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


This directory
(Three_Body_Stillinger_Weber_Zhang_Silicene_Model1_Si__MO_800412945727_000)
contains a parameterization of the Stillinger-Weber potential [1] optimized for 
Silicene (single-layer Si sheets) [2] based on the KIM Model Driver 
Three_Body_Stillinger_Weber.  According to the authors, the potential
"accurately reproduces the low buckling structure of silicene and the full phonon dispersion curves obtained from ab initio calculations" [2]. 
The authors provide two sets of parameters. This parameterization corresponds 
to the parameter set referred to as "Optimized SW1" in [2].

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 the Model based on the specified KIM Model
    Driver

README
    This file

Three_Body_Stillinger_Weber_Zhang_Silicine_Model1_Si.params
    Parameters file providing the Stillinger-Weber parameters for Si

   This file must have the follwing format:

     Line 1: A
     Line 2: B
     Line 3: p
     Line 4: q
     Line 5: a
     Line 6: lambda
     Line 7: gamma
     Line 8: sigma in Angstrom
     Line 9: epsilon in ev
     Line 10: costheta_0

Any additional lines will be silently ignored.

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. X. Zhang, H. Xie, M. Hu, H. Bao, S. Yue, G. Qin and G. Su, "Thermal conductivity of silicene calculated using an optimized Stillinger-Weber potential", Phys. Rev. B, vol 89, 054310, 2014.

Description:
/*******************************************************************************

* For three-body potential any potential energy function for N-particle system can be written in the
* following form of two-body and three-body terms:
     F(1, 2, ...., N)   = sum_{i; 1 <= i < j <= N} phi_two(r; r = r_ij)
                          + sum_{i; 1 <= i \neq j < k <= N} phi_three(r_ij, r_ik, r_jk);

* For Stillinger-Weber, two-body term phi_two is

     phi_two(r) = epsilon * f_2(r_cap; r_cap = r/sigma); where f_2 is

     f_2(r_cap) = A * ( B*r_cap^(-p) - r_cap^-q ) * exp(1/(r_cap - a)); when  r_cap <  a
                = 0   when r_cap >= a

* and three-body term phi_three is

     phi_three(r_ij, r_ik, r_jk) = epsilon * f_3(r1_cap, r2_cap, r3_cap); where

     r1_cap = r_ij/sigma, r2_cap = r_ik/sigma, r3_cap = r_jk/sigma,      and

     f_3(r1_cap, r2_cap, r3_cap) = lambda * (exp(gamma((1/(r1_cap - a)) + (1/(r2_cap - a))))) * (costheta_jik - costheta_0)^2;  when r1_cap < a && r2_cap < a
                                 = 0;                                                                                           otherwise

     costheta_jik = (r_ij^2 + r_ik^2 - r_jk^2) / (2*r_ij*r_ik).

*******************************************************************************/