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# pair_style table command

Accelerator Variants: table/gpu, table/kk, table/omp

## Syntax

    pair_style table style N keyword ...

- 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

## 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

## Description

Style table creates interpolation tables from potential energy and force values listed in a file(s) as a function of distance. When performing dynamics or minimization, the interpolation tables are used to evaluate energy and forces for pairwise interactions between particles, similar to how analytic formulas are used for other pair styles.

The interpolation tables are created as a pre-computation by fitting cubic splines to the file values and interpolating energy and force values at each of N distances. During a simulation, the tables are used to interpolate energy and force values as needed for each pair of particles separated by a distance R. The interpolation is done in one of 4 styles: lookup, linear, spline, or bitmap.

For the lookup style, the distance R is used to find the nearest table entry, which is the energy or force.

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

For the spline style, cubic spline coefficients are computed and stored for each of the N values in the table, one set of splines for energy, another for force. Note that these splines are different than the ones used to pre-compute the N values. Those splines were fit to the Nfile values in the tabulated file, where often Nfile < N. The distance R is used to find the appropriate set of spline coefficients which are used to evaluate a cubic polynomial which computes the energy or force.

For the bitmap style, the specified N is used to create interpolation tables that are 2^N in length. The distance R is used to index into the table via a fast bit-mapping technique due to (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 command as in the examples above.

- filename

- keyword

- cutoff (distance units)

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 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 ensure 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. Note that it is up to you to ensure the tabulated values for each pair of atom types has the correct functional form to be compatible with the matching long-range solver.

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.

- Always use the pair_write command to produce a plot of what the final interpolated potential looks like. This can show up interpolation “features” you may not like.

- Start with the linear style; it’s the style least likely to have problems.

- 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.

- Make sure that your tabulated forces and tabulated energies are consistent (dE/dr = -F) over the entire range of r values. LAMMPS will warn if this is not the case.

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

Suitable tables in the correct format for use with these pair styles can be created by LAMMPS itself using the pair_write command. In combination with the pair styles python, lepton, or lepton/coul this can be a powerful mechanism to implement and test tables for use with LAMMPS. Another option to generate tables is the Python code in the `tools/tabulate` folder of the LAMMPS source code distribution.

The format of a tabulated file has an (optional) header followed by a series of one or more sections, defined as follows (without the parenthesized comments). The header must start with a # character and the DATE: and UNITS: tags will be parsed and used:

    # DATE: 2020-06-10  UNITS: real  CONTRIBUTOR: ... (header line)
    # Morse potential for Fe   (one or more comment or blank lines)

    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

A section begins with a non-blank line whose first 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 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 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. This is because the internal table abscissa is always RSQ (separation distance squared), for efficient lookup.

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.

Note

If you use “R” or “RSQ”, the tabulated distance values in the file are effectively ignored, and replaced by new values as described in the previous paragraph. If the distance value in the table is not very close to the new value (i.e. round-off difference), then you will be assigning energy/force values to a different distance, which is probably not what you want. LAMMPS will warn if this is occurring.

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 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 third 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 first value is the index from 1 to N, the second value is r (in distance units), the third value is the energy (in energy units), and the fourth 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.

Styles with a 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 on the Accelerator packages page. 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 GPU, INTEL, KOKKOS, OPENMP, and OPT packages, respectively. They are only enabled if LAMMPS was built with those packages. See the Build package page 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 when you invoke LAMMPS, or you can use the suffix command in your input script.

See the Accelerator packages page for more instructions on how to use the accelerated styles effectively.

## 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 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, 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 command. It does not support the inner, middle, outer keywords.

## Restrictions

none

## Related commands

pair_coeff, pair_write

## Default

none

(Wolff) Wolff and Rudd, Comp Phys Comm, 120, 200-32 (1999).