lammps/doc/pair_table.txt

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pair_style table command :h3

[Syntax:]

pair_style table style N :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 :ul

[Examples:]

pair_style table linear 1000
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 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 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 "(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, or in the data file or restart files read by the
"read_data"_read_data.html or "read_restart"_read_restart.html
commands:

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.

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

Make sure the tabulated potential you are feeding to LAMMPS is not
pathological. :l,ule

:line

The format of a tabulated file is 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; its value is the number of table
entries that follow.  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.
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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[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).