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<div class="section" id="pair-style-lj-cut-command">
<span id="index-0"></span><h1>pair_style lj/cut command</h1>
</div>
<div class="section" id="pair-style-lj-cut-gpu-command">
<h1>pair_style lj/cut/gpu command</h1>
</div>
<div class="section" id="pair-style-lj-cut-intel-command">
<h1>pair_style lj/cut/intel command</h1>
</div>
<div class="section" id="pair-style-lj-cut-kk-command">
<h1>pair_style lj/cut/kk command</h1>
</div>
<div class="section" id="pair-style-lj-cut-opt-command">
<h1>pair_style lj/cut/opt command</h1>
</div>
<div class="section" id="pair-style-lj-cut-omp-command">
<h1>pair_style lj/cut/omp command</h1>
</div>
<div class="section" id="pair-style-lj-cut-coul-cut-command">
<h1>pair_style lj/cut/coul/cut command</h1>
</div>
<div class="section" id="pair-style-lj-cut-coul-cut-gpu-command">
<h1>pair_style lj/cut/coul/cut/gpu command</h1>
</div>
<div class="section" id="pair-style-lj-cut-coul-cut-omp-command">
<h1>pair_style lj/cut/coul/cut/omp command</h1>
</div>
<div class="section" id="pair-style-lj-cut-coul-debye-command">
<h1>pair_style lj/cut/coul/debye command</h1>
</div>
<div class="section" id="pair-style-lj-cut-coul-debye-gpu-command">
<h1>pair_style lj/cut/coul/debye/gpu command</h1>
</div>
<div class="section" id="pair-style-lj-cut-coul-debye-kk-command">
<h1>pair_style lj/cut/coul/debye/kk command</h1>
</div>
<div class="section" id="pair-style-lj-cut-coul-debye-omp-command">
<h1>pair_style lj/cut/coul/debye/omp command</h1>
</div>
<div class="section" id="pair-style-lj-cut-coul-dsf-command">
<h1>pair_style lj/cut/coul/dsf command</h1>
</div>
<div class="section" id="pair-style-lj-cut-coul-dsf-gpu-command">
<h1>pair_style lj/cut/coul/dsf/gpu command</h1>
</div>
<div class="section" id="pair-style-lj-cut-coul-dsf-kk-command">
<h1>pair_style lj/cut/coul/dsf/kk command</h1>
</div>
<div class="section" id="pair-style-lj-cut-coul-dsf-omp-command">
<h1>pair_style lj/cut/coul/dsf/omp command</h1>
</div>
<div class="section" id="pair-style-lj-cut-coul-long-command">
<h1>pair_style lj/cut/coul/long command</h1>
</div>
<div class="section" id="pair-style-lj-cut-coul-long-cs-command">
<h1>pair_style lj/cut/coul/long/cs command</h1>
</div>
<div class="section" id="pair-style-lj-cut-coul-long-gpu-command">
<h1>pair_style lj/cut/coul/long/gpu command</h1>
</div>
<div class="section" id="pair-style-lj-cut-coul-long-intel-command">
<h1>pair_style lj/cut/coul/long/intel command</h1>
</div>
<div class="section" id="pair-style-lj-cut-coul-long-opt-command">
<h1>pair_style lj/cut/coul/long/opt command</h1>
</div>
<div class="section" id="pair-style-lj-cut-coul-long-omp-command">
<h1>pair_style lj/cut/coul/long/omp command</h1>
</div>
<div class="section" id="pair-style-lj-cut-coul-msm-command">
<h1>pair_style lj/cut/coul/msm command</h1>
</div>
<div class="section" id="pair-style-lj-cut-coul-msm-gpu-command">
<h1>pair_style lj/cut/coul/msm/gpu command</h1>
</div>
<div class="section" id="pair-style-lj-cut-coul-msm-omp-command">
<h1>pair_style lj/cut/coul/msm/omp command</h1>
</div>
<div class="section" id="pair-style-lj-cut-tip4p-cut-command">
<h1>pair_style lj/cut/tip4p/cut command</h1>
</div>
<div class="section" id="pair-style-lj-cut-tip4p-cut-omp-command">
<h1>pair_style lj/cut/tip4p/cut/omp command</h1>
</div>
<div class="section" id="pair-style-lj-cut-tip4p-long-command">
<h1>pair_style lj/cut/tip4p/long command</h1>
</div>
<div class="section" id="pair-style-lj-cut-tip4p-long-omp-command">
<h1>pair_style lj/cut/tip4p/long/omp command</h1>
</div>
<div class="section" id="pair-style-lj-cut-tip4p-long-opt-command">
<h1>pair_style lj/cut/tip4p/long/opt command</h1>
<div class="section" id="syntax">
<h2>Syntax</h2>
<pre class="literal-block">
pair_style style args
</pre>
<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/long/cs</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)
</pre>
</div>
<div class="section" id="examples">
<h2>Examples</h2>
<pre class="literal-block">
pair_style lj/cut 2.5
pair_coeff * * 1 1
pair_coeff 1 1 1 1.1 2.8
</pre>
<pre class="literal-block">
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>
<pre class="literal-block">
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>
<pre class="literal-block">
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>
<pre class="literal-block">
pair_style lj/cut/coul/long 10.0
pair_style lj/cut/coul/long/cs 10.0
pair_style lj/cut/coul/long 10.0 8.0
pair_style lj/cut/coul/long/cs 10.0 8.0
pair_coeff * * 100.0 3.0
pair_coeff 1 1 100.0 3.5 9.0
</pre>
<pre class="literal-block">
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>
<pre class="literal-block">
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>
<pre class="literal-block">
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 class="section" id="description">
<h2>Description</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"><span class="doc">dielectric</span></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 class="std std-ref">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"><span class="doc">kspace_style</span></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>Style <em>lj/cut/coul/long/cs</em> is identical to <em>lj/cut/coul/long</em> except
that a term is added for the <a class="reference internal" href="Section_howto.html#howto-25"><span class="std std-ref">core/shell model</span></a> to allow charges on core and shell
particles to be separated by r = 0.0.</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 class="std std-ref">(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 note">
<p class="first admonition-title">Note</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 class="std std-ref">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"><span class="doc">pair_coeff</span></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"><span class="doc">read_data</span></a>
or <a class="reference internal" href="read_restart.html"><span class="doc">read_restart</span></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>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"><span class="doc">Section_accelerate</span></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 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 class="std std-ref">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 class="std std-ref">-suffix command-line switch</span></a> when you invoke LAMMPS, or you can
use the <a class="reference internal" href="suffix.html"><span class="doc">suffix</span></a> command in your input script.</p>
<p>See <a class="reference internal" href="Section_accelerate.html"><span class="doc">Section_accelerate</span></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"><span class="doc">pair_modify</span></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"><span class="doc">pair_modify</span></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"><span class="doc">pair_modify</span></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"><span class="doc">binary restart files</span></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"><span class="doc">run_style respa</span></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"><span class="doc">run_style</span></a> command for details.</p>
</div>
<hr class="docutils" />
<div class="section" id="restrictions">
<h2>Restrictions</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 class="std std-ref">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</h2>
<p><a class="reference internal" href="pair_coeff.html"><span class="doc">pair_coeff</span></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>
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