diff --git a/doc/src/Eqs/pair_atm.jpg b/doc/src/Eqs/pair_atm.jpg deleted file mode 100644 index d2e6d704e9..0000000000 Binary files a/doc/src/Eqs/pair_atm.jpg and /dev/null differ diff --git a/doc/src/Eqs/pair_atm.tex b/doc/src/Eqs/pair_atm.tex deleted file mode 100644 index fce1db99b8..0000000000 --- a/doc/src/Eqs/pair_atm.tex +++ /dev/null @@ -1,9 +0,0 @@ -\documentclass[12pt]{article} - -\begin{document} - -\begin{equation} -E=\nu\frac{1+3\cos\gamma_1\cos\gamma_2\cos\gamma_3}{r_{12}^3r_{23}^3r_{31}^3} -\end{equation} - -\end{document} diff --git a/doc/src/pair_atm.rst b/doc/src/pair_atm.rst index 6118b0943f..aff3692e49 100644 --- a/doc/src/pair_atm.rst +++ b/doc/src/pair_atm.rst @@ -1,13 +1,13 @@ -.. index:: pair\_style atm +.. index:: pair_style atm -pair\_style atm command -======================= +pair_style atm command +====================== Syntax """""" -.. parsed-literal:: +.. code-block:: LAMMPS pair_style atm cutoff cutoff_triple @@ -18,13 +18,13 @@ Examples """""""" -.. parsed-literal:: +.. code-block:: LAMMPS pair_style atm 4.5 2.5 - pair_coeff \* \* \* 0.072 + 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 * * 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 @@ -36,91 +36,95 @@ Description The *atm* style computes a 3-body :ref:`Axilrod-Teller-Muto ` potential for the energy E of a system of atoms as -.. image:: Eqs/pair_atm.jpg - :align: center +.. math:: -where nu is the three-body interaction strength. The distances -between pairs of atoms r12, r23, r31 and the angles gamma1, gamma2, -gamma3 are as shown in this diagram: + 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 I,J,K, there +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 nu value is -the same for all those permutations of the atom types of I,J,K +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 ` command as in the example above. -The potential for a triplet of atom is calculated only if all 3 -distances r12, r23, r31 between the 3 atoms satisfy rIJ < cutoff. -In addition, the product of the 3 distances r12\*r23\*r31 < -cutoff\_triple\^3 is required, which excludes from calculation the -triplets with small contribution to the interaction. +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 3 atoms satisfy +:math:`r_{IJ} < \text{cutoff}`. In addition, the product of the 3 distances +:math:`r_{12} r_{23} r_{31} < \text{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 :doc:`pair_coeff ` command as in the examples above, or in the restart files read by the :doc:`read_restart ` commands: -* K = atom type of the third atom (1 to Ntypes) -* nu = prefactor (energy/distance\^9 units) +* :math:`K` = atom type of the third atom (1 to :math:`N_{\text{types}}`) +* :math:`\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 2nd example above. J <= 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: nu123, nu132, nu213, nu231, nu312, nu321. This -enforces the symmetry discussed above. +:math:`K` can be specified in one of two ways. An explicit numeric value can +be used, as in the 2nd example above. :math:`J \leq K` is required. 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 N = 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 <= K are -considered; if asterisks imply type triplets where K < J, they are +"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 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: +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: -.. parsed-literal:: +.. code-block:: LAMMPS - pair_coeff \* \* \* 0.25 + 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. -.. parsed-literal:: +.. code-block:: LAMMPS pair_coeff 1 1 1 0.25 -For a simulation with two atom types, four pair\_coeff commands will +For a simulation with two atom types, four pair_coeff commands will specify all possible nu values: -.. parsed-literal:: +.. 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 +For a simulation with three atom types, ten pair_coeff commands will specify all possible nu values: -.. parsed-literal:: +.. code-block:: LAMMPS pair_coeff 1 1 1 nu1 pair_coeff 1 1 2 nu2 @@ -133,12 +137,12 @@ specify all possible nu values: 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 +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 I,J +styles, it is required to specify a pair_coeff command for all :math:`I,J` combinations, else an error will result. @@ -150,16 +154,16 @@ combinations, else an error will result. This pair styles do not support the :doc:`pair_modify ` mix, shift, table, and tail options. -This pair style writes its information to :doc:`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 :doc:`pair_style hybrid/overlay ` -command then pair\_coeff commands need to be re-specified -in the restart input script. +This pair style writes its information to :doc:`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 :doc:`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 :doc:`run_style respa ` command. It does not support the -*inner*\ , *middle*\ , *outer* keywords. +*inner* , *middle* , *outer* keywords. ----------