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<li><a class="reference internal" href="#">pair_style resquared command</a></li>
<li><a class="reference internal" href="#pair-style-resquared-gpu-command">pair_style resquared/gpu command</a></li>
<li><a class="reference internal" href="#pair-style-resquared-omp-command">pair_style resquared/omp command</a><ul>
<li><a class="reference internal" href="#syntax">Syntax</a></li>
<li><a class="reference internal" href="#examples">Examples</a></li>
<li><a class="reference internal" href="#description">Description</a></li>
<li><a class="reference internal" href="#restrictions">Restrictions</a></li>
<li><a class="reference internal" href="#related-commands">Related commands</a></li>
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<div class="section" id="pair-style-resquared-command">
<span id="index-0"></span><h1>pair_style resquared command</h1>
</div>
<div class="section" id="pair-style-resquared-gpu-command">
<h1>pair_style resquared/gpu command</h1>
</div>
<div class="section" id="pair-style-resquared-omp-command">
<h1>pair_style resquared/omp command</h1>
<div class="section" id="syntax">
<h2>Syntax</h2>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">pair_style</span> <span class="n">resquared</span> <span class="n">cutoff</span>
</pre></div>
</div>
<ul class="simple">
<li>cutoff = global cutoff for interactions (distance units)</li>
</ul>
</div>
<div class="section" id="examples">
<h2>Examples</h2>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">pair_style</span> <span class="n">resquared</span> <span class="mf">10.0</span>
<span class="n">pair_coeff</span> <span class="o">*</span> <span class="o">*</span> <span class="mf">1.0</span> <span class="mf">1.0</span> <span class="mf">1.7</span> <span class="mf">3.4</span> <span class="mf">3.4</span> <span class="mf">1.0</span> <span class="mf">1.0</span> <span class="mf">1.0</span>
</pre></div>
</div>
</div>
<div class="section" id="description">
<h2>Description</h2>
<p>Style <em>resquared</em> computes the RE-squared anisotropic interaction
<a class="reference internal" href="#everaers"><span class="std std-ref">(Everaers)</span></a>, <a class="reference internal" href="#babadi"><span class="std std-ref">(Babadi)</span></a> between pairs of
ellipsoidal and/or spherical Lennard-Jones particles. For ellipsoidal
interactions, the potential considers the ellipsoid as being comprised
of small spheres of size sigma. LJ particles are a single sphere of
size sigma. The distinction is made to allow the pair style to make
efficient calculations of ellipsoid/solvent interactions.</p>
<p>Details for the equations used are given in the references below and
in <a class="reference external" href="PDF/pair_resquared_extra.pdf">this supplementary document</a>.</p>
<p>Use of this pair style requires the NVE, NVT, or NPT fixes with the
<em>asphere</em> extension (e.g. <a class="reference internal" href="fix_nve_asphere.html"><span class="doc">fix nve/asphere</span></a>) in
order to integrate particle rotation. Additionally, <a class="reference internal" href="atom_style.html"><span class="doc">atom_style ellipsoid</span></a> should be used since it defines the
rotational state and the size and shape of each ellipsoidal particle.</p>
<p>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:</p>
<ul class="simple">
<li>A12 = Energy Prefactor/Hamaker constant (energy units)</li>
<li>sigma = atomic interaction diameter (distance units)</li>
<li>epsilon_i_a = relative well depth of type I for side-to-side interactions</li>
<li>epsilon_i_b = relative well depth of type I for face-to-face interactions</li>
<li>epsilon_i_c = relative well depth of type I for end-to-end interactions</li>
<li>epsilon_j_a = relative well depth of type J for side-to-side interactions</li>
<li>epsilon_j_b = relative well depth of type J for face-to-face interactions</li>
<li>epsilon_j_c = relative well depth of type J for end-to-end interactions</li>
<li>cutoff (distance units)</li>
</ul>
<p>The parameters used depend on the type of the interacting particles,
i.e. ellipsoids or LJ spheres. The type of a particle is determined
by the diameters specified for its 3 shape paramters. If all 3 shape
parameters = 0.0, then the particle is treated as an LJ sphere. The
epsilon_i_* or epsilon_j_* parameters are ignored for LJ spheres. If
the 3 shape paraemters are &gt; 0.0, then the particle is treated as an
ellipsoid (even if the 3 parameters are equal to each other).</p>
<p>A12 specifies the energy prefactor which depends on the types of the
two interacting particles.</p>
<p>For ellipsoid/ellipsoid interactions, the interaction is computed by
the formulas in the supplementary docuement referenced above. A12 is
the Hamaker constant as described in <a class="reference internal" href="#everaers"><span class="std std-ref">(Everaers)</span></a>. In LJ
units:</p>
<img alt="_images/pair_resquared.jpg" class="align-center" src="_images/pair_resquared.jpg" />
<p>where rho gives the number density of the spherical particles
composing the ellipsoids and epsilon_LJ determines the interaction
strength of the spherical particles.</p>
<p>For ellipsoid/LJ sphere interactions, the interaction is also computed
by the formulas in the supplementary docuement referenced above. A12
has a modifed form (see <a class="reference external" href="PDF/pair_resquared_extra.pdf">here</a> for
details):</p>
<img alt="_images/pair_resquared2.jpg" class="align-center" src="_images/pair_resquared2.jpg" />
<p>For ellipsoid/LJ sphere interactions, a correction to the distance-
of-closest approach equation has been implemented to reduce the error
from two particles of disparate sizes; see <a class="reference external" href="PDF/pair_resquared_extra.pdf">this supplementary document</a>.</p>
<p>For LJ sphere/LJ sphere interactions, the interaction is computed
using the standard Lennard-Jones formula, which is much cheaper to
compute than the ellipsoidal formulas. A12 is used as epsilon in the
standard LJ formula:</p>
<img alt="_images/pair_resquared3.jpg" class="align-center" src="_images/pair_resquared3.jpg" />
<p>and the specified <em>sigma</em> is used as the sigma in the standard LJ
formula.</p>
<p>When one of both of the interacting particles are ellipsoids, then
<em>sigma</em> specifies the diameter of the continuous distribution of
constituent particles within each ellipsoid used to model the
RE-squared potential. Note that this is a different meaning for
<em>sigma</em> than the <a class="reference internal" href="pair_gayberne.html"><span class="doc">pair_style gayberne</span></a> potential
uses.</p>
<p>The epsilon_i and epsilon_j coefficients are defined for atom types,
not for pairs of atom types. Thus, in a series of pair_coeff
commands, they only need to be specified once for each atom type.</p>
<p>Specifically, if any of epsilon_i_a, epsilon_i_b, epsilon_i_c are
non-zero, the three values are assigned to atom type I. If all the
epsilon_i values are zero, they are ignored. If any of epsilon_j_a,
epsilon_j_b, epsilon_j_c are non-zero, the three values are assigned
to atom type J. If all three epsilon_i values are zero, they are
ignored. Thus the typical way to define the epsilon_i and epsilon_j
coefficients is to list their values in &#8220;pair_coeff I J&#8221; commands when
I = J, but set them to 0.0 when I != J. If you do list them when I !=
J, you should insure they are consistent with their values in other
pair_coeff commands.</p>
<p>Note that if this potential is being used as a sub-style of
<a class="reference internal" href="pair_hybrid.html"><span class="doc">pair_style hybrid</span></a>, and there is no &#8220;pair_coeff I I&#8221;
setting made for RE-squared for a particular type I (because I-I
interactions are computed by another hybrid pair potential), then you
still need to insure the epsilon a,b,c coefficients are assigned to
that type in a &#8220;pair_coeff I J&#8221; command.</p>
<p>For large uniform molecules it has been shown that the epsilon_*_*
energy parameters are approximately representable in terms of local
contact curvatures <a class="reference internal" href="#everaers"><span class="std std-ref">(Everaers)</span></a>:</p>
<img alt="_images/pair_resquared4.jpg" class="align-center" src="_images/pair_resquared4.jpg" />
<p>where a, b, and c give the particle diameters.</p>
<p>The last coefficient is optional. If not specified, the global cutoff
specified in the pair_style command is used.</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 <span class="xref std std-ref">Making LAMMPS</span> 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 <span class="xref std std-ref">-suffix command-line switch</span> 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 can be mixed, but only for sphere pairs. The
default mix value is <em>geometric</em>. See the &#8220;pair_modify&#8221; command for
details. Other type pairs cannot be mixed, due to the different
meanings of the energy prefactors used to calculate the interactions
and the implicit dependence of the ellipsoid-sphere interaction on the
equation for the Hamaker constant presented here. Mixing of sigma and
epsilon followed by calculation of the energy prefactors using the
equations above is recommended.</p>
<p>This pair styles supports 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, but only for sphere-sphere interactions. There is no
shifting performed for ellipsoidal interactions due to the anisotropic
dependence of the interaction.</p>
<p>The <a class="reference internal" href="pair_modify.html"><span class="doc">pair_modify</span></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"><span class="doc">pair_modify</span></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"><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>This pair style can only be used via the <em>pair</em> keyword of the
<a class="reference internal" href="run_style.html"><span class="doc">run_style respa</span></a> command. It does not support the
<em>inner</em>, <em>middle</em>, <em>outer</em> keywords of the <a class="reference internal" href="run_style.html"><span class="doc">run_style command</span></a>.</p>
</div>
<hr class="docutils" />
<div class="section" id="restrictions">
<h2>Restrictions</h2>
<p>This style is part of the ASPHERE package. It is only enabled if
LAMMPS was built with that package. See the <span class="xref std std-ref">Making LAMMPS</span> section for more info.</p>
<p>This pair style requires that atoms be ellipsoids as defined by the
<a class="reference internal" href="atom_style.html"><span class="doc">atom_style ellipsoid</span></a> command.</p>
<p>Particles acted on by the potential can be finite-size aspherical or
spherical particles, or point particles. Spherical particles have all
3 of their shape parameters equal to each other. Point particles have
all 3 of their shape parameters equal to 0.0.</p>
<p>The distance-of-closest-approach approximation used by LAMMPS becomes
less accurate when high-aspect ratio ellipsoids are used.</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>, <a class="reference internal" href="fix_nve_asphere.html"><span class="doc">fix nve/asphere</span></a>,
<a class="reference internal" href="compute_temp_asphere.html"><span class="doc">compute temp/asphere</span></a>, <a class="reference internal" href="pair_gayberne.html"><span class="doc">pair_style gayberne</span></a></p>
<p><strong>Default:</strong> none</p>
<hr class="docutils" />
<p id="everaers"><strong>(Everaers)</strong> Everaers and Ejtehadi, Phys Rev E, 67, 041710 (2003).</p>
<p id="babadi"><strong>(Berardi)</strong> Babadi, Ejtehadi, Everaers, J Comp Phys, 219, 770-779 (2006).</p>
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