<p>where x is the improper angle, x0 is its equilibrium value, and K is a
prefactor.</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 X
is the angle between the plane of I,J,K and the plane of J,K,L.
Alternatively, you can think of atoms J,K,L as being in a plane, and
atom I above the plane, and X as a measure of how far out-of-plane I
is with respect to the other 3 atoms.</p>
<p>Note that defining 4 atoms to interact in this way, does not mean that
bonds necessarily exist between I-J, J-K, or K-L, as they would in a
linear dihedral. Normally, the bonds I-J, I-K, I-L would exist for an
improper to be defined between the 4 atoms.</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>X0 (degrees)</li>
</ul>
<p>X0 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>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 5</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 <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 5</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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