lammps/doc/pair_table.txt

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pair_style table command :h3
pair_style table/gpu command :h3
pair_style table/kk command :h3
pair_style table/omp command :h3

[Syntax:]

pair_style table style N keyword ... :pre

style = {lookup} or {linear} or {spline} or {bitmap} = method of interpolation
N = use N values in {lookup}, {linear}, {spline} tables
N = use 2^N values in {bitmap} tables
zero or more keywords may be appended
keyword = {ewald} or {pppm} or {msm} or {dispersion} or {tip4p} :ul

[Examples:]

pair_style table linear 1000
pair_style table linear 1000 pppm
pair_style table bitmap 12
pair_coeff * 3 morse.table ENTRY1
pair_coeff * 3 morse.table ENTRY1 7.0 :pre

[Description:]

Style {table} creates interpolation tables of length {N} from pair
potential and force values listed in a file(s) as a function of
distance.  The files are read by the "pair_coeff"_pair_coeff.html
command.

The interpolation tables are created by fitting cubic splines to the
file values and interpolating energy and force values at each of {N}
distances.  During a simulation, these tables are used to interpolate
energy and force values as needed.  The interpolation is done in one
of 4 styles: {lookup}, {linear}, {spline}, or {bitmap}.

For the {lookup} style, the distance between 2 atoms is used to find
the nearest table entry, which is the energy or force.

For the {linear} style, the pair distance is used to find 2
surrounding table values from which an energy or force is computed by
linear interpolation.

For the {spline} style, a cubic spline coefficients are computed and
stored at each of the {N} values in the table.  The pair distance is
used to find the appropriate set of coefficients which are used to
evaluate a cubic polynomial which computes the energy or force.

For the {bitmap} style, the N means to create interpolation tables
that are 2^N in length.  The pair distance is used to index into the
table via a fast bit-mapping technique due to "(Wolff)"_#Wolff, and a
linear interpolation is performed between adjacent table values.

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.

filename
keyword
cutoff (distance units) :ul

The filename specifies a file containing tabulated energy and force
values.  The keyword specifies a section of the file.  The cutoff is
an optional coefficient.  If not specified, the outer cutoff in the
table itself (see below) will be used to build an interpolation table
that extend to the largest tabulated distance.  If specified, only
file values up to the cutoff are used to create the interpolation
table.  The format of this file is described below.

If your tabulated potential(s) are designed to be used as the
short-range part of one of the long-range solvers specified by the
"kspace_style"_kspace_style.html command, then you must use one or
more of the optional keywords listed above for the pair_style command.
These are {ewald} or {pppm} or {msm} or {dispersion} or {tip4p}.  This
is so LAMMPS can insure the short-range potential and long-range
solver are compatible with each other, as it does for other
short-range pair styles, such as "pair_style
lj/cut/coul/long"_pair_lj.html.  Note that it is up to you to insure
the tabulated values for each pair of atom types has the correct
functional form to be compatible with the matching long-range solver.

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Here are some guidelines for using the pair_style table command to
best effect:

Vary the number of table points; you may need to use more than you think
to get good resolution. :ulb,l

Always use the "pair_write"_pair_write.html command to produce a plot
of what the final interpolated potential looks like.  This can show up
interpolation "features" you may not like. :l

Start with the linear style; it's the style least likely to have problems. :l

Use {N} in the pair_style command equal to the "N" in the tabulation
file, and use the "RSQ" or "BITMAP" parameter, so additional interpolation
is not needed.  See discussion below. :l

Make sure that your tabulated forces and tabulated energies are consistent 
(dE/dr = -F) along the entire range of r values. :l

Use as large an inner cutoff as possible.  This avoids fitting splines
to very steep parts of the potential. :l,ule

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The format of a tabulated file is a series of one or more sections,
defined as follows (without the parenthesized comments):

# Morse potential for Fe   (one or more comment or blank lines) :pre

MORSE_FE                   (keyword is first text on line)
N 500 R 1.0 10.0           (N, R, RSQ, BITMAP, FPRIME parameters)
                           (blank)
1 1.0 25.5 102.34          (index, r, energy, force)
2 1.02 23.4 98.5
...
500 10.0 0.001 0.003 :pre

A section begins with a non-blank line whose 1st character is not a
"#"; blank lines or lines starting with "#" can be used as comments
between sections.  The first line begins with a keyword which
identifies the section.  The line can contain additional text, but the
initial text must match the argument specified in the pair_coeff
command.  The next line lists (in any order) one or more parameters
for the table.  Each parameter is a keyword followed by one or more
numeric values.

The parameter "N" is required and its value is the number of table
entries that follow.  Note that this may be different than the {N}
specified in the "pair_style table"_pair_style.html command.  Let
Ntable = {N} in the pair_style command, and Nfile = "N" in the
tabulated file.  What LAMMPS does is a preliminary interpolation by
creating splines using the Nfile tabulated values as nodal points.  It
uses these to interpolate as needed to generate energy and force
values at Ntable different points.  The resulting tables of length
Ntable are then used as described above, when computing energy and
force for individual pair distances.  This means that if you want the
interpolation tables of length Ntable to match exactly what is in the
tabulated file (with effectively no preliminary interpolation), you
should set Ntable = Nfile, and use the "RSQ" or "BITMAP" parameter.
The internal table abscissa is RSQ (separation distance squared).

All other parameters are optional.  If "R" or "RSQ" or "BITMAP" does
not appear, then the distances in each line of the table are used
as-is to perform spline interpolation.  In this case, the table values
can be spaced in {r} uniformly or however you wish to position table
values in regions of large gradients.

If used, the parameters "R" or "RSQ" are followed by 2 values {rlo}
and {rhi}.  If specified, the distance associated with each energy and
force value is computed from these 2 values (at high accuracy), rather
than using the (low-accuracy) value listed in each line of the table.
The distance values in the table file are ignored in this case.
For "R", distances uniformly spaced between {rlo} and {rhi} are
computed; for "RSQ", squared distances uniformly spaced between
{rlo*rlo} and {rhi*rhi} are computed.

If used, the parameter "BITMAP" is also followed by 2 values {rlo} and
{rhi}.  These values, along with the "N" value determine the ordering
of the N lines that follow and what distance is associated with each.
This ordering is complex, so it is not documented here, since this
file is typically produced by the "pair_write"_pair_write.html command
with its {bitmap} option.  When the table is in BITMAP format, the "N"
parameter in the file must be equal to 2^M where M is the value
specified in the pair_style command.  Also, a cutoff parameter cannot
be used as an optional 3rd argument in the pair_coeff command; the
entire table extent as specified in the file must be used.

If used, the parameter "FPRIME" is followed by 2 values {fplo} and
{fphi} which are the derivative of the force at the innermost and
outermost distances listed in the table.  These values are needed by
the spline construction routines.  If not specified by the "FPRIME"
parameter, they are estimated (less accurately) by the first 2 and
last 2 force values in the table.  This parameter is not used by
BITMAP tables.

Following a blank line, the next N lines list the tabulated values.
On each line, the 1st value is the index from 1 to N, the 2nd value is
r (in distance units), the 3rd value is the energy (in energy units),
and the 4th is the force (in force units).  The r values must increase
from one line to the next (unless the BITMAP parameter is specified).

Note that one file can contain many sections, each with a tabulated
potential.  LAMMPS reads the file section by section until it finds
one that matches the specified keyword.

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Styles with a {cuda}, {gpu}, {intel}, {kk}, {omp}, or {opt} suffix are
functionally the same as the corresponding style without the suffix.
They have been optimized to run faster, depending on your available
hardware, as discussed in "Section_accelerate"_Section_accelerate.html
of the manual.  The accelerated styles take the same arguments and
should produce the same results, except for round-off and precision
issues.

These accelerated styles are part of the USER-CUDA, GPU, USER-INTEL,
KOKKOS, USER-OMP and OPT packages, respectively.  They are only
enabled if LAMMPS was built with those packages.  See the "Making
LAMMPS"_Section_start.html#start_3 section for more info.

You can specify the accelerated styles explicitly in your input script
by including their suffix, or you can use the "-suffix command-line
switch"_Section_start.html#start_7 when you invoke LAMMPS, or you can
use the "suffix"_suffix.html command in your input script.

See "Section_accelerate"_Section_accelerate.html of the manual for
more instructions on how to use the accelerated styles effectively.

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

This pair style does not support mixing.  Thus, coefficients for all
I,J pairs must be specified explicitly.

The "pair_modify"_pair_modify.html shift, table, and tail options are
not relevant for this pair style.

This pair style writes the settings for the "pair_style table" command
to "binary restart files"_restart.html, so a pair_style command does
not need to specified in an input script that reads a restart file.
However, the coefficient information is not stored in the restart
file, since it is tabulated in the potential files.  Thus, pair_coeff
commands do need to be specified in the restart input script.

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.

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[Restrictions:] none

[Related commands:]

"pair_coeff"_pair_coeff.html

[Default:] none

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:link(Wolff)
[(Wolff)] Wolff and Rudd, Comp Phys Comm, 120, 200-32 (1999).