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### pair_style table command

Syntax:

    pair_style table style N

- 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

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

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 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 (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.

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, so additional interpolation is not needed. See discussion below.
- Use as large an inner cutoff as possible. This avoids fitting splines to very steep parts of the potential.

The format of a tabulated file is as follows (without the parenthesized comments):

    # 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 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 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.

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 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.

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

Default: none

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