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<div class="section" id="compute-orientorder-atom-command">
<span id="index-0"></span><h1>compute orientorder/atom command<a class="headerlink" href="#compute-orientorder-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 orientorder/atom 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>orientorder/atom = style name of this compute command</li>
<li>one or more keyword/value pairs may be appended</li>
</ul>
<pre class="literal-block">
keyword = <em>cutoff</em> or <em>nnn</em> or <em>ql</em>
<em>cutoff</em> value = distance cutoff
<em>nnn</em> value = number of nearest neighbors
<em>degrees</em> values = nlvalues, l1, l2,...
</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 orientorder/atom
compute 1 all orientorder/atom degrees 5 4 6 8 10 12 nnn NULL cutoff 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>Define a computation that calculates a set of bond-orientational
order parameters <em>Ql</em> for each atom in a group. These order parameters
were introduced by <a class="reference internal" href="#steinhardt"><span>Steinhardt et al.</span></a> as a way to
characterize the local orientational order in atomic structures.
For each atom, <em>Ql</em> is a real number defined as follows:</p>
<img alt="_images/orientorder.jpg" class="align-center" src="_images/orientorder.jpg" />
<p>The first equation defines the spherical harmonic order parameters.
These are complex number components of the 3D analog of the 2D order
parameter <em>qn</em>, which is implemented as LAMMPS compute
<a class="reference internal" href="compute_hexorder_atom.html"><em>hexorder/atom</em></a>.
The summation is over the <em>nnn</em> nearest
neighbors of the central atom.
The angles theta and phi are the standard spherical polar angles
defining the direction of the bond vector <em>rij</em>.
The second equation defines <em>Ql</em>, which is a
rotationally invariant scalar quantity obtained by summing
over all the components of degree <em>l</em>.</p>
<p>The optional keyword <em>cutoff</em> defines the distance cutoff
used when searching for neighbors. The default value, also
the maximum allowable value, is the cutoff specified
by the pair style.</p>
<p>The optional keyword <em>nnn</em> defines the number of nearest
neighbors used to calculate <em>Ql</em>. The default value is 12.
If the value is NULL, then all neighbors up to the
specified distance cutoff are used.</p>
<p>The optional keyword <em>degrees</em> defines the list of order parameters to
be computed. The first argument <em>nlvalues</em> is the number of order
parameters. This is followed by that number of integers giving the
degree of each order parameter. Because <a href="#id1"><span class="problematic" id="id2">*</span></a>Q*2 and all odd-degree
order parameters are zero for atoms in cubic crystals
(see <a class="reference internal" href="#steinhardt"><span>Steinhardt</span></a>), the default order parameters
are <a href="#id3"><span class="problematic" id="id4">*</span></a>Q*4, <a href="#id5"><span class="problematic" id="id6">*</span></a>Q*6, <a href="#id7"><span class="problematic" id="id8">*</span></a>Q*8, <a href="#id9"><span class="problematic" id="id10">*</span></a>Q*10, and <a href="#id11"><span class="problematic" id="id12">*</span></a>Q*12. For the
FCC crystal with <a href="#id13"><span class="problematic" id="id14">*</span></a>nnn*=12, <a href="#id15"><span class="problematic" id="id16">*</span></a>Q*4 = sqrt(7/3)/8 = 0.19094....
The numerical values of all order parameters up to <a href="#id17"><span class="problematic" id="id18">*</span></a>Q*12
for a range of commonly encountered high-symmetry structures are given
in Table I of <a class="reference internal" href="#mickel"><span>Mickel et al.</span></a>.</p>
<p>The value of <em>Ql</em> is set to zero for atoms not in the
specified compute group, as well as for atoms that have less than
<em>nnn</em> neighbors within the distance cutoff.</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>
<div class="admonition note">
<p class="first admonition-title">Note</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 order parameter. This
difficulty can be circumvented by writing a dump file, and using the
<a class="reference internal" href="rerun.html"><em>rerun</em></a> command to compute the order parameter 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><strong>Output info:</strong></p>
<p>This compute calculates a per-atom array with <em>nlvalues</em> columns, giving the
<em>Ql</em> values for each atom, which are real numbers on the range 0 &lt;= <em>Ql</em> &lt;= 1.</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>
<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_coord_atom.html"><em>compute coord/atom</em></a>, <a class="reference internal" href="compute_centro_atom.html"><em>compute centro/atom</em></a>, <a class="reference internal" href="compute_hexorder_atom.html"><em>compute hexorder/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 option defaults are <em>cutoff</em> = pair style cutoff, <em>nnn</em> = 12, <em>degrees</em> = 5 4 6 8 9 10 12 i.e. <a href="#id19"><span class="problematic" id="id20">*</span></a>Q*4, <a href="#id21"><span class="problematic" id="id22">*</span></a>Q*6, <a href="#id23"><span class="problematic" id="id24">*</span></a>Q*8, <a href="#id25"><span class="problematic" id="id26">*</span></a>Q*10, and <a href="#id27"><span class="problematic" id="id28">*</span></a>Q*12.</p>
<hr class="docutils" />
<p id="mickel"><span id="steinhardt"></span><strong>(Steinhardt)</strong> P. Steinhardt, D. Nelson, and M. Ronchetti, Phys. Rev. B 28, 784 (1983).</p>
<p><strong>(Mickel)</strong> W. Mickel, S. C. Kapfer, G. E. Schroeder-Turkand, K. Mecke, J. Chem. Phys. 138, 044501 (2013).</p>
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