# pair_style atm command¶

## Syntax¶

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¶

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 Axilrod-Teller-Muto potential for the energy E of a system of atoms as

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

where $$\nu$$ is the three-body interaction strength. The distances between pairs of atoms $$r_{12}$$, $$r_{23}$$, $$r_{31}$$ and the angles $$\gamma_1$$, $$\gamma_2$$, $$\gamma_3$$ are as shown in this diagram: Note that for the interaction between a triplet of atoms $$I,J,K$$, there is no “central” atom. The interaction is symmetric with respect to permutation of the three atoms. Thus the $$\nu$$ value is the same for all those permutations of the atom types of $$I,J,K$$ 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 pair_style hybrid/overlay command as in the example above.

The potential for a triplet of atom is calculated only if all 3 distances $$r_{12}$$, $$r_{23}$$, $$r_{31}$$ between the 3 atoms satisfy $$r_{IJ} < \text{cutoff}$$. In addition, the product of the 3 distances $$r_{12} r_{23} r_{31}$$ < cutoff_triple $$^3$$ 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 pair_coeff command as in the examples above, or in the restart files read by the read_restart commands:

• $$K$$ = atom type of the third atom (1 to $$N_{\text{types}}$$)

• $$\nu$$ = prefactor (energy/distance^9 units)

$$K$$ can be specified in one of two ways. An explicit numeric value can be used, as in the second example above. $$J \leq K$$ is required. LAMMPS sets the coefficients for the other 5 symmetric interactions to the same values. E.g. if $$I = 1$$, $$J = 2$$, $$K = 3$$, then these 6 values are set to the specified $$\nu$$: $$\nu_{123}$$, $$\nu_{132}$$, $$\nu_{213}$$, $$\nu_{231}$$, $$\nu_{312}$$, $$\nu_{321}$$. 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 $$N$$ equals the number of atom types, then an asterisk with no numeric values means all types from 1 to $$N$$. A leading asterisk means all types from 1 to $$n$$ (inclusive). A trailing asterisk means all types from $$n$$ to $$N$$ (inclusive). A middle asterisk means all types from $$m$$ to $$n$$ (inclusive). Note that only type triplets with $$J \leq K$$ are considered; if asterisks imply type triplets where $$K < J$$, they are ignored.

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

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.

pair_coeff 1 1 1 0.25


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

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:

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 $$\nu$$ 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 $$K$$ types. If some $$I,J,K$$ 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 $$I,J$$ combinations, else an error will result.

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

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

This pair style writes its information to binary restart files, 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 pair_style hybrid/overlay 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 run_style respa command. It does not support the inner , middle , 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 Build package doc page for more info.

## Default¶

none

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