to their list of
 outputs if the simulation box volume changes during the simulation.</p>
 <p>The values printed by the various keywords are instantaneous values,
 calculated on the current timestep.  Time-averaged quantities, which
 include values from previous timesteps, can be output by using the
 f_ID keyword and accessing a fix that does time-averaging such as the
 <a class="reference internal" href="fix_ave_time.html"><em>fix ave/time</em></a> command.</p>
 <p>Options invoked by the <a class="reference internal" href="thermo_modify.html"><em>thermo_modify</em></a> command can
 be used to set the one- or multi-line format of the print-out, the
 normalization of thermodynamic output (total values versus per-atom
 values for extensive quantities (ones which scale with the number of
 atoms in the system), and the numeric precision of each printed value.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">When you use a &#8220;thermo_style&#8221; command, all
 thermodynamic settings are restored to their default values, including
 those previously set by a <a class="reference internal" href="thermo_modify.html"><em>thermo_modify</em></a> command.
 Thus if your input script specifies a thermo_style command, you should
 use the thermo_modify command after it.</p>
 </div>
 <hr class="docutils" />
 <p>Several of the thermodynamic quantities require a temperature to be
 computed: &#8220;temp&#8221;, &#8220;press&#8221;, &#8220;ke&#8221;, &#8220;etotal&#8221;, &#8220;enthalpy&#8221;, &#8220;pxx&#8221;, etc.  By
 default this is done by using a <em>temperature</em> compute which is created
 when LAMMPS starts up, as if this command had been issued:</p>
 <div class="highlight-python"><div class="highlight"><pre>compute thermo_temp all temp
 </pre></div>
 </div>
 <p>See the <a class="reference internal" href="compute_temp.html"><em>compute temp</em></a> command for details.  Note
 that the ID of this compute is <em>thermo_temp</em> and the group is <em>all</em>.
 You can change the attributes of this temperature (e.g. its
 degrees-of-freedom) via the <a class="reference internal" href="compute_modify.html"><em>compute_modify</em></a>
 command.  Alternatively, you can directly assign a new compute (that
 calculates temperature) which you have defined, to be used for
 calculating any thermodynamic quantity that requires a temperature.
 This is done via the <a class="reference internal" href="thermo_modify.html"><em>thermo_modify</em></a> command.</p>
 <p>Several of the thermodynamic quantities require a pressure to be
 computed: &#8220;press&#8221;, &#8220;enthalpy&#8221;, &#8220;pxx&#8221;, etc.  By default this is done by
 using a <em>pressure</em> compute which is created when LAMMPS starts up, as
 if this command had been issued:</p>
 <div class="highlight-python"><div class="highlight"><pre>compute thermo_press all pressure thermo_temp
 </pre></div>
 </div>
 <p>See the <a class="reference internal" href="compute_pressure.html"><em>compute pressure</em></a> command for details.
 Note that the ID of this compute is <em>thermo_press</em> and the group is
 <em>all</em>.  You can change the attributes of this pressure via the
 <a class="reference internal" href="compute_modify.html"><em>compute_modify</em></a> command.  Alternatively, you can
 directly assign a new compute (that calculates pressure) which you
 have defined, to be used for calculating any thermodynamic quantity
 that requires a pressure.  This is done via the
 <a class="reference internal" href="thermo_modify.html"><em>thermo_modify</em></a> command.</p>
 <p>Several of the thermodynamic quantities require a potential energy to
 be computed: &#8220;pe&#8221;, &#8220;etotal&#8221;, &#8220;ebond&#8221;, etc.  This is done by using a
 <em>pe</em> compute which is created when LAMMPS starts up, as if this
 command had been issued:</p>
 <div class="highlight-python"><div class="highlight"><pre>compute thermo_pe all pe
 </pre></div>
 </div>
 <p>See the <a class="reference internal" href="compute_pe.html"><em>compute pe</em></a> command for details.  Note that
 the ID of this compute is <em>thermo_pe</em> and the group is <em>all</em>.  You can
 change the attributes of this potential energy via the
 <a class="reference internal" href="compute_modify.html"><em>compute_modify</em></a> command.</p>
 <hr class="docutils" />
 <p>The kinetic energy of the system <em>ke</em> is inferred from the temperature
 of the system with 1/2 Kb T of energy for each degree of freedom.
 Thus, using different <a class="reference internal" href="compute.html"><em>compute commands</em></a> for calculating
 temperature, via the <a class="reference internal" href="thermo_modify.html"><em>thermo_modify temp</em></a> command,
 may yield different kinetic energies, since different computes that
 calculate temperature can subtract out different non-thermal
 components of velocity and/or include different degrees of freedom
 (translational, rotational, etc).</p>
 <p>The potential energy of the system <em>pe</em> will include contributions
 from fixes if the <a class="reference internal" href="fix_modify.html"><em>fix_modify thermo</em></a> option is set
 for a fix that calculates such a contribution.  For example, the <a class="reference internal" href="fix_wall.html"><em>fix wall/lj93</em></a> fix calculates the energy of atoms
 interacting with the wall.  See the doc pages for &#8220;individual fixes&#8221;
 to see which ones contribute.</p>
 <p>A long-range tail correction <em>etail</em> for the VanderWaal pairwise
 energy will be non-zero only if the <a class="reference internal" href="pair_modify.html"><em>pair_modify tail</em></a> option is turned on.  The <em>etail</em> contribution
 is included in <em>evdwl</em>, <em>pe</em>, and <em>etotal</em>, and the corresponding tail
 correction to the pressure is included in <em>press</em> and <em>pxx</em>, <em>pyy</em>,
 etc.</p>
 <hr class="docutils" />
 <p>The <em>step</em>, <em>elapsed</em>, and <em>elaplong</em> keywords refer to timestep
 count.  <em>Step</em> is the current timestep, or iteration count when a
 <a class="reference internal" href="minimize.html"><em>minimization</em></a> is being performed.  <em>Elapsed</em> is the
 number of timesteps elapsed since the beginning of this run.
 <em>Elaplong</em> is the number of timesteps elapsed since the beginning of
 an initial run in a series of runs.  See the <em>start</em> and <em>stop</em>
 keywords for the <a class="reference internal" href="run.html"><em>run</em></a> for info on how to invoke a series of
 runs that keep track of an initial starting time.  If these keywords
 are not used, then <em>elapsed</em> and <em>elaplong</em> are the same value.</p>
 <p>The <em>dt</em> keyword is the current timestep size in time
 <a class="reference internal" href="units.html"><em>units</em></a>.  The <em>time</em> keyword is the current elapsed
 simulation time, also in time <a class="reference internal" href="units.html"><em>units</em></a>, which is simply
 (step*dt) if the timestep size has not changed and the timestep has
 not been reset.  If the timestep has changed (e.g. via <a class="reference internal" href="fix_dt_reset.html"><em>fix dt/reset</em></a>) or the timestep has been reset (e.g. via
 the &#8220;reset_timestep&#8221; command), then the simulation time is effectively
 a cummulative value up to the current point.</p>
 <p>The <em>cpu</em> keyword is elapsed CPU seconds since the beginning of this
 run.  The <em>tpcpu</em> and <em>spcpu</em> keywords are measures of how fast your
 simulation is currently running.  The <em>tpcpu</em> keyword is simulation
 time per CPU second, where simulation time is in time
 <a class="reference internal" href="units.html"><em>units</em></a>.  E.g. for metal units, the <em>tpcpu</em> value would be
 picoseconds per CPU second.  The <em>spcpu</em> keyword is the number of
 timesteps per CPU second.  Both quantities are on-the-fly metrics,
 measured relative to the last time they were invoked.  Thus if you are
 printing out thermodyamic output every 100 timesteps, the two keywords
 will continually output the time and timestep rate for the last 100
 steps.  The <em>tpcpu</em> keyword does not attempt to track any changes in
 timestep size, e.g. due to using the <a class="reference internal" href="fix_dt_reset.html"><em>fix dt/reset</em></a>
 command.</p>
 <p>The <em>cpuremain</em> keyword estimates the CPU time remaining in the
 current run, based on the time elapsed thus far.  It will only be a
 good estimate if the CPU time/timestep for the rest of the run is
 similar to the preceding timesteps.  On the initial timestep the value
 will be 0.0 since there is no history to estimate from.  For a
 minimization run performed by the &#8220;minimize&#8221; command, the estimate is
 based on the <em>maxiter</em> parameter, assuming the minimization will
 proceed for the maximum number of allowed iterations.</p>
 <p>The <em>part</em> keyword is useful for multi-replica or multi-partition
 simulations to indicate which partition this output and this file
 corresponds to, or for use in a <a class="reference internal" href="variable.html"><em>variable</em></a> to append to
 a filename for output specific to this partition.  See <a class="reference internal" href="Section_start.html#start-7"><span>Section_start 7</span></a> of the manual for details on running in
 multi-partition mode.</p>
 <p>The <em>fmax</em> and <em>fnorm</em> keywords are useful for monitoring the progress
 of an <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.  The <em>fmax</em> keyword
 calculates the maximum force in any dimension on any atom in the
 system, or the infinity-norm of the force vector for the system.  The
 <em>fnorm</em> keyword calculates the 2-norm or length of the force vector.</p>
 <p>The <em>nbuild</em> and <em>ndanger</em> keywords are useful for monitoring neighbor
 list builds during a run.  Note that both these values are also
 printed with the end-of-run statistics.  The <em>nbuild</em> keyword is the
 number of re-builds during the current run.  The <em>ndanger</em> keyword is
 the number of re-builds that LAMMPS considered potentially
 &#8220;dangerous&#8221;.  If atom movement triggered neighbor list rebuilding (see
 the <a class="reference internal" href="neigh_modify.html"><em>neigh_modify</em></a> command), then dangerous
 reneighborings are those that were triggered on the first timestep
 atom movement was checked for.  If this count is non-zero you may wish
 to reduce the delay factor to insure no force interactions are missed
 by atoms moving beyond the neighbor skin distance before a rebuild
 takes place.</p>
 <p>The keywords <em>cella</em>, <em>cellb</em>, <em>cellc</em>, <em>cellalpha</em>, <em>cellbeta</em>,
 <em>cellgamma</em>, correspond to the usual crystallographic quantities that
 define the periodic unit cell of a crystal.  See <a class="reference internal" href="Section_howto.html#howto-12"><span>this section</span></a> of the doc pages for a geometric
 description of triclinic periodic cells, including a precise defintion
 of these quantities in terms of the internal LAMMPS cell dimensions
 <em>lx</em>, <em>ly</em>, <em>lz</em>, <em>yz</em>, <em>xz</em>, <em>xy</em>.</p>
 <hr class="docutils" />
 <p>The <em>c_ID</em> and <em>c_ID[I]</em> and <em>c_ID[I][J]</em> keywords allow global
 values calculated by a compute to be output.  As discussed on the
 <a class="reference internal" href="compute.html"><em>compute</em></a> doc page, computes can calculate global,
 per-atom, or local values.  Only global values can be referenced by
 this command.  However, per-atom compute values can be referenced in a
 <a class="reference internal" href="variable.html"><em>variable</em></a> and the variable referenced by thermo_style
 custom, as discussed below.</p>
 <p>The ID in the keyword should be replaced by the actual ID of a compute
 that has been defined elsewhere in the input script.  See the
 <a class="reference internal" href="compute.html"><em>compute</em></a> command for details.  If the compute calculates
 a global scalar, vector, or array, then the keyword formats with 0, 1,
 or 2 brackets will reference a scalar value from the compute.</p>
 <p>Note that some computes calculate &#8220;intensive&#8221; global quantities like
 temperature; others calculate &#8220;extensive&#8221; global quantities like
 kinetic energy that are summed over all atoms in the compute group.
 Intensive quantities are printed directly without normalization by
 thermo_style custom.  Extensive quantities may be normalized by the
 total number of atoms in the simulation (NOT the number of atoms in
 the compute group) when output, depending on the <a class="reference internal" href="thermo_modify.html"><em>thermo_modify norm</em></a> option being used.</p>
 <p>The <em>f_ID</em> and <em>f_ID[I]</em> and <em>f_ID[I][J]</em> keywords allow global
 values calculated by a fix to be output.  As discussed on the
 <a class="reference internal" href="fix.html"><em>fix</em></a> doc page, fixes can calculate global, per-atom, or
 local values.  Only global values can be referenced by this command.
 However, per-atom fix values can be referenced in a
 <a class="reference internal" href="variable.html"><em>variable</em></a> and the variable referenced by thermo_style
 custom, as discussed below.</p>
 <p>The ID in the keyword should be replaced by the actual ID of a fix
 that has been defined elsewhere in the input script.  See the
 <a class="reference internal" href="fix.html"><em>fix</em></a> command for details.  If the fix calculates a global
 scalar, vector, or array, then the keyword formats with 0, 1, or 2
 brackets will reference a scalar value from the fix.</p>
 <p>Note that some fixes calculate &#8220;intensive&#8221; global quantities like
 timestep size; others calculate &#8220;extensive&#8221; global quantities like
 energy that are summed over all atoms in the fix group.  Intensive
 quantities are printed directly without normalization by thermo_style
 custom.  Extensive quantities may be normalized by the total number of
 atoms in the simulation (NOT the number of atoms in the fix group)
 when output, depending on the <a class="reference internal" href="thermo_modify.html"><em>thermo_modify norm</em></a>
 option being used.</p>
 <p>The <em>v_name</em> keyword allow the current value of a variable to be
 output.  The name in the keyword should be replaced by the variable
 name that has been defined elsewhere in the input script.  Only
 equal-style variables can be referenced.  See the
 <a class="reference internal" href="variable.html"><em>variable</em></a> command for details.  Variables of style
 <em>equal</em> can reference per-atom properties or thermodynamic keywords,
 or they can invoke other computes, fixes, or variables when evaluated,
 so this is a very general means of creating thermodynamic output.</p>
 <p>Note that equal-style variables are assumed to be &#8220;intensive&#8221; global
 quantities, which are thus printed as-is, without normalization by
 thermo_style custom.  You can include a division by &#8220;natoms&#8221; in the
 variable formula if this is not the case.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>This command must come after the simulation box is defined by a
 <a class="reference internal" href="read_data.html"><em>read_data</em></a>, <a class="reference internal" href="read_restart.html"><em>read_restart</em></a>, or
 <a class="reference internal" href="create_box.html"><em>create_box</em></a> command.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="thermo.html"><em>thermo</em></a>, <a class="reference internal" href="thermo_modify.html"><em>thermo_modify</em></a>,
 <a class="reference internal" href="fix_modify.html"><em>fix_modify</em></a>, <a class="reference internal" href="compute_temp.html"><em>compute temp</em></a>,
 <a class="reference internal" href="compute_pressure.html"><em>compute pressure</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>thermo_style one
 </pre></div>
 </div>
 </div>
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   <div class="section" id="variable-command">
 <span id="index-0"></span><h1>variable command<a class="headerlink" href="#variable-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>variable name style args ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>name = name of variable to define</li>
 <li>style = <em>delete</em> or <em>index</em> or <em>loop</em> or <em>world</em> or <em>universe</em> or
 <em>uloop</em> or <em>string</em> or <em>format</em> or <em>getenv</em> or <em>file</em> or <em>atomfile</em> or <em>python</em> or <em>equal</em> or <em>atom</em></li>
 </ul>
 <pre class="literal-block">
 <em>delete</em> = no args
-  <em>index</em> args = one or more strings
-  <em>loop</em> args = N
-    N = integer size of loop, loop from 1 to N inclusive
-  <em>loop</em> args = N pad
-    N = integer size of loop, loop from 1 to N inclusive
-    pad = all values will be same length, e.g. 001, 002, ..., 100
-  <em>loop</em> args = N1 N2
-    N1,N2 = loop from N1 to N2 inclusive
-  <em>loop</em> args = N1 N2 pad
-    N1,N2 = loop from N1 to N2 inclusive
-    pad = all values will be same length, e.g. 050, 051, ..., 100
-  <em>world</em> args = one string for each partition of processors
-  <em>universe</em> args = one or more strings
-  <em>uloop</em> args = N
-    N = integer size of loop
-  <em>uloop</em> args = N pad
-    N = integer size of loop
-    pad = all values will be same length, e.g. 001, 002, ..., 100
-  <em>string</em> arg = one string
-  <em>format</em> args = vname fstr
-    vname = name of equal-style variable to evaluate
-    fstr = C-style format string
-  <em>getenv</em> arg = one string
-  <em>file</em> arg = filename
-  <em>atomfile</em> arg = filename
-  <em>python</em> arg = function
-  <em>equal</em> or <em>atom</em> args = one formula containing numbers, thermo keywords, math operations, group functions, atom values and vectors, compute/fix/variable references
-    numbers = 0.0, 100, -5.4, 2.8e-4, etc
-    constants = PI
-    thermo keywords = vol, ke, press, etc from <a class="reference internal" href="thermo_style.html"><em>thermo_style</em></a>
-    math operators = (), -x, x+y, x-y, x*y, x/y, x^y, x%y,
-                     x == y, x != y, x &amp;lt y, x &amp;lt= y, x &amp;gt y, x &amp;gt= y, x &amp;&amp; y, x || y, !x
-    math functions = sqrt(x), exp(x), ln(x), log(x), abs(x),
-                     sin(x), cos(x), tan(x), asin(x), acos(x), atan(x), atan2(y,x),
-                     random(x,y,z), normal(x,y,z), ceil(x), floor(x), round(x)
-                     ramp(x,y), stagger(x,y), logfreq(x,y,z), logfreq2(x,y,z),
-                  stride(x,y,z), stride2(x,y,z,a,b,c),
-                  vdisplace(x,y), swiggle(x,y,z), cwiggle(x,y,z)
-    group functions = count(group), mass(group), charge(group),
-                   xcm(group,dim), vcm(group,dim), fcm(group,dim),
-                   bound(group,dir), gyration(group), ke(group),
-                   angmom(group,dim), torque(group,dim),
-                      inertia(group,dimdim), omega(group,dim)
-    region functions = count(group,region), mass(group,region), charge(group,region),
-                   xcm(group,dim,region), vcm(group,dim,region), fcm(group,dim,region),
-                   bound(group,dir,region), gyration(group,region), ke(group,reigon),
-                   angmom(group,dim,region), torque(group,dim,region),
-                   inertia(group,dimdim,region), omega(group,dim,region)
-    special functions = sum(x), min(x), max(x), ave(x), trap(x), slope(x), gmask(x), rmask(x), grmask(x,y), next(x)
-    atom value = id[i], mass[i], type[i], mol[i], x[i], y[i], z[i], vx[i], vy[i], vz[i], fx[i], fy[i], fz[i], q[i]
-    atom vector = id, mass, type, mol, x, y, z, vx, vy, vz, fx, fy, fz, q
-    compute references = c_ID, c_ID[i], c_ID[i][j]
-    fix references = f_ID, f_ID[i], f_ID[i][j]
-    variable references = v_name, v_name[i]
+<em>index</em> args = one or more strings
+<em>loop</em> args = N
+  N = integer size of loop, loop from 1 to N inclusive
+<em>loop</em> args = N pad
+  N = integer size of loop, loop from 1 to N inclusive
+  pad = all values will be same length, e.g. 001, 002, ..., 100
+<em>loop</em> args = N1 N2
+  N1,N2 = loop from N1 to N2 inclusive
+<em>loop</em> args = N1 N2 pad
+  N1,N2 = loop from N1 to N2 inclusive
+  pad = all values will be same length, e.g. 050, 051, ..., 100
+<em>world</em> args = one string for each partition of processors
+<em>universe</em> args = one or more strings
+<em>uloop</em> args = N
+  N = integer size of loop
+<em>uloop</em> args = N pad
+  N = integer size of loop
+  pad = all values will be same length, e.g. 001, 002, ..., 100
+<em>string</em> arg = one string
+<em>format</em> args = vname fstr
+  vname = name of equal-style variable to evaluate
+  fstr = C-style format string
+<em>getenv</em> arg = one string
+<em>file</em> arg = filename
+<em>atomfile</em> arg = filename
+<em>python</em> arg = function
+<em>equal</em> or <em>atom</em> args = one formula containing numbers, thermo keywords, math operations, group functions, atom values and vectors, compute/fix/variable references
+  numbers = 0.0, 100, -5.4, 2.8e-4, etc
+  constants = PI
+  thermo keywords = vol, ke, press, etc from <a class="reference internal" href="thermo_style.html"><em>thermo_style</em></a>
+  math operators = (), -x, x+y, x-y, x*y, x/y, x^y, x%y,
+                   x == y, x != y, x &amp;lt y, x &amp;lt= y, x &amp;gt y, x &amp;gt= y, x &amp;&amp; y, x || y, !x
+  math functions = sqrt(x), exp(x), ln(x), log(x), abs(x),
+                   sin(x), cos(x), tan(x), asin(x), acos(x), atan(x), atan2(y,x),
+                   random(x,y,z), normal(x,y,z), ceil(x), floor(x), round(x)
+                   ramp(x,y), stagger(x,y), logfreq(x,y,z), logfreq2(x,y,z),
+                stride(x,y,z), stride2(x,y,z,a,b,c),
+                vdisplace(x,y), swiggle(x,y,z), cwiggle(x,y,z)
+  group functions = count(group), mass(group), charge(group),
+                 xcm(group,dim), vcm(group,dim), fcm(group,dim),
+                 bound(group,dir), gyration(group), ke(group),
+                 angmom(group,dim), torque(group,dim),
+                    inertia(group,dimdim), omega(group,dim)
+  region functions = count(group,region), mass(group,region), charge(group,region),
+                 xcm(group,dim,region), vcm(group,dim,region), fcm(group,dim,region),
+                 bound(group,dir,region), gyration(group,region), ke(group,reigon),
+                 angmom(group,dim,region), torque(group,dim,region),
+                 inertia(group,dimdim,region), omega(group,dim,region)
+  special functions = sum(x), min(x), max(x), ave(x), trap(x), slope(x), gmask(x), rmask(x), grmask(x,y), next(x)
+  atom value = id[i], mass[i], type[i], mol[i], x[i], y[i], z[i], vx[i], vy[i], vz[i], fx[i], fy[i], fz[i], q[i]
+  atom vector = id, mass, type, mol, x, y, z, vx, vy, vz, fx, fy, fz, q
+  compute references = c_ID, c_ID[i], c_ID[i][j]
+  fix references = f_ID, f_ID[i], f_ID[i][j]
+  variable references = v_name, v_name[i]
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>variable x index run1 run2 run3 run4 run5 run6 run7 run8
 variable LoopVar loop $n
 variable beta equal temp/3.0
 variable b1 equal x[234]+0.5*vol
 variable b1 equal &quot;x[234] + 0.5*vol&quot;
 variable b equal xcm(mol1,x)/2.0
 variable b equal c_myTemp
 variable b atom x*y/vol
 variable foo string myfile
 variable myPy python increase
 variable f file values.txt
 variable temp world 300.0 310.0 320.0 ${Tfinal}
 variable x universe 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
 variable x uloop 15 pad
 variable str format x %.6g
 variable x delete
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>This command assigns one or more strings to a variable name for
 evaluation later in the input script or during a simulation.</p>
 <p>Variables can thus be useful in several contexts.  A variable can be
 defined and then referenced elsewhere in an input script to become
 part of a new input command.  For variable styles that store multiple
 strings, the <a class="reference internal" href="next.html"><em>next</em></a> command can be used to increment which
 string is assigned to the variable.  Variables of style <em>equal</em> store
 a formula which when evaluated produces a single numeric value which
 can be output either directly (see the <a class="reference internal" href="print.html"><em>print</em></a>, <a class="reference internal" href="fix_print.html"><em>fix print</em></a>, and <a class="reference internal" href="run.html"><em>run every</em></a> commands) or as part
 of thermodynamic output (see the <a class="reference internal" href="thermo_style.html"><em>thermo_style</em></a>
 command), or used as input to an averaging fix (see the <a class="reference internal" href="fix_ave_time.html"><em>fix ave/time</em></a> command).  Variables of style <em>atom</em> store
 a formula which when evaluated produces one numeric value per atom
 which can be output to a dump file (see the <a class="reference internal" href="dump.html"><em>dump custom</em></a>
 command) or used as input to an averaging fix (see the <a class="reference internal" href="fix_ave_spatial.html"><em>fix ave/spatial</em></a> and <a class="reference internal" href="fix_ave_atom.html"><em>fix ave/atom</em></a>
 commands).  Variables of style <em>atomfile</em> can be used anywhere in an
 input script that atom-style variables are used; they get their
 per-atom values from a file rather than from a formula.  Variables can
 be hooked to Python functions using code you provide, so that the
 variable gets its value from the evaluation of the Python code.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">As discussed in <a class="reference internal" href="Section_commands.html#cmd-2"><span>Section 3.2</span></a>
 of the manual, an input script can use &#8220;immediate&#8221; variables, specified
 as $(formula) with parenthesis, where the formula has the same syntax
 as equal-style variables described on this page.  This is a convenient
 way to evaluate a formula immediately without using the variable command
 to define a named variable and then evaluate that variable. See below
 for a more detailed discussion of this feature.</p>
 </div>
 <p>In the discussion that follows, the &#8220;name&#8221; of the variable is the
 arbitrary string that is the 1st argument in the variable command.
 This name can only contain alphanumeric characters and underscores.
 The &#8220;string&#8221; is one or more of the subsequent arguments.  The &#8220;string&#8221;
 can be simple text as in the 1st example above, it can contain other
 variables as in the 2nd example, or it can be a formula as in the 3rd
 example.  The &#8220;value&#8221; is the numeric quantity resulting from
 evaluation of the string.  Note that the same string can generate
 different values when it is evaluated at different times during a
 simulation.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">When the input script line is encountered that defines
 a variable of style <em>equal</em> or <em>atom</em> or <em>python</em> that contains a
 formula or Python code, the formula is NOT immediately evaluated.
 It will be evaluated every time when the variable is <strong>used</strong> instead.
 If you simply want to evaluate a formula in place you can use as
 so-called. See the section below about &#8220;Immediate Evaluation
 of Variables&#8221; for more details on the topic.  This is also true of
 a <em>format</em> style variable since it evaluates another variable when
 it is invoked.</p>
 </div>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">Variables of style <em>equal</em> and <em>atom</em> can be used as
 inputs to various other LAMMPS commands which evaluate their formulas
 as needed, e.g. at different timesteps during a <a class="reference internal" href="run.html"><em>run</em></a>.
 Variables of style <em>python</em> can be used in place of an equal-style
 variable so long as the associated Python function, as defined by the
 <a class="reference internal" href="python.html"><em>python</em></a> command, returns a numeric value.  Thus any
 command that states it can use an equal-style variable as an argument,
 can also use such a python-style variable.  This means that when the
 LAMMPS command evaluates the variable, the Python function will be
 executed.</p>
 </div>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">When a variable command is encountered in the input
 script and the variable name has already been specified, the command
 is ignored.  This means variables can NOT be re-defined in an input
 script (with two exceptions, read further).  This is to allow an input
 script to be processed multiple times without resetting the variables;
 see the <a class="reference internal" href="jump.html"><em>jump</em></a> or <a class="reference internal" href="include.html"><em>include</em></a> commands.  It also
 means that using the <a class="reference internal" href="Section_start.html#start-7"><span>command-line switch</span></a>
 -var will override a corresponding index variable setting in the input
 script.</p>
 </div>
 <p>There are two exceptions to this rule.  First, variables of style
 <em>string</em>, <em>getenv</em>, <em>equal</em>, <em>atom</em>, and <em>python</em> ARE redefined each
 time the command is encountered.  This allows these style of variables
 to be redefined multiple times in an input script.  In a loop, this
 means the formula associated with an <em>equal</em> or <em>atom</em> style variable
 can change if it contains a substitution for another variable, e.g. $x
 or v_x.</p>
 <p>Second, as described below, if a variable is iterated on to the end of
 its list of strings via the <a class="reference internal" href="next.html"><em>next</em></a> command, it is removed
 from the list of active variables, and is thus available to be
 re-defined in a subsequent variable command.  The <em>delete</em> style does
 the same thing.</p>
 <hr class="docutils" />
 <p><a class="reference internal" href="Section_commands.html#cmd-2"><span>This section</span></a> of the manual explains how
 occurrences of a variable name in an input script line are replaced by
 the variable&#8217;s string.  The variable name can be referenced as $x if
 the name &#8220;x&#8221; is a single character, or as ${LoopVar} if the name
 &#8220;LoopVar&#8221; is one or more characters.</p>
 <p>As described below, for variable styles <em>index</em>, <em>loop</em>, <em>file</em>,
 <em>universe</em>, and <em>uloop</em>, which string is assigned to a variable can be
 incremented via the <a class="reference internal" href="next.html"><em>next</em></a> command.  When there are no more
 strings to assign, the variable is exhausted and a flag is set that
 causes the next <a class="reference internal" href="jump.html"><em>jump</em></a> command encountered in the input
 script to be skipped.  This enables the construction of simple loops
 in the input script that are iterated over and then exited from.</p>
 <p>As explained above, an exhausted variable can be re-used in an input
 script.  The <em>delete</em> style also removes the variable, the same as if
 it were exhausted, allowing it to be redefined later in the input
 script or when the input script is looped over.  This can be useful
 when breaking out of a loop via the <a class="reference internal" href="if.html"><em>if</em></a> and <a class="reference internal" href="jump.html"><em>jump</em></a>
 commands before the variable would become exhausted.  For example,</p>
 <div class="highlight-python"><div class="highlight"><pre>label            loop
 variable    a loop 5
 print            &quot;A = $a&quot;
 if       &quot;$a &gt; 2&quot; then &quot;jump in.script break&quot;
 next     a
 jump     in.script loop
 label            break
 variable    a delete
 </pre></div>
 </div>
 <hr class="docutils" />
 <p>This section describes how all the various variable styles are defined
 and what they store.  Except for the <em>equal</em> and <em>atom</em> styles,
 which are explaine in the next section.</p>
 <p>Many of the styles store one or more strings.  Note that a single
 string can contain spaces (multiple words), if it is enclosed in
 quotes in the variable command.  When the variable is substituted for
 in another input script command, its returned string will then be
 interpreted as multiple arguments in the expanded command.</p>
 <p>For the <em>index</em> style, one or more strings are specified.  Initially,
 the 1st string is assigned to the variable.  Each time a
 <a class="reference internal" href="next.html"><em>next</em></a> command is used with the variable name, the next
 string is assigned.  All processors assign the same string to the
 variable.</p>
 <p><em>Index</em> style variables with a single string value can also be set by
 using the command-line switch -var; see <a class="reference internal" href="Section_start.html#start-7"><span>this section</span></a> for details.</p>
 <p>The <em>loop</em> style is identical to the <em>index</em> style except that the
 strings are the integers from 1 to N inclusive, if only one argument N
 is specified.  This allows generation of a long list of runs
 (e.g. 1000) without having to list N strings in the input script.
 Initially, the string &#8220;1&#8221; is assigned to the variable.  Each time a
 <a class="reference internal" href="next.html"><em>next</em></a> command is used with the variable name, the next
 string (&#8220;2&#8221;, &#8220;3&#8221;, etc) is assigned.  All processors assign the same
 string to the variable.  The <em>loop</em> style can also be specified with
 two arguments N1 and N2.  In this case the loop runs from N1 to N2
 inclusive, and the string N1 is initially assigned to the variable.
 N1 &lt;= N2 and N2 &gt;= 0 is required.</p>
 <p>For the <em>world</em> style, one or more strings are specified.  There must
 be one string for each processor partition or &#8220;world&#8221;.  See <a class="reference internal" href="Section_start.html#start-7"><span>this section</span></a> of the manual for information on
 running LAMMPS with multiple partitions via the &#8220;-partition&#8221;
 command-line switch.  This variable command assigns one string to each
 world.  All processors in the world are assigned the same string.  The
 next command cannot be used with <em>equal</em> style variables, since there
 is only one value per world.  This style of variable is useful when
 you wish to run different simulations on different partitions, or when
 performing a parallel tempering simulation (see the
 <a class="reference internal" href="temper.html"><em>temper</em></a> command), to assign different temperatures to
 different partitions.</p>
 <p>For the <em>universe</em> style, one or more strings are specified.  There
 must be at least as many strings as there are processor partitions or
 &#8220;worlds&#8221;.  See <a class="reference internal" href="Section_start.html#start-7"><span>this page</span></a> for information
 on running LAMMPS with multiple partitions via the &#8220;-partition&#8221;
 command-line switch.  This variable command initially assigns one
 string to each world.  When a <a class="reference internal" href="next.html"><em>next</em></a> command is encountered
 using this variable, the first processor partition to encounter it, is
 assigned the next available string.  This continues until all the
 variable strings are consumed.  Thus, this command can be used to run
 50 simulations on 8 processor partitions.  The simulations will be run
 one after the other on whatever partition becomes available, until
 they are all finished.  <em>Universe</em> style variables are incremented
 using the files &#8220;tmp.lammps.variable&#8221; and &#8220;tmp.lammps.variable.lock&#8221;
 which you will see in your directory during such a LAMMPS run.</p>
 <p>The <em>uloop</em> style is identical to the <em>universe</em> style except that the
 strings are the integers from 1 to N.  This allows generation of long
 list of runs (e.g. 1000) without having to list N strings in the input
 script.</p>
 <p>For the <em>string</em> style, a single string is assigned to the variable.
 The only difference between this and using the <em>index</em> style with a
 single string is that a variable with <em>string</em> style can be redefined.
 E.g. by another command later in the input script, or if the script is
 read again in a loop.</p>
 <p>For the <em>format</em> style, an equal-style variable is specified along
 with a C-style format string, e.g. &#8220;%f&#8221; or &#8220;%.10g&#8221;, which must be
 appropriate for formatting a double-precision floating-point value.
 This allows an equal-style variable to be formatted specifically for
 output as a string, e.g. by the <a class="reference internal" href="print.html"><em>print</em></a> command, if the
 default format &#8220;%.15g&#8221; has too much precision.</p>
 <p>For the <em>getenv</em> style, a single string is assigned to the variable
 which should be the name of an environment variable.  When the
 variable is evaluated, it returns the value of the environment
 variable, or an empty string if it not defined.  This style of
 variable can be used to adapt the behavior of LAMMPS input scripts via
 environment variable settings, or to retrieve information that has
 been previously stored with the <a class="reference internal" href="shell.html"><em>shell putenv</em></a> command.
 Note that because environment variable settings are stored by the
 operating systems, they persist beyond a <a class="reference internal" href="clear.html"><em>clear</em></a> command.</p>
 <p>For the <em>file</em> style, a filename is provided which contains a list of
 strings to assign to the variable, one per line.  The strings can be
 numeric values if desired.  See the discussion of the next() function
 below for equal-style variables, which will convert the string of a
 file-style variable into a numeric value in a formula.</p>
 <p>When a file-style variable is defined, the file is opened and the
 string on the first line is read and stored with the variable.  This
 means the variable can then be evaluated as many times as desired and
 will return that string.  There are two ways to cause the next string
 from the file to be read: use the <a class="reference internal" href="next.html"><em>next</em></a> command or the
 next() function in an equal- or atom-style variable, as discussed
 below.</p>
 <p>The rules for formatting the file are as follows.  A comment character
 &#8220;#&#8221; can be used anywhere on a line; text starting with the comment
 character is stripped.  Blank lines are skipped.  The first &#8220;word&#8221; of
 a non-blank line, delimited by white space, is the &#8220;string&#8221; assigned
 to the variable.</p>
 <p>For the <em>atomfile</em> style, a filename is provided which contains one or
 more sets of values, to assign on a per-atom basis to the variable.
 The format of the file is described below.</p>
 <p>When an atomfile-style variable is defined, the file is opened and the
 first set of per-atom values are read and stored with the variable.
 This means the variable can then be evaluated as many times as desired
 and will return those values.  There are two ways to cause the next
 set of per-atom values from the file to be read: use the
 <a class="reference internal" href="next.html"><em>next</em></a> command or the next() function in an atom-style
 variable, as discussed below.</p>
 <p>The rules for formatting the file are as follows.  Each time a set of
 per-atom values is read, a non-blank line is searched for in the file.
 A comment character &#8220;#&#8221; can be used anywhere on a line; text starting
 with the comment character is stripped.  Blank lines are skipped.  The
 first &#8220;word&#8221; of a non-blank line, delimited by white space, is read as
 the count N of per-atom lines to immediately follow.  N can be be the
 total number of atoms in the system, or only a subset.  The next N
 lines have the following format</p>
 <div class="highlight-python"><div class="highlight"><pre>ID value
 </pre></div>
 </div>
 <p>where ID is an atom ID and value is the per-atom numeric value that
 will be assigned to that atom.  IDs can be listed in any order.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">Every time a set of per-atom lines is read, the value
 for all atoms is first set to 0.0.  Thus values for atoms whose ID
 does not appear in the set, will remain 0.0.</p>
 </div>
 <p>For the <em>python</em> style a Python function name is provided.  This needs
 to match a function name specified in a <a class="reference internal" href="python.html"><em>python</em></a> command
 which returns a value to this variable as defined by its <em>return</em>
 keyword.  For exampe these two commands would be self-consistent:</p>
 <div class="highlight-python"><div class="highlight"><pre>variable foo python myMultiply
 python myMultiply return v_foo format f file funcs.py
 </pre></div>
 </div>
 <p>The two commands can appear in either order so long as both are
 specified before the Python function is invoked for the first time.</p>
 <p>Each time the variable is evaluated, the associated Python function is
 invoked, and the value it returns is also returned by the variable.
 Since the Python function can use other LAMMPS variables as input, or
 query interal LAMMPS quantities to perform its computation, this means
 the variable can return a different value each time it is evaluated.</p>
 <p>The type of value stored in the variable is determined by the <em>format</em>
 keyword of the <a class="reference internal" href="python.html"><em>python</em></a> command.  It can be an integer
 (i), floating point (f), or string (s) value.  As mentioned above, if
 it is a numeric value (integer or floating point), then the
 python-style variable can be used in place of an equal-style variable
 anywhere in an input script, e.g. as an argument to another command
 that allows for equal-style variables.</p>
 <hr class="docutils" />
 <p>For the <em>equal</em> and <em>atom</em> styles, a single string is specified which
 represents a formula that will be evaluated afresh each time the
 variable is used.  If you want spaces in the string, enclose it in
 double quotes so the parser will treat it as a single argument.  For
 <em>equal</em> style variables the formula computes a scalar quantity, which
 becomes the value of the variable whenever it is evaluated.  For
 <em>atom</em> style variables the formula computes one quantity for each
 atom whenever it is evaluated.</p>
 <p>Note that <em>equal</em> and <em>atom</em> variables can produce different values at
 different stages of the input script or at different times during a
 run.  For example, if an <em>equal</em> variable is used in a <a class="reference internal" href="fix_print.html"><em>fix print</em></a> command, different values could be printed each
 timestep it was invoked.  If you want a variable to be evaluated
 immediately, so that the result is stored by the variable instead of
 the string, see the section below on &#8220;Immediate Evaluation of
 Variables&#8221;.</p>
 <p>The next command cannot be used with <em>equal</em> or <em>atom</em> style
 variables, since there is only one string.</p>
 <p>The formula for an <em>equal</em> or <em>atom</em> variable can contain a variety
 of quantities.  The syntax for each kind of quantity is simple, but
 multiple quantities can be nested and combined in various ways to
 build up formulas of arbitrary complexity.  For example, this is a
 valid (though strange) variable formula:</p>
 <div class="highlight-python"><div class="highlight"><pre>variable x equal &quot;pe + c_MyTemp / vol^(1/3)&quot;
 </pre></div>
 </div>
 <p>Specifically, an formula can contain numbers, thermo keywords, math
 operators, math functions, group functions, region functions, atom
 values, atom vectors, compute references, fix references, and
 references to other variables.</p>
 <hr class="docutils" />
 <p>Most of the formula elements produce a scalar value.  A few produce a
 per-atom vector of values.  These are the atom vectors, compute
 references that represent a per-atom vector, fix references that
 represent a per-atom vector, and variables that are atom-style
 variables.  Math functions that operate on scalar values produce a
 scalar value; math function that operate on per-atom vectors do so
 element-by-element and produce a per-atom vector.</p>
 <p>A formula for equal-style variables cannot use any formula element
 that produces a per-atom vector.  A formula for an atom-style variable
 can use formula elements that produce either a scalar value or a
 per-atom vector.  Atom-style variables are evaluated by other commands
 that define a <a class="reference internal" href="group.html"><em>group</em></a> on which they operate, e.g. a
 <a class="reference internal" href="dump.html"><em>dump</em></a> or <a class="reference internal" href="compute.html"><em>compute</em></a> or <a class="reference internal" href="fix.html"><em>fix</em></a> command.
 When they invoke the atom-style variable, only atoms in the group are
 inlcuded in the formula evaluation.  The variable evaluates to 0.0 for
 atoms not in the group.</p>
 <p>The thermo keywords allowed in a formula are those defined by the
 <a class="reference internal" href="thermo_style.html"><em>thermo_style custom</em></a> command.  Thermo keywords that
 require a <a class="reference internal" href="compute.html"><em>compute</em></a> to calculate their values such as
 &#8220;temp&#8221; or &#8220;press&#8221;, use computes stored and invoked by the
 <a class="reference internal" href="thermo_style.html"><em>thermo_style</em></a> command.  This means that you can
 only use those keywords in a variable if the style you are using with
 the thermo_style command (and the thermo keywords associated with that
 style) also define and use the needed compute.  Note that some thermo
 keywords use a compute indirectly to calculate their value (e.g. the
 enthalpy keyword uses temp, pe, and pressure).  If a variable is
 evaluated directly in an input script (not during a run), then the
 values accessed by the thermo keyword must be current.  See the
 discussion below about &#8220;Variable Accuracy&#8221;.</p>
 <hr class="docutils" />
 <div class="section" id="math-operators">
 <h3>Math Operators<a class="headerlink" href="#math-operators" title="Permalink to this headline">¶</a></h3>
 <p>Math operators are written in the usual way, where the &#8220;x&#8221; and &#8220;y&#8221; in
 the examples can themselves be arbitrarily complex formulas, as in the
 examples above.  In this syntax, &#8220;x&#8221; and &#8220;y&#8221; can be scalar values or
 per-atom vectors.  For example, &#8220;ke/natoms&#8221; is the division of two
 scalars, where &#8220;vy+vz&#8221; is the element-by-element sum of two per-atom
 vectors of y and z velocities.</p>
 <p>Operators are evaluated left to right and have the usual C-style
 precedence: unary minus and unary logical NOT operator &#8221;!&#8221; have the
 highest precedence, exponentiation &#8220;^&#8221; is next; multiplication and
 division and the modulo operator &#8220;%&#8221; are next; addition and
 subtraction are next; the 4 relational operators &#8220;&lt;&#8221;, &#8220;&lt;=&#8221;, &#8220;&gt;&#8221;, and
 &#8220;&gt;=&#8221; are next; the two remaining relational operators &#8220;==&#8221; and &#8221;!=&#8221;
 are next; then the logical AND operator &#8220;&amp;&amp;&#8221;; and finally the logical
 OR operator &#8220;||&#8221; has the lowest precedence.  Parenthesis can be used
 to group one or more portions of a formula and/or enforce a different
 order of evaluation than what would occur with the default precedence.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">Because a unary minus is higher precedence than
 exponentiation, the formula &#8220;-2^2&#8221; will evaluate to 4, not -4.  This
 convention is compatible with some programming languages, but not
 others.  As mentioned, this behavior can be easily overridden with
 parenthesis; the formula &#8220;-(2^2)&#8221; will evaluate to -4.</p>
 </div>
 <p>The 6 relational operators return either a 1.0 or 0.0 depending on
 whether the relationship between x and y is TRUE or FALSE.  For
 example the expression x&lt;10.0 in an atom-style variable formula will
 return 1.0 for all atoms whose x-coordinate is less than 10.0, and 0.0
 for the others.  The logical AND operator will return 1.0 if both its
 arguments are non-zero, else it returns 0.0.  The logical OR operator
 will return 1.0 if either of its arguments is non-zero, else it
 returns 0.0.  The logical NOT operator returns 1.0 if its argument is
 0.0, else it returns 0.0.</p>
 <p>These relational and logical operators can be used as a masking or
 selection operation in a formula.  For example, the number of atoms
 whose properties satifsy one or more criteria could be calculated by
 taking the returned per-atom vector of ones and zeroes and passing it
 to the <a class="reference internal" href="compute_reduce.html"><em>compute reduce</em></a> command.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="math-functions">
 <h3>Math Functions<a class="headerlink" href="#math-functions" title="Permalink to this headline">¶</a></h3>
 <p>Math functions are specified as keywords followed by one or more
 parenthesized arguments &#8220;x&#8221;, &#8220;y&#8221;, &#8220;z&#8221;, each of which can themselves be
 arbitrarily complex formulas.  In this syntax, the arguments can
 represent scalar values or per-atom vectors.  In the latter case, the
 math operation is performed on each element of the vector.  For
 example, &#8220;sqrt(natoms)&#8221; is the sqrt() of a scalar, where &#8220;sqrt(y*z)&#8221;
 yields a per-atom vector with each element being the sqrt() of the
 product of one atom&#8217;s y and z coordinates.</p>
 <p>Most of the math functions perform obvious operations.  The ln() is
 the natural log; log() is the base 10 log.</p>
 <p>The random(x,y,z) function takes 3 arguments: x = lo, y = hi, and z =
 seed.  It generates a uniform random number between lo and hi.  The
 normal(x,y,z) function also takes 3 arguments: x = mu, y = sigma, and
 z = seed.  It generates a Gaussian variate centered on mu with
 variance sigma^2.  In both cases the seed is used the first time the
 internal random number generator is invoked, to initialize it.  For
 equal-style variables, every processor uses the same seed so that they
 each generate the same sequence of random numbers.  For atom-style
 variables, a unique seed is created for each processor, based on the
 specified seed.  This effectively generates a different random number
 for each atom being looped over in the atom-style variable.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">Internally, there is just one random number generator
 for all equal-style variables and one for all atom-style variables.
 If you define multiple variables (of each style) which use the
 random() or normal() math functions, then the internal random number
 generators will only be initialized once, which means only one of the
 specified seeds will determine the sequence of generated random
 numbers.</p>
 </div>
 <p>The ceil(), floor(), and round() functions are those in the C math
 library.  Ceil() is the smallest integer not less than its argument.
 Floor() if the largest integer not greater than its argument.  Round()
 is the nearest integer to its argument.</p>
 <p>The ramp(x,y) function uses the current timestep to generate a value
 linearly intepolated between the specified x,y values over the course
 of a run, according to this formula:</p>
 <div class="highlight-python"><div class="highlight"><pre><span class="n">value</span> <span class="o">=</span> <span class="n">x</span> <span class="o">+</span> <span class="p">(</span><span class="n">y</span><span class="o">-</span><span class="n">x</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">timestep</span><span class="o">-</span><span class="n">startstep</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">stopstep</span><span class="o">-</span><span class="n">startstep</span><span class="p">)</span>
 </pre></div>
 </div>
 <p>The run begins on startstep and ends on stopstep.  Startstep and
 stopstep can span multiple runs, using the <em>start</em> and <em>stop</em> keywords
 of the <a class="reference internal" href="run.html"><em>run</em></a> command.  See the <a class="reference internal" href="run.html"><em>run</em></a> command for
 details of how to do this.</p>
 <p>The stagger(x,y) function uses the current timestep to generate a new
 timestep.  X,y &gt; 0 and x &gt; y are required.  The generated timesteps
 increase in a staggered fashion, as the sequence
 x,x+y,2x,2x+y,3x,3x+y,etc.  For any current timestep, the next
 timestep in the sequence is returned.  Thus if stagger(1000,100) is
 used in a variable by the <a class="reference internal" href="dump_modify.html"><em>dump_modify every</em></a>
 command, it will generate the sequence of output timesteps:</p>
 <div class="highlight-python"><div class="highlight"><pre><span class="mi">100</span><span class="p">,</span><span class="mi">1000</span><span class="p">,</span><span class="mi">1100</span><span class="p">,</span><span class="mi">2000</span><span class="p">,</span><span class="mi">2100</span><span class="p">,</span><span class="mi">3000</span><span class="p">,</span><span class="n">etc</span>
 </pre></div>
 </div>
 <p>The logfreq(x,y,z) function uses the current timestep to generate a
 new timestep.  X,y,z &gt; 0 and y &lt; z are required.  The generated
 timesteps are on a base-z logarithmic scale, starting with x, and the
 y value is how many of the z-1 possible timesteps within one
 logarithmic interval are generated.  I.e. the timesteps follow the
 sequence x,2x,3x,...y*x,x*z,2x*z,3x*z,...y*x*z,x*z^2,2x*z^2,etc.  For
 any current timestep, the next timestep in the sequence is returned.
 Thus if logfreq(100,4,10) is used in a variable by the <a class="reference internal" href="dump_modify.html"><em>dump_modify every</em></a> command, it will generate this sequence of
 output timesteps:</p>
 <div class="highlight-python"><div class="highlight"><pre><span class="mi">100</span><span class="p">,</span><span class="mi">200</span><span class="p">,</span><span class="mi">300</span><span class="p">,</span><span class="mi">400</span><span class="p">,</span><span class="mi">1000</span><span class="p">,</span><span class="mi">2000</span><span class="p">,</span><span class="mi">3000</span><span class="p">,</span><span class="mi">4000</span><span class="p">,</span><span class="mi">10000</span><span class="p">,</span><span class="mi">20000</span><span class="p">,</span><span class="n">etc</span>
 </pre></div>
 </div>
 <p>The logfreq2(x,y,z) function is similar to logfreq, except a single
 logarithmic interval is divided into y equally-spaced timesteps and
 all of them are output.  Y &lt; z is not required.  Thus, if
 logfreq2(100,18,10) is used in a variable by the <a class="reference internal" href="dump_modify.html"><em>dump_modify every</em></a> command, then the interval between 100 and
 1000 is divided as 900/18 = 50 steps, and it will generate the
 sequence of output timesteps:</p>
 <div class="highlight-python"><div class="highlight"><pre><span class="mi">100</span><span class="p">,</span><span class="mi">150</span><span class="p">,</span><span class="mi">200</span><span class="p">,</span><span class="o">...</span><span class="mi">950</span><span class="p">,</span><span class="mi">1000</span><span class="p">,</span><span class="mi">1500</span><span class="p">,</span><span class="mi">2000</span><span class="p">,</span><span class="o">...</span><span class="mi">9500</span><span class="p">,</span><span class="mi">10000</span><span class="p">,</span><span class="mi">15000</span><span class="p">,</span><span class="n">etc</span>
 </pre></div>
 </div>
 <p>The stride(x,y,z) function uses the current timestep to generate a new
 timestep.  X,y &gt;= 0 and z &gt; 0 and x &lt;= y are required.  The generated
 timesteps increase in increments of z, from x to y, i.e. it generates
 the sequece x,x+z,x+2z,...,y.  If y-x is not a multiple of z, then
 similar to the way a for loop operates, the last value will be one
 that does not exceed y.  For any current timestep, the next timestep
 in the sequence is returned.  Thus if stride(1000,2000,100) is used
 in a variable by the <a class="reference internal" href="dump_modify.html"><em>dump_modify every</em></a> command, it
 will generate the sequence of output timesteps:</p>
 <div class="highlight-python"><div class="highlight"><pre><span class="mi">1000</span><span class="p">,</span><span class="mi">1100</span><span class="p">,</span><span class="mi">1200</span><span class="p">,</span> <span class="o">...</span> <span class="p">,</span><span class="mi">1900</span><span class="p">,</span><span class="mi">2000</span>
 </pre></div>
 </div>
 <p>The stride2(x,y,z,a,b,c) function is similar to the stride() function
 except it generates two sets of strided timesteps, one at a coarser
 level and one at a finer level.  Thus it is useful for debugging,
 e.g. to produce output every timestep at the point in simulation when
 a problem occurs.  X,y &gt;= 0 and z &gt; 0 and x &lt;= y are required, as are
 a,b &gt;= 0 and c &gt; 0 and a &lt; b.  Also, a &gt;= x and b &lt;= y are required so
 that the second stride is inside the first.  The generated timesteps
 increase in increments of z, starting at x, until a is reached.  At
 that point the timestep increases in increments of c, from a to b,
 then after b, increments by z are resumed until y is reached.  For any
 current timestep, the next timestep in the sequence is returned.  Thus
 if stride(1000,2000,100,1350,1360,1) is used in a variable by the
 <a class="reference internal" href="dump_modify.html"><em>dump_modify every</em></a> command, it will generate the
 sequence of output timesteps:</p>
 <div class="highlight-python"><div class="highlight"><pre>1000,1100,1200,1300,1350,1351,1352, ... 1359,1360,1400,1500, ... ,2000
 </pre></div>
 </div>
 <p>The vdisplace(x,y) function takes 2 arguments: x = value0 and y =
 velocity, and uses the elapsed time to change the value by a linear
 displacement due to the applied velocity over the course of a run,
 according to this formula:</p>
 <div class="highlight-python"><div class="highlight"><pre><span class="n">value</span> <span class="o">=</span> <span class="n">value0</span> <span class="o">+</span> <span class="n">velocity</span><span class="o">*</span><span class="p">(</span><span class="n">timestep</span><span class="o">-</span><span class="n">startstep</span><span class="p">)</span><span class="o">*</span><span class="n">dt</span>
 </pre></div>
 </div>
 <p>where dt = the timestep size.</p>
 <p>The run begins on startstep.  Startstep can span multiple runs, using
 the <em>start</em> keyword of the <a class="reference internal" href="run.html"><em>run</em></a> command.  See the
 <a class="reference internal" href="run.html"><em>run</em></a> command for details of how to do this.  Note that the
 <a class="reference internal" href="thermo_style.html"><em>thermo_style</em></a> keyword elaplong =
 timestep-startstep.</p>
 <p>The swiggle(x,y,z) and cwiggle(x,y,z) functions each take 3 arguments:
 x = value0, y = amplitude, z = period.  They use the elapsed time to
 oscillate the value by a sin() or cos() function over the course of a
 run, according to one of these formulas, where omega = 2 PI / period:</p>
 <div class="highlight-python"><div class="highlight"><pre><span class="n">value</span> <span class="o">=</span> <span class="n">value0</span> <span class="o">+</span> <span class="n">Amplitude</span> <span class="o">*</span> <span class="n">sin</span><span class="p">(</span><span class="n">omega</span><span class="o">*</span><span class="p">(</span><span class="n">timestep</span><span class="o">-</span><span class="n">startstep</span><span class="p">)</span><span class="o">*</span><span class="n">dt</span><span class="p">)</span>
 <span class="n">value</span> <span class="o">=</span> <span class="n">value0</span> <span class="o">+</span> <span class="n">Amplitude</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">cos</span><span class="p">(</span><span class="n">omega</span><span class="o">*</span><span class="p">(</span><span class="n">timestep</span><span class="o">-</span><span class="n">startstep</span><span class="p">)</span><span class="o">*</span><span class="n">dt</span><span class="p">))</span>
 </pre></div>
 </div>
 <p>where dt = the timestep size.</p>
 <p>The run begins on startstep.  Startstep can span multiple runs, using
 the <em>start</em> keyword of the <a class="reference internal" href="run.html"><em>run</em></a> command.  See the
 <a class="reference internal" href="run.html"><em>run</em></a> command for details of how to do this.  Note that the
 <a class="reference internal" href="thermo_style.html"><em>thermo_style</em></a> keyword elaplong =
 timestep-startstep.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="group-and-region-functions">
 <h3>Group and Region Functions<a class="headerlink" href="#group-and-region-functions" title="Permalink to this headline">¶</a></h3>
 <p>Group functions are specified as keywords followed by one or two
 parenthesized arguments.  The first argument <em>ID</em> is the group-ID.
 The <em>dim</em> argument, if it exists, is <em>x</em> or <em>y</em> or <em>z</em>.  The <em>dir</em>
 argument, if it exists, is <em>xmin</em>, <em>xmax</em>, <em>ymin</em>, <em>ymax</em>, <em>zmin</em>, or
 <em>zmax</em>.  The <em>dimdim</em> argument, if it exists, is <em>xx</em> or <em>yy</em> or <em>zz</em>
 or <em>xy</em> or <em>yz</em> or <em>xz</em>.</p>
 <p>The group function count() is the number of atoms in the group.  The
 group functions mass() and charge() are the total mass and charge of
 the group.  Xcm() and vcm() return components of the position and
 velocity of the center of mass of the group.  Fcm() returns a
 component of the total force on the group of atoms.  Bound() returns
 the min/max of a particular coordinate for all atoms in the group.
 Gyration() computes the radius-of-gyration of the group of atoms.  See
 the <a class="reference internal" href="compute_gyration.html"><em>compute gyration</em></a> command for a definition
 of the formula.  Angmom() returns components of the angular momentum
 of the group of atoms around its center of mass.  Torque() returns
 components of the torque on the group of atoms around its center of
 mass, based on current forces on the atoms.  Inertia() returns one of
 6 components of the symmetric inertia tensor of the group of atoms
 around its center of mass, ordered as Ixx,Iyy,Izz,Ixy,Iyz,Ixz.
 Omega() returns components of the angular velocity of the group of
 atoms around its center of mass.</p>
 <p>Region functions are specified exactly the same way as group functions
 except they take an extra final argument <em>IDR</em> which is the region ID.
 The function is computed for all atoms that are in both the group and
 the region.  If the group is &#8220;all&#8221;, then the only criteria for atom
 inclusion is that it be in the region.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="special-functions">
 <h3>Special Functions<a class="headerlink" href="#special-functions" title="Permalink to this headline">¶</a></h3>
 <p>Special functions take specific kinds of arguments, meaning their
 arguments cannot be formulas themselves.</p>
 <p>The sum(x), min(x), max(x), ave(x), trap(x), and slope(x) functions
 each take 1 argument which is of the form &#8220;c_ID&#8221; or &#8220;c_ID[N]&#8221; or
 &#8220;f_ID&#8221; or &#8220;f_ID[N]&#8221;.  The first two are computes and the second two
 are fixes; the ID in the reference should be replaced by the ID of a
 compute or fix defined elsewhere in the input script.  The compute or
 fix must produce either a global vector or array.  If it produces a
 global vector, then the notation without &#8220;[N]&#8221; should be used.  If
 it produces a global array, then the notation with &#8220;[N]&#8221; should be
 used, when N is an integer, to specify which column of the global
 array is being referenced.</p>
 <p>These functions operate on the global vector of inputs and reduce it
 to a single scalar value.  This is analagous to the operation of the
 <a class="reference internal" href="compute_reduce.html"><em>compute reduce</em></a> command, which invokes the same
 functions on per-atom and local vectors.</p>
 <p>The sum() function calculates the sum of all the vector elements.  The
 min() and max() functions find the minimum and maximum element
 respectively.  The ave() function is the same as sum() except that it
 divides the result by the length of the vector.</p>
 <p>The trap() function is the same as sum() except the first and last
 elements are multiplied by a weighting factor of 1/2 when performing
 the sum.  This effectively implements an integration via the
 trapezoidal rule on the global vector of data.  I.e. consider a set of
 points, equally spaced by 1 in their x coordinate: (1,V1), (2,V2),
 ..., (N,VN), where the Vi are the values in the global vector of
 length N.  The integral from 1 to N of these points is trap().  When
 appropriately normalized by the timestep size, this function is useful
 for calculating integrals of time-series data, like that generated by
 the <a class="reference internal" href="fix_ave_correlate.html"><em>fix ave/correlate</em></a> command.</p>
 <p>The slope() function uses linear regression to fit a line to the set
 of points, equally spaced by 1 in their x coordinate: (1,V1), (2,V2),
 ..., (N,VN), where the Vi are the values in the global vector of
 length N.  The returned value is the slope of the line.  If the line
 has a single point or is vertical, it returns 1.0e20.</p>
 <p>The gmask(x) function takes 1 argument which is a group ID.  It
 can only be used in atom-style variables.  It returns a 1 for
 atoms that are in the group, and a 0 for atoms that are not.</p>
 <p>The rmask(x) function takes 1 argument which is a region ID.  It can
 only be used in atom-style variables.  It returns a 1 for atoms that
 are in the geometric region, and a 0 for atoms that are not.</p>
 <p>The grmask(x,y) function takes 2 arguments.  The first is a group ID,
 and the second is a region ID.  It can only be used in atom-style
 variables.  It returns a 1 for atoms that are in both the group and
 region, and a 0 for atoms that are not in both.</p>
 <p>The next(x) function takes 1 argument which is a variable ID (not
 &#8220;v_foo&#8221;, just &#8220;foo&#8221;).  It must be for a file-style or atomfile-style
 variable.  Each time the next() function is invoked (i.e. each time
 the equal-style or atom-style variable is evaluated), the following
 steps occur.</p>
 <p>For file-style variables, the current string value stored by the
 file-style variable is converted to a numeric value and returned by
 the function.  And the next string value in the file is read and
 stored.  Note that if the line previously read from the file was not a
 numeric string, then it will typically evaluate to 0.0, which is
 likely not what you want.</p>
 <p>For atomfile-style variables, the current per-atom values stored by
 the atomfile-style variable are returned by the function.  And the
 next set of per-atom values in the file is read and stored.</p>
 <p>Since file-style and atomfile-style variables read and store the first
 line of the file or first set of per-atoms values when they are
 defined in the input script, these are the value(s) that will be
 returned the first time the next() function is invoked.  If next() is
 invoked more times than there are lines or sets of lines in the file,
 the variable is deleted, similar to how the <a class="reference internal" href="next.html"><em>next</em></a> command
 operates.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="atom-values-and-vectors">
 <h3>Atom Values and Vectors<a class="headerlink" href="#atom-values-and-vectors" title="Permalink to this headline">¶</a></h3>
 <p>Atom values take an integer argument I from 1 to N, where I is the
 atom-ID, e.g. x[243], which means use the x coordinate of the atom
 with ID = 243.  Or they can take a variable name, specified as v_name,
 where name is the name of the variable, like x[v_myIndex].  The
 variable can be of any style except atom or atom-file variables.  The
 variable is evaluated and the result is expected to be numeric and is
 cast to an integer (i.e. 3.4 becomes 3), to use an an index, which
 must be a value from 1 to N.  Note that a &#8220;formula&#8221; cannot be used as
 the argument between the brackets, e.g. x[243+10] or
 x[v_myIndex+1] are not allowed.  To do this a single variable can be
 defined that contains the needed formula.</p>
 <p>Note that the 0 &lt; atom-ID &lt;= N, where N is the largest atom ID
 in the system.  If an ID is specified for an atom that does not
 currently exist, then the generated value is 0.0.</p>
 <p>Atom vectors generate one value per atom, so that a reference like
 &#8220;vx&#8221; means the x-component of each atom&#8217;s velocity will be used when
 evaluating the variable.</p>
 <p>The meaning of the different atom values and vectors is mostly
 self-explanatory.  Mol refers to the molecule ID of an atom, and is
 only defined if an <a class="reference internal" href="atom_style.html"><em>atom_style</em></a> is being used that
 defines molecule IDs.</p>
 <p>Note that many other atom attributes can be used as inputs to a
 variable by using the <a class="reference internal" href="compute_property_atom.html"><em>compute property/atom</em></a> command and then specifying
 a quantity from that compute.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="compute-references">
 <h3>Compute References<a class="headerlink" href="#compute-references" title="Permalink to this headline">¶</a></h3>
 <p>Compute references access quantities calculated by a
 <a class="reference internal" href="compute.html"><em>compute</em></a>.  The ID in the reference should be replaced by
 the ID of a compute defined elsewhere in the input script.  As
 discussed in the doc page for the <a class="reference internal" href="compute.html"><em>compute</em></a> command,
 computes can produce global, per-atom, or local values.  Only global
 and per-atom values can be used in a variable.  Computes can also
 produce a scalar, vector, or array.  An equal-style variable can only
 use scalar values, which means a global scalar, or an element of a
 global or per-atom vector or array.  Atom-style variables can use the
 same scalar values.  They can also use per-atom vector values.  A
 vector value can be a per-atom vector itself, or a column of an
 per-atom array.  See the doc pages for individual computes to see what
 kind of values they produce.</p>
 <p>Examples of different kinds of compute references are as follows.
 There is no ambiguity as to what a reference means, since computes
 only produce global or per-atom quantities, never both.</p>
 <table border="1" class="docutils">
 <colgroup>
 <col width="10%" />
 <col width="90%" />
 </colgroup>
 <tbody valign="top">
 <tr class="row-odd"><td>c_ID</td>
 <td>global scalar, or per-atom vector</td>
 </tr>
 <tr class="row-even"><td>c_ID[I]</td>
 <td>Ith element of global vector, or atom I&#8217;s value in per-atom vector, or Ith column from per-atom array</td>
 </tr>
 <tr class="row-odd"><td>c_ID[I][J]</td>
 <td>I,J element of global array, or atom I&#8217;s Jth value in per-atom array</td>
 </tr>
 </tbody>
 </table>
 <p>For I and J, integers can be specified or a variable name, specified
 as v_name, where name is the name of the variable.  The rules for this
 syntax are the same as for the &#8220;Atom Values and Vectors&#8221; discussion
 above.</p>
 <p>If a variable containing a compute is evaluated directly in an input
 script (not during a run), then the values accessed by the compute
 must be current.  See the discussion below about &#8220;Variable Accuracy&#8221;.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="fix-references">
 <h3>Fix References<a class="headerlink" href="#fix-references" title="Permalink to this headline">¶</a></h3>
 <p>Fix references access quantities calculated by a <a class="reference internal" href="compute.html"><em>fix</em></a>.
 The ID in the reference should be replaced by the ID of a fix defined
 elsewhere in the input script.  As discussed in the doc page for the
 <a class="reference internal" href="fix.html"><em>fix</em></a> command, fixes can produce global, per-atom, or local
 values.  Only global and per-atom values can be used in a variable.
 Fixes can also produce a scalar, vector, or array.  An equal-style
 variable can only use scalar values, which means a global scalar, or
 an element of a global or per-atom vector or array.  Atom-style
 variables can use the same scalar values.  They can also use per-atom
 vector values.  A vector value can be a per-atom vector itself, or a
 column of an per-atom array.  See the doc pages for individual fixes
 to see what kind of values they produce.</p>
 <p>The different kinds of fix references are exactly the same as the
 compute references listed in the above table, where &#8220;<a href="#id1"><span class="problematic" id="id2">c_</span></a>&#8221; is replaced
 by &#8220;<a href="#id3"><span class="problematic" id="id4">f_</span></a>&#8221;.  Again, there is no ambiguity as to what a reference means,
 since fixes only produce global or per-atom quantities, never both.</p>
 <table border="1" class="docutils">
 <colgroup>
 <col width="10%" />
 <col width="90%" />
 </colgroup>
 <tbody valign="top">
 <tr class="row-odd"><td>f_ID</td>
 <td>global scalar, or per-atom vector</td>
 </tr>
 <tr class="row-even"><td>f_ID[I]</td>
 <td>Ith element of global vector, or atom I&#8217;s value in per-atom vector, or Ith column from per-atom array</td>
 </tr>
 <tr class="row-odd"><td>f_ID[I][J]</td>
 <td>I,J element of global array, or atom I&#8217;s Jth value in per-atom array</td>
 </tr>
 </tbody>
 </table>
 <p>For I and J, integers can be specified or a variable name, specified
 as v_name, where name is the name of the variable.  The rules for this
 syntax are the same as for the &#8220;Atom Values and Vectors&#8221; discussion
 above.</p>
 <p>If a variable containing a fix is evaluated directly in an input
 script (not during a run), then the values accessed by the fix should
 be current.  See the discussion below about &#8220;Variable Accuracy&#8221;.</p>
 <p>Note that some fixes only generate quantities on certain timesteps.
 If a variable attempts to access the fix on non-allowed timesteps, an
 error is generated.  For example, the <a class="reference internal" href="fix_ave_time.html"><em>fix ave/time</em></a>
 command may only generate averaged quantities every 100 steps.  See
 the doc pages for individual fix commands for details.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="variable-references">
 <h3>Variable References<a class="headerlink" href="#variable-references" title="Permalink to this headline">¶</a></h3>
 <p>Variable references access quantities stored or calculated by other
 variables, which will cause those variables to be evaluated.  The name
 in the reference should be replaced by the name of a variable defined
 elsewhere in the input script.</p>
 <p>As discussed on this doc page, equal-style variables generate a global
 scalar numeric value; atom-style and atomfile-style variables generate
 a per-atom vector of numeric values; all other variables store a
 string.  The formula for an equal-style variable can use any style of
 variable except an atom-style or atomfile-style (unless only a single
 value from the variable is accessed via a subscript).  If a
 string-storing variable is used, the string is converted to a numeric
 value.  Note that this will typically produce a 0.0 if the string is
 not a numeric string, which is likely not what you want.  The formula
 for an atom-style variable can use any style of variable, including
 other atom-style or atomfile-style variables.</p>
 <p>Examples of different kinds of variable references are as follows.
 There is no ambiguity as to what a reference means, since variables
 produce only a global scalar or a per-atom vector, never both.</p>
 <table border="1" class="docutils">
 <colgroup>
 <col width="24%" />
 <col width="76%" />
 </colgroup>
 <tbody valign="top">
 <tr class="row-odd"><td>v_name</td>
 <td>scalar, or per-atom vector</td>
 </tr>
 <tr class="row-even"><td>v_name[I]</td>
 <td>atom I&#8217;s value in per-atom vector</td>
 </tr>
 </tbody>
 </table>
 <p>For I, an integer can be specified or a variable name, specified as
 v_name, where name is the name of the variable.  The rules for this
 syntax are the same as for the &#8220;Atom Values and Vectors&#8221; discussion
 above.</p>
 <hr class="docutils" />
 <p><strong>Immediate Evaluation of Variables:</strong></p>
 <p>If you want an equal-style variable to be evaluated immediately, it
 may be the case that you do not need to define a variable at all.  See
 <a class="reference internal" href="Section_commands.html#cmd-2"><span>Section 3.2</span></a> of the manual, which
 describes the use of &#8220;immediate&#8221; variables in an input script,
 specified as $(formula) with parenthesis, where the formula has the
 same syntax as equal-style variables described on this page.  This
 effectively evaluates a formula immediately without using the variable
 command to define a named variable.</p>
 <p>More generally, there is a difference between referencing a variable
 with a leading $ sign (e.g. $x or ${abc}) versus with a leading &#8220;<a href="#id5"><span class="problematic" id="id6">v_</span></a>&#8221;
 (e.g. v_x or v_abc).  The former can be used in any input script
 command, including a variable command.  The input script parser
 evaluates the reference variable immediately and substitutes its value
 into the command.  As explained in <span class="xref std std-ref">Section commands 3.2</span> for &#8220;Parsing rules&#8221;, you can also use
 un-named &#8220;immediate&#8221; variables for this purpose.  For example, a
 string like this $((xlo+xhi)/2+sqrt(v_area)) in an input script
 command evaluates the string between the parenthesis as an equal-style
 variable formula.</p>
 <p>Referencing a variable with a leading &#8220;<a href="#id7"><span class="problematic" id="id8">v_</span></a>&#8221; is an optional or required
 kind of argument for some commands (e.g. the <a class="reference internal" href="fix_ave_spatial.html"><em>fix ave/spatial</em></a> or <a class="reference internal" href="dump.html"><em>dump custom</em></a> or
 <a class="reference internal" href="thermo_style.html"><em>thermo_style</em></a> commands) if you wish it to evaluate
 a variable periodically during a run.  It can also be used in a
 variable formula if you wish to reference a second variable.  The
 second variable will be evaluated whenever the first variable is
 evaluated.</p>
 <p>As an example, suppose you use this command in your input script to
 define the variable &#8220;v&#8221; as</p>
 <div class="highlight-python"><div class="highlight"><pre>variable v equal vol
 </pre></div>
 </div>
 <p>before a run where the simulation box size changes.  You might think
 this will assign the initial volume to the variable &#8220;v&#8221;.  That is not
 the case.  Rather it assigns a formula which evaluates the volume
 (using the thermo_style keyword &#8220;vol&#8221;) to the variable &#8220;v&#8221;.  If you
 use the variable &#8220;v&#8221; in some other command like <a class="reference internal" href="fix_ave_time.html"><em>fix ave/time</em></a> then the current volume of the box will be
 evaluated continuously during the run.</p>
 <p>If you want to store the initial volume of the system, you can do it
 this way:</p>
 <div class="highlight-python"><div class="highlight"><pre>variable v equal vol
 variable v0 equal $v
 </pre></div>
 </div>
 <p>The second command will force &#8220;v&#8221; to be evaluated (yielding the
 initial volume) and assign that value to the variable &#8220;v0&#8221;.  Thus the
 command</p>
 <div class="highlight-python"><div class="highlight"><pre>thermo_style custom step v_v v_v0
 </pre></div>
 </div>
 <p>would print out both the current and initial volume periodically
 during the run.</p>
 <p>Note that it is a mistake to enclose a variable formula in double
 quotes if it contains variables preceeded by $ signs.  For example,</p>
 <div class="highlight-python"><div class="highlight"><pre>variable vratio equal &quot;${vfinal}/${v0}&quot;
 </pre></div>
 </div>
 <p>This is because the quotes prevent variable substitution (see <a class="reference internal" href="Section_commands.html#cmd-2"><span>this section</span></a> on parsing input script
 commands), and thus an error will occur when the formula for &#8220;vratio&#8221;
 is evaluated later.</p>
 <hr class="docutils" />
 <p><strong>Variable Accuracy:</strong></p>
 <p>Obviously, LAMMPS attempts to evaluate variables containing formulas
 (<em>equal</em> and <em>atom</em> style variables) accurately whenever the
 evaluation is performed.  Depending on what is included in the
 formula, this may require invoking a <a class="reference internal" href="compute.html"><em>compute</em></a>, either
 directly or indirectly via a thermo keyword, or accessing a value
 previously calculated by a compute, or accessing a value calculated
 and stored by a <a class="reference internal" href="fix.html"><em>fix</em></a>.  If the compute is one that calculates
 the pressure or energy of the system, then these quantities need to be
 tallied during the evaluation of the interatomic potentials (pair,
 bond, etc) on timesteps that the variable will need the values.</p>
 <p>LAMMPS keeps track of all of this during a <a class="reference internal" href="run.html"><em>run</em></a> or <a class="reference internal" href="minimize.html"><em>energy minimization</em></a>.  An error will be generated if you
 attempt to evaluate a variable on timesteps when it cannot produce
 accurate values.  For example, if a <a class="reference internal" href="thermo_style.html"><em>thermo_style custom</em></a> command prints a variable which accesses
 values stored by a <a class="reference internal" href="fix_ave_time.html"><em>fix ave/time</em></a> command and the
 timesteps on which thermo output is generated are not multiples of the
 averaging frequency used in the fix command, then an error will occur.</p>
 <p>An input script can also request variables be evaluated before or
 after or in between runs, e.g. by including them in a
 <a class="reference internal" href="print.html"><em>print</em></a> command.  In this case, if a compute is needed to
 evaluate a variable (either directly or indirectly), LAMMPS will not
 invoke the compute, but it will use a value previously calculated by
 the compute, and can do this only if it was invoked on the current
 timestep.  Fixes will always provide a quantity needed by a variable,
 but the quantity may or may not be current.  This leads to one of
 three kinds of behavior:</p>
 <p>(1) The variable may be evaluated accurately.  If it contains
 references to a compute or fix, and these values were calculated on
 the last timestep of a preceeding run, then they will be accessed and
 used by the variable and the result will be accurate.</p>
 <p>(2) LAMMPS may not be able to evaluate the variable and will generate
 an error message stating so.  For example, if the variable requires a
 quantity from a <a class="reference internal" href="compute.html"><em>compute</em></a> that has not been invoked on
 the current timestep, LAMMPS will generate an error.  This means, for
 example, that such a variable cannot be evaluated before the first run
 has occurred.  Likewise, in between runs, a variable containing a
 compute cannot be evaluated unless the compute was invoked on the last
 timestep of the preceding run, e.g. by thermodynamic output.</p>
 <p>One way to get around this problem is to perform a 0-timestep run
 before using the variable.  For example, these commands</p>
 <div class="highlight-python"><div class="highlight"><pre>variable t equal temp
 print &quot;Initial temperature = $t&quot;
 run 1000
 </pre></div>
 </div>
 <p>will generate an error if the run is the first run specified in the
 input script, because generating a value for the &#8220;t&#8221; variable requires
 a compute for calculating the temperature to be invoked.</p>
 <p>However, this sequence of commands would be fine:</p>
 <div class="highlight-python"><div class="highlight"><pre>run 0
 variable t equal temp
 print &quot;Initial temperature = $t&quot;
 run 1000
 </pre></div>
 </div>
 <p>The 0-timestep run initializes and invokes various computes, including
 the one for temperature, so that the value it stores is current and
 can be accessed by the variable &#8220;t&#8221; after the run has completed.  Note
 that a 0-timestep run does not alter the state of the system, so it
 does not change the input state for the 1000-timestep run that
 follows.  Also note that the 0-timestep run must actually use and
 invoke the compute in question (e.g. via <a class="reference internal" href="thermo_style.html"><em>thermo</em></a> or
 <a class="reference internal" href="dump.html"><em>dump</em></a> output) in order for it to enable the compute to be
 used in a variable after the run.  Thus if you are trying to print a
 variable that uses a compute you have defined, you can insure it is
 invoked on the last timestep of the preceding run by including it in
 thermodynamic output.</p>
 <p>Unlike computes, <a class="reference internal" href="fix.html"><em>fixes</em></a> will never generate an error if
 their values are accessed by a variable in between runs.  They always
 return some value to the variable.  However, the value may not be what
 you expect if the fix has not yet calculated the quantity of interest
 or it is not current.  For example, the <a class="reference internal" href="fix_indent.html"><em>fix indent</em></a>
 command stores the force on the indenter.  But this is not computed
 until a run is performed.  Thus if a variable attempts to print this
 value before the first run, zeroes will be output.  Again, performing
 a 0-timestep run before printing the variable has the desired effect.</p>
 <p>(3) The variable may be evaluated incorrectly and LAMMPS may have no
 way to detect this has occurred.  Consider the following sequence of
 commands:</p>
 <div class="highlight-python"><div class="highlight"><pre>pair_coeff 1 1 1.0 1.0
 run 1000
 pair_coeff 1 1 1.5 1.0
 variable e equal pe
 print &quot;Final potential energy = $e&quot;
 </pre></div>
 </div>
 <p>The first run is performed using one setting for the pairwise
 potential defined by the <a class="reference internal" href="pair_style.html"><em>pair_style</em></a> and
 <a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a> commands.  The potential energy is
 evaluated on the final timestep and stored by the <a class="reference internal" href="compute_pe.html"><em>compute pe</em></a> compute (this is done by the
 <a class="reference internal" href="thermo_style.html"><em>thermo_style</em></a> command).  Then a pair coefficient is
 changed, altering the potential energy of the system.  When the
 potential energy is printed via the &#8220;e&#8221; variable, LAMMPS will use the
 potential energy value stored by the <a class="reference internal" href="compute_pe.html"><em>compute pe</em></a>
 compute, thinking it is current.  There are many other commands which
 could alter the state of the system between runs, causing a variable
 to evaluate incorrectly.</p>
 <p>The solution to this issue is the same as for case (2) above, namely
 perform a 0-timestep run before the variable is evaluated to insure
 the system is up-to-date.  For example, this sequence of commands
 would print a potential energy that reflected the changed pairwise
 coefficient:</p>
 <div class="highlight-python"><div class="highlight"><pre>pair_coeff 1 1 1.0 1.0
 run 1000
 pair_coeff 1 1 1.5 1.0
 run 0
 variable e equal pe
 print &quot;Final potential energy = $e&quot;
 </pre></div>
 </div>
 </div>
 </div>
 <hr class="docutils" />
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>Indexing any formula element by global atom ID, such as an atom value,
 requires the atom style to use a global mapping in order to look up
 the vector indices.  By default, only atom styles with molecular
 information create global maps.  The <a class="reference internal" href="atom_modify.html"><em>atom_modify map</em></a> command can override the default.</p>
 <p>All <em>universe</em>- and <em>uloop</em>-style variables defined in an input script
 must have the same number of values.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="next.html"><em>next</em></a>, <a class="reference internal" href="jump.html"><em>jump</em></a>, <a class="reference internal" href="include.html"><em>include</em></a>,
 <a class="reference internal" href="temper.html"><em>temper</em></a>, <a class="reference internal" href="fix_print.html"><em>fix print</em></a>, <a class="reference internal" href="print.html"><em>print</em></a></p>
 <p><strong>Default:</strong> none</p>
 </div>
 </div>
 
 
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   <div class="section" id="velocity-command">
 <span id="index-0"></span><h1>velocity command<a class="headerlink" href="#velocity-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>velocity group-ID style args keyword value ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>group-ID = ID of group of atoms whose velocity will be changed</li>
 <li>style = <em>create</em> or <em>set</em> or <em>scale</em> or <em>ramp</em> or <em>zero</em></li>
 </ul>
 <pre class="literal-block">
 <em>create</em> args = temp seed
-    temp = temperature value (temperature units)
-    seed = random # seed (positive integer)
-  <em>set</em> args = vx vy vz
-    vx,vy,vz = velocity value or NULL (velocity units)
-    any of vx,vy,vz van be a variable (see below)
-  <em>scale</em> arg = temp
-    temp = temperature value (temperature units)
-  <em>ramp</em> args = vdim vlo vhi dim clo chi
-    vdim = <em>vx</em> or <em>vy</em> or <em>vz</em>
-    vlo,vhi = lower and upper velocity value (velocity units)
-    dim = <em>x</em> or <em>y</em> or <em>z</em>
-    clo,chi = lower and upper coordinate bound (distance units)
-  <em>zero</em> arg = <em>linear</em> or <em>angular</em>
-    <em>linear</em> = zero the linear momentum
-    <em>angular</em> = zero the angular momentum
+  temp = temperature value (temperature units)
+  seed = random # seed (positive integer)
+<em>set</em> args = vx vy vz
+  vx,vy,vz = velocity value or NULL (velocity units)
+  any of vx,vy,vz van be a variable (see below)
+<em>scale</em> arg = temp
+  temp = temperature value (temperature units)
+<em>ramp</em> args = vdim vlo vhi dim clo chi
+  vdim = <em>vx</em> or <em>vy</em> or <em>vz</em>
+  vlo,vhi = lower and upper velocity value (velocity units)
+  dim = <em>x</em> or <em>y</em> or <em>z</em>
+  clo,chi = lower and upper coordinate bound (distance units)
+<em>zero</em> arg = <em>linear</em> or <em>angular</em>
+  <em>linear</em> = zero the linear momentum
+  <em>angular</em> = zero the angular momentum
 </pre>
 <ul class="simple">
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>dist</em> or <em>sum</em> or <em>mom</em> or <em>rot</em> or <em>temp</em> or <em>bias</em> or <em>loop</em> or <em>units</em></li>
 </ul>
 <pre class="literal-block">
 <em>dist</em> value = <em>uniform</em> or <em>gaussian</em>
-  <em>sum</em> value = <em>no</em> or <em>yes</em>
-  <em>mom</em> value = <em>no</em> or <em>yes</em>
-  <em>rot</em> value = <em>no</em> or <em>yes</em>
-  <em>temp</em> value = temperature compute ID
-  <em>bias</em> value = <em>no</em> or <em>yes</em>
-  <em>loop</em> value = <em>all</em> or <em>local</em> or <em>geom</em>
-  <em>rigid</em> value = fix-ID
-    fix-ID = ID of rigid body fix
-  <em>units</em> value = <em>box</em> or <em>lattice</em>
+<em>sum</em> value = <em>no</em> or <em>yes</em>
+<em>mom</em> value = <em>no</em> or <em>yes</em>
+<em>rot</em> value = <em>no</em> or <em>yes</em>
+<em>temp</em> value = temperature compute ID
+<em>bias</em> value = <em>no</em> or <em>yes</em>
+<em>loop</em> value = <em>all</em> or <em>local</em> or <em>geom</em>
+<em>rigid</em> value = fix-ID
+  fix-ID = ID of rigid body fix
+<em>units</em> value = <em>box</em> or <em>lattice</em>
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>velocity all create 300.0 4928459 rot yes dist gaussian
 velocity border set NULL 4.0 v_vz sum yes units box
 velocity flow scale 300.0
 velocity flow ramp vx 0.0 5.0 y 5 25 temp mytemp
 velocity all zero linear
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Set or change the velocities of a group of atoms in one of several
 styles.  For each style, there are required arguments and optional
 keyword/value parameters.  Not all options are used by each style.
 Each option has a default as listed below.</p>
 <p>The <em>create</em> style generates an ensemble of velocities using a random
 number generator with the specified seed as the specified temperature.</p>
 <p>The <em>set</em> style sets the velocities of all atoms in the group to the
 specified values.  If any component is specified as NULL, then it is
 not set.  Any of the vx,vy,vz velocity components can be specified as
 an equal-style or atom-style <a class="reference internal" href="variable.html"><em>variable</em></a>.  If the value
 is a variable, it should be specified as v_name, where name is the
 variable name.  In this case, the variable will be evaluated, and its
 value used to determine the velocity component.  Note that if a
 variable is used, the velocity it calculates must be in box units, not
 lattice units; see the discussion of the <em>units</em> keyword below.</p>
 <p>Equal-style variables can specify formulas with various mathematical
 functions, and include <a class="reference internal" href="thermo_style.html"><em>thermo_style</em></a> command
 keywords for the simulation box parameters or other parameters.</p>
 <p>Atom-style variables can specify the same formulas as equal-style
 variables but can also include per-atom values, such as atom
 coordinates.  Thus it is easy to specify a spatially-dependent
 velocity field.</p>
 <p>The <em>scale</em> style computes the current temperature of the group of
 atoms and then rescales the velocities to the specified temperature.</p>
 <p>The <em>ramp</em> style is similar to that used by the <a class="reference internal" href="compute_temp_ramp.html"><em>compute temp/ramp</em></a> command.  Velocities ramped
 uniformly from vlo to vhi are applied to dimension vx, or vy, or vz.
 The value assigned to a particular atom depends on its relative
 coordinate value (in dim) from clo to chi.  For the example above, an
 atom with y-coordinate of 10 (1/4 of the way from 5 to 25), would be
 assigned a x-velocity of 1.25 (1/4 of the way from 0.0 to 5.0).  Atoms
 outside the coordinate bounds (less than 5 or greater than 25 in this
 case), are assigned velocities equal to vlo or vhi (0.0 or 5.0 in this
 case).</p>
 <p>The <em>zero</em> style adjusts the velocities of the group of atoms so that
 the aggregate linear or angular momentum is zero.  No other changes
 are made to the velocities of the atoms.  If the <em>rigid</em> option is
 specified (see below), then the zeroing is performed on individual
 rigid bodies, as defined by the <a class="reference internal" href="fix_rigid.html"><em>fix rigid or fix rigid/small</em></a> commands.  In other words, zero linear
 will set the linear momentum of each rigid body to zero, and zero
 angular will set the angular momentum of each rigid body to zero.
 This is done by adjusting the velocities of the atoms in each rigid
 body.</p>
 <p>All temperatures specified in the velocity command are in temperature
 units; see the <a class="reference internal" href="units.html"><em>units</em></a> command.  The units of velocities and
 coordinates depend on whether the <em>units</em> keyword is set to <em>box</em> or
 <em>lattice</em>, as discussed below.</p>
 <p>For all styles, no atoms are assigned z-component velocities if the
 simulation is 2d; see the <a class="reference internal" href="dimension.html"><em>dimension</em></a> command.</p>
 <hr class="docutils" />
 <p>The keyword/value options are used in the following ways by the
 various styles.</p>
 <p>The <em>dist</em> keyword is used by <em>create</em>.  The ensemble of generated
 velocities can be a <em>uniform</em> distribution from some minimum to
 maximum value, scaled to produce the requested temperature.  Or it can
 be a <em>gaussian</em> distribution with a mean of 0.0 and a sigma scaled to
 produce the requested temperature.</p>
 <p>The <em>sum</em> keyword is used by all styles, except <em>zero</em>.  The new
 velocities will be added to the existing ones if sum = yes, or will
 replace them if sum = no.</p>
 <p>The <em>mom</em> and <em>rot</em> keywords are used by <em>create</em>.  If mom = yes, the
 linear momentum of the newly created ensemble of velocities is zeroed;
 if rot = yes, the angular momentum is zeroed.</p>
 <p><a href="#id1"><span class="problematic" id="id2">*</span></a>line</p>
 <p>If specified, the <em>temp</em> keyword is used by <em>create</em> and <em>scale</em> to
 specify a <a class="reference internal" href="compute.html"><em>compute</em></a> that calculates temperature in a
 desired way, e.g. by first subtracting out a velocity bias, as
 discussed in <a class="reference internal" href="Section_howto.html#howto-15"><span>Section howto 16</span></a> of the doc
 pages.  If this keyword is not specified, <em>create</em> and <em>scale</em>
 calculate temperature using a compute that is defined internally as
 follows:</p>
 <div class="highlight-python"><div class="highlight"><pre>compute velocity_temp group-ID temp
 </pre></div>
 </div>
 <p>where group-ID is the same ID used in the velocity command. i.e. the
 group of atoms whose velocity is being altered.  This compute is
 deleted when the velocity command is finished.  See the <a class="reference internal" href="compute_temp.html"><em>compute temp</em></a> command for details.  If the calculated
 temperature should have degrees-of-freedom removed due to fix
 constraints (e.g. SHAKE or rigid-body constraints), then the
 appropriate fix command must be specified before the velocity command
 is issued.</p>
 <p>The <em>bias</em> keyword with a <em>yes</em> setting is used by <em>create</em> and
 <em>scale</em>, but only if the <em>temp</em> keyword is also used to specify a
 <a class="reference internal" href="compute.html"><em>compute</em></a> that calculates temperature in a desired way.
 If the temperature compute also calculates a velocity bias, the the
 bias is subtracted from atom velocities before the <em>create</em> and
 <em>scale</em> operations are performed.  After the operations, the bias is
 added back to the atom velocities.  See <a class="reference internal" href="Section_howto.html#howto-15"><span>Section howto 16</span></a> of the doc pages for more discussion
 of temperature computes with biases.  Note that the velocity bias is
 only applied to atoms in the temperature compute specified with the
 <em>temp</em> keyword.</p>
 <p>As an example, assume atoms are currently streaming in a flow
 direction (which could be separately initialized with the <em>ramp</em>
 style), and you wish to initialize their thermal velocity to a desired
 temperature.  In this context thermal velocity means the per-particle
 velocity that remains when the streaming velocity is subtracted.  This
 can be done using the <em>create</em> style with the <em>temp</em> keyword
 specifying the ID of a <a class="reference internal" href="compute_temp_ramp.html"><em>compute temp/ramp</em></a> or
 <a class="reference internal" href="compute_temp_profile.html"><em>compute temp/profile</em></a> command, and the
 <em>bias</em> keyword set to a <em>yes</em> value.</p>
 <hr class="docutils" />
 <p>The <em>loop</em> keyword is used by <em>create</em> in the following ways.</p>
 <p>If loop = all, then each processor loops over all atoms in the
 simulation to create velocities, but only stores velocities for atoms
 it owns.  This can be a slow loop for a large simulation.  If atoms
 were read from a data file, the velocity assigned to a particular atom
 will be the same, independent of how many processors are being used.
 This will not be the case if atoms were created using the
 <a class="reference internal" href="create_atoms.html"><em>create_atoms</em></a> command, since atom IDs will likely
 be assigned to atoms differently.</p>
 <p>If loop = local, then each processor loops over only its atoms to
 produce velocities.  The random number seed is adjusted to give a
 different set of velocities on each processor.  This is a fast loop,
 but the velocity assigned to a particular atom will depend on which
 processor owns it.  Thus the results will always be different when a
 simulation is run on a different number of processors.</p>
 <p>If loop = geom, then each processor loops over only its atoms.  For
 each atom a unique random number seed is created, based on the atom&#8217;s
 xyz coordinates.  A velocity is generated using that seed.  This is a
 fast loop and the velocity assigned to a particular atom will be the
 same, independent of how many processors are used.  However, the set
 of generated velocities may be more correlated than if the <em>all</em> or
 <em>local</em> keywords are used.</p>
 <p>Note that the <em>loop geom</em> keyword will not necessarily assign
 identical velocities for two simulations run on different machines.
 This is because the computations based on xyz coordinates are
 sensitive to tiny differences in the double-precision value for a
 coordinate as stored on a particular machine.</p>
 <hr class="docutils" />
 <p>The <em>rigid</em> keyword only has meaning when used with the <em>zero</em> style.
 It allows specification of a fix-ID for one of the <a class="reference internal" href="fix_rigid.html"><em>rigid-body fix</em></a> variants which defines a set of rigid bodies.  The
 zeroing of linear or angular momentum is then performed for each rigid
 body defined by the fix, as described above.</p>
 <p>The <em>units</em> keyword is used by <em>set</em> and <em>ramp</em>.  If units = box,
 the velocities and coordinates specified in the velocity command are
 in the standard units described by the <a class="reference internal" href="units.html"><em>units</em></a> command
 (e.g. Angstroms/fmsec for real units).  If units = lattice, velocities
 are in units of lattice spacings per time (e.g. spacings/fmsec) and
 coordinates are in lattice spacings.  The <a class="reference internal" href="lattice.html"><em>lattice</em></a>
 command must have been previously used to define the lattice spacing.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>Assigning a temperature via the <em>create</em> style to a system with <a class="reference internal" href="fix_rigid.html"><em>rigid bodies</em></a> or <a class="reference internal" href="fix_shake.html"><em>SHAKE constraints</em></a> may not
 have the desired outcome for two reasons.  First, the velocity command
 can be invoked before all of the relevant fixes are created and
 initialized and the number of adjusted degrees of freedom (DOFs) is
 known.  Thus it is not possible to compute the target temperature
 correctly.  Second, the assigned velocities may be partially canceled
 when constraints are first enforced, leading to a different
 temperature than desired.  A workaround for this is to perform a <a class="reference internal" href="run.html"><em>run 0</em></a> command, which insures all DOFs are accounted for
 properly, and then rescale the temperature to the desired value before
 performing a simulation.  For example:</p>
 <div class="highlight-python"><div class="highlight"><pre>velocity all create 300.0 12345
 run 0                             # temperature may not be 300K
 velocity all scale 300.0          # now it should be
 </pre></div>
 </div>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="fix_rigid.html"><em>fix rigid</em></a>, <a class="reference internal" href="fix_shake.html"><em>fix shake</em></a>,
 <a class="reference internal" href="lattice.html"><em>lattice</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The keyword defaults are dist = uniform, sum = no, mom = yes, rot =
 no, bias = no, loop = all, and units = lattice.  The temp and rigid
 keywords are not defined by default.</p>
 </div>
 </div>
 
 
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   <div class="section" id="write-data-command">
 <span id="index-0"></span><h1>write_data command<a class="headerlink" href="#write-data-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>write_data file keyword value ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>file = name of data file to write out</li>
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>pair</em> or <em>nocoeff</em></li>
 </ul>
 <pre class="literal-block">
 <em>nocoeff</em> = do not write out force field info
-  <em>pair</em> value = <em>ii</em> or <em>ij</em>
-    <em>ii</em> = write one line of pair coefficient info per atom type
-    <em>ij</em> = write one line of pair coefficient info per IJ atom type pair
+<em>pair</em> value = <em>ii</em> or <em>ij</em>
+  <em>ii</em> = write one line of pair coefficient info per atom type
+  <em>ij</em> = write one line of pair coefficient info per IJ atom type pair
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>write_data data.polymer
 write_data data.*
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Write a data file in text format of the current state of the
 simulation.  Data files can be read by the <a class="reference internal" href="read_data.html"><em>read data</em></a>
 command to begin a simulation.  The <a class="reference internal" href="read_data.html"><em>read_data</em></a> command
 also describes their format.</p>
 <p>Similar to <a class="reference internal" href="dump.html"><em>dump</em></a> files, the data filename can contain a &#8220;*&#8221;
 wild-card character.  The &#8220;*&#8221; is replaced with the current timestep
 value.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">The write-data command is not yet fully implemented in
 two respects.  First, most pair styles do not yet write their
 coefficient information into the data file.  This means you will need
 to specify that information in your input script that reads the data
 file, via the <a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a> command.  Second, a few of
 the <a class="reference internal" href="atom_style.html"><em>atom styles</em></a> (body, ellipsoid, line, tri) that
 store auxiliary &#8220;bonus&#8221; information about aspherical particles, do not
 yet write the bonus info into the data file.  Both these
 functionalities will be added to the write_data command later.</p>
 </div>
 <p>Because a data file is in text format, if you use a data file written
 out by this command to restart a simulation, the initial state of the
 new run will be slightly different than the final state of the old run
 (when the file was written) which was represented internally by LAMMPS
 in binary format.  A new simulation which reads the data file will
 thus typically diverge from a simulation that continued in the
 original input script.</p>
 <p>If you want to do more exact restarts, using binary files, see the
 <a class="reference internal" href="restart.html"><em>restart</em></a>, <a class="reference internal" href="write_restart.html"><em>write_restart</em></a>, and
 <a class="reference internal" href="read_restart.html"><em>read_restart</em></a> commands.  You can also convert
 binary restart files to text data files, after a simulation has run,
 using the <a class="reference internal" href="Section_start.html#start-7"><span>-r command-line switch</span></a>.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">Only limited information about a simulation is stored
 in a data file.  For example, no information about atom
 <a class="reference internal" href="group.html"><em>groups</em></a> and <a class="reference internal" href="fix.html"><em>fixes</em></a> are stored.  <a class="reference internal" href="read_restart.html"><em>Binary restart files</em></a> store more information.</p>
 </div>
 <p>Bond interactions (angle, etc) that have been turned off by the <a class="reference internal" href="fix_shake.html"><em>fix shake</em></a> or <a class="reference internal" href="delete_bonds.html"><em>delete_bonds</em></a> command will
 be written to a data file as if they are turned on.  This means they
 will need to be turned off again in a new run after the data file is
 read.</p>
 <p>Bonds that are broken (e.g. by a bond-breaking potential) are not
 written to the data file.  Thus these bonds will not exist when the
 data file is read.</p>
 <hr class="docutils" />
 <p>The <em>nocoeff</em> keyword requests that no force field parameters should
 be written to the data file. This can be very helpful, if one wants
 to make significant changes to the force field or if the parameters
 are read in separately anyway, e.g. from an include file.</p>
 <p>The <em>pair</em> keyword lets you specify in what format the pair
 coefficient information is written into the data file.  If the value
 is specified as <em>ii</em>, then one line per atom type is written, to
 specify the coefficients for each of the I=J interactions.  This means
 that no cross-interactions for I != J will be specified in the data
 file and the pair style will apply its mixing rule, as documented on
 individual <a class="reference internal" href="pair_style.html"><em>pair_style</em></a> doc pages.  Of course this
 behavior can be overridden in the input script after reading the data
 file, by specifying additional <a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a> commands
 for any desired I,J pairs.</p>
 <p>If the value is specified as <em>ij</em>, then one line of coefficients is
 written for all I,J pairs where I &lt;= J.  These coefficients will
 include any specific settings made in the input script up to that
 point.  The presence of these I != J coefficients in the data file
 will effectively turn off the default mixing rule for the pair style.
 Again, the coefficient values in the data file can can be overridden
 in the input script after reading the data file, by specifying
 additional <a class="reference internal" href="pair_coeff.html"><em>pair_coeff</em></a> commands for any desired I,J
 pairs.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>This command requires inter-processor communication to migrate atoms
 before the data file is written.  This means that your system must be
 ready to perform a simulation before using this command (force fields
 setup, atom masses initialized, etc).</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="read_data.html"><em>read_data</em></a>, <a class="reference internal" href="write_restart.html"><em>write_restart</em></a></p>
 </div>
 <div class="section" id="default">
 <h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
 <p>The option defaults are pair = ii.</p>
 </div>
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   <div class="section" id="write-restart-command">
 <span id="index-0"></span><h1>write_restart command<a class="headerlink" href="#write-restart-command" title="Permalink to this headline">¶</a></h1>
 <div class="section" id="syntax">
 <h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>write_restart file keyword value ...
 </pre></div>
 </div>
 <ul class="simple">
 <li>file = name of file to write restart information to</li>
 <li>zero or more keyword/value pairs may be appended</li>
 <li>keyword = <em>fileper</em> or <em>nfile</em></li>
 </ul>
 <pre class="literal-block">
 <em>fileper</em> arg = Np
-    Np = write one file for every this many processors
-  <em>nfile</em> arg = Nf
-    Nf = write this many files, one from each of Nf processors
+  Np = write one file for every this many processors
+<em>nfile</em> arg = Nf
+  Nf = write this many files, one from each of Nf processors
 </pre>
 </div>
 <div class="section" id="examples">
 <h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
 <div class="highlight-python"><div class="highlight"><pre>write_restart restart.equil
 write_restart restart.equil.mpiio
 write_restart poly.%.* nfile 10
 </pre></div>
 </div>
 </div>
 <div class="section" id="description">
 <h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
 <p>Write a binary restart file of the current state of the simulation.</p>
 <p>During a long simulation, the <a class="reference internal" href="restart.html"><em>restart</em></a> command is
 typically used to output restart files periodically.  The
 write_restart command is useful after a minimization or whenever you
 wish to write out a single current restart file.</p>
 <p>Similar to <a class="reference internal" href="dump.html"><em>dump</em></a> files, the restart filename can contain
 two wild-card characters.  If a &#8220;*&#8221; appears in the filename, it is
 replaced with the current timestep value.  If a &#8220;%&#8221; character appears
 in the filename, then one file is written by each processor and the
 &#8220;%&#8221; character is replaced with the processor ID from 0 to P-1.  An
 additional file with the &#8220;%&#8221; replaced by &#8220;base&#8221; is also written, which
 contains global information.  For example, the files written for
 filename restart.% would be restart.base, restart.0, restart.1, ...
 restart.P-1.  This creates smaller files and can be a fast mode of
 output and subsequent input on parallel machines that support parallel
 I/O.  The optional <em>fileper</em> and <em>nfile</em> keywords discussed below can
 alter the number of files written.</p>
 <p>The restart file can also be written in parallel as one large binary
 file via the MPI-IO library, which is part of the MPI standard for
 versions 2.0 and above.  Using MPI-IO requires two steps.  First,
 build LAMMPS with its MPIIO package installed, e.g.</p>
 <div class="highlight-python"><div class="highlight"><pre>make yes-mpiio    # installs the MPIIO package
 make g++          # build LAMMPS for your platform
 </pre></div>
 </div>
 <p>Second, use a restart filename which contains &#8221;.mpiio&#8221;.  Note that it
 does not have to end in &#8221;.mpiio&#8221;, just contain those characters.
 Unlike MPI-IO dump files, a particular restart file must be both
 written and read using MPI-IO.</p>
 <p>Restart files can be read by a <a class="reference internal" href="read_restart.html"><em>read_restart</em></a>
 command to restart a simulation from a particular state.  Because the
 file is binary (to enable exact restarts), it may not be readable on
 another machine.  In this case, you can use the <a class="reference internal" href="Section_start.html#start-7"><span>-r command-line switch</span></a> to convert a restart file to a data
 file.</p>
 <div class="admonition warning">
 <p class="first admonition-title">Warning</p>
 <p class="last">Although the purpose of restart files is to enable
 restarting a simulation from where it left off, not all information
 about a simulation is stored in the file.  For example, the list of
 fixes that were specified during the initial run is not stored, which
 means the new input script must specify any fixes you want to use.
 Even when restart information is stored in the file, as it is for some
 fixes, commands may need to be re-specified in the new input script,
 in order to re-use that information. Details are usually given in
 the documentation of the respective command. Also, see the
 <a class="reference internal" href="read_restart.html"><em>read_restart</em></a> command for general information
 about what is stored in a restart file.</p>
 </div>
 <hr class="docutils" />
 <p>The optional <em>nfile</em> or <em>fileper</em> keywords can be used in conjunction
 with the &#8220;%&#8221; wildcard character in the specified restart file name.
 As explained above, the &#8220;%&#8221; character causes the restart file to be
 written in pieces, one piece for each of P processors.  By default P =
 the number of processors the simulation is running on.  The <em>nfile</em> or
 <em>fileper</em> keyword can be used to set P to a smaller value, which can
 be more efficient when running on a large number of processors.</p>
 <p>The <em>nfile</em> keyword sets P to the specified Nf value.  For example, if
 Nf = 4, and the simulation is running on 100 processors, 4 files will
 be written, by processors 0,25,50,75.  Each will collect information
 from itself and the next 24 processors and write it to a restart file.</p>
 <p>For the <em>fileper</em> keyword, the specified value of Np means write one
 file for every Np processors.  For example, if Np = 4, every 4th
 processor (0,4,8,12,etc) will collect information from itself and the
 next 3 processors and write it to a restart file.</p>
 </div>
 <hr class="docutils" />
 <div class="section" id="restrictions">
 <h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
 <p>This command requires inter-processor communication to migrate atoms
 before the restart file is written.  This means that your system must
 be ready to perform a simulation before using this command (force
 fields setup, atom masses initialized, etc).</p>
 <p>To write and read restart files in parallel with MPI-IO, the MPIIO
 package must be installed.</p>
 </div>
 <div class="section" id="related-commands">
 <h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
 <p><a class="reference internal" href="restart.html"><em>restart</em></a>, <a class="reference internal" href="read_restart.html"><em>read_restart</em></a>,
 <a class="reference internal" href="write_data.html"><em>write_data</em></a></p>
 <p><strong>Default:</strong> none</p>
 </div>
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