.. index:: pair_style atm

pair_style atm command
======================

Syntax
""""""

.. code-block:: LAMMPS

   pair_style atm cutoff cutoff_triple

* cutoff = cutoff for each pair in 3-body interaction (distance units)
* cutoff_triple = additional cutoff applied to product of 3 pairwise distances (distance units)

Examples
""""""""

.. code-block:: LAMMPS

   pair_style atm 4.5 2.5
   pair_coeff * * * 0.072

   pair_style hybrid/overlay lj/cut 6.5 atm 4.5 2.5
   pair_coeff * * lj/cut 1.0 1.0
   pair_coeff 1 1 atm 1 0.064
   pair_coeff 1 1 atm 2 0.080
   pair_coeff 1 2 atm 2 0.100
   pair_coeff 2 2 atm 2 0.125

Description
"""""""""""

The *atm* style computes a 3-body :ref:`Axilrod-Teller-Muto <Axilrod>`
potential for the energy E of a system of atoms as

.. math::

   E & = \nu\frac{1+3\cos\gamma_1\cos\gamma_2\cos\gamma_3}{r_{12}^3r_{23}^3r_{31}^3} \\

where :math:`\nu` is the three-body interaction strength.  The distances
between pairs of atoms :math:`r_{12}`, :math:`r_{23}`, :math:`r_{31}` and the angles :math:`\gamma_1`, :math:`\gamma_2`,
:math:`\gamma_3` are as shown in this diagram:

.. image:: JPG/pair_atm_dia.jpg
   :align: center

Note that for the interaction between a triplet of atoms :math:`I,J,K`, there
is no "central" atom.  The interaction is symmetric with respect to
permutation of the three atoms. Thus the :math:`\nu` value is
the same for all those permutations of the atom types of :math:`I,J,K`
and needs to be specified only once, as discussed below.

The *atm* potential is typically used in combination with a two-body
potential using the :doc:`pair_style hybrid/overlay <pair_hybrid>`
command as in the example above.

The potential for a triplet of atom is calculated only if all 3 distances
:math:`r_{12}`, :math:`r_{23}`, :math:`r_{31}` between the three atoms satisfy
:math:`r_{IJ} < \text{cutoff}`.  In addition, the product of the 3 distances
:math:`r_{12} r_{23} r_{31}` < cutoff_triple :math:`^3` is required, which
excludes from calculation the triplets with small contribution to the
interaction.

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, or in the restart files read by the
:doc:`read_restart <read_restart>` commands:

* :math:`K` = atom type of the third atom (1 to :math:`N_{\text{types}}`)
* :math:`\nu` = prefactor (energy/distance\^9 units)

:math:`K` can be specified in one of two ways.  An explicit numeric value
or type label can be used, as in the second example above.   LAMMPS
sets the coefficients for the other 5 symmetric interactions to the same
values.  E.g. if :math:`I = 1`, :math:`J = 2`, :math:`K = 3`, then these 6
values are set to the specified :math:`\nu`: :math:`\nu_{123}`,
:math:`\nu_{132}`, :math:`\nu_{213}`, :math:`\nu_{231}`, :math:`\nu_{312}`,
:math:`\nu_{321}`.  This enforces the symmetry discussed above.

A wildcard asterisk can be used for K to set the coefficients for
multiple triplets of atom types.  This takes the form "\*" or "\*n" or
"n\*" or "m\*n".  If :math:`N` equals the number of atom types, then an asterisk with
no numeric values means all types from 1 to :math:`N`.  A leading asterisk
means all types from 1 to :math:`n` (inclusive).  A trailing asterisk means
all types from :math:`n` to :math:`N` (inclusive).  A middle asterisk means all types
from :math:`m` to :math:`n` (inclusive).  Note that only type triplets with :math:`J \leq K` are
considered; if asterisks imply type triplets where :math:`K < J`, they are
ignored.

Note that a pair_coeff command can override a previous setting for the
same :math:`I,J,K` triplet.  For example, these commands set :math:`\nu` for all :math:`I,J.K`
triplets, then overwrite nu for just the :math:`I,J,K = 2,3,4` triplet:

.. code-block:: LAMMPS

   pair_coeff * * * 0.25
   pair_coeff 2 3 4 0.1

Note that for a simulation with a single atom type, only a single
entry is required, e.g.

.. code-block:: LAMMPS

   pair_coeff 1 1 1 0.25

For a simulation with two atom types, four pair_coeff commands will
specify all possible nu values:

.. code-block:: LAMMPS

   pair_coeff 1 1 1 nu1
   pair_coeff 1 1 2 nu2
   pair_coeff 1 2 2 nu3
   pair_coeff 2 2 2 nu4

For a simulation with three atom types, ten pair_coeff commands will
specify all possible nu values:

.. code-block:: LAMMPS

   pair_coeff 1 1 1 nu1
   pair_coeff 1 1 2 nu2
   pair_coeff 1 1 3 nu3
   pair_coeff 1 2 2 nu4
   pair_coeff 1 2 3 nu5
   pair_coeff 1 3 3 nu6
   pair_coeff 2 2 2 nu7
   pair_coeff 2 2 3 nu8
   pair_coeff 2 3 3 nu9
   pair_coeff 3 3 3 nu10

By default the :math:`\nu` value for all triplets is set to 0.0.  Thus it is
not required to provide pair_coeff commands that enumerate triplet
interactions for all :math:`K` types.  If some :math:`I,J,K` combination is not
specified, then there will be no 3-body ATM interactions for that
combination and all its permutations.  However, as with all pair
styles, it is required to specify a pair_coeff command for all :math:`I,J`
combinations, else an error will result.

----------

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

This pair style do not support the :doc:`pair_modify <pair_modify>`
mix, shift, table, and tail options.

This pair style writes its information to :doc:`binary restart files
<restart>`, so pair_style and pair_coeff commands do not need to be specified
in an input script that reads a restart file.  However, if the *atm* potential
is used in combination with other potentials using the :doc:`pair_style
hybrid/overlay <pair_hybrid>` command then pair_coeff commands need to be
re-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*, and *outer* keywords.

----------

Restrictions
""""""""""""

This pair style is part of the MANYBODY package.  It is only enabled
if LAMMPS was built with that package.  See the :doc:`Build package <Build_package>` page for more info.

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

:doc:`pair_coeff <pair_coeff>`

Default
"""""""

none

----------

.. _Axilrod:

**(Axilrod)**
Axilrod and Teller, J Chem Phys, 11, 299 (1943);
Muto, Nippon Sugaku-Buturigakkwaishi 17, 629 (1943).
