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<li class="toctree-l2"><a class="reference internal" href="improper_inversion_harmonic.html">improper_style inversion/harmonic command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="improper_none.html">improper_style none command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="improper_ring.html">improper_style ring command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="improper_sqdistharm.html">improper_style sqdistharm command</a></li>
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<li class="toctree-l2"><a class="reference internal" href="improper_umbrella.html">improper_style umbrella command</a></li>
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<p><span class="math notranslate nohighlight">\(\renewcommand{\AA}{\text{Å}}\)</span></p>
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<section id="improper-style-harmonic-command">
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<span id="index-3"></span><span id="index-2"></span><span id="index-1"></span><span id="index-0"></span><h1>improper_style harmonic command<a class="headerlink" href="#improper-style-harmonic-command" title="Link to this heading"></a></h1>
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<p>Accelerator Variants: <em>harmonic/intel</em>, <em>harmonic/kk</em>, <em>harmonic/omp</em></p>
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<section id="syntax">
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<h2>Syntax<a class="headerlink" href="#syntax" title="Link to this heading"></a></h2>
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<div class="highlight-LAMMPS notranslate"><div class="highlight"><pre><span></span><span class="k">improper_style</span><span class="w"> </span><span class="n">harmonic</span>
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</pre></div>
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</div>
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</section>
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<section id="examples">
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<h2>Examples<a class="headerlink" href="#examples" title="Link to this heading"></a></h2>
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<div class="highlight-LAMMPS notranslate"><div class="highlight"><pre><span></span><span class="k">improper_style</span><span class="w"> </span><span class="n">harmonic</span>
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<span class="k">improper_coeff</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="m">100.0</span><span class="w"> </span><span class="m">0</span>
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</pre></div>
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</div>
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</section>
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<section id="description">
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<h2>Description<a class="headerlink" href="#description" title="Link to this heading"></a></h2>
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<p>The <em>harmonic</em> improper style uses the potential</p>
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<div class="math notranslate nohighlight">
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\[E = K (\chi - \chi_0)^2\]</div>
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<p>where <span class="math notranslate nohighlight">\(\chi\)</span> is the improper angle, <span class="math notranslate nohighlight">\(\chi_0\)</span> is its equilibrium
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value, and <span class="math notranslate nohighlight">\(K\)</span> is a prefactor. Note that the usual 1/2 factor is
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included in <span class="math notranslate nohighlight">\(K\)</span>.</p>
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<p>If the 4 atoms in an improper quadruplet (listed in the data file read
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by the <a class="reference internal" href="read_data.html"><span class="doc">read_data</span></a> command) are ordered I,J,K,L then
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<span class="math notranslate nohighlight">\(\chi\)</span>
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is the angle between the plane of I,J,K and the plane of J,K,L.
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Alternatively, you can think of atoms J,K,L as being in a plane, and
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atom I above the plane, and <span class="math notranslate nohighlight">\(\chi\)</span> as a measure of how far out-of-plane
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I is with respect to the other 3 atoms.</p>
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<p>Note that defining 4 atoms to interact in this way, does not mean that
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bonds necessarily exist between I-J, J-K, or K-L, as they would in a
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linear dihedral. Normally, the bonds I-J, I-K, I-L would exist for an
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improper to be defined between the 4 atoms.</p>
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<p>The following coefficients must be defined for each improper type via
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the <a class="reference internal" href="improper_coeff.html"><span class="doc">improper_coeff</span></a> command as in the example
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above, or in the data file or restart files read by the
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<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>
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commands:</p>
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<ul class="simple">
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<li><p><span class="math notranslate nohighlight">\(K\)</span> (energy)</p></li>
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<li><p><span class="math notranslate nohighlight">\(\chi_0\)</span> (degrees)</p></li>
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</ul>
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<p><span class="math notranslate nohighlight">\(\chi_0\)</span> is specified in degrees, but LAMMPS converts it to
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radians internally; hence <span class="math notranslate nohighlight">\(K\)</span> is effectively energy per
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radian^2.</p>
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<hr class="docutils" />
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<p>Styles with a <em>gpu</em>, <em>intel</em>, <em>kk</em>, <em>omp</em>, or <em>opt</em> suffix are
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functionally the same as the corresponding style without the suffix.
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They have been optimized to run faster, depending on your available
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hardware, as discussed on the <a class="reference internal" href="Speed_packages.html"><span class="doc">Accelerator packages</span></a>
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page. The accelerated styles take the same arguments and should
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produce the same results, except for round-off and precision issues.</p>
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<p>These accelerated styles are part of the GPU, INTEL, KOKKOS,
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OPENMP, and OPT packages, respectively. They are only enabled if
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LAMMPS was built with those packages. See the <a class="reference internal" href="Build_package.html"><span class="doc">Build package</span></a> page for more info.</p>
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<p>You can specify the accelerated styles explicitly in your input script
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by including their suffix, or you can use the <a class="reference internal" href="Run_options.html"><span class="doc">-suffix command-line switch</span></a> when you invoke LAMMPS, or you can use the
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<a class="reference internal" href="suffix.html"><span class="doc">suffix</span></a> command in your input script.</p>
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<p>See the <a class="reference internal" href="Speed_packages.html"><span class="doc">Accelerator packages</span></a> page for more
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instructions on how to use the accelerated styles effectively.</p>
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</section>
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<hr class="docutils" />
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<section id="restrictions">
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<h2>Restrictions<a class="headerlink" href="#restrictions" title="Link to this heading"></a></h2>
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<p>This improper style can only be used if LAMMPS was built with the
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MOLECULE package. See the <a class="reference internal" href="Build_package.html"><span class="doc">Build package</span></a> doc page
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for more info.</p>
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</section>
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<section id="related-commands">
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<h2>Related commands<a class="headerlink" href="#related-commands" title="Link to this heading"></a></h2>
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<p><a class="reference internal" href="improper_coeff.html"><span class="doc">improper_coeff</span></a></p>
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</section>
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<section id="default">
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<h2>Default<a class="headerlink" href="#default" title="Link to this heading"></a></h2>
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<p>none</p>
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