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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 langevin/drude command
	</H3>
	<P><B>Syntax:</B>
	</P>
	<PRE>fix ID group-ID langevin/drude Tcom damp_com seed_com Tdrude damp_drude seed_drude keyword values ...
	</PRE>
	<UL><LI>ID, group-ID are documented in <A HREF = "fix.html">fix</A> command

	<LI>langevin/drude = style name of this fix command

	<LI>Tcom = desired temperature of the centers of mass (temperature units)

	<LI>damp_com = damping parameter for the thermostat on centers of mass (time units)

	<LI>seed_com = random number seed to use for white noise of the thermostat on centers of mass (positive integer)

	<LI>Tdrude = desired temperature of the Drude oscillators (temperature units)

	<LI>damp_drude = damping parameter for the thermostat on Drude oscillators (time units)

	<LI>seed_drude = random number seed to use for white noise of the thermostat on Drude oscillators (positive integer)

	<LI>zero or more keyword/value pairs may be appended

	<LI>keyword = <I>zero</I>

	<PRE> <I>zero</I> value = <I>no</I> or <I>yes</I>
	<I>no</I> = do not set total random force on centers of mass to zero
	<I>yes</I> = set total random force on centers of mass to zero
	</PRE>

	</UL>
	<P><B>Examples:</B>
	</P>
	<PRE>fix 3 all langevin/drude 300.0 100.0 19377 1.0 20.0 83451
	fix 1 all langevin/drude 298.15 100.0 19377 5.0 10.0 83451 zero yes
	</PRE>
	<P><B>Description:</B>
	</P>
	<P>Apply two Langevin thermostats as described in <A HREF = "#Jiang">(Jiang)</A> for
	thermalizing the reduced degrees of freedom of Drude oscillators.
	This link describes how to use the <A HREF = "tutorial_drude.html">thermalized Drude oscillator
	model</A> in LAMMPS and polarizable models in LAMMPS
	are discussed in <A HREF = "Section_howto.html#howto_25">this Section</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>
	Velocities:
	\begin{equation} V' = \frac {M\, V + m\, v} {M'} \end{equation}
	\begin{equation} v' = v - V \end{equation}
	Masses:
	\begin{equation} M' = M + m \end{equation}
	\begin{equation} m' = \frac {M\, m } {M'} \end{equation}
	The Langevin forces are computed as
	\begin{equation} F' = - \frac {M'} {\mathtt{damp\_com}}\, V' + F_r' \end{equation}
	\begin{equation} f' = - \frac {m'} {\mathtt{damp\_drude}}\, v' + f_r' \end{equation}
	\(F_r'\) is a random force proportional to
	\(\sqrt { \frac {2\, k_B \mathtt{Tcom}\, m'}
	{\mathrm dt\, \mathtt{damp\_com} }
	} \).
	<BR>
	\(f_r'\) is a random force proportional to
	\(\sqrt { \frac {2\, k_B \mathtt{Tdrude}\, m'}
	{\mathrm dt\, \mathtt{damp\_drude} }
	} \).
	<BR>
	<P>Then the real forces acting on the particles are computed from the inverse
	transform:
	\begin{equation} F = \frac M {M'}\, F' - f' \end{equation}
	\begin{equation} f = \frac m {M'}\, F' + f' \end{equation}
	</P>
	<P>This fix also thermostates non-polarizable atoms in the group at
	temperature <I>Tcom</I>, 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>
	<P>IMPORTANT NOTE: Like the <A HREF = "fix_langevin.html">fix langevin</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 HREF = "fix_nve.html">fix nve</A> or <A HREF = "fix_nh.html">fix nph</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 HREF = "fix_nh.html">fix
	nvt</A> or <A HREF = "fix_temp_rescale.html">fix temp/rescale</A> commands.
	</P>
	<P>See <A HREF = "Section_howto.html#howto_16">this howto section</A> of the manual for
	a discussion of different ways to compute temperature and perform
	thermostating.
	</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 thermostatted as if they had
	a massless Drude partner (electron).
	</P>
	<P>IMPORTANT NOTE: Ghost atoms need to know their velocity for this fix
	to act correctly. You must use the <A HREF = "comm_modify.html">comm_modify</A>
	command to enable this, e.g.
	</P>
	<PRE>comm_modify vel yes
	</PRE>
	<HR>

	<P><I>Tcom</I> is the target temperature of the centers of mass, which would
	be used to thermostate the non-polarizable atoms. <I>Tdrude</I> is the
	(normally low) target temperature of the core-Drude particle pairs
	(dipoles). <I>Tcom</I> and <I>Tdrude</I> can be specified as an equal-style
	<A HREF = "variable.html">variable</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 HREF = "thermo_style.html">thermo_style</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 HREF = "compute.html">compute commands</A> that remove a "bias" 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 HREF = "fix_modify.html">fix_modify</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 HREF = "compute.html">compute commands</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><I>damp_com</I> 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 HREF = "units.html">units</A>
	command). <I>damp_drude</I> is the characteristic time for reaching
	thermal equilibrium of the dipoles. It is typically a few timesteps.
	</P>
	<P>The number <I>seed_com</I> and <I>seed_drude</I> 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 <I>zero</I> 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 <I>zero</I> is set to <I>yes</I>, 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 relatice coordinates, respectively, can be
	calculated using the <A HREF = "compute_temp_drude.html">compute temp/drude</A>
	command.
	</P>
	<HR>

	<P>Usage example for rigid bodies in the NPT ensemble:
	</P>
	<PRE>comm_modify vel yes
	fix TEMP all langevin/drude 300. 100. 1256 1. 20. 13977 zero yes
	fix NPH ATOMS rigid/nph/small molecule iso 1. 1. 500.
	fix NVE DRUDES nve
	thermo_style custom step cpu etotal ke pe ebond ecoul elong press vol temp c_TATOM c_TDRUDE f_TEMP[1] f_TEMP[2]
	</PRE>
	<P>Comments:
	</P>
	<UL><LI>Drude particles should not be in the rigid group, otherwise the Drude
	<LI>oscillators will be frozen and the system will lose its
	<LI>polarizability. <I>zero yes</I> avoids a drift of the center of mass of
	<LI>the system, but is a bit slower. use two different random seeds to
	<LI>avoid unphysical correlations. temperature is controlled by the fix
	<LI><I>langevin/drude</I>, so the time-integration fixes do not thermostate.
	<LI>don't forget to time-integrate both cores and Drude particles.
	<LI>pressure is time-integrated only once by using <I>nve</I> for Drude
	<LI>particles and <I>nph</I> for atoms/cores (or vice versa). Do not use <I>nph</I>
	<LI>for both. contrary to the alternative thermostating using Nose-Hoover
	<LI>thermostat fix <I>npt</I> and fix <I>drude/transform</I>, the <I>fix_modify</I>
	<LI>command is not required here, because the fix <I>nph</I> computes the
	<LI>global pressure even if its group is <I>ATOMS</I>. This is what we want. If
	<LI>we thermostated <I>ATOMS</I> using <I>npt</I>, the pressure should be the global
	<LI>one, but the temperature should be only that of the cores. That's why
	<LI>the command <I>fix_modify</I> should be called in that case. f_TEMP[1]
	<LI>and f_TEMP[2] contain the reduced temperatures of the cores/atoms
	<LI>and of the Drude particles (see below). They should be 300. and 1. on
	<LI>average here.
	</UL>
	<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>. Because the state of the random number generator
	is not saved in restart files, this means you cannot do "exact"
	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 HREF = "fix_modify.html">fix_modify</A> <I>temp</I> option is supported by this
	fix. You can use it to assign a temperature <A HREF = "compute.html">compute</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 HREF = "minimize.html">energy minimization</A>.
	</P>
	<P><B>Restrictions:</B> none
	</P>
	<P><B>Related commands:</B>
	</P>
	<P><A HREF = "fix_langevin.html">fix langevin</A>,
	<A HREF = "fix_drude.html">fix drude</A>,
	<A HREF = "fix_drude_transform.html">fix drude/transform</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>
	</P>
	<P>The option defaults are zero = no.
	</P>
	<HR>

	<A NAME = "Jiang"></A>

	<P><B>(Jiang)</B> Jiang, Hardy, Phillips, MacKerell, Schulten, and Roux, J
	Phys Chem Lett, 2, 87-92 (2011).
	</P>
	</HTML>

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