# pair_style atm command ## Syntax ``` 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 ``` 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 [Axilrod-Teller-Muto](Axilrod) potential for the energy E of a system of atoms as $$\begin{aligned} E & = \nu\frac{1+3\cos\gamma_1\cos\gamma_2\cos\gamma_3}{r_{12}^3r_{23}^3r_{31}^3} \\ \end{aligned}$$ 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: ![image](JPG/pair_atm_dia.jpg){.align-center} 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](pair_hybrid) 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](pair_coeff) command as in the examples above, or in the restart files read by the [read_restart](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: ``` 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. ``` 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: ``` 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: ``` 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 $\nu$ 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](pair_modify) mix, shift, table, and tail options. This pair style writes its information to [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 [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 [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 [Build package](Build_package) page for more info. ## Related commands [pair_coeff](pair_coeff) ## Default none ------------------------------------------------------------------------ ::: {#Axilrod} **(Axilrod)** Axilrod and Teller, J Chem Phys, 11, 299 (1943); Muto, Nippon Sugaku-Buturigakkwaishi 17, 629 (1943). :::