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# pair_style python command

## Syntax

    pair_style python cutoff

cutoff = global cutoff for interactions in python potential classes

## Examples

    pair_style python 2.5
    pair_coeff * * py_pot.LJCutMelt lj

    pair_style python 10.0
    pair_coeff * * py_pot.HarmonicCut A B

    pair_style hybrid/overlay coul/long 12.0 python 12.0
    pair_coeff * * coul/long
    pair_coeff * * python py_pot.LJCutSPCE OW NULL

## Description

The python pair style provides a way to define pairwise additive potential functions as python script code that is loaded into LAMMPS from a python file which must contain specific python class definitions. This allows to rapidly evaluate different potential functions without having to modify and re-compile LAMMPS. Due to python being an interpreted language, however, the performance of this pair style is going to be significantly slower (often between 20x and 100x) than corresponding compiled code. This penalty can be significantly reduced through generating tabulations from the python code through the pair_write command, which is supported by this style.

Only a single pair_coeff command is used with the python pair style which specifies a python class inside a python module or a file that LAMMPS will look up in the current directory, a folder pointed to by the `LAMMPS_POTENTIALS` environment variable or somewhere in your python path. A single python module can hold multiple python pair class definitions. The class definitions itself have to follow specific rules that are explained below.

Atom types in the python class are specified through symbolic constants, typically strings. These are mapped to LAMMPS atom types by specifying N additional arguments after the class name in the pair_coeff command, where N must be the number of currently defined atom types:

As an example, imagine a file py_pot.py has a python potential class names LJCutMelt with parameters and potential functions for a two Lennard-Jones atom types labeled as ‘LJ1’ and ‘LJ2’. In your LAMMPS input and you would have defined 3 atom types, out of which the first two are supposed to be using the ‘LJ1’ parameters and the third the ‘LJ2’ parameters, then you would use the following pair_coeff command:

    pair_coeff * * py_pot.LJCutMelt LJ1 LJ1 LJ2

The first two arguments must be * * so as to span all LAMMPS atom types. The first two LJ1 arguments map LAMMPS atom types 1 and 2 to the LJ1 atom type in the LJCutMelt class of the py_pot.py file. The final LJ2 argument maps LAMMPS atom type 3 to the LJ2 atom type the python file. If a mapping value is specified as NULL, the mapping is not performed, any pair interaction with this atom type will be skipped. This can be used when a python potential is used as part of the hybrid or hybrid/overlay pair style. The NULL values are then placeholders for atom types that will be used with other potentials.

The python potential file has to start with the following code:

    from __future__ import print_function

    class LAMMPSPairPotential(object):
        def __init__(self):
            self.pmap=dict()
            self.units='lj'
        def map_coeff(self,name,ltype):
            self.pmap[ltype]=name
        def check_units(self,units):
            if (units != self.units):
               raise Exception("Conflicting units: %s vs. %s" % (self.units,units))

Any classes with definitions of specific potentials have to be derived from this class and should be initialize in a similar fashion to the example given below.

Note

The class constructor has to set up a data structure containing the potential parameters supported by this class. It should also define a variable self.units containing a string matching one of the options of LAMMPS’ units command, which is used to verify, that the potential definition in the python class and in the LAMMPS input match.

Here is an example for a single type Lennard-Jones potential class LJCutMelt in reduced units, which defines an atom type lj for which the parameters epsilon and sigma are both 1.0:

    class LJCutMelt(LAMMPSPairPotential):
        def __init__(self):
            super(LJCutMelt,self).__init__()
            # set coeffs: 48*eps*sig**12, 24*eps*sig**6,
            #              4*eps*sig**12,  4*eps*sig**6
            self.units = 'lj'
            self.coeff = {'lj'  : {'lj'  : (48.0,24.0,4.0,4.0)}}

The class also has to provide two methods for the computation of the potential energy and forces, which have be named compute_force, and compute_energy, which both take 3 numerical arguments:

- rsq = the square of the distance between a pair of atoms (float)

- itype = the (numerical) type of the first atom

- jtype = the (numerical) type of the second atom

This functions need to compute the (scaled) force and the energy, respectively, and use the result as return value. The functions need to use the pmap dictionary to convert the LAMMPS atom type number to the symbolic value of the internal potential parameter data structure. Following the LJCutMelt example, here are the two functions:

    def compute_force(self,rsq,itype,jtype):
         coeff = self.coeff[self.pmap[itype]][self.pmap[jtype]]
         r2inv  = 1.0/rsq
         r6inv  = r2inv*r2inv*r2inv
         lj1 = coeff[0]
         lj2 = coeff[1]
         return (r6inv * (lj1*r6inv - lj2))*r2inv

     def compute_energy(self,rsq,itype,jtype):
         coeff = self.coeff[self.pmap[itype]][self.pmap[jtype]]
         r2inv  = 1.0/rsq
         r6inv  = r2inv*r2inv*r2inv
         lj3 = coeff[2]
         lj4 = coeff[3]
         return (r6inv * (lj3*r6inv - lj4))

Note

for consistency with the C++ pair styles in LAMMPS, the compute_force function follows the conventions of the Pair::single() methods and does not return the pairwise force directly, but the force divided by the distance between the two atoms, so this value only needs to be multiplied by delta x, delta y, and delta z to conveniently obtain the three components of the force vector between these two atoms.

Below is a more complex example using real units and defines an interaction equivalent to:

    units real
    pair_style harmonic/cut
    pair_coeff 1 1 0.2 9.0
    pair_coeff 2 2 0.4 9.0

This uses the default geometric mixing. The equivalent input with pair style python is:

    units real
    pair_style python 10.0
    pair_coeff * * py_pot.Harmonic A B

Note that while for pair style harmonic/cut the cutoff is implicitly set to the minimum of the harmonic potential, for pair style python a global cutoff must be set and it must be equal or larger to the implicit cutoff of the potential in python, which has to explicitly return zero force and energy beyond the cutoff. Also, the mixed parameters have to be explicitly provided. The corresponding python code is:

    class Harmonic(LAMMPSPairPotential):
        def __init__(self):
            super(Harmonic,self).__init__()
            self.units = 'real'
            # set coeffs: K, r0
            self.coeff = {'A'  : {'A'  : (0.2,9.0),
                                  'B'  : (math.sqrt(0.2*0.4),9.0)},
                          'B'  : {'A'  : (math.sqrt(0.2*0.4),9.0),
                                  'B'  : (0.4,9.0)}}

        def compute_force(self,rsq,itype,jtype):
            coeff = self.coeff[self.pmap[itype]][self.pmap[jtype]]
            r = math.sqrt(rsq)
            delta = coeff[1]-r
            if (r < coeff[1]):
                return 2.0*delta*coeff[0]/r
            else:
                return 0.0

        def compute_energy(self,rsq,itype,jtype):
            coeff = self.coeff[self.pmap[itype]][self.pmap[jtype]]
            r = math.sqrt(rsq)
            delta = coeff[1]-r
            if (r < coeff[1]):
                return delta*delta*coeff[0]
            else:
                return 0.0

Performance Impact

The evaluation of scripted python code will slow down the computation of pairwise interactions quite significantly. However, this performance penalty can be worked around through using the python pair style not for the actual simulation, but to generate tabulated potentials using the pair_write command. This will also enable GPU or multi-thread acceleration through the GPU, KOKKOS, or OPENMP package versions of the table pair style. Please see below for a LAMMPS input example demonstrating how to build a table file:

    pair_style python 2.5
    pair_coeff * * py_pot.LJCutMelt lj
    shell rm -f lj.table
    pair_write  1 1 2000 rsq 0.01 2.5 lj.table lj

Note that it is strongly recommended to try to delete the potential table file before generating it. Since the pair_write command will always append to a table file, while pair style table will use the first match. Thus when changing the potential function in the python class, the table pair style will still read the old variant unless the table file is first deleted.

After switching the pair style to table, the potential tables need to be assigned to the LAMMPS atom types like this:

    pair_style      table linear 2000
    pair_coeff      1  1  lj.table lj

This can also be done for more complex systems. Please see the examples/python folders for a few more examples.

## Mixing, shift, table, tail correction, restart, rRESPA info

Mixing of potential parameters has to be handled inside the provided python module. The python pair style simply assumes that force and energy computation can be correctly performed for all pairs of atom types as they are mapped to the atom type labels inside the python potential class.

This pair style does not support the pair_modify shift, table, and tail options.

This pair style does not write its information to binary restart files, since it is stored in potential files. Thus, you need to re-specify the pair_style and pair_coeff commands in an input script that reads a restart file.

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

This pair style is part of the PYTHON package. It is only enabled if LAMMPS was built with that package. See the Build package page for more info.

## Related commands

pair_coeff, pair_write, pair style table

## Default

none