#
# CDDL HEADER START
#
# The contents of this file are subject to the terms of the Common Development
# and Distribution License Version 1.0 (the "License").
#
# You can obtain a copy of the license at
# http://www.opensource.org/licenses/CDDL-1.0.  See the License for the
# specific language governing permissions and limitations under the License.
#
# When distributing Covered Code, include this CDDL HEADER in each file and
# include the License file in a prominent location with the name LICENSE.CDDL.
# If applicable, add the following below this CDDL HEADER, with the fields
# enclosed by brackets "[]" replaced with your own identifying information:
#
# Portions Copyright (c) [yyyy] [name of copyright owner]. All rights reserved.
#
# CDDL HEADER END
#

#
# Copyright (c) 2012, Regents of the University of Minnesota.  All rights reserved.
#
# Contributors:
#    Ryan S. Elliott
#    Ellad B. Tadmor
#    Mingjian Wen

#
# Release: This file is part of the openkim-api-vX.X.X package.
#


This directory (Three_Body_Stillinger_Weber__MD_335816936951_002) contains Stillinger-Weber(SW) potential
Model Driver written in C.


1. This is a direct extention of the standard Stillinger-Weber potential to support multiple species.
   Usage of a subset of the supported species is valid. For example, if there are 3 species A, B and C
   in the parameter file, the use of single species A (or B or C) or two species A and B (or A and C,
   or B and C) are fine.


2. The functional form has been rewritten so as to separate the parameters to avoid inconvenience of using  
   this Model Dirver.  The varible 'epsilon' in the standard SW potential is a dummy variable, so it is 
   combined with 'A' and 'lambda'.  The 'cutoff' of the standard SW potential is determined implicitly
   by 'cutoff' = 'a*sigma', where 'a' is a potential parameter.  In this Model Driver, the 'cutoff' is
   defined explicitly.  By doing this, if 'sigma' is updated through 'PARAM_FREE_sigma' there is no needed
   to update 'cutoff'.

   Above all, compared to the standard SW potential, the following redefinitions have been made:
   A      := A*epsilon
   lambda := lambda*epsion
   gamma  := gamma*sigma
   rcut   := a*sigma

   Besides, an approximation is made:
   lambda_ijk = sqrt(lambda_ij)*sqrt(lambda_ik),

   and also we assume that the ideal angle 'thetea0' is the same between all 3-body interactions. 

   Then the SW potential for multiple species can be written as:
  
   E = sum_{i,j>i} phi_2(rij) + sum_{i, j!=i, k>j} phi_3(rij, rik, theta)

   phi_2(rij)           = Aij*(Bij(rij/sigma_ij)^(-p) - (rij/sigma_ij)^(-q))
                          * exp(sigma_ij/(rij - rcutij))

   phi_3(rij,rik,theta) = sqrt(lambda_ij)*sqrt(lambda_ik)(cos[theta] - cos[theta0])^2 
                          *  exp(gamma_ij/(rij - rcutij) + gamma_ik/(rik - rcutik))


3. One parameter file is needed, and the parameters should be given as:
     first line: number of species

   Then each line lists the following 9 parameters for the interaction between two species:
     A(in ev) B p q sigma(in Angstrom) lambda(in eV) gamma(in Angstorm) costheta_0 cutoff

   Note that one should list all the interactions for one species and then proceed to list all the
   interaction for the next species.  For example, if there are 3 species, then the parameters should
   be in the following order,
     (1,1)
     (1,2)   # (2,1) is the same as (1,2), so only list it once here
     (1,3)
     (2,2)
     (2,3)
     (3,3)
     where, (i,j) means the parameters for species i and species j.  There should be N*(N+1)/2 such 
     lines for N species. 


The Model Driver complies with the KIM API standard, using four neihgbor handling methods: MI_OPBC_F,
NEIGH_PURE_F, NEIGH_RVEC_F, and CLUSTER and iterator or locator mode. It publishes its parameters
and supports optional computation of 'energy', 'forces', 'particleEnergy', 'process_dEdr',
and 'process_dE2dr2'. Its initializaton routine takes a KIM API object pointer and a pointer to a string 
that contains all parameters which define a KIM Model based on this KIM Model Driver.


References:

1. F. H. Stillinger and T. A. Weber, "Computer simulation of local order in condensed phases of silicon",
   Phys. Rev. B, vol. 31, 5262-5271, 1985

2. Ellad B. Tadmor and Ronald E. Miller, Modeling Materials: Continuum, Atomistic and Multiscale Techniques,
   Cambridge University Press, 2011

3. X. W. Zhou, D. K. Ward, and J. E. Martin, et al, "Stillinger-Weber potential for the II-VI elements 
   Zn-Cd-Hg-S-Se-Te" Phys. Rev. B, 88, 085309, 2013.


The following files are in this directory:

LICENSE.CDDL
     The Common Development and Distribution License (CDDL) Version 1.0 file

Makefile
    makefile to compile and build executables with GNU or Intel compilers

README
    This file

Three_Body_Stillinger_Weber.c
    C file that contains the implementation of the 3-body Stillinger-Weber potential Model Driver

Three_Body_Stillinger_Weber.kim.tpl
    Template KIM descriptor file containing all variables and methods that are
    exposed by the driver through the KIM API interface.  This file will be
    used (by the make system) to generate a KIM descriptor file for each KIM
    Model based on this Model Driver.