<p>A spring force is applied independently to each atom in the group to
tether it to its initial position. The initial position for each atom
is its location at the time the fix command was issued. More details
about the springs are available in <aclass="reference internal"href="fix_spring_self.html"><spanclass="doc">fix spring/self</span></a>. The forces on the atoms are
dynamically scaled during the simulation, the rescaling is done in the
<p>This function has zero slope as lambda approaches its extreme values
(0 and 1), according to (<aclass="reference internal"href="#dekoning96"><spanclass="std std-ref">de Koning96)</span></a> this results in
smaller fluctuations on the integral to be computed on the
thermodynamic integration.</p>
<divclass="admonition note">
<pclass="first admonition-title">Note</p>
<pclass="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 <aclass="reference external"href="fix_langevin_html">fix langevin</a>
and <aclass="reference internal"href="velocity.html"><spanclass="doc">velocity</span></a>. The use of the Nose-Hoover thermostat
(<aclass="reference internal"href="fix_nh.html"><spanclass="doc">fix nvt</span></a>) 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 (<aclass="reference external"href="fix_langevin.html"">fix langevin</a>) works fine.</p>
</div>
<p><strong>Restart, fix_modify, output, run start/stop, minimize info:</strong></p>
<p>This fix writes the original coordinates of tethered atoms to <aclass="reference internal"href="restart.html"><spanclass="doc">binary restart files</span></a>, so that the spring effect will be the
same in a restarted simulation. See the <aclass="reference internal"href="read_restart.html"><spanclass="doc">read restart</span></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 <aclass="reference internal"href="fix_modify.html"><spanclass="doc">fix modify</span></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 <aclass="reference internal"href="thermo_style.html"><spanclass="doc">thermodynamic output</span></a>.</p>
<p>This fix computes a global scalar and a global vector quantities which
can be accessed by various <aclass="reference internal"href="Section_howto.html#howto-15"><spanclass="std std-ref">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 <aclass="reference internal"href="run.html"><spanclass="doc">run</span></a> command.</p>
<p>The forces due to this fix are imposed during an energy minimization,
invoked by the <aclass="reference internal"href="minimize.html"><spanclass="doc">minimize</span></a> command.</p>
<divclass="admonition note">
<pclass="first admonition-title">Note</p>
<pclass="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 <aclass="reference internal"href="fix_modify.html"><spanclass="doc">fix modify</span></a><em>energy</em> option for
this fix.</p>
</div>
<p>An example script using this command is provided in the
<p>This command is part of the USER-MISC package. It is 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>
</div>
<divclass="section"id="default">
<h2>Default</h2>
<p>The keyword default is function = 1.</p>
<hrclass="docutils"/>
<pid="frenkel"><strong>(Frenkel)</strong> Daan Frenkel and Anthony J. C. Ladd, J. Chem. Phys. 81, 3188
(1984).</p>
<pid="watanabe"><strong>(Watanabe)</strong> M. Watanabe and W. P. Reinhardt, Phys Rev Lett, 65, 3301 (1990).</p>
<pid="dekoning96"><strong>(de Koning 96)</strong> M. de Koning and A. Antonelli, Phys Rev E, 53, 465 (1996).</p>
<pid="dekoning97"><strong>(de Koning 97)</strong> M. de Koning and A. Antonelli, Phys Rev B, 55, 735 (1997).</p>
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