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<CENTER><A HREF = "http://lammps.sandia.gov">LAMMPS WWW Site</A> - <A HREF = "Manual.html">LAMMPS Documentation</A> - <A HREF = "Section_commands.html#comm">LAMMPS Commands</A>
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<H3>fix drude/transform/direct command
</H3>
<H3>fix drude/transform/inverse command
</H3>
<P><B>Syntax:</B>
</P>
<PRE>fix ID group-ID style keyword value ...
</PRE>
<UL><LI>ID, group-ID are documented in <A HREF = "fix.html">fix</A> command
<LI>style = <I>drude/transform/direct</I> or <I>drude/transform/inverse</I>
</UL>
<P><B>Examples:</B>
</P>
<PRE>fix 3 all drude/transform/direct
fix 1 all drude/transform/inverse
</PRE>
<P><B>Description:</B>
</P>
<P>Transform the coordinates of Drude oscillators from real to reduced
and back for thermalizing the Drude oscillators as described in
<A HREF = "#Lamoureux">(Lamoureux)</A> using a Nose-Hoover thermostat. This fix is
designed to be used with the <A HREF = "tutorial_drude.html">thermalized Drude oscillator
model</A>. Polarizable models in LAMMPS are
described in <A HREF = "Section_howto.html#howto_25">this Section</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: \begin{equation} M' = M + m \end{equation}
\begin{equation} m' = \frac {M\, m } {M'} \end{equation}
Positions: \begin{equation} X' = \frac {M\, X + m\, x} {M'}
\end{equation} \begin{equation} x' = x - X \end{equation}
Velocities: \begin{equation} V' = \frac {M\, V + m\, v} {M'}
\end{equation} \begin{equation} v' = v - V \end{equation}
Forces: \begin{equation} F' = F + f \end{equation}
\begin{equation} f' = \frac { M\, f - m\, F} {M'}
\end{equation}
</P>
<P>This transform conserves the total kinetic energy
\begin{equation} \frac 1 2 \, (M\, V^2\ + m\, v^2)
= \frac 1 2 \, (M'\, V'^2\ + m'\, v'^2) \end{equation}
and the virial defined with absolute positions
\begin{equation} X\, F + x\, f = X'\, F' + x'\, f' \end{equation}
</P>
<HR>
<P>This fix requires each atom know whether it is a Drude particle or
not. You must therefore use the <A HREF = "fix_drude.html">fix drude</A> command to
specify the Drude status of each atom type.
</P>
<P>IMPORTANT NOTE: 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 not be transformed.
</P>
<HR>
<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 HREF = "fix_nve.html">fix nve</A> or <A HREF = "fix_nh.html">fix
npt</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>
<P>IMPORTANT NOTE: The <I>fix drude/transform/direct</I> command must appear
before any Nose-Hoover thermostating fixes. The <I>fix
drude/transform/inverse</I> command must appear after any Nose-Hoover
thermostating fixes.
</P>
<P>Example:
</P>
<PRE>fix fDIRECT all drude/transform/direct
fix fNVT gCORES nvt temp 300.0 300.0 100.0
fix fNVT gDRUDES nvt temp 1.0 1.0 100.0
fix fINVERSE all drude/transform/inverse
compute TDRUDE all temp/drude
thermo_style custom step cpu etotal ke pe ebond ecoul elong press vol temp c_TDRUDE[1] c_TDRUDE[2]
</PRE>
<P>In this example, <I>gCORES</I> is the group of the atom cores and <I>gDRUDES</I>
is the group of the Drude particles (electrons). The centers of mass
of the Drude oscillators will be thermostated at 300.0 and the
internal degrees of freedom will be thermostated at 1.0. The
temperatures of cores and Drude particles, in center-of-mass and
relatice coordinates, are calculated using <A HREF = "compute_temp_drude.html">compute
temp/drude</A>
</P>
<P>In addition, if you want to use a barostat to simulate a system at
constant pressure, only one of the Nose-Hoover fixes must be <I>npt</I>,
the other one should be <I>nvt</I>. You must add a <I>compute temp/com</I> and a
<I>fix_modify</I> command so that the temperature of the <I>npt</I> fix be just
that of its group but the pressure be the overall pressure
<I>thermo_press</I>.
</P>
<P>Example:
</P>
<PRE>compute cTEMP_CORE gCORES temp/com
fix fDIRECT all drude/transform/direct
fix fNPT gCORES npt temp 298.0 298.0 100.0 iso 1.0 1.0 500.0
fix_modify fNPT temp cTEMP_CORE press thermo_press
fix fNVT gDRUDES nvt temp 5.0 5.0 100.0
fix fINVERSE all drude/transform/inverse
</PRE>
<P>In this example, <I>gCORES</I> is the group of the atom cores and <I>gDRUDES</I>
is the group of the Drude particles. The centers of mass of the Drude
oscillators will be thermostated at 298.0 and the internal degrees of
freedom will be thermostated at 5.0. The whole system will be
barostated at 1.0.
</P>
<P>In order to avoid the flying ice cube problem (irreversible transfer
of linear momentum to the center of mass of the system), you may need
to add a <I>fix momentum</I> command like such as
</P>
<PRE>fix fMOMENTUM all momentum 100 linear 1 1 1
</PRE>
<HR>
<P><B>Restart, fix_modify, output, run start/stop, minimize info:</B>
</P>
<P>No information about this fix is written to <A HREF = "restart.html">binary restart
files</A>.
</P>
<P><B>Restrictions:</B> none
</P>
<P><B>Related commands:</B>
</P>
<P><A HREF = "fix_drude.html">fix drude</A>,
<A HREF = "fix_langevin_drude.html">fix langevin/drude</A>,
<A HREF = "compute_temp_drude.html">compute temp/drude</A>,
<A HREF = "pair_thole.html">pair_style thole</A>
</P>
<P><B>Default:</B> none
</P>
<HR>
<A NAME = "Lamoureux"></A>
<P><B>(Lamoureux)</B> Lamoureux and Roux, J Chem Phys, 119, 3025-3039 (2003).
</P>
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