#
# 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) 2013--2019, Regents of the University of Minnesota.
# All rights reserved.
#
# Contributors:
#    Ellad B. Tadmor
#

Spring-modified Lennard-Jones (SLJ) pair potential model for Ar.

V = 0.5 \sum_i \sum_j eps_i eps_j 4 [ (sig/r_ij)^12 - (sig/r_ij)^6 ] (1)

where
      eps_i = 0.5 \sum_k spring (r_ik)^2                             (2)

The potential parameters are `sig` and the spring constant `sig`.

This potential uses two cutoffs and requires neighbors of padding
atoms for the summ in (2).

The loops in (2) are over all atoms for which r_ik < cutoff1

The loops in (1) are over all atoms for which r_ij < cutoff2

For the Ar parameterization, cutoff1 is set so that only nearest
neighbors contribute in the equilibrium 0K fcc structure, and
cutoff2 is set to include the third neighbor distance. The potential
is discontinuous at both cutoffs. It is designed for testing purposes
only.

The equilibrium spacing for the fcc structure predicted by the SLJ potential is

a0 = 2^(1/3)/sqrt(3) * (94297/491)^(1/6) sig = 1.74724 sig

The first, second and third neighbor distances in fcc are then:

r_NN1 = a0/sqrt(2)   = 1.235 sig
r_NN2 = a0           = 1.747 sig
r_NN3 = a0*sqrt(3/2) = 2.140 sig

The parameters `sig` and `spring` are selected to reproduce the experimental
properties of fcc argon:

a0  = 5.26 A
E_c = 0.0104 eV
