<p>This function has zero slope as lambda approaches its extreme values
(0 and 1), according to (<a class="reference internal" href="#dekoning96"><span>de Koning96)</span></a> this results in
smaller fluctuations on the integral to be computed on the
thermodynamic integration.</p>
<div class="admonition warning">
<p class="first admonition-title">Warning</p>
<p class="last">It is importante to keep the center of mass fixed
during the thermodynamic integration, a non-zero total velocity will
result in divergencies during the integration due to the fact that the
atoms are ‘attatched’ to its equilibrium positions by the Einstein
crystal. Check the option <em>zero</em> of <a class="reference external" href="fix_langevin_html">fix langevin</a>
and <a class="reference internal" href="velocity.html"><em>velocity</em></a>. The use of the Nose-Hoover thermostat
(<code class="xref doc docutils literal"><span class="pre">fix</span> <span class="pre">nvt</span></code>) is NOT recommended due to its well documented
issues with the canonical sampling of harmonic degrees of freedom
(notice that the <em>chain</em> option will NOT solve this problem). The
Langevin thermostat (<a class="reference external" href="fix_langevin.html"">fix langevin</a>) works fine.</p>
<h2>Restart, fix_modify, output, run start/stop, minimize info<a class="headerlink" href="#restart-fix-modify-output-run-start-stop-minimize-info" title="Permalink to this headline">¶</a></h2>
<p>This fix writes the original coordinates of tethered atoms to <a class="reference internal" href="restart.html"><em>binary restart files</em></a>, so that the spring effect will be the
same in a restarted simulation. See the <a class="reference internal" href="read_restart.html"><em>read restart</em></a> command for info on how to re-specify a fix
in an input script that reads a restart file, so that the operation of
the fix continues in an uninterrupted fashion.</p>
<p>The <a class="reference internal" href="fix_modify.html"><em>fix modify</em></a> <em>energy</em> option is supported by this
fix to add the energy stored in the per-atom springs to the system’s
potential energy as part of <a class="reference internal" href="thermo_style.html"><em>thermodynamic output</em></a>.</p>
<p>This fix computes a global scalar and a global vector quantities which
can be accessed by various <a class="reference internal" href="Section_howto.html#howto-15"><span>output commands</span></a>. The scalar is an energy which
is the sum of the spring energy for each atom, where the per-atom
energy is 0.5 * K * r^2. The vector has 2 positions, the first one is
the coupling parameter lambda and the second one is the time
derivative of lambda. The scalar and vector values calculated by this
fix are “extensive”.</p>
<p>No parameter of this fix can be used with the <em>start/stop</em> keywords of
the <a class="reference internal" href="run.html"><em>run</em></a> command.</p>
<p>The forces due to this fix are imposed during an energy minimization,
invoked by the <a class="reference internal" href="minimize.html"><em>minimize</em></a> command.</p>
<div class="admonition warning">
<p class="first admonition-title">Warning</p>
<p class="last">If you want the per-atom spring energy to be included
in the total potential energy of the system (the quantity being
minimized), you MUST enable the <a class="reference internal" href="fix_modify.html"><em>fix modify</em></a> <em>energy</em>
option for this fix.</p>
</div>
<p>An example script using this command is provided in the
examples/USER/misc/ti directory.</p>
</div>
<div class="section" id="related-commands">
<h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
<h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
<p>This command is part of the USER-MISC package. It is only enabled if
LAMMPS was built with those packages. See the <a class="reference internal" href="Section_start.html#start-3"><span>Making LAMMPS</span></a> section for more info.</p>
</div>
<div class="section" id="default">
<h2>Default<a class="headerlink" href="#default" title="Permalink to this headline">¶</a></h2>
<p>The keyword default is function = 1.</p>
<hr class="docutils" />
<p id="frenkel"><strong>(Frenkel)</strong> Daan Frenkel and Anthony J. C. Ladd, J. Chem. Phys. 81, 3188
(1984).</p>
<p id="watanabe"><strong>(Watanabe)</strong> M. Watanabe and W. P. Reinhardt, Phys Rev Lett, 65, 3301 (1990).</p>
<p id="dekoning96"><strong>(de Koning 96)</strong> M. de Koning and A. Antonelli, Phys Rev E, 53, 465 (1996).</p>
<p id="dekoning97"><strong>(de Koning 97)</strong> M. de Koning and A. Antonelli, Phys Rev B, 55, 735 (1997).</p>
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