.. index:: pair_style table
.. index:: pair_style table/gpu
.. index:: pair_style table/kk
.. index:: pair_style table/omp

pair_style table command
========================

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

Syntax
""""""

.. code-block:: LAMMPS

   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
""""""""

.. code-block:: LAMMPS

   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
:ref:`(Wolff) <Wolff2>`, and a linear interpolation is performed between
adjacent table values.

The following coefficients must be defined for each pair of atoms
types via the :doc:`pair_coeff <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
:doc:`kspace_style <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 :doc:`pair_style lj/cut/coul/long <pair_lj_cut_coul>`.  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 :doc:`pair_write <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 :doc:`pair_write <pair_write>`
command.  In combination with the pair styles :doc:`python <pair_python>`,
:doc:`lepton, or lepton/coul <pair_lepton>` 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:

.. parsed-literal::

   # 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 :doc:`pair_style table <pair_style>` 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 :doc:`pair_write <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.

----------

.. include:: accel_styles.rst

----------

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 :doc:`pair_modify <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 :doc:`binary restart files <restart>`, 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
:doc:`run_style respa <run_style>` command.  It does not support the
*inner*, *middle*, *outer* keywords.

----------

Restrictions
""""""""""""
none

Related commands
""""""""""""""""

:doc:`pair_coeff <pair_coeff>`, :doc:`pair_write <pair_write>`

Default
"""""""

none

----------

.. _Wolff2:

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