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<li><a class="reference internal" href="#">fix langevin/drude command</a><ul>
<li><a class="reference internal" href="#syntax">Syntax</a></li>
<li><a class="reference internal" href="#examples">Examples</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="#restrictions">Restrictions</a></li>
<li><a class="reference internal" href="#related-commands">Related commands</a></li>
<li><a class="reference internal" href="#default">Default</a></li>
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<div class="section" id="fix-langevin-drude-command">
<span id="index-0"></span><h1>fix langevin/drude 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">langevin</span><span class="o">/</span><span class="n">drude</span> <span class="n">Tcom</span> <span class="n">damp_com</span> <span class="n">seed_com</span> <span class="n">Tdrude</span> <span class="n">damp_drude</span> <span class="n">seed_drude</span> <span class="n">keyword</span> <span class="n">values</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>langevin/drude = style name of this fix command</li>
<li>Tcom = desired temperature of the centers of mass (temperature units)</li>
<li>damp_com = damping parameter for the thermostat on centers of mass (time units)</li>
<li>seed_com = random number seed to use for white noise of the thermostat on centers of mass (positive integer)</li>
<li>Tdrude = desired temperature of the Drude oscillators (temperature units)</li>
<li>damp_drude = damping parameter for the thermostat on Drude oscillators (time units)</li>
<li>seed_drude = random number seed to use for white noise of the thermostat on Drude oscillators (positive integer)</li>
<li>zero or more keyword/value pairs may be appended</li>
<li>keyword = <em>zero</em></li>
</ul>
<pre class="literal-block">
<em>zero</em> value = <em>no</em> or <em>yes</em>
<em>no</em> = do not set total random force on centers of mass to zero
<em>yes</em> = set total random force on centers of mass to zero
</pre>
</div>
<div class="section" id="examples">
<h2>Examples</h2>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">fix</span> <span class="mi">3</span> <span class="nb">all</span> <span class="n">langevin</span><span class="o">/</span><span class="n">drude</span> <span class="mf">300.0</span> <span class="mf">100.0</span> <span class="mi">19377</span> <span class="mf">1.0</span> <span class="mf">20.0</span> <span class="mi">83451</span>
<span class="n">fix</span> <span class="mi">1</span> <span class="nb">all</span> <span class="n">langevin</span><span class="o">/</span><span class="n">drude</span> <span class="mf">298.15</span> <span class="mf">100.0</span> <span class="mi">19377</span> <span class="mf">5.0</span> <span class="mf">10.0</span> <span class="mi">83451</span> <span class="n">zero</span> <span class="n">yes</span>
</pre></div>
</div>
</div>
<div class="section" id="description">
<h2>Description</h2>
<p>Apply two Langevin thermostats as described in <a class="reference internal" href="tutorial_drude.html#jiang"><span class="std std-ref">(Jiang)</span></a> for
thermalizing the reduced degrees of freedom of Drude oscillators.
This link describes how to use the <a class="reference internal" href="tutorial_drude.html"><span class="doc">thermalized Drude oscillator model</span></a> in LAMMPS and polarizable models in LAMMPS
are discussed in <a class="reference internal" href="Section_howto.html#howto-25"><span class="std std-ref">this Section</span></a>.</p>
<p>Drude oscillators are a way to simulate polarizables atoms, by
splitting them into a core and a Drude particle bound by a harmonic
bond. The thermalization works by transforming the particles degrees
of freedom by these equations. In these equations upper case denotes
atomic or center of mass values and lower case denotes Drude particle
or dipole values. Primes denote the transformed (reduced) values,
while bare letters denote the original values.</p>
<p>Velocities:</p>
<div class="math">
\[\begin{equation} V' = \frac {M\, V + m\, v} {M'} \end{equation}\]</div>
<div class="math">
\[\begin{equation} v' = v - V \end{equation}\]</div>
<p>Masses:</p>
<div class="math">
\[\begin{equation} M' = M + m \end{equation}\]</div>
<div class="math">
\[\begin{equation} m' = \frac {M\, m } {M'} \end{equation}\]</div>
<p>The Langevin forces are computed as</p>
<div class="math">
\[\begin{equation} F' = - \frac {M'} {\mathtt{damp\_com}}\, V' + F_r' \end{equation}\]</div>
<div class="math">
\[\begin{equation} f' = - \frac {m'} {\mathtt{damp\_drude}}\, v' + f_r' \end{equation}\]</div>
<p><span class="math">\(F_r'\)</span> is a random force proportional to
<span class="math">\(\sqrt { \frac {2\, k_B \mathtt{Tcom}\, m'} {\mathrm dt\, \mathtt{damp\_com} } }\)</span>. <a href="#id1"><span class="problematic" id="id2">:b:math:`f_r&#8217;`</span></a> is a random force proportional to
<span class="math">\(\sqrt { \frac {2\, k_B \mathtt{Tdrude}\, m'} {\mathrm dt\, \mathtt{damp\_drude} } }\)</span>.
Then the real forces acting on the particles are computed from the inverse
transform:</p>
<div class="math">
\[\begin{equation} F = \frac M {M'}\, F' - f' \end{equation}\]</div>
<div class="math">
\[\begin{equation} f = \frac m {M'}\, F' + f' \end{equation}\]</div>
<p>This fix also thermostates non-polarizable atoms in the group at
temperature <em>Tcom</em>, as if they had a massless Drude partner. The
Drude particles themselves need not be in the group. The center of
mass and the dipole are thermostated iff the core atom is in the
group.</p>
<p>Note that the thermostat effect of this fix is applied to only the
translational degrees of freedom of the particles, which is an
important consideration if finite-size particles, which have
rotational degrees of freedom, are being thermostated. The
translational degrees of freedom can also have a bias velocity removed
from them before thermostating takes place; see the description below.</p>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<p class="last">Like the <a class="reference internal" href="fix_langevin.html"><span class="doc">fix langevin</span></a> command, this fix does
NOT perform time integration. It only modifies forces to effect
thermostating. Thus you must use a separate time integration fix, like
<a class="reference internal" href="fix_nve.html"><span class="doc">fix nve</span></a> or <a class="reference internal" href="fix_nh.html"><span class="doc">fix nph</span></a> to actually update the
velocities and positions of atoms using the modified forces.
Likewise, this fix should not normally be used on atoms that also have
their temperature controlled by another fix - e.g. by <a class="reference internal" href="fix_nh.html"><span class="doc">fix nvt</span></a> or <a class="reference internal" href="fix_temp_rescale.html"><span class="doc">fix temp/rescale</span></a> commands.</p>
</div>
<p>See <a class="reference internal" href="Section_howto.html#howto-16"><span class="std std-ref">this howto section</span></a> of the manual for
a discussion of different ways to compute temperature and perform
thermostating.</p>
<hr class="docutils" />
<p>This fix requires each atom know whether it is a Drude particle or
not. You must therefore use the <a class="reference internal" href="fix_drude.html"><span class="doc">fix drude</span></a> command to
specify the Drude status of each atom type.</p>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<p class="last">only the Drude core atoms need to be in the group specified for
this fix. A Drude electron will be transformed together with its cores
even if it is not itself in the group. It is safe to include Drude
electrons or non-polarizable atoms in the group. The non-polarizable
atoms will simply be thermostatted as if they had a massless Drude
partner (electron).</p>
</div>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<p class="last">Ghost atoms need to know their velocity for this fix to act
correctly. You must use the <a class="reference internal" href="comm_modify.html"><span class="doc">comm_modify</span></a> command to
enable this, e.g.</p>
</div>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">comm_modify</span> <span class="n">vel</span> <span class="n">yes</span>
</pre></div>
</div>
<hr class="docutils" />
<p><em>Tcom</em> is the target temperature of the centers of mass, which would
be used to thermostate the non-polarizable atoms. <em>Tdrude</em> is the
(normally low) target temperature of the core-Drude particle pairs
(dipoles). <em>Tcom</em> and <em>Tdrude</em> can be specified as an equal-style
<a class="reference internal" href="variable.html"><span class="doc">variable</span></a>. If the value is a variable, it should be
specified as v_name, where name is the variable name. In this case,
the variable will be evaluated each timestep, and its value used to
determine the target temperature.</p>
<p>Equal-style variables can specify formulas with various mathematical
functions, and include <a class="reference internal" href="thermo_style.html"><span class="doc">thermo_style</span></a> command
keywords for the simulation box parameters and timestep and elapsed
time. Thus it is easy to specify a time-dependent temperature.</p>
<p>Like other fixes that perform thermostating, this fix can be used with
<a class="reference internal" href="compute.html"><span class="doc">compute commands</span></a> that remove a &#8220;bias&#8221; from the atom
velocities. E.g. removing the center-of-mass velocity from a group of
atoms. This is not done by default, but only if the
<a class="reference internal" href="fix_modify.html"><span class="doc">fix_modify</span></a> command is used to assign a temperature
compute to this fix that includes such a bias term. See the doc pages
for individual <a class="reference internal" href="compute.html"><span class="doc">compute commands</span></a> to determine which ones
include a bias. In this case, the thermostat works in the following
manner: bias is removed from each atom, thermostating is performed on
the remaining thermal degrees of freedom, and the bias is added back
in. NOTE: this feature has not been tested.</p>
<p>Note: The temperature thermostating the core-Drude particle pairs
should be chosen low enough, so as to mimic as closely as possible the
self-consistent minimization. It must however be high enough, so that
the dipoles can follow the local electric field exerted by the
neighbouring atoms. The optimal value probably depends on the
temperature of the centers of mass and on the mass of the Drude
particles.</p>
<p><em>damp_com</em> is the characteristic time for reaching thermal equilibrium
of the centers of mass. For example, a value of 100.0 means to relax
the temperature of the centers of mass in a timespan of (roughly) 100
time units (tau or fmsec or psec - see the <a class="reference internal" href="units.html"><span class="doc">units</span></a>
command). <em>damp_drude</em> is the characteristic time for reaching
thermal equilibrium of the dipoles. It is typically a few timesteps.</p>
<p>The number <em>seed_com</em> and <em>seed_drude</em> are positive integers. They set
the seeds of the Marsaglia random number generators used for
generating the random forces on centers of mass and on the
dipoles. Each processor uses the input seed to generate its own unique
seed and its own stream of random numbers. Thus the dynamics of the
system will not be identical on two runs on different numbers of
processors.</p>
<p>The keyword <em>zero</em> can be used to eliminate drift due to the
thermostat on centers of mass. Because the random forces on different
centers of mass are independent, they do not sum exactly to zero. As
a result, this fix applies a small random force to the entire system,
and the momentum of the total center of mass of the system undergoes a
slow random walk. If the keyword <em>zero</em> is set to <em>yes</em>, the total
random force on the centers of mass is set exactly to zero by
subtracting off an equal part of it from each center of mass in the
group. As a result, the total center of mass of a system with zero
initial momentum will not drift over time.</p>
<p>The actual temperatures of cores and Drude particles, in
center-of-mass and relative coordinates, respectively, can be
calculated using the <a class="reference internal" href="compute_temp_drude.html"><span class="doc">compute temp/drude</span></a>
command.</p>
<hr class="docutils" />
<p>Usage example for rigid bodies in the NPT ensemble:</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">comm_modify</span> <span class="n">vel</span> <span class="n">yes</span>
<span class="n">fix</span> <span class="n">TEMP</span> <span class="nb">all</span> <span class="n">langevin</span><span class="o">/</span><span class="n">drude</span> <span class="mf">300.</span> <span class="mf">100.</span> <span class="mi">1256</span> <span class="mf">1.</span> <span class="mf">20.</span> <span class="mi">13977</span> <span class="n">zero</span> <span class="n">yes</span>
<span class="n">fix</span> <span class="n">NPH</span> <span class="n">ATOMS</span> <span class="n">rigid</span><span class="o">/</span><span class="n">nph</span><span class="o">/</span><span class="n">small</span> <span class="n">molecule</span> <span class="n">iso</span> <span class="mf">1.</span> <span class="mf">1.</span> <span class="mf">500.</span>
<span class="n">fix</span> <span class="n">NVE</span> <span class="n">DRUDES</span> <span class="n">nve</span>
<span class="n">compute</span> <span class="n">TDRUDE</span> <span class="nb">all</span> <span class="n">temp</span><span class="o">/</span><span class="n">drude</span>
<span class="n">thermo_style</span> <span class="n">custom</span> <span class="n">step</span> <span class="n">cpu</span> <span class="n">etotal</span> <span class="n">ke</span> <span class="n">pe</span> <span class="n">ebond</span> <span class="n">ecoul</span> <span class="n">elong</span> <span class="n">press</span> <span class="n">vol</span> <span class="n">temp</span> <span class="n">c_TDRUDE</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="n">c_TDRUDE</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span>
</pre></div>
</div>
<p>Comments:</p>
<ul class="simple">
<li>Drude particles should not be in the rigid group, otherwise the Drude
oscillators will be frozen and the system will lose its
polarizability.</li>
<li><em>zero yes</em> avoids a drift of the center of mass of
the system, but is a bit slower.</li>
<li>Use two different random seeds to avoid unphysical correlations.</li>
<li>Temperature is controlled by the fix <em>langevin/drude</em>, so the
time-integration fixes do not thermostate. Don&#8217;t forget to
time-integrate both cores and Drude particles.</li>
<li>Pressure is time-integrated only once by using <em>nve</em> for Drude
particles and <em>nph</em> for atoms/cores (or vice versa). Do not use <em>nph</em>
for both.</li>
<li>The temperatures of cores and Drude particles are calculated by
<a class="reference internal" href="compute_temp_drude.html"><span class="doc">compute temp/drude</span></a></li>
<li>Contrary to the alternative thermostating using Nose-Hoover thermostat
fix <em>npt</em> and <a class="reference internal" href="fix_drude_transform.html"><span class="doc">fix drude/transform</span></a>, the
<em>fix_modify</em> command is not required here, because the fix <em>nph</em>
computes the global pressure even if its group is <em>ATOMS</em>. This is
what we want. If we thermostated <em>ATOMS</em> using <em>npt</em>, the pressure
should be the global one, but the temperature should be only that of
the cores. That&#8217;s why the command <em>fix_modify</em> should be called in
that case.</li>
</ul>
</div>
<hr class="docutils" />
<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>No information about this fix is written to <a class="reference internal" href="restart.html"><span class="doc">binary restart files</span></a>. Because the state of the random number generator
is not saved in restart files, this means you cannot do &#8220;exact&#8221;
restarts with this fix, where the simulation continues on the same as
if no restart had taken place. However, in a statistical sense, a
restarted simulation should produce the same behavior.</p>
<p>The <a class="reference internal" href="fix_modify.html"><span class="doc">fix_modify</span></a> <em>temp</em> option is supported by this
fix. You can use it to assign a temperature <a class="reference internal" href="compute.html"><span class="doc">compute</span></a>
you have defined to this fix which will be used in its thermostating
procedure, as described above. For consistency, the group used by the
compute should include the group of this fix and the Drude particles.</p>
<p>This fix is not invoked during <a class="reference internal" href="minimize.html"><span class="doc">energy minimization</span></a>.</p>
</div>
<div class="section" id="restrictions">
<h2>Restrictions</h2>
<blockquote>
<div>none</div></blockquote>
</div>
<div class="section" id="related-commands">
<h2>Related commands</h2>
<p><a class="reference internal" href="fix_langevin.html"><span class="doc">fix langevin</span></a>,
<a class="reference internal" href="fix_drude.html"><span class="doc">fix drude</span></a>,
<a class="reference internal" href="fix_drude_transform.html"><span class="doc">fix drude/transform</span></a>,
<a class="reference internal" href="compute_temp_drude.html"><span class="doc">compute temp/drude</span></a>,
<a class="reference internal" href="pair_thole.html"><span class="doc">pair_style thole</span></a></p>
</div>
<div class="section" id="default">
<h2>Default</h2>
<p>The option defaults are zero = no.</p>
<hr class="docutils" />
<p id="jiang"><strong>(Jiang)</strong> Jiang, Hardy, Phillips, MacKerell, Schulten, and Roux, J
Phys Chem Lett, 2, 87-92 (2011).</p>
</div>
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