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fix_qeq.html
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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 qeq/point command
</H3>
<H3>fix qeq/shielded command
</H3>
<H3>fix qeq/slater command
</H3>
<H3>fix qeq/dynamic command
</H3>
<P><B>Syntax:</B>
</P>
<PRE>fix ID group-ID style Nevery cutoff tolerance maxiter qfile
</PRE>
<UL><LI>ID, group-ID are documented in <A HREF = "fix.html">fix</A> command
<LI>style = <I>qeq/point</I> or <I>qeq/shielded</I> or <I>qeq/slater</I> or <I>qeq/dynamic</I>
<LI>Nevery = perform charge equilibration every this many steps
<LI>cutoff = global cutoff for charge-charge interactions (distance unit)
<LI>tolerance = precision to which charges will be equilibrated
<LI>maxiter = maximum iterations to perform charge equilibration
<LI>qfile = a filename with QEq parameters
</UL>
<P><B>Examples:</B>
</P>
<PRE>fix 1 all qeq/point 1 10 1.0e-6 200 param.qeq1
fix 1 qeq qeq/shielded 1 8 1.0e-6 100 param.qeq2
fix 1 all qeq/slater 5 10 1.0e-6 100 params
fix 1 qeq qeq/dynamic 1 12 1.0e-3 100 my_qeq
</PRE>
<P><B>Description:</B>
</P>
<P>Perform the charge equilibration (QEq) method as described in <A HREF = "#Rappe">(Rappe
and Goddard)</A> and formulated in <A HREF = "#Nakano">(Nakano)</A> (also known
as the matrix inversion method) and in <A HREF = "#Rick">(Rick and Stuart)</A> (also
known as the extended Lagrangian method) based on the
electronegativity equilization principle.
</P>
<P>These fixes can be used with any <A HREF = "pair_style.html">pair style</A> in
LAMMPS, so long as per-atom charges are defined. The most typical
use-case is in conjunction with a <A HREF = "pair_style.html">pair style</A> that
performs charge equilibration periodically (e.g. every timestep), such
as the ReaxFF or Streitz-Mintmire potential (the latter is not yet
implemented in LAMMPS). But these fixes can also be used with
potentials that normally assume per-atom charges are fixed, e.g. a
<A HREF = "pair_buck.html">Buckingham</A> or <A HREF = "pair_lj.html">LJ/Coulombic</A> potential.
</P>
<P>Because the charge equilibration calculation is effectively
independent of the pair style, these fixes can also be used to perform
a one-time assignment of charges to atoms. For example, you could
define the QEq fix, perform a zero-timestep run via the <A HREF = "run.html">run</A>
command without any pair style defined which would set per-atom
charges (based on the current atom configuration), then remove the fix
via the <A HREF = "unfix.html">unfix</A> command before performing further dynamics.
</P>
<P>IMPORTANT NOTE: Computing and using charge values different from
published values defined for a fixed-charge potential like Buckingham
or CHARMM or AMBER, can have a strong effect on energies and forces,
and produces a different model than the published versions.
</P>
<P>IMPORTANT NOTE: The <A HREF = "fix_qeq_comb.html">fix qeq/comb</A> command must
still be used to perform charge equliibration with the <A HREF = "pair_comb.html">COMB
potential</A>. The <A HREF = "fix_qeq_reax.html">fix qeq/reax</A>
command can be used to perform charge equilibration with the <A HREF = "pair_reax_c.html">ReaxFF
force field</A>, although fix qeq/shielded yields the
same results as fix qeq/reax if <I>Nevery</I>, <I>cutoff</I>, and <I>tolerance</I> are
the same. Eventually the fix qeq/reax command will be deprecated.
</P>
<P>The QEq method minimizes the electrostatic energy of the system (or
equalizes the derivative of energy with respect to charge of all the
atoms) by adjusting the partial charge on individual atoms based on
interactions with their neighbors within <I>cutoff</I>. It reqires a few
parameters, in <I>metal</I> units, for each atom type which provided in a
file specified by <I>qfile</I>. The file has the following format
</P>
<PRE>1 chi eta gamma zeta qcore
2 chi eta gamma zeta qcore
...
Ntype chi eta gamma zeta qcore
</PRE>
<P>There is one line per atom type with the following parameters.
Only a subset of the parameters is used by each QEq style as descibed
below, thus the others can be set to 0.0 if desired.
</P>
<UL><LI><I>chi</I> = electronegativity in energy units
<LI><I>eta</I> = self-Coulomb potential in energy units
<LI><I>gamma</I> = shielded Coulomb constant defined by <A HREF = "#vanDuin">ReaxFF force field</A> in distance units
<LI><I>zeta</I> = Slater type orbital exponent defined by the <A HREF = "#Streitz">Streitz-Mintmire</A> potential in reverse distance units
<LI><I>qcore</I> = charge of the nucleus defined by the <A HREF = "#Streitz">Streitz-Mintmire potential</A> potential in charge units
</UL>
<P>The <I>qeq/point</I> style describes partial charges on atoms as point
charges. Interaction between a pair of charged particles is 1/r,
which is the simplest description of the interaction between charges.
Only the <I>chi</I> and <I>eta</I> parameters from the <I>qfile</I> file are used.
Note that Coulomb catastrophe can occur if repulsion between the pair
of charged particles is too weak. This style solves partial charges
on atoms via the matrix inversion method. A tolerance of 1.0e-6 is
usually a good number.
</P>
<P>The <I>qeq/shielded</I> style describes partial charges on atoms also as
point charges, but uses a shielded Coulomb potential to describe the
interaction between a pair of charged particles. Interaction through
the shielded Coulomb is given by equation (13) of the <A HREF = "#vanDuin">ReaxFF force
field</A> paper. The shielding accounts for charge overlap
between charged particles at small separation. This style is the same
as <A HREF = "fix_qeq_reax.html">fix qeq/reax</A>, and can be used with <A HREF = "pair_reax_c.html">pair_style
reax/c</A>. Only the <I>chi</I>, <I>eta</I>, and <I>gamma</I>
parameters from the <I>qfile</I> file are used. This style solves partial
charges on atoms via the matrix inversion method. A tolerance of
1.0e-6 is usually a good number.
</P>
<P>The <I>qeq/slater</I> style describes partial charges on atoms as spherical
charge densities centered around atoms via the Slater 1<I>s</I> orbital, so
that the interaction between a pair of charged particles is the
product of two Slater 1<I>s</I> orbitals. The expression for the Slater
1<I>s</I> orbital is given under equation (6) of the
<A HREF = "#Streitz">Streitz-Mintmire</A> paper. Only the <I>chi</I>, <I>eta</I>, <I>zeta</I>, and
<I>qcore</I> parameters from the <I>qfile</I> file are used. This style solves
partial charges on atoms via the matrix inversion method. A tolerance
of 1.0e-6 is usually a good number.
</P>
<P>The <I>qeq/dynamic</I> style describes partial charges on atoms as point
charges that interact through 1/r, but the extended Lagrangian method
is used to solve partial charges on atoms. Only the <I>chi</I> and <I>eta</I>
parameters from the <I>qfile</I> file are used. Note that Coulomb
catastrophe can occur if repulsion between the pair of charged
particles is too weak. A tolerance of 1.0e-3 is usually a good
number.
</P>
<P>Note that <I>qeq/point</I>, <I>qeq/shielded</I>, and <I>qeq/slater</I> describe
different charge models, whereas the matrix inversion method and the
extended Lagrangian method (<I>qeq/dynamic</I>) are different solvers.
</P>
<P>Note that the <I>qeq/point</I> and the <I>qeq/dynamic</I> styles both describe
charges as point charges that interact through 1/r relationship, but
solve partial charges on atoms using different solvers. Styles
<I>qeq/point</I> and the <I>qeq/dynamic</I> should yield comparable results if
the QEq parameters and <I>Nevery</I>, <I>cutoff</I>, and <I>tolerance</I> are the
same. Style <I>qeq/point</I> is typically faster, but <I>qeq/dynamic</I> scales
better on larger sizes.
</P>
<P>IMPORTANT NOTE: To avoid the evaluation of the derivative of charge
with respect to position, which is typically ill-defined, the system
should have a zero net charge.
</P>
<P>IMPORTANT NOTE: Developing QEq parameters (chi, eta, gamma, zeta, and
qcore) is an "art". Charges on atoms are not guaranteed to
equilibrate with arbitrary choices of these parameters. We do not
develop these QEq paramters. See the examples/qeq directory for some
examples.
</P>
<P><B>Restart, fix_modify, output, run start/stop, minimize info:</B>
</P>
<P>No information about these fixes is written to <A HREF = "restart.html">binary restart
files</A>. No global scalar or vector or per-atom
quantities are stored by these fixes for access by various <A HREF = "Section_howto.html#howto_15">output
commands</A>. No parameter of these fixes
can be used with the <I>start/stop</I> keywords of the <A HREF = "run.html">run</A>
command.
</P>
<P>Thexe fixes are invoked during <A HREF = "minimize.html">energy minimization</A>.
</P>
<P><B>Restrictions:</B>
</P>
<P>These fixes are part of the QEQ package. They are only enabled if
LAMMPS was built with that package. See the <A HREF = "Section_start.html#start_3">Making
LAMMPS</A> section for more info.
</P>
<P><B>Related commands:</B>
</P>
<P><A HREF = "fix_qeq_reax.html">fix qeq/reax</A>, <A HREF = "fix_qeq_comb.html">fix qeq/comb</A>
</P>
<P><B>Default:</B> none
</P>
<HR>
<A NAME = "Rappe"></A>
<P><B>(Rappe and Goddard)</B> A. K. Rappe and W. A. Goddard III, J Physical
Chemistry, 95, 3358-3363 (1991).
</P>
<A NAME = "Nakano"></A>
<P><B>(Nakano)</B> A. Nakano, Computer Physics Communications, 104, 59-69 (1997).
</P>
<A NAME = "Rick"></A>
<P><B>(Rick and Stuart)</B> S. W. Rick, S. J. Stuart, B. J. Berne, J Chemical Physics
101, 16141 (1994).
</P>
<A NAME = "Streitz"></A>
<P><B>(Streitz-Mintmire)</B> F. H. Streitz, J. W. Mintmire, Physical Review B, 50,
16, 11996 (1994)
</P>
<A NAME = "vanDuin"></A>
<P><B>(ReaxFF)</B> A. C. T. van Duin, S. Dasgupta, F. Lorant, W. A. Goddard III, J
Physical Chemistry, 105, 9396-9049 (2001)
</P>
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