"LAMMPS WWW Site"_lws - "LAMMPS Documentation"_ld - "LAMMPS Commands"_lc :c

:link(lws,http://lammps.sandia.gov)
:link(ld,Manual.html)
:link(lc,Section_commands.html#comm)

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pair_style resquared command :h3

[Syntax:]

pair_style resquared cutoff :pre

cutoff = global cutoff for interactions (distance units) :ul

[Examples:]

pair_style resquared 10.0
pair_coeff * * 1.0 1.0 1.7 3.4 3.4 1.0 1.0 1.0 :pre

[Description:]

Style {resquared} computes the RE-squared anisotropic interaction
"(Everaers)"_#Everaers, "(Babadi)"_#Babadi between pairs of
ellipsoidal and/or spherical Lennard-Jones particles.  For ellipsoidal
interactions, the potential considers the ellipsoid as being comprised
of small spheres of size sigma.  LJ particles are a single sphere of
size sigma.  The distinction is made to allow the pair style to make
efficient calculations of ellipsoid/solvent interactions.

Details for the equations used are given in the references below and
in "this supplementary document"_PDF/pair_resquared_extra.pdf.

Use of this pair style requires the NVE, NVT, or NPT fixes with the
{asphere} extension (e.g. "fix nve/asphere"_fix_nve_asphere.html) in
order to integrate particle rotation.  Additionally, "atom_style
ellipsoid"_atom_style.html should be used since it defines the
rotational state of the ellipsoidal particles.  The size and shape of
the ellipsoidal particles are defined by the "shape"_shape.html
command.

The following coefficients must be defined for each pair of atoms
types via the "pair_coeff"_pair_coeff.html command as in the examples
above, or in the data file or restart files read by the
"read_data"_read_data.html or "read_restart"_read_restart.html
commands:

A12 = Energy Prefactor/Hamaker constant (energy units)
sigma = atomic interaction diameter (distance units)
epsilon_i_a = relative well depth of type I for side-to-side interactions
epsilon_i_b = relative well depth of type I for face-to-face interactions
epsilon_i_c = relative well depth of type I for end-to-end interactions
epsilon_j_a = relative well depth of type J for side-to-side interactions
epsilon_j_b = relative well depth of type J for face-to-face interactions
epsilon_j_c = relative well depth of type J for end-to-end interactions
cutoff (distance units) :ul

The last coefficient is optional.  If not specified, the global
cutoff specified in the pair_style command is used.

As described above, {sigma} is the size of the small spheres which are
integrated over to create the potential.  Note that this is a
different meaning for {sigma} than the "pair_style
gayberne"_pair_gayberne.html potential uses.

The parameters used depend on the type of the interacting particles,
i.e. ellipsoid or LJ sphere.  The type of particle is determined by
the diameters specified with the "shape"_shape.html command.  LJ
spheres have diameters equal to zero and thus represent a single
particle with size sigma.  The epsilon_i_* or epsilon_j_* parameters
are ignored for LJ sphere interactions.  The interactions between two
LJ sphere particles are computed using the standard Lennard-Jones
formula.

For ellipsoid-LJ sphere interactions, a correction to the distance-
of-closest approach equation has been implemented to reduce the error
from disparate sizes; see "this supplementary
document"_PDF/pair_resquared_extra.pdf.

A12 specifies the energy prefactor which depends on the type of
particles interacting.  For ellipsoid-ellipsoid interactions, A12 is
the Hamaker constant as described in "(Everaers)"_#Everaers. In LJ
units:

:c,image(Eqs/pair_resquared.jpg)

where rho gives the number density of the spherical particles
composing the ellipsoids and epsilon_LJ determines the interaction
strength of the spherical particles.

For ellipsoid-LJ sphere interactions, A12 gives the energy prefactor
(see "here"_PDF/pair_resquared_extra.pdf for details:

:c,image(Eqs/pair_resquared2.jpg)

For LJ sphere-LJ sphere interactions, A12 is the standard epsilon used
in Lennard-Jones pair styles:

:c,image(Eqs/pair_resquared3.jpg)

sigma specifies the diameter of the continuous distribution of
constituent particles within each ellipsoid used to model the
RE-squared potential. 

For large uniform molecules it has been shown that the epsilon_*_*
energy parameters are approximately representable in terms of local
contact curvatures "(Everaers)"_#Everaers:

:c,image(Eqs/pair_resquared4.jpg)

where a, b, and c give the particle diameters.

The last coefficient is optional.  If not specified, the global cutoff
specified in the pair_style command is used.

The epsilon_i and epsilon_j coefficients are actually defined for atom
types, not for pairs of atom types.  Thus, in a series of pair_coeff
commands, they only need to be specified once for each atom type.

Specifically, if any of epsilon_i_a, epsilon_i_b, epsilon_i_c are
non-zero, the three values are assigned to atom type I.  If all the
epsilon_i values are zero, they are ignored.  If any of epsilon_j_a,
epsilon_j_b, epsilon_j_c are non-zero, the three values are assigned
to atom type J.  If all three epsilon_i values are zero, they are
ignored.  Thus the typical way to define the epsilon_i and epsilon_j
coefficients is to list their values in "pair_coeff I J" commands when
I = J, but set them to 0.0 when I != J.  If you do list them when I !=
J, you should insure they are consistent with their values in other
pair_coeff commands.

Note that if this potential is being used as a sub-style of
"pair_style hybrid"_pair_hybrid.html, and there is no "pair_coeff I I"
setting made for RE-squared for a particular type I (because I-I
interactions are computed by another hybrid pair potential), then you
still need to insure the epsilon a,b,c coefficients are assigned to
that type in a "pair_coeff I J" command.

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[Mixing, shift, table, tail correction, restart, rRESPA info]:

For atom type pairs I,J and I != J, the epsilon and sigma coefficients
and cutoff distance can be mixed, but only for LJ sphere pairs.  The
default mix value is {geometric}.  See the "pair_modify" command for
details.  Other type pairs cannot be mixed, due to the different
meanings of the energy prefactors used to calculate the interactions
and the implicit dependence of the ellipsoid-LJ sphere interaction on
the equation for the Hamaker constant presented here.  Mixing of sigma
and epsilon followed by calculation of the energy prefactors using the
equations above is recommended.

This pair styles supports the "pair_modify"_pair_modify.html shift
option for the energy of the Lennard-Jones portion of the pair
interaction, but only for sphere-sphere interactions.  There is no
shifting performed for ellipsoidal interactions due to the anisotropic
dependence of the interaction.

The "pair_modify"_pair_modify.html table option is not relevant
for this pair style.

This pair style does not support the "pair_modify"_pair_modify.html
tail option for adding long-range tail corrections to energy and
pressure.

This pair style writes its information to "binary restart
files"_restart.html, so pair_style and pair_coeff commands do not need
to be specified in an input script that reads a restart file.

This pair style can only be used via the {pair} keyword of the
"run_style respa"_run_style.html command.  It does not support the
{inner}, {middle}, {outer} keywords of the "run_style
command"_run_style.html.

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[Restrictions:]

This style is part of the "asphere" package.  It is only enabled if
LAMMPS was built with that package.  See the "Making
LAMMPS"_Section_start.html#2_3 section for more info.

This pair style requires that atoms store torque and a quaternion to
represent their orientation, as defined by the
"atom_style"_atom_style.html.  It also require they store a per-type
"shape"_shape.html.  The particles cannot store a per-particle
diameter.

Particles acted on by the potential can be extended aspherical or
spherical particles, or point particles.

The distance-of-closest-approach approximation used by LAMMPS becomes 
less accurate when high-aspect ratio ellipsoids are used.

[Related commands:]

"pair_coeff"_pair_coeff.html, "fix nve/asphere"_fix_nve_asphere.html,
"compute temp/asphere"_compute_temp_asphere.html, "pair_style
gayberne"_pair_gayberne.html

[Default:] none

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:link(Everaers)
[(Everaers)] Everaers and Ejtehadi, Phys Rev E, 67, 041710 (2003).

:link(Babadi)
[(Berardi)] Babadi, Ejtehadi, Everaers, J Comp Phys, 219, 770-779 (2006).
