<p>Transform the coordinates of Drude oscillators from real to reduced
and back for thermalizing the Drude oscillators as described in
<a class="reference internal" href="tutorial_drude.html#lamoureux"><span class="std std-ref">(Lamoureux)</span></a> using a Nose-Hoover thermostat. This fix is
designed to be used with the <a class="reference internal" href="tutorial_drude.html"><span class="doc">thermalized Drude oscillator model</span></a>. Polarizable models in LAMMPS are
described 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 pair of atoms representing a single
polarizable atom. Ideally, the mass of Drude particles would vanish
and their positions would be determined self-consistently by iterative
minimization of the energy, the cores’ positions being fixed. It is
however more efficient and it yields comparable results, if the Drude
oscillators (the motion of the Drude particle relative to the core)
are thermalized at a low temperature. In that case, the Drude
particles need a small mass.</p>
<p>The thermostats act on the reduced degrees of freedom, which are
defined by the following equations. Note that 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>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>Positions:</p>
<div class="math">
\[\begin{equation} X' = \frac {M\, X + m\, x} {M'}\end{equation}\]</div>
<div class="math">
\[\begin{equation} x' = x - X \end{equation}\]</div>
<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>Forces:</p>
<div class="math">
\[\begin{equation} F' = F + f \end{equation}\]</div>
<div class="math">
\[\begin{equation} f' = \frac { M\, f - m\, F} {M'}\end{equation}\]</div>
<p>This transform conserves the total kinetic energy</p>
<p>and the virial defined with absolute positions</p>
<div class="math">
\[\begin{equation} X\, F + x\, f = X'\, F' + x'\, f' \end{equation}\]</div>
<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 core
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 not be transformed.</p>
</div>
<hr class="docutils" />
<p>This fix does NOT perform time integration. It only transform masses,
coordinates, velocities and forces. Thus you must use separate time
integration fixes, 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 npt</span></a> to actually update the velocities and positions of
atoms. In order to thermalize the reduced degrees of freedom at
different temperatures, two Nose-Hoover thermostats must be defined,
acting on two distinct groups.</p>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<p class="last">The <em>fix drude/transform/direct</em> command must appear before any
Nose-Hoover thermostating fixes. The <em>fix drude/transform/inverse</em>
command must appear after any Nose-Hoover thermostating fixes.</p>
<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>.</p>
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