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<li><a class="reference internal" href="#">fix ti/spring command</a><ul>
<li><a class="reference internal" href="#syntax">Syntax</a></li>
<li><a class="reference internal" href="#description">Description</a></li>
<li><a class="reference internal" href="#restart-fix-modify-output-run-start-stop-minimize-info">Restart, fix_modify, output, run start/stop, minimize info</a></li>
<li><a class="reference internal" href="#related-commands">Related commands</a></li>
<li><a class="reference internal" href="#restrictions">Restrictions</a></li>
<li><a class="reference internal" href="#default">Default</a></li>
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<div class="section" id="fix-ti-spring-command">
<span id="index-0"></span><h1>fix ti/spring command</h1>
<div class="section" id="syntax">
<h2>Syntax</h2>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">fix</span> <span class="n">ID</span> <span class="n">group</span><span class="o">-</span><span class="n">ID</span> <span class="n">ti</span><span class="o">/</span><span class="n">spring</span> <span class="n">K</span> <span class="n">t_switch</span> <span class="n">t_equil</span> <span class="n">keyword</span> <span class="n">value</span> <span class="o">...</span>
</pre></div>
</div>
<ul class="simple">
<li>ID, group-ID are documented in <a class="reference internal" href="fix.html"><span class="doc">fix</span></a> command</li>
<li>ti/spring = style name of this fix command</li>
<li>K = spring constant (force/distance units)</li>
<li>t_switch/t_equil = number of steps of the switching/equilibration procedure</li>
<li>zero or more keyword/value pairs may be appended to args</li>
<li>keyword = <em>function</em></li>
</ul>
<pre class="literal-block">
<em>function</em> value = function-ID
function-ID = ID of the switching function (1 or 2)
</pre>
<p><strong>Example:</strong></p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">fix</span> <span class="n">ref</span> <span class="nb">all</span> <span class="n">ti</span><span class="o">/</span><span class="n">spring</span> <span class="mf">50.0</span> <span class="mi">2000</span> <span class="mi">1000</span> <span class="n">function</span> <span class="mi">2</span>
</pre></div>
</div>
</div>
<div class="section" id="description">
<h2>Description</h2>
<p>This fix allows you to compute the free energy of solids by performing
a thermodynamic integration between the solid of interest and an
Einstein crystal <a class="reference internal" href="#frenkel"><span class="std std-ref">(Frenkel)</span></a>. The thermodynamic integration
is performed using the nonequilibrium method of Adiabatic Switching
<a class="reference internal" href="#watanabe"><span class="std std-ref">(Watanabe,</span></a> <a class="reference internal" href="#dekoning96"><span class="std std-ref">de Koning96)</span></a>.</p>
<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 <a class="reference internal" href="fix_spring_self.html"><span class="doc">fix spring/self</span></a>. The forces on the atoms are
dynamically scaled during the simulation, the rescaling is done in the
following manner:</p>
<img alt="_images/fix_ti_spring_force.jpg" class="align-center" src="_images/fix_ti_spring_force.jpg" />
<p>where F_harm is the force due to the springs, F_solid is the total
force on the atoms due to the interatomic potential and lambda is the
coupling parameter of the thermodynamic integration.</p>
<p>The fix acts as follows: during the first <em>t_equil</em> steps after the
fix is defined the value of lambda is zero, this is the period to
equilibrate the system in the lambda = 0 state. After this the value
of lambda changes continuously from 0 to 1 according to the function
defined using the keyword <em>function</em> (described below), this is done
in <em>t_switch</em> steps. Then comes the second equilibration period of
<em>t_equil</em> to equilibrate the system in the lambda = 1 state. After
that the switching back to the lambda = 0 state is made using
<em>t_switch</em> timesteps and following the same switching function. After
this period the value of lambda is kept equal to zero and the fix has
no action in the dynamics of the system anymore.</p>
<p>The description of thermodynamic integration in both directions is
done in <a class="reference internal" href="#dekoning97"><span class="std std-ref">de Koning97</span></a>, the main reason is to try to
eliminate the dissipated heat due to the nonequilibrium process.</p>
<p>The <em>function</em> keyword allows the use of two different switching
rates, the option <em>1</em> results in a constant rescaling where the lambda
parameter changes at a constant rate during the switching time
according to the switching function</p>
<img alt="_images/fix_ti_spring_function_1.jpg" class="align-center" src="_images/fix_ti_spring_function_1.jpg" />
<p>where tau is the scaled time variable t/t_switch. The option number
<em>2</em> performs the switching at a rate defined by the following
switching function</p>
<img alt="_images/fix_ti_spring_function_2.jpg" class="align-center" src="_images/fix_ti_spring_function_2.jpg" />
<p>This function has zero slope as lambda approaches its extreme values
(0 and 1), according to (<a class="reference internal" href="#dekoning96"><span class="std std-ref">de Koning96)</span></a> this results in
smaller fluctuations on the integral to be computed on the
thermodynamic integration.</p>
<div class="admonition note">
<p class="first admonition-title">Note</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
&#8216;attatched&#8217; 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"><span class="doc">velocity</span></a>. The use of the Nose-Hoover thermostat
(<a class="reference internal" href="fix_nh.html"><span class="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 (<a class="reference external" href="fix_langevin.html&quot;">fix langevin</a>) works fine.</p>
</div>
</div>
<div class="section" id="restart-fix-modify-output-run-start-stop-minimize-info">
<h2>Restart, fix_modify, output, run start/stop, minimize info</h2>
<p>This fix writes the original coordinates of tethered atoms to <a class="reference internal" href="restart.html"><span class="doc">binary restart files</span></a>, so that the spring effect will be the
same in a restarted simulation. See the <a class="reference internal" href="read_restart.html"><span class="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 <a class="reference internal" href="fix_modify.html"><span class="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&#8217;s
potential energy as part of <a class="reference internal" href="thermo_style.html"><span class="doc">thermodynamic output</span></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 class="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 &#8220;extensive&#8221;.</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"><span class="doc">run</span></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"><span class="doc">minimize</span></a> command.</p>
<div class="admonition note">
<p class="first admonition-title">Note</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"><span class="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
examples/USER/misc/ti directory.</p>
</div>
<div class="section" id="related-commands">
<h2>Related commands</h2>
<p><a class="reference internal" href="fix_spring.html"><span class="doc">fix spring</span></a>, <a class="reference internal" href="fix_ti_rs.html"><span class="doc">fix ti/rs</span></a></p>
</div>
<div class="section" id="restrictions">
<h2>Restrictions</h2>
<p>This command is part of the USER-MISC package. It is only enabled if
LAMMPS was built with those packages. See the <span class="xref std std-ref">Making LAMMPS</span> section for more info.</p>
</div>
<div class="section" id="default">
<h2>Default</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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