<p>where K is a prefactor, theta is the angle formed by the atoms
specified by (i,j,k,l) indices and theta0 its equilibrium value.</p>
<p>If the 4 atoms in an improper quadruplet (listed in the data file read
by the <aclass="reference internal"href="read_data.html"><spanclass="doc">read_data</span></a> command) are ordered i,j,k,l then
<ahref="#id1"><spanclass="problematic"id="id2">theta_</span></a><em>ijl</em> is the angle between atoms i,j and l, <ahref="#id3"><spanclass="problematic"id="id4">theta_</span></a><em>ijk</em> is the
angle between atoms i,j and k, <ahref="#id5"><spanclass="problematic"id="id6">theta_</span></a><em>kjl</em> is the angle between atoms
j,k, and l.</p>
<p>The “ring” improper style implements the improper potential introduced
by Destree et al., in Equation (9) of <aclass="reference internal"href="#destree"><spanclass="std std-ref">(Destree)</span></a>. This
potential does not affect small amplitude vibrations but is used in an
ad-hoc way to prevent the onset of accidentially large amplitude
fluctuations leading to the occurrence of a planar conformation of the
three bonds i-j, j-k and j-l, an intermediate conformation toward the
chiral inversion of a methine carbon. In the “Impropers” section of
data file four atoms: i, j, k and l are specified with i,j and l lying
on the backbone of the chain and k specifying the chirality of j.</p>
<p>The following coefficients must be defined for each improper type via
the <aclass="reference internal"href="improper_coeff.html"><spanclass="doc">improper_coeff</span></a> command as in the example
above, or in the data file or restart files read by the
<aclass="reference internal"href="read_data.html"><spanclass="doc">read_data</span></a> or <aclass="reference internal"href="read_restart.html"><spanclass="doc">read_restart</span></a>
commands:</p>
<ulclass="simple">
<li>K (energy/radian^2)</li>
<li>theta0 (degrees)</li>
</ul>
<p>theta0 is specified in degrees, but LAMMPS converts it to radians
internally; hence the units of K are in energy/radian^2.</p>
<hrclass="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 <aclass="reference internal"href="Section_accelerate.html"><spanclass="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 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 <aclass="reference internal"href="Section_start.html#start-3"><spanclass="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 <aclass="reference internal"href="Section_start.html#start-7"><spanclass="std std-ref">-suffix command-line switch</span></a> when you invoke LAMMPS, or you can
use the <aclass="reference internal"href="suffix.html"><spanclass="doc">suffix</span></a> command in your input script.</p>
<p>See <aclass="reference internal"href="Section_accelerate.html"><spanclass="doc">Section_accelerate</span></a> of the manual for
more instructions on how to use the accelerated styles effectively.</p>
</div>
<hrclass="docutils"/>
<divclass="section"id="restrictions">
<h2>Restrictions</h2>
<p>This improper style can only be used if LAMMPS was built with the
USER-MISC package. See the <aclass="reference internal"href="Section_start.html#start-3"><spanclass="std std-ref">Making LAMMPS</span></a>
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