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pair_bop.cpp
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/* ----------------------------------------------------------------------
LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
http://lammps.sandia.gov, Sandia National Laboratories
Steve Plimpton, sjplimp@sandia.gov
Copyright (2003) Sandia Corporation. Under the terms of Contract
DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
certain rights in this software. This software is distributed under
the GNU General Public License.
See the README file in the top-level LAMMPS directory.
------------------------------------------------------------------------- */
/* ----------------------------------------------------------------------
Contributing authors: D.K. Ward (donward@sandia.gov) and X.W. Zhou (Sandia)
------------------------------------------------------------------------- */
/* ----------------------------------------------------------------------
The formulation for this work follows (a) D.G. Pettifor, et al., Mat.
Sci. and Eng. A365, 2-13, (2004);(b) D.A. Murdick, et al., Phys.
Rev. B 73, 045206 (2006);(c) D.G. Pettifor and I.I. Oleinik., Phys
Rev. Lett. 84, 4124 (2000); (d) D.K. Ward, et al., Phys. Rev. B 85,
115206 (2012).
Copyright (2012) Sandia Corporation. Under the terms of Contract DE-
AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
rights in this software.
pairbop v 1.0 comes with no warranty of any kind. pairbop v 1.0 is a
copyrighted code that is distributed free-of-charge, under the terms
of the GNU Public License (GPL). See "Open-Source
Rules"_http://lammps.sandia.gov/open_source.html
------------------------------------------------------------------------- */
#include "math.h"
#include "stdio.h"
#include "stdlib.h"
#include "string.h"
#include "mpi.h"
#include "pair_bop.h"
#include "atom.h"
#include "neighbor.h"
#include "neigh_request.h"
#include "force.h"
#include "timer.h"
#include "comm.h"
#include "domain.h"
#include "neighbor.h"
#include "neigh_list.h"
#include "neigh_request.h"
#include "memory.h"
#include "error.h"
#include "math_special.h"
using namespace LAMMPS_NS;
using namespace MathSpecial;
#define MAXLINE 1024
#define EPSILON 1.0e-6
/* ---------------------------------------------------------------------- */
PairBOP::PairBOP(LAMMPS *lmp) : Pair(lmp)
{
single_enable = 0;
one_coeff = 1;
manybody_flag = 1;
map = NULL;
pi_a = NULL;
pro_delta = NULL;
pi_delta = NULL;
pi_p = NULL;
pi_c = NULL;
sigma_r0 = NULL;
pi_r0 = NULL;
phi_r0 = NULL;
sigma_rc = NULL;
pi_rc = NULL;
phi_rc = NULL;
r1 = NULL;
sigma_beta0 = NULL;
pi_beta0 = NULL;
phi0 = NULL;
sigma_n = NULL;
pi_n = NULL;
phi_m = NULL;
sigma_nc = NULL;
pi_nc = NULL;
phi_nc = NULL;
pro = NULL;
sigma_delta = NULL;
sigma_c = NULL;
sigma_a = NULL;
sigma_g0 = NULL;
sigma_g1 = NULL;
sigma_g2 = NULL;
sigma_g3 = NULL;
sigma_g4 = NULL;
sigma_f = NULL;
sigma_k = NULL;
small3 = NULL;
rcut = NULL;
dr = NULL;
rdr = NULL;
disij = NULL;
rij = NULL;
cosAng = NULL;
betaS = NULL;
dBetaS = NULL;
betaP = NULL;
dBetaP = NULL;
repul = NULL;
dRepul = NULL;
itypeSigBk = NULL;
nSigBk = NULL;
sigB = NULL;
sigB1 = NULL;
itypePiBk = NULL;
nPiBk = NULL;
piB = NULL;
pBetaS = NULL;
pBetaS1 = NULL;
pBetaS2 = NULL;
pBetaS3 = NULL;
pBetaS4 = NULL;
pBetaS5 = NULL;
pBetaS6 = NULL;
pBetaP = NULL;
pBetaP1 = NULL;
pBetaP2 = NULL;
pBetaP3 = NULL;
pBetaP4 = NULL;
pBetaP5 = NULL;
pBetaP6 = NULL;
pRepul = NULL;
pRepul1 = NULL;
pRepul2 = NULL;
pRepul3 = NULL;
pRepul4 = NULL;
pRepul5 = NULL;
pRepul6 = NULL;
FsigBO = NULL;
FsigBO1 = NULL;
FsigBO2 = NULL;
FsigBO3 = NULL;
FsigBO4 = NULL;
FsigBO5 = NULL;
FsigBO6 = NULL;
rcmin = NULL;
rcmax = NULL;
rcmaxp = NULL;
setflag = NULL;
cutsq = NULL;
cutghost = NULL;
ghostneigh = 1;
bt_sg=NULL;
bt_pi=NULL;
}
/* ----------------------------------------------------------------------
check if allocated, since class can be destructed when incomplete
------------------------------------------------------------------------- */
PairBOP::~PairBOP()
{
int i;
if(allocated) {
memory_theta_destroy();
if (otfly==0) memory->destroy(cos_index);
delete [] map;
memory->destroy(BOP_index);
memory->destroy(rcut);
memory->destroy(dr);
memory->destroy(rdr);
memory->destroy(setflag);
memory->destroy(cutsq);
memory->destroy(cutghost);
memory->destroy(pBetaS);
memory->destroy(pBetaS1);
memory->destroy(pBetaS2);
memory->destroy(pBetaS3);
memory->destroy(pBetaS4);
memory->destroy(pBetaS5);
memory->destroy(pBetaS6);
memory->destroy(pBetaP);
memory->destroy(pBetaP1);
memory->destroy(pBetaP2);
memory->destroy(pBetaP3);
memory->destroy(pBetaP4);
memory->destroy(pBetaP5);
memory->destroy(pBetaP6);
memory->destroy(pRepul);
memory->destroy(pRepul1);
memory->destroy(pRepul2);
memory->destroy(pRepul3);
memory->destroy(pRepul4);
memory->destroy(pRepul5);
memory->destroy(pRepul6);
memory->destroy(FsigBO);
memory->destroy(FsigBO1);
memory->destroy(FsigBO2);
memory->destroy(FsigBO3);
memory->destroy(FsigBO4);
memory->destroy(FsigBO5);
memory->destroy(FsigBO6);
if(table==0) {
memory->destroy(pi_a);
memory->destroy(pro_delta);
memory->destroy(pi_delta);
memory->destroy(pi_p);
memory->destroy(pi_c);
memory->destroy(sigma_r0);
memory->destroy(pi_r0);
memory->destroy(phi_r0);
memory->destroy(sigma_rc);
memory->destroy(pi_rc);
memory->destroy(phi_rc);
memory->destroy(r1);
memory->destroy(sigma_beta0);
memory->destroy(pi_beta0);
memory->destroy(phi0);
memory->destroy(sigma_n);
memory->destroy(pi_n);
memory->destroy(phi_m);
memory->destroy(sigma_nc);
memory->destroy(pi_nc);
memory->destroy(phi_nc);
memory->destroy(pro);
memory->destroy(sigma_delta);
memory->destroy(sigma_c);
memory->destroy(sigma_a);
memory->destroy(sigma_g0);
memory->destroy(sigma_g1);
memory->destroy(sigma_g2);
memory->destroy(sigma_g3);
memory->destroy(sigma_g4);
memory->destroy(sigma_f);
memory->destroy(sigma_k);
memory->destroy(small3);
}
else {
memory->destroy(pi_a);
memory->destroy(pro_delta);
memory->destroy(pi_delta);
memory->destroy(pi_p);
memory->destroy(pi_c);
memory->destroy(r1);
memory->destroy(pro);
memory->destroy(sigma_delta);
memory->destroy(sigma_c);
memory->destroy(sigma_a);
memory->destroy(sigma_g0);
memory->destroy(sigma_g1);
memory->destroy(sigma_g2);
memory->destroy(sigma_f);
memory->destroy(sigma_k);
memory->destroy(small3);
}
}
if(allocate_sigma) {
destroy_sigma();
}
if(allocate_pi) {
destroy_pi();
}
}
/* ---------------------------------------------------------------------- */
void PairBOP::compute(int eflag, int vflag)
{
int ago,delay,every;
int i,j,ii,jj,iij;
int n,inum,temp_ij,ks;
int itype,jtype,i_tag,j_tag;
int *ilist,*iilist,*numneigh;
int **firstneigh;
double dpr1,ps;
double ftmp1,ftmp2,ftmp3,dE;
double dis_ij[3],rsq_ij,r_ij;
double betaS_ij,dBetaS_ij;
double betaP_ij,dBetaP_ij;
double repul_ij,dRepul_ij;
double totE;
double **f = atom->f;
double **x = atom->x;
int *type = atom->type;
int *tag = atom->tag;
int newton_pair = force->newton_pair;
int nlocal = atom->nlocal;
int nall = nlocal + atom->nghost;
inum = list->inum;
ilist = list->ilist;
numneigh = list->numneigh;
firstneigh = list->firstneigh;
ago=neighbor->ago;
delay=neighbor->delay;
every=neighbor->every;
if (eflag || vflag) ev_setup(eflag,vflag);
else evflag = vflag_fdotr = 0;
// BOP Neighbor lists must be updated every time
// atoms are moved between processors
if ((ago ==0)||bop_step==0||(ago>=delay&&(ago%every)==0)||(nall>maxnall))
gneigh();
// For non on the fly calculations cos and derivatives
// are calculated in advance and stored
if(otfly==0) theta();
else theta_mod();
// Calculate Sigma Bond-Order
if(a_flag==1) {
if (otfly==0) sigmaBo_noa();
else sigmaBo_noa_otf();
}
else {
if (otfly==0) sigmaBo();
else sigmaBo_otf();
}
// Calculate Pi Bond-Order
if (otfly==0) PiBo();
else PiBo_otf();
n=0;
totE=0;
for (ii = 0; ii < inum; ii++) {
i=ilist[ii];
i_tag=tag[i];
itype=map[type[i]]+1;
iilist=firstneigh[i];
for(jj=0;jj<numneigh[i];jj++) {
temp_ij=BOP_index[i]+jj;
j=iilist[jj];
j_tag=tag[j];
jtype=map[type[j]]+1;
if(j_tag>=i_tag) {
if(otfly==0) {
if(neigh_flag[temp_ij]) {
dpr1=(dRepul[temp_ij]-2.0*dBetaS[temp_ij]*sigB[n]
-2.0*dBetaP[temp_ij]*piB[n])/rij[temp_ij];
ftmp1=dpr1*disij[0][temp_ij];
ftmp2=dpr1*disij[1][temp_ij];
ftmp3=dpr1*disij[2][temp_ij];
f[i][0]=f[i][0]+ftmp1;
f[i][1]=f[i][1]+ftmp2;
f[i][2]=f[i][2]+ftmp3;
f[j][0]=f[j][0]-ftmp1;
f[j][1]=f[j][1]-ftmp2;
f[j][2]=f[j][2]-ftmp3;
// add repulsive and bond order components to total energy
// (d) Eq.1
dE=-2.0*betaS[temp_ij]*sigB[n]-2.0*betaP[temp_ij]*piB[n];
totE+=dE+repul[temp_ij];
if(evflag) {
ev_tally_full(i,repul[temp_ij],dE,0.0,0.0,0.0,0.0);
ev_tally_full(j,repul[temp_ij],dE,0.0,0.0,0.0,0.0);
ev_tally_xyz(i,j,nlocal,newton_pair,0.0,0.0,-ftmp1,-ftmp2,-ftmp3,
disij[0][temp_ij],disij[1][temp_ij],disij[2][temp_ij]);
}
n++;
}
}
else {
if(itype==jtype)
iij=itype-1;
else if(itype<jtype)
iij=itype*bop_types-itype*(itype+1)/2+jtype-1;
else
iij=jtype*bop_types-jtype*(jtype+1)/2+itype-1;
dis_ij[0]=x[j][0]-x[i][0];
dis_ij[1]=x[j][1]-x[i][1];
dis_ij[2]=x[j][2]-x[i][2];
rsq_ij=dis_ij[0]*dis_ij[0]
+dis_ij[1]*dis_ij[1]
+dis_ij[2]*dis_ij[2];
r_ij=sqrt(rsq_ij);
if(r_ij<=rcut[iij]) {
ps=r_ij*rdr[iij]+1.0;
ks=(int)ps;
if(nr-1<ks)
ks=nr-1;
ps=ps-ks;
if(ps>1.0)
ps=1.0;
betaS_ij=((pBetaS3[iij][ks-1]*ps+pBetaS2[iij][ks-1])*ps
+pBetaS1[iij][ks-1])*ps+pBetaS[iij][ks-1];
dBetaS_ij=(pBetaS6[iij][ks-1]*ps+pBetaS5[iij][ks-1])*ps
+pBetaS4[iij][ks-1];
betaP_ij=((pBetaP3[iij][ks-1]*ps+pBetaP2[iij][ks-1])*ps
+pBetaP1[iij][ks-1])*ps+pBetaP[iij][ks-1];
dBetaP_ij=(pBetaP6[iij][ks-1]*ps+pBetaP5[iij][ks-1])*ps
+pBetaP4[iij][ks-1];
repul_ij=((pRepul3[iij][ks-1]*ps+pRepul2[iij][ks-1])*ps
+pRepul1[iij][ks-1])*ps+pRepul[iij][ks-1];
dRepul_ij=(pRepul6[iij][ks-1]*ps+pRepul5[iij][ks-1])*ps
+pRepul4[iij][ks-1];
dpr1=(dRepul_ij-2.0*dBetaS_ij*sigB[n]
-2.0*dBetaP_ij*piB[n])/r_ij;
ftmp1=dpr1*dis_ij[0];
ftmp2=dpr1*dis_ij[1];
ftmp3=dpr1*dis_ij[2];
f[i][0]=f[i][0]+ftmp1;
f[i][1]=f[i][1]+ftmp2;
f[i][2]=f[i][2]+ftmp3;
f[j][0]=f[j][0]-ftmp1;
f[j][1]=f[j][1]-ftmp2;
f[j][2]=f[j][2]-ftmp3;
// add repulsive and bond order components to total energy
// (d) Eq. 1
dE=-2.0*betaS_ij*sigB[n]-2.0*betaP_ij*piB[n];
totE+=dE+repul_ij;
if(evflag) {
ev_tally_full(i,repul_ij,dE,0.0,0.0,0.0,0.0);
ev_tally_full(j,repul_ij,dE,0.0,0.0,0.0,0.0);
ev_tally_xyz(i,j,nlocal,newton_pair,0.0,0.0,-ftmp1,-ftmp2,-ftmp3,
dis_ij[0],dis_ij[1],dis_ij[2]);
}
n++;
}
}
}
}
}
if (vflag_fdotr) virial_fdotr_compute();
bop_step = 1;
}
/* ----------------------------------------------------------------------
allocate all arrays
------------------------------------------------------------------------- */
void PairBOP::allocate()
{
allocated = 1;
int n = atom->ntypes;
memory->create(rcut,npairs,"BOP:rcut");
memory->create(dr,npairs,"BOP:dr");
memory->create(rdr,npairs,"BOP:dr");
memory->create(setflag,n+1,n+1,"pair:setflag");
memory->create(cutsq,n+1,n+1,"pair:cutsq");
memory->create(cutghost,n+1,n+1,"pair:cutghost");
memory->create(pBetaS,npairs,nr,"BOP:pBetaS");
memory->create(pBetaS1,npairs,nr,"BOP:pBetaS1");
memory->create(pBetaS2,npairs,nr,"BOP:pBetaS2");
memory->create(pBetaS3,npairs,nr,"BOP:pBetaS3");
memory->create(pBetaS4,npairs,nr,"BOP:pBetaS4");
memory->create(pBetaS5,npairs,nr,"BOP:pBetaS5");
memory->create(pBetaS6,npairs,nr,"BOP:pBetaS6");
memory->create(pBetaP,npairs,nr,"BOP:pBetaP");
memory->create(pBetaP1,npairs,nr,"BOP:pBetaP1");
memory->create(pBetaP2,npairs,nr,"BOP:pBetaP2");
memory->create(pBetaP3,npairs,nr,"BOP:pBetaP3");
memory->create(pBetaP4,npairs,nr,"BOP:pBetaP4");
memory->create(pBetaP5,npairs,nr,"BOP:pBetaP5");
memory->create(pBetaP6,npairs,nr,"BOP:pBetaP6");
memory->create(pRepul,npairs,nr,"BOP:pRepul");
memory->create(pRepul1,npairs,nr,"BOP:pRepul1");
memory->create(pRepul2,npairs,nr,"BOP:pRepul2");
memory->create(pRepul3,npairs,nr,"BOP:pRepul3");
memory->create(pRepul4,npairs,nr,"BOP:pRepul4");
memory->create(pRepul5,npairs,nr,"BOP:pRepul5");
memory->create(pRepul6,npairs,nr,"BOP:pRepul6");
memory->create(FsigBO,npairs,nBOt,"BOP:FsigBO");
memory->create(FsigBO1,npairs,nBOt,"BOP:FsigBO1");
memory->create(FsigBO2,npairs,nBOt,"BOP:FsigBO2");
memory->create(FsigBO3,npairs,nBOt,"BOP:FsigBO3");
memory->create(FsigBO4,npairs,nBOt,"BOP:FsigBO4");
memory->create(FsigBO5,npairs,nBOt,"BOP:FsigBO5");
memory->create(FsigBO6,npairs,nBOt,"BOP:FsigBO6");
}
/* ----------------------------------------------------------------------
global settings
------------------------------------------------------------------------- */
void PairBOP::settings(int narg, char **arg)
{
table = 0;
otfly = 1;
a_flag = 0;
int iarg = 0;
while (iarg < narg) {
if (strcmp(arg[iarg],"table") == 0) {
table = 1;
iarg++;
} else if (strcmp(arg[iarg],"save") == 0) {
otfly = 0;
iarg++;
} else if (strcmp(arg[iarg],"sigmaoff") == 0) {
a_flag = 1;
iarg++;
} else error->all(FLERR,"Illegal pair_style command");
}
}
/* ----------------------------------------------------------------------
set coeffs for one or more type pairs(Updated: D.K. Ward 05/06/10)
------------------------------------------------------------------------- */
void PairBOP::coeff(int narg, char **arg)
{
int i,j,n;
MPI_Comm_rank(world,&me);
map = new int[atom->ntypes+1];
if (narg < 3 + atom->ntypes)
error->all(FLERR,"Incorrect args for pair coefficients");
// ensure I,J args are * *
if (strcmp(arg[0],"*") != 0 || strcmp(arg[1],"*") != 0)
error->all(FLERR,"Incorrect args for pair coefficients");
// read the potential file
nr=2000;
nBOt=2000;
bop_step=0;
nb_pi=0;
nb_sg=0;
allocate_sigma=0;
allocate_pi=0;
allocate_neigh=0;
update_list=0;
if (table == 0) read_file(arg[2]);
else read_table(arg[2]);
if (table == 0) {
setPbetaS();
setPbetaP();
setPrepul();
setSign();
}
// match element names to BOP word types
if (me == 0) {
for (i = 3; i < narg; i++) {
if (strcmp(arg[i],"NULL") == 0) {
map[i-2] = -1;
continue;
}
for (j = 0; j < bop_types; j++)
if (strcmp(arg[i],words[j]) == 0) break;
map[i-2] = j;
}
}
MPI_Bcast(&map[1],atom->ntypes,MPI_INT,0,world);
if (me == 0) {
if (words) {
for (i = 0; i < bop_types; i++) delete [] words[i];
delete [] words;
}
}
// clear setflag since coeff() called once with I,J = * *
n = atom->ntypes;
for (int i = 1; i <= n; i++)
for (int j = i; j <= n; j++)
setflag[i][j] = 0;
// set setflag i,j for type pairs where both are mapped to elements
int count = 0;
for (int i = 1; i <= n; i++)
for (int j = i; j <= n; j++)
if (map[i] >= 0 && map[j] >= 0) {
setflag[i][j] = 1;
count++;
}
if (count == 0) error->all(FLERR,"Incorrect args for pair coefficients");
}
/* ----------------------------------------------------------------------
init specific to this pair style
------------------------------------------------------------------------- */
void PairBOP::init_style()
{
if (atom->tag_enable == 0)
error->all(FLERR,"Pair style BOP requires atom IDs");
if (force->newton_pair == 0)
error->all(FLERR,"Pair style BOP requires newton pair on");
// check that user sets comm->cutghostuser to 3x the max BOP cutoff
if (comm->cutghostuser < 3.0*cutmax - EPSILON) {
char str[128];
sprintf(str,"Pair style bop requires comm ghost cutoff "
"at least 3x larger than %g",cutmax);
error->all(FLERR,str);
}
// need a full neighbor list and neighbors of ghosts
int irequest = neighbor->request(this);
neighbor->requests[irequest]->half = 0;
neighbor->requests[irequest]->full = 1;
neighbor->requests[irequest]->ghost = 1;
}
/* ---------------------------------------------------------------------- */
double PairBOP::init_one(int i, int j)
{
if (setflag[i][j] == 0) error->all(FLERR,"All pair coeffs are not set");
int ii = map[i]+1;
int jj = map[j]+1;
int ij;
if (ii==jj) ij=ii-1;
else if (ii<jj) ij=ii*bop_types-ii*(ii+1)/2+jj-1;
else ij=jj*bop_types-jj*(jj+1)/2+ii-1;
cutghost[i][j] = rcut[ij];
cutghost[j][i] = cutghost[i][j];
cutsq[i][j] = rcut[ij]*rcut[ij];
cutsq[j][i] = cutsq[i][j];
return rcut[ij];
}
/* ----------------------------------------------------------------------
create BOP neighbor list from main neighbor list
BOP neighbor list stores neighbors of ghost atoms
BOP requires neighbor's of k if k is a neighbor of
j and j is a neighbor of i
------------------------------------------------------------------------- */
void PairBOP::gneigh()
{
int i,ii;
int *ilist,*numneigh;
int **firstneigh;
int nlocal = atom->nlocal;
int nall = nlocal + atom->nghost;
if(allocate_neigh==0) {
memory->create (BOP_index,nall,"BOP_index");
if (otfly==0) memory->create (cos_index,nall,"cos_index");
allocate_neigh=1;
}
else {
memory->grow (BOP_index,nall,"BOP_index");
if (otfly==0) memory->grow (cos_index,nall,"cos_index");
allocate_neigh=1;
}
ilist = list->ilist;
numneigh = list->numneigh;
firstneigh = list->firstneigh;
if(bop_step==0) {
maxneigh=0;
maxnall=0;
}
neigh_total=0;
cos_total=0;
for (ii = 0; ii < nall; ii++) {
if(i<nlocal) {
i=ilist[ii];
if(numneigh[i]>maxneigh) maxneigh=numneigh[i];
}
else {
i=ii;
if(numneigh[i]>maxneigh) maxneigh=numneigh[i];
}
BOP_index[i]=neigh_total;
neigh_total+=numneigh[i];
if(otfly==0) {
cos_index[i]=cos_total;
cos_total+=numneigh[i]*(numneigh[i]-1)/2;
}
}
maxnall=nall;
}
/* ---------------------------------------------------------------------- */
void PairBOP::theta()
{
int i,j,k,ii,jj,kk;
int itype,jtype,i12;
int temp_ij,temp_ik,temp_ijk;
int n,nlocal,nall,ks;
int *ilist,*numneigh;
int *iilist;
int **firstneigh;
double rj2,rk2,rsq,ps;
double rj1k1,rj2k2,rj2k1,rj1k2;
double **x = atom->x;
int *type = atom->type;
nlocal = atom->nlocal;
nall = nlocal+atom->nghost;
ilist = list->ilist;
firstneigh = list->firstneigh;
numneigh = list->numneigh;
if(update_list!=0)
memory_theta_grow();
else
memory_theta_create();
for (ii = 0; ii < nall; ii++) {
if(ii<nlocal)
i= ilist[ii];
else
i=ii;
itype = map[type[i]]+1;
iilist=firstneigh[i];
for(jj=0;jj<numneigh[i];jj++) {
j=iilist[jj];
temp_ij=BOP_index[i]+jj;
jtype = map[type[j]]+1;
if(itype==jtype)
i12=itype-1;
else if(itype<jtype)
i12=itype*bop_types-itype*(itype+1)/2+jtype-1;
else
i12=jtype*bop_types-jtype*(jtype+1)/2+itype-1;
if(i12>=npairs) {
error->one(FLERR,"Too many atom pairs for pair bop");
}
disij[0][temp_ij]=x[j][0]-x[i][0];
disij[1][temp_ij]=x[j][1]-x[i][1];
disij[2][temp_ij]=x[j][2]-x[i][2];
rsq=disij[0][temp_ij]*disij[0][temp_ij]
+disij[1][temp_ij]*disij[1][temp_ij]
+disij[2][temp_ij]*disij[2][temp_ij];
rij[temp_ij]=sqrt(rsq);
if(rij[temp_ij]<=rcut[i12])
neigh_flag[temp_ij]=1;
else
neigh_flag[temp_ij]=0;
ps=rij[temp_ij]*rdr[i12]+1.0;
ks=(int)ps;
if(nr-1<ks)
ks=nr-1;
ps=ps-ks;
if(ps>1.0)
ps=1.0;
betaS[temp_ij]=((pBetaS3[i12][ks-1]*ps+pBetaS2[i12][ks-1])*ps
+pBetaS1[i12][ks-1])*ps+pBetaS[i12][ks-1];
dBetaS[temp_ij]=(pBetaS6[i12][ks-1]*ps+pBetaS5[i12][ks-1])*ps
+pBetaS4[i12][ks-1];
betaP[temp_ij]=((pBetaP3[i12][ks-1]*ps+pBetaP2[i12][ks-1])*ps
+pBetaP1[i12][ks-1])*ps+pBetaP[i12][ks-1];
dBetaP[temp_ij]=(pBetaP6[i12][ks-1]*ps+pBetaP5[i12][ks-1])*ps
+pBetaP4[i12][ks-1];
repul[temp_ij]=((pRepul3[i12][ks-1]*ps+pRepul2[i12][ks-1])*ps
+pRepul1[i12][ks-1])*ps+pRepul[i12][ks-1];
dRepul[temp_ij]=(pRepul6[i12][ks-1]*ps+pRepul5[i12][ks-1])*ps
+pRepul4[i12][ks-1];
}
}
for (ii = 0; ii < nall; ii++) {
n=0;
if(ii<nlocal)
i= ilist[ii];
else
i=ii;
iilist=firstneigh[i];
for(jj=0;jj<numneigh[i];jj++) {
j=iilist[jj];
temp_ij=BOP_index[i]+jj;
rj2=rij[temp_ij]*rij[temp_ij];
for(kk=jj+1;kk<numneigh[i];kk++) {
if(cos_index[i]+n>=cos_total) {
error->one(FLERR,"Too many atom triplets for pair bop");
}
temp_ik=BOP_index[i]+kk;
temp_ijk=cos_index[i]+n;
if(temp_ijk>=cos_total) {
error->one(FLERR,"Too many atom triplets for pair bop");
}
rk2=rij[temp_ik]*rij[temp_ik];
rj1k1=rij[temp_ij]*rij[temp_ik];
rj2k2=rj1k1*rj1k1;
rj2k1=rj1k1*rij[temp_ij];
rj1k2=rj1k1*rij[temp_ik];
k=iilist[kk];
if(temp_ijk>=cos_total) {
error->one(FLERR,"Too many atom triplets for pair bop");
}
cosAng[temp_ijk]=(disij[0][temp_ij]*disij[0][temp_ik]+disij[1][temp_ij]
*disij[1][temp_ik]+disij[2][temp_ij]*disij[2][temp_ik])/rj1k1;
dcAng[temp_ijk][0][0]=(disij[0][temp_ik]*rj1k1-cosAng[temp_ijk]
*disij[0][temp_ij]*rk2)/(rj2k2);
dcAng[temp_ijk][1][0]=(disij[1][temp_ik]*rj1k1-cosAng[temp_ijk]
*disij[1][temp_ij]*rk2)/(rj2k2);
dcAng[temp_ijk][2][0]=(disij[2][temp_ik]*rj1k1-cosAng[temp_ijk]
*disij[2][temp_ij]*rk2)/(rj2k2);
dcAng[temp_ijk][0][1]=(disij[0][temp_ij]*rj1k1-cosAng[temp_ijk]
*disij[0][temp_ik]*rj2)/(rj2k2);
dcAng[temp_ijk][1][1]=(disij[1][temp_ij]*rj1k1-cosAng[temp_ijk]
*disij[1][temp_ik]*rj2)/(rj2k2);
dcAng[temp_ijk][2][1]=(disij[2][temp_ij]*rj1k1-cosAng[temp_ijk]
*disij[2][temp_ik]*rj2)/(rj2k2);
n++;
}
}
}
}
/* ---------------------------------------------------------------------- */
void PairBOP::theta_mod()
{
if(update_list!=0)
memory_theta_grow();
else
memory_theta_create();
}
/* ---------------------------------------------------------------------- */
/* The formulation differs slightly to avoid negative square roots
in the calculation of Sigma^(1/2) of (a) Eq. 6 and (b) Eq. 11 */
void PairBOP::sigmaBo()
{
int nb_t,new_n_tot;
int n,i,j,k,kp,m,pp,kkp;
int iij,ji,ki;
int itmp,jtmp,ktmp,ltmp,mtmp;
int i_tag,j_tag;
int ngi,ngj,ngk,nglkp,ngli,nglj,ngl;
int ngji,ngjk,nikj,ngki,ngkj,ngjkp;
int ngkpk,ngkpj,ngkkp,nglk;
int njik,nijk,nikkp,nkp,nijkp;
int nkikp,njikp,nk0;
int njkpk,nkjkp,njkkp;
int jNeik,kNeii,kNeij,kNeikp;
int kpNeij,kpNeik;
int new1,new2,nlocal;
int inum,*ilist,*iilist,*jlist,*klist,*kplist;
int **firstneigh,*numneigh;
int temp_ji,temp_ikp,temp_ki,temp_kkp;
int temp_ij,temp_ik,temp_jkp,temp_kk,temp_jk;
int ang_ijkp,ang_ikkp,ang_jkpk,ang_kjkp;
int ang_ijk,ang_ikj,ang_jikp,ang_jkkp;
int ang_jik,ang_kikp;
int nb_ij,nb_ik,nb_ikp;
int nb_jk,nb_jkp,nb_kkp;
int kp_nsearch,nsearch;
int sig_flag,setting,ncmp,ks;
int itype,jtype,ktype,kptype;
int bt_i,bt_j,bt_ij;
int kp_index,same_ikp,same_jkp;
int same_kkp,same_jkpj;
double AA,BB,CC,DD,EE,EE1,FF;
double AAC,BBC,CCC,DDC,EEC,FFC,GGC;
double AACFF,UT,bndtmp,UTcom;
double amean,gmean0,gmean1,gmean2,ps;
double gfactor1,gprime1,gsqprime,factorsq;
double gfactorsq,gfactor2,gprime2;
double gfactorsq2,gsqprime2;
double gfactor3,gprime3,gfactor,rfactor;
double drfactor,gfactor4,gprime4,agpdpr3;
double rfactor0,rfactorrt,rfactor1rt,rfactor1;
double rcm1,rcm2,gcm1,gcm2,gcm3;
double agpdpr1,agpdpr2,app1,app2,app3,app4;
double dsigB1,dsigB2;
double part0,part1,part2,part3,part4;
double psign,bndtmp0,pp1;
double bndtmp1,bndtmp2,bndtmp3,bndtmp4,bndtmp5;
double ftmp[3];
double **x = atom->x;
double **f = atom->f;
int *tag = atom->tag;
int newton_pair = force->newton_pair;
int *type = atom->type;
nlocal = atom->nlocal;
int nall = nlocal+atom->nghost;
firstneigh = list->firstneigh;
numneigh = list->numneigh;
inum = list->inum;
ilist = list->ilist;
n=0;
//loop over all local atoms
if(nb_sg>16) {
nb_sg=16;
}
if(nb_sg==0) {
nb_sg=(maxneigh)*(maxneigh/2);
}
if(allocate_sigma) {
destroy_sigma();
}
create_sigma(nb_sg);
for(itmp=0;itmp<inum;itmp++) {
i = ilist[itmp];
i_tag=tag[i];
itype = map[type[i]]+1;
//j is loop over all neighbors of i
for(jtmp=0;jtmp<numneigh[i];jtmp++) {
temp_ij=BOP_index[i]+jtmp;
if(neigh_flag[temp_ij]) {
for(m=0;m<nb_sg;m++) {
for(pp=0;pp<3;pp++) {
bt_sg[m].dAA[pp]=0.0;
bt_sg[m].dBB[pp]=0.0;
bt_sg[m].dCC[pp]=0.0;
bt_sg[m].dDD[pp]=0.0;
bt_sg[m].dEE[pp]=0.0;
bt_sg[m].dEE1[pp]=0.0;
bt_sg[m].dFF[pp]=0.0;
bt_sg[m].dAAC[pp]=0.0;
bt_sg[m].dBBC[pp]=0.0;
bt_sg[m].dCCC[pp]=0.0;
bt_sg[m].dDDC[pp]=0.0;
bt_sg[m].dEEC[pp]=0.0;
bt_sg[m].dFFC[pp]=0.0;
bt_sg[m].dGGC[pp]=0.0;
bt_sg[m].dUT[pp]=0.0;
bt_sg[m].dSigB1[pp]=0.0;
bt_sg[m].dSigB[pp]=0.0;
}
bt_sg[m].i=-1;
bt_sg[m].j=-1;
bt_sg[m].temp=-1;
}
nb_t=0;
iilist=firstneigh[i];
j=iilist[jtmp];
jlist=firstneigh[j];
for(ki=0;ki<numneigh[j];ki++) {
temp_ki=BOP_index[j]+ki;
if(x[jlist[ki]][0]==x[i][0]) {
if(x[jlist[ki]][1]==x[i][1]) {
if(x[jlist[ki]][2]==x[i][2]) {
break;
}
}
}
}
j_tag=tag[j];
jtype = map[type[j]]+1;
nb_ij=nb_t;
nb_t++;
if(nb_t>nb_sg) {
new_n_tot=nb_sg+maxneigh;
grow_sigma(nb_sg,new_n_tot);
nb_sg=new_n_tot;
}
bt_sg[nb_ij].temp=temp_ij;
bt_sg[nb_ij].i=i;
bt_sg[nb_ij].j=j;
if(j_tag>=i_tag) {
if(itype==jtype)
iij=itype-1;
else if(itype<jtype)
iij=itype*bop_types-itype*(itype+1)/2+jtype-1;
else
iij=jtype*bop_types-jtype*(jtype+1)/2+itype-1;
for(ji=0;ji<numneigh[j];ji++) {
temp_ji=BOP_index[j]+ji;
if(x[jlist[ji]][0]==x[i][0]) {
if(x[jlist[ji]][1]==x[i][1]) {
if(x[jlist[ji]][2]==x[i][2]) {
break;
}
}
}
}
nSigBk[n]=0;
//AA-EE1 are the components making up Eq. 30 (a)
AA=0.0;
BB=0.0;
CC=0.0;
DD=0.0;
EE=0.0;
EE1=0.0;
//FF is the Beta_sigma^2 term
FF=betaS[temp_ij]*betaS[temp_ij];
//agpdpr1 is derivative of FF w.r.t. r_ij
agpdpr1=2.0*betaS[temp_ij]*dBetaS[temp_ij]/rij[temp_ij];
//dXX derivatives are taken with respect to all pairs contributing to the energy
//nb_ij is derivative w.r.t. ij pair
bt_sg[nb_ij].dFF[0]=agpdpr1*disij[0][temp_ij];
bt_sg[nb_ij].dFF[1]=agpdpr1*disij[1][temp_ij];
bt_sg[nb_ij].dFF[2]=agpdpr1*disij[2][temp_ij];
//k is loop over all neighbors of i again with j neighbor of i
for(ktmp=0;ktmp<numneigh[i];ktmp++) {
temp_ik=BOP_index[i]+ktmp;
if(neigh_flag[temp_ik]) {
if(ktmp!=jtmp) {
if(jtmp<ktmp) {
njik=jtmp*(2*numneigh[i]-jtmp-1)/2+(ktmp-jtmp)-1;
ngj=0;
ngk=1;
}
else {
njik=ktmp*(2*numneigh[i]-ktmp-1)/2+(jtmp-ktmp)-1;
ngj=1;
ngk=0;
}
k=iilist[ktmp];
ktype = map[type[k]]+1;
//find neighbor of k that is equal to i
klist=firstneigh[k];
for(kNeii=0;kNeii<numneigh[k];kNeii++) {
temp_ki=BOP_index[k]+kNeii;
if(x[klist[kNeii]][0]==x[i][0]) {
if(x[klist[kNeii]][1]==x[i][1]) {
if(x[klist[kNeii]][2]==x[i][2]) {
break;
}
}
}
}
//find neighbor of i that is equal to k
for(jNeik=0;jNeik<numneigh[j];jNeik++) {
temp_jk=BOP_index[j]+jNeik;
if(x[jlist[jNeik]][0]==x[k][0]) {
if(x[jlist[jNeik]][1]==x[k][1]) {
if(x[jlist[jNeik]][2]==x[k][2]) {
break;
}
}
}
}
//find neighbor of k that is equal to j
for(kNeij=0;kNeij<numneigh[k];kNeij++) {
if(x[klist[kNeij]][0]==x[j][0]) {
if(x[klist[kNeij]][1]==x[j][1]) {
if(x[klist[kNeij]][2]==x[j][2]) {
break;
}
}
}
}
sig_flag=0;
for(nsearch=0;nsearch<nSigBk[n];nsearch++) {
ncmp=itypeSigBk[n][nsearch];
if(x[ncmp][0]==x[k][0]) {
if(x[ncmp][1]==x[k][1]) {
if(x[ncmp][2]==x[k][2]) {
nk0=nsearch;
sig_flag=1;
break;
}
}
}
}
if(sig_flag==0) {
nSigBk[n]=nSigBk[n]+1;
nk0=nSigBk[n]-1;
itypeSigBk[n][nk0]=k;
}
nb_ik=nb_t;
nb_t++;
if(nb_t>nb_sg) {
new_n_tot=nb_sg+maxneigh;
grow_sigma(nb_sg,new_n_tot);
nb_sg=new_n_tot;
}
bt_sg[nb_ik].temp=temp_ik;
bt_sg[nb_ik].i=i;
bt_sg[nb_ik].j=k;
nb_jk=nb_t;
nb_t++;
if(nb_t>nb_sg) {
new_n_tot=nb_sg+maxneigh;
grow_sigma(nb_sg,new_n_tot);
nb_sg=new_n_tot;
}
bt_sg[nb_jk].temp=temp_jk;
bt_sg[nb_jk].i=j;
bt_sg[nb_jk].j=k;
ang_jik=cos_index[i]+njik;
gmean0=sigma_g0[jtype-1][itype-1][ktype-1];
gmean1=sigma_g1[jtype-1][itype-1][ktype-1];
gmean2=sigma_g2[jtype-1][itype-1][ktype-1];
amean=cosAng[ang_jik];
gfactor1=gmean0+gmean1*amean
+gmean2*amean*amean;
gfactorsq=gfactor1*gfactor1;
gprime1=gmean1+2.0*gmean2*amean;
gsqprime=2.0*gfactor1*gprime1;
//AA is Eq. 34 (a) or Eq. 10 (c) for the i atom
//1st CC is Eq. 11 (c) for i atom where j & k=neighbor of i
AA=AA+gfactorsq*betaS[temp_ik]*betaS[temp_ik];
CC=CC+gfactorsq*betaS[temp_ik]*betaS[temp_ik]*betaS[temp_ik]*betaS[temp_ik];
//agpdpr1 is derivative of AA w.r.t. Beta(rik)
//agpdpr2 is derivative of CC 1st term w.r.t. Beta(rik)
//app1 is derivative of AA w.r.t. cos(theta_jik)
//app2 is derivative of CC 1st term w.r.t. cos(theta_jik)
agpdpr1=2.0*gfactorsq*betaS[temp_ik]*dBetaS[temp_ik]/rij[temp_ik];
agpdpr1=2.0*betaS[temp_ik]*betaS[temp_ik]*agpdpr1;
app1=betaS[temp_ik]*betaS[temp_ik]*gsqprime;
app1=betaS[temp_ik]*betaS[temp_ik]*app1;
bt_sg[nb_ij].dAA[0]+=
app1*dcAng[ang_jik][0][ngj];
bt_sg[nb_ij].dAA[1]+=
app1*dcAng[ang_jik][1][ngj];
bt_sg[nb_ij].dAA[2]+=
app1*dcAng[ang_jik][2][ngj];
bt_sg[nb_ij].dCC[0]+=
app2*dcAng[ang_jik][0][ngj];
bt_sg[nb_ij].dCC[1]+=
app2*dcAng[ang_jik][1][ngj];
bt_sg[nb_ij].dCC[2]+=
app2*dcAng[ang_jik][2][ngj];
bt_sg[nb_ik].dAA[0]+=
app1*dcAng[ang_jik][0][ngk]
+agpdpr1*disij[0][temp_ik];
bt_sg[nb_ik].dAA[1]+=
app1*dcAng[ang_jik][1][ngk]
+agpdpr1*disij[1][temp_ik];
bt_sg[nb_ik].dAA[2]+=
app1*dcAng[ang_jik][2][ngk]
+agpdpr1*disij[2][temp_ik];
bt_sg[nb_ik].dCC[0]+=
app2*dcAng[ang_jik][0][ngk]
+agpdpr2*disij[0][temp_ik];
bt_sg[nb_ik].dCC[1]+=
app2*dcAng[ang_jik][1][ngk]
+agpdpr2*disij[1][temp_ik];
bt_sg[nb_ik].dCC[2]+=
app2*dcAng[ang_jik][2][ngk]
+agpdpr2*disij[2][temp_ik];
//k' is loop over neighbors all neighbors of j with k a neighbor
//of i and j a neighbor of i and determine which k' is k
kp_index=0;
for(ltmp=0;ltmp<numneigh[j];ltmp++) {
temp_jkp=BOP_index[j]+ltmp;
kp=jlist[ltmp];
if(x[kp][0]==x[k][0]) {
if(x[kp][1]==x[k][1]) {
if(x[kp][2]==x[k][2]) {
kp_index=1;
break;
}
}
}
}
if(kp_index) {
//loop over neighbors of k
for(mtmp=0;mtmp<numneigh[k];mtmp++) {
kp=klist[mtmp];
if(x[kp][0]==x[j][0]) {
if(x[kp][1]==x[j][1]) {
if(x[kp][2]==x[j][2]) {
break;
}
}
}
}
if(ki<ltmp) {
nijk=ki*(2*numneigh[j]-ki-1)/2+(ltmp-ki)-1;
ngji=0;
ngjk=1;
}
else {
nijk=ltmp*(2*numneigh[j]-ltmp-1)/2+(ki-ltmp)-1;
ngji=1;
ngjk=0;
}
if(kNeii<mtmp) {
nikj=kNeii*(2*numneigh[k]-kNeii-1)/2+(mtmp-kNeii)-1;
ngki=0;
ngkj=1;
}
else {
nikj=mtmp*(2*numneigh[k]-mtmp-1)/2+(kNeii-mtmp)-1;
ngki=1;
ngkj=0;
}
ang_ijk=cos_index[j]+nijk;
gmean0=sigma_g0[itype-1][jtype-1][ktype-1];
gmean1=sigma_g1[itype-1][jtype-1][ktype-1];
gmean2=sigma_g2[itype-1][jtype-1][ktype-1];
amean=cosAng[ang_ijk];
gfactor2=gmean0+gmean1*amean
+gmean2*amean*amean;
gprime2=gmean1+2.0*gmean2*amean;
gmean0=sigma_g0[itype-1][ktype-1][jtype-1];
gmean1=sigma_g1[itype-1][ktype-1][jtype-1];
gmean2=sigma_g2[itype-1][ktype-1][jtype-1];
ang_ikj=cos_index[k]+nikj;
amean=cosAng[ang_ikj];
gfactor3=gmean0+gmean1*amean
+gmean2*amean*amean;
gprime3=gmean1+2.0*gmean2*amean;
gfactor=gfactor1*gfactor2*gfactor3;
rfactor=betaS[temp_ik]*betaS[temp_jkp];
//EE1 is (b) Eq. 12
EE1=EE1+gfactor*rfactor;
//rcm2 is derivative of EE1 w.r.t Beta(r_jk')
//gcm1 is derivative of EE1 w.r.t cos(theta_jik)
//gcm2 is derivative of EE1 w.r.t cos(theta_ijk)
//gcm3 is derivative of EE1 w.r.t cos(theta_ikj)
rcm1=gfactor*betaS[temp_jkp]*dBetaS[temp_ik]/rij[temp_ik];
rcm2=gfactor*betaS[temp_ik]*dBetaS[temp_jkp]/rij[temp_jkp];
gcm1=rfactor*gprime1*gfactor2*gfactor3;
gcm2=rfactor*gfactor1*gprime2*gfactor3;
gcm3=rfactor*gfactor1*gfactor2*gprime3;
bt_sg[nb_ij].dEE1[0]+=
gcm1*dcAng[ang_jik][0][ngj]
-gcm2*dcAng[ang_ijk][0][ngji];
bt_sg[nb_ij].dEE1[1]+=
gcm1*dcAng[ang_jik][1][ngj]
-gcm2*dcAng[ang_ijk][1][ngji];
bt_sg[nb_ij].dEE1[2]+=
gcm1*dcAng[ang_jik][2][ngj]
-gcm2*dcAng[ang_ijk][2][ngji];
bt_sg[nb_ik].dEE1[0]+=
gcm1*dcAng[ang_jik][0][ngk]
+rcm1*disij[0][temp_ik]
-gcm3*dcAng[ang_ikj][0][ngki];
bt_sg[nb_ik].dEE1[1]+=
gcm1*dcAng[ang_jik][1][ngk]
+rcm1*disij[1][temp_ik]
-gcm3*dcAng[ang_ikj][1][ngki];
bt_sg[nb_ik].dEE1[2]+=
gcm1*dcAng[ang_jik][2][ngk]
+rcm1*disij[2][temp_ik]
-gcm3*dcAng[ang_ikj][2][ngki];
bt_sg[nb_jk].dEE1[0]+=
gcm2*dcAng[ang_ijk][0][ngjk]
+rcm2*disij[0][temp_jkp]
-gcm3*dcAng[ang_ikj][0][ngkj];
bt_sg[nb_jk].dEE1[1]+=
gcm2*dcAng[ang_ijk][1][ngjk]
+rcm2*disij[1][temp_jkp]
-gcm3*dcAng[ang_ikj][1][ngkj];
bt_sg[nb_jk].dEE1[2]+=
gcm2*dcAng[ang_ijk][2][ngjk]
+rcm2*disij[2][temp_jkp]
-gcm3*dcAng[ang_ikj][2][ngkj];
}
// k and k' and j are all different neighbors of i
for(ltmp=0;ltmp<ktmp;ltmp++) {
if(ltmp!=jtmp) {
temp_ikp=BOP_index[i]+ltmp;
if(neigh_flag[temp_ikp]) {
kp=iilist[ltmp];
kptype = map[type[kp]]+1;
for(nsearch=0;nsearch<nSigBk[n];nsearch++) {
ncmp=itypeSigBk[n][nsearch];
if(x[ncmp][0]==x[kp][0]) {
if(x[ncmp][1]==x[kp][1]) {
if(x[ncmp][2]==x[kp][2]) {
break;
}
}
}
}
if(jtmp<ltmp) {
njikp=jtmp*(2*numneigh[i]-jtmp-1)/2+(ltmp-jtmp)-1;
nglj=0;
ngl=1;
}
else {
njikp=ltmp*(2*numneigh[i]-ltmp-1)/2+(jtmp-ltmp)-1;
nglj=1;
ngl=0;
}
if(ktmp<ltmp) {
nkikp=ktmp*(2*numneigh[i]-ktmp-1)/2+(ltmp-ktmp)-1;
nglk=0;
nglkp=1;
}
else {
nkikp=ltmp*(2*numneigh[i]-ltmp-1)/2+(ktmp-ltmp)-1;
nglk=1;
nglkp=0;
}
ang_jikp=cos_index[i]+njikp;
nb_ikp=nb_t;
nb_t++;
if(nb_t>nb_sg) {
new_n_tot=nb_sg+maxneigh;
grow_sigma(nb_sg,new_n_tot);
nb_sg=new_n_tot;
}
bt_sg[nb_ikp].temp=temp_ikp;
bt_sg[nb_ikp].i=i;
bt_sg[nb_ikp].j=kp;
gmean0=sigma_g0[jtype-1][itype-1][kptype-1];
gmean1=sigma_g1[jtype-1][itype-1][kptype-1];
gmean2=sigma_g2[jtype-1][itype-1][kptype-1];
amean=cosAng[ang_jikp];
gfactor2=gmean0+gmean1*amean
+gmean2*amean*amean;
gprime2=gmean1+2.0*gmean2*amean;
gmean0=sigma_g0[ktype-1][itype-1][kptype-1];
gmean1=sigma_g1[ktype-1][itype-1][kptype-1];
gmean2=sigma_g2[ktype-1][itype-1][kptype-1];
ang_kikp=cos_index[i]+nkikp;
amean=cosAng[ang_kikp];
gfactor3=gmean0+gmean1*amean
+gmean2*amean*amean;
gprime3=gmean1+2.0*gmean2*amean;
gfactor=gfactor1*gfactor2*gfactor3;
rfactorrt=betaS[temp_ik]*betaS[temp_ikp];
rfactor=rfactorrt*rfactorrt;
//2nd CC is second term of Eq. 11 (c) for i atom where j , k & k' =neighbor of i
CC=CC+2.0*gfactor*rfactor;
//agpdpr1 is derivative of CC 2nd term w.r.t. Beta(r_ik)
//agpdpr2 is derivative of CC 2nd term w.r.t. Beta(r_ik')
//app1 is derivative of CC 2nd term w.r.t. cos(theta_jik)
//app2 is derivative of CC 2nd term w.r.t. cos(theta_jik')
//app3 is derivative of CC 2nd term w.r.t. cos(theta_kik')
agpdpr1=4.0*gfactor*rfactorrt*betaS[temp_ikp]
*dBetaS[temp_ik]/rij[temp_ik];
agpdpr2=4.0*gfactor*rfactorrt*betaS[temp_ik]
*dBetaS[temp_ikp]/rij[temp_ikp];
app1=2.0*rfactor*gfactor2*gfactor3*gprime1;
app2=2.0*rfactor*gfactor1*gfactor3*gprime2;
app3=2.0*rfactor*gfactor1*gfactor2*gprime3;
bt_sg[nb_ij].dCC[0]+=
app1*dcAng[ang_jik][0][ngj]
+app2*dcAng[ang_jikp][0][nglj];
bt_sg[nb_ij].dCC[1]+=
app1*dcAng[ang_jik][1][ngj]
+app2*dcAng[ang_jikp][1][nglj];
bt_sg[nb_ij].dCC[2]+=
app1*dcAng[ang_jik][2][ngj]
+app2*dcAng[ang_jikp][2][nglj];
bt_sg[nb_ik].dCC[0]+=
app1*dcAng[ang_jik][0][ngk]
+app3*dcAng[ang_kikp][0][nglk]
+agpdpr1*disij[0][temp_ik];
bt_sg[nb_ik].dCC[1]+=
app1*dcAng[ang_jik][1][ngk]
+app3*dcAng[ang_kikp][1][nglk]
+agpdpr1*disij[1][temp_ik];
bt_sg[nb_ik].dCC[2]+=
app1*dcAng[ang_jik][2][ngk]
+app3*dcAng[ang_kikp][2][nglk]
+agpdpr1*disij[2][temp_ik];
bt_sg[nb_ikp].dCC[0]+=
app2*dcAng[ang_jikp][0][ngl]
+app3*dcAng[ang_kikp][0][nglkp]
+agpdpr2*disij[0][temp_ikp];
bt_sg[nb_ikp].dCC[1]+=
app2*dcAng[ang_jikp][1][ngl]
+app3*dcAng[ang_kikp][1][nglkp]
+agpdpr2*disij[1][temp_ikp];
bt_sg[nb_ikp].dCC[2]+=
app2*dcAng[ang_jikp][2][ngl]
+app3*dcAng[ang_kikp][2][nglkp]
+agpdpr2*disij[2][temp_ikp];
}
}
}
// j and k are different neighbors of i and k' is a neighbor k not equal to i
for(ltmp=0;ltmp<numneigh[k];ltmp++) {
temp_kkp=BOP_index[k]+ltmp;
if(neigh_flag[temp_kkp]) {
kp=klist[ltmp];;
kptype = map[type[kp]]+1;
same_ikp=0;
same_jkp=0;
if(x[i][0]==x[kp][0]) {
if(x[i][1]==x[kp][1]) {
if(x[i][2]==x[kp][2]) {
same_ikp=1;
}
}
}
if(x[j][0]==x[kp][0]) {
if(x[j][1]==x[kp][1]) {
if(x[j][2]==x[kp][2]) {
same_jkp=1;
}
}
}
if(!same_ikp&&!same_jkp) {
if(kNeii<ltmp) {
nikkp=kNeii*(2*numneigh[k]-kNeii-1)/2+(ltmp-kNeii)-1;
nglkp=1;
ngli=0;
}
else {
nikkp=ltmp*(2*numneigh[k]-ltmp-1)/2+(kNeii-ltmp)-1;
nglkp=0;
ngli=1;
}
sig_flag=0;
for(nsearch=0;nsearch<nSigBk[n];nsearch++) {
ncmp=itypeSigBk[n][nsearch];
if(x[ncmp][0]==x[kp][0]) {
if(x[ncmp][1]==x[kp][1]) {
if(x[ncmp][2]==x[kp][2]) {
sig_flag=1;
nkp=nsearch;
break;
}
}
}
}
if(sig_flag==0) {
nSigBk[n]=nSigBk[n]+1;
nkp=nSigBk[n]-1;
itypeSigBk[n][nkp]=kp;
}
ang_ikkp=cos_index[k]+nikkp;
nb_kkp=nb_t;
nb_t++;
if(nb_t>nb_sg) {
new_n_tot=nb_sg+maxneigh;
grow_sigma(nb_sg,new_n_tot);
nb_sg=new_n_tot;
}
bt_sg[nb_kkp].temp=temp_kkp;
bt_sg[nb_kkp].i=k;
bt_sg[nb_kkp].j=kp;
gmean0=sigma_g0[itype-1][ktype-1][kptype-1];
gmean1=sigma_g1[itype-1][ktype-1][kptype-1];
gmean2=sigma_g2[itype-1][ktype-1][kptype-1];
amean=cosAng[ang_ikkp];
gfactor2=gmean0+gmean1*amean
+gmean2*amean*amean;
gprime2=gmean1+2.0*gmean2*amean;
gfactorsq2=gfactor2*gfactor2;
gsqprime2=2.0*gfactor2*gprime2;
gfactor=gfactorsq*gfactorsq2;
rfactorrt=betaS[temp_ik]*betaS[temp_kkp];
rfactor=rfactorrt*rfactorrt;
//3rd CC is third term of Eq. 11 (c) for i atom
//where j , k =neighbor of i & k' =neighbor of k
CC=CC+gfactor*rfactor;
agpdpr1=2.0*gfactor*rfactorrt*betaS[temp_kkp]
*dBetaS[temp_ik]/rij[temp_ik];
agpdpr2=2.0*gfactor*rfactorrt*betaS[temp_ik]
*dBetaS[temp_kkp]/rij[temp_kkp];
app1=rfactor*gfactorsq2*gsqprime;
app2=rfactor*gfactorsq*gsqprime2;
bt_sg[nb_ij].dCC[0]+=
app1*dcAng[ang_jik][0][ngj];
bt_sg[nb_ij].dCC[1]+=
app1*dcAng[ang_jik][1][ngj];
bt_sg[nb_ij].dCC[2]+=
app1*dcAng[ang_jik][2][ngj];
bt_sg[nb_ik].dCC[0]+=
app1*dcAng[ang_jik][0][ngk]
+agpdpr1*disij[0][temp_ik]
-app2*dcAng[ang_ikkp][0][ngli];
bt_sg[nb_ik].dCC[1]+=
app1*dcAng[ang_jik][1][ngk]
+agpdpr1*disij[1][temp_ik]
-app2*dcAng[ang_ikkp][1][ngli];
bt_sg[nb_ik].dCC[2]+=
app1*dcAng[ang_jik][2][ngk]
+agpdpr1*disij[2][temp_ik]
-app2*dcAng[ang_ikkp][2][ngli];
bt_sg[nb_kkp].dCC[0]+=
app2*dcAng[ang_ikkp][0][nglkp]
+agpdpr2*disij[0][temp_kkp];
bt_sg[nb_kkp].dCC[1]+=
app2*dcAng[ang_ikkp][1][nglkp]
+agpdpr2*disij[1][temp_kkp];
bt_sg[nb_kkp].dCC[2]+=
app2*dcAng[ang_ikkp][2][nglkp]
+agpdpr2*disij[2][temp_kkp];
}
}
}
//j and k are different neighbors of i and k' is a neighbor j not equal to k
kplist=firstneigh[kp];
for(ltmp=0;ltmp<numneigh[j];ltmp++) {
sig_flag=0;
temp_jkp=BOP_index[j]+ltmp;
if(neigh_flag[temp_jkp]) {
kp=jlist[ltmp];
kptype = map[type[kp]]+1;
same_jkp=0;
same_kkp=0;
for(kpNeij=0;kpNeij<numneigh[kp];kpNeij++) {
if(x[j][0]==x[kp][0]) {
if(x[j][1]==x[kp][1]) {
if(x[j][2]==x[kp][2]) {
same_jkp=1;
break;
}
}
}
}
for(kpNeik=0;kpNeik<numneigh[kp];kpNeik++) {
if(x[k][0]==x[kp][0]) {
if(x[k][1]==x[kp][1]) {
if(x[k][2]==x[kp][2]) {
same_kkp=1;
break;
}
}
}
}
if(!same_kkp&&!same_jkp) {
for(kNeikp=0;kNeikp<numneigh[k];kNeikp++) {
temp_kkp=BOP_index[k]+kNeikp;
kkp=klist[kNeikp];
if(x[kkp][0]==x[kp][0]) {
if(x[kkp][1]==x[kp][1]) {
if(x[kkp][2]==x[kp][2]) {
sig_flag=1;
break;
}
}
}
}
if(sig_flag==1) {
for(nsearch=0;nsearch<numneigh[kp];nsearch++) {
kp_nsearch=BOP_index[kp]+nsearch;
ncmp=kplist[nsearch];
if(x[ncmp][0]==x[j][0]) {
if(x[ncmp][1]==x[j][1]) {
if(x[ncmp][2]==x[j][2]) {
kpNeij=nsearch;
}
}
}
if(x[ncmp][0]==x[k][0]) {
if(x[ncmp][1]==x[k][1]) {
if(x[ncmp][2]==x[k][2]) {
kpNeik=nsearch;
}
}
}
}
if(ji<ltmp) {
nijkp=(ji)*numneigh[j]-(ji+1)*(ji+2)/2+ltmp;
ngji=0;
ngjkp=1;
}
else {
nijkp=(ltmp)*numneigh[j]-(ltmp+1)*(ltmp+2)/2+ji;
ngji=1;
ngjkp=0;
}
if(kNeii<kNeikp) {
nikkp=(kNeii)*numneigh[k]-(kNeii+1)*(kNeii+2)/2+kNeikp;
ngki=0;
ngkkp=1;
}
else {
nikkp=(kNeikp)*numneigh[k]-(kNeikp+1)*(kNeikp+2)/2+kNeii;
ngki=1;
ngkkp=0;
}
if(kpNeij<kpNeik) {
njkpk=(kpNeij)*numneigh[kp]-(kpNeij+1)*(kpNeij+2)/2+kpNeik;
ngkpj=0;
ngkpk=1;
}
else {
njkpk=(kpNeik)*numneigh[kp]-(kpNeik+1)*(kpNeik+2)/2+kpNeij;
ngkpj=1;
ngkpk=0;
}
sig_flag=0;
for(nsearch=0;nsearch<nSigBk[n];nsearch++) {
ncmp=itypeSigBk[n][nsearch];
if(x[ncmp][0]==x[kp][0]) {
if(x[ncmp][1]==x[kp][1]) {
if(x[ncmp][2]==x[kp][2]) {
nkp=nsearch;
sig_flag=1;
break;
}
}
}
}
if(sig_flag==0) {
nSigBk[n]=nSigBk[n]+1;
nkp=nSigBk[n]-1;
itypeSigBk[n][nkp]=kp;
}
ang_ijkp=cos_index[j]+nijkp;
ang_ikkp=cos_index[k]+nikkp;
ang_jkpk=cos_index[kp]+njkpk;
nb_jkp=nb_t;
nb_t++;
if(nb_t>nb_sg) {
new_n_tot=nb_sg+maxneigh;
grow_sigma(nb_sg,new_n_tot);
nb_sg=new_n_tot;
}
bt_sg[nb_jkp].temp=temp_jkp;
bt_sg[nb_jkp].i=j;
bt_sg[nb_jkp].j=kp;
nb_kkp=nb_t;
nb_t++;
if(nb_t>nb_sg) {
new_n_tot=nb_sg+maxneigh;
grow_sigma(nb_sg,new_n_tot);
nb_sg=new_n_tot;
}
bt_sg[nb_kkp].temp=temp_kkp;
bt_sg[nb_kkp].i=k;
bt_sg[nb_kkp].j=kp;
gmean0=sigma_g0[itype-1][jtype-1][kptype-1];
gmean1=sigma_g1[itype-1][jtype-1][kptype-1];
gmean2=sigma_g2[itype-1][jtype-1][kptype-1];
amean=cosAng[ang_ijkp];
gfactor2=gmean0+gmean1*amean
+gmean2*amean*amean;
gprime2=gmean1+2.0*gmean2*amean;
gmean0=sigma_g0[itype-1][ktype-1][kptype-1];
gmean1=sigma_g1[itype-1][ktype-1][kptype-1];
gmean2=sigma_g2[itype-1][ktype-1][kptype-1];
amean=cosAng[ang_ikkp];
gfactor3=gmean0+gmean1*amean
+gmean2*amean*amean;
gprime3=gmean1+2.0*gmean2*amean;
gmean0=sigma_g0[jtype-1][kptype-1][ktype-1];
gmean1=sigma_g1[jtype-1][kptype-1][ktype-1];
gmean2=sigma_g2[jtype-1][kptype-1][ktype-1];
amean=cosAng[ang_jkpk];
gfactor4=gmean0+gmean1*amean
+gmean2*amean*amean;
gprime4=gmean1+2.0*gmean2*amean;
gfactor=gfactor1*gfactor2*gfactor3*gfactor4;
rfactor0=(betaS[temp_ik]+small2)*(betaS[temp_jkp]+small2)
*(betaS[temp_kkp]+small2);
rfactor=pow(rfactor0,2.0/3.0);
drfactor=2.0/3.0*pow(rfactor0,-1.0/3.0);
//EE is Eq. 25(notes)
EE=EE+gfactor*rfactor;
//agpdpr1 is derivative of agpdpr1 w.r.t. Beta(r_ik)
//agpdpr2 is derivative of agpdpr1 w.r.t. Beta(r_jk')
//agpdpr3 is derivative of agpdpr1 w.r.t. Beta(r_kk')
//app1 is derivative of agpdpr1 w.r.t. cos(theta_jik)
//app2 is derivative of agpdpr1 w.r.t. cos(theta_ijk')
//app3 is derivative of agpdpr1 w.r.t. cos(theta_ikk')
//app4 is derivative of agpdpr1 w.r.t. cos(theta_jk'k)
agpdpr1=gfactor*drfactor*(betaS[temp_jkp]+small2)*(betaS[temp_kkp]
+small2)*dBetaS[temp_ik]/rij[temp_ik];
agpdpr2=gfactor*drfactor*(betaS[temp_ik]+small2)*(betaS[temp_kkp]
+small2)*dBetaS[temp_jkp]/rij[temp_jkp];
agpdpr3=gfactor*drfactor*(betaS[temp_ik]+small2)*(betaS[temp_jkp]
+small2)*dBetaS[temp_kkp]/rij[temp_kkp];
app1=rfactor*gfactor2*gfactor3*gfactor4*gprime1;
app2=rfactor*gfactor1*gfactor3*gfactor4*gprime2;
app3=rfactor*gfactor1*gfactor2*gfactor4*gprime3;
app4=rfactor*gfactor1*gfactor2*gfactor3*gprime4;
bt_sg[nb_ij].dEE[0]+=
app1*dcAng[ang_jik][0][ngj]
-app2*dcAng[ang_ijkp][0][ngji];
bt_sg[nb_ij].dEE[1]+=
app1*dcAng[ang_jik][1][ngj]
-app2*dcAng[ang_ijkp][1][ngji];
bt_sg[nb_ij].dEE[2]+=
app1*dcAng[ang_jik][2][ngj]
-app2*dcAng[ang_ijkp][2][ngji];
bt_sg[nb_ik].dEE[0]+=
app1*dcAng[ang_jik][0][ngk]
+agpdpr1*disij[0][temp_ik]
-app3*dcAng[ang_ikkp][0][ngki];
bt_sg[nb_ik].dEE[1]+=
app1*dcAng[ang_jik][1][ngk]
+agpdpr1*disij[1][temp_ik]
-app3*dcAng[ang_ikkp][1][ngki];
bt_sg[nb_ik].dEE[2]+=
app1*dcAng[ang_jik][2][ngk]
+agpdpr1*disij[2][temp_ik]
-app3*dcAng[ang_ikkp][2][ngki];
bt_sg[nb_jkp].dEE[0]+=
app2*dcAng[ang_ijkp][0][ngjkp]
+agpdpr2*disij[0][temp_jkp]
-app4*dcAng[ang_jkpk][0][ngkpj];
bt_sg[nb_jkp].dEE[1]+=
app2*dcAng[ang_ijkp][1][ngjkp]
+agpdpr2*disij[1][temp_jkp]
-app4*dcAng[ang_jkpk][1][ngkpj];
bt_sg[nb_jkp].dEE[2]+=
app2*dcAng[ang_ijkp][2][ngjkp]
+agpdpr2*disij[2][temp_jkp]
-app4*dcAng[ang_jkpk][2][ngkpj];
bt_sg[nb_kkp].dEE[0]+=
app3*dcAng[ang_ikkp][0][ngkkp]
+agpdpr3*disij[0][temp_kkp]
-app4*dcAng[ang_jkpk][0][ngkpk];
bt_sg[nb_kkp].dEE[1]+=
app3*dcAng[ang_ikkp][1][ngkkp]
+agpdpr3*disij[1][temp_kkp]
-app4*dcAng[ang_jkpk][1][ngkpk];
bt_sg[nb_kkp].dEE[2]+=
app3*dcAng[ang_ikkp][2][ngkkp]
+agpdpr3*disij[2][temp_kkp]
-app4*dcAng[ang_jkpk][2][ngkpk];
}
}
}
}
}
}
}
//j is a neighbor of i and k is a neighbor of j not equal to i
for(ktmp=0;ktmp<numneigh[j];ktmp++) {
if(ktmp!=ji) {
if(ktmp<ji) {
njik=ktmp*(2*numneigh[j]-ktmp-1)/2+(ji-ktmp)-1;
ngi=1;
ngk=0;
}
else {
njik=ji*(2*numneigh[j]-ji-1)/2+(ktmp-ji)-1;
ngi=0;
ngk=1;
}
temp_jk=BOP_index[j]+ktmp;
if(neigh_flag[temp_jk]) {
k=jlist[ktmp];
ktype=map[type[k]]+1;
klist=firstneigh[k];
for(kNeij=0;kNeij<numneigh[k];kNeij++) {
if(x[klist[kNeij]][0]==x[j][0]) {
if(x[klist[kNeij]][1]==x[j][1]) {
if(x[klist[kNeij]][2]==x[j][2]) {
break;
}
}
}
}
sig_flag=0;
for(nsearch=0;nsearch<nSigBk[n];nsearch++) {
ncmp=itypeSigBk[n][nsearch];
if(x[ncmp][0]==x[k][0]) {
if(x[ncmp][1]==x[k][1]) {
if(x[ncmp][2]==x[k][2]) {
new1=nsearch;
sig_flag=1;
break;
}
}
}
}
if(sig_flag==0) {
nSigBk[n]=nSigBk[n]+1;
new1=nSigBk[n]-1;
itypeSigBk[n][new1]=k;
}
ang_ijk=cos_index[j]+njik;
nb_jk=nb_t;
nb_t++;
if(nb_t>nb_sg) {
new_n_tot=nb_sg+maxneigh;
grow_sigma(nb_sg,new_n_tot);
nb_sg=new_n_tot;
}
bt_sg[nb_jk].temp=temp_jk;
bt_sg[nb_jk].i=j;
bt_sg[nb_jk].j=k;
gmean0=sigma_g0[itype-1][jtype-1][ktype-1];
gmean1=sigma_g1[itype-1][jtype-1][ktype-1];
gmean2=sigma_g2[itype-1][jtype-1][ktype-1];
amean=cosAng[ang_ijk];
gfactor1=gmean0+gmean1*amean
+gmean2*amean*amean;
gprime1=gmean1+2.0*gmean2*amean;
gfactorsq=gfactor1*gfactor1;
gsqprime=2.0*gfactor1*gprime1;
rfactor1rt=betaS[temp_jk]*betaS[temp_jk];
rfactor1=rfactor1rt*rfactor1rt;
//BB is Eq. 34 (a) or Eq. 10 (c) for the j atom
//1st DD is Eq. 11 (c) for j atom where i & k=neighbor of j
BB=BB+gfactorsq*rfactor1rt;
DD=DD+gfactorsq*rfactor1;
//agpdpr1 is derivative of BB w.r.t. Beta(r_jk)
//app1 is derivative of BB w.r.t. cos(theta_ijk)
agpdpr1=2.0*gfactorsq*betaS[temp_jk]*dBetaS[temp_jk]/rij[temp_jk];
app1=rfactor1rt*gsqprime;
bt_sg[nb_ij].dBB[0]-=
app1*dcAng[ang_ijk][0][ngi];
bt_sg[nb_ij].dBB[1]-=
app1*dcAng[ang_ijk][1][ngi];
bt_sg[nb_ij].dBB[2]-=
app1*dcAng[ang_ijk][2][ngi];
bt_sg[nb_ij].dDD[0]-=
app2*dcAng[ang_ijk][0][ngi];
bt_sg[nb_ij].dDD[1]-=
app2*dcAng[ang_ijk][1][ngi];
bt_sg[nb_ij].dDD[2]-=
app2*dcAng[ang_ijk][2][ngi];
bt_sg[nb_jk].dBB[0]+=
app1*dcAng[ang_ijk][0][ngk]
+agpdpr1*disij[0][temp_jk];
bt_sg[nb_jk].dBB[1]+=
app1*dcAng[ang_ijk][1][ngk]
+agpdpr1*disij[1][temp_jk];
bt_sg[nb_jk].dBB[2]+=
app1*dcAng[ang_ijk][2][ngk]
+agpdpr1*disij[2][temp_jk];
bt_sg[nb_jk].dDD[0]+=
app2*dcAng[ang_ijk][0][ngk]
+agpdpr2*disij[0][temp_jk];
bt_sg[nb_jk].dDD[1]+=
app2*dcAng[ang_ijk][1][ngk]
+agpdpr2*disij[1][temp_jk];
bt_sg[nb_jk].dDD[2]+=
app2*dcAng[ang_ijk][2][ngk]
+agpdpr2*disij[2][temp_jk];
//j is a neighbor of i, k and k' prime different neighbors of j not equal to i
for(ltmp=0;ltmp<ktmp;ltmp++) {
if(ltmp!=ji) {
temp_jkp=BOP_index[j]+ltmp;
if(neigh_flag[temp_jkp]) {
kp=jlist[ltmp];
kptype=map[type[kp]]+1;
for(nsearch=0;nsearch<nSigBk[n];nsearch++) {
ncmp=itypeSigBk[n][nsearch];
if(x[ncmp][0]==x[kp][0]) {
if(x[ncmp][1]==x[kp][1]) {
if(x[ncmp][2]==x[kp][2]) {
new2=nsearch;
break;
}
}
}
}
if(ji<ltmp) {
nijkp=ji*(2*numneigh[j]-ji-1)/2+(ltmp-ji)-1;
ngli=0;
ngl=1;
}
else {
nijkp=ltmp*(2*numneigh[j]-ltmp-1)/2+(ji-ltmp)-1;
ngli=1;
ngl=0;
}
if(ktmp<ltmp) {
nkjkp=ktmp*(2*numneigh[j]-ktmp-1)/2+(ltmp-ktmp)-1;
ngjk=0;
ngjkp=1;
}
else {
nkjkp=ltmp*(2*numneigh[j]-ltmp-1)/2+(ktmp-ltmp)-1;
ngjk=1;
ngjkp=0;
}
ang_ijkp=cos_index[j]+nijkp;
ang_kjkp=cos_index[j]+nkjkp;
gmean0=sigma_g0[itype-1][jtype-1][kptype-1];
gmean1=sigma_g1[itype-1][jtype-1][kptype-1];
gmean2=sigma_g2[itype-1][jtype-1][kptype-1];
amean=cosAng[ang_ijkp];
gfactor2=gmean0+gmean1*amean
+gmean2*amean*amean;
gprime2=gmean1+2.0*gmean2*amean;
gmean0=sigma_g0[ktype-1][jtype-1][kptype-1];
gmean1=sigma_g1[ktype-1][jtype-1][kptype-1];
gmean2=sigma_g2[ktype-1][jtype-1][kptype-1];
amean=cosAng[ang_kjkp];
gfactor3=gmean0+gmean1*amean
+gmean2*amean*amean;
gprime3=gmean1+2.0*gmean2*amean;
gfactor=gfactor1*gfactor2*gfactor3;
rfactorrt=betaS[temp_jk]*betaS[temp_jkp];
rfactor=rfactorrt*rfactorrt;
//2nd DD is Eq. 11 (c) for j atom where i , k & k'=neighbor of j
DD=DD+2.0*gfactor*rfactor;
//agpdpr1 is derivative of DD w.r.t. Beta(r_jk)
//agpdpr2 is derivative of DD w.r.t. Beta(r_jk')
//app1 is derivative of DD w.r.t. cos(theta_ijk)
//app2 is derivative of DD w.r.t. cos(theta_ijkp)
//app3 is derivative of DD w.r.t. cos(theta_kjkp)
agpdpr1=4.0*gfactor*rfactorrt*betaS[temp_jkp]
*dBetaS[temp_jk]/rij[temp_jk];
agpdpr2=4.0*gfactor*rfactorrt*betaS[temp_jk]
*dBetaS[temp_jkp]/rij[temp_jkp];
app1=2.0*rfactor*gfactor2*gfactor3*gprime1;
app2=2.0*rfactor*gfactor1*gfactor3*gprime2;
app3=2.0*rfactor*gfactor1*gfactor2*gprime3;
bt_sg[nb_ij].dDD[0]-=
app1*dcAng[ang_ijk][0][ngi]
+app2*dcAng[ang_ijkp][0][ngli];
bt_sg[nb_ij].dDD[1]-=
app1*dcAng[ang_ijk][1][ngi]
+app2*dcAng[ang_ijkp][1][ngli];
bt_sg[nb_ij].dDD[2]-=
app1*dcAng[ang_ijk][2][ngi]
+app2*dcAng[ang_ijkp][2][ngli];
bt_sg[nb_jk].dDD[0]+=
app1*dcAng[ang_ijk][0][ngk]
+app3*dcAng[ang_kjkp][0][ngjk]
+agpdpr1*disij[0][temp_jk];
bt_sg[nb_jk].dDD[1]+=
app1*dcAng[ang_ijk][1][ngk]
+app3*dcAng[ang_kjkp][1][ngjk]
+agpdpr1*disij[1][temp_jk];
bt_sg[nb_jk].dDD[2]+=
app1*dcAng[ang_ijk][2][ngk]
+app3*dcAng[ang_kjkp][2][ngjk]
+agpdpr1*disij[2][temp_jk];
bt_sg[nb_jkp].dDD[0]+=
app2*dcAng[ang_ijkp][0][ngl]
+app3*dcAng[ang_kjkp][0][ngjkp]
+agpdpr2*disij[0][temp_jkp];
bt_sg[nb_jkp].dDD[1]+=
app2*dcAng[ang_ijkp][1][ngl]
+app3*dcAng[ang_kjkp][1][ngjkp]
+agpdpr2*disij[1][temp_jkp];
bt_sg[nb_jkp].dDD[2]+=
app2*dcAng[ang_ijkp][2][ngl]
+app3*dcAng[ang_kjkp][2][ngjkp]
+agpdpr2*disij[2][temp_jkp];
}
}
}
//j is a neighbor of i, k is a neighbor of j not equal to i and k'
//is a neighbor of k not equal to j or i
for(ltmp=0;ltmp<numneigh[k];ltmp++) {
temp_kkp=BOP_index[k]+ltmp;
if(neigh_flag[temp_kkp]) {
kp=klist[ltmp];
kptype=map[type[kp]]+1;
same_ikp=0;
same_jkp=0;
if(x[i][0]==x[kp][0]) {
if(x[i][1]==x[kp][1]) {
if(x[i][2]==x[kp][2]) {
same_ikp=1;
}
}
}
if(x[j][0]==x[kp][0]) {
if(x[j][1]==x[kp][1]) {
if(x[j][2]==x[kp][2]) {
same_jkp=1;
}
}
}
if(!same_ikp&&!same_jkp) {
for(kNeij=0;kNeij<numneigh[k];kNeij++) {
if(x[klist[kNeij]][0]==x[j][0]) {
if(x[klist[kNeij]][1]==x[j][1]) {
if(x[klist[kNeij]][2]==x[j][2]) {
break;
}
}
}
}
if(kNeij<ltmp) {
njkkp=kNeij*(2*numneigh[k]-kNeij-1)/2+(ltmp-kNeij)-1;
nglkp=1;
nglj=0;
}
else {
njkkp=ltmp*(2*numneigh[k]-ltmp-1)/2+(kNeij-ltmp)-1;
nglkp=0;
nglj=1;
}
sig_flag=0;
for(nsearch=0;nsearch<nSigBk[n];nsearch++) {
ncmp=itypeSigBk[n][nsearch];
if(x[ncmp][0]==x[kp][0]) {
if(x[ncmp][1]==x[kp][1]) {
if(x[ncmp][2]==x[kp][2]) {
new2=nsearch;
sig_flag=1;
break;
}
}
}
}
if(sig_flag==0) {
nSigBk[n]=nSigBk[n]+1;
new2=nSigBk[n]-1;
itypeSigBk[n][new2]=kp;
}
ang_jkkp=cos_index[k]+njkkp;
nb_kkp=nb_t;
nb_t++;
if(nb_t>nb_sg) {
new_n_tot=nb_sg+maxneigh;
grow_sigma(nb_sg,new_n_tot);
nb_sg=new_n_tot;
}
bt_sg[nb_kkp].temp=temp_kkp;
bt_sg[nb_kkp].i=k;
bt_sg[nb_kkp].j=kp;
gmean0=sigma_g0[jtype-1][ktype-1][kptype-1];
gmean1=sigma_g1[jtype-1][ktype-1][kptype-1];
gmean2=sigma_g2[jtype-1][ktype-1][kptype-1];
amean=cosAng[ang_jkkp];
gfactor2=gmean0+gmean1*amean
+gmean2*amean*amean;
gprime2=gmean1+2.0*gmean2*amean;
gfactorsq2=gfactor2*gfactor2;
gsqprime2=2.0*gfactor2*gprime2;
gfactor=gfactorsq*gfactorsq2;
rfactorrt=betaS[temp_jk]*betaS[temp_kkp];
rfactor=rfactorrt*rfactorrt;
//3rd DD is Eq. 11 (c) for j atom where i & k=neighbor of j & k'=neighbor of k
DD=DD+gfactor*rfactor;
//agpdpr1 is derivative of DD 3rd term w.r.t. Beta(r_jk)
//agpdpr2 is derivative of DD 3rd term w.r.t. Beta(r_kk')
//app1 is derivative of DD 3rd term w.r.t. cos(theta_ijk)
//app2 is derivative of DD 3rd term w.r.t. cos(theta_jkkp)
agpdpr1=2.0*gfactor*rfactorrt*betaS[temp_kkp]
*dBetaS[temp_jk]/rij[temp_jk];
agpdpr2=2.0*gfactor*rfactorrt*betaS[temp_jk]
*dBetaS[temp_kkp]/rij[temp_kkp];
app1=rfactor*gfactorsq2*gsqprime;
app2=rfactor*gfactorsq*gsqprime2;
bt_sg[nb_ij].dDD[0]-=
app1*dcAng[ang_ijk][0][ngi];
bt_sg[nb_ij].dDD[1]-=
app1*dcAng[ang_ijk][1][ngi];
bt_sg[nb_ij].dDD[2]-=
app1*dcAng[ang_ijk][2][ngi];
bt_sg[nb_jk].dDD[0]+=
app1*dcAng[ang_ijk][0][ngk]
+agpdpr1*disij[0][temp_jk]
-app2*dcAng[ang_jkkp][0][nglj];
bt_sg[nb_jk].dDD[1]+=
app1*dcAng[ang_ijk][1][ngk]
+agpdpr1*disij[1][temp_jk]
-app2*dcAng[ang_jkkp][1][nglj];
bt_sg[nb_jk].dDD[2]+=
app1*dcAng[ang_ijk][2][ngk]
+agpdpr1*disij[2][temp_jk]
-app2*dcAng[ang_jkkp][2][nglj];
bt_sg[nb_kkp].dDD[0]+=
app2*dcAng[ang_jkkp][0][nglkp]
+agpdpr2*disij[0][temp_kkp];
bt_sg[nb_kkp].dDD[1]+=
app2*dcAng[ang_jkkp][1][nglkp]
+agpdpr2*disij[1][temp_kkp];
bt_sg[nb_kkp].dDD[2]+=
app2*dcAng[ang_jkkp][2][nglkp]
+agpdpr2*disij[2][temp_kkp];
}
}
}
}
}
}
sig_flag=0;
if(FF<=0.000001) {
sigB[n]=0.0;
sig_flag=1;
}
if(sig_flag==0) {
if(AA<0.0)
AA=0.0;
if(BB<0.0)
BB=0.0;
if(CC<0.0)
CC=0.0;
if(DD<0.0)
DD=0.0;
// AA and BB are the representations of (a) Eq. 34 and (b) Eq. 9
// for atoms i and j respectively
AAC=AA+BB;
BBC=AA*BB;
CCC=AA*AA+BB*BB;
DDC=CC+DD;
//EEC is a modified form of (a) Eq. 33
EEC=(DDC-CCC)/(AAC+2.0*small1);
for(m=0;m<nb_t;m++) {
if((bt_sg[m].i>-1)&&(bt_sg[m].j>-1)) {
bt_i=bt_sg[m].i;
bt_j=bt_sg[m].j;
bt_sg[m].dAAC[0]=bt_sg[m].dAA[0]
+bt_sg[m].dBB[0];
bt_sg[m].dAAC[1]=bt_sg[m].dAA[1]
+bt_sg[m].dBB[1];
bt_sg[m].dAAC[2]=bt_sg[m].dAA[2]
+bt_sg[m].dBB[2];
bt_sg[m].dBBC[0]=bt_sg[m].dAA[0]*BB
+AA*bt_sg[m].dBB[0];
bt_sg[m].dBBC[1]=bt_sg[m].dAA[1]*BB
+AA*bt_sg[m].dBB[1];
bt_sg[m].dBBC[2]=bt_sg[m].dAA[2]*BB
+AA*bt_sg[m].dBB[2];
bt_sg[m].dCCC[0]=2.0*AA*bt_sg[m].dAA[0]
+2.0*BB*bt_sg[m].dBB[0];
bt_sg[m].dCCC[1]=2.0*AA*bt_sg[m].dAA[1]
+2.0*BB*bt_sg[m].dBB[1];
bt_sg[m].dCCC[2]=2.0*AA*bt_sg[m].dAA[2]
+2.0*BB*bt_sg[m].dBB[2];
bt_sg[m].dDDC[0]=bt_sg[m].dCC[0]
+bt_sg[m].dDD[0];
bt_sg[m].dDDC[1]=bt_sg[m].dCC[1]
+bt_sg[m].dDD[1];
bt_sg[m].dDDC[2]=bt_sg[m].dCC[2]
+bt_sg[m].dDD[2];
bt_sg[m].dEEC[0]=(bt_sg[m].dDDC[0]
-bt_sg[m].dCCC[0]
-EEC*bt_sg[m].dAAC[0])*AACFF;
bt_sg[m].dEEC[1]=(bt_sg[m].dDDC[1]
-bt_sg[m].dCCC[1]
-EEC*bt_sg[m].dAAC[1])*AACFF;
bt_sg[m].dEEC[2]=(bt_sg[m].dDDC[2]
-bt_sg[m].dCCC[2]
-EEC*bt_sg[m].dAAC[2])*AACFF;
}
}
UT=EEC*FF+BBC+small3[iij];
UT=1.0/sqrt(UT);
// FFC is slightly modified form of (a) Eq. 31
// GGC is slightly modified form of (a) Eq. 32
// bndtmp is a slightly modified form of (a) Eq. 30 and (b) Eq. 8
FFC=BBC*UT;
GGC=EEC*UT;
bndtmp=(FF+sigma_delta[iij]*sigma_delta[iij])
+sigma_c[iij]*AAC+small4;
UTcom=-0.5*UT*UT*UT;
for(m=0;m<nb_t;m++) {
if((bt_sg[m].i>-1)&&(bt_sg[m].j>-1)) {
bt_sg[m].dUT[0]=UTcom*(bt_sg[m].dEEC[0]*FF
+EEC*bt_sg[m].dFF[0]+bt_sg[m].dBBC[0]);
bt_sg[m].dUT[1]=UTcom*(bt_sg[m].dEEC[1]*FF
+EEC*bt_sg[m].dFF[1]+bt_sg[m].dBBC[1]);
bt_sg[m].dUT[2]=UTcom*(bt_sg[m].dEEC[2]*FF
+EEC*bt_sg[m].dFF[2]+bt_sg[m].dBBC[2]);
bt_sg[m].dFFC[0]=bt_sg[m].dBBC[0]*UT
+BBC*bt_sg[m].dUT[0];
bt_sg[m].dFFC[1]=bt_sg[m].dBBC[1]*UT
+BBC*bt_sg[m].dUT[1];
bt_sg[m].dFFC[2]=bt_sg[m].dBBC[2]*UT
+BBC*bt_sg[m].dUT[2];
bt_sg[m].dGGC[0]=bt_sg[m].dEEC[0]*UT
+EEC*bt_sg[m].dUT[0];
bt_sg[m].dGGC[1]=bt_sg[m].dEEC[1]*UT
+EEC*bt_sg[m].dUT[1];
bt_sg[m].dGGC[2]=bt_sg[m].dEEC[2]*UT
+EEC*bt_sg[m].dUT[2];
}
}
psign=1.0;
if(1.0+sigma_a[iij]*GGC<0.0)
psign=-1.0;
bndtmp0=1.0/sqrt(bndtmp);
sigB1[n]=psign*betaS[temp_ij]*(1.0+sigma_a[iij]*GGC)*bndtmp0;
bndtmp=-0.5*bndtmp0*bndtmp0*bndtmp0;
bndtmp1=psign*(1.0+sigma_a[iij]*GGC)*bndtmp0+psign*betaS[temp_ij]
*(1.0+sigma_a[iij]*GGC)*bndtmp*2.0*betaS[temp_ij]*(1.0
+sigma_a[iij]*GGC)*(1.0+sigma_a[iij]*GGC);
bndtmp1=bndtmp1*dBetaS[temp_ij]/rij[temp_ij];
bndtmp2=psign*betaS[temp_ij]*(1.0+sigma_a[iij]*GGC)*bndtmp*sigma_c[iij];
bndtmp3=psign*betaS[temp_ij]*(1.0+sigma_a[iij]*GGC)
*bndtmp*sigma_c[iij]*sigma_a[iij];
bndtmp4=psign*betaS[temp_ij]*(1.0+sigma_a[iij]*GGC)
*bndtmp*sigma_c[iij]*sigma_a[iij]*(2.0+GGC);
bndtmp5=sigma_a[iij]*psign*betaS[temp_ij]*bndtmp0
+psign*betaS[temp_ij]*(1.0+sigma_a[iij]*GGC)*bndtmp
*(2.0*(FF+sigma_delta[iij]*sigma_delta[iij])*(1.0
+sigma_a[iij]*GGC)*sigma_a[iij]+sigma_c[iij]*sigma_a[iij]*FFC);
setting=0;
for(m=0;m<nb_t;m++) {
if((bt_sg[m].i>-1)&&(bt_sg[m].j>-1)) {
temp_kk=bt_sg[m].temp;
if(temp_kk==temp_ij&&setting==0) {
bt_sg[m].dSigB1[0]=bndtmp1*disij[0][temp_ij]
+(bndtmp2*bt_sg[m].dAAC[0]
+bndtmp3*bt_sg[m].dEE[0]
+bndtmp4*bt_sg[m].dFFC[0]
+bndtmp5*bt_sg[m].dGGC[0]);
bt_sg[m].dSigB1[1]=bndtmp1*disij[1][temp_ij]
+(bndtmp2*bt_sg[m].dAAC[1]
+bndtmp3*bt_sg[m].dEE[1]
+bndtmp4*bt_sg[m].dFFC[1]
+bndtmp5*bt_sg[m].dGGC[1]);
bt_sg[m].dSigB1[2]=bndtmp1*disij[2][temp_ij]
+(bndtmp2*bt_sg[m].dAAC[2]
+bndtmp3*bt_sg[m].dEE[2]
+bndtmp4*bt_sg[m].dFFC[2]
+bndtmp5*bt_sg[m].dGGC[2]);
setting=1;
}
else if(temp_kk==temp_ji&&setting==0) {
bt_sg[m].dSigB1[0]=-bndtmp1*disij[0][temp_ij]
+(bndtmp2*bt_sg[m].dAAC[0]
+bndtmp3*bt_sg[m].dEE[0]
+bndtmp4*bt_sg[m].dFFC[0]
+bndtmp5*bt_sg[m].dGGC[0]);
bt_sg[m].dSigB1[1]=-bndtmp1*disij[1][temp_ij]
+(bndtmp2*bt_sg[m].dAAC[1]
+bndtmp3*bt_sg[m].dEE[1]
+bndtmp4*bt_sg[m].dFFC[1]
+bndtmp5*bt_sg[m].dGGC[1]);
bt_sg[m].dSigB1[2]=-bndtmp1*disij[2][temp_ij]
+(bndtmp2*bt_sg[m].dAAC[2]
+bndtmp3*bt_sg[m].dEE[2]
+bndtmp4*bt_sg[m].dFFC[2]
+bndtmp5*bt_sg[m].dGGC[2]);
setting=1;
}
else {
bt_sg[m].dSigB1[0]=(bndtmp2*bt_sg[m].dAAC[0]
+bndtmp3*bt_sg[m].dEE[0]
+bndtmp4*bt_sg[m].dFFC[0]
+bndtmp5*bt_sg[m].dGGC[0]);
bt_sg[m].dSigB1[1]=(bndtmp2*bt_sg[m].dAAC[1]
+bndtmp3*bt_sg[m].dEE[1]
+bndtmp4*bt_sg[m].dFFC[1]
+bndtmp5*bt_sg[m].dGGC[1]);
bt_sg[m].dSigB1[2]=(bndtmp2*bt_sg[m].dAAC[2]
+bndtmp3*bt_sg[m].dEE[2]
+bndtmp4*bt_sg[m].dFFC[2]
+bndtmp5*bt_sg[m].dGGC[2]);
}
}
}
//This loop is to ensure there is not an error for atoms with no neighbors (deposition)
if(nb_t==0) {
if(j>i) {
bt_sg[0].dSigB1[0]=bndtmp1*disij[0][temp_ij];
bt_sg[0].dSigB1[1]=bndtmp1*disij[1][temp_ij];
bt_sg[0].dSigB1[2]=bndtmp1*disij[2][temp_ij];
}
else {
bt_sg[0].dSigB1[0]=-bndtmp1*disij[0][temp_ij];
bt_sg[0].dSigB1[1]=-bndtmp1*disij[1][temp_ij];
bt_sg[0].dSigB1[2]=-bndtmp1*disij[2][temp_ij];
}
for(pp=0;pp<3;pp++) {
bt_sg[0].dAA[pp]=0.0;
bt_sg[0].dBB[pp]=0.0;
bt_sg[0].dCC[pp]=0.0;
bt_sg[0].dDD[pp]=0.0;
bt_sg[0].dEE[pp]=0.0;
bt_sg[0].dEE1[pp]=0.0;
bt_sg[0].dFF[pp]=0.0;
bt_sg[0].dAAC[pp]=0.0;
bt_sg[0].dBBC[pp]=0.0;
bt_sg[0].dCCC[pp]=0.0;
bt_sg[0].dDDC[pp]=0.0;
bt_sg[0].dEEC[pp]=0.0;
bt_sg[0].dFFC[pp]=0.0;
bt_sg[0].dGGC[pp]=0.0;
bt_sg[0].dUT[pp]=0.0;
bt_sg[0].dSigB1[pp]=0.0;
bt_sg[0].dSigB[pp]=0.0;
}
bt_sg[0].i=i;
bt_sg[0].j=j;
bt_sg[0].temp=temp_ij;
nb_t++;
if(nb_t>nb_sg) {
new_n_tot=nb_sg+maxneigh;
grow_sigma(nb_sg,new_n_tot);
nb_sg=new_n_tot;
}
}
ps=sigB1[n]*rdBO+1.0;
ks=(int)ps;
if(nBOt-1<ks)
ks=nBOt-1;
ps=ps-ks;
if(ps>1.0)
ps=1.0;
dsigB1=((FsigBO3[iij][ks-1]*ps+FsigBO2[iij][ks-1])*ps
+FsigBO1[iij][ks-1])*ps+FsigBO[iij][ks-1];
dsigB2=(FsigBO6[iij][ks-1]*ps+FsigBO5[iij][ks-1])*ps+FsigBO4[iij][ks-1];
part0=(FF+0.5*AAC+small5);
part1=(sigma_f[iij]-0.5)*sigma_k[iij];
part2=1.0-part1*EE1/part0;
part3=dsigB1*part1/part0;
part4=part3/part0*EE1;
// sigB is the final expression for (a) Eq. 6 and (b) Eq. 11
sigB[n]=dsigB1*part2;
pp1=2.0*betaS[temp_ij];
for(m=0;m<nb_t;m++) {
if((bt_sg[m].i>-1)&&(bt_sg[m].j>-1)) {
temp_kk=bt_sg[m].temp;
bt_ij=bt_sg[m].temp;
bt_i=bt_sg[m].i;
bt_j=bt_sg[m].j;
for(pp=0;pp<3;pp++) {
bt_sg[m].dSigB[pp]=dsigB2*part2*bt_sg[m].dSigB1[pp]
-part3*bt_sg[m].dEE1[pp]
+part4*(bt_sg[m].dFF[pp]
+0.5*bt_sg[m].dAAC[pp]);
}
for(pp=0;pp<3;pp++) {
ftmp[pp]=pp1*bt_sg[m].dSigB[pp];
f[bt_i][pp]-=ftmp[pp];
f[bt_j][pp]+=ftmp[pp];
}
if(evflag) {
ev_tally_xyz(bt_i,bt_j,nlocal,newton_pair,0.0,0.0,ftmp[0],ftmp[1]
,ftmp[2],disij[0][bt_ij],disij[1][bt_ij],disij[2][bt_ij]);
}
}
}
}
n++;
}
}
}
}
if(allocate_sigma)
destroy_sigma();
}
/* ---------------------------------------------------------------------- */
void PairBOP::sigmaBo_noa()
{
int nb_t,new_n_tot;
int n,i,j,k,kp,m,pp;
int iij,ji,ki;
int itmp,jtmp,ktmp,ltmp,mtmp;
int i_tag,j_tag;
int ngi,ngj,ngk,ngli,nglj,ngl;
int ngji,ngjk,nikj,ngki,ngkj;
int njik,nijk,nikkp,nkp,nijkp;
int nkikp,njikp,nk0,nkjkp,njkkp;
int jNeik,kNeii,kNeij;
int new1,new2,nlocal,nsearch;
int inum,*ilist,*iilist,*jlist,*klist;
int **firstneigh,*numneigh;
int temp_ji,temp_ikp,temp_ki,temp_kkp;
int temp_ij,temp_ik,temp_jkp,temp_kk,temp_jk;
int ang_ijkp,ang_ikkp,ang_kjkp;
int ang_ijk,ang_ikj,ang_jikp,ang_jkkp;
int ang_jik,ang_kikp;
int nb_ij,nb_ik,nb_jk;
int sig_flag,setting,ncmp,ks;
int itype,jtype,ktype,kptype;
int bt_i,bt_j,bt_ij;
int kp_index,same_ikp,same_jkp;
double AA,BB,CC,DD,EE,EE1,FF;
double AAC,BBC,CCC,DDC,EEC,FFC,GGC;
double AACFF,UT,bndtmp,UTcom;
double amean,gmean0,gmean1,gmean2,ps;
double gfactor1,gprime1,gsqprime,factorsq;
double gfactorsq,gfactor2,gprime2;
double gfactorsq2,gsqprime2;
double gfactor3,gprime3,gfactor,rfactor;
double drfactor,gfactor4,gprime4,agpdpr3;
double rfactor0,rfactorrt,rfactor1rt,rfactor1;
double rcm1,rcm2,gcm1,gcm2,gcm3;
double agpdpr1,agpdpr2,app1,app2,app3,app4;
double dsigB1,dsigB2;
double part0,part1,part2,part3,part4;
double psign,bndtmp0,pp1,bndtmp1,bndtmp2;
double ftmp[3];
double **x = atom->x;
double **f = atom->f;
int *tag = atom->tag;
int newton_pair = force->newton_pair;
int *type = atom->type;
nlocal = atom->nlocal;
int nall = nlocal+atom->nghost;
firstneigh = list->firstneigh;
numneigh = list->numneigh;
inum = list->inum;
ilist = list->ilist;
n=0;
//loop over all local atoms
if(nb_sg>16) {
nb_sg=16;
}
if(nb_sg==0) {
nb_sg=(maxneigh)*(maxneigh/2);
}
if(allocate_sigma) {
destroy_sigma();
}
create_sigma(nb_sg);
for(itmp=0;itmp<inum;itmp++) {
i = ilist[itmp];
i_tag=tag[i];
itype = map[type[i]]+1;
//j is loop over all neighbors of i
for(jtmp=0;jtmp<numneigh[i];jtmp++) {
temp_ij=BOP_index[i]+jtmp;
if(neigh_flag[temp_ij]) {
for(m=0;m<nb_sg;m++) {
for(pp=0;pp<3;pp++) {
bt_sg[m].dAA[pp]=0.0;
bt_sg[m].dBB[pp]=0.0;
bt_sg[m].dEE1[pp]=0.0;
bt_sg[m].dFF[pp]=0.0;
bt_sg[m].dAAC[pp]=0.0;
bt_sg[m].dSigB1[pp]=0.0;
bt_sg[m].dSigB[pp]=0.0;
}
bt_sg[m].i=-1;
bt_sg[m].j=-1;
}
nb_t=0;
iilist=firstneigh[i];
j=iilist[jtmp];
jlist=firstneigh[j];
for(ki=0;ki<numneigh[j];ki++) {
temp_ki=BOP_index[j]+ki;
if(x[jlist[ki]][0]==x[i][0]) {
if(x[jlist[ki]][1]==x[i][1]) {
if(x[jlist[ki]][2]==x[i][2]) {
break;
}
}
}
}
j_tag=tag[j];
jtype = map[type[j]]+1;
nb_ij=nb_t;
nb_t++;
if(nb_t>nb_sg) {
new_n_tot=nb_sg+maxneigh;
grow_sigma(nb_sg,new_n_tot);
nb_sg=new_n_tot;
}
bt_sg[nb_ij].temp=temp_ij;
bt_sg[nb_ij].i=i;
bt_sg[nb_ij].j=j;
if(j_tag>=i_tag) {
if(itype==jtype)
iij=itype-1;
else if(itype<jtype)
iij=itype*bop_types-itype*(itype+1)/2+jtype-1;
else
iij=jtype*bop_types-jtype*(jtype+1)/2+itype-1;
for(ji=0;ji<numneigh[j];ji++) {
temp_ji=BOP_index[j]+ji;
if(x[jlist[ji]][0]==x[i][0]) {
if(x[jlist[ji]][1]==x[i][1]) {
if(x[jlist[ji]][2]==x[i][2]) {
break;
}
}
}
}
nSigBk[n]=0;
//AA-EE1 are the components making up Eq. 30 (a)
AA=0.0;
BB=0.0;
CC=0.0;
DD=0.0;
EE1=0.0;
//FF is the Beta_sigma^2 term
FF=betaS[temp_ij]*betaS[temp_ij];
//agpdpr1 is derivative of FF w.r.t. r_ij
agpdpr1=2.0*betaS[temp_ij]*dBetaS[temp_ij]/rij[temp_ij];
//dXX derivatives are taken with respect to all pairs contributing to the energy
//nb_ij is derivative w.r.t. ij pair
bt_sg[nb_ij].dFF[0]=agpdpr1*disij[0][temp_ij];
bt_sg[nb_ij].dFF[1]=agpdpr1*disij[1][temp_ij];
bt_sg[nb_ij].dFF[2]=agpdpr1*disij[2][temp_ij];
//k is loop over all neighbors of i again with j neighbor of i
for(ktmp=0;ktmp<numneigh[i];ktmp++) {
temp_ik=BOP_index[i]+ktmp;
if(neigh_flag[temp_ik]) {
if(ktmp!=jtmp) {
if(jtmp<ktmp) {
njik=jtmp*(2*numneigh[i]-jtmp-1)/2+(ktmp-jtmp)-1;
ngj=0;
ngk=1;
}
else {
njik=ktmp*(2*numneigh[i]-ktmp-1)/2+(jtmp-ktmp)-1;
ngj=1;
ngk=0;
}
k=iilist[ktmp];
ktype = map[type[k]]+1;
//find neighbor of k that is equal to i
klist=firstneigh[k];
for(kNeii=0;kNeii<numneigh[k];kNeii++) {
temp_ki=BOP_index[k]+kNeii;
if(x[klist[kNeii]][0]==x[i][0]) {
if(x[klist[kNeii]][1]==x[i][1]) {
if(x[klist[kNeii]][2]==x[i][2]) {
break;
}
}
}
}
//find neighbor of i that is equal to k
for(jNeik=0;jNeik<numneigh[j];jNeik++) {
temp_jk=BOP_index[j]+jNeik;
if(x[jlist[jNeik]][0]==x[k][0]) {
if(x[jlist[jNeik]][1]==x[k][1]) {
if(x[jlist[jNeik]][2]==x[k][2]) {
break;
}
}
}
}
//find neighbor of k that is equal to j
for(kNeij=0;kNeij<numneigh[k];kNeij++) {
if(x[klist[kNeij]][0]==x[j][0]) {
if(x[klist[kNeij]][1]==x[j][1]) {
if(x[klist[kNeij]][2]==x[j][2]) {
break;
}
}
}
}
sig_flag=0;
for(nsearch=0;nsearch<nSigBk[n];nsearch++) {
ncmp=itypeSigBk[n][nsearch];
if(x[ncmp][0]==x[k][0]) {
if(x[ncmp][1]==x[k][1]) {
if(x[ncmp][2]==x[k][2]) {
nk0=nsearch;
sig_flag=1;
break;
}
}
}
}
if(sig_flag==0) {
nSigBk[n]=nSigBk[n]+1;
nk0=nSigBk[n]-1;
itypeSigBk[n][nk0]=k;
}
nb_ik=nb_t;
nb_t++;
if(nb_t>nb_sg) {
new_n_tot=nb_sg+maxneigh;
grow_sigma(nb_sg,new_n_tot);
nb_sg=new_n_tot;
}
bt_sg[nb_ik].temp=temp_ik;
bt_sg[nb_ik].i=i;
bt_sg[nb_ik].j=k;
nb_jk=nb_t;
nb_t++;
if(nb_t>nb_sg) {
new_n_tot=nb_sg+maxneigh;
grow_sigma(nb_sg,new_n_tot);
nb_sg=new_n_tot;
}
bt_sg[nb_jk].temp=temp_jk;
bt_sg[nb_jk].i=j;
bt_sg[nb_jk].j=k;
ang_jik=cos_index[i]+njik;
if(ang_jik>=cos_total) {
error->one(FLERR,"Too many atom triplets for pair bop");
}
gmean0=sigma_g0[jtype-1][itype-1][ktype-1];
gmean1=sigma_g1[jtype-1][itype-1][ktype-1];
gmean2=sigma_g2[jtype-1][itype-1][ktype-1];
amean=cosAng[ang_jik];
gfactor1=gmean0+gmean1*amean
+gmean2*amean*amean;
gfactorsq=gfactor1*gfactor1;
gprime1=gmean1+2.0*gmean2*amean;
gsqprime=2.0*gfactor1*gprime1;
//AA is Eq. 34 (a) or Eq. 10 (c) for the i atom
//1st CC is Eq. 11 (c) for i atom where j & k=neighbor of i
AA=AA+gfactorsq*betaS[temp_ik]*betaS[temp_ik];
CC=CC+gfactorsq*betaS[temp_ik]*betaS[temp_ik]*betaS[temp_ik]*betaS[temp_ik];
//agpdpr1 is derivative of AA w.r.t. Beta(rik)
//agpdpr2 is derivative of CC 1st term w.r.t. Beta(rik)
//app1 is derivative of AA w.r.t. cos(theta_jik)
//app2 is derivative of CC 1st term w.r.t. cos(theta_jik)
agpdpr1=2.0*gfactorsq*betaS[temp_ik]*dBetaS[temp_ik]/rij[temp_ik];
app1=betaS[temp_ik]*betaS[temp_ik]*gsqprime;
bt_sg[nb_ij].dAA[0]+=
app1*dcAng[ang_jik][0][ngj];
bt_sg[nb_ij].dAA[1]+=
app1*dcAng[ang_jik][1][ngj];
bt_sg[nb_ij].dAA[2]+=
app1*dcAng[ang_jik][2][ngj];
bt_sg[nb_ik].dAA[0]+=
app1*dcAng[ang_jik][0][ngk]
+agpdpr1*disij[0][temp_ik];
bt_sg[nb_ik].dAA[1]+=
app1*dcAng[ang_jik][1][ngk]
+agpdpr1*disij[1][temp_ik];
bt_sg[nb_ik].dAA[2]+=
app1*dcAng[ang_jik][2][ngk]
+agpdpr1*disij[2][temp_ik];
//k' is loop over neighbors all neighbors of j with k a neighbor
//of i and j a neighbor of i and determine which k' is k
kp_index=0;
for(ltmp=0;ltmp<numneigh[j];ltmp++) {
temp_jkp=BOP_index[j]+ltmp;
kp=jlist[ltmp];
if(x[kp][0]==x[k][0]) {
if(x[kp][1]==x[k][1]) {
if(x[kp][2]==x[k][2]) {
kp_index=1;
break;
}
}
}
}
if(kp_index) {
//loop over neighbors of k
for(mtmp=0;mtmp<numneigh[k];mtmp++) {
kp=klist[mtmp];
if(x[kp][0]==x[j][0]) {
if(x[kp][1]==x[j][1]) {
if(x[kp][2]==x[j][2]) {
break;
}
}
}
}
if(ki<ltmp) {
nijk=ki*(2*numneigh[j]-ki-1)/2+(ltmp-ki)-1;
ngji=0;
ngjk=1;
}
else {
nijk=ltmp*(2*numneigh[j]-ltmp-1)/2+(ki-ltmp)-1;
ngji=1;
ngjk=0;
}
if(kNeii<mtmp) {
nikj=kNeii*(2*numneigh[k]-kNeii-1)/2+(mtmp-kNeii)-1;
ngki=0;
ngkj=1;
}
else {
nikj=mtmp*(2*numneigh[k]-mtmp-1)/2+(kNeii-mtmp)-1;
ngki=1;
ngkj=0;
}
ang_ijk=cos_index[j]+nijk;
if(ang_ijk>=cos_total) {
error->one(FLERR,"Too many atom triplets for pair bop");
}
gmean0=sigma_g0[itype-1][jtype-1][ktype-1];
gmean1=sigma_g1[itype-1][jtype-1][ktype-1];
gmean2=sigma_g2[itype-1][jtype-1][ktype-1];
amean=cosAng[ang_ijk];
gfactor2=gmean0+gmean1*amean
+gmean2*amean*amean;
gprime2=gmean1+2.0*gmean2*amean;
gmean0=sigma_g0[itype-1][ktype-1][jtype-1];
gmean1=sigma_g1[itype-1][ktype-1][jtype-1];
gmean2=sigma_g2[itype-1][ktype-1][jtype-1];
ang_ikj=cos_index[k]+nikj;
if(ang_ikj>=cos_total) {
error->one(FLERR,"Too many atom triplets for pair bop");
}
amean=cosAng[ang_ikj];
gfactor3=gmean0+gmean1*amean
+gmean2*amean*amean;
gprime3=gmean1+2.0*gmean2*amean;
gfactor=gfactor1*gfactor2*gfactor3;
rfactor=betaS[temp_ik]*betaS[temp_jkp];
//EE1 is (b) Eq. 12
EE1=EE1+gfactor*rfactor;
//rcm2 is derivative of EE1 w.r.t Beta(r_jk')
//gcm1 is derivative of EE1 w.r.t cos(theta_jik)
//gcm2 is derivative of EE1 w.r.t cos(theta_ijk)
//gcm3 is derivative of EE1 w.r.t cos(theta_ikj)
rcm1=gfactor*betaS[temp_jkp]*dBetaS[temp_ik]/rij[temp_ik];
rcm2=gfactor*betaS[temp_ik]*dBetaS[temp_jkp]/rij[temp_jkp];
gcm1=rfactor*gprime1*gfactor2*gfactor3;
gcm2=rfactor*gfactor1*gprime2*gfactor3;
gcm3=rfactor*gfactor1*gfactor2*gprime3;
bt_sg[nb_ij].dEE1[0]+=
gcm1*dcAng[ang_jik][0][ngj]
-gcm2*dcAng[ang_ijk][0][ngji];
bt_sg[nb_ij].dEE1[1]+=
gcm1*dcAng[ang_jik][1][ngj]
-gcm2*dcAng[ang_ijk][1][ngji];
bt_sg[nb_ij].dEE1[2]+=
gcm1*dcAng[ang_jik][2][ngj]
-gcm2*dcAng[ang_ijk][2][ngji];
bt_sg[nb_ik].dEE1[0]+=
gcm1*dcAng[ang_jik][0][ngk]
+rcm1*disij[0][temp_ik]
-gcm3*dcAng[ang_ikj][0][ngki];
bt_sg[nb_ik].dEE1[1]+=
gcm1*dcAng[ang_jik][1][ngk]
+rcm1*disij[1][temp_ik]
-gcm3*dcAng[ang_ikj][1][ngki];
bt_sg[nb_ik].dEE1[2]+=
gcm1*dcAng[ang_jik][2][ngk]
+rcm1*disij[2][temp_ik]
-gcm3*dcAng[ang_ikj][2][ngki];
bt_sg[nb_jk].dEE1[0]+=
gcm2*dcAng[ang_ijk][0][ngjk]
+rcm2*disij[0][temp_jkp]
-gcm3*dcAng[ang_ikj][0][ngkj];
bt_sg[nb_jk].dEE1[1]+=
gcm2*dcAng[ang_ijk][1][ngjk]
+rcm2*disij[1][temp_jkp]
-gcm3*dcAng[ang_ikj][1][ngkj];
bt_sg[nb_jk].dEE1[2]+=
gcm2*dcAng[ang_ijk][2][ngjk]
+rcm2*disij[2][temp_jkp]
-gcm3*dcAng[ang_ikj][2][ngkj];
}
// k and k' and j are all different neighbors of i
for(ltmp=0;ltmp<ktmp;ltmp++) {
if(ltmp!=jtmp) {
temp_ikp=BOP_index[i]+ltmp;
if(neigh_flag[temp_ikp]) {
kp=iilist[ltmp];
kptype = map[type[kp]]+1;
for(nsearch=0;nsearch<nSigBk[n];nsearch++) {
ncmp=itypeSigBk[n][nsearch];
if(x[ncmp][0]==x[kp][0]) {
if(x[ncmp][1]==x[kp][1]) {
if(x[ncmp][2]==x[kp][2]) {
break;
}
}
}
}
if(jtmp<ltmp) {
njikp=jtmp*(2*numneigh[i]-jtmp-1)/2+(ltmp-jtmp)-1;
nglj=0;
ngl=1;
}
else {
njikp=ltmp*(2*numneigh[i]-ltmp-1)/2+(jtmp-ltmp)-1;
nglj=1;
ngl=0;
}
if(ktmp<ltmp) {
nkikp=ktmp*(2*numneigh[i]-ktmp-1)/2+(ltmp-ktmp)-1;
}
else {
nkikp=ltmp*(2*numneigh[i]-ltmp-1)/2+(ktmp-ltmp)-1;
}
ang_jikp=cos_index[i]+njikp;
if(ang_jikp>=cos_total) {
error->one(FLERR,"Too many atom triplets for pair bop");
}
gmean0=sigma_g0[jtype-1][itype-1][kptype-1];
gmean1=sigma_g1[jtype-1][itype-1][kptype-1];
gmean2=sigma_g2[jtype-1][itype-1][kptype-1];
amean=cosAng[ang_jikp];
gfactor2=gmean0+gmean1*amean
+gmean2*amean*amean;
gprime2=gmean1+2.0*gmean2*amean;
gmean0=sigma_g0[ktype-1][itype-1][kptype-1];
gmean1=sigma_g1[ktype-1][itype-1][kptype-1];
gmean2=sigma_g2[ktype-1][itype-1][kptype-1];
ang_kikp=cos_index[i]+nkikp;
if(ang_kikp>=cos_total) {
error->one(FLERR,"Too many atom triplets for pair bop");
}
amean=cosAng[ang_kikp];
gfactor3=gmean0+gmean1*amean
+gmean2*amean*amean;
gprime3=gmean1+2.0*gmean2*amean;
gfactor=gfactor1*gfactor2*gfactor3;
rfactorrt=betaS[temp_ik]*betaS[temp_ikp];
rfactor=rfactorrt*rfactorrt;
//2nd CC is second term of Eq. 11 (c) for i atom where j , k & k' =neighbor of i
CC=CC+2.0*gfactor*rfactor;
}
}
}
// j and k are different neighbors of i and k' is a neighbor k not equal to i
for(ltmp=0;ltmp<numneigh[k];ltmp++) {
temp_kkp=BOP_index[k]+ltmp;
if(neigh_flag[temp_kkp]) {
kp=klist[ltmp];;
kptype = map[type[kp]]+1;
same_ikp=0;
same_jkp=0;
if(x[i][0]==x[kp][0]) {
if(x[i][1]==x[kp][1]) {
if(x[i][2]==x[kp][2]) {
same_ikp=1;
}
}
}
if(x[j][0]==x[kp][0]) {
if(x[j][1]==x[kp][1]) {
if(x[j][2]==x[kp][2]) {
same_jkp=1;
}
}
}
if(!same_ikp&&!same_jkp) {
if(kNeii<ltmp) {
nikkp=kNeii*(2*numneigh[k]-kNeii-1)/2+(ltmp-kNeii)-1;
ngli=0;
}
else {
nikkp=ltmp*(2*numneigh[k]-ltmp-1)/2+(kNeii-ltmp)-1;
ngli=1;
}
sig_flag=0;
for(nsearch=0;nsearch<nSigBk[n];nsearch++) {
ncmp=itypeSigBk[n][nsearch];
if(x[ncmp][0]==x[kp][0]) {
if(x[ncmp][1]==x[kp][1]) {
if(x[ncmp][2]==x[kp][2]) {
sig_flag=1;
nkp=nsearch;
break;
}
}
}
}
if(sig_flag==0) {
nSigBk[n]=nSigBk[n]+1;
nkp=nSigBk[n]-1;
itypeSigBk[n][nkp]=kp;
}
ang_ikkp=cos_index[k]+nikkp;
if(ang_ikkp>=cos_total) {
error->one(FLERR,"Too many atom triplets for pair bop");
}
gmean0=sigma_g0[itype-1][ktype-1][kptype-1];
gmean1=sigma_g1[itype-1][ktype-1][kptype-1];
gmean2=sigma_g2[itype-1][ktype-1][kptype-1];
amean=cosAng[ang_ikkp];
gfactor2=gmean0+gmean1*amean
+gmean2*amean*amean;
gprime2=gmean1+2.0*gmean2*amean;
gfactorsq2=gfactor2*gfactor2;
gsqprime2=2.0*gfactor2*gprime2;
gfactor=gfactorsq*gfactorsq2;
rfactorrt=betaS[temp_ik]*betaS[temp_kkp];
rfactor=rfactorrt*rfactorrt;
//3rd CC is third term of Eq. 11 (c) for i atom
//where j , k =neighbor of i & k' =neighbor of k
CC=CC+gfactor*rfactor;
}
}
}
}
}
}
//j is a neighbor of i and k is a neighbor of j not equal to i
for(ktmp=0;ktmp<numneigh[j];ktmp++) {
if(ktmp!=ji) {
if(ktmp<ji) {
njik=ktmp*(2*numneigh[j]-ktmp-1)/2+(ji-ktmp)-1;
ngi=1;
ngk=0;
}
else {
njik=ji*(2*numneigh[j]-ji-1)/2+(ktmp-ji)-1;
ngi=0;
ngk=1;
}
temp_jk=BOP_index[j]+ktmp;
if(neigh_flag[temp_jk]) {
k=jlist[ktmp];
ktype=map[type[k]]+1;
klist=firstneigh[k];
for(kNeij=0;kNeij<numneigh[k];kNeij++) {
if(x[klist[kNeij]][0]==x[j][0]) {
if(x[klist[kNeij]][1]==x[j][1]) {
if(x[klist[kNeij]][2]==x[j][2]) {
break;
}
}
}
}
sig_flag=0;
for(nsearch=0;nsearch<nSigBk[n];nsearch++) {
ncmp=itypeSigBk[n][nsearch];
if(x[ncmp][0]==x[k][0]) {
if(x[ncmp][1]==x[k][1]) {
if(x[ncmp][2]==x[k][2]) {
new1=nsearch;
sig_flag=1;
break;
}
}
}
}
if(sig_flag==0) {
nSigBk[n]=nSigBk[n]+1;
new1=nSigBk[n]-1;
itypeSigBk[n][new1]=k;
}
ang_ijk=cos_index[j]+njik;
if(ang_ijk>=cos_total) {
error->one(FLERR,"Too many atom triplets for pair bop");
}
nb_jk=nb_t;
nb_t++;
if(nb_t>nb_sg) {
new_n_tot=nb_sg+maxneigh;
grow_sigma(nb_sg,new_n_tot);
nb_sg=new_n_tot;
}
bt_sg[nb_jk].temp=temp_jk;
bt_sg[nb_jk].i=j;
bt_sg[nb_jk].j=k;
gmean0=sigma_g0[itype-1][jtype-1][ktype-1];
gmean1=sigma_g1[itype-1][jtype-1][ktype-1];
gmean2=sigma_g2[itype-1][jtype-1][ktype-1];
amean=cosAng[ang_ijk];
gfactor1=gmean0+gmean1*amean
+gmean2*amean*amean;
gprime1=gmean1+2.0*gmean2*amean;
gfactorsq=gfactor1*gfactor1;
gsqprime=2.0*gfactor1*gprime1;
rfactor1rt=betaS[temp_jk]*betaS[temp_jk];
rfactor1=rfactor1rt*rfactor1rt;
//BB is Eq. 34 (a) or Eq. 10 (c) for the j atom
//1st DD is Eq. 11 (c) for j atom where i & k=neighbor of j
BB=BB+gfactorsq*rfactor1rt;
DD=DD+gfactorsq*rfactor1;
//agpdpr1 is derivative of BB w.r.t. Beta(r_jk)
//app1 is derivative of BB w.r.t. cos(theta_ijk)
agpdpr1=2.0*gfactorsq*betaS[temp_jk]*dBetaS[temp_jk]/rij[temp_jk];
app1=rfactor1rt*gsqprime;
bt_sg[nb_ij].dBB[0]-=
app1*dcAng[ang_ijk][0][ngi];
bt_sg[nb_ij].dBB[1]-=
app1*dcAng[ang_ijk][1][ngi];
bt_sg[nb_ij].dBB[2]-=
app1*dcAng[ang_ijk][2][ngi];
bt_sg[nb_jk].dBB[0]+=
app1*dcAng[ang_ijk][0][ngk]
+agpdpr1*disij[0][temp_jk];
bt_sg[nb_jk].dBB[1]+=
app1*dcAng[ang_ijk][1][ngk]
+agpdpr1*disij[1][temp_jk];
bt_sg[nb_jk].dBB[2]+=
app1*dcAng[ang_ijk][2][ngk]
+agpdpr1*disij[2][temp_jk];
//j is a neighbor of i, k and k' prime different neighbors of j not equal to i
for(ltmp=0;ltmp<ktmp;ltmp++) {
if(ltmp!=ji) {
temp_jkp=BOP_index[j]+ltmp;
if(neigh_flag[temp_jkp]) {
kp=jlist[ltmp];
kptype=map[type[kp]]+1;
for(nsearch=0;nsearch<nSigBk[n];nsearch++) {
ncmp=itypeSigBk[n][nsearch];
if(x[ncmp][0]==x[kp][0]) {
if(x[ncmp][1]==x[kp][1]) {
if(x[ncmp][2]==x[kp][2]) {
new2=nsearch;
break;
}
}
}
}
if(ji<ltmp) {
nijkp=ji*(2*numneigh[j]-ji-1)/2+(ltmp-ji)-1;
ngli=0;
ngl=1;
}
else {
nijkp=ltmp*(2*numneigh[j]-ltmp-1)/2+(ji-ltmp)-1;
ngli=1;
ngl=0;
}
if(ktmp<ltmp) {
nkjkp=ktmp*(2*numneigh[j]-ktmp-1)/2+(ltmp-ktmp)-1;
ngjk=0;
}
else {
nkjkp=ltmp*(2*numneigh[j]-ltmp-1)/2+(ktmp-ltmp)-1;
ngjk=1;
}
ang_ijkp=cos_index[j]+nijkp;
if(ang_ijkp>=cos_total) {
error->one(FLERR,"Too many atom triplets for pair bop");
}
ang_kjkp=cos_index[j]+nkjkp;
if(ang_kjkp>=cos_total) {
error->one(FLERR,"Too many atom triplets for pair bop");
}
gmean0=sigma_g0[itype-1][jtype-1][kptype-1];
gmean1=sigma_g1[itype-1][jtype-1][kptype-1];
gmean2=sigma_g2[itype-1][jtype-1][kptype-1];
amean=cosAng[ang_ijkp];
gfactor2=gmean0+gmean1*amean
+gmean2*amean*amean;
gprime2=gmean1+2.0*gmean2*amean;
gmean0=sigma_g0[ktype-1][jtype-1][kptype-1];
gmean1=sigma_g1[ktype-1][jtype-1][kptype-1];
gmean2=sigma_g2[ktype-1][jtype-1][kptype-1];
amean=cosAng[ang_kjkp];
gfactor3=gmean0+gmean1*amean
+gmean2*amean*amean;
gprime3=gmean1+2.0*gmean2*amean;
gfactor=gfactor1*gfactor2*gfactor3;
rfactorrt=betaS[temp_jk]*betaS[temp_jkp];
rfactor=rfactorrt*rfactorrt;
//2nd DD is Eq. 11 (c) for j atom where i , k & k'=neighbor of j
DD=DD+2.0*gfactor*rfactor;
}
}
}
//j is a neighbor of i, k is a neighbor of j not equal to i and k'
//is a neighbor of k not equal to j or i
for(ltmp=0;ltmp<numneigh[k];ltmp++) {
temp_kkp=BOP_index[k]+ltmp;
if(neigh_flag[temp_kkp]) {
kp=klist[ltmp];
kptype=map[type[kp]]+1;
same_ikp=0;
same_jkp=0;
if(x[i][0]==x[kp][0]) {
if(x[i][1]==x[kp][1]) {
if(x[i][2]==x[kp][2]) {
same_ikp=1;
}
}
}
if(x[j][0]==x[kp][0]) {
if(x[j][1]==x[kp][1]) {
if(x[j][2]==x[kp][2]) {
same_jkp=1;
}
}
}
if(!same_ikp&&!same_jkp) {
for(kNeij=0;kNeij<numneigh[k];kNeij++) {
if(x[klist[kNeij]][0]==x[j][0]) {
if(x[klist[kNeij]][1]==x[j][1]) {
if(x[klist[kNeij]][2]==x[j][2]) {
break;
}
}
}
}
if(kNeij<ltmp) {
njkkp=kNeij*(2*numneigh[k]-kNeij-1)/2+(ltmp-kNeij)-1;
nglj=0;
}
else {
njkkp=ltmp*(2*numneigh[k]-ltmp-1)/2+(kNeij-ltmp)-1;
nglj=1;
}
sig_flag=0;
for(nsearch=0;nsearch<nSigBk[n];nsearch++) {
ncmp=itypeSigBk[n][nsearch];
if(x[ncmp][0]==x[kp][0]) {
if(x[ncmp][1]==x[kp][1]) {
if(x[ncmp][2]==x[kp][2]) {
new2=nsearch;
sig_flag=1;
break;
}
}
}
}
if(sig_flag==0) {
nSigBk[n]=nSigBk[n]+1;
new2=nSigBk[n]-1;
itypeSigBk[n][new2]=kp;
}
ang_jkkp=cos_index[k]+njkkp;
if(ang_jkkp>=cos_total) {
error->one(FLERR,"Too many atom triplets for pair bop");
}
gmean0=sigma_g0[jtype-1][ktype-1][kptype-1];
gmean1=sigma_g1[jtype-1][ktype-1][kptype-1];
gmean2=sigma_g2[jtype-1][ktype-1][kptype-1];
amean=cosAng[ang_jkkp];
gfactor2=gmean0+gmean1*amean
+gmean2*amean*amean;
gprime2=gmean1+2.0*gmean2*amean;
gfactorsq2=gfactor2*gfactor2;
gsqprime2=2.0*gfactor2*gprime2;
gfactor=gfactorsq*gfactorsq2;
rfactorrt=betaS[temp_jk]*betaS[temp_kkp];
rfactor=rfactorrt*rfactorrt;
//3rd DD is Eq. 11 (c) for j atom where i & k=neighbor of j & k'=neighbor of k
DD=DD+gfactor*rfactor;
}
}
}
}
}
}
sig_flag=0;
if(sig_flag==0) {
// AA and BB are the representations of (a) Eq. 34 and (b) Eq. 9
// for atoms i and j respectively
AAC=AA+BB;
BBC=AA*BB;
CCC=AA*AA+BB*BB;
DDC=CC+DD;
//EEC is a modified form of (a) Eq. 33
EEC=(DDC-CCC)/(AAC+2.0*small1);
for(m=0;m<nb_t;m++) {
if((bt_sg[m].i>-1)&&(bt_sg[m].j>-1)) {
bt_i=bt_sg[m].i;
bt_j=bt_sg[m].j;
bt_sg[m].dAAC[0]=bt_sg[m].dAA[0]
+bt_sg[m].dBB[0];
bt_sg[m].dAAC[1]=bt_sg[m].dAA[1]
+bt_sg[m].dBB[1];
bt_sg[m].dAAC[2]=bt_sg[m].dAA[2]
+bt_sg[m].dBB[2];
}
}
UT=EEC*FF+BBC+small3[iij];
UT=1.0/sqrt(UT);
// FFC is slightly modified form of (a) Eq. 31
// GGC is slightly modified form of (a) Eq. 32
// bndtmp is a slightly modified form of (a) Eq. 30 and (b) Eq. 8
bndtmp=(FF+sigma_delta[iij]*sigma_delta[iij])
+sigma_c[iij]*AAC+small4;
UTcom=-0.5*UT*UT*UT;
psign=1.0;
bndtmp0=1.0/sqrt(bndtmp);
sigB1[n]=psign*betaS[temp_ij]*bndtmp0;
bndtmp=-0.5*bndtmp0*bndtmp0*bndtmp0;
bndtmp1=psign*bndtmp0+psign*betaS[temp_ij]
*bndtmp*2.0*betaS[temp_ij];
bndtmp1=bndtmp1*dBetaS[temp_ij]/rij[temp_ij];
bndtmp2=psign*betaS[temp_ij]*bndtmp*sigma_c[iij];
setting=0;
for(m=0;m<nb_t;m++) {
if((bt_sg[m].i>-1)&&(bt_sg[m].j>-1)) {
temp_kk=bt_sg[m].temp;
if(temp_kk==temp_ij&&setting==0) {
bt_sg[m].dSigB1[0]=bndtmp1*disij[0][temp_ij]
+(bndtmp2*bt_sg[m].dAAC[0]);
bt_sg[m].dSigB1[1]=bndtmp1*disij[1][temp_ij]
+(bndtmp2*bt_sg[m].dAAC[1]);
bt_sg[m].dSigB1[2]=bndtmp1*disij[2][temp_ij]
+(bndtmp2*bt_sg[m].dAAC[2]);
setting=1;
}
else if(temp_kk==temp_ji&&setting==0) {
bt_sg[m].dSigB1[0]=-bndtmp1*disij[0][temp_ij]
+(bndtmp2*bt_sg[m].dAAC[0]);
bt_sg[m].dSigB1[1]=-bndtmp1*disij[1][temp_ij]
+(bndtmp2*bt_sg[m].dAAC[1]);
bt_sg[m].dSigB1[2]=-bndtmp1*disij[2][temp_ij]
+(bndtmp2*bt_sg[m].dAAC[2]);
setting=1;
}
else {
bt_sg[m].dSigB1[0]=(bndtmp2*bt_sg[m].dAAC[0]);
bt_sg[m].dSigB1[1]=(bndtmp2*bt_sg[m].dAAC[1]);
bt_sg[m].dSigB1[2]=(bndtmp2*bt_sg[m].dAAC[2]);
}
}
}
//This loop is to ensure there is not an error for atoms with no neighbors (deposition)
if(nb_t==0) {
if(j>i) {
bt_sg[0].dSigB1[0]=bndtmp1*disij[0][temp_ij];
bt_sg[0].dSigB1[1]=bndtmp1*disij[1][temp_ij];
bt_sg[0].dSigB1[2]=bndtmp1*disij[2][temp_ij];
}
else {
bt_sg[0].dSigB1[0]=-bndtmp1*disij[0][temp_ij];
bt_sg[0].dSigB1[1]=-bndtmp1*disij[1][temp_ij];
bt_sg[0].dSigB1[2]=-bndtmp1*disij[2][temp_ij];
}
for(pp=0;pp<3;pp++) {
bt_sg[0].dAA[pp]=0.0;
bt_sg[0].dBB[pp]=0.0;
bt_sg[0].dEE1[pp]=0.0;
bt_sg[0].dFF[pp]=0.0;
bt_sg[0].dAAC[pp]=0.0;
bt_sg[0].dSigB[pp]=0.0;
}
bt_sg[0].i=i;
bt_sg[0].j=j;
bt_sg[0].temp=temp_ij;
nb_t++;
if(nb_t>nb_sg) {
new_n_tot=nb_sg+maxneigh;
grow_sigma(nb_sg,new_n_tot);
nb_sg=new_n_tot;
}
}
ps=sigB1[n]*rdBO+1.0;
ks=(int)ps;
if(nBOt-1<ks)
ks=nBOt-1;
ps=ps-ks;
if(ps>1.0)
ps=1.0;
dsigB1=((FsigBO3[iij][ks-1]*ps+FsigBO2[iij][ks-1])*ps
+FsigBO1[iij][ks-1])*ps+FsigBO[iij][ks-1];
dsigB2=(FsigBO6[iij][ks-1]*ps+FsigBO5[iij][ks-1])*ps+FsigBO4[iij][ks-1];
part0=(FF+0.5*AAC+small5);
part1=(sigma_f[iij]-0.5)*sigma_k[iij];
part2=1.0-part1*EE1/part0;
part3=dsigB1*part1/part0;
part4=part3/part0*EE1;
// sigB is the final expression for (a) Eq. 6 and (b) Eq. 11
sigB[n]=dsigB1*part2;
pp1=2.0*betaS[temp_ij];
for(m=0;m<nb_t;m++) {
if((bt_sg[m].i>-1)&&(bt_sg[m].j>-1)) {
temp_kk=bt_sg[m].temp;
bt_ij=bt_sg[m].temp;
bt_i=bt_sg[m].i;
bt_j=bt_sg[m].j;
for(pp=0;pp<3;pp++) {
bt_sg[m].dSigB[pp]=dsigB2*part2*bt_sg[m].dSigB1[pp]
-part3*bt_sg[m].dEE1[pp]
+part4*(bt_sg[m].dFF[pp]
+0.5*bt_sg[m].dAAC[pp]);
}
for(pp=0;pp<3;pp++) {
ftmp[pp]=pp1*bt_sg[m].dSigB[pp];
f[bt_i][pp]-=ftmp[pp];
f[bt_j][pp]+=ftmp[pp];
}
if(evflag) {
ev_tally_xyz(bt_i,bt_j,nlocal,newton_pair,0.0,0.0,ftmp[0],ftmp[1]
,ftmp[2],disij[0][bt_ij],disij[1][bt_ij],disij[2][bt_ij]);
}
}
}
}
n++;
}
}
}
}
destroy_sigma();
}
/* ---------------------------------------------------------------------- */
/* The formulation differs slightly to avoid negative square roots
in the calculation of Theta_pi,ij of (a) Eq. 36 and (b) Eq. 18 */
void PairBOP::sigmaBo_otf()
{
int nb_t,new_n_tot;
int n,i,j,k,kp,m,pp,kpj,kpk,kkp;
int itmp,jtmp,ktmp,ltmp,mtmp;
int i_tag,j_tag;
int kp1,kp2,kp1type;
int iij,iik,ijk,ikkp,ji,iikp,ijkp;
int nkp;
int nk0;
int jNeik,kNeii,kNeij,kNeikp;
int kpNeij,kpNeik;
int new1,new2,nlocal;
int inum,*ilist,*iilist,*jlist,*klist,*kplist;
int **firstneigh,*numneigh;
int temp_ij,temp_ik,temp_jkp,temp_kk,temp_jk;
int temp_ji,temp_kpj,temp_kkp;
int temp_ikp,temp_kpk;
int nb_ij,nb_ik,nb_ikp;
int nb_jk,nb_jkp,nb_kkp;
int kp_nsearch,nsearch;
int sig_flag,setting,ncmp,ks;
int itype,jtype,ktype,kptype;
int bt_i,bt_j;
int same_ikp,same_jkp,same_kpk;
int same_jkpj,same_kkpk;
double AA,BB,CC,DD,EE,EE1,FF;
double AAC,BBC,CCC,DDC,EEC,FFC,GGC;
double AACFF,UT,bndtmp,UTcom;
double amean,gmean0,gmean1,gmean2,ps;
double gfactor1,gprime1,gsqprime,factorsq;
double gfactorsq,gfactor2,gprime2;
double gfactorsq2,gsqprime2;
double gfactor3,gprime3,gfactor,rfactor;
double drfactor,gfactor4,gprime4,agpdpr3;
double rfactor0,rfactorrt,rfactor1rt,rfactor1;
double rcm1,rcm2,gcm1,gcm2,gcm3;
double agpdpr1,agpdpr2,app1,app2,app3,app4;
double dsigB1,dsigB2;
double part0,part1,part2,part3,part4;
double psign,bndtmp0,pp1;
double bndtmp1,bndtmp2,bndtmp3,bndtmp4,bndtmp5;
double dis_ij[3],rsq_ij,r_ij;
double betaS_ij,dBetaS_ij;
double betaP_ij,dBetaP_ij;
double dis_ik[3],rsq_ik,r_ik;
double betaS_ik,dBetaS_ik;
double betaP_ik,dBetaP_ik;
double dis_ikp[3],rsq_ikp,r_ikp;
double betaS_ikp,dBetaS_ikp;
double betaP_ikp,dBetaP_ikp;
double dis_jk[3],rsq_jk,r_jk;
double betaS_jk,dBetaS_jk;
double betaP_jk,dBetaP_jk;
double dis_jkp[3],rsq_jkp,r_jkp;
double betaS_jkp,dBetaS_jkp;
double betaP_jkp,dBetaP_jkp;
double dis_kkp[3],rsq_kkp,r_kkp;
double betaS_kkp,dBetaS_kkp;
double betaP_kkp,dBetaP_kkp;
double cosAng_jik,dcA_jik[3][2];
double cosAng_jikp,dcA_jikp[3][2];
double cosAng_kikp,dcA_kikp[3][2];
double cosAng_ijk,dcA_ijk[3][2];
double cosAng_ijkp,dcA_ijkp[3][2];
double cosAng_kjkp,dcA_kjkp[3][2];
double cosAng_ikj,dcA_ikj[3][2];
double cosAng_ikkp,dcA_ikkp[3][2];
double cosAng_jkkp,dcA_jkkp[3][2];
double cosAng_jkpk,dcA_jkpk[3][2];
double ftmp[3],xtmp[3];
double **x = atom->x;
double **f = atom->f;
int *tag = atom->tag;
int newton_pair = force->newton_pair;
int *type = atom->type;
nlocal = atom->nlocal;
int nall = nlocal + atom->nghost;
inum = list->inum;
ilist = list->ilist;
numneigh = list->numneigh;
firstneigh = list->firstneigh;
n=0;
if(nb_sg==0) {
nb_sg=(maxneigh)*(maxneigh/2);
}
if(allocate_sigma) {
destroy_sigma();
}
create_sigma(nb_sg);
for(itmp=0;itmp<inum;itmp++) {
i = ilist[itmp];
i_tag=tag[i];
itype = map[type[i]]+1;
//j is loop over all neighbors of i
for(jtmp=0;jtmp<numneigh[i];jtmp++) {
for(m=0;m<nb_sg;m++) {
for(pp=0;pp<3;pp++) {
bt_sg[m].dAA[pp]=0.0;
bt_sg[m].dBB[pp]=0.0;
bt_sg[m].dCC[pp]=0.0;
bt_sg[m].dDD[pp]=0.0;
bt_sg[m].dEE[pp]=0.0;
bt_sg[m].dEE1[pp]=0.0;
bt_sg[m].dFF[pp]=0.0;
bt_sg[m].dAAC[pp]=0.0;
bt_sg[m].dBBC[pp]=0.0;
bt_sg[m].dCCC[pp]=0.0;
bt_sg[m].dDDC[pp]=0.0;
bt_sg[m].dEEC[pp]=0.0;
bt_sg[m].dFFC[pp]=0.0;
bt_sg[m].dGGC[pp]=0.0;
bt_sg[m].dUT[pp]=0.0;
bt_sg[m].dSigB1[pp]=0.0;
bt_sg[m].dSigB[pp]=0.0;
}
bt_sg[m].i=-1;
bt_sg[m].j=-1;
bt_sg[m].temp=-1;
}
nb_t=0;
iilist=firstneigh[i];
temp_ij=BOP_index[i]+jtmp;
j=iilist[jtmp];
jlist=firstneigh[j];
j_tag=tag[j];
jtype = map[type[j]]+1;
nb_ij=nb_t;
nb_t++;
if(nb_t>nb_sg) {
new_n_tot=nb_sg+maxneigh;
grow_sigma(nb_sg,new_n_tot);
nb_sg=new_n_tot;
}
bt_sg[nb_ij].temp=temp_ij;
bt_sg[nb_ij].i=i;
bt_sg[nb_ij].j=j;
if(j_tag>=i_tag) {
if(itype==jtype)
iij=itype-1;
else if(itype<jtype)
iij=itype*bop_types-itype*(itype+1)/2+jtype-1;
else
iij=jtype*bop_types-jtype*(jtype+1)/2+itype-1;
for(ji=0;ji<numneigh[j];ji++) {
temp_ji=BOP_index[j]+ji;
if(x[jlist[ji]][0]==x[i][0]) {
if(x[jlist[ji]][1]==x[i][1]) {
if(x[jlist[ji]][2]==x[i][2]) {
break;
}
}
}
}
dis_ij[0]=x[j][0]-x[i][0];
dis_ij[1]=x[j][1]-x[i][1];
dis_ij[2]=x[j][2]-x[i][2];
rsq_ij=dis_ij[0]*dis_ij[0]
+dis_ij[1]*dis_ij[1]
+dis_ij[2]*dis_ij[2];
r_ij=sqrt(rsq_ij);
if(r_ij<rcut[iij]) {
ps=r_ij*rdr[iij]+1.0;
ks=(int)ps;
if(nr-1<ks)
ks=nr-1;
ps=ps-ks;
if(ps>1.0)
ps=1.0;
betaS_ij=((pBetaS3[iij][ks-1]*ps+pBetaS2[iij][ks-1])*ps
+pBetaS1[iij][ks-1])*ps+pBetaS[iij][ks-1];
dBetaS_ij=(pBetaS6[iij][ks-1]*ps+pBetaS5[iij][ks-1])*ps
+pBetaS4[iij][ks-1];
betaP_ij=((pBetaP3[iij][ks-1]*ps+pBetaP2[iij][ks-1])*ps
+pBetaP1[iij][ks-1])*ps+pBetaP[iij][ks-1];
dBetaP_ij=(pBetaP6[iij][ks-1]*ps+pBetaP5[iij][ks-1])*ps
+pBetaP4[iij][ks-1];
nSigBk[n]=0;
//AA-EE1 are the components making up Eq. 30 (a)
AA=0.0;
BB=0.0;
CC=0.0;
DD=0.0;
EE=0.0;
EE1=0.0;
//FF is the Beta_sigma^2 term
FF=betaS_ij*betaS_ij;
//agpdpr1 is derivative of FF w.r.t. r_ij
agpdpr1=2.0*betaS_ij*dBetaS_ij/r_ij;
//dXX derivatives are taken with respect to all pairs contributing to the energy
//nb_ij is derivative w.r.t. ij pair
bt_sg[nb_ij].dFF[0]=agpdpr1*dis_ij[0];
bt_sg[nb_ij].dFF[1]=agpdpr1*dis_ij[1];
bt_sg[nb_ij].dFF[2]=agpdpr1*dis_ij[2];
//k is loop over all neighbors of i again with j neighbor of i
for(ktmp=0;ktmp<numneigh[i];ktmp++) {
temp_ik=BOP_index[i]+ktmp;
if(ktmp!=jtmp) {
k=iilist[ktmp];
klist=firstneigh[k];
ktype = map[type[k]]+1;
if(itype==ktype)
iik=itype-1;
else if(itype<ktype)
iik=itype*bop_types-itype*(itype+1)/2+ktype-1;
else
iik=ktype*bop_types-ktype*(ktype+1)/2+itype-1;
//find neighbor of k that is equal to i
for(kNeii=0;kNeii<numneigh[k];kNeii++) {
if(x[klist[kNeii]][0]==x[i][0]) {
if(x[klist[kNeii]][1]==x[i][1]) {
if(x[klist[kNeii]][2]==x[i][2]) {
break;
}
}
}
}
dis_ik[0]=x[k][0]-x[i][0];
dis_ik[1]=x[k][1]-x[i][1];
dis_ik[2]=x[k][2]-x[i][2];
rsq_ik=dis_ik[0]*dis_ik[0]
+dis_ik[1]*dis_ik[1]
+dis_ik[2]*dis_ik[2];
r_ik=sqrt(rsq_ik);
if(r_ik<=rcut[iik]) {
ps=r_ik*rdr[iik]+1.0;
ks=(int)ps;
if(nr-1<ks)
ks=nr-1;
ps=ps-ks;
if(ps>1.0)
ps=1.0;
betaS_ik=((pBetaS3[iik][ks-1]*ps+pBetaS2[iik][ks-1])*ps
+pBetaS1[iik][ks-1])*ps+pBetaS[iik][ks-1];
dBetaS_ik=(pBetaS6[iik][ks-1]*ps+pBetaS5[iik][ks-1])*ps
+pBetaS4[iik][ks-1];
betaP_ik=((pBetaP3[iik][ks-1]*ps+pBetaP2[iik][ks-1])*ps
+pBetaP1[iik][ks-1])*ps+pBetaP[iik][ks-1];
dBetaP_ik=(pBetaP6[iik][ks-1]*ps+pBetaP5[iik][ks-1])*ps
+pBetaP4[iik][ks-1];
//find neighbor of i that is equal to k
for(jNeik=0;jNeik<numneigh[j];jNeik++) {
temp_jk=BOP_index[j]+jNeik;
if(x[jlist[jNeik]][0]==x[k][0]) {
if(x[jlist[jNeik]][1]==x[k][1]) {
if(x[jlist[jNeik]][2]==x[k][2]) {
break;
}
}
}
}
//find neighbor of k that is equal to j
for(kNeij=0;kNeij<numneigh[k];kNeij++) {
if(x[klist[kNeij]][0]==x[j][0]) {
if(x[klist[kNeij]][1]==x[j][1]) {
if(x[klist[kNeij]][2]==x[j][2]) {
break;
}
}
}
}
dis_jk[0]=x[k][0]-x[j][0];
dis_jk[1]=x[k][1]-x[j][1];
dis_jk[2]=x[k][2]-x[j][2];
rsq_jk=dis_jk[0]*dis_jk[0]
+dis_jk[1]*dis_jk[1]
+dis_jk[2]*dis_jk[2];
r_jk=sqrt(rsq_jk);
sig_flag=0;
for(nsearch=0;nsearch<nSigBk[n];nsearch++) {
ncmp=itypeSigBk[n][nsearch];
if(x[ncmp][0]==x[k][0]) {
if(x[ncmp][1]==x[k][1]) {
if(x[ncmp][2]==x[k][2]) {
nk0=nsearch;
sig_flag=1;
break;
}
}
}
}
if(sig_flag==0) {
nSigBk[n]=nSigBk[n]+1;
nk0=nSigBk[n]-1;
itypeSigBk[n][nk0]=k;
}
nb_ik=nb_t;
nb_t++;
if(nb_t>nb_sg) {
new_n_tot=nb_sg+maxneigh;
grow_sigma(nb_sg,new_n_tot);
nb_sg=new_n_tot;
}
bt_sg[nb_ik].temp=temp_ik;
bt_sg[nb_ik].i=i;
bt_sg[nb_ik].j=k;
nb_jk=nb_t;
nb_t++;
if(nb_t>nb_sg) {
new_n_tot=nb_sg+maxneigh;
grow_sigma(nb_sg,new_n_tot);
nb_sg=new_n_tot;
}
bt_sg[nb_jk].temp=temp_jk;
bt_sg[nb_jk].i=j;
bt_sg[nb_jk].j=k;
cosAng_jik=(dis_ij[0]*dis_ik[0]+dis_ij[1]*dis_ik[1]
+dis_ij[2]*dis_ik[2])/(r_ij*r_ik);
dcA_jik[0][0]=(dis_ik[0]*r_ij*r_ik-cosAng_jik
*dis_ij[0]*r_ik*r_ik)/(r_ij*r_ij*r_ik*r_ik);
dcA_jik[1][0]=(dis_ik[1]*r_ij*r_ik-cosAng_jik
*dis_ij[1]*r_ik*r_ik)/(r_ij*r_ij*r_ik*r_ik);
dcA_jik[2][0]=(dis_ik[2]*r_ij*r_ik-cosAng_jik
*dis_ij[2]*r_ik*r_ik)/(r_ij*r_ij*r_ik*r_ik);
dcA_jik[0][1]=(dis_ij[0]*r_ij*r_ik-cosAng_jik
*dis_ik[0]*r_ij*r_ij)/(r_ij*r_ij*r_ik*r_ik);
dcA_jik[1][1]=(dis_ij[1]*r_ij*r_ik-cosAng_jik
*dis_ik[1]*r_ij*r_ij)/(r_ij*r_ij*r_ik*r_ik);
dcA_jik[2][1]=(dis_ij[2]*r_ij*r_ik-cosAng_jik
*dis_ik[2]*r_ij*r_ij)/(r_ij*r_ij*r_ik*r_ik);
gmean0=sigma_g0[jtype-1][itype-1][ktype-1];
gmean1=sigma_g1[jtype-1][itype-1][ktype-1];
gmean2=sigma_g2[jtype-1][itype-1][ktype-1];
amean=cosAng_jik;
gfactor1=gmean0+gmean1*amean
+gmean2*amean*amean;
gfactorsq=gfactor1*gfactor1;
gprime1=gmean1+2.0*gmean2*amean;
gsqprime=2.0*gfactor1*gprime1;
//AA is Eq. 34 (a) or Eq. 10 (c) for the i atom
//1st CC is Eq. 11 (c) for i atom where j & k=neighbor of i
AA=AA+gfactorsq*betaS_ik*betaS_ik;
CC=CC+gfactorsq*betaS_ik*betaS_ik*betaS_ik*betaS_ik;
//agpdpr1 is derivative of AA w.r.t. Beta(rik)
//app1 is derivative of AA w.r.t. cos(theta_jik)
agpdpr1=2.0*gfactorsq*betaS_ik*dBetaS_ik/r_ik;
app1=betaS_ik*betaS_ik*gsqprime;
bt_sg[nb_ij].dAA[0]+=
app1*dcA_jik[0][0];
bt_sg[nb_ij].dAA[1]+=
app1*dcA_jik[1][0];
bt_sg[nb_ij].dAA[2]+=
app1*dcA_jik[2][0];
bt_sg[nb_ij].dCC[0]+=
app2*dcA_jik[0][0];
bt_sg[nb_ij].dCC[1]+=
app2*dcA_jik[1][0];
bt_sg[nb_ij].dCC[2]+=
app2*dcA_jik[2][0];
bt_sg[nb_ik].dAA[0]+=
app1*dcA_jik[0][1]
+agpdpr1*dis_ik[0];
bt_sg[nb_ik].dAA[1]+=
app1*dcA_jik[1][1]
+agpdpr1*dis_ik[1];
bt_sg[nb_ik].dAA[2]+=
app1*dcA_jik[2][1]
+agpdpr1*dis_ik[2];
bt_sg[nb_ik].dCC[0]+=
app2*dcA_jik[0][1]
+agpdpr2*dis_ik[0];
bt_sg[nb_ik].dCC[1]+=
app2*dcA_jik[1][1]
+agpdpr2*dis_ik[1];
bt_sg[nb_ik].dCC[2]+=
app2*dcA_jik[2][1]
+agpdpr2*dis_ik[2];
//k' is loop over neighbors all neighbors of j with k a neighbor
//of i and j a neighbor of i and determine which k' is k
same_kpk=0;
for(ltmp=0;ltmp<numneigh[j];ltmp++) {
temp_jkp=BOP_index[j]+ltmp;
kp1=jlist[ltmp];
kp1type=map[type[kp1]]+1;
if(x[kp1][0]==x[k][0]) {
if(x[kp1][1]==x[k][1]) {
if(x[kp1][2]==x[k][2]) {
same_kpk=1;
break;
}
}
}
}
if(same_kpk){
//loop over neighbors of k
for(mtmp=0;mtmp<numneigh[k];mtmp++) {
temp_kpj=BOP_index[k]+mtmp;
kp2=klist[mtmp];
if(x[kp2][0]==x[k][0]) {
if(x[kp2][1]==x[k][1]) {
if(x[kp2][2]==x[k][2]) {
break;
}
}
}
}
if(jtype==ktype)
ijk=jtype-1;
else if(jtype < ktype)
ijk=jtype*bop_types-jtype*(jtype+1)/2+ktype-1;
else
ijk=ktype*bop_types-ktype*(ktype+1)/2+jtype-1;
if(jtype==kp1type)
ijkp=jtype-1;
else if(jtype<kp1type)
ijkp=jtype*bop_types-jtype*(jtype+1)/2+kp1type-1;
else
ijkp=kp1type*bop_types-kp1type*(kp1type+1)/2+jtype-1;
dis_jkp[0]=x[kp1][0]-x[j][0];
dis_jkp[1]=x[kp1][1]-x[j][1];
dis_jkp[2]=x[kp1][2]-x[j][2];
rsq_jkp=dis_jkp[0]*dis_jkp[0]
+dis_jkp[1]*dis_jkp[1]
+dis_jkp[2]*dis_jkp[2];
r_jkp=sqrt(rsq_jkp);
if(r_jkp<=rcut[ijkp]) {
ps=r_jkp*rdr[ijkp]+1.0;
ks=(int)ps;
if(nr-1<ks)
ks=nr-1;
ps=ps-ks;
if(ps>1.0)
ps=1.0;
betaS_jkp=((pBetaS3[ijkp][ks-1]*ps+pBetaS2[ijkp][ks-1])*ps
+pBetaS1[ijkp][ks-1])*ps+pBetaS[ijkp][ks-1];
dBetaS_jkp=(pBetaS6[ijkp][ks-1]*ps+pBetaS5[ijkp][ks-1])*ps
+pBetaS4[ijkp][ks-1];
betaP_jkp=((pBetaP3[ijkp][ks-1]*ps+pBetaP2[ijkp][ks-1])*ps
+pBetaP1[ijkp][ks-1])*ps+pBetaP[ijkp][ks-1];
dBetaP_jkp=(pBetaP6[ijkp][ks-1]*ps+pBetaP5[ijkp][ks-1])*ps
+pBetaP4[ijkp][ks-1];
cosAng_ijk=(-dis_ij[0]*dis_jk[0]-dis_ij[1]*dis_jk[1]
-dis_ij[2]*dis_jk[2])/(r_ij*r_jk);
dcA_ijk[0][0]=(dis_jk[0]*r_ij*r_jk-cosAng_ijk
*-dis_ij[0]*r_jk*r_jk)/(r_ij*r_ij*r_jk*r_jk);
dcA_ijk[1][0]=(dis_jk[1]*r_ij*r_jk-cosAng_ijk
*-dis_ij[1]*r_jk*r_jk)/(r_ij*r_ij*r_jk*r_jk);
dcA_ijk[2][0]=(dis_jk[2]*r_ij*r_jk-cosAng_ijk
*-dis_ij[2]*r_jk*r_jk)/(r_ij*r_ij*r_jk*r_jk);
dcA_ijk[0][1]=(-dis_ij[0]*r_ij*r_jk-cosAng_ijk
*dis_jk[0]*r_ij*r_ij)/(r_ij*r_ij*r_jk*r_jk);
dcA_ijk[1][1]=(-dis_ij[1]*r_ij*r_jk-cosAng_ijk
*dis_jk[1]*r_ij*r_ij)/(r_ij*r_ij*r_jk*r_jk);
dcA_ijk[2][1]=(-dis_ij[2]*r_ij*r_jk-cosAng_ijk
*dis_jk[2]*r_ij*r_ij)/(r_ij*r_ij*r_jk*r_jk);
gmean0=sigma_g0[itype-1][jtype-1][ktype-1];
gmean1=sigma_g1[itype-1][jtype-1][ktype-1];
gmean2=sigma_g2[itype-1][jtype-1][ktype-1];
amean=cosAng_ijk;
gfactor2=gmean0+gmean1*amean
+gmean2*amean*amean;
gprime2=gmean1+2.0*gmean2*amean;
gmean0=sigma_g0[itype-1][ktype-1][jtype-1];
gmean1=sigma_g1[itype-1][ktype-1][jtype-1];
gmean2=sigma_g2[itype-1][ktype-1][jtype-1];
cosAng_ikj=(dis_ik[0]*dis_jk[0]+dis_ik[1]*dis_jk[1]
+dis_ik[2]*dis_jk[2])/(r_ik*r_jk);
dcA_ikj[0][0]=(-dis_jk[0]*r_ik*r_jk-cosAng_ikj
*-dis_ik[0]*r_jk*r_jk)/(r_ik*r_ik*r_jk*r_jk);
dcA_ikj[1][0]=(-dis_jk[1]*r_ik*r_jk-cosAng_ikj
*-dis_ik[1]*r_jk*r_jk)/(r_ik*r_ik*r_jk*r_jk);
dcA_ikj[2][0]=(-dis_jk[2]*r_ik*r_jk-cosAng_ikj
*-dis_ik[2]*r_jk*r_jk)/(r_ik*r_ik*r_jk*r_jk);
dcA_ikj[0][1]=(-dis_ik[0]*r_ik*r_jk-cosAng_ikj
*-dis_jk[0]*r_ik*r_ik)/(r_ik*r_ik*r_jk*r_jk);
dcA_ikj[1][1]=(-dis_ik[1]*r_ik*r_jk-cosAng_ikj
*-dis_jk[1]*r_ik*r_ik)/(r_ik*r_ik*r_jk*r_jk);
dcA_ikj[2][1]=(-dis_ik[2]*r_ik*r_jk-cosAng_ikj
*-dis_jk[2]*r_ik*r_ik)/(r_ik*r_ik*r_jk*r_jk);
amean=cosAng_ikj;
gfactor3=gmean0+gmean1*amean
+gmean2*amean*amean;
gprime3=gmean1+2.0*gmean2*amean;
gfactor=gfactor1*gfactor2*gfactor3;
rfactor=betaS_ik*betaS_jkp;
//EE1 is (b) Eq. 12
EE1=EE1+gfactor*rfactor;
//rcm1 is derivative of EE1 w.r.t Beta(r_ik)
//rcm2 is derivative of EE1 w.r.t Beta(r_jk')
//gcm1 is derivative of EE1 w.r.t cos(theta_jik)
//gcm2 is derivative of EE1 w.r.t cos(theta_ijk)
//gcm3 is derivative of EE1 w.r.t cos(theta_ikj)
rcm1=gfactor*betaS_jkp*dBetaS_ik/r_ik;
rcm2=gfactor*betaS_ik*dBetaS_jkp/r_jkp;
gcm1=rfactor*gprime1*gfactor2*gfactor3;
gcm2=rfactor*gfactor1*gprime2*gfactor3;
gcm3=rfactor*gfactor1*gfactor2*gprime3;
bt_sg[nb_ij].dEE1[0]+=
gcm1*dcA_jik[0][0]
-gcm2*dcA_ijk[0][0];
bt_sg[nb_ij].dEE1[1]+=
gcm1*dcA_jik[1][0]
-gcm2*dcA_ijk[1][0];
bt_sg[nb_ij].dEE1[2]+=
gcm1*dcA_jik[2][0]
-gcm2*dcA_ijk[2][0];
bt_sg[nb_ik].dEE1[0]+=
gcm1*dcA_jik[0][1]
+rcm1*dis_ik[0]
-gcm3*dcA_ikj[0][0];
bt_sg[nb_ik].dEE1[1]+=
gcm1*dcA_jik[1][1]
+rcm1*dis_ik[1]
-gcm3*dcA_ikj[1][0];
bt_sg[nb_ik].dEE1[2]+=
gcm1*dcA_jik[2][1]
+rcm1*dis_ik[2]
-gcm3*dcA_ikj[2][0];
bt_sg[nb_jk].dEE1[0]+=
gcm2*dcA_ijk[0][1]
+rcm2*dis_jkp[0]
-gcm3*dcA_ikj[0][1];
bt_sg[nb_jk].dEE1[1]+=
gcm2*dcA_ijk[1][1]
+rcm2*dis_jkp[1]
-gcm3*dcA_ikj[1][1];
bt_sg[nb_jk].dEE1[2]+=
gcm2*dcA_ijk[2][1]
+rcm2*dis_jkp[2]
-gcm3*dcA_ikj[2][1];
}
}
// k and k' and j are all different neighbors of i
for(ltmp=0;ltmp<ktmp;ltmp++) {
if(ltmp!=jtmp) {
temp_ikp=BOP_index[i]+ltmp;
kp=iilist[ltmp];;
kptype = map[type[kp]]+1;
if(itype==kptype)
iikp=itype-1;
else if(itype<kptype)
iikp=itype*bop_types-itype*(itype+1)/2+kptype-1;
else
iikp=kptype*bop_types-kptype*(kptype+1)/2+itype-1;
for(nsearch=0;nsearch<nSigBk[n];nsearch++) {
ncmp=itypeSigBk[n][nsearch];
if(x[ncmp][0]==x[kp][0]) {
if(x[ncmp][1]==x[kp][1]) {
if(x[ncmp][2]==x[kp][2]) {
break;
}
}
}
}
dis_ikp[0]=x[kp][0]-x[i][0];
dis_ikp[1]=x[kp][1]-x[i][1];
dis_ikp[2]=x[kp][2]-x[i][2];
rsq_ikp=dis_ikp[0]*dis_ikp[0]
+dis_ikp[1]*dis_ikp[1]
+dis_ikp[2]*dis_ikp[2];
r_ikp=sqrt(rsq_ikp);
if(r_ikp<=rcut[iikp]) {
ps=r_ikp*rdr[iikp]+1.0;
ks=(int)ps;
if(nr-1<ks)
ks=nr-1;
ps=ps-ks;
if(ps>1.0)
ps=1.0;
betaS_ikp=((pBetaS3[iikp][ks-1]*ps+pBetaS2[iikp][ks-1])*ps
+pBetaS1[iikp][ks-1])*ps+pBetaS[iikp][ks-1];
dBetaS_ikp=(pBetaS6[iikp][ks-1]*ps+pBetaS5[iikp][ks-1])*ps
+pBetaS4[iikp][ks-1];
betaP_ikp=((pBetaP3[iikp][ks-1]*ps+pBetaP2[iikp][ks-1])*ps
+pBetaP1[iikp][ks-1])*ps+pBetaP[iikp][ks-1];
dBetaP_ikp=(pBetaP6[iikp][ks-1]*ps+pBetaP5[iikp][ks-1])*ps
+pBetaP4[iikp][ks-1];
nb_ikp=nb_t;
nb_t++;
if(nb_t>nb_sg) {
new_n_tot=nb_sg+maxneigh;
grow_sigma(nb_sg,new_n_tot);
nb_sg=new_n_tot;
}
bt_sg[nb_ikp].temp=temp_ikp;
bt_sg[nb_ikp].i=i;
bt_sg[nb_ikp].j=kp;
gmean0=sigma_g0[jtype-1][itype-1][kptype-1];
gmean1=sigma_g1[jtype-1][itype-1][kptype-1];
gmean2=sigma_g2[jtype-1][itype-1][kptype-1];
cosAng_jikp=(dis_ij[0]*dis_ikp[0]+dis_ij[1]*dis_ikp[1]
+dis_ij[2]*dis_ikp[2])/(r_ij*r_ikp);
dcA_jikp[0][0]=(dis_ikp[0]*r_ij*r_ikp-cosAng_jikp
*dis_ij[0]*r_ikp*r_ikp)/(r_ij*r_ij*r_ikp*r_ikp);
dcA_jikp[1][0]=(dis_ikp[1]*r_ij*r_ikp-cosAng_jikp
*dis_ij[1]*r_ikp*r_ikp)/(r_ij*r_ij*r_ikp*r_ikp);
dcA_jikp[2][0]=(dis_ikp[2]*r_ij*r_ikp-cosAng_jikp
*dis_ij[2]*r_ikp*r_ikp)/(r_ij*r_ij*r_ikp*r_ikp);
dcA_jikp[0][1]=(dis_ij[0]*r_ij*r_ikp-cosAng_jikp
*dis_ikp[0]*r_ij*r_ij)/(r_ij*r_ij*r_ikp*r_ikp);
dcA_jikp[1][1]=(dis_ij[1]*r_ij*r_ikp-cosAng_jikp
*dis_ikp[1]*r_ij*r_ij)/(r_ij*r_ij*r_ikp*r_ikp);
dcA_jikp[2][1]=(dis_ij[2]*r_ij*r_ikp-cosAng_jikp
*dis_ikp[2]*r_ij*r_ij)/(r_ij*r_ij*r_ikp*r_ikp);
cosAng_kikp=(dis_ik[0]*dis_ikp[0]+dis_ik[1]*dis_ikp[1]
+dis_ik[2]*dis_ikp[2])/(r_ik*r_ikp);
dcA_kikp[0][0]=(dis_ikp[0]*r_ik*r_ikp-cosAng_kikp
*dis_ik[0]*r_ikp*r_ikp)/(r_ik*r_ik*r_ikp*r_ikp);
dcA_kikp[1][0]=(dis_ikp[1]*r_ik*r_ikp-cosAng_kikp
*dis_ik[1]*r_ikp*r_ikp)/(r_ik*r_ik*r_ikp*r_ikp);
dcA_kikp[2][0]=(dis_ikp[2]*r_ik*r_ikp-cosAng_kikp
*dis_ik[2]*r_ikp*r_ikp)/(r_ik*r_ik*r_ikp*r_ikp);
dcA_kikp[0][1]=(dis_ik[0]*r_ik*r_ikp-cosAng_kikp
*dis_ikp[0]*r_ik*r_ik)/(r_ik*r_ik*r_ikp*r_ikp);
dcA_kikp[1][1]=(dis_ik[1]*r_ik*r_ikp-cosAng_kikp
*dis_ikp[1]*r_ik*r_ik)/(r_ik*r_ik*r_ikp*r_ikp);
dcA_kikp[2][1]=(dis_ik[2]*r_ik*r_ikp-cosAng_kikp
*dis_ikp[2]*r_ik*r_ik)/(r_ik*r_ik*r_ikp*r_ikp);
amean=cosAng_jikp;
gfactor2=gmean0+gmean1*amean
+gmean2*amean*amean;
gprime2=gmean1+2.0*gmean2*amean;
gmean0=sigma_g0[ktype-1][itype-1][kptype-1];
gmean1=sigma_g1[ktype-1][itype-1][kptype-1];
gmean2=sigma_g2[ktype-1][itype-1][kptype-1];
amean=cosAng_kikp;
gfactor3=gmean0+gmean1*amean
+gmean2*amean*amean;
gprime3=gmean1+2.0*gmean2*amean;
gfactor=gfactor1*gfactor2*gfactor3;
rfactorrt=betaS_ik*betaS_ikp;
rfactor=rfactorrt*rfactorrt;
//2nd CC is second term of Eq. 11 (c) for i atom where j , k & k' =neighbor of i
CC=CC+2.0*gfactor*rfactor;
//agpdpr1 is derivative of CC 2nd term w.r.t. Beta(r_ik)
//agpdpr2 is derivative of CC 2nd term w.r.t. Beta(r_ik')
//app1 is derivative of CC 2nd term w.r.t. cos(theta_jik)
//app2 is derivative of CC 2nd term w.r.t. cos(theta_jik')
//app3 is derivative of CC 2nd term w.r.t. cos(theta_kik')
agpdpr1=4.0*gfactor*rfactorrt*betaS_ikp
*dBetaS_ik/r_ik;
agpdpr2=4.0*gfactor*rfactorrt*betaS_ik
*dBetaS_ikp/r_ikp;
app1=2.0*rfactor*gfactor2*gfactor3*gprime1;
app2=2.0*rfactor*gfactor1*gfactor3*gprime2;
app3=2.0*rfactor*gfactor1*gfactor2*gprime3;
bt_sg[nb_ij].dCC[0]+=
app1*dcA_jik[0][0]
+app2*dcA_jikp[0][0];
bt_sg[nb_ij].dCC[1]+=
app1*dcA_jik[1][0]
+app2*dcA_jikp[1][0];
bt_sg[nb_ij].dCC[2]+=
app1*dcA_jik[2][0]
+app2*dcA_jikp[2][0];
bt_sg[nb_ik].dCC[0]+=
app1*dcA_jik[0][1]
+app3*dcA_kikp[0][0]
+agpdpr1*dis_ik[0];
bt_sg[nb_ik].dCC[1]+=
app1*dcA_jik[1][1]
+app3*dcA_kikp[1][0]
+agpdpr1*dis_ik[1];
bt_sg[nb_ik].dCC[2]+=
app1*dcA_jik[2][1]
+app3*dcA_kikp[2][0]
+agpdpr1*dis_ik[2];
bt_sg[nb_ikp].dCC[0]=
app2*dcA_jikp[0][1]
+app3*dcA_kikp[0][1]
+agpdpr2*dis_ikp[0];
bt_sg[nb_ikp].dCC[1]=
app2*dcA_jikp[1][1]
+app3*dcA_kikp[1][1]
+agpdpr2*dis_ikp[1];
bt_sg[nb_ikp].dCC[2]=
app2*dcA_jikp[2][1]
+app3*dcA_kikp[2][1]
+agpdpr2*dis_ikp[2];
}
}
}
// j and k are different neighbors of i and k' is a neighbor k not equal to i
for(ltmp=0;ltmp<numneigh[k];ltmp++) {
temp_kkp=BOP_index[k]+ltmp;
kp=klist[ltmp];;
kptype = map[type[kp]]+1;
same_ikp=0;
same_jkp=0;
if(x[i][0]==x[kp][0]) {
if(x[i][1]==x[kp][1]) {
if(x[i][2]==x[kp][2]) {
same_ikp=1;
}
}
}
if(x[j][0]==x[kp][0]) {
if(x[j][1]==x[kp][1]) {
if(x[j][2]==x[kp][2]) {
same_jkp=1;
}
}
}
if(!same_ikp&&!same_jkp) {
if(ktype==kptype)
ikkp=ktype-1;
else if(ktype<kptype)
ikkp=ktype*bop_types-ktype*(ktype+1)/2+kptype-1;
else
ikkp=kptype*bop_types-kptype*(kptype+1)/2+ktype-1;
dis_kkp[0]=x[kp][0]-x[k][0];
dis_kkp[1]=x[kp][1]-x[k][1];
dis_kkp[2]=x[kp][2]-x[k][2];
rsq_kkp=dis_kkp[0]*dis_kkp[0]
+dis_kkp[1]*dis_kkp[1]
+dis_kkp[2]*dis_kkp[2];
r_kkp=sqrt(rsq_kkp);
if(r_kkp<=rcut[ikkp]) {
ps=r_kkp*rdr[ikkp]+1.0;
ks=(int)ps;
if(nr-1<ks)
ks=nr-1;
ps=ps-ks;
if(ps>1.0)
ps=1.0;
betaS_kkp=((pBetaS3[ikkp][ks-1]*ps+pBetaS2[ikkp][ks-1])*ps
+pBetaS1[ikkp][ks-1])*ps+pBetaS[ikkp][ks-1];
dBetaS_kkp=(pBetaS6[ikkp][ks-1]*ps+pBetaS5[ikkp][ks-1])*ps
+pBetaS4[ikkp][ks-1];
betaP_kkp=((pBetaP3[ikkp][ks-1]*ps+pBetaP2[ikkp][ks-1])*ps
+pBetaP1[ikkp][ks-1])*ps+pBetaP[ikkp][ks-1];
dBetaP_kkp=(pBetaP6[ikkp][ks-1]*ps+pBetaP5[ikkp][ks-1])*ps
+pBetaP4[ikkp][ks-1];
sig_flag=0;
for(nsearch=0;nsearch<nSigBk[n];nsearch++) {
ncmp=itypeSigBk[n][nsearch];
if(x[ncmp][0]==x[kp][0]) {
if(x[ncmp][1]==x[kp][1]) {
if(x[ncmp][2]==x[kp][2]) {
sig_flag=1;
nkp=nsearch;
break;
}
}
}
}
if(sig_flag==0) {
nSigBk[n]=nSigBk[n]+1;
nkp=nSigBk[n]-1;
itypeSigBk[n][nkp]=kp;
}
cosAng_ikkp=(-dis_ik[0]*dis_kkp[0]-dis_ik[1]*dis_kkp[1]
-dis_ik[2]*dis_kkp[2])/(r_ik*r_kkp);
dcA_ikkp[0][0]=(dis_kkp[0]*r_ik*r_kkp-cosAng_ikkp
*-dis_ik[0]*r_kkp*r_kkp)/(r_ik*r_ik*r_kkp*r_kkp);
dcA_ikkp[1][0]=(dis_kkp[1]*r_ik*r_kkp-cosAng_ikkp
*-dis_ik[1]*r_kkp*r_kkp)/(r_ik*r_ik*r_kkp*r_kkp);
dcA_ikkp[2][0]=(dis_kkp[2]*r_ik*r_kkp-cosAng_ikkp
*-dis_ik[2]*r_kkp*r_kkp)/(r_ik*r_ik*r_kkp*r_kkp);
dcA_ikkp[0][1]=(-dis_ik[0]*r_ik*r_kkp-cosAng_ikkp
*dis_kkp[0]*r_ik*r_ik)/(r_ik*r_ik*r_kkp*r_kkp);
dcA_ikkp[1][1]=(-dis_ik[1]*r_ik*r_kkp-cosAng_ikkp
*dis_kkp[1]*r_ik*r_ik)/(r_ik*r_ik*r_kkp*r_kkp);
dcA_ikkp[2][1]=(-dis_ik[2]*r_ik*r_kkp-cosAng_ikkp
*dis_kkp[2]*r_ik*r_ik)/(r_ik*r_ik*r_kkp*r_kkp);
nb_kkp=nb_t;
nb_t++;
if(nb_t>nb_sg) {
new_n_tot=nb_sg+maxneigh;
grow_sigma(nb_sg,new_n_tot);
nb_sg=new_n_tot;
}
bt_sg[nb_kkp].temp=temp_kkp;
bt_sg[nb_kkp].i=k;
bt_sg[nb_kkp].j=kp;
gmean0=sigma_g0[itype-1][ktype-1][kptype-1];
gmean1=sigma_g1[itype-1][ktype-1][kptype-1];
gmean2=sigma_g2[itype-1][ktype-1][kptype-1];
amean=cosAng_ikkp;
gfactor2=gmean0+gmean1*amean
+gmean2*amean*amean;
gprime2=gmean1+2.0*gmean2*amean;
gfactorsq2=gfactor2*gfactor2;
gsqprime2=2.0*gfactor2*gprime2;
gfactor=gfactorsq*gfactorsq2;
rfactorrt=betaS_ik*betaS_kkp;
rfactor=rfactorrt*rfactorrt;
//3rd CC is third term of Eq. 11 (c) for i atom
//where j , k =neighbor of i & k' =neighbor of k
CC=CC+gfactor*rfactor;
//agpdpr1 is derivative of CC 3rd term w.r.t. Beta(r_ik)
//agpdpr2 is derivative of CC 3rd term w.r.t. Beta(r_kk')
//app1 is derivative of CC 3rd term w.r.t. cos(theta_jik)
//app2 is derivative of CC 3rd term w.r.t. cos(theta_ikk')
agpdpr1=2.0*gfactor*rfactorrt*betaS_kkp
*dBetaS_ik/r_ik;
agpdpr2=2.0*gfactor*rfactorrt*betaS_ik
*dBetaS_kkp/r_kkp;
app1=rfactor*gfactorsq2*gsqprime;
app2=rfactor*gfactorsq*gsqprime2;
bt_sg[nb_ij].dCC[0]+=
app1*dcA_jik[0][0];
bt_sg[nb_ij].dCC[1]+=
app1*dcA_jik[1][0];
bt_sg[nb_ij].dCC[2]+=
app1*dcA_jik[2][0];
bt_sg[nb_ik].dCC[0]+=
app1*dcA_jik[0][1]
+agpdpr1*dis_ik[0]
-app2*dcA_ikkp[0][0];
bt_sg[nb_ik].dCC[1]+=
app1*dcA_jik[1][1]
+agpdpr1*dis_ik[1]
-app2*dcA_ikkp[1][0];
bt_sg[nb_ik].dCC[2]+=
app1*dcA_jik[2][1]
+agpdpr1*dis_ik[2]
-app2*dcA_ikkp[2][0];
bt_sg[nb_kkp].dCC[0]+=
app2*dcA_ikkp[0][1]
+agpdpr2*dis_kkp[0];
bt_sg[nb_kkp].dCC[1]+=
app2*dcA_ikkp[1][1]
+agpdpr2*dis_kkp[1];
bt_sg[nb_kkp].dCC[2]+=
app2*dcA_ikkp[2][1]
+agpdpr2*dis_kkp[2];
}
}
}
//j and k are different neighbors of i and k' is a neighbor j not equal to k
for(ltmp=0;ltmp<numneigh[j];ltmp++) {
sig_flag=0;
temp_jkp=BOP_index[j]+ltmp;
kp=jlist[ltmp];
kptype = map[type[kp]]+1;
kplist=firstneigh[kp];
same_kkpk=0;
same_jkpj=0;
for(kpNeij=0;kpNeij<numneigh[kp];kpNeij++) {
temp_kpj=BOP_index[kp]+kpNeij;
kpj=kplist[kpNeij];
if(x[j][0]==x[kpj][0]) {
if(x[j][1]==x[kpj][1]) {
if(x[j][2]==x[kpj][2]) {
same_jkpj=1;
break;
}
}
}
}
for(kpNeik=0;kpNeik<numneigh[kp];kpNeik++) {
temp_kpk=BOP_index[kp]+kpNeik;
kpk=kplist[kpNeik];
if(x[k][0]==x[kpk][0]) {
if(x[k][1]==x[kpk][1]) {
if(x[k][2]==x[kpk][2]) {
same_kkpk=1;
break;
}
}
}
}
if(!same_jkpj&&!same_kkpk) {
same_kkpk=0;
for(kNeikp=0;kNeikp<numneigh[k];kNeikp++) {
temp_kkp=BOP_index[k]+kNeikp;
kkp=kplist[kNeikp];
if(x[kp][0]==x[kkp][0]) {
if(x[kp][1]==x[kkp][1]) {
if(x[kp][2]==x[kkp][2]) {
sig_flag=1;
break;
}
}
}
}
if(sig_flag==1) {
for(nsearch=0;nsearch<numneigh[kp];nsearch++) {
kp_nsearch=BOP_index[kp]+nsearch;
ncmp=kplist[nsearch];
if(x[ncmp][0]==x[j][0]) {
if(x[ncmp][1]==x[j][1]) {
if(x[ncmp][2]==x[j][2]) {
kpNeij=nsearch;
}
}
}
if(x[ncmp][0]==x[k][0]) {
if(x[ncmp][1]==x[k][1]) {
if(x[ncmp][2]==x[k][2]) {
kpNeik=nsearch;
}
}
}
}
if(jtype==kptype)
ijkp=jtype-1;
else if(jtype<kptype)
ijkp=jtype*bop_types-jtype*(jtype+1)/2+kptype-1;
else
ijkp=kptype*bop_types-kptype*(kptype+1)/2+jtype-1;
if(ktype==kptype)
ikkp=ktype-1;
else if(ktype<kptype)
ikkp=ktype*bop_types-ktype*(ktype+1)/2+kptype-1;
else
ikkp=kptype*bop_types-kptype*(kptype+1)/2+ktype-1;
dis_jkp[0]=x[kp][0]-x[j][0];
dis_jkp[1]=x[kp][1]-x[j][1];
dis_jkp[2]=x[kp][2]-x[j][2];
rsq_jkp=dis_jkp[0]*dis_jkp[0]
+dis_jkp[1]*dis_jkp[1]
+dis_jkp[2]*dis_jkp[2];
r_jkp=sqrt(rsq_jkp);
ps=r_jkp*rdr[ijkp]+1.0;
ks=(int)ps;
if(nr-1<ks)
ks=nr-1;
ps=ps-ks;
if(ps>1.0)
ps=1.0;
betaS_jkp=((pBetaS3[ijkp][ks-1]*ps+pBetaS2[ijkp][ks-1])*ps
+pBetaS1[ijkp][ks-1])*ps+pBetaS[ijkp][ks-1];
dBetaS_jkp=(pBetaS6[ijkp][ks-1]*ps+pBetaS5[ijkp][ks-1])*ps
+pBetaS4[ijkp][ks-1];
betaP_jkp=((pBetaP3[ijkp][ks-1]*ps+pBetaP2[ijkp][ks-1])*ps
+pBetaP1[ijkp][ks-1])*ps+pBetaP[ijkp][ks-1];
dBetaP_jkp=(pBetaP6[ijkp][ks-1]*ps+pBetaP5[ijkp][ks-1])*ps
+pBetaP4[ijkp][ks-1];
dis_kkp[0]=x[kp][0]-x[k][0];
dis_kkp[1]=x[kp][1]-x[k][1];
dis_kkp[2]=x[kp][2]-x[k][2];
rsq_kkp=dis_kkp[0]*dis_kkp[0]
+dis_kkp[1]*dis_kkp[1]
+dis_kkp[2]*dis_kkp[2];
r_kkp=sqrt(rsq_kkp);
ps=r_kkp*rdr[ikkp]+1.0;
ks=(int)ps;
if(nr-1<ks)
ks=nr-1;
ps=ps-ks;
if(ps>1.0)
ps=1.0;
betaS_kkp=((pBetaS3[ikkp][ks-1]*ps+pBetaS2[ikkp][ks-1])*ps
+pBetaS1[ikkp][ks-1])*ps+pBetaS[ikkp][ks-1];
dBetaS_kkp=(pBetaS6[ikkp][ks-1]*ps+pBetaS5[ikkp][ks-1])*ps
+pBetaS4[ikkp][ks-1];
betaP_kkp=((pBetaP3[ikkp][ks-1]*ps+pBetaP2[ikkp][ks-1])*ps
+pBetaP1[ikkp][ks-1])*ps+pBetaP[ikkp][ks-1];
dBetaP_kkp=(pBetaP6[ikkp][ks-1]*ps+pBetaP5[ikkp][ks-1])*ps
+pBetaP4[ikkp][ks-1];
cosAng_ijkp=(-dis_ij[0]*dis_jkp[0]-dis_ij[1]*dis_jkp[1]
-dis_ij[2]*dis_jkp[2])/(r_ij*r_jkp);
dcA_ijkp[0][0]=(dis_jkp[0]*r_ij*r_jkp-cosAng_ijkp
*-dis_ij[0]*r_jkp*r_jkp)/(r_ij*r_ij*r_jkp*r_jkp);
dcA_ijkp[1][0]=(dis_jkp[1]*r_ij*r_jkp-cosAng_ijkp
*-dis_ij[1]*r_jkp*r_jkp)/(r_ij*r_ij*r_jkp*r_jkp);
dcA_ijkp[2][0]=(dis_jkp[2]*r_ij*r_jkp-cosAng_ijkp
*-dis_ij[2]*r_jkp*r_jkp)/(r_ij*r_ij*r_jkp*r_jkp);
dcA_ijkp[0][1]=(-dis_ij[0]*r_ij*r_jkp-cosAng_ijkp
*dis_jkp[0]*r_ij*r_ij)/(r_ij*r_ij*r_jkp*r_jkp);
dcA_ijkp[1][1]=(-dis_ij[1]*r_ij*r_jkp-cosAng_ijkp
*dis_jkp[1]*r_ij*r_ij)/(r_ij*r_ij*r_jkp*r_jkp);
dcA_ijkp[2][1]=(-dis_ij[2]*r_ij*r_jkp-cosAng_ijkp
*dis_jkp[2]*r_ij*r_ij)/(r_ij*r_ij*r_jkp*r_jkp);
cosAng_ikkp=(-dis_ik[0]*dis_kkp[0]-dis_ik[1]*dis_kkp[1]
-dis_ik[2]*dis_kkp[2])/(r_ik*r_kkp);
dcA_ikkp[0][0]=(dis_kkp[0]*r_ik*r_kkp-cosAng_ikkp
*-dis_ik[0]*r_kkp*r_kkp)/(r_ik*r_ik*r_kkp*r_kkp);
dcA_ikkp[1][0]=(dis_kkp[1]*r_ik*r_kkp-cosAng_ikkp
*-dis_ik[1]*r_kkp*r_kkp)/(r_ik*r_ik*r_kkp*r_kkp);
dcA_ikkp[2][0]=(dis_kkp[2]*r_ik*r_kkp-cosAng_ikkp
*-dis_ik[2]*r_kkp*r_kkp)/(r_ik*r_ik*r_kkp*r_kkp);
dcA_ikkp[0][1]=(-dis_ik[0]*r_ik*r_kkp-cosAng_ikkp
*dis_kkp[0]*r_ik*r_ik)/(r_ik*r_ik*r_kkp*r_kkp);
dcA_ikkp[1][1]=(-dis_ik[1]*r_ik*r_kkp-cosAng_ikkp
*dis_kkp[1]*r_ik*r_ik)/(r_ik*r_ik*r_kkp*r_kkp);
dcA_ikkp[2][1]=(-dis_ik[2]*r_ik*r_kkp-cosAng_ikkp
*dis_kkp[2]*r_ik*r_ik)/(r_ik*r_ik*r_kkp*r_kkp);
cosAng_jkpk=(dis_jkp[0]*dis_kkp[0]+dis_jkp[1]*dis_kkp[1]
+dis_jkp[2]*dis_kkp[2])/(r_jkp*r_kkp);
dcA_jkpk[0][0]=(-dis_kkp[0]*r_jkp*r_kkp-cosAng_jkpk
*-dis_jkp[0]*r_kkp*r_kkp)/(r_jkp*r_jkp*r_kkp*r_kkp);
dcA_jkpk[1][0]=(-dis_kkp[1]*r_jkp*r_kkp-cosAng_jkpk
*-dis_jkp[1]*r_kkp*r_kkp)/(r_jkp*r_jkp*r_kkp*r_kkp);
dcA_jkpk[2][0]=(-dis_kkp[2]*r_jkp*r_kkp-cosAng_jkpk
*-dis_jkp[2]*r_kkp*r_kkp)/(r_jkp*r_jkp*r_kkp*r_kkp);
dcA_jkpk[0][1]=(-dis_jkp[0]*r_jkp*r_kkp-cosAng_jkpk
*-dis_kkp[0]*r_jkp*r_jkp)/(r_jkp*r_jkp*r_kkp*r_kkp);
dcA_jkpk[1][1]=(-dis_jkp[1]*r_jkp*r_kkp-cosAng_jkpk
*-dis_kkp[1]*r_jkp*r_jkp)/(r_jkp*r_jkp*r_kkp*r_kkp);
dcA_jkpk[2][1]=(-dis_jkp[2]*r_jkp*r_kkp-cosAng_jkpk
*-dis_kkp[2]*r_jkp*r_jkp)/(r_jkp*r_jkp*r_kkp*r_kkp);
sig_flag=0;
for(nsearch=0;nsearch<nSigBk[n];nsearch++) {
ncmp=itypeSigBk[n][nsearch];
if(x[ncmp][0]==x[kp][0]) {
if(x[ncmp][1]==x[kp][1]) {
if(x[ncmp][2]==x[kp][2]) {
nkp=nsearch;
sig_flag=1;
break;
}
}
}
}
if(sig_flag==0) {
nSigBk[n]=nSigBk[n]+1;
nkp=nSigBk[n]-1;
itypeSigBk[n][nkp]=kp;
}
temp_kpk=BOP_index[kp]+kpNeik;
nb_jkp=nb_t;
nb_t++;
if(nb_t>nb_sg) {
new_n_tot=nb_sg+maxneigh;
grow_sigma(nb_sg,new_n_tot);
nb_sg=new_n_tot;
}
bt_sg[nb_jkp].temp=temp_jkp;
bt_sg[nb_jkp].i=j;
bt_sg[nb_jkp].j=kp;
nb_kkp=nb_t;
nb_t++;
if(nb_t>nb_sg) {
new_n_tot=nb_sg+maxneigh;
grow_sigma(nb_sg,new_n_tot);
nb_sg=new_n_tot;
}
bt_sg[nb_kkp].temp=temp_kkp;
bt_sg[nb_kkp].i=k;
bt_sg[nb_kkp].j=kp;
gmean0=sigma_g0[itype-1][jtype-1][kptype-1];
gmean1=sigma_g1[itype-1][jtype-1][kptype-1];
gmean2=sigma_g2[itype-1][jtype-1][kptype-1];
amean=cosAng_ijkp;
gfactor2=gmean0+gmean1*amean
+gmean2*amean*amean;
gprime2=gmean1+2.0*gmean2*amean;
gmean0=sigma_g0[itype-1][ktype-1][kptype-1];
gmean1=sigma_g1[itype-1][ktype-1][kptype-1];
gmean2=sigma_g2[itype-1][ktype-1][kptype-1];
amean=cosAng_ikkp;
gfactor3=gmean0+gmean1*amean
+gmean2*amean*amean;
gprime3=gmean1+2.0*gmean2*amean;
gmean0=sigma_g0[jtype-1][kptype-1][ktype-1];
gmean1=sigma_g1[jtype-1][kptype-1][ktype-1];
gmean2=sigma_g2[jtype-1][kptype-1][ktype-1];
amean=cosAng_jkpk;
gfactor4=gmean0+gmean1*amean
+gmean2*amean*amean;
gprime4=gmean1+2.0*gmean2*amean;
gfactor=gfactor1*gfactor2*gfactor3*gfactor4;
rfactor0=(betaS_ik+small2)*(betaS_jkp+small2)
*(betaS_kkp+small2);
rfactor=pow(rfactor0,2.0/3.0);
drfactor=2.0/3.0*pow(rfactor0,-1.0/3.0);
//EE is Eq. 25(notes)
EE=EE+gfactor*rfactor;
//agpdpr1 is derivative of agpdpr1 w.r.t. Beta(r_ik)
//agpdpr2 is derivative of agpdpr1 w.r.t. Beta(r_jk')
//agpdpr3 is derivative of agpdpr1 w.r.t. Beta(r_kk')
//app1 is derivative of agpdpr1 w.r.t. cos(theta_jik)
//app2 is derivative of agpdpr1 w.r.t. cos(theta_ijk')
//app3 is derivative of agpdpr1 w.r.t. cos(theta_ikk')
//app4 is derivative of agpdpr1 w.r.t. cos(theta_jk'k)
agpdpr1=gfactor*drfactor*(betaS_jkp+small2)*(betaS_kkp
+small2)*dBetaS_ik/r_ik;
agpdpr2=gfactor*drfactor*(betaS_ik+small2)*(betaS_kkp
+small2)*dBetaS_jkp/r_jkp;
agpdpr3=gfactor*drfactor*(betaS_ik+small2)*(betaS_jkp
+small2)*dBetaS_kkp/r_kkp;
app1=rfactor*gfactor2*gfactor3*gfactor4*gprime1;
app2=rfactor*gfactor1*gfactor3*gfactor4*gprime2;
app3=rfactor*gfactor1*gfactor2*gfactor4*gprime3;
app4=rfactor*gfactor1*gfactor2*gfactor3*gprime4;
bt_sg[nb_ij].dEE[0]+=
app1*dcA_jik[0][0]
-app2*dcA_ijkp[0][0];
bt_sg[nb_ij].dEE[1]+=
app1*dcA_jik[1][0]
-app2*dcA_ijkp[1][0];
bt_sg[nb_ij].dEE[2]+=
app1*dcA_jik[2][0]
-app2*dcA_ijkp[2][0];
bt_sg[nb_ik].dEE[0]+=
app1*dcA_jik[0][1]
+agpdpr1*dis_ik[0]
-app3*dcA_ikkp[0][0];
bt_sg[nb_ik].dEE[1]+=
app1*dcA_jik[1][1]
+agpdpr1*dis_ik[1]
-app3*dcA_ikkp[1][0];
bt_sg[nb_ik].dEE[2]+=
app1*dcA_jik[2][1]
+agpdpr1*dis_ik[2]
-app3*dcA_ikkp[2][0];
bt_sg[nb_jkp].dEE[0]+=
app2*dcA_ijkp[0][1]
+agpdpr2*dis_jkp[0]
-app4*dcA_jkpk[0][0];
bt_sg[nb_jkp].dEE[1]+=
app2*dcA_ijkp[1][1]
+agpdpr2*dis_jkp[1]
-app4*dcA_jkpk[1][0];
bt_sg[nb_jkp].dEE[2]+=
app2*dcA_ijkp[2][1]
+agpdpr2*dis_jkp[2]
-app4*dcA_jkpk[2][0];
bt_sg[nb_kkp].dEE[0]+=
app3*dcA_ikkp[0][1]
+agpdpr3*dis_kkp[0]
-app4*dcA_jkpk[0][1];
bt_sg[nb_kkp].dEE[1]+=
app3*dcA_ikkp[1][1]
+agpdpr3*dis_kkp[1]
-app4*dcA_jkpk[1][1];
bt_sg[nb_kkp].dEE[2]+=
app3*dcA_ikkp[2][1]
+agpdpr3*dis_kkp[2]
-app4*dcA_jkpk[2][1];
}
}
}
}
}
}
//j is a neighbor of i and k is a neighbor of j not equal to i
for(ktmp=0;ktmp<numneigh[j];ktmp++) {
if(ktmp!=ji) {
temp_jk=BOP_index[j]+ktmp;
k=jlist[ktmp];
klist=firstneigh[k];
ktype=map[type[k]]+1;
for(kNeij=0;kNeij<numneigh[k];kNeij++) {
if(x[klist[kNeij]][0]==x[j][0]) {
if(x[klist[kNeij]][1]==x[j][1]) {
if(x[klist[kNeij]][2]==x[j][2]) {
break;
}
}
}
}
if(jtype==ktype)
ijk=jtype-1;
else if(jtype<ktype)
ijk=jtype*bop_types-jtype*(jtype+1)/2+ktype-1;
else
ijk=ktype*bop_types-ktype*(ktype+1)/2+jtype-1;
sig_flag=0;
for(nsearch=0;nsearch<nSigBk[n];nsearch++) {
ncmp=itypeSigBk[n][nsearch];
if(x[ncmp][0]==x[k][0]) {
if(x[ncmp][1]==x[k][1]) {
if(x[ncmp][2]==x[k][2]) {
new1=nsearch;
sig_flag=1;
break;
}
}
}
}
if(sig_flag==0) {
nSigBk[n]=nSigBk[n]+1;
new1=nSigBk[n]-1;
itypeSigBk[n][new1]=k;
}
dis_jk[0]=x[k][0]-x[j][0];
dis_jk[1]=x[k][1]-x[j][1];
dis_jk[2]=x[k][2]-x[j][2];
rsq_jk=dis_jk[0]*dis_jk[0]
+dis_jk[1]*dis_jk[1]
+dis_jk[2]*dis_jk[2];
r_jk=sqrt(rsq_jk);
if(r_jk<=rcut[ijk]) {
ps=r_jk*rdr[ijk]+1.0;
ks=(int)ps;
if(nr-1<ks)
ks=nr-1;
ps=ps-ks;
if(ps>1.0)
ps=1.0;
betaS_jk=((pBetaS3[ijk][ks-1]*ps+pBetaS2[ijk][ks-1])*ps
+pBetaS1[ijk][ks-1])*ps+pBetaS[ijk][ks-1];
dBetaS_jk=(pBetaS6[ijk][ks-1]*ps+pBetaS5[ijk][ks-1])*ps
+pBetaS4[ijk][ks-1];
betaP_jk=((pBetaP3[ijk][ks-1]*ps+pBetaP2[ijk][ks-1])*ps
+pBetaP1[ijk][ks-1])*ps+pBetaP[ijk][ks-1];
dBetaP_jk=(pBetaP6[ijk][ks-1]*ps+pBetaP5[ijk][ks-1])*ps
+pBetaP4[ijk][ks-1];
cosAng_ijk=(-dis_ij[0]*dis_jk[0]-dis_ij[1]*dis_jk[1]
-dis_ij[2]*dis_jk[2])/(r_ij*r_jk);
dcA_ijk[0][0]=(dis_jk[0]*r_ij*r_jk-cosAng_ijk
*-dis_ij[0]*r_jk*r_jk)/(r_ij*r_ij*r_jk*r_jk);
dcA_ijk[1][0]=(dis_jk[1]*r_ij*r_jk-cosAng_ijk
*-dis_ij[1]*r_jk*r_jk)/(r_ij*r_ij*r_jk*r_jk);
dcA_ijk[2][0]=(dis_jk[2]*r_ij*r_jk-cosAng_ijk
*-dis_ij[2]*r_jk*r_jk)/(r_ij*r_ij*r_jk*r_jk);
dcA_ijk[0][1]=(-dis_ij[0]*r_ij*r_jk-cosAng_ijk
*dis_jk[0]*r_ij*r_ij)/(r_ij*r_ij*r_jk*r_jk);
dcA_ijk[1][1]=(-dis_ij[1]*r_ij*r_jk-cosAng_ijk
*dis_jk[1]*r_ij*r_ij)/(r_ij*r_ij*r_jk*r_jk);
dcA_ijk[2][1]=(-dis_ij[2]*r_ij*r_jk-cosAng_ijk
*dis_jk[2]*r_ij*r_ij)/(r_ij*r_ij*r_jk*r_jk);
nb_jk=nb_t;
nb_t++;
if(nb_t>nb_sg) {
new_n_tot=nb_sg+maxneigh;
grow_sigma(nb_sg,new_n_tot);
nb_sg=new_n_tot;
}
bt_sg[nb_jk].temp=temp_jk;
bt_sg[nb_jk].i=j;
bt_sg[nb_jk].j=k;
gmean0=sigma_g0[itype-1][jtype-1][ktype-1];
gmean1=sigma_g1[itype-1][jtype-1][ktype-1];
gmean2=sigma_g2[itype-1][jtype-1][ktype-1];
amean=cosAng_ijk;
gfactor1=gmean0+gmean1*amean
+gmean2*amean*amean;
gprime1=gmean1+2.0*gmean2*amean;
gfactorsq=gfactor1*gfactor1;
gsqprime=2.0*gfactor1*gprime1;
rfactor1rt=betaS_jk*betaS_jk;
rfactor1=rfactor1rt*rfactor1rt;
//BB is Eq. 34 (a) or Eq. 10 (c) for the j atom
//1st DD is Eq. 11 (c) for j atom where i & k=neighbor of j
BB=BB+gfactorsq*rfactor1rt;
DD=DD+gfactorsq*rfactor1;
//agpdpr1 is derivative of BB w.r.t. Beta(r_jk)
//app1 is derivative of BB w.r.t. cos(theta_ijk)
agpdpr1=2.0*gfactorsq*betaS_jk*dBetaS_jk/r_jk;
agpdpr2=2.0*rfactor1rt*agpdpr1;
app1=rfactor1rt*gsqprime;
app2=rfactor1rt*app1;
bt_sg[nb_ij].dBB[0]-=
app1*dcA_ijk[0][0];
bt_sg[nb_ij].dBB[1]-=
app1*dcA_ijk[1][0];
bt_sg[nb_ij].dBB[2]-=
app1*dcA_ijk[2][0];
bt_sg[nb_ij].dDD[0]-=
app2*dcA_ijk[0][0];
bt_sg[nb_ij].dDD[1]-=
app2*dcA_ijk[1][0];
bt_sg[nb_ij].dDD[2]-=
app2*dcA_ijk[2][0];
bt_sg[nb_jk].dBB[0]+=
app1*dcA_ijk[0][1]
+agpdpr1*dis_jk[0];
bt_sg[nb_jk].dBB[1]+=
app1*dcA_ijk[1][1]
+agpdpr1*dis_jk[1];
bt_sg[nb_jk].dBB[2]+=
app1*dcA_ijk[2][1]
+agpdpr1*dis_jk[2];
bt_sg[nb_jk].dDD[0]+=
app2*dcA_ijk[0][1]
+agpdpr2*dis_jk[0];
bt_sg[nb_jk].dDD[1]+=
app2*dcA_ijk[1][1]
+agpdpr2*dis_jk[1];
bt_sg[nb_jk].dDD[2]+=
app2*dcA_ijk[2][1]
+agpdpr2*dis_jk[2];
//j is a neighbor of i, k and k' prime different neighbors of j not equal to i
for(ltmp=0;ltmp<ktmp;ltmp++) {
if(ltmp!=ji) {
temp_jkp=BOP_index[j]+ltmp;
kp=jlist[ltmp];
kptype=map[type[kp]]+1;
if(jtype==kptype)
ijkp=jtype-1;
else if(jtype<kptype)
ijkp=jtype*bop_types-jtype*(jtype+1)/2+kptype-1;
else
ijkp=kptype*bop_types-kptype*(kptype+1)/2+jtype-1;
for(nsearch=0;nsearch<nSigBk[n];nsearch++) {
ncmp=itypeSigBk[n][nsearch];
if(x[ncmp][0]==x[kp][0]) {
if(x[ncmp][1]==x[kp][1]) {
if(x[ncmp][2]==x[kp][2]) {
new2=nsearch;
break;
}
}
}
}
dis_jkp[0]=x[kp][0]-x[j][0];
dis_jkp[1]=x[kp][1]-x[j][1];
dis_jkp[2]=x[kp][2]-x[j][2];
rsq_jkp=dis_jkp[0]*dis_jkp[0]
+dis_jkp[1]*dis_jkp[1]
+dis_jkp[2]*dis_jkp[2];
r_jkp=sqrt(rsq_jkp);
if(r_jkp<=rcut[ijkp]) {
ps=r_jkp*rdr[ijkp]+1.0;
ks=(int)ps;
if(nr-1<ks)
ks=nr-1;
ps=ps-ks;
if(ps>1.0)
ps=1.0;
betaS_jkp=((pBetaS3[ijkp][ks-1]*ps+pBetaS2[ijkp][ks-1])*ps
+pBetaS1[ijkp][ks-1])*ps+pBetaS[ijkp][ks-1];
dBetaS_jkp=(pBetaS6[ijkp][ks-1]*ps+pBetaS5[ijkp][ks-1])*ps
+pBetaS4[ijkp][ks-1];
betaP_jkp=((pBetaP3[ijkp][ks-1]*ps+pBetaP2[ijkp][ks-1])*ps
+pBetaP1[ijkp][ks-1])*ps+pBetaP[ijkp][ks-1];
dBetaP_jkp=(pBetaP6[ijkp][ks-1]*ps+pBetaP5[ijkp][ks-1])*ps
+pBetaP4[ijkp][ks-1];
cosAng_ijkp=(-dis_ij[0]*dis_jkp[0]-dis_ij[1]*dis_jkp[1]
-dis_ij[2]*dis_jkp[2])/(r_ij*r_jkp);
dcA_ijkp[0][0]=(dis_jkp[0]*r_ij*r_jkp-cosAng_ijkp
*-dis_ij[0]*r_jkp*r_jkp)/(r_ij*r_ij*r_jkp*r_jkp);
dcA_ijkp[1][0]=(dis_jkp[1]*r_ij*r_jkp-cosAng_ijkp
*-dis_ij[1]*r_jkp*r_jkp)/(r_ij*r_ij*r_jkp*r_jkp);
dcA_ijkp[2][0]=(dis_jkp[2]*r_ij*r_jkp-cosAng_ijkp
*-dis_ij[2]*r_jkp*r_jkp)/(r_ij*r_ij*r_jkp*r_jkp);
dcA_ijkp[0][1]=(-dis_ij[0]*r_ij*r_jkp-cosAng_ijkp
*dis_jkp[0]*r_ij*r_ij)/(r_ij*r_ij*r_jkp*r_jkp);
dcA_ijkp[1][1]=(-dis_ij[1]*r_ij*r_jkp-cosAng_ijkp
*dis_jkp[1]*r_ij*r_ij)/(r_ij*r_ij*r_jkp*r_jkp);
dcA_ijkp[2][1]=(-dis_ij[2]*r_ij*r_jkp-cosAng_ijkp
*dis_jkp[2]*r_ij*r_ij)/(r_ij*r_ij*r_jkp*r_jkp);
cosAng_kjkp=(dis_jk[0]*dis_jkp[0]+dis_jk[1]*dis_jkp[1]
+dis_jk[2]*dis_jkp[2])/(r_jk*r_jkp);
dcA_kjkp[0][0]=(dis_jkp[0]*r_jk*r_jkp-cosAng_kjkp
*dis_jk[0]*r_jkp*r_jkp)/(r_jk*r_jk*r_jkp*r_jkp);
dcA_kjkp[1][0]=(dis_jkp[1]*r_jk*r_jkp-cosAng_kjkp
*dis_jk[1]*r_jkp*r_jkp)/(r_jk*r_jk*r_jkp*r_jkp);
dcA_kjkp[2][0]=(dis_jkp[2]*r_jk*r_jkp-cosAng_kjkp
*dis_jk[2]*r_jkp*r_jkp)/(r_jk*r_jk*r_jkp*r_jkp);
dcA_kjkp[0][1]=(dis_jk[0]*r_jk*r_jkp-cosAng_kjkp
*dis_jkp[0]*r_jk*r_jk)/(r_jk*r_jk*r_jkp*r_jkp);
dcA_kjkp[1][1]=(dis_jk[1]*r_jk*r_jkp-cosAng_kjkp
*dis_jkp[1]*r_jk*r_jk)/(r_jk*r_jk*r_jkp*r_jkp);
dcA_kjkp[2][1]=(dis_jk[2]*r_jk*r_jkp-cosAng_kjkp
*dis_jkp[2]*r_jk*r_jk)/(r_jk*r_jk*r_jkp*r_jkp);
nb_jkp=nb_t;
nb_t++;
if(nb_t>nb_sg) {
new_n_tot=nb_sg+maxneigh;
grow_sigma(nb_sg,new_n_tot);
nb_sg=new_n_tot;
}
bt_sg[nb_jkp].temp=temp_jkp;
bt_sg[nb_jkp].i=j;
bt_sg[nb_jkp].j=kp;
gmean0=sigma_g0[itype-1][jtype-1][kptype-1];
gmean1=sigma_g1[itype-1][jtype-1][kptype-1];
gmean2=sigma_g2[itype-1][jtype-1][kptype-1];
amean=cosAng_ijkp;
gfactor2=gmean0+gmean1*amean
+gmean2*amean*amean;
gprime2=gmean1+2.0*gmean2*amean;
gmean0=sigma_g0[ktype-1][jtype-1][kptype-1];
gmean1=sigma_g1[ktype-1][jtype-1][kptype-1];
gmean2=sigma_g2[ktype-1][jtype-1][kptype-1];
amean=cosAng_kjkp;
gfactor3=gmean0+gmean1*amean
+gmean2*amean*amean;
gprime3=gmean1+2.0*gmean2*amean;
gfactor=gfactor1*gfactor2*gfactor3;
rfactorrt=betaS_jk*betaS_jkp;
rfactor=rfactorrt*rfactorrt;
//2nd DD is Eq. 11 (c) for j atom where i , k & k'=neighbor of j
DD=DD+2.0*gfactor*rfactor;
//agpdpr1 is derivative of DD w.r.t. Beta(r_jk)
//agpdpr2 is derivative of DD w.r.t. Beta(r_jk')
//app1 is derivative of DD w.r.t. cos(theta_ijk)
//app2 is derivative of DD w.r.t. cos(theta_ijkp)
//app3 is derivative of DD w.r.t. cos(theta_kjkp)
agpdpr1=4.0*gfactor*rfactorrt*betaS_jkp
*dBetaS_jk/r_jk;
agpdpr2=4.0*gfactor*rfactorrt*betaS_jk
*dBetaS_jkp/r_jkp;
app1=2.0*rfactor*gfactor2*gfactor3*gprime1;
app2=2.0*rfactor*gfactor1*gfactor3*gprime2;
app3=2.0*rfactor*gfactor1*gfactor2*gprime3;
bt_sg[nb_ij].dDD[0]-=
app1*dcA_ijk[0][0]
+app2*dcA_ijkp[0][0];
bt_sg[nb_ij].dDD[1]-=
app1*dcA_ijk[1][0]
+app2*dcA_ijkp[1][0];
bt_sg[nb_ij].dDD[2]-=
app1*dcA_ijk[2][0]
+app2*dcA_ijkp[2][0];
bt_sg[nb_jk].dDD[0]+=
app1*dcA_ijk[0][1]
+app3*dcA_kjkp[0][0]
+agpdpr1*dis_jk[0];
bt_sg[nb_jk].dDD[1]+=
app1*dcA_ijk[1][1]
+app3*dcA_kjkp[1][0]
+agpdpr1*dis_jk[1];
bt_sg[nb_jk].dDD[2]+=
app1*dcA_ijk[2][1]
+app3*dcA_kjkp[2][0]
+agpdpr1*dis_jk[2];
bt_sg[nb_jkp].dDD[0]+=
app2*dcA_ijkp[0][1]
+app3*dcA_kjkp[0][1]
+agpdpr2*dis_jkp[0];
bt_sg[nb_jkp].dDD[1]+=
app2*dcA_ijkp[1][1]
+app3*dcA_kjkp[1][1]
+agpdpr2*dis_jkp[1];
bt_sg[nb_jkp].dDD[2]+=
app2*dcA_ijkp[2][1]
+app3*dcA_kjkp[2][1]
+agpdpr2*dis_jkp[2];
}
}
}
//j is a neighbor of i, k is a neighbor of j not equal to i and k'
//is a neighbor of k not equal to j or i
for(ltmp=0;ltmp<numneigh[k];ltmp++) {
temp_kkp=BOP_index[k]+ltmp;
kp=klist[ltmp];
kptype=map[type[kp]]+1;
same_ikp=0;
same_jkp=0;
if(x[i][0]==x[kp][0]) {
if(x[i][1]==x[kp][1]) {
if(x[i][2]==x[kp][2]) {
same_ikp=1;
}
}
}
if(x[j][0]==x[kp][0]) {
if(x[j][1]==x[kp][1]) {
if(x[j][2]==x[kp][2]) {
same_jkp=1;
}
}
}
if(!same_ikp&&!same_jkp) {
if(ktype==kptype)
ikkp=ktype-1;
else if(ktype<kptype)
ikkp=ktype*bop_types-ktype*(ktype+1)/2+kptype-1;
else
ikkp=kptype*bop_types-kptype*(kptype+1)/2+ktype-1;
for(kNeij=0;kNeij<numneigh[k];kNeij++) {
if(x[klist[kNeij]][0]==x[j][0]) {
if(x[klist[kNeij]][1]==x[j][1]) {
if(x[klist[kNeij]][2]==x[j][2]) {
break;
}
}
}
}
sig_flag=0;
for(nsearch=0;nsearch<nSigBk[n];nsearch++) {
ncmp=itypeSigBk[n][nsearch];
if(x[ncmp][0]==x[kp][0]) {
if(x[ncmp][1]==x[kp][1]) {
if(x[ncmp][2]==x[kp][2]) {
new2=nsearch;
sig_flag=1;
break;
}
}
}
}
if(sig_flag==0) {
nSigBk[n]=nSigBk[n]+1;
new2=nSigBk[n]-1;
itypeSigBk[n][new2]=kp;
}
dis_kkp[0]=x[kp][0]-x[k][0];
dis_kkp[1]=x[kp][1]-x[k][1];
dis_kkp[2]=x[kp][2]-x[k][2];
rsq_kkp=dis_kkp[0]*dis_kkp[0]
+dis_kkp[1]*dis_kkp[1]
+dis_kkp[2]*dis_kkp[2];
r_kkp=sqrt(rsq_kkp);
if(r_kkp<=rcut[ikkp]) {
ps=r_kkp*rdr[ikkp]+1.0;
ks=(int)ps;
if(nr-1<ks)
ks=nr-1;
ps=ps-ks;
if(ps>1.0)
ps=1.0;
betaS_kkp=((pBetaS3[ikkp][ks-1]*ps+pBetaS2[ikkp][ks-1])*ps
+pBetaS1[ikkp][ks-1])*ps+pBetaS[ikkp][ks-1];
dBetaS_kkp=(pBetaS6[ikkp][ks-1]*ps+pBetaS5[ikkp][ks-1])*ps
+pBetaS4[ikkp][ks-1];
betaP_kkp=((pBetaP3[ikkp][ks-1]*ps+pBetaP2[ikkp][ks-1])*ps
+pBetaP1[ikkp][ks-1])*ps+pBetaP[ikkp][ks-1];
dBetaP_kkp=(pBetaP6[ikkp][ks-1]*ps+pBetaP5[ikkp][ks-1])*ps
+pBetaP4[ikkp][ks-1];
cosAng_jkkp=(-dis_jk[0]*dis_kkp[0]-dis_jk[1]*dis_kkp[1]
-dis_jk[2]*dis_kkp[2])/(r_jk*r_kkp);
dcA_jkkp[0][0]=(dis_kkp[0]*r_jk*r_kkp-cosAng_jkkp
*-dis_jk[0]*r_kkp*r_kkp)/(r_jk*r_jk*r_kkp*r_kkp);
dcA_jkkp[1][0]=(dis_kkp[1]*r_jk*r_kkp-cosAng_jkkp
*-dis_jk[1]*r_kkp*r_kkp)/(r_jk*r_jk*r_kkp*r_kkp);
dcA_jkkp[2][0]=(dis_kkp[2]*r_jk*r_kkp-cosAng_jkkp
*-dis_jk[2]*r_kkp*r_kkp)/(r_jk*r_jk*r_kkp*r_kkp);
dcA_jkkp[0][1]=(-dis_jk[0]*r_jk*r_kkp-cosAng_jkkp
*dis_kkp[0]*r_jk*r_jk)/(r_jk*r_jk*r_kkp*r_kkp);
dcA_jkkp[1][1]=(-dis_jk[1]*r_jk*r_kkp-cosAng_jkkp
*dis_kkp[1]*r_jk*r_jk)/(r_jk*r_jk*r_kkp*r_kkp);
dcA_jkkp[2][1]=(-dis_jk[2]*r_jk*r_kkp-cosAng_jkkp
*dis_kkp[2]*r_jk*r_jk)/(r_jk*r_jk*r_kkp*r_kkp);
nb_kkp=nb_t;
nb_t++;
if(nb_t>nb_sg) {
new_n_tot=nb_sg+maxneigh;
grow_sigma(nb_sg,new_n_tot);
nb_sg=new_n_tot;
}
bt_sg[nb_kkp].temp=temp_kkp;
bt_sg[nb_kkp].i=k;
bt_sg[nb_kkp].j=kp;
gmean0=sigma_g0[jtype-1][ktype-1][kptype-1];
gmean1=sigma_g1[jtype-1][ktype-1][kptype-1];
gmean2=sigma_g2[jtype-1][ktype-1][kptype-1];
amean=cosAng_jkkp;
gfactor2=gmean0+gmean1*amean
+gmean2*amean*amean;
gprime2=gmean1+2.0*gmean2*amean;
gfactorsq2=gfactor2*gfactor2;
gsqprime2=2.0*gfactor2*gprime2;
gfactor=gfactorsq*gfactorsq2;
rfactorrt=betaS_jk*betaS_kkp;
rfactor=rfactorrt*rfactorrt;
//3rd DD is Eq. 11 (c) for j atom where i & k=neighbor of j & k'=neighbor of k
DD=DD+gfactor*rfactor;
//agpdpr1 is derivative of DD 3rd term w.r.t. Beta(r_jk)
//agpdpr2 is derivative of DD 3rd term w.r.t. Beta(r_kk')
//app1 is derivative of DD 3rd term w.r.t. cos(theta_ijk)
//app2 is derivative of DD 3rd term w.r.t. cos(theta_jkkp)
agpdpr1=2.0*gfactor*rfactorrt*betaS_kkp
*dBetaS_jk/r_jk;
agpdpr2=2.0*gfactor*rfactorrt*betaS_jk
*dBetaS_kkp/r_kkp;
app1=rfactor*gfactorsq2*gsqprime;
app2=rfactor*gfactorsq*gsqprime2;
bt_sg[nb_ij].dDD[0]-=
app1*dcA_ijk[0][0];
bt_sg[nb_ij].dDD[1]-=
app1*dcA_ijk[1][0];
bt_sg[nb_ij].dDD[2]-=
app1*dcA_ijk[2][0];
bt_sg[nb_jk].dDD[0]+=
app1*dcA_ijk[0][1]
+agpdpr1*dis_jk[0]
-app2*dcA_jkkp[0][0];
bt_sg[nb_jk].dDD[1]+=
app1*dcA_ijk[1][1]
+agpdpr1*dis_jk[1]
-app2*dcA_jkkp[1][0];
bt_sg[nb_jk].dDD[2]+=
app1*dcA_ijk[2][1]
+agpdpr1*dis_jk[2]
-app2*dcA_jkkp[2][0];
bt_sg[nb_kkp].dDD[0]+=
app2*dcA_jkkp[0][1]
+agpdpr2*dis_kkp[0];
bt_sg[nb_kkp].dDD[1]+=
app2*dcA_jkkp[1][1]
+agpdpr2*dis_kkp[1];
bt_sg[nb_kkp].dDD[2]+=
app2*dcA_jkkp[2][1]
+agpdpr2*dis_kkp[2];
}
}
}
}
}
}
sig_flag=0;
if(FF<=0.000001) {
sigB[n]=0.0;
sig_flag=1;
}
if(sig_flag==0) {
if(AA<0.0)
AA=0.0;
if(BB<0.0)
BB=0.0;
if(CC<0.0)
CC=0.0;
if(DD<0.0)
DD=0.0;
// AA and BB are the representations of (a) Eq. 34 and (b) Eq. 9
// for atoms i and j respectively
AAC=AA+BB;
BBC=AA*BB;
CCC=AA*AA+BB*BB;
DDC=CC+DD;
//EEC is a modified form of (a) Eq. 33
EEC=(DDC-CCC)/(AAC+2.0*small1);
AACFF=1.0/(AAC+2.0*small1);
for(m=0;m<nb_t;m++) {
if((bt_sg[m].i>-1)&&(bt_sg[m].j>-1)) {
bt_sg[m].dAAC[0]=bt_sg[m].dAA[0]
+bt_sg[m].dBB[0];
bt_sg[m].dAAC[1]=bt_sg[m].dAA[1]
+bt_sg[m].dBB[1];
bt_sg[m].dAAC[2]=bt_sg[m].dAA[2]
+bt_sg[m].dBB[2];
bt_sg[m].dBBC[0]=bt_sg[m].dAA[0]*BB
+AA*bt_sg[m].dBB[0];
bt_sg[m].dBBC[1]=bt_sg[m].dAA[1]*BB
+AA*bt_sg[m].dBB[1];
bt_sg[m].dBBC[2]=bt_sg[m].dAA[2]*BB
+AA*bt_sg[m].dBB[2];
bt_sg[m].dCCC[0]=2.0*AA*bt_sg[m].dAA[0]
+2.0*BB*bt_sg[m].dBB[0];
bt_sg[m].dCCC[1]=2.0*AA*bt_sg[m].dAA[1]
+2.0*BB*bt_sg[m].dBB[1];
bt_sg[m].dCCC[2]=2.0*AA*bt_sg[m].dAA[2]
+2.0*BB*bt_sg[m].dBB[2];
bt_sg[m].dDDC[0]=bt_sg[m].dCC[0]
+bt_sg[m].dDD[0];
bt_sg[m].dDDC[1]=bt_sg[m].dCC[1]
+bt_sg[m].dDD[1];
bt_sg[m].dDDC[2]=bt_sg[m].dCC[2]
+bt_sg[m].dDD[2];
bt_sg[m].dEEC[0]=(bt_sg[m].dDDC[0]
-bt_sg[m].dCCC[0]
-EEC*bt_sg[m].dAAC[0])*AACFF;
bt_sg[m].dEEC[1]=(bt_sg[m].dDDC[1]
-bt_sg[m].dCCC[1]
-EEC*bt_sg[m].dAAC[1])*AACFF;
bt_sg[m].dEEC[2]=(bt_sg[m].dDDC[2]
-bt_sg[m].dCCC[2]
-EEC*bt_sg[m].dAAC[2])*AACFF;
}
}
UT=EEC*FF+BBC+small3[iij];
UT=1.0/sqrt(UT);
// FFC is slightly modified form of (a) Eq. 31
// GGC is slightly modified form of (a) Eq. 32
// bndtmp is a slightly modified form of (a) Eq. 30 and (b) Eq. 8
FFC=BBC*UT;
GGC=EEC*UT;
bndtmp=(FF+sigma_delta[iij]*sigma_delta[iij])*(1.0+sigma_a[iij]*GGC)
*(1.0+sigma_a[iij]*GGC)+sigma_c[iij]*(AAC+sigma_a[iij]*EE
+sigma_a[iij]*FFC*(2.0+GGC))+small4;
UTcom=-0.5*UT*UT*UT;
for(m=0;m<nb_t;m++) {
if((bt_sg[m].i>-1)&&(bt_sg[m].j>-1)) {
bt_sg[m].dUT[0]=UTcom*(bt_sg[m].dEEC[0]*FF
+EEC*bt_sg[m].dFF[0]+bt_sg[m].dBBC[0]);
bt_sg[m].dUT[1]=UTcom*(bt_sg[m].dEEC[1]*FF
+EEC*bt_sg[m].dFF[1]+bt_sg[m].dBBC[1]);
bt_sg[m].dUT[2]=UTcom*(bt_sg[m].dEEC[2]*FF
+EEC*bt_sg[m].dFF[2]+bt_sg[m].dBBC[2]);
bt_sg[m].dFFC[0]=bt_sg[m].dBBC[0]*UT
+BBC*bt_sg[m].dUT[0];
bt_sg[m].dFFC[1]=bt_sg[m].dBBC[1]*UT
+BBC*bt_sg[m].dUT[1];
bt_sg[m].dFFC[2]=bt_sg[m].dBBC[2]*UT
+BBC*bt_sg[m].dUT[2];
bt_sg[m].dGGC[0]=bt_sg[m].dEEC[0]*UT
+EEC*bt_sg[m].dUT[0];
bt_sg[m].dGGC[1]=bt_sg[m].dEEC[1]*UT
+EEC*bt_sg[m].dUT[1];
bt_sg[m].dGGC[2]=bt_sg[m].dEEC[2]*UT
+EEC*bt_sg[m].dUT[2];
}
}
psign=1.0;
if(1.0+sigma_a[iij]*GGC<0.0)
psign=-1.0;
bndtmp0=1.0/sqrt(bndtmp);
sigB1[n]=psign*betaS_ij*(1.0+sigma_a[iij]*GGC)*bndtmp0;
bndtmp=-0.5*bndtmp0*bndtmp0*bndtmp0;
bndtmp1=psign*(1.0+sigma_a[iij]*GGC)*bndtmp0+psign*betaS_ij
*(1.0+sigma_a[iij]*GGC)*bndtmp*2.0*betaS_ij*(1.0
+sigma_a[iij]*GGC)*(1.0+sigma_a[iij]*GGC);
bndtmp1=bndtmp1*dBetaS_ij/r_ij;
bndtmp2=psign*betaS_ij*(1.0+sigma_a[iij]*GGC)*bndtmp*sigma_c[iij];
bndtmp3=psign*betaS_ij*(1.0+sigma_a[iij]*GGC)
*bndtmp*sigma_c[iij]*sigma_a[iij];
bndtmp4=psign*betaS_ij*(1.0+sigma_a[iij]*GGC)
*bndtmp*sigma_c[iij]*sigma_a[iij]*(2.0+GGC);
bndtmp5=sigma_a[iij]*psign*betaS_ij*bndtmp0
+psign*betaS_ij*(1.0+sigma_a[iij]*GGC)*bndtmp
*(2.0*(FF+sigma_delta[iij]*sigma_delta[iij])*(1.0
+sigma_a[iij]*GGC)*sigma_a[iij]+sigma_c[iij]*sigma_a[iij]*FFC);
setting=0;
for(m=0;m<nb_t;m++) {
if((bt_sg[m].i>-1)&&(bt_sg[m].j>-1)) {
temp_kk=bt_sg[m].temp;
if(temp_kk==temp_ij&&setting==0) {
bt_sg[m].dSigB1[0]=bndtmp1*dis_ij[0]
+(bndtmp2*bt_sg[m].dAAC[0]
+bndtmp3*bt_sg[m].dEE[0]
+bndtmp4*bt_sg[m].dFFC[0]
+bndtmp5*bt_sg[m].dGGC[0]);
bt_sg[m].dSigB1[1]=bndtmp1*dis_ij[1]
+(bndtmp2*bt_sg[m].dAAC[1]
+bndtmp3*bt_sg[m].dEE[1]
+bndtmp4*bt_sg[m].dFFC[1]
+bndtmp5*bt_sg[m].dGGC[1]);
bt_sg[m].dSigB1[2]=bndtmp1*dis_ij[2]
+(bndtmp2*bt_sg[m].dAAC[2]
+bndtmp3*bt_sg[m].dEE[2]
+bndtmp4*bt_sg[m].dFFC[2]
+bndtmp5*bt_sg[m].dGGC[2]);
setting=1;
}
else if(temp_kk==temp_ji&&setting==0) {
bt_sg[m].dSigB1[0]=-bndtmp1*dis_ij[0]
+(bndtmp2*bt_sg[m].dAAC[0]
+bndtmp3*bt_sg[m].dEE[0]
+bndtmp4*bt_sg[m].dFFC[0]
+bndtmp5*bt_sg[m].dGGC[0]);
bt_sg[m].dSigB1[1]=-bndtmp1*dis_ij[1]
+(bndtmp2*bt_sg[m].dAAC[1]
+bndtmp3*bt_sg[m].dEE[1]
+bndtmp4*bt_sg[m].dFFC[1]
+bndtmp5*bt_sg[m].dGGC[1]);
bt_sg[m].dSigB1[2]=-bndtmp1*dis_ij[2]
+(bndtmp2*bt_sg[m].dAAC[2]
+bndtmp3*bt_sg[m].dEE[2]
+bndtmp4*bt_sg[m].dFFC[2]
+bndtmp5*bt_sg[m].dGGC[2]);
setting=1;
}
else {
bt_sg[m].dSigB1[0]=(bndtmp2*bt_sg[m].dAAC[0]
+bndtmp3*bt_sg[m].dEE[0]
+bndtmp4*bt_sg[m].dFFC[0]
+bndtmp5*bt_sg[m].dGGC[0]);
bt_sg[m].dSigB1[1]=(bndtmp2*bt_sg[m].dAAC[1]
+bndtmp3*bt_sg[m].dEE[1]
+bndtmp4*bt_sg[m].dFFC[1]
+bndtmp5*bt_sg[m].dGGC[1]);
bt_sg[m].dSigB1[2]=(bndtmp2*bt_sg[m].dAAC[2]
+bndtmp3*bt_sg[m].dEE[2]
+bndtmp4*bt_sg[m].dFFC[2]
+bndtmp5*bt_sg[m].dGGC[2]);
}
}
}
//This loop is to ensure there is not an error for atoms with no neighbors (deposition)
if(nb_t==0) {
if(j>i) {
bt_sg[0].dSigB1[0]=bndtmp1*dis_ij[0];
bt_sg[0].dSigB1[1]=bndtmp1*dis_ij[1];
bt_sg[0].dSigB1[2]=bndtmp1*dis_ij[2];
}
else {
bt_sg[0].dSigB1[0]=-bndtmp1*dis_ij[0];
bt_sg[0].dSigB1[1]=-bndtmp1*dis_ij[1];
bt_sg[0].dSigB1[2]=-bndtmp1*dis_ij[2];
}
for(pp=0;pp<3;pp++) {
bt_sg[0].dAA[pp]=0.0;
bt_sg[0].dBB[pp]=0.0;
bt_sg[0].dCC[pp]=0.0;
bt_sg[0].dDD[pp]=0.0;
bt_sg[0].dEE[pp]=0.0;
bt_sg[0].dEE1[pp]=0.0;
bt_sg[0].dFF[pp]=0.0;
bt_sg[0].dAAC[pp]=0.0;
bt_sg[0].dBBC[pp]=0.0;
bt_sg[0].dCCC[pp]=0.0;
bt_sg[0].dDDC[pp]=0.0;
bt_sg[0].dEEC[pp]=0.0;
bt_sg[0].dFFC[pp]=0.0;
bt_sg[0].dGGC[pp]=0.0;
bt_sg[0].dUT[pp]=0.0;
bt_sg[0].dSigB1[pp]=0.0;
bt_sg[0].dSigB[pp]=0.0;
}
bt_sg[0].i=i;
bt_sg[0].j=j;
bt_sg[0].temp=temp_ij;
nb_t++;
if(nb_t>nb_sg) {
new_n_tot=nb_sg+maxneigh;
grow_sigma(nb_sg,new_n_tot);
nb_sg=new_n_tot;
}
}
ps=sigB1[n]*rdBO+1.0;
ks=(int)ps;
if(nBOt-1<ks)
ks=nBOt-1;
ps=ps-ks;
if(ps>1.0)
ps=1.0;
dsigB1=((FsigBO3[iij][ks-1]*ps+FsigBO2[iij][ks-1])*ps
+FsigBO1[iij][ks-1])*ps+FsigBO[iij][ks-1];
dsigB2=(FsigBO6[iij][ks-1]*ps+FsigBO5[iij][ks-1])*ps+FsigBO4[iij][ks-1];
part0=(FF+0.5*AAC+small5);
part1=(sigma_f[iij]-0.5)*sigma_k[iij];
part2=1.0-part1*EE1/part0;
part3=dsigB1*part1/part0;
part4=part3/part0*EE1;
// sigB is the final expression for (a) Eq. 6 and (b) Eq. 11
sigB[n]=dsigB1*part2;
pp1=2.0*betaS_ij;
for(m=0;m<nb_t;m++) {
if((bt_sg[m].i>-1)&&(bt_sg[m].j>-1)) {
temp_kk=bt_sg[m].temp;
bt_i=bt_sg[m].i;
bt_j=bt_sg[m].j;
xtmp[0]=x[bt_j][0]-x[bt_i][0];
xtmp[1]=x[bt_j][1]-x[bt_i][1];
xtmp[2]=x[bt_j][2]-x[bt_i][2];
for(pp=0;pp<3;pp++) {
bt_sg[m].dSigB[pp]=dsigB2*part2*bt_sg[m].dSigB1[pp]
-part3*bt_sg[m].dEE1[pp]
+part4*(bt_sg[m].dFF[pp]
+0.5*bt_sg[m].dAAC[pp]);
}
for(pp=0;pp<3;pp++) {
ftmp[pp]=pp1*bt_sg[m].dSigB[pp];
f[bt_i][pp]-=ftmp[pp];
f[bt_j][pp]+=ftmp[pp];
}
if(evflag) {
ev_tally_xyz(bt_i,bt_j,nlocal,newton_pair,0.0,0.0,ftmp[0],ftmp[1]
,ftmp[2],xtmp[0],xtmp[1],xtmp[2]);
}
}
}
}
n++;
}
}
}
}
destroy_sigma();
}
/* ---------------------------------------------------------------------- */
/* The formulation differs slightly to avoid negative square roots
in the calculation of Theta_pi,ij of (a) Eq. 36 and (b) Eq. 18
see (d) */
void PairBOP::sigmaBo_noa_otf()
{
int nb_t,new_n_tot;
int n,i,j,k,kp,m,pp;
int itmp,jtmp,ktmp,ltmp,mtmp;
int i_tag,j_tag;
int kp1,kp2,kp1type;
int iij,iik,ijk,ikkp,ji,iikp,ijkp;
int nkp;
int nk0;
int jNeik,kNeii,kNeij;
int new1,new2,nlocal;
int inum,*ilist,*iilist,*jlist,*klist;
int **firstneigh,*numneigh;
int temp_ij,temp_ik,temp_jkp,temp_kk,temp_jk;
int temp_ji,temp_kkp;
int temp_kpk;
int nb_ij,nb_ik,nb_ikp;
int nb_jk,nb_jkp,nb_kkp;
int kp_nsearch,nsearch;
int sig_flag,setting,ncmp,ks;
int itype,jtype,ktype,kptype;
int bt_i,bt_j,bt_ij;
int kp_index,same_ikp,same_jkp,same_kpk;
double AA,BB,CC,DD,EE,EE1,FF;
double AAC,BBC,CCC,DDC,EEC,FFC,GGC;
double AACFF,UT,bndtmp,UTcom;
double amean,gmean0,gmean1,gmean2,ps;
double gfactor1,gprime1,gsqprime,factorsq;
double gfactorsq,gfactor2,gprime2;
double gfactorsq2,gsqprime2;
double gfactor3,gprime3,gfactor,rfactor;
double drfactor,gfactor4,gprime4,agpdpr3;
double rfactor0,rfactorrt,rfactor1rt,rfactor1;
double rcm1,rcm2,gcm1,gcm2,gcm3;
double agpdpr1,agpdpr2,app1,app2,app3,app4;
double dsigB1,dsigB2;
double part0,part1,part2,part3,part4;
double psign,bndtmp0,pp1;
double bndtmp1,bndtmp2;
double dis_ij[3],rsq_ij,r_ij;
double betaS_ij,dBetaS_ij;
double betaP_ij,dBetaP_ij;
double dis_ik[3],rsq_ik,r_ik;
double betaS_ik,dBetaS_ik;
double betaP_ik,dBetaP_ik;
double dis_ikp[3],rsq_ikp,r_ikp;
double betaS_ikp,dBetaS_ikp;
double betaP_ikp,dBetaP_ikp;
double dis_jk[3],rsq_jk,r_jk;
double betaS_jk,dBetaS_jk;
double betaP_jk,dBetaP_jk;
double dis_jkp[3],rsq_jkp,r_jkp;
double betaS_jkp,dBetaS_jkp;
double betaP_jkp,dBetaP_jkp;
double dis_kkp[3],rsq_kkp,r_kkp;
double betaS_kkp,dBetaS_kkp;
double betaP_kkp,dBetaP_kkp;
double cosAng_jik,dcA_jik[3][2];
double cosAng_jikp,dcA_jikp[3][2];
double cosAng_kikp,dcA_kikp[3][2];
double cosAng_ijk,dcA_ijk[3][2];
double cosAng_ijkp,dcA_ijkp[3][2];
double cosAng_kjkp,dcA_kjkp[3][2];
double cosAng_ikj,dcA_ikj[3][2];
double cosAng_ikkp,dcA_ikkp[3][2];
double cosAng_jkkp,dcA_jkkp[3][2];
double cosAng_jkpk,dcA_jkpk[3][2];
double ftmp[3],xtmp[3];
double **x = atom->x;
double **f = atom->f;
int *tag = atom->tag;
int newton_pair = force->newton_pair;
int *type = atom->type;
nlocal = atom->nlocal;
int nall = nlocal + atom->nghost;
inum = list->inum;
ilist = list->ilist;
numneigh = list->numneigh;
firstneigh = list->firstneigh;
n=0;
if(nb_sg==0) {
nb_sg=4;
}
if(allocate_sigma) {
destroy_sigma();
}
create_sigma(nb_sg);
for(itmp=0;itmp<inum;itmp++) {
i = ilist[itmp];
i_tag=tag[i];
itype = map[type[i]]+1;
//j is loop over all neighbors of i
for(jtmp=0;jtmp<numneigh[i];jtmp++) {
for(m=0;m<nb_sg;m++) {
for(pp=0;pp<3;pp++) {
bt_sg[m].dAA[pp]=0.0;
bt_sg[m].dBB[pp]=0.0;
bt_sg[m].dEE1[pp]=0.0;
bt_sg[m].dFF[pp]=0.0;
bt_sg[m].dAAC[pp]=0.0;
bt_sg[m].dSigB1[pp]=0.0;
bt_sg[m].dSigB[pp]=0.0;
}
bt_sg[m].i=-1;
bt_sg[m].j=-1;
}
nb_t=0;
iilist=firstneigh[i];
temp_ij=BOP_index[i]+jtmp;
j=iilist[jtmp];
jlist=firstneigh[j];
j_tag=tag[j];
jtype = map[type[j]]+1;
nb_ij=nb_t;
nb_t++;
if(nb_t>nb_sg) {
new_n_tot=nb_sg+maxneigh;
grow_sigma(nb_sg,new_n_tot);
nb_sg=new_n_tot;
}
bt_sg[nb_ij].temp=temp_ij;
bt_sg[nb_ij].i=i;
bt_sg[nb_ij].j=j;
if(j_tag>=i_tag) {
if(itype==jtype)
iij=itype-1;
else if(itype<jtype)
iij=itype*bop_types-itype*(itype+1)/2+jtype-1;
else
iij=jtype*bop_types-jtype*(jtype+1)/2+itype-1;
for(ji=0;ji<numneigh[j];ji++) {
temp_ji=BOP_index[j]+ji;
if(x[jlist[ji]][0]==x[i][0]) {
if(x[jlist[ji]][1]==x[i][1]) {
if(x[jlist[ji]][2]==x[i][2]) {
break;
}
}
}
}
dis_ij[0]=x[j][0]-x[i][0];
dis_ij[1]=x[j][1]-x[i][1];
dis_ij[2]=x[j][2]-x[i][2];
rsq_ij=dis_ij[0]*dis_ij[0]
+dis_ij[1]*dis_ij[1]
+dis_ij[2]*dis_ij[2];
r_ij=sqrt(rsq_ij);
if(r_ij<rcut[iij]) {
ps=r_ij*rdr[iij]+1.0;
ks=(int)ps;
if(nr-1<ks)
ks=nr-1;
ps=ps-ks;
if(ps>1.0)
ps=1.0;
betaS_ij=((pBetaS3[iij][ks-1]*ps+pBetaS2[iij][ks-1])*ps
+pBetaS1[iij][ks-1])*ps+pBetaS[iij][ks-1];
dBetaS_ij=(pBetaS6[iij][ks-1]*ps+pBetaS5[iij][ks-1])*ps
+pBetaS4[iij][ks-1];
betaP_ij=((pBetaP3[iij][ks-1]*ps+pBetaP2[iij][ks-1])*ps
+pBetaP1[iij][ks-1])*ps+pBetaP[iij][ks-1];
dBetaP_ij=(pBetaP6[iij][ks-1]*ps+pBetaP5[iij][ks-1])*ps
+pBetaP4[iij][ks-1];
nSigBk[n]=0;
//AA-EE1 are the components making up Eq. 30 (a)
AA=0.0;
BB=0.0;
CC=0.0;
DD=0.0;
EE=0.0;
EE1=0.0;
//FF is the Beta_sigma^2 term
FF=betaS_ij*betaS_ij;
//agpdpr1 is derivative of FF w.r.t. r_ij
agpdpr1=2.0*betaS_ij*dBetaS_ij/r_ij;
//dXX derivatives are taken with respect to all pairs contributing to the energy
//nb_ij is derivative w.r.t. ij pair
bt_sg[nb_ij].dFF[0]=agpdpr1*dis_ij[0];
bt_sg[nb_ij].dFF[1]=agpdpr1*dis_ij[1];
bt_sg[nb_ij].dFF[2]=agpdpr1*dis_ij[2];
//k is loop over all neighbors of i again with j neighbor of i
for(ktmp=0;ktmp<numneigh[i];ktmp++) {
temp_ik=BOP_index[i]+ktmp;
if(ktmp!=jtmp) {
k=iilist[ktmp];
klist=firstneigh[k];
ktype = map[type[k]]+1;
if(itype==ktype)
iik=itype-1;
else if(itype<ktype)
iik=itype*bop_types-itype*(itype+1)/2+ktype-1;
else
iik=ktype*bop_types-ktype*(ktype+1)/2+itype-1;
//find neighbor of k that is equal to i
for(kNeii=0;kNeii<numneigh[k];kNeii++) {
if(x[klist[kNeii]][0]==x[i][0]) {
if(x[klist[kNeii]][1]==x[i][1]) {
if(x[klist[kNeii]][2]==x[i][2]) {
break;
}
}
}
}
dis_ik[0]=x[k][0]-x[i][0];
dis_ik[1]=x[k][1]-x[i][1];
dis_ik[2]=x[k][2]-x[i][2];
rsq_ik=dis_ik[0]*dis_ik[0]
+dis_ik[1]*dis_ik[1]
+dis_ik[2]*dis_ik[2];
r_ik=sqrt(rsq_ik);
if(r_ik<=rcut[iik]) {
ps=r_ik*rdr[iik]+1.0;
ks=(int)ps;
if(nr-1<ks)
ks=nr-1;
ps=ps-ks;
if(ps>1.0)
ps=1.0;
betaS_ik=((pBetaS3[iik][ks-1]*ps+pBetaS2[iik][ks-1])*ps
+pBetaS1[iik][ks-1])*ps+pBetaS[iik][ks-1];
dBetaS_ik=(pBetaS6[iik][ks-1]*ps+pBetaS5[iik][ks-1])*ps
+pBetaS4[iik][ks-1];
betaP_ik=((pBetaP3[iik][ks-1]*ps+pBetaP2[iik][ks-1])*ps
+pBetaP1[iik][ks-1])*ps+pBetaP[iik][ks-1];
dBetaP_ik=(pBetaP6[iik][ks-1]*ps+pBetaP5[iik][ks-1])*ps
+pBetaP4[iik][ks-1];
//find neighbor of i that is equal to k
for(jNeik=0;jNeik<numneigh[j];jNeik++) {
temp_jk=BOP_index[j]+jNeik;
if(x[jlist[jNeik]][0]==x[k][0]) {
if(x[jlist[jNeik]][1]==x[k][1]) {
if(x[jlist[jNeik]][2]==x[k][2]) {
break;
}
}
}
}
//find neighbor of k that is equal to j
for(kNeij=0;kNeij<numneigh[k];kNeij++) {
if(x[klist[kNeij]][0]==x[j][0]) {
if(x[klist[kNeij]][1]==x[j][1]) {
if(x[klist[kNeij]][2]==x[j][2]) {
break;
}
}
}
}
dis_jk[0]=x[k][0]-x[j][0];
dis_jk[1]=x[k][1]-x[j][1];
dis_jk[2]=x[k][2]-x[j][2];
rsq_jk=dis_jk[0]*dis_jk[0]
+dis_jk[1]*dis_jk[1]
+dis_jk[2]*dis_jk[2];
r_jk=sqrt(rsq_jk);
sig_flag=0;
for(nsearch=0;nsearch<nSigBk[n];nsearch++) {
ncmp=itypeSigBk[n][nsearch];
if(x[ncmp][0]==x[k][0]) {
if(x[ncmp][1]==x[k][1]) {
if(x[ncmp][2]==x[k][2]) {
nk0=nsearch;
sig_flag=1;
break;
}
}
}
}
if(sig_flag==0) {
nSigBk[n]=nSigBk[n]+1;
nk0=nSigBk[n]-1;
itypeSigBk[n][nk0]=k;
}
nb_ik=nb_t;
nb_t++;
if(nb_t>nb_sg) {
new_n_tot=nb_sg+maxneigh;
grow_sigma(nb_sg,new_n_tot);
nb_sg=new_n_tot;
}
bt_sg[nb_ik].temp=temp_ik;
bt_sg[nb_ik].i=i;
bt_sg[nb_ik].j=k;
nb_jk=nb_t;
nb_t++;
if(nb_t>nb_sg) {
new_n_tot=nb_sg+maxneigh;
grow_sigma(nb_sg,new_n_tot);
nb_sg=new_n_tot;
}
bt_sg[nb_jk].temp=temp_jk;
bt_sg[nb_jk].i=j;
bt_sg[nb_jk].j=k;
cosAng_jik=(dis_ij[0]*dis_ik[0]+dis_ij[1]*dis_ik[1]
+dis_ij[2]*dis_ik[2])/(r_ij*r_ik);
dcA_jik[0][0]=(dis_ik[0]*r_ij*r_ik-cosAng_jik
*dis_ij[0]*r_ik*r_ik)/(r_ij*r_ij*r_ik*r_ik);
dcA_jik[1][0]=(dis_ik[1]*r_ij*r_ik-cosAng_jik
*dis_ij[1]*r_ik*r_ik)/(r_ij*r_ij*r_ik*r_ik);
dcA_jik[2][0]=(dis_ik[2]*r_ij*r_ik-cosAng_jik
*dis_ij[2]*r_ik*r_ik)/(r_ij*r_ij*r_ik*r_ik);
dcA_jik[0][1]=(dis_ij[0]*r_ij*r_ik-cosAng_jik
*dis_ik[0]*r_ij*r_ij)/(r_ij*r_ij*r_ik*r_ik);
dcA_jik[1][1]=(dis_ij[1]*r_ij*r_ik-cosAng_jik
*dis_ik[1]*r_ij*r_ij)/(r_ij*r_ij*r_ik*r_ik);
dcA_jik[2][1]=(dis_ij[2]*r_ij*r_ik-cosAng_jik
*dis_ik[2]*r_ij*r_ij)/(r_ij*r_ij*r_ik*r_ik);
gmean0=sigma_g0[jtype-1][itype-1][ktype-1];
gmean1=sigma_g1[jtype-1][itype-1][ktype-1];
gmean2=sigma_g2[jtype-1][itype-1][ktype-1];
amean=cosAng_jik;
gfactor1=gmean0+gmean1*amean
+gmean2*amean*amean;
gfactorsq=gfactor1*gfactor1;
gprime1=gmean1+2.0*gmean2*amean;
gsqprime=2.0*gfactor1*gprime1;
//AA is Eq. 34 (a) or Eq. 10 (c) for the i atom
//1st CC is Eq. 11 (c) for i atom where j & k=neighbor of i
AA=AA+gfactorsq*betaS_ik*betaS_ik;
CC=CC+gfactorsq*betaS_ik*betaS_ik*betaS_ik*betaS_ik;
//agpdpr1 is derivative of AA w.r.t. Beta(rik)
//app1 is derivative of AA w.r.t. cos(theta_jik)
agpdpr1=2.0*gfactorsq*betaS_ik*dBetaS_ik/r_ik;
app1=betaS_ik*betaS_ik*gsqprime;
bt_sg[nb_ij].dAA[0]+=
app1*dcA_jik[0][0];
bt_sg[nb_ij].dAA[1]+=
app1*dcA_jik[1][0];
bt_sg[nb_ij].dAA[2]+=
app1*dcA_jik[2][0];
bt_sg[nb_ik].dAA[0]+=
app1*dcA_jik[0][1]
+agpdpr1*dis_ik[0];
bt_sg[nb_ik].dAA[1]+=
app1*dcA_jik[1][1]
+agpdpr1*dis_ik[1];
bt_sg[nb_ik].dAA[2]+=
app1*dcA_jik[2][1]
+agpdpr1*dis_ik[2];
//k' is loop over neighbors all neighbors of j with k a neighbor
//of i and j a neighbor of i and determine which k' is k
same_kpk=0;
for(ltmp=0;ltmp<numneigh[j];ltmp++) {
temp_jkp=BOP_index[j]+ltmp;
kp1=jlist[ltmp];
kp1type=map[type[kp1]]+1;
if(x[kp1][0]==x[k][0]) {
if(x[kp1][1]==x[k][1]) {
if(x[kp1][2]==x[k][2]) {
same_kpk=1;
break;
}
}
}
}
if(same_kpk){
//loop over neighbors of k
for(mtmp=0;mtmp<numneigh[k];mtmp++) {
kp2=klist[mtmp];
if(x[kp2][0]==x[k][0]) {
if(x[kp2][1]==x[k][1]) {
if(x[kp2][2]==x[k][2]) {
break;
}
}
}
}
if(jtype==ktype)
ijk=jtype-1;
else if(jtype < ktype)
ijk=jtype*bop_types-jtype*(jtype+1)/2+ktype-1;
else
ijk=ktype*bop_types-ktype*(ktype+1)/2+jtype-1;
if(jtype==kp1type)
ijkp=jtype-1;
else if(jtype<kp1type)
ijkp=jtype*bop_types-jtype*(jtype+1)/2+kp1type-1;
else
ijkp=kp1type*bop_types-kp1type*(kp1type+1)/2+jtype-1;
dis_jkp[0]=x[kp1][0]-x[j][0];
dis_jkp[1]=x[kp1][1]-x[j][1];
dis_jkp[2]=x[kp1][2]-x[j][2];
rsq_jkp=dis_jkp[0]*dis_jkp[0]
+dis_jkp[1]*dis_jkp[1]
+dis_jkp[2]*dis_jkp[2];
r_jkp=sqrt(rsq_jkp);
if(r_jkp<=rcut[ijkp]) {
ps=r_jkp*rdr[ijkp]+1.0;
ks=(int)ps;
if(nr-1<ks)
ks=nr-1;
ps=ps-ks;
if(ps>1.0)
ps=1.0;
betaS_jkp=((pBetaS3[ijkp][ks-1]*ps+pBetaS2[ijkp][ks-1])*ps
+pBetaS1[ijkp][ks-1])*ps+pBetaS[ijkp][ks-1];
dBetaS_jkp=(pBetaS6[ijkp][ks-1]*ps+pBetaS5[ijkp][ks-1])*ps
+pBetaS4[ijkp][ks-1];
betaP_jkp=((pBetaP3[ijkp][ks-1]*ps+pBetaP2[ijkp][ks-1])*ps
+pBetaP1[ijkp][ks-1])*ps+pBetaP[ijkp][ks-1];
dBetaP_jkp=(pBetaP6[ijkp][ks-1]*ps+pBetaP5[ijkp][ks-1])*ps
+pBetaP4[ijkp][ks-1];
cosAng_ijk=(-dis_ij[0]*dis_jk[0]-dis_ij[1]*dis_jk[1]
-dis_ij[2]*dis_jk[2])/(r_ij*r_jk);
dcA_ijk[0][0]=(dis_jk[0]*r_ij*r_jk-cosAng_ijk
*-dis_ij[0]*r_jk*r_jk)/(r_ij*r_ij*r_jk*r_jk);
dcA_ijk[1][0]=(dis_jk[1]*r_ij*r_jk-cosAng_ijk
*-dis_ij[1]*r_jk*r_jk)/(r_ij*r_ij*r_jk*r_jk);
dcA_ijk[2][0]=(dis_jk[2]*r_ij*r_jk-cosAng_ijk
*-dis_ij[2]*r_jk*r_jk)/(r_ij*r_ij*r_jk*r_jk);
dcA_ijk[0][1]=(-dis_ij[0]*r_ij*r_jk-cosAng_ijk
*dis_jk[0]*r_ij*r_ij)/(r_ij*r_ij*r_jk*r_jk);
dcA_ijk[1][1]=(-dis_ij[1]*r_ij*r_jk-cosAng_ijk
*dis_jk[1]*r_ij*r_ij)/(r_ij*r_ij*r_jk*r_jk);
dcA_ijk[2][1]=(-dis_ij[2]*r_ij*r_jk-cosAng_ijk
*dis_jk[2]*r_ij*r_ij)/(r_ij*r_ij*r_jk*r_jk);
gmean0=sigma_g0[itype-1][jtype-1][ktype-1];
gmean1=sigma_g1[itype-1][jtype-1][ktype-1];
gmean2=sigma_g2[itype-1][jtype-1][ktype-1];
amean=cosAng_ijk;
gfactor2=gmean0+gmean1*amean
+gmean2*amean*amean;
gprime2=gmean1+2.0*gmean2*amean;
gmean0=sigma_g0[itype-1][ktype-1][jtype-1];
gmean1=sigma_g1[itype-1][ktype-1][jtype-1];
gmean2=sigma_g2[itype-1][ktype-1][jtype-1];
cosAng_ikj=(dis_ik[0]*dis_jk[0]+dis_ik[1]*dis_jk[1]
+dis_ik[2]*dis_jk[2])/(r_ik*r_jk);
dcA_ikj[0][0]=(-dis_jk[0]*r_ik*r_jk-cosAng_ikj
*-dis_ik[0]*r_jk*r_jk)/(r_ik*r_ik*r_jk*r_jk);
dcA_ikj[1][0]=(-dis_jk[1]*r_ik*r_jk-cosAng_ikj
*-dis_ik[1]*r_jk*r_jk)/(r_ik*r_ik*r_jk*r_jk);
dcA_ikj[2][0]=(-dis_jk[2]*r_ik*r_jk-cosAng_ikj
*-dis_ik[2]*r_jk*r_jk)/(r_ik*r_ik*r_jk*r_jk);
dcA_ikj[0][1]=(-dis_ik[0]*r_ik*r_jk-cosAng_ikj
*-dis_jk[0]*r_ik*r_ik)/(r_ik*r_ik*r_jk*r_jk);
dcA_ikj[1][1]=(-dis_ik[1]*r_ik*r_jk-cosAng_ikj
*-dis_jk[1]*r_ik*r_ik)/(r_ik*r_ik*r_jk*r_jk);
dcA_ikj[2][1]=(-dis_ik[2]*r_ik*r_jk-cosAng_ikj
*-dis_jk[2]*r_ik*r_ik)/(r_ik*r_ik*r_jk*r_jk);
amean=cosAng_ikj;
gfactor3=gmean0+gmean1*amean
+gmean2*amean*amean;
gprime3=gmean1+2.0*gmean2*amean;
gfactor=gfactor1*gfactor2*gfactor3;
rfactor=betaS_ik*betaS_jkp;
//EE1 is (b) Eq. 12
EE1=EE1+gfactor*rfactor;
//rcm1 is derivative of EE1 w.r.t Beta(r_ik)
//rcm2 is derivative of EE1 w.r.t Beta(r_jk')
//gcm1 is derivative of EE1 w.r.t cos(theta_jik)
//gcm2 is derivative of EE1 w.r.t cos(theta_ijk)
//gcm3 is derivative of EE1 w.r.t cos(theta_ikj)
rcm1=gfactor*betaS_jkp*dBetaS_ik/r_ik;
rcm2=gfactor*betaS_ik*dBetaS_jkp/r_jkp;
gcm1=rfactor*gprime1*gfactor2*gfactor3;
gcm2=rfactor*gfactor1*gprime2*gfactor3;
gcm3=rfactor*gfactor1*gfactor2*gprime3;
bt_sg[nb_ij].dEE1[0]+=
gcm1*dcA_jik[0][0]
-gcm2*dcA_ijk[0][0];
bt_sg[nb_ij].dEE1[1]+=
gcm1*dcA_jik[1][0]
-gcm2*dcA_ijk[1][0];
bt_sg[nb_ij].dEE1[2]+=
gcm1*dcA_jik[2][0]
-gcm2*dcA_ijk[2][0];
bt_sg[nb_ik].dEE1[0]+=
gcm1*dcA_jik[0][1]
+rcm1*dis_ik[0]
-gcm3*dcA_ikj[0][0];
bt_sg[nb_ik].dEE1[1]+=
gcm1*dcA_jik[1][1]
+rcm1*dis_ik[1]
-gcm3*dcA_ikj[1][0];
bt_sg[nb_ik].dEE1[2]+=
gcm1*dcA_jik[2][1]
+rcm1*dis_ik[2]
-gcm3*dcA_ikj[2][0];
bt_sg[nb_jk].dEE1[0]+=
gcm2*dcA_ijk[0][1]
+rcm2*dis_jkp[0]
-gcm3*dcA_ikj[0][1];
bt_sg[nb_jk].dEE1[1]+=
gcm2*dcA_ijk[1][1]
+rcm2*dis_jkp[1]
-gcm3*dcA_ikj[1][1];
bt_sg[nb_jk].dEE1[2]+=
gcm2*dcA_ijk[2][1]
+rcm2*dis_jkp[2]
-gcm3*dcA_ikj[2][1];
}
}
// k and k' and j are all different neighbors of i
for(ltmp=0;ltmp<ktmp;ltmp++) {
if(ltmp!=jtmp) {
kp=iilist[ltmp];;
kptype = map[type[kp]]+1;
if(itype==kptype)
iikp=itype-1;
else if(itype<kptype)
iikp=itype*bop_types-itype*(itype+1)/2+kptype-1;
else
iikp=kptype*bop_types-kptype*(kptype+1)/2+itype-1;
for(nsearch=0;nsearch<nSigBk[n];nsearch++) {
ncmp=itypeSigBk[n][nsearch];
if(x[ncmp][0]==x[kp][0]) {
if(x[ncmp][1]==x[kp][1]) {
if(x[ncmp][2]==x[kp][2]) {
break;
}
}
}
}
dis_ikp[0]=x[kp][0]-x[i][0];
dis_ikp[1]=x[kp][1]-x[i][1];
dis_ikp[2]=x[kp][2]-x[i][2];
rsq_ikp=dis_ikp[0]*dis_ikp[0]
+dis_ikp[1]*dis_ikp[1]
+dis_ikp[2]*dis_ikp[2];
r_ikp=sqrt(rsq_ikp);
if(r_ikp<=rcut[iikp]) {
ps=r_ikp*rdr[iikp]+1.0;
ks=(int)ps;
if(nr-1<ks)
ks=nr-1;
ps=ps-ks;
if(ps>1.0)
ps=1.0;
betaS_ikp=((pBetaS3[iikp][ks-1]*ps+pBetaS2[iikp][ks-1])*ps
+pBetaS1[iikp][ks-1])*ps+pBetaS[iikp][ks-1];
dBetaS_ikp=(pBetaS6[iikp][ks-1]*ps+pBetaS5[iikp][ks-1])*ps
+pBetaS4[iikp][ks-1];
betaP_ikp=((pBetaP3[iikp][ks-1]*ps+pBetaP2[iikp][ks-1])*ps
+pBetaP1[iikp][ks-1])*ps+pBetaP[iikp][ks-1];
dBetaP_ikp=(pBetaP6[iikp][ks-1]*ps+pBetaP5[iikp][ks-1])*ps
+pBetaP4[iikp][ks-1];
gmean0=sigma_g0[jtype-1][itype-1][kptype-1];
gmean1=sigma_g1[jtype-1][itype-1][kptype-1];
gmean2=sigma_g2[jtype-1][itype-1][kptype-1];
cosAng_jikp=(dis_ij[0]*dis_ikp[0]+dis_ij[1]*dis_ikp[1]
+dis_ij[2]*dis_ikp[2])/(r_ij*r_ikp);
cosAng_kikp=(dis_ik[0]*dis_ikp[0]+dis_ik[1]*dis_ikp[1]
+dis_ik[2]*dis_ikp[2])/(r_ik*r_ikp);
amean=cosAng_jikp;
gfactor2=gmean0+gmean1*amean
+gmean2*amean*amean;
gprime2=gmean1+2.0*gmean2*amean;
gmean0=sigma_g0[ktype-1][itype-1][kptype-1];
gmean1=sigma_g1[ktype-1][itype-1][kptype-1];
gmean2=sigma_g2[ktype-1][itype-1][kptype-1];
amean=cosAng_kikp;
gfactor3=gmean0+gmean1*amean
+gmean2*amean*amean;
gprime3=gmean1+2.0*gmean2*amean;
gfactor=gfactor1*gfactor2*gfactor3;
rfactorrt=betaS_ik*betaS_ikp;
rfactor=rfactorrt*rfactorrt;
//2nd CC is second term of Eq. 11 (c) for i atom where j , k & k' =neighbor of i
CC=CC+2.0*gfactor*rfactor;
}
}
}
// j and k are different neighbors of i and k' is a neighbor k not equal to i
for(ltmp=0;ltmp<numneigh[k];ltmp++) {
temp_kkp=BOP_index[k]+ltmp;
kp=klist[ltmp];;
kptype = map[type[kp]]+1;
same_ikp=0;
same_jkp=0;
if(x[i][0]==x[kp][0]) {
if(x[i][1]==x[kp][1]) {
if(x[i][2]==x[kp][2]) {
same_ikp=1;
}
}
}
if(x[j][0]==x[kp][0]) {
if(x[j][1]==x[kp][1]) {
if(x[j][2]==x[kp][2]) {
same_jkp=1;
}
}
}
if(!same_ikp&&!same_jkp) {
if(ktype==kptype)
ikkp=ktype-1;
else if(ktype<kptype)
ikkp=ktype*bop_types-ktype*(ktype+1)/2+kptype-1;
else
ikkp=kptype*bop_types-kptype*(kptype+1)/2+ktype-1;
dis_kkp[0]=x[kp][0]-x[k][0];
dis_kkp[1]=x[kp][1]-x[k][1];
dis_kkp[2]=x[kp][2]-x[k][2];
rsq_kkp=dis_kkp[0]*dis_kkp[0]
+dis_kkp[1]*dis_kkp[1]
+dis_kkp[2]*dis_kkp[2];
r_kkp=sqrt(rsq_kkp);
if(r_kkp<=rcut[ikkp]) {
ps=r_kkp*rdr[ikkp]+1.0;
ks=(int)ps;
if(nr-1<ks)
ks=nr-1;
ps=ps-ks;
if(ps>1.0)
ps=1.0;
betaS_kkp=((pBetaS3[ikkp][ks-1]*ps+pBetaS2[ikkp][ks-1])*ps
+pBetaS1[ikkp][ks-1])*ps+pBetaS[ikkp][ks-1];
dBetaS_kkp=(pBetaS6[ikkp][ks-1]*ps+pBetaS5[ikkp][ks-1])*ps
+pBetaS4[ikkp][ks-1];
betaP_kkp=((pBetaP3[ikkp][ks-1]*ps+pBetaP2[ikkp][ks-1])*ps
+pBetaP1[ikkp][ks-1])*ps+pBetaP[ikkp][ks-1];
dBetaP_kkp=(pBetaP6[ikkp][ks-1]*ps+pBetaP5[ikkp][ks-1])*ps
+pBetaP4[ikkp][ks-1];
sig_flag=0;
for(nsearch=0;nsearch<nSigBk[n];nsearch++) {
ncmp=itypeSigBk[n][nsearch];
if(x[ncmp][0]==x[kp][0]) {
if(x[ncmp][1]==x[kp][1]) {
if(x[ncmp][2]==x[kp][2]) {
sig_flag=1;
nkp=nsearch;
break;
}
}
}
}
if(sig_flag==0) {
nSigBk[n]=nSigBk[n]+1;
nkp=nSigBk[n]-1;
itypeSigBk[n][nkp]=kp;
}
cosAng_ikkp=(-dis_ik[0]*dis_kkp[0]-dis_ik[1]*dis_kkp[1]
-dis_ik[2]*dis_kkp[2])/(r_ik*r_kkp);
gmean0=sigma_g0[itype-1][ktype-1][kptype-1];
gmean1=sigma_g1[itype-1][ktype-1][kptype-1];
gmean2=sigma_g2[itype-1][ktype-1][kptype-1];
amean=cosAng_ikkp;
gfactor2=gmean0+gmean1*amean
+gmean2*amean*amean;
gprime2=gmean1+2.0*gmean2*amean;
gfactorsq2=gfactor2*gfactor2;
gsqprime2=2.0*gfactor2*gprime2;
gfactor=gfactorsq*gfactorsq2;
rfactorrt=betaS_ik*betaS_kkp;
rfactor=rfactorrt*rfactorrt;
//3rd CC is third term of Eq. 11 (c) for i atom
//where j , k =neighbor of i & k' =neighbor of k
CC=CC+gfactor*rfactor;
}
}
}
}
}
}
//j is a neighbor of i and k is a neighbor of j not equal to i
for(ktmp=0;ktmp<numneigh[j];ktmp++) {
if(ktmp!=ji) {
temp_jk=BOP_index[j]+ktmp;
k=jlist[ktmp];
klist=firstneigh[k];
ktype=map[type[k]]+1;
for(kNeij=0;kNeij<numneigh[k];kNeij++) {
if(x[klist[kNeij]][0]==x[j][0]) {
if(x[klist[kNeij]][1]==x[j][1]) {
if(x[klist[kNeij]][2]==x[j][2]) {
break;
}
}
}
}
if(jtype==ktype)
ijk=jtype-1;
else if(jtype<ktype)
ijk=jtype*bop_types-jtype*(jtype+1)/2+ktype-1;
else
ijk=ktype*bop_types-ktype*(ktype+1)/2+jtype-1;
sig_flag=0;
for(nsearch=0;nsearch<nSigBk[n];nsearch++) {
ncmp=itypeSigBk[n][nsearch];
if(x[ncmp][0]==x[k][0]) {
if(x[ncmp][1]==x[k][1]) {
if(x[ncmp][2]==x[k][2]) {
new1=nsearch;
sig_flag=1;
break;
}
}
}
}
if(sig_flag==0) {
nSigBk[n]=nSigBk[n]+1;
new1=nSigBk[n]-1;
itypeSigBk[n][new1]=k;
}
dis_jk[0]=x[k][0]-x[j][0];
dis_jk[1]=x[k][1]-x[j][1];
dis_jk[2]=x[k][2]-x[j][2];
rsq_jk=dis_jk[0]*dis_jk[0]
+dis_jk[1]*dis_jk[1]
+dis_jk[2]*dis_jk[2];
r_jk=sqrt(rsq_jk);
if(r_jk<=rcut[ijk]) {
ps=r_jk*rdr[ijk]+1.0;
ks=(int)ps;
if(nr-1<ks)
ks=nr-1;
ps=ps-ks;
if(ps>1.0)
ps=1.0;
betaS_jk=((pBetaS3[ijk][ks-1]*ps+pBetaS2[ijk][ks-1])*ps
+pBetaS1[ijk][ks-1])*ps+pBetaS[ijk][ks-1];
dBetaS_jk=(pBetaS6[ijk][ks-1]*ps+pBetaS5[ijk][ks-1])*ps
+pBetaS4[ijk][ks-1];
betaP_jk=((pBetaP3[ijk][ks-1]*ps+pBetaP2[ijk][ks-1])*ps
+pBetaP1[ijk][ks-1])*ps+pBetaP[ijk][ks-1];
dBetaP_jk=(pBetaP6[ijk][ks-1]*ps+pBetaP5[ijk][ks-1])*ps
+pBetaP4[ijk][ks-1];
cosAng_ijk=(-dis_ij[0]*dis_jk[0]-dis_ij[1]*dis_jk[1]
-dis_ij[2]*dis_jk[2])/(r_ij*r_jk);
dcA_ijk[0][0]=(dis_jk[0]*r_ij*r_jk-cosAng_ijk
*-dis_ij[0]*r_jk*r_jk)/(r_ij*r_ij*r_jk*r_jk);
dcA_ijk[1][0]=(dis_jk[1]*r_ij*r_jk-cosAng_ijk
*-dis_ij[1]*r_jk*r_jk)/(r_ij*r_ij*r_jk*r_jk);
dcA_ijk[2][0]=(dis_jk[2]*r_ij*r_jk-cosAng_ijk
*-dis_ij[2]*r_jk*r_jk)/(r_ij*r_ij*r_jk*r_jk);
dcA_ijk[0][1]=(-dis_ij[0]*r_ij*r_jk-cosAng_ijk
*dis_jk[0]*r_ij*r_ij)/(r_ij*r_ij*r_jk*r_jk);
dcA_ijk[1][1]=(-dis_ij[1]*r_ij*r_jk-cosAng_ijk
*dis_jk[1]*r_ij*r_ij)/(r_ij*r_ij*r_jk*r_jk);
dcA_ijk[2][1]=(-dis_ij[2]*r_ij*r_jk-cosAng_ijk
*dis_jk[2]*r_ij*r_ij)/(r_ij*r_ij*r_jk*r_jk);
nb_jk=nb_t;
nb_t++;
if(nb_t>nb_sg) {
new_n_tot=nb_sg+maxneigh;
grow_sigma(nb_sg,new_n_tot);
nb_sg=new_n_tot;
}
bt_sg[nb_jk].temp=temp_jk;
bt_sg[nb_jk].i=j;
bt_sg[nb_jk].j=k;
gmean0=sigma_g0[itype-1][jtype-1][ktype-1];
gmean1=sigma_g1[itype-1][jtype-1][ktype-1];
gmean2=sigma_g2[itype-1][jtype-1][ktype-1];
amean=cosAng_ijk;
gfactor1=gmean0+gmean1*amean
+gmean2*amean*amean;
gprime1=gmean1+2.0*gmean2*amean;
gfactorsq=gfactor1*gfactor1;
gsqprime=2.0*gfactor1*gprime1;
rfactor1rt=betaS_jk*betaS_jk;
rfactor1=rfactor1rt*rfactor1rt;
//BB is Eq. 34 (a) or Eq. 10 (c) for the j atom
//1st DD is Eq. 11 (c) for j atom where i & k=neighbor of j
BB=BB+gfactorsq*rfactor1rt;
DD=DD+gfactorsq*rfactor1;
//agpdpr1 is derivative of BB w.r.t. Beta(r_jk)
//app1 is derivative of BB w.r.t. cos(theta_ijk)
agpdpr1=2.0*gfactorsq*betaS_jk*dBetaS_jk/r_jk;
app1=rfactor1rt*gsqprime;
bt_sg[nb_ij].dBB[0]-=
app1*dcA_ijk[0][0];
bt_sg[nb_ij].dBB[1]-=
app1*dcA_ijk[1][0];
bt_sg[nb_ij].dBB[2]-=
app1*dcA_ijk[2][0];
bt_sg[nb_jk].dBB[0]+=
app1*dcA_ijk[0][1]
+agpdpr1*dis_jk[0];
bt_sg[nb_jk].dBB[1]+=
app1*dcA_ijk[1][1]
+agpdpr1*dis_jk[1];
bt_sg[nb_jk].dBB[2]+=
app1*dcA_ijk[2][1]
+agpdpr1*dis_jk[2];
//j is a neighbor of i, k and k' prime different neighbors of j not equal to i
for(ltmp=0;ltmp<ktmp;ltmp++) {
if(ltmp!=ji) {
temp_jkp=BOP_index[j]+ltmp;
kp=jlist[ltmp];
kptype=map[type[kp]]+1;
if(jtype==kptype)
ijkp=jtype-1;
else if(jtype<kptype)
ijkp=jtype*bop_types-jtype*(jtype+1)/2+kptype-1;
else
ijkp=kptype*bop_types-kptype*(kptype+1)/2+jtype-1;
for(nsearch=0;nsearch<nSigBk[n];nsearch++) {
ncmp=itypeSigBk[n][nsearch];
if(x[ncmp][0]==x[kp][0]) {
if(x[ncmp][1]==x[kp][1]) {
if(x[ncmp][2]==x[kp][2]) {
new2=nsearch;
break;
}
}
}
}
dis_jkp[0]=x[kp][0]-x[j][0];
dis_jkp[1]=x[kp][1]-x[j][1];
dis_jkp[2]=x[kp][2]-x[j][2];
rsq_jkp=dis_jkp[0]*dis_jkp[0]
+dis_jkp[1]*dis_jkp[1]
+dis_jkp[2]*dis_jkp[2];
r_jkp=sqrt(rsq_jkp);
if(r_jkp<=rcut[ijkp]) {
ps=r_jkp*rdr[ijkp]+1.0;
ks=(int)ps;
if(nr-1<ks)
ks=nr-1;
ps=ps-ks;
if(ps>1.0)
ps=1.0;
betaS_jkp=((pBetaS3[ijkp][ks-1]*ps+pBetaS2[ijkp][ks-1])*ps
+pBetaS1[ijkp][ks-1])*ps+pBetaS[ijkp][ks-1];
dBetaS_jkp=(pBetaS6[ijkp][ks-1]*ps+pBetaS5[ijkp][ks-1])*ps
+pBetaS4[ijkp][ks-1];
betaP_jkp=((pBetaP3[ijkp][ks-1]*ps+pBetaP2[ijkp][ks-1])*ps
+pBetaP1[ijkp][ks-1])*ps+pBetaP[ijkp][ks-1];
dBetaP_jkp=(pBetaP6[ijkp][ks-1]*ps+pBetaP5[ijkp][ks-1])*ps
+pBetaP4[ijkp][ks-1];
cosAng_ijkp=(-dis_ij[0]*dis_jkp[0]-dis_ij[1]*dis_jkp[1]
-dis_ij[2]*dis_jkp[2])/(r_ij*r_jkp);
dcA_ijkp[0][0]=(dis_jkp[0]*r_ij*r_jkp-cosAng_ijkp
*-dis_ij[0]*r_jkp*r_jkp)/(r_ij*r_ij*r_jkp*r_jkp);
dcA_ijkp[1][0]=(dis_jkp[1]*r_ij*r_jkp-cosAng_ijkp
*-dis_ij[1]*r_jkp*r_jkp)/(r_ij*r_ij*r_jkp*r_jkp);
dcA_ijkp[2][0]=(dis_jkp[2]*r_ij*r_jkp-cosAng_ijkp
*-dis_ij[2]*r_jkp*r_jkp)/(r_ij*r_ij*r_jkp*r_jkp);
dcA_ijkp[0][1]=(-dis_ij[0]*r_ij*r_jkp-cosAng_ijkp
*dis_jkp[0]*r_ij*r_ij)/(r_ij*r_ij*r_jkp*r_jkp);
dcA_ijkp[1][1]=(-dis_ij[1]*r_ij*r_jkp-cosAng_ijkp
*dis_jkp[1]*r_ij*r_ij)/(r_ij*r_ij*r_jkp*r_jkp);
dcA_ijkp[2][1]=(-dis_ij[2]*r_ij*r_jkp-cosAng_ijkp
*dis_jkp[2]*r_ij*r_ij)/(r_ij*r_ij*r_jkp*r_jkp);
cosAng_kjkp=(dis_jk[0]*dis_jkp[0]+dis_jk[1]*dis_jkp[1]
+dis_jk[2]*dis_jkp[2])/(r_jk*r_jkp);
dcA_kjkp[0][0]=(dis_jkp[0]*r_jk*r_jkp-cosAng_kjkp
*dis_jk[0]*r_jkp*r_jkp)/(r_jk*r_jk*r_jkp*r_jkp);
dcA_kjkp[1][0]=(dis_jkp[1]*r_jk*r_jkp-cosAng_kjkp
*dis_jk[1]*r_jkp*r_jkp)/(r_jk*r_jk*r_jkp*r_jkp);
dcA_kjkp[2][0]=(dis_jkp[2]*r_jk*r_jkp-cosAng_kjkp
*dis_jk[2]*r_jkp*r_jkp)/(r_jk*r_jk*r_jkp*r_jkp);
dcA_kjkp[0][1]=(dis_jk[0]*r_jk*r_jkp-cosAng_kjkp
*dis_jkp[0]*r_jk*r_jk)/(r_jk*r_jk*r_jkp*r_jkp);
dcA_kjkp[1][1]=(dis_jk[1]*r_jk*r_jkp-cosAng_kjkp
*dis_jkp[1]*r_jk*r_jk)/(r_jk*r_jk*r_jkp*r_jkp);
dcA_kjkp[2][1]=(dis_jk[2]*r_jk*r_jkp-cosAng_kjkp
*dis_jkp[2]*r_jk*r_jk)/(r_jk*r_jk*r_jkp*r_jkp);
nb_jkp=nb_t;
nb_t++;
if(nb_t>nb_sg) {
new_n_tot=nb_sg+maxneigh;
grow_sigma(nb_sg,new_n_tot);
nb_sg=new_n_tot;
}
bt_sg[nb_jkp].temp=temp_jkp;
bt_sg[nb_jkp].i=j;
bt_sg[nb_jkp].j=kp;
gmean0=sigma_g0[itype-1][jtype-1][kptype-1];
gmean1=sigma_g1[itype-1][jtype-1][kptype-1];
gmean2=sigma_g2[itype-1][jtype-1][kptype-1];
amean=cosAng_ijkp;
gfactor2=gmean0+gmean1*amean
+gmean2*amean*amean;
gprime2=gmean1+2.0*gmean2*amean;
gmean0=sigma_g0[ktype-1][jtype-1][kptype-1];
gmean1=sigma_g1[ktype-1][jtype-1][kptype-1];
gmean2=sigma_g2[ktype-1][jtype-1][kptype-1];
amean=cosAng_kjkp;
gfactor3=gmean0+gmean1*amean
+gmean2*amean*amean;
gprime3=gmean1+2.0*gmean2*amean;
gfactor=gfactor1*gfactor2*gfactor3;
rfactorrt=betaS_jk*betaS_jkp;
rfactor=rfactorrt*rfactorrt;
//2nd DD is Eq. 11 (c) for j atom where i , k & k'=neighbor of j
DD=DD+2.0*gfactor*rfactor;
}
}
}
//j is a neighbor of i, k is a neighbor of j not equal to i and k'
//is a neighbor of k not equal to j or i
for(ltmp=0;ltmp<numneigh[k];ltmp++) {
temp_kkp=BOP_index[k]+ltmp;
kp=klist[ltmp];
kptype=map[type[kp]]+1;
same_ikp=0;
same_jkp=0;
if(x[i][0]==x[kp][0]) {
if(x[i][1]==x[kp][1]) {
if(x[i][2]==x[kp][2]) {
same_ikp=1;
}
}
}
if(x[j][0]==x[kp][0]) {
if(x[j][1]==x[kp][1]) {
if(x[j][2]==x[kp][2]) {
same_jkp=1;
}
}
}
if(!same_ikp&&!same_jkp) {
if(ktype==kptype)
ikkp=ktype-1;
else if(ktype<kptype)
ikkp=ktype*bop_types-ktype*(ktype+1)/2+kptype-1;
else
ikkp=kptype*bop_types-kptype*(kptype+1)/2+ktype-1;
for(kNeij=0;kNeij<numneigh[k];kNeij++) {
if(x[klist[kNeij]][0]==x[j][0]) {
if(x[klist[kNeij]][1]==x[j][1]) {
if(x[klist[kNeij]][2]==x[j][2]) {
break;
}
}
}
}
sig_flag=0;
for(nsearch=0;nsearch<nSigBk[n];nsearch++) {
ncmp=itypeSigBk[n][nsearch];
if(x[ncmp][0]==x[kp][0]) {
if(x[ncmp][1]==x[kp][1]) {
if(x[ncmp][2]==x[kp][2]) {
new2=nsearch;
sig_flag=1;
break;
}
}
}
}
if(sig_flag==0) {
nSigBk[n]=nSigBk[n]+1;
new2=nSigBk[n]-1;
itypeSigBk[n][new2]=kp;
}
dis_kkp[0]=x[kp][0]-x[k][0];
dis_kkp[1]=x[kp][1]-x[k][1];
dis_kkp[2]=x[kp][2]-x[k][2];
rsq_kkp=dis_kkp[0]*dis_kkp[0]
+dis_kkp[1]*dis_kkp[1]
+dis_kkp[2]*dis_kkp[2];
r_kkp=sqrt(rsq_kkp);
if(r_kkp<=rcut[ikkp]) {
ps=r_kkp*rdr[ikkp]+1.0;
ks=(int)ps;
if(nr-1<ks)
ks=nr-1;
ps=ps-ks;
if(ps>1.0)
ps=1.0;
betaS_kkp=((pBetaS3[ikkp][ks-1]*ps+pBetaS2[ikkp][ks-1])*ps
+pBetaS1[ikkp][ks-1])*ps+pBetaS[ikkp][ks-1];
dBetaS_kkp=(pBetaS6[ikkp][ks-1]*ps+pBetaS5[ikkp][ks-1])*ps
+pBetaS4[ikkp][ks-1];
betaP_kkp=((pBetaP3[ikkp][ks-1]*ps+pBetaP2[ikkp][ks-1])*ps
+pBetaP1[ikkp][ks-1])*ps+pBetaP[ikkp][ks-1];
dBetaP_kkp=(pBetaP6[ikkp][ks-1]*ps+pBetaP5[ikkp][ks-1])*ps
+pBetaP4[ikkp][ks-1];
cosAng_jkkp=(-dis_jk[0]*dis_kkp[0]-dis_jk[1]*dis_kkp[1]
-dis_jk[2]*dis_kkp[2])/(r_jk*r_kkp);
dcA_jkkp[0][0]=(dis_kkp[0]*r_jk*r_kkp-cosAng_jkkp
*-dis_jk[0]*r_kkp*r_kkp)/(r_jk*r_jk*r_kkp*r_kkp);
dcA_jkkp[1][0]=(dis_kkp[1]*r_jk*r_kkp-cosAng_jkkp
*-dis_jk[1]*r_kkp*r_kkp)/(r_jk*r_jk*r_kkp*r_kkp);
dcA_jkkp[2][0]=(dis_kkp[2]*r_jk*r_kkp-cosAng_jkkp
*-dis_jk[2]*r_kkp*r_kkp)/(r_jk*r_jk*r_kkp*r_kkp);
dcA_jkkp[0][1]=(-dis_jk[0]*r_jk*r_kkp-cosAng_jkkp
*dis_kkp[0]*r_jk*r_jk)/(r_jk*r_jk*r_kkp*r_kkp);
dcA_jkkp[1][1]=(-dis_jk[1]*r_jk*r_kkp-cosAng_jkkp
*dis_kkp[1]*r_jk*r_jk)/(r_jk*r_jk*r_kkp*r_kkp);
dcA_jkkp[2][1]=(-dis_jk[2]*r_jk*r_kkp-cosAng_jkkp
*dis_kkp[2]*r_jk*r_jk)/(r_jk*r_jk*r_kkp*r_kkp);
nb_kkp=nb_t;
nb_t++;
if(nb_t>nb_sg) {
new_n_tot=nb_sg+maxneigh;
grow_sigma(nb_sg,new_n_tot);
nb_sg=new_n_tot;
}
bt_sg[nb_kkp].temp=temp_kkp;
bt_sg[nb_kkp].i=k;
bt_sg[nb_kkp].j=kp;
gmean0=sigma_g0[jtype-1][ktype-1][kptype-1];
gmean1=sigma_g1[jtype-1][ktype-1][kptype-1];
gmean2=sigma_g2[jtype-1][ktype-1][kptype-1];
amean=cosAng_jkkp;
gfactor2=gmean0+gmean1*amean
+gmean2*amean*amean;
gprime2=gmean1+2.0*gmean2*amean;
gfactorsq2=gfactor2*gfactor2;
gsqprime2=2.0*gfactor2*gprime2;
gfactor=gfactorsq*gfactorsq2;
rfactorrt=betaS_jk*betaS_kkp;
rfactor=rfactorrt*rfactorrt;
//3rd DD is Eq. 11 (c) for j atom where i & k=neighbor of j & k'=neighbor of k
DD=DD+gfactor*rfactor;
}
}
}
}
}
}
sig_flag=0;
if(FF<=0.000001) {
sigB[n]=0.0;
sig_flag=1;
}
if(sig_flag==0) {
if(AA<0.0)
AA=0.0;
if(BB<0.0)
BB=0.0;
if(CC<0.0)
CC=0.0;
if(DD<0.0)
DD=0.0;
// AA and BB are the representations of (a) Eq. 34 and (b) Eq. 9
// for atoms i and j respectively
AAC=AA+BB;
BBC=AA*BB;
CCC=AA*AA+BB*BB;
DDC=CC+DD;
//EEC is a modified form of (a) Eq. 33
EEC=(DDC-CCC)/(AAC+2.0*small1);
for(m=0;m<nb_t;m++) {
if((bt_sg[m].i>-1)&&(bt_sg[m].j>-1)) {
bt_sg[m].dAAC[0]=bt_sg[m].dAA[0]
+bt_sg[m].dBB[0];
bt_sg[m].dAAC[1]=bt_sg[m].dAA[1]
+bt_sg[m].dBB[1];
bt_sg[m].dAAC[2]=bt_sg[m].dAA[2]
+bt_sg[m].dBB[2];
}
}
UT=EEC*FF+BBC+small3[iij];
UT=1.0/sqrt(UT);
// FFC is slightly modified form of (a) Eq. 31
// GGC is slightly modified form of (a) Eq. 32
// bndtmp is a slightly modified form of (a) Eq. 30 and (b) Eq. 8
FFC=BBC*UT;
GGC=EEC*UT;
bndtmp=(FF+sigma_delta[iij]*sigma_delta[iij])
+sigma_c[iij]*AAC+small4;
UTcom=-0.5*UT*UT*UT;
psign=1.0;
bndtmp0=1.0/sqrt(bndtmp);
sigB1[n]=psign*betaS_ij*bndtmp0;
bndtmp=-0.5*bndtmp0*bndtmp0*bndtmp0;
bndtmp1=psign*bndtmp0+psign*betaS_ij
*bndtmp*2.0*betaS_ij;
bndtmp1=bndtmp1*dBetaS_ij/r_ij;
bndtmp2=psign*betaS_ij*bndtmp*sigma_c[iij];
setting=0;
for(m=0;m<nb_t;m++) {
if((bt_sg[m].i>-1)&&(bt_sg[m].j>-1)) {
temp_kk=bt_sg[m].temp;
if(temp_kk==temp_ij&&setting==0) {
bt_sg[m].dSigB1[0]=bndtmp1*dis_ij[0]
+(bndtmp2*bt_sg[m].dAAC[0]);
bt_sg[m].dSigB1[1]=bndtmp1*dis_ij[1]
+(bndtmp2*bt_sg[m].dAAC[1]);
bt_sg[m].dSigB1[2]=bndtmp1*dis_ij[2]
+(bndtmp2*bt_sg[m].dAAC[2]);
setting=1;
}
else if(temp_kk==temp_ji&&setting==0) {
bt_sg[m].dSigB1[0]=-bndtmp1*dis_ij[0]
+(bndtmp2*bt_sg[m].dAAC[0]);
bt_sg[m].dSigB1[1]=-bndtmp1*dis_ij[1]
+(bndtmp2*bt_sg[m].dAAC[1]);
bt_sg[m].dSigB1[2]=-bndtmp1*dis_ij[2]
+(bndtmp2*bt_sg[m].dAAC[2]);
setting=1;
}
else {
bt_sg[m].dSigB1[0]=(bndtmp2*bt_sg[m].dAAC[0]);
bt_sg[m].dSigB1[1]=(bndtmp2*bt_sg[m].dAAC[1]);
bt_sg[m].dSigB1[2]=(bndtmp2*bt_sg[m].dAAC[2]);
}
}
}
//This loop is to ensure there is not an error for atoms with no neighbors (deposition)
if(nb_t==0) {
if(j>i) {
bt_sg[0].dSigB1[0]=bndtmp1*dis_ij[0];
bt_sg[0].dSigB1[1]=bndtmp1*dis_ij[1];
bt_sg[0].dSigB1[2]=bndtmp1*dis_ij[2];
}
else {
bt_sg[0].dSigB1[0]=-bndtmp1*dis_ij[0];
bt_sg[0].dSigB1[1]=-bndtmp1*dis_ij[1];
bt_sg[0].dSigB1[2]=-bndtmp1*dis_ij[2];
}
for(pp=0;pp<3;pp++) {
bt_sg[0].dAA[pp]=0.0;
bt_sg[0].dBB[pp]=0.0;
bt_sg[0].dEE1[pp]=0.0;
bt_sg[0].dFF[pp]=0.0;
bt_sg[0].dAAC[pp]=0.0;
bt_sg[0].dSigB[pp]=0.0;
}
bt_sg[0].i=i;
bt_sg[0].j=j;
bt_sg[0].temp=temp_ij;
nb_t++;
if(nb_t>nb_sg) {
new_n_tot=nb_sg+maxneigh;
grow_sigma(nb_sg,new_n_tot);
nb_sg=new_n_tot;
}
}
ps=sigB1[n]*rdBO+1.0;
ks=(int)ps;
if(nBOt-1<ks)
ks=nBOt-1;
ps=ps-ks;
if(ps>1.0)
ps=1.0;
dsigB1=((FsigBO3[iij][ks-1]*ps+FsigBO2[iij][ks-1])*ps
+FsigBO1[iij][ks-1])*ps+FsigBO[iij][ks-1];
dsigB2=(FsigBO6[iij][ks-1]*ps+FsigBO5[iij][ks-1])*ps+FsigBO4[iij][ks-1];
part0=(FF+0.5*AAC+small5);
part1=(sigma_f[iij]-0.5)*sigma_k[iij];
part2=1.0-part1*EE1/part0;
part3=dsigB1*part1/part0;
part4=part3/part0*EE1;
// sigB is the final expression for (a) Eq. 6 and (b) Eq. 11
sigB[n]=dsigB1*part2;
pp1=2.0*betaS_ij;
for(m=0;m<nb_t;m++) {
if((bt_sg[m].i>-1)&&(bt_sg[m].j>-1)) {
temp_kk=bt_sg[m].temp;
bt_ij=bt_sg[m].temp;
bt_i=bt_sg[m].i;
bt_j=bt_sg[m].j;
xtmp[0]=x[bt_j][0]-x[bt_i][0];
xtmp[1]=x[bt_j][1]-x[bt_i][1];
xtmp[2]=x[bt_j][2]-x[bt_i][2];
for(pp=0;pp<3;pp++) {
bt_sg[m].dSigB[pp]=dsigB2*part2*bt_sg[m].dSigB1[pp]
-part3*bt_sg[m].dEE1[pp]
+part4*(bt_sg[m].dFF[pp]
+0.5*bt_sg[m].dAAC[pp]);
}
for(pp=0;pp<3;pp++) {
ftmp[pp]=pp1*bt_sg[m].dSigB[pp];
f[bt_i][pp]-=ftmp[pp];
f[bt_j][pp]+=ftmp[pp];
}
if(evflag) {
ev_tally_xyz(bt_i,bt_j,nlocal,newton_pair,0.0,0.0,ftmp[0],ftmp[1]
,ftmp[2],xtmp[0],xtmp[1],xtmp[2]);
}
}
}
}
n++;
}
}
}
}
destroy_sigma();
}
/* ---------------------------------------------------------------------- */
void PairBOP::PiBo()
{
int new_n_tot;
int i,j,k,kp,m,n,pp,nb_t;
int iij,ji,ki;
int nsearch,ncmp;
int i_tag,j_tag;
int njik,ngj,ngk,nglj,ngl,ngi;
int nkjkp,nijkp,ngli,nkikp,njikp;
int itmp,ltmp,jtmp,ktmp;
int nlocal,pi_flag;
int inum,*ilist,*iilist,*jlist;
int **firstneigh,*numneigh;
int itype,jtype;
int temp_ij,temp_ik,temp_ikp;
int temp_ji,temp_jki,temp_jk,temp_jkp;
int ang_jikp,ang_kikp,ang_ijk;
int ang_ijkp,ang_kjkp,ang_jik;
int nb_ij,nb_ik,nb_jk,nb_ikp,nb_jkp;
int bt_ij,bt_i,bt_j;
double AA,BB,CC,DD,EE,FF;
double cosSq,sinFactor,cosFactor;
double cosSq1,dotV,BBrt,AB1,AB2;
double BBrtR,ABrtR,ABrtR1,ABrtR2;
double angFactor,angFactor1,angFactor2;
double angFactor3,angFactor4,angRfactor;
double dAngR1,dAngR2,agpdpr3;
double agpdpr1,agpdpr2,app1,app2,app3;
double betaCapSq1,dbetaCapSq1;
double betaCapSq2,dbetaCapSq2;
double betaCapSum,ftmp[3];
double dPiB1,dPiB2,dPiB3,pp2;
double **f = atom->f;
double **x = atom->x;
int *type = atom->type;
int *tag = atom->tag;
int newton_pair = force->newton_pair;
nlocal = atom->nlocal;
inum = list->inum;
ilist = list->ilist;
numneigh = list->numneigh;
firstneigh = list->firstneigh;
n=0;
// Loop over all local atoms for i
if(nb_pi>16) {
nb_pi=16;
}
if(nb_pi==0) {
nb_pi=(maxneigh)*(maxneigh/2);
}
if(allocate_pi) {
destroy_pi();
}
create_pi(nb_pi);
for(itmp=0;itmp<inum;itmp++) {
nb_t=0;
i = ilist[itmp];
itype = map[type[i]]+1;
i_tag=tag[i];
// j is a loop over all neighbors of i
iilist=firstneigh[i];
for(jtmp=0;jtmp<numneigh[i];jtmp++) {
temp_ij=BOP_index[i]+jtmp;
if(neigh_flag[temp_ij]) {
for(m=0;m<nb_pi;m++) {
for(pp=0;pp<3;pp++) {
bt_pi[m].dAA[pp]=0.0;
bt_pi[m].dBB[pp]=0.0;
bt_pi[m].dPiB[pp]=0.0;
}
bt_pi[m].i=-1;
bt_pi[m].j=-1;
}
j=iilist[jtmp];
jlist=firstneigh[j];
jtype=map[type[j]]+1;
j_tag=tag[j];
nb_t=0;
ftmp[0]=0.0;
ftmp[1]=0.0;
ftmp[2]=0.0;
nb_ij=nb_t;
nb_t++;
if(nb_t>nb_pi) {
new_n_tot=nb_pi+maxneigh;
grow_pi(nb_pi,new_n_tot);
nb_pi=new_n_tot;
}
bt_pi[nb_ij].i=i;
bt_pi[nb_ij].j=j;
bt_pi[nb_ij].temp=temp_ij;
if(j_tag>=i_tag) {
if(itype==jtype)
iij=itype-1;
else if(itype<jtype)
iij=itype*bop_types-itype*(itype+1)/2+jtype-1;
else
iij=jtype*bop_types-jtype*(jtype+1)/2+itype-1;
AA=0.0;
BB=0.0;
nPiBk[n]=0;
for(ji=0;ji<numneigh[j];ji++) {
temp_ji=BOP_index[j]+ji;
if(x[jlist[ji]][0]==x[i][0]) {
if(x[jlist[ji]][1]==x[i][1]) {
if(x[jlist[ji]][2]==x[i][2]) {
break;
}
}
}
}
// j and k are different neighbors of i
for(ktmp=0;ktmp<numneigh[i];ktmp++) {
if(ktmp!=jtmp) {
temp_ik=BOP_index[i]+ktmp;
if(neigh_flag[temp_ik]) {
k=iilist[ktmp];
if(jtmp<ktmp) {
njik=jtmp*(2*numneigh[i]-jtmp-1)/2+(ktmp-jtmp)-1;
ngj=0;
ngk=1;
}
else {
njik=ktmp*(2*numneigh[i]-ktmp-1)/2+(jtmp-ktmp)-1;
ngj=1;
ngk=0;
}
ang_jik=cos_index[i]+njik;
if(ang_jik>=cos_total) {
error->one(FLERR,"Too many atom triplets for pair bop");
}
nb_ik=nb_t;
nb_t++;
if(nb_t>nb_pi) {
new_n_tot=nb_pi+maxneigh;
grow_pi(nb_pi,new_n_tot);
nb_pi=new_n_tot;
}
bt_pi[nb_ik].i=i;
bt_pi[nb_ik].j=k;
bt_pi[nb_ik].temp=temp_ik;
cosSq=cosAng[ang_jik]*cosAng[ang_jik];
sinFactor=.5*(1.0-cosSq)*pi_p[itype-1]*betaS[temp_ik];
cosFactor=.5*(1.0+cosSq)*betaP[temp_ik];
betaCapSq1=pi_p[itype-1]*betaS[temp_ik]*betaS[temp_ik]-betaP[temp_ik]
*betaP[temp_ik];
dbetaCapSq1=2.0*pi_p[itype-1]*betaS[temp_ik]*dBetaS[temp_ik]
-2.0*betaP[temp_ik]*dBetaP[temp_ik];
//AA is Eq. 37 (a) and Eq. 19 (b) or i atoms
//1st BB is first term of Eq. 38 (a) where j and k =neighbors i
AA=AA+sinFactor*betaS[temp_ik]+cosFactor*betaP[temp_ik];
BB=BB+.25*(1.0-cosSq)*(1.0-cosSq)*betaCapSq1*betaCapSq1;
//agpdpr1 is derivative of AA w.r.t. for atom i w.r.t. Beta(r_ik)
//agpdpr2 is derivative of BB w.r.t. for atom i w.r.t. Beta(r_ik)
//app1 is derivative of AA w.r.t. for atom i w.r.t. cos(theta_jik)
//app2 is derivative of BB w.r.t. for atom i w.r.t. cos(theta_jik)
agpdpr1=(2.0*sinFactor*dBetaS[temp_ik]+2.0*cosFactor
*dBetaP[temp_ik])/rij[temp_ik];
app1=cosAng[ang_jik]*(-pi_p[itype-1]*betaS[temp_ik]*betaS[temp_ik]
+betaP[temp_ik]*betaP[temp_ik]);
app2=-(1.0-cosSq)*cosAng[ang_jik]*betaCapSq1*betaCapSq1;
agpdpr2=.5*(1.0-cosSq)*(1.0-cosSq)*betaCapSq1*dbetaCapSq1/rij[temp_ik];
itypePiBk[n][nPiBk[n]]=k;
bt_pi[nb_ij].dAA[0]+=
app1*dcAng[ang_jik][0][ngj];
bt_pi[nb_ij].dAA[1]+=
app1*dcAng[ang_jik][1][ngj];
bt_pi[nb_ij].dAA[2]+=
app1*dcAng[ang_jik][2][ngj];
bt_pi[nb_ij].dBB[0]+=
app2*dcAng[ang_jik][0][ngj];
bt_pi[nb_ij].dBB[1]+=
app2*dcAng[ang_jik][1][ngj];
bt_pi[nb_ij].dBB[2]+=
app2*dcAng[ang_jik][2][ngj];
bt_pi[nb_ik].dAA[0]+=
agpdpr1*disij[0][temp_ik]
+app1*dcAng[ang_jik][0][ngk];
bt_pi[nb_ik].dAA[1]+=
agpdpr1*disij[1][temp_ik]
+app1*dcAng[ang_jik][1][ngk];
bt_pi[nb_ik].dAA[2]+=
agpdpr1*disij[2][temp_ik]
+app1*dcAng[ang_jik][2][ngk];
bt_pi[nb_ik].dBB[0]+=
app2*dcAng[ang_jik][0][ngk]
+agpdpr2*disij[0][temp_ik];
bt_pi[nb_ik].dBB[1]+=
app2*dcAng[ang_jik][1][ngk]
+agpdpr2*disij[1][temp_ik];
bt_pi[nb_ik].dBB[2]+=
app2*dcAng[ang_jik][2][ngk]
+agpdpr2*disij[2][temp_ik];
// j and k and k' are different neighbors of i
for(ltmp=0;ltmp<ktmp;ltmp++) {
if(ltmp!=jtmp) {
temp_ikp=BOP_index[i]+ltmp;
if(neigh_flag[temp_ikp]) {
kp=iilist[ltmp];
for(nsearch=0;nsearch<nPiBk[n];nsearch++) {
ncmp=itypePiBk[n][nsearch];
if(x[ncmp][0]==x[kp][0]) {
if(x[ncmp][1]==x[kp][1]) {
if(x[ncmp][2]==x[kp][2]) {
break;
}
}
}
}
nkikp=ltmp*(2*numneigh[i]-ltmp-1)/2+(ktmp-ltmp)-1;
if(jtmp<ltmp) {
njikp=jtmp*(2*numneigh[i]-jtmp-1)/2+(ltmp-jtmp)-1;
nglj=0;
ngl=1;
}
else {
njikp=ltmp*(2*numneigh[i]-ltmp-1)/2+(jtmp-ltmp)-1;
nglj=1;
ngl=0;
}
ang_jikp=cos_index[i]+njikp;
if(ang_jikp>=cos_total) {
error->one(FLERR,"Too many atom triplets for pair bop");
}
nb_ikp=nb_t;
nb_t++;
if(nb_t>nb_pi) {
new_n_tot=nb_pi+maxneigh;
grow_pi(nb_pi,new_n_tot);
nb_pi=new_n_tot;
}
bt_pi[nb_ikp].i=i;
bt_pi[nb_ikp].j=kp;
bt_pi[nb_ikp].temp=temp_ikp;
ang_kikp=cos_index[i]+nkikp;
if(ang_kikp>=cos_total) {
error->one(FLERR,"Too many atom triplets for pair bop");
}
betaCapSq2=pi_p[itype-1]*betaS[temp_ikp]*betaS[temp_ikp]
-betaP[temp_ikp]*betaP[temp_ikp];
dbetaCapSq2=2.0*pi_p[itype-1]*betaS[temp_ikp]*dBetaS[temp_ikp]
-2.0*betaP[temp_ikp]*dBetaP[temp_ikp];
cosSq1=cosAng[ang_jikp]*cosAng[ang_jikp];
angFactor=cosAng[ang_kikp]-cosAng[ang_jikp]*cosAng[ang_jik];
angFactor1=4.0*angFactor;
angFactor2=-angFactor1*cosAng[ang_jikp]
+2.0*cosAng[ang_jik]*(1.0-cosSq1);
angFactor3=-angFactor1*cosAng[ang_jik]
+2.0*cosAng[ang_jikp]*(1.0-cosSq);
angFactor4=2.0*angFactor*angFactor-(1.0-cosSq)*(1.0-cosSq1);
betaCapSum=.5*betaCapSq1*betaCapSq2;
//2nd BB is third term of Eq. 38 (a) where j , k and k'=neighbors i
BB=BB+betaCapSum*angFactor4;
//agpdpr1 is derivative of BB w.r.t. for atom i w.r.t. Beta(r_ik)
//agpdpr2 is derivative of BB w.r.t. for atom i w.r.t. Beta(r_ik')
//app1 is derivative of BB 3rd term w.r.t. cos(theta_kik')
//app2 is derivative of BB 3rd term w.r.t. cos(theta_jik)
//app3 is derivative of BB 3rd term w.r.t. cos(theta_jik')
app1=betaCapSum*angFactor1;
app2=betaCapSum*angFactor2;
app3=betaCapSum*angFactor3;
agpdpr1=.5*angFactor4*dbetaCapSq1*betaCapSq2/rij[temp_ik];
agpdpr2=.5*angFactor4*betaCapSq1*dbetaCapSq2/rij[temp_ikp];
bt_pi[nb_ij].dBB[0]+=
app2*dcAng[ang_jik][0][ngj]
+app3*dcAng[ang_jikp][0][nglj];
bt_pi[nb_ij].dBB[1]+=
app2*dcAng[ang_jik][1][ngj]
+app3*dcAng[ang_jikp][1][nglj];
bt_pi[nb_ij].dBB[2]+=
app2*dcAng[ang_jik][2][ngj]
+app3*dcAng[ang_jikp][2][nglj];
bt_pi[nb_ik].dBB[0]+=
agpdpr1*disij[0][temp_ik]
+app1*dcAng[ang_kikp][0][1]
+app2*dcAng[ang_jik][0][ngk];
bt_pi[nb_ik].dBB[1]+=
agpdpr1*disij[1][temp_ik]
+app1*dcAng[ang_kikp][1][1]
+app2*dcAng[ang_jik][1][ngk];
bt_pi[nb_ik].dBB[2]+=
agpdpr1*disij[2][temp_ik]
+app1*dcAng[ang_kikp][2][1]
+app2*dcAng[ang_jik][2][ngk];
bt_pi[nb_ikp].dBB[0]+=
agpdpr2*disij[0][temp_ikp]
+app1*dcAng[ang_kikp][0][0]
+app3*dcAng[ang_jikp][0][ngl];
bt_pi[nb_ikp].dBB[1]+=
agpdpr2*disij[1][temp_ikp]
+app1*dcAng[ang_kikp][1][0]
+app3*dcAng[ang_jikp][1][ngl];
bt_pi[nb_ikp].dBB[2]+=
agpdpr2*disij[2][temp_ikp]
+app1*dcAng[ang_kikp][2][0]
+app3*dcAng[ang_jikp][2][ngl];
}
}
}
nPiBk[n]=nPiBk[n]+1;
}
}
}
//j is a neighbor of i and k is a neighbor of j and equal to i
for(ki=0;ki<numneigh[j];ki++) {
temp_jki=BOP_index[j]+ki;
k=jlist[ki];
if(x[k][0]==x[i][0]) {
if(x[k][1]==x[i][1]) {
if(x[k][2]==x[i][2]) {
break;
}
}
}
}
//j is a neighbor of i and k is a neighbor of j not equal to i
for(ktmp=0;ktmp<numneigh[j];ktmp++) {
if(ktmp!=ki) {
temp_jk=BOP_index[j]+ktmp;
if(neigh_flag[temp_jk]) {
k=jlist[ktmp];
pi_flag=0;
for(nsearch=0;nsearch<nPiBk[n];nsearch++) {
ncmp=itypePiBk[n][nsearch];
if(x[ncmp][0]==x[k][0]) {
if(x[ncmp][1]==x[k][1]) {
if(x[ncmp][2]==x[k][2]) {
pi_flag=1;
break;
}
}
}
}
if(pi_flag==0) {
itypePiBk[n][nPiBk[n]]=k;
}
if(ktmp<ki) {
njik=ktmp*(2*numneigh[j]-ktmp-1)/2+(ki-ktmp)-1;
ngi=1;
ngk=0;
}
else {
njik=ki*(2*numneigh[j]-ki-1)/2+(ktmp-ki)-1;
ngi=0;
ngk=1;
}
ang_ijk=cos_index[j]+njik;
if(ang_ijk>=cos_total) {
error->one(FLERR,"Too many atom triplets for pair bop");
}
nb_jk=nb_t;
nb_t++;
if(nb_t>nb_pi) {
new_n_tot=nb_pi+maxneigh;
grow_pi(nb_pi,new_n_tot);
nb_pi=new_n_tot;
}
bt_pi[nb_jk].i=j;
bt_pi[nb_jk].j=k;
bt_pi[nb_jk].temp=temp_jk;
cosSq=cosAng[ang_ijk]*cosAng[ang_ijk];
sinFactor=.5*(1.0-cosSq)*pi_p[jtype-1]*betaS[temp_jk];
cosFactor=.5*(1.0+cosSq)*betaP[temp_jk];
betaCapSq1=pi_p[jtype-1]*betaS[temp_jk]*betaS[temp_jk]
-betaP[temp_jk]*betaP[temp_jk];
dbetaCapSq1=2.0*pi_p[jtype-1]*betaS[temp_jk]*dBetaS[temp_jk]
-2.0*betaP[temp_jk]*dBetaP[temp_jk];
//AA is Eq. 37 (a) and Eq. 19 (b) for j atoms
//3rd BB is 2nd term of Eq. 38 (a) where i and k =neighbors j
AA=AA+sinFactor*betaS[temp_jk]+cosFactor*betaP[temp_jk];
BB=BB+.25*(1.0-cosSq)*(1.0-cosSq)*betaCapSq1*betaCapSq1;
//agpdpr1 is derivative of AA for atom j w.r.t. Beta(r_jk)
//agpdpr2 is derivative of BB for atom j w.r.t. Beta(r_jk)
//app1 is derivative of AA for j atom w.r.t. cos(theta_ijk)
//app2 is derivative of BB 2nd term w.r.t. cos(theta_ijk)
agpdpr1=(2.0*sinFactor*dBetaS[temp_jk]+2.0*cosFactor
*dBetaP[temp_jk])/rij[temp_jk];
agpdpr2=.5*(1.0-cosSq)*(1.0-cosSq)*betaCapSq1*dbetaCapSq1/rij[temp_jk];
app1=cosAng[ang_ijk]*(-pi_p[jtype-1]*betaS[temp_jk]*betaS[temp_jk]
+betaP[temp_jk]*betaP[temp_jk]);
app2=-(1.0-cosSq)*cosAng[ang_ijk]*betaCapSq1*betaCapSq1;
bt_pi[nb_ij].dAA[0]-=
app1*dcAng[ang_ijk][0][ngi];
bt_pi[nb_ij].dAA[1]-=
app1*dcAng[ang_ijk][1][ngi];
bt_pi[nb_ij].dAA[2]-=
app1*dcAng[ang_ijk][2][ngi];
bt_pi[nb_ij].dBB[0]-=
app2*dcAng[ang_ijk][0][ngi];
bt_pi[nb_ij].dBB[1]-=
app2*dcAng[ang_ijk][1][ngi];
bt_pi[nb_ij].dBB[2]-=
app2*dcAng[ang_ijk][2][ngi];
bt_pi[nb_jk].dAA[0]+=
agpdpr1*disij[0][temp_jk]
+app1*dcAng[ang_ijk][0][ngk];
bt_pi[nb_jk].dAA[1]+=
agpdpr1*disij[1][temp_jk]
+app1*dcAng[ang_ijk][1][ngk];
bt_pi[nb_jk].dAA[2]+=
agpdpr1*disij[2][temp_jk]
+app1*dcAng[ang_ijk][2][ngk];
bt_pi[nb_jk].dBB[0]+=
app2*dcAng[ang_ijk][0][ngk]
+agpdpr2*disij[0][temp_jk];
bt_pi[nb_jk].dBB[1]+=
app2*dcAng[ang_ijk][1][ngk]
+agpdpr2*disij[1][temp_jk];
bt_pi[nb_jk].dBB[2]+=
app2*dcAng[ang_ijk][2][ngk]
+agpdpr2*disij[2][temp_jk];
//j is a neighbor of i and k and k' are different neighbors of j not equal to i
for(ltmp=0;ltmp<ktmp;ltmp++) {
if(ltmp!=ki) {
temp_jkp=BOP_index[j]+ltmp;
if(neigh_flag[temp_jkp]) {
kp=jlist[ltmp];
for(nsearch=0;nsearch<nPiBk[n];nsearch++) {
ncmp=itypePiBk[n][nsearch];
if(x[ncmp][0]==x[kp][0]) {
if(x[ncmp][1]==x[kp][1]) {
if(x[ncmp][2]==x[kp][2]) {
break;
}
}
}
}
nkjkp=ltmp*(2*numneigh[j]-ltmp-1)/2+(ktmp-ltmp)-1;
if(ki<ltmp) {
nijkp=ki*(2*numneigh[j]-ki-1)/2+(ltmp-ki)-1;
ngli=0;
ngl=1;
}
else {
nijkp=ltmp*(2*numneigh[j]-ltmp-1)/2+(ki-ltmp)-1;
ngli=1;
ngl=0;
}
ang_ijkp=cos_index[j]+nijkp;
if(ang_ijkp>=cos_total) {
error->one(FLERR,"Too many atom triplets for pair bop");
}
ang_kjkp=cos_index[j]+nkjkp;
if(ang_kjkp>=cos_total) {
error->one(FLERR,"Too many atom triplets for pair bop");
}
nb_jkp=nb_t;
nb_t++;
if(nb_t>nb_pi) {
new_n_tot=nb_pi+maxneigh;
grow_pi(nb_pi,new_n_tot);
nb_pi=new_n_tot;
}
bt_pi[nb_jkp].i=j;
bt_pi[nb_jkp].j=kp;
bt_pi[nb_jkp].temp=temp_jkp;
betaCapSq2=pi_p[jtype-1]*betaS[temp_jkp]*betaS[temp_jkp]
-betaP[temp_jkp]*betaP[temp_jkp];
dbetaCapSq2=2.0*pi_p[jtype-1]*betaS[temp_jkp]*dBetaS[temp_jkp]
-2.0*betaP[temp_jkp]*dBetaP[temp_jkp];
cosSq1=cosAng[ang_ijkp]*cosAng[ang_ijkp];
angFactor=cosAng[ang_kjkp]-cosAng[ang_ijkp]*cosAng[ang_ijk];
angFactor1=4.0*angFactor;
angFactor2=-angFactor1*cosAng[ang_ijkp]
+2.0*cosAng[ang_ijk]*(1.0-cosSq1);
angFactor3=-angFactor1*cosAng[ang_ijk]
+2.0*cosAng[ang_ijkp]*(1.0-cosSq);
angFactor4=2.0*angFactor*angFactor-(1.0-cosSq)*(1.0-cosSq1);
betaCapSum=.5*betaCapSq1*betaCapSq2;
//4th BB is 4th term of Eq. 38 (a) where i , k and k' =neighbors j
BB=BB+betaCapSum*angFactor4;
//app1 is derivative of BB 4th term w.r.t. cos(theta_kjk')
//app2 is derivative of BB 4th term w.r.t. cos(theta_ijk)
//app3 is derivative of BB 4th term w.r.t. cos(theta_ijk')
//agpdpr1 is derivative of BB 4th term for atom j w.r.t. Beta(r_jk)
//agpdpr2 is derivative of BB 4th term for atom j w.r.t. Beta(r_jk')
app1=betaCapSum*angFactor1;
app2=betaCapSum*angFactor2;
app3=betaCapSum*angFactor3;
agpdpr1=.5*angFactor4*dbetaCapSq1*betaCapSq2/rij[temp_jk];
agpdpr2=.5*angFactor4*betaCapSq1*dbetaCapSq2/rij[temp_jkp];
bt_pi[nb_ij].dBB[0]-=
app3*dcAng[ang_ijkp][0][ngli]
+app2*dcAng[ang_ijk][0][ngi];
bt_pi[nb_ij].dBB[1]-=
app3*dcAng[ang_ijkp][1][ngli]
+app2*dcAng[ang_ijk][1][ngi];
bt_pi[nb_ij].dBB[2]-=
app3*dcAng[ang_ijkp][2][ngli]
+app2*dcAng[ang_ijk][2][ngi];
bt_pi[nb_jk].dBB[0]+=
agpdpr1*disij[0][temp_jk]
+app1*dcAng[ang_kjkp][0][1]
+app2*dcAng[ang_ijk][0][ngk];
bt_pi[nb_jk].dBB[1]+=
agpdpr1*disij[1][temp_jk]
+app1*dcAng[ang_kjkp][1][1]
+app2*dcAng[ang_ijk][1][ngk];
bt_pi[nb_jk].dBB[2]+=
agpdpr1*disij[2][temp_jk]
+app1*dcAng[ang_kjkp][2][1]
+app2*dcAng[ang_ijk][2][ngk];
bt_pi[nb_jkp].dBB[0]+=
agpdpr2*disij[0][temp_jkp]
+app1*dcAng[ang_kjkp][0][0]
+app3*dcAng[ang_ijkp][0][ngl];
bt_pi[nb_jkp].dBB[1]+=
agpdpr2*disij[1][temp_jkp]
+app1*dcAng[ang_kjkp][1][0]
+app3*dcAng[ang_ijkp][1][ngl];
bt_pi[nb_jkp].dBB[2]+=
agpdpr2*disij[2][temp_jkp]
+app1*dcAng[ang_kjkp][2][0]
+app3*dcAng[ang_ijkp][2][ngl];
}
}
}
//j and k' are different neighbors of i and k is a neighbor of j not equal to i
for(ltmp=0;ltmp<numneigh[i];ltmp++) {
if(ltmp!=jtmp) {
temp_ikp=BOP_index[i]+ltmp;
if(neigh_flag[temp_ikp]) {
kp=iilist[ltmp];
for(nsearch=0;nsearch<nPiBk[n];nsearch++) {
ncmp=itypePiBk[n][nsearch];
if(x[ncmp][0]==x[kp][0]) {
if(x[ncmp][1]==x[kp][1]) {
if(x[ncmp][2]==x[kp][2]) {
break;
}
}
}
}
if(ltmp<jtmp) {
njikp=ltmp*(2*numneigh[i]-ltmp-1)/2+(jtmp-ltmp)-1;
ngl=1;
nglj=0;
}
else {
njikp=jtmp*(2*numneigh[i]-jtmp-1)/2+(ltmp-jtmp)-1;
ngl=0;
nglj=1;
}
ang_jikp=cos_index[i]+njikp;
if(ang_jikp>=cos_total) {
error->one(FLERR,"Too many atom triplets for pair bop");
}
nb_ikp=nb_t;
nb_t++;
if(nb_t>nb_pi) {
new_n_tot=nb_pi+maxneigh;
grow_pi(nb_pi,new_n_tot);
nb_pi=new_n_tot;
}
bt_pi[nb_ikp].i=i;
bt_pi[nb_ikp].j=kp;
bt_pi[nb_ikp].temp=temp_ikp;
betaCapSq2=pi_p[itype-1]*betaS[temp_ikp]*betaS[temp_ikp]
-betaP[temp_ikp]*betaP[temp_ikp];
dbetaCapSq2=2.0*pi_p[itype-1]*betaS[temp_ikp]*dBetaS[temp_ikp]
-2.0*betaP[temp_ikp]*dBetaP[temp_ikp];
dotV=(disij[0][temp_jk]*disij[0][temp_ikp]+disij[1][temp_jk]
*disij[1][temp_ikp]+disij[2][temp_jk]*disij[2][temp_ikp])
/(rij[temp_jk]*rij[temp_ikp]);
cosSq1=cosAng[ang_jikp]*cosAng[ang_jikp];
angFactor=dotV+cosAng[ang_jikp]*cosAng[ang_ijk];
angRfactor=4.0*angFactor*dotV;
dAngR1=-angRfactor/rij[temp_jk];
dAngR2=-angRfactor/rij[temp_ikp];
angFactor1=4.0*angFactor*cosAng[ang_jikp]
+2.0*cosAng[ang_ijk]*(1.0-cosSq1);
angFactor2=4.0*angFactor*cosAng[ang_ijk]
+2.0*cosAng[ang_jikp]*(1.0-cosSq);
angFactor3=2.0*angFactor*angFactor-(1.0-cosSq)*(1.0-cosSq1);
betaCapSum=.5*betaCapSq1*betaCapSq2;
//5th BB is 5th term of Eq. 38 (a) Eq. 21 (b) where i , k and k' =neighbors j
BB=BB+betaCapSum*angFactor3;
//app1 is derivative of BB 5th term w.r.t. cos(theta_ijk)
//app2 is derivative of BB 5th term w.r.t. cos(theta_jik')
//agpdpr1 is derivative of BB 5th term for atom j w.r.t. Beta(r_jk)
//agpdpr2 is derivative of BB 5th term for atom j w.r.t. Beta(r_ik')
//agpdpr3 is derivative of BB 5th term for atom j w.r.t. dot(r_ik',r_ij)
app1=betaCapSum*angFactor1;
app2=betaCapSum*angFactor2;
agpdpr1=(.5*angFactor3*dbetaCapSq1*betaCapSq2
+betaCapSum*dAngR1)/rij[temp_jk];
agpdpr2=(.5*angFactor3*betaCapSq1*dbetaCapSq2
+betaCapSum*dAngR2)/rij[temp_ikp];
agpdpr3=4.0*betaCapSum*angFactor/(rij[temp_ikp]*rij[temp_jk]);
bt_pi[nb_ij].dBB[0]+=
+app2*dcAng[ang_jikp][0][ngl]
-app1*dcAng[ang_ijk][0][ngi];
bt_pi[nb_ij].dBB[1]+=
+app2*dcAng[ang_jikp][1][ngl]
-app1*dcAng[ang_ijk][1][ngi];
bt_pi[nb_ij].dBB[2]+=
+app2*dcAng[ang_jikp][2][ngl]
-app1*dcAng[ang_ijk][2][ngi];
bt_pi[nb_ikp].dBB[0]+=
agpdpr2*disij[0][temp_ikp]
+agpdpr3*disij[0][temp_jk]
+app2*dcAng[ang_jikp][0][nglj];
bt_pi[nb_ikp].dBB[1]+=
agpdpr2*disij[1][temp_ikp]
+agpdpr3*disij[1][temp_jk]
+app2*dcAng[ang_jikp][1][nglj];
bt_pi[nb_ikp].dBB[2]+=
agpdpr2*disij[2][temp_ikp]
+agpdpr3*disij[2][temp_jk]
+app2*dcAng[ang_jikp][2][nglj];
bt_pi[nb_jk].dBB[0]+=
agpdpr1*disij[0][temp_jk]
+agpdpr3*disij[0][temp_ikp]
+app1*dcAng[ang_ijk][0][ngk];
bt_pi[nb_jk].dBB[1]+=
agpdpr1*disij[1][temp_jk]
+agpdpr3*disij[1][temp_ikp]
+app1*dcAng[ang_ijk][1][ngk];
bt_pi[nb_jk].dBB[2]+=
agpdpr1*disij[2][temp_jk]
+agpdpr3*disij[2][temp_ikp]
+app1*dcAng[ang_ijk][2][ngk];
}
}
}
if(pi_flag==0)
nPiBk[n]=nPiBk[n]+1;
}
}
}
CC=betaP[temp_ij]*betaP[temp_ij]+pi_delta[iij]*pi_delta[iij];
BBrt=sqrt(BB+small6);
AB1=CC+pi_c[iij]*(AA+BBrt)+small7;
AB2=CC+pi_c[iij]*(AA-BBrt+sqrt(small6))+small7;
BBrtR=1.0/BBrt;
ABrtR1=1.0/sqrt(AB1);
ABrtR2=1.0/sqrt(AB2);
// piB is similary formulation to (a) Eq. 36 and (b) Eq. 18
piB[n]=(ABrtR1+ABrtR2)*pi_a[iij]*betaP[temp_ij];
dPiB1=-.5*(cube(ABrtR1)+cube(ABrtR2))*pi_c[iij]*pi_a[iij]*betaP[temp_ij];
dPiB2=.25*BBrtR*(cube(ABrtR2)-cube(ABrtR1))*pi_c[iij]*pi_a[iij]*betaP[temp_ij];
dPiB3=((ABrtR1+ABrtR2)*pi_a[iij]-(cube(ABrtR1)+cube(ABrtR2))*pi_a[iij]
*betaP[temp_ij]*betaP[temp_ij])*dBetaP[temp_ij]/rij[temp_ij];
n++;
pp2=2.0*betaP[temp_ij];
for(m=0;m<nb_t;m++) {
bt_ij=bt_pi[m].temp;
bt_i=bt_pi[m].i;
bt_j=bt_pi[m].j;
for(pp=0;pp<3;pp++) {
bt_pi[m].dPiB[pp]=
+dPiB1*bt_pi[m].dAA[pp]
+dPiB2*bt_pi[m].dBB[pp];
ftmp[pp]=pp2*bt_pi[m].dPiB[pp];
f[bt_i][pp]-=ftmp[pp];
f[bt_j][pp]+=ftmp[pp];
}
if(evflag) {
ev_tally_xyz(bt_i,bt_j,nlocal,newton_pair,0.0,0.0,ftmp[0],ftmp[1]
,ftmp[2],disij[0][bt_ij],disij[1][bt_ij],disij[2][bt_ij]);
}
}
for(pp=0;pp<3;pp++) {
ftmp[pp]=pp2*dPiB3*disij[pp][temp_ij];
f[i][pp]-=ftmp[pp];
f[j][pp]+=ftmp[pp];
}
if(evflag) {
ev_tally_xyz(i,j,nlocal,newton_pair,0.0,0.0,ftmp[0],ftmp[1]
,ftmp[2],disij[0][temp_ij],disij[1][temp_ij],disij[2][temp_ij]);
}
}
}
}
}
destroy_pi();
}
/* ---------------------------------------------------------------------- */
void PairBOP::PiBo_otf()
{
int new_n_tot;
int i,j,k,kp,m,n,pp,nb_t;
int iij,iik,iikp,ji,ki,ijkp,ijk;
int nsearch,ncmp;
int i_tag,j_tag;
int itmp,ltmp,jtmp,ktmp;
int pi_flag,ks;
int nlocal;
int inum,*ilist,*iilist,*jlist;
int **firstneigh,*numneigh;
int itype,jtype,ktype,kptype;
int temp_ij,temp_ik,temp_ikp;
int temp_jk,temp_jkp;
int nb_ij,nb_ik,nb_jk,nb_ikp,nb_jkp;
int bt_i,bt_j;
double AA,BB,CC,DD,EE,FF;
double cosSq,sinFactor,cosFactor;
double cosSq1,dotV,BBrt,AB1,AB2;
double BBrtR,ABrtR,ABrtR1,ABrtR2;
double angFactor,angFactor1,angFactor2;
double angFactor3,angFactor4,angRfactor;
double dAngR1,dAngR2,agpdpr3;
double agpdpr1,agpdpr2,app1,app2,app3;
double betaCapSq1,dbetaCapSq1;
double betaCapSq2,dbetaCapSq2;
double betaCapSum,ps;
double ftmp[3],xtmp[3];
double dPiB1,dPiB2,dPiB3,pp2;
double dis_ij[3],rsq_ij,r_ij;
double betaP_ij,dBetaP_ij;
double dis_ik[3],rsq_ik,r_ik;
double betaS_ik,dBetaS_ik;
double betaP_ik,dBetaP_ik;
double dis_ikp[3],rsq_ikp,r_ikp;
double betaS_ikp,dBetaS_ikp;
double betaP_ikp,dBetaP_ikp;
double dis_jk[3],rsq_jk,r_jk;
double betaS_jk,dBetaS_jk;
double betaP_jk,dBetaP_jk;
double dis_jkp[3],rsq_jkp,r_jkp;
double betaS_jkp,dBetaS_jkp;
double betaP_jkp,dBetaP_jkp;
double cosAng_jik,dcA_jik[3][2];
double cosAng_jikp,dcA_jikp[3][2];
double cosAng_kikp,dcA_kikp[3][2];
double cosAng_ijk,dcA_ijk[3][2];
double cosAng_ijkp,dcA_ijkp[3][2];
double cosAng_kjkp,dcA_kjkp[3][2];
int newton_pair = force->newton_pair;
double **f = atom->f;
double **x = atom->x;
int *type = atom->type;
int *tag = atom->tag;
nlocal = atom->nlocal;
numneigh = list->numneigh;
firstneigh = list->firstneigh;
inum = list->inum;
ilist = list->ilist;
n=0;
if(nb_pi>16) {
nb_pi=16;
}
if(nb_pi==0) {
nb_pi=(maxneigh)*(maxneigh/2);
}
// Loop over all local atoms for i
if(allocate_pi) {
destroy_pi();
}
create_pi(nb_pi);
for(itmp=0;itmp<inum;itmp++) {
nb_t=0;
i = ilist[itmp];
itype = map[type[i]]+1;
i_tag=tag[i];
// j is a loop over all neighbors of i
iilist=firstneigh[i];
for(jtmp=0;jtmp<numneigh[i];jtmp++) {
for(m=0;m<nb_pi;m++) {
for(pp=0;pp<3;pp++) {
bt_pi[m].dAA[pp]=0.0;
bt_pi[m].dBB[pp]=0.0;
bt_pi[m].dPiB[pp]=0.0;
}
bt_pi[m].i=-1;
bt_pi[m].j=-1;
}
temp_ij=BOP_index[i]+jtmp;
j=iilist[jtmp];
jlist=firstneigh[j];
jtype=map[type[j]]+1;
j_tag=tag[j];
nb_t=0;
ftmp[0]=0.0;
ftmp[1]=0.0;
ftmp[2]=0.0;
if(j_tag>=i_tag) {
if(itype==jtype)
iij=itype-1;
else if(itype<jtype)
iij=itype*bop_types-itype*(itype+1)/2+jtype-1;
else
iij=jtype*bop_types-jtype*(jtype+1)/2+itype-1;
AA=0.0;
BB=0.0;
nPiBk[n]=0;
for(ji=0;ji<numneigh[j];ji++) {
if(x[jlist[ji]][0]==x[i][0]) {
if(x[jlist[ji]][1]==x[i][1]) {
if(x[jlist[ji]][2]==x[i][2]) {
break;
}
}
}
}
nb_ij=nb_t;
nb_t++;
if(nb_t>nb_pi) {
new_n_tot=nb_pi+maxneigh;
grow_pi(nb_pi,new_n_tot);
nb_pi=new_n_tot;
}
bt_pi[nb_ij].i=i;
bt_pi[nb_ij].j=j;
bt_pi[nb_ij].temp=temp_ij;
dis_ij[0]=x[j][0]-x[i][0];
dis_ij[1]=x[j][1]-x[i][1];
dis_ij[2]=x[j][2]-x[i][2];
rsq_ij=dis_ij[0]*dis_ij[0]
+dis_ij[1]*dis_ij[1]
+dis_ij[2]*dis_ij[2];
r_ij=sqrt(rsq_ij);
if(r_ij<=rcut[iij]) {
ps=r_ij*rdr[iij]+1.0;
ks=(int)ps;
if(nr-1<ks)
ks=nr-1;
ps=ps-ks;
if(ps>1.0)
ps=1.0;
betaP_ij=((pBetaP3[iij][ks-1]*ps+pBetaP2[iij][ks-1])*ps
+pBetaP1[iij][ks-1])*ps+pBetaP[iij][ks-1];
dBetaP_ij=(pBetaP6[iij][ks-1]*ps+pBetaP5[iij][ks-1])*ps
+pBetaP4[iij][ks-1];
// j and k are different neighbors of i
for(ktmp=0;ktmp<numneigh[i];ktmp++) {
if(ktmp!=jtmp) {
temp_ik=BOP_index[i]+ktmp;
k=iilist[ktmp];
ktype=map[type[k]]+1;
if(itype==ktype)
iik=itype-1;
else if(itype<ktype)
iik=itype*bop_types-itype*(itype+1)/2+ktype-1;
else
iik=ktype*bop_types-ktype*(ktype+1)/2+itype-1;
dis_ik[0]=x[k][0]-x[i][0];
dis_ik[1]=x[k][1]-x[i][1];
dis_ik[2]=x[k][2]-x[i][2];
rsq_ik=dis_ik[0]*dis_ik[0]
+dis_ik[1]*dis_ik[1]
+dis_ik[2]*dis_ik[2];
r_ik=sqrt(rsq_ik);
if(r_ik<=rcut[iik]) {
ps=r_ik*rdr[iik]+1.0;
ks=(int)ps;
if(nr-1<ks)
ks=nr-1;
ps=ps-ks;
if(ps>1.0)
ps=1.0;
betaS_ik=((pBetaS3[iik][ks-1]*ps+pBetaS2[iik][ks-1])*ps
+pBetaS1[iik][ks-1])*ps+pBetaS[iik][ks-1];
dBetaS_ik=(pBetaS6[iik][ks-1]*ps+pBetaS5[iik][ks-1])*ps
+pBetaS4[iik][ks-1];
betaP_ik=((pBetaP3[iik][ks-1]*ps+pBetaP2[iik][ks-1])*ps
+pBetaP1[iik][ks-1])*ps+pBetaP[iik][ks-1];
dBetaP_ik=(pBetaP6[iik][ks-1]*ps+pBetaP5[iik][ks-1])*ps
+pBetaP4[iik][ks-1];
cosAng_jik=(dis_ij[0]*dis_ik[0]+dis_ij[1]*dis_ik[1]
+dis_ij[2]*dis_ik[2])/(r_ij*r_ik);
dcA_jik[0][0]=(dis_ik[0]*r_ij*r_ik-cosAng_jik
*dis_ij[0]*r_ik*r_ik)/(r_ij*r_ij*r_ik*r_ik);
dcA_jik[1][0]=(dis_ik[1]*r_ij*r_ik-cosAng_jik
*dis_ij[1]*r_ik*r_ik)/(r_ij*r_ij*r_ik*r_ik);
dcA_jik[2][0]=(dis_ik[2]*r_ij*r_ik-cosAng_jik
*dis_ij[2]*r_ik*r_ik)/(r_ij*r_ij*r_ik*r_ik);
dcA_jik[0][1]=(dis_ij[0]*r_ij*r_ik-cosAng_jik
*dis_ik[0]*r_ij*r_ij)/(r_ij*r_ij*r_ik*r_ik);
dcA_jik[1][1]=(dis_ij[1]*r_ij*r_ik-cosAng_jik
*dis_ik[1]*r_ij*r_ij)/(r_ij*r_ij*r_ik*r_ik);
dcA_jik[2][1]=(dis_ij[2]*r_ij*r_ik-cosAng_jik
*dis_ik[2]*r_ij*r_ij)/(r_ij*r_ij*r_ik*r_ik);
nb_ik=nb_t;
nb_t++;
if(nb_t>nb_pi) {
new_n_tot=nb_pi+maxneigh;
grow_pi(nb_pi,new_n_tot);
nb_pi=new_n_tot;
}
bt_pi[nb_ik].i=i;
bt_pi[nb_ik].j=k;
bt_pi[nb_ik].temp=temp_ik;
cosSq=cosAng_jik*cosAng_jik;
sinFactor=.5*(1.0-cosSq)*pi_p[itype-1]*betaS_ik;
cosFactor=.5*(1.0+cosSq)*betaP_ik;
betaCapSq1=pi_p[itype-1]*betaS_ik*betaS_ik-betaP_ik
*betaP_ik;
dbetaCapSq1=2.0*pi_p[itype-1]*betaS_ik*dBetaS_ik
-2.0*betaP_ik*dBetaP_ik;
//AA is Eq. 37 (a) and Eq. 19 (b) or i atoms
//1st BB is first term of Eq. 38 (a) where j and k =neighbors i
AA=AA+sinFactor*betaS_ik+cosFactor*betaP_ik;
BB=BB+.25*(1.0-cosSq)*(1.0-cosSq)*betaCapSq1*betaCapSq1;
//agpdpr1 is derivative of AA w.r.t. for atom i w.r.t. Beta(r_ik)
//agpdpr2 is derivative of BB w.r.t. for atom i w.r.t. Beta(r_ik)
//app1 is derivative of AA w.r.t. for atom i w.r.t. cos(theta_jik)
//app2 is derivative of BB w.r.t. for atom i w.r.t. cos(theta_jik)
agpdpr1=(2.0*sinFactor*dBetaS_ik+2.0*cosFactor
*dBetaP_ik)/r_ik;
app1=cosAng_jik*(-pi_p[itype-1]*betaS_ik*betaS_ik
+betaP_ik*betaP_ik);
app2=-(1.0-cosSq)*cosAng_jik*betaCapSq1*betaCapSq1;
agpdpr2=.5*(1.0-cosSq)*(1.0-cosSq)*betaCapSq1*dbetaCapSq1/r_ik;
itypePiBk[n][nPiBk[n]]=k;
bt_pi[nb_ij].dAA[0]+=
app1*dcA_jik[0][0];
bt_pi[nb_ij].dAA[1]+=
app1*dcA_jik[1][0];
bt_pi[nb_ij].dAA[2]+=
app1*dcA_jik[2][0];
bt_pi[nb_ij].dBB[0]+=
app2*dcA_jik[0][0];
bt_pi[nb_ij].dBB[1]+=
app2*dcA_jik[1][0];
bt_pi[nb_ij].dBB[2]+=
app2*dcA_jik[2][0];
bt_pi[nb_ik].dAA[0]+=
agpdpr1*dis_ik[0]
+app1*dcA_jik[0][1];
bt_pi[nb_ik].dAA[1]+=
agpdpr1*dis_ik[1]
+app1*dcA_jik[1][1];
bt_pi[nb_ik].dAA[2]+=
agpdpr1*dis_ik[2]
+app1*dcA_jik[2][1];
bt_pi[nb_ik].dBB[0]+=
app2*dcA_jik[0][1]
+agpdpr2*dis_ik[0];
bt_pi[nb_ik].dBB[1]+=
app2*dcA_jik[1][1]
+agpdpr2*dis_ik[1];
bt_pi[nb_ik].dBB[2]+=
app2*dcA_jik[2][1]
+agpdpr2*dis_ik[2];
// j and k and k' are different neighbors of i
for(ltmp=0;ltmp<ktmp;ltmp++) {
if(ltmp!=jtmp) {
temp_ikp=BOP_index[i]+ltmp;
kp=iilist[ltmp];
kptype=map[type[kp]]+1;
for(nsearch=0;nsearch<nPiBk[n];nsearch++) {
ncmp=itypePiBk[n][nsearch];
if(x[ncmp][0]==x[kp][0]) {
if(x[ncmp][1]==x[kp][1]) {
if(x[ncmp][2]==x[kp][2]) {
break;
}
}
}
}
if(itype==kptype)
iikp=itype-1;
else if(itype<kptype)
iikp=itype*bop_types-itype*(itype+1)/2+kptype-1;
else
iikp=kptype*bop_types-kptype*(kptype+1)/2+itype-1;
dis_ikp[0]=x[kp][0]-x[i][0];
dis_ikp[1]=x[kp][1]-x[i][1];
dis_ikp[2]=x[kp][2]-x[i][2];
rsq_ikp=dis_ikp[0]*dis_ikp[0]
+dis_ikp[1]*dis_ikp[1]
+dis_ikp[2]*dis_ikp[2];
r_ikp=sqrt(rsq_ikp);
if(r_ikp<=rcut[iikp]) {
ps=r_ikp*rdr[iikp]+1.0;
ks=(int)ps;
if(nr-1<ks)
ks=nr-1;
ps=ps-ks;
if(ps>1.0)
ps=1.0;
betaS_ikp=((pBetaS3[iikp][ks-1]*ps+pBetaS2[iikp][ks-1])*ps
+pBetaS1[iikp][ks-1])*ps+pBetaS[iikp][ks-1];
dBetaS_ikp=(pBetaS6[iikp][ks-1]*ps+pBetaS5[iikp][ks-1])*ps
+pBetaS4[iikp][ks-1];
betaP_ikp=((pBetaP3[iikp][ks-1]*ps+pBetaP2[iikp][ks-1])*ps
+pBetaP1[iikp][ks-1])*ps+pBetaP[iikp][ks-1];
dBetaP_ikp=(pBetaP6[iikp][ks-1]*ps+pBetaP5[iikp][ks-1])*ps
+pBetaP4[iikp][ks-1];
cosAng_jikp=(dis_ij[0]*dis_ikp[0]+dis_ij[1]*dis_ikp[1]
+dis_ij[2]*dis_ikp[2])/(r_ij*r_ikp);
dcA_jikp[0][0]=(dis_ikp[0]*r_ij*r_ikp-cosAng_jikp
*dis_ij[0]*r_ikp*r_ikp)/(r_ij*r_ij*r_ikp*r_ikp);
dcA_jikp[1][0]=(dis_ikp[1]*r_ij*r_ikp-cosAng_jikp
*dis_ij[1]*r_ikp*r_ikp)/(r_ij*r_ij*r_ikp*r_ikp);
dcA_jikp[2][0]=(dis_ikp[2]*r_ij*r_ikp-cosAng_jikp
*dis_ij[2]*r_ikp*r_ikp)/(r_ij*r_ij*r_ikp*r_ikp);
dcA_jikp[0][1]=(dis_ij[0]*r_ij*r_ikp-cosAng_jikp
*dis_ikp[0]*r_ij*r_ij)/(r_ij*r_ij*r_ikp*r_ikp);
dcA_jikp[1][1]=(dis_ij[1]*r_ij*r_ikp-cosAng_jikp
*dis_ikp[1]*r_ij*r_ij)/(r_ij*r_ij*r_ikp*r_ikp);
dcA_jikp[2][1]=(dis_ij[2]*r_ij*r_ikp-cosAng_jikp
*dis_ikp[2]*r_ij*r_ij)/(r_ij*r_ij*r_ikp*r_ikp);
cosAng_kikp=(dis_ik[0]*dis_ikp[0]+dis_ik[1]*dis_ikp[1]
+dis_ik[2]*dis_ikp[2])/(r_ik*r_ikp);
dcA_kikp[0][0]=(dis_ikp[0]*r_ik*r_ikp-cosAng_kikp
*dis_ik[0]*r_ikp*r_ikp)/(r_ik*r_ik*r_ikp*r_ikp);
dcA_kikp[1][0]=(dis_ikp[1]*r_ik*r_ikp-cosAng_kikp
*dis_ik[1]*r_ikp*r_ikp)/(r_ik*r_ik*r_ikp*r_ikp);
dcA_kikp[2][0]=(dis_ikp[2]*r_ik*r_ikp-cosAng_kikp
*dis_ik[2]*r_ikp*r_ikp)/(r_ik*r_ik*r_ikp*r_ikp);
dcA_kikp[0][1]=(dis_ik[0]*r_ik*r_ikp-cosAng_kikp
*dis_ikp[0]*r_ik*r_ik)/(r_ik*r_ik*r_ikp*r_ikp);
dcA_kikp[1][1]=(dis_ik[1]*r_ik*r_ikp-cosAng_kikp
*dis_ikp[1]*r_ik*r_ik)/(r_ik*r_ik*r_ikp*r_ikp);
dcA_kikp[2][1]=(dis_ik[2]*r_ik*r_ikp-cosAng_kikp
*dis_ikp[2]*r_ik*r_ik)/(r_ik*r_ik*r_ikp*r_ikp);
nb_ikp=nb_t;
nb_t++;
if(nb_t>nb_pi) {
new_n_tot=nb_pi+maxneigh;
grow_pi(nb_pi,new_n_tot);
nb_pi=new_n_tot;
}
bt_pi[nb_ikp].i=i;
bt_pi[nb_ikp].j=kp;
bt_pi[nb_ikp].temp=temp_ikp;
betaCapSq2=pi_p[itype-1]*betaS_ikp*betaS_ikp
-betaP_ikp*betaP_ikp;
dbetaCapSq2=2.0*pi_p[itype-1]*betaS_ikp*dBetaS_ikp
-2.0*betaP_ikp*dBetaP_ikp;
cosSq1=cosAng_jikp*cosAng_jikp;
angFactor=cosAng_kikp-cosAng_jikp*cosAng_jik;
angFactor1=4.0*angFactor;
angFactor2=-angFactor1*cosAng_jikp
+2.0*cosAng_jik*(1.0-cosSq1);
angFactor3=-angFactor1*cosAng_jik
+2.0*cosAng_jikp*(1.0-cosSq);
angFactor4=2.0*angFactor*angFactor-(1.0-cosSq)*(1.0-cosSq1);
betaCapSum=.5*betaCapSq1*betaCapSq2;
//2nd BB is third term of Eq. 38 (a) where j , k and k'=neighbors i
BB=BB+betaCapSum*angFactor4;
//agpdpr1 is derivative of BB w.r.t. for atom i w.r.t. Beta(r_ik)
//agpdpr2 is derivative of BB w.r.t. for atom i w.r.t. Beta(r_ik')
//app1 is derivative of BB 3rd term w.r.t. cos(theta_kik')
//app2 is derivative of BB 3rd term w.r.t. cos(theta_jik)
//app3 is derivative of BB 3rd term w.r.t. cos(theta_jik')
app1=betaCapSum*angFactor1;
app2=betaCapSum*angFactor2;
app3=betaCapSum*angFactor3;
agpdpr1=.5*angFactor4*dbetaCapSq1*betaCapSq2/r_ik;
agpdpr2=.5*angFactor4*betaCapSq1*dbetaCapSq2/r_ikp;
bt_pi[nb_ij].dBB[0]+=
app2*dcA_jik[0][0]
+app3*dcA_jikp[0][0];
bt_pi[nb_ij].dBB[1]+=
app2*dcA_jik[1][0]
+app3*dcA_jikp[1][0];
bt_pi[nb_ij].dBB[2]+=
app2*dcA_jik[2][0]
+app3*dcA_jikp[2][0];
bt_pi[nb_ik].dBB[0]+=
agpdpr1*dis_ik[0]
+app1*dcA_kikp[0][0]
+app2*dcA_jik[0][1];
bt_pi[nb_ik].dBB[1]+=
agpdpr1*dis_ik[1]
+app1*dcA_kikp[1][0]
+app2*dcA_jik[1][1];
bt_pi[nb_ik].dBB[2]+=
agpdpr1*dis_ik[2]
+app1*dcA_kikp[2][0]
+app2*dcA_jik[2][1];
bt_pi[nb_ikp].dBB[0]+=
agpdpr2*dis_ikp[0]
+app1*dcA_kikp[0][1]
+app3*dcA_jikp[0][1];
bt_pi[nb_ikp].dBB[1]+=
agpdpr2*dis_ikp[1]
+app1*dcA_kikp[1][1]
+app3*dcA_jikp[1][1];
bt_pi[nb_ikp].dBB[2]+=
agpdpr2*dis_ikp[2]
+app1*dcA_kikp[2][1]
+app3*dcA_jikp[2][1];
}
}
}
nPiBk[n]=nPiBk[n]+1;
}
}
}
//j is a neighbor of i and k is a neighbor of j and equal to i
for(ki=0;ki<numneigh[j];ki++) {
k=jlist[ki];
if(x[k][0]==x[i][0]) {
if(x[k][1]==x[i][1]) {
if(x[k][2]==x[i][2]) {
break;
}
}
}
}
//j is a neighbor of i and k is a neighbor of j not equal to i
for(ktmp=0;ktmp<numneigh[j];ktmp++) {
if(ktmp!=ki) {
temp_jk=BOP_index[j]+ktmp;
k=jlist[ktmp];
ktype=map[type[k]]+1;
pi_flag=0;
for(nsearch=0;nsearch<nPiBk[n];nsearch++) {
ncmp=itypePiBk[n][nsearch];
if(x[ncmp][0]==x[k][0]) {
if(x[ncmp][1]==x[k][1]) {
if(x[ncmp][2]==x[k][2]) {
pi_flag=1;
break;
}
}
}
}
if(pi_flag==0) {
itypePiBk[n][nPiBk[n]]=k;
}
if(jtype==ktype)
ijk=jtype-1;
else if(jtype<ktype)
ijk=jtype*bop_types-jtype*(jtype+1)/2+ktype-1;
else
ijk=ktype*bop_types-ktype*(ktype+1)/2+jtype-1;
dis_jk[0]=x[k][0]-x[j][0];
dis_jk[1]=x[k][1]-x[j][1];
dis_jk[2]=x[k][2]-x[j][2];
rsq_jk=dis_jk[0]*dis_jk[0]
+dis_jk[1]*dis_jk[1]
+dis_jk[2]*dis_jk[2];
r_jk=sqrt(rsq_jk);
if(r_jk<=rcut[ijk]) {
ps=r_jk*rdr[ijk]+1.0;
ks=(int)ps;
if(nr-1<ks)
ks=nr-1;
ps=ps-ks;
if(ps>1.0)
ps=1.0;
betaS_jk=((pBetaS3[ijk][ks-1]*ps+pBetaS2[ijk][ks-1])*ps
+pBetaS1[ijk][ks-1])*ps+pBetaS[ijk][ks-1];
dBetaS_jk=(pBetaS6[ijk][ks-1]*ps+pBetaS5[ijk][ks-1])*ps
+pBetaS4[ijk][ks-1];
betaP_jk=((pBetaP3[ijk][ks-1]*ps+pBetaP2[ijk][ks-1])*ps
+pBetaP1[ijk][ks-1])*ps+pBetaP[ijk][ks-1];
dBetaP_jk=(pBetaP6[ijk][ks-1]*ps+pBetaP5[ijk][ks-1])*ps
+pBetaP4[ijk][ks-1];
cosAng_ijk=(-dis_ij[0]*dis_jk[0]-dis_ij[1]*dis_jk[1]
-dis_ij[2]*dis_jk[2])/(r_ij*r_jk);
dcA_ijk[0][0]=(dis_jk[0]*r_ij*r_jk-cosAng_ijk
*-dis_ij[0]*r_jk*r_jk)/(r_ij*r_ij*r_jk*r_jk);
dcA_ijk[1][0]=(dis_jk[1]*r_ij*r_jk-cosAng_ijk
*-dis_ij[1]*r_jk*r_jk)/(r_ij*r_ij*r_jk*r_jk);
dcA_ijk[2][0]=(dis_jk[2]*r_ij*r_jk-cosAng_ijk
*-dis_ij[2]*r_jk*r_jk)/(r_ij*r_ij*r_jk*r_jk);
dcA_ijk[0][1]=(-dis_ij[0]*r_ij*r_jk-cosAng_ijk
*dis_jk[0]*r_ij*r_ij)/(r_ij*r_ij*r_jk*r_jk);
dcA_ijk[1][1]=(-dis_ij[1]*r_ij*r_jk-cosAng_ijk
*dis_jk[1]*r_ij*r_ij)/(r_ij*r_ij*r_jk*r_jk);
dcA_ijk[2][1]=(-dis_ij[2]*r_ij*r_jk-cosAng_ijk
*dis_jk[2]*r_ij*r_ij)/(r_ij*r_ij*r_jk*r_jk);
nb_jk=nb_t;
nb_t++;
if(nb_t>nb_pi) {
new_n_tot=nb_pi+maxneigh;
grow_pi(nb_pi,new_n_tot);
nb_pi=new_n_tot;
}
bt_pi[nb_jk].i=j;
bt_pi[nb_jk].j=k;
bt_pi[nb_jk].temp=temp_jk;
cosSq=cosAng_ijk*cosAng_ijk;
sinFactor=.5*(1.0-cosSq)*pi_p[jtype-1]*betaS_jk;
cosFactor=.5*(1.0+cosSq)*betaP_jk;
betaCapSq1=pi_p[jtype-1]*betaS_jk*betaS_jk
-betaP_jk*betaP_jk;
dbetaCapSq1=2.0*pi_p[jtype-1]*betaS_jk*dBetaS_jk
-2.0*betaP_jk*dBetaP_jk;
//AA is Eq. 37 (a) and Eq. 19 (b) for j atoms
//3rd BB is 2nd term of Eq. 38 (a) where i and k =neighbors j
AA=AA+sinFactor*betaS_jk+cosFactor*betaP_jk;
BB=BB+.25*(1.0-cosSq)*(1.0-cosSq)*betaCapSq1*betaCapSq1;
agpdpr1=(2.0*sinFactor*dBetaS_jk+2.0*cosFactor
*dBetaP_jk)/r_jk;
//agpdpr1 is derivative of AA for atom j w.r.t. Beta(r_jk)
//agpdpr2 is derivative of BB for atom j w.r.t. Beta(r_jk)
//app1 is derivative of AA for j atom w.r.t. cos(theta_ijk)
//app2 is derivative of BB 2nd term w.r.t. cos(theta_ijk)
agpdpr2=.5*(1.0-cosSq)*(1.0-cosSq)*betaCapSq1*dbetaCapSq1/r_jk;
app1=cosAng_ijk*(-pi_p[jtype-1]*betaS_jk*betaS_jk
+betaP_jk*betaP_jk);
app2=-(1.0-cosSq)*cosAng_ijk*betaCapSq1*betaCapSq1;
bt_pi[nb_ij].dAA[0]-=
app1*dcA_ijk[0][0];
bt_pi[nb_ij].dAA[1]-=
app1*dcA_ijk[1][0];
bt_pi[nb_ij].dAA[2]-=
app1*dcA_ijk[2][0];
bt_pi[nb_ij].dBB[0]-=
app2*dcA_ijk[0][0];
bt_pi[nb_ij].dBB[1]-=
app2*dcA_ijk[1][0];
bt_pi[nb_ij].dBB[2]-=
app2*dcA_ijk[2][0];
bt_pi[nb_jk].dAA[0]+=
agpdpr1*dis_jk[0]
+app1*dcA_ijk[0][1];
bt_pi[nb_jk].dAA[1]+=
agpdpr1*dis_jk[1]
+app1*dcA_ijk[1][1];
bt_pi[nb_jk].dAA[2]+=
agpdpr1*dis_jk[2]
+app1*dcA_ijk[2][1];
bt_pi[nb_jk].dBB[0]+=
app2*dcA_ijk[0][1]
+agpdpr2*dis_jk[0];
bt_pi[nb_jk].dBB[1]+=
app2*dcA_ijk[1][1]
+agpdpr2*dis_jk[1];
bt_pi[nb_jk].dBB[2]+=
app2*dcA_ijk[2][1]
+agpdpr2*dis_jk[2];
//j is a neighbor of i and k and k' are different neighbors of j not equal to i
for(ltmp=0;ltmp<ktmp;ltmp++) {
if(ltmp!=ki) {
temp_jkp=BOP_index[j]+ltmp;
kp=jlist[ltmp];
kptype=map[type[kp]]+1;
for(nsearch=0;nsearch<nPiBk[n];nsearch++) {
ncmp=itypePiBk[n][nsearch];
if(x[ncmp][0]==x[kp][0]) {
if(x[ncmp][1]==x[kp][1]) {
if(x[ncmp][2]==x[kp][2]) {
break;
}
}
}
}
if(jtype==kptype)
ijkp=jtype-1;
else if(jtype<kptype)
ijkp=jtype*bop_types-jtype*(jtype+1)/2+kptype-1;
else
ijkp=kptype*bop_types-kptype*(kptype+1)/2+jtype-1;
dis_jkp[0]=x[kp][0]-x[j][0];
dis_jkp[1]=x[kp][1]-x[j][1];
dis_jkp[2]=x[kp][2]-x[j][2];
rsq_jkp=dis_jkp[0]*dis_jkp[0]
+dis_jkp[1]*dis_jkp[1]
+dis_jkp[2]*dis_jkp[2];
r_jkp=sqrt(rsq_jkp);
if(r_jkp<=rcut[ijkp]) {
ps=r_jkp*rdr[ijkp]+1.0;
ks=(int)ps;
if(nr-1<ks)
ks=nr-1;
ps=ps-ks;
if(ps>1.0)
ps=1.0;
betaS_jkp=((pBetaS3[ijkp][ks-1]*ps+pBetaS2[ijkp][ks-1])*ps
+pBetaS1[ijkp][ks-1])*ps+pBetaS[ijkp][ks-1];
dBetaS_jkp=(pBetaS6[ijkp][ks-1]*ps+pBetaS5[ijkp][ks-1])*ps
+pBetaS4[ijkp][ks-1];
betaP_jkp=((pBetaP3[ijkp][ks-1]*ps+pBetaP2[ijkp][ks-1])*ps
+pBetaP1[ijkp][ks-1])*ps+pBetaP[ijkp][ks-1];
dBetaP_jkp=(pBetaP6[ijkp][ks-1]*ps+pBetaP5[ijkp][ks-1])*ps
+pBetaP4[ijkp][ks-1];
cosAng_ijkp=(-dis_ij[0]*dis_jkp[0]-dis_ij[1]*dis_jkp[1]
-dis_ij[2]*dis_jkp[2])/(r_ij*r_jkp);
dcA_ijkp[0][0]=(dis_jkp[0]*r_ij*r_jkp-cosAng_ijkp
*-dis_ij[0]*r_jkp*r_jkp)/(r_ij*r_ij*r_jkp*r_jkp);
dcA_ijkp[1][0]=(dis_jkp[1]*r_ij*r_jkp-cosAng_ijkp
*-dis_ij[1]*r_jkp*r_jkp)/(r_ij*r_ij*r_jkp*r_jkp);
dcA_ijkp[2][0]=(dis_jkp[2]*r_ij*r_jkp-cosAng_ijkp
*-dis_ij[2]*r_jkp*r_jkp)/(r_ij*r_ij*r_jkp*r_jkp);
dcA_ijkp[0][1]=(-dis_ij[0]*r_ij*r_jkp-cosAng_ijkp
*dis_jkp[0]*r_ij*r_ij)/(r_ij*r_ij*r_jkp*r_jkp);
dcA_ijkp[1][1]=(-dis_ij[1]*r_ij*r_jkp-cosAng_ijkp
*dis_jkp[1]*r_ij*r_ij)/(r_ij*r_ij*r_jkp*r_jkp);
dcA_ijkp[2][1]=(-dis_ij[2]*r_ij*r_jkp-cosAng_ijkp
*dis_jkp[2]*r_ij*r_ij)/(r_ij*r_ij*r_jkp*r_jkp);
cosAng_kjkp=(dis_jk[0]*dis_jkp[0]+dis_jk[1]*dis_jkp[1]
+dis_jk[2]*dis_jkp[2])/(r_jk*r_jkp);
dcA_kjkp[0][0]=(dis_jkp[0]*r_jk*r_jkp-cosAng_kjkp
*dis_jk[0]*r_jkp*r_jkp)/(r_jk*r_jk*r_jkp*r_jkp);
dcA_kjkp[1][0]=(dis_jkp[1]*r_jk*r_jkp-cosAng_kjkp
*dis_jk[1]*r_jkp*r_jkp)/(r_jk*r_jk*r_jkp*r_jkp);
dcA_kjkp[2][0]=(dis_jkp[2]*r_jk*r_jkp-cosAng_kjkp
*dis_jk[2]*r_jkp*r_jkp)/(r_jk*r_jk*r_jkp*r_jkp);
dcA_kjkp[0][1]=(dis_jk[0]*r_jk*r_jkp-cosAng_kjkp
*dis_jkp[0]*r_jk*r_jk)/(r_jk*r_jk*r_jkp*r_jkp);
dcA_kjkp[1][1]=(dis_jk[1]*r_jk*r_jkp-cosAng_kjkp
*dis_jkp[1]*r_jk*r_jk)/(r_jk*r_jk*r_jkp*r_jkp);
dcA_kjkp[2][1]=(dis_jk[2]*r_jk*r_jkp-cosAng_kjkp
*dis_jkp[2]*r_jk*r_jk)/(r_jk*r_jk*r_jkp*r_jkp);
nb_jkp=nb_t;
nb_t++;
if(nb_t>nb_pi) {
new_n_tot=nb_pi+maxneigh;
grow_pi(nb_pi,new_n_tot);
nb_pi=new_n_tot;
}
bt_pi[nb_jkp].i=j;
bt_pi[nb_jkp].j=kp;
bt_pi[nb_jkp].temp=temp_jkp;
betaCapSq2=pi_p[jtype-1]*betaS_jkp*betaS_jkp
-betaP_jkp*betaP_jkp;
dbetaCapSq2=2.0*pi_p[jtype-1]*betaS_jkp*dBetaS_jkp
-2.0*betaP_jkp*dBetaP_jkp;
cosSq1=cosAng_ijkp*cosAng_ijkp;
angFactor=cosAng_kjkp-cosAng_ijkp*cosAng_ijk;
angFactor1=4.0*angFactor;
angFactor2=-angFactor1*cosAng_ijkp
+2.0*cosAng_ijk*(1.0-cosSq1);
angFactor3=-angFactor1*cosAng_ijk
+2.0*cosAng_ijkp*(1.0-cosSq);
angFactor4=2.0*angFactor*angFactor-(1.0-cosSq)*(1.0-cosSq1);
betaCapSum=.5*betaCapSq1*betaCapSq2;
//4th BB is 4th term of Eq. 38 (a) where i , k and k' =neighbors j
BB=BB+betaCapSum*angFactor4;
//app1 is derivative of BB 4th term w.r.t. cos(theta_kjk')
//app2 is derivative of BB 4th term w.r.t. cos(theta_ijk)
//app3 is derivative of BB 4th term w.r.t. cos(theta_ijk')
//agpdpr1 is derivative of BB 4th term for atom j w.r.t. Beta(r_jk)
//agpdpr2 is derivative of BB 4th term for atom j w.r.t. Beta(r_jk')
app1=betaCapSum*angFactor1;
app2=betaCapSum*angFactor2;
app3=betaCapSum*angFactor3;
agpdpr1=.5*angFactor4*dbetaCapSq1*betaCapSq2/r_jk;
agpdpr2=.5*angFactor4*betaCapSq1*dbetaCapSq2/r_jkp;
bt_pi[nb_ij].dBB[0]-=
app3*dcA_ijkp[0][0]
+app2*dcA_ijk[0][0];
bt_pi[nb_ij].dBB[1]-=
app3*dcA_ijkp[1][0]
+app2*dcA_ijk[1][0];
bt_pi[nb_ij].dBB[2]-=
app3*dcA_ijkp[2][0]
+app2*dcA_ijk[2][0];
bt_pi[nb_jk].dBB[0]+=
agpdpr1*dis_jk[0]
+app1*dcA_kjkp[0][0]
+app2*dcA_ijk[0][1];
bt_pi[nb_jk].dBB[1]+=
agpdpr1*dis_jk[1]
+app1*dcA_kjkp[1][0]
+app2*dcA_ijk[1][1];
bt_pi[nb_jk].dBB[2]+=
agpdpr1*dis_jk[2]
+app1*dcA_kjkp[2][0]
+app2*dcA_ijk[2][1];
bt_pi[nb_jkp].dBB[0]+=
agpdpr2*dis_jkp[0]
+app1*dcA_kjkp[0][1]
+app3*dcA_ijkp[0][1];
bt_pi[nb_jkp].dBB[1]+=
agpdpr2*dis_jkp[1]
+app1*dcA_kjkp[1][1]
+app3*dcA_ijkp[1][1];
bt_pi[nb_jkp].dBB[2]+=
agpdpr2*dis_jkp[2]
+app1*dcA_kjkp[2][1]
+app3*dcA_ijkp[2][1];
}
}
}
//j and k' are different neighbors of i and k is a neighbor of j not equal to i
for(ltmp=0;ltmp<numneigh[i];ltmp++) {
if(ltmp!=jtmp) {
temp_ikp=BOP_index[i]+ltmp;
kp=iilist[ltmp];
kptype=map[type[kp]]+1;
for(nsearch=0;nsearch<nPiBk[n];nsearch++) {
ncmp=itypePiBk[n][nsearch];
if(x[ncmp][0]==x[kp][0]) {
if(x[ncmp][1]==x[kp][1]) {
if(x[ncmp][2]==x[kp][2]) {
break;
}
}
}
}
if(itype==kptype)
iikp=itype-1;
else if(itype<kptype)
iikp=itype*bop_types-itype*(itype+1)/2+kptype-1;
else
iikp=kptype*bop_types-kptype*(kptype+1)/2+itype-1;
dis_ikp[0]=x[kp][0]-x[i][0];
dis_ikp[1]=x[kp][1]-x[i][1];
dis_ikp[2]=x[kp][2]-x[i][2];
rsq_ikp=dis_ikp[0]*dis_ikp[0]
+dis_ikp[1]*dis_ikp[1]
+dis_ikp[2]*dis_ikp[2];
r_ikp=sqrt(rsq_ikp);
if(r_ikp<=rcut[iikp]) {
ps=r_ikp*rdr[iikp]+1.0;
ks=(int)ps;
if(nr-1<ks)
ks=nr-1;
ps=ps-ks;
if(ps>1.0)
ps=1.0;
betaS_ikp=((pBetaS3[iikp][ks-1]*ps+pBetaS2[iikp][ks-1])*ps
+pBetaS1[iikp][ks-1])*ps+pBetaS[iikp][ks-1];
dBetaS_ikp=(pBetaS6[iikp][ks-1]*ps+pBetaS5[iikp][ks-1])*ps
+pBetaS4[iikp][ks-1];
betaP_ikp=((pBetaP3[iikp][ks-1]*ps+pBetaP2[iikp][ks-1])*ps
+pBetaP1[iikp][ks-1])*ps+pBetaP[iikp][ks-1];
dBetaP_ikp=(pBetaP6[iikp][ks-1]*ps+pBetaP5[iikp][ks-1])*ps
+pBetaP4[iikp][ks-1];
cosAng_jikp=(dis_ij[0]*dis_ikp[0]+dis_ij[1]*dis_ikp[1]
+dis_ij[2]*dis_ikp[2])/(r_ij*r_ikp);
dcA_jikp[0][0]=(dis_ikp[0]*r_ij*r_ikp-cosAng_jikp
*dis_ij[0]*r_ikp*r_ikp)/(r_ij*r_ij*r_ikp*r_ikp);
dcA_jikp[1][0]=(dis_ikp[1]*r_ij*r_ikp-cosAng_jikp
*dis_ij[1]*r_ikp*r_ikp)/(r_ij*r_ij*r_ikp*r_ikp);
dcA_jikp[2][0]=(dis_ikp[2]*r_ij*r_ikp-cosAng_jikp
*dis_ij[2]*r_ikp*r_ikp)/(r_ij*r_ij*r_ikp*r_ikp);
dcA_jikp[0][1]=(dis_ij[0]*r_ij*r_ikp-cosAng_jikp
*dis_ikp[0]*r_ij*r_ij)/(r_ij*r_ij*r_ikp*r_ikp);
dcA_jikp[1][1]=(dis_ij[1]*r_ij*r_ikp-cosAng_jikp
*dis_ikp[1]*r_ij*r_ij)/(r_ij*r_ij*r_ikp*r_ikp);
dcA_jikp[2][1]=(dis_ij[2]*r_ij*r_ikp-cosAng_jikp
*dis_ikp[2]*r_ij*r_ij)/(r_ij*r_ij*r_ikp*r_ikp);
nb_ikp=nb_t;
nb_t++;
if(nb_t>nb_pi) {
new_n_tot=nb_pi+maxneigh;
grow_pi(nb_pi,new_n_tot);
nb_pi=new_n_tot;
}
bt_pi[nb_ikp].i=i;
bt_pi[nb_ikp].j=kp;
bt_pi[nb_ikp].temp=temp_ikp;
betaCapSq2=pi_p[itype-1]*betaS_ikp*betaS_ikp
-betaP_ikp*betaP_ikp;
dbetaCapSq2=2.0*pi_p[itype-1]*betaS_ikp*dBetaS_ikp
-2.0*betaP_ikp*dBetaP_ikp;
dotV=(dis_jk[0]*dis_ikp[0]+dis_jk[1]
*dis_ikp[1]+dis_jk[2]*dis_ikp[2])
/(r_jk*r_ikp);
cosSq1=cosAng_jikp*cosAng_jikp;
angFactor=dotV+cosAng_jikp*cosAng_ijk;
angRfactor=4.0*angFactor*dotV;
dAngR1=-angRfactor/r_jk;
dAngR2=-angRfactor/r_ikp;
angFactor1=4.0*angFactor*cosAng_jikp
+2.0*cosAng_ijk*(1.0-cosSq1);
angFactor2=4.0*angFactor*cosAng_ijk
+2.0*cosAng_jikp*(1.0-cosSq);
angFactor3=2.0*angFactor*angFactor-(1.0-cosSq)*(1.0-cosSq1);
betaCapSum=.5*betaCapSq1*betaCapSq2;
//5th BB is 5th term of Eq. 38 (a) Eq. 21 (b) where i , k and k' =neighbors j
BB=BB+betaCapSum*angFactor3;
//app1 is derivative of BB 5th term w.r.t. cos(theta_ijk)
//app2 is derivative of BB 5th term w.r.t. cos(theta_jik')
//agpdpr1 is derivative of BB 5th term for atom j w.r.t. Beta(r_jk)
//agpdpr2 is derivative of BB 5th term for atom j w.r.t. Beta(r_ik')
//agpdpr3 is derivative of BB 5th term for atom j w.r.t. dot(r_ik',r_ij)
app1=betaCapSum*angFactor1;
app2=betaCapSum*angFactor2;
agpdpr1=(.5*angFactor3*dbetaCapSq1*betaCapSq2
+betaCapSum*dAngR1)/r_jk;
agpdpr2=(.5*angFactor3*betaCapSq1*dbetaCapSq2
+betaCapSum*dAngR2)/r_ikp;
agpdpr3=4.0*betaCapSum*angFactor/(r_ikp*r_jk);
bt_pi[nb_ij].dBB[0]+=
+app2*dcA_jikp[0][0]
-app1*dcA_ijk[0][0];
bt_pi[nb_ij].dBB[1]+=
+app2*dcA_jikp[1][0]
-app1*dcA_ijk[1][0];
bt_pi[nb_ij].dBB[2]+=
+app2*dcA_jikp[2][0]
-app1*dcA_ijk[2][0];
bt_pi[nb_ikp].dBB[0]+=
agpdpr2*dis_ikp[0]
+agpdpr3*dis_jk[0]
+app2*dcA_jikp[0][1];
bt_pi[nb_ikp].dBB[1]+=
agpdpr2*dis_ikp[1]
+agpdpr3*dis_jk[1]
+app2*dcA_jikp[1][1];
bt_pi[nb_ikp].dBB[2]+=
agpdpr2*dis_ikp[2]
+agpdpr3*dis_jk[2]
+app2*dcA_jikp[2][1];
bt_pi[nb_jk].dBB[0]+=
agpdpr1*dis_jk[0]
+agpdpr3*dis_ikp[0]
+app1*dcA_ijk[0][1];
bt_pi[nb_jk].dBB[1]+=
agpdpr1*dis_jk[1]
+agpdpr3*dis_ikp[1]
+app1*dcA_ijk[1][1];
bt_pi[nb_jk].dBB[2]+=
agpdpr1*dis_jk[2]
+agpdpr3*dis_ikp[2]
+app1*dcA_ijk[2][1];
}
}
}
if(pi_flag==0)
nPiBk[n]=nPiBk[n]+1;
}
}
}
CC=betaP_ij*betaP_ij+pi_delta[iij]*pi_delta[iij];
BBrt=sqrt(BB+small6);
AB1=CC+pi_c[iij]*(AA+BBrt)+small7;
AB2=CC+pi_c[iij]*(AA-BBrt+sqrt(small6))+small7;
BBrtR=1.0/BBrt;
ABrtR1=1.0/sqrt(AB1);
ABrtR2=1.0/sqrt(AB2);
// piB is similary formulation to (a) Eq. 36 and (b) Eq. 18
piB[n]=(ABrtR1+ABrtR2)*pi_a[iij]*betaP_ij;
dPiB1=-.5*(cube(ABrtR1)+cube(ABrtR2))*pi_c[iij]*pi_a[iij]*betaP_ij;
dPiB2=.25*BBrtR*(cube(ABrtR2)-cube(ABrtR1))*pi_c[iij]*pi_a[iij]*betaP_ij;
dPiB3=((ABrtR1+ABrtR2)*pi_a[iij]-(cube(ABrtR1)+cube(ABrtR2))*pi_a[iij]
*betaP_ij*betaP_ij)*dBetaP_ij/r_ij;
n++;
pp2=2.0*betaP_ij;
for(m=0;m<nb_t;m++) {
bt_i=bt_pi[m].i;
bt_j=bt_pi[m].j;
xtmp[0]=x[bt_j][0]-x[bt_i][0];
xtmp[1]=x[bt_j][1]-x[bt_i][1];
xtmp[2]=x[bt_j][2]-x[bt_i][2];
for(pp=0;pp<3;pp++) {
bt_pi[m].dPiB[pp]=
+dPiB1*bt_pi[m].dAA[pp]
+dPiB2*bt_pi[m].dBB[pp];
ftmp[pp]=pp2*bt_pi[m].dPiB[pp];
f[bt_i][pp]-=ftmp[pp];
f[bt_j][pp]+=ftmp[pp];
}
if(evflag) {
ev_tally_xyz(bt_i,bt_j,nlocal,newton_pair,0.0,0.0,ftmp[0],ftmp[1]
,ftmp[2],xtmp[0],xtmp[1],xtmp[2]);
}
}
for(pp=0;pp<3;pp++) {
ftmp[pp]=pp2*dPiB3*dis_ij[pp];
f[i][pp]-=ftmp[pp];
f[j][pp]+=ftmp[pp];
}
if(evflag) {
ev_tally_xyz(i,j,nlocal,newton_pair,0.0,0.0,ftmp[0],ftmp[1]
,ftmp[2],dis_ij[0],dis_ij[1],dis_ij[2]);
}
}
}
}
}
destroy_pi();
}
/* ----------------------------------------------------------------------
read BOP potential file
------------------------------------------------------------------------- */
void PairBOP::read_file(char *filename)
{
int i,j,k;
int ij,ii,jj;
int buf1;
int n;
double buf2;
char s[MAXLINE];
char buf[2];
MPI_Comm_rank(world,&me);
// read file on proc 0
rcore=0.1;
if (me == 0) {
FILE *fp = open_potential(filename);
if (fp == NULL) {
char str[128];
sprintf(str,"Cannot open BOP potential file %s",filename);
error->one(FLERR,str);
}
// read parameters
fgets(s,MAXLINE,fp);
fgets(s,MAXLINE,fp);
sscanf(s,"%d",&bop_types);
fclose(fp);
npairs=bop_types*(bop_types+1)/2;
}
MPI_Bcast(&bop_types,1,MPI_INT,0,world);
MPI_Bcast(&npairs,1,MPI_INT,0,world);
allocate();
memory->create(pi_a,npairs,"BOP:pi_a");
memory->create(pro_delta,bop_types,"BOP:pro_delta");
memory->create(pi_delta,npairs,"BOP:pi_delta");
memory->create(pi_p,bop_types,"BOP:pi_p");
memory->create(pi_c,npairs,"BOP:pi_c");
memory->create(sigma_r0,npairs,"BOP:sigma_r0");
memory->create(pi_r0,npairs,"BOP:pi_r0");
memory->create(phi_r0,npairs,"BOP:phi_r0");
memory->create(sigma_rc,npairs,"BOP:sigma_rc");
memory->create(pi_rc,npairs,"BOP:pi_rc");
memory->create(phi_rc,npairs,"BOP:phi_rc");
memory->create(r1,npairs,"BOP:r1");
memory->create(sigma_beta0,npairs,"BOP:sigma_beta0");
memory->create(pi_beta0,npairs,"BOP:pi_beta0");
memory->create(phi0,npairs,"BOP:phi0");
memory->create(sigma_n,npairs,"BOP:sigma_n");
memory->create(pi_n,npairs,"BOP:pi_n");
memory->create(phi_m,npairs,"BOP:phi_m");
memory->create(sigma_nc,npairs,"BOP:sigma_nc");
memory->create(pi_nc,npairs,"BOP:pi_nc");
memory->create(phi_nc,npairs,"BOP:phi_nc");
memory->create(pro,bop_types,"BOP:pro");
memory->create(sigma_delta,npairs,"BOP:sigma_delta");
memory->create(sigma_c,npairs,"BOP:sigma_c");
memory->create(sigma_a,npairs,"BOP:sigma_a");
memory->create(sigma_g0,bop_types
,bop_types,bop_types,"BOP:sigma_g0");
memory->create(sigma_g1,bop_types
,bop_types,bop_types,"BOP:sigma_g1");
memory->create(sigma_g2,bop_types
,bop_types,bop_types,"BOP:sigma_g2");
memory->create(sigma_g3,bop_types
,bop_types,bop_types,"BOP:sigma_g3");
memory->create(sigma_g4,bop_types
,bop_types,bop_types,"BOP:sigma_g4");
memory->create(sigma_f,npairs,"BOP:sigma_f");
memory->create(sigma_k,npairs,"BOP:sigma_k");
memory->create(small3,npairs,"BOP:small3");
if (me == 0) {
words = new char*[bop_types];
for(i=0;i<bop_types;i++) words[i]=NULL;
FILE *fp = open_potential(filename);
if (fp == NULL) {
char str[128];
sprintf(str,"Cannot open BOP potential file %s",filename);
error->one(FLERR,str);
}
fgets(s,MAXLINE,fp);
fgets(s,MAXLINE,fp);
for(i=0;i<bop_types;i++) {
fgets(s,MAXLINE,fp);
sscanf(s,"%d %lf %s",&buf1,&buf2,buf);
n= strlen(buf)+1;
words[i] = new char[n];
strcpy(words[i],buf);
}
fgets(s,MAXLINE,fp);
fgets(s,MAXLINE,fp);
fgets(s,MAXLINE,fp);
sscanf(s,"%lf%lf%lf%lf%lf%lf%lf",&small1,&small2,&small3g,&small4
,&small5,&small6,&small7);
fgets(s,MAXLINE,fp);
sscanf(s,"%d%lf%lf",&ncutoff,&rbig,&rsmall);
fgets(s,MAXLINE,fp);
sscanf(s,"%lf%lf%d",&which,&alpha,&nfunc);
fgets(s,MAXLINE,fp);
sscanf(s,"%lf%lf%lf",&alpha1,&beta1,&gamma1);
fgets(s,MAXLINE,fp);
sscanf(s,"%lf%lf",&alpha2,&beta2);
fgets(s,MAXLINE,fp);
sscanf(s,"%lf%lf",&alpha3,&beta3);
fgets(s,MAXLINE,fp);
fgets(s,MAXLINE,fp);
for(i=0;i<bop_types;i++) {
fgets(s,MAXLINE,fp);
sscanf(s,"%lf%lf%lf",&pro[i],&pro_delta[i],&pi_p[i]);
}
fgets(s,MAXLINE,fp);
fgets(s,MAXLINE,fp);
cutmax=0;
for(i=0;i<bop_types;i++) {
ii=i+1;
for(j=i;j<bop_types;j++) {
jj=j+1;
if(ii==jj)
ij=ii-1;
else if(ii<jj)
ij=ii*bop_types-ii*(ii+1)/2+jj-1;
else
ij=jj*bop_types-jj*(jj+1)/2+ii-1;
fgets(s,MAXLINE,fp);
sscanf(s,"%lf%lf%lf%lf",&sigma_r0[ij],&sigma_rc[ij],&r1[ij],&rcut[ij]);
if(rcut[ij]>cutmax)
cutmax=rcut[ij];
pi_r0[ij]=sigma_r0[ij];
phi_r0[ij]=sigma_r0[ij];
pi_rc[ij]=sigma_rc[ij];
phi_rc[ij]=sigma_rc[ij];
fgets(s,MAXLINE,fp);
sscanf(s,"%lf%lf%lf",&phi_m[ij],&sigma_n[ij],&sigma_nc[ij]);
pi_n[ij]=sigma_n[ij];
pi_nc[ij]=sigma_nc[ij];
phi_nc[ij]=sigma_nc[ij];
fgets(s,MAXLINE,fp);
sscanf(s,"%lf%lf%lf",&phi0[ij],&sigma_beta0[ij],&pi_beta0[ij]);
fgets(s,MAXLINE,fp);
sscanf(s,"%lf%lf%lf",&sigma_a[ij],&sigma_c[ij],&sigma_delta[ij]);
fgets(s,MAXLINE,fp);
sscanf(s,"%lf%lf%lf",&pi_a[ij],&pi_c[ij],&pi_delta[ij]);
fgets(s,MAXLINE,fp);
sscanf(s,"%lf%lf%lf",&sigma_f[ij],&sigma_k[ij],&small3[ij]);
}
}
fgets(s,MAXLINE,fp);
fgets(s,MAXLINE,fp);
for(i=0;i<bop_types;i++) {
for(j=0;j<bop_types;j++) {
for(k=j;k<bop_types;k++) {
fgets(s,MAXLINE,fp);
sscanf(s,"%lf%lf%lf",&sigma_g0[j][i][k],&sigma_g1[j][i][k]
,&sigma_g2[j][i][k]);
sigma_g0[k][i][j]=sigma_g0[j][i][k];
sigma_g1[k][i][j]=sigma_g1[j][i][k];
sigma_g2[k][i][j]=sigma_g2[j][i][k];
}
}
}
for(i=0;i<npairs;i++) {
dr[i]=rcut[i]/(nr-1.0);
rdr[i]=1.0/dr[i];
}
fclose(fp);
}
MPI_Bcast(&small1,1,MPI_DOUBLE,0,world);
MPI_Bcast(&small2,1,MPI_DOUBLE,0,world);
MPI_Bcast(&small3g,1,MPI_DOUBLE,0,world);
MPI_Bcast(&small4,1,MPI_DOUBLE,0,world);
MPI_Bcast(&small5,1,MPI_DOUBLE,0,world);
MPI_Bcast(&small6,1,MPI_DOUBLE,0,world);
MPI_Bcast(&small7,1,MPI_DOUBLE,0,world);
MPI_Bcast(&ncutoff,1,MPI_INT,0,world);
MPI_Bcast(&rbig,1,MPI_DOUBLE,0,world);
MPI_Bcast(&rsmall,1,MPI_DOUBLE,0,world);
MPI_Bcast(&which,1,MPI_DOUBLE,0,world);
MPI_Bcast(&alpha,1,MPI_DOUBLE,0,world);
MPI_Bcast(&nfunc,1,MPI_INT,0,world);
MPI_Bcast(&alpha1,1,MPI_DOUBLE,0,world);
MPI_Bcast(&beta1,1,MPI_DOUBLE,0,world);
MPI_Bcast(&gamma1,1,MPI_DOUBLE,0,world);
MPI_Bcast(&alpha2,1,MPI_DOUBLE,0,world);
MPI_Bcast(&beta2,1,MPI_DOUBLE,0,world);
MPI_Bcast(&alpha3,1,MPI_DOUBLE,0,world);
MPI_Bcast(&beta3,1,MPI_DOUBLE,0,world);
MPI_Bcast(&pro[0],bop_types,MPI_DOUBLE,0,world);
MPI_Bcast(&pro_delta[0],bop_types,MPI_DOUBLE,0,world);
MPI_Bcast(&pi_p[0],bop_types,MPI_DOUBLE,0,world);
MPI_Bcast(&sigma_r0[0],npairs,MPI_DOUBLE,0,world);
MPI_Bcast(&sigma_rc[0],npairs,MPI_DOUBLE,0,world);
MPI_Bcast(&r1[0],npairs,MPI_DOUBLE,0,world);
MPI_Bcast(&rcut[0],npairs,MPI_DOUBLE,0,world);
MPI_Bcast(&cutmax,1,MPI_DOUBLE,0,world);
MPI_Bcast(&pi_r0[0],npairs,MPI_DOUBLE,0,world);
MPI_Bcast(&phi_r0[0],npairs,MPI_DOUBLE,0,world);
MPI_Bcast(&pi_rc[0],npairs,MPI_DOUBLE,0,world);
MPI_Bcast(&phi_rc[0],npairs,MPI_DOUBLE,0,world);
MPI_Bcast(&phi_m[0],npairs,MPI_DOUBLE,0,world);
MPI_Bcast(&sigma_n[0],npairs,MPI_DOUBLE,0,world);
MPI_Bcast(&sigma_nc[0],npairs,MPI_DOUBLE,0,world);
MPI_Bcast(&pi_n[0],npairs,MPI_DOUBLE,0,world);
MPI_Bcast(&pi_nc[0],npairs,MPI_DOUBLE,0,world);
MPI_Bcast(&phi_nc[0],npairs,MPI_DOUBLE,0,world);
MPI_Bcast(&phi0[0],npairs,MPI_DOUBLE,0,world);
MPI_Bcast(&sigma_beta0[0],npairs,MPI_DOUBLE,0,world);
MPI_Bcast(&pi_beta0[0],npairs,MPI_DOUBLE,0,world);
MPI_Bcast(&sigma_a[0],npairs,MPI_DOUBLE,0,world);
MPI_Bcast(&sigma_c[0],npairs,MPI_DOUBLE,0,world);
MPI_Bcast(&sigma_delta[0],npairs,MPI_DOUBLE,0,world);
MPI_Bcast(&pi_a[0],npairs,MPI_DOUBLE,0,world);
MPI_Bcast(&pi_c[0],npairs,MPI_DOUBLE,0,world);
MPI_Bcast(&pi_delta[0],npairs,MPI_DOUBLE,0,world);
MPI_Bcast(&sigma_f[0],npairs,MPI_DOUBLE,0,world);
MPI_Bcast(&sigma_k[0],npairs,MPI_DOUBLE,0,world);
MPI_Bcast(&small3[0],npairs,MPI_DOUBLE,0,world);
MPI_Bcast(&sigma_g0[0][0][0],bop_types*bop_types*bop_types,MPI_DOUBLE,0,world);
MPI_Bcast(&sigma_g1[0][0][0],bop_types*bop_types*bop_types,MPI_DOUBLE,0,world);
MPI_Bcast(&sigma_g2[0][0][0],bop_types*bop_types*bop_types,MPI_DOUBLE,0,world);
MPI_Bcast(&sigma_g3[0][0][0],bop_types*bop_types*bop_types,MPI_DOUBLE,0,world);
MPI_Bcast(&sigma_g4[0][0][0],bop_types*bop_types*bop_types,MPI_DOUBLE,0,world);
MPI_Bcast(&dr[0],npairs,MPI_DOUBLE,0,world);
MPI_Bcast(&rdr[0],npairs,MPI_DOUBLE,0,world);
}
/* ---------------------------------------------------------------------- */
void PairBOP::read_table(char *filename)
{
int i,j,k,n;
int buf1;
double buf2;
char s[MAXLINE],buf[2];
MPI_Comm_rank(world,&me);
if (me == 0) {
FILE *fp = open_potential(filename);
if (fp == NULL) {
char str[128];
sprintf(str,"Cannot open BOP potential file %s",filename);
error->one(FLERR,str);
}
fgets(s,MAXLINE,fp);
sscanf(s,"%d",&bop_types);
words = new char*[bop_types];
for(i=0;i<bop_types;i++) words[i]=NULL;
for(i=0;i<bop_types;i++) {
fgets(s,MAXLINE,fp);
sscanf(s,"%d %lf %s",&buf1,&buf2,buf);
n= strlen(buf)+1;
words[i] = new char[n];
strcpy(words[i],buf);
}
fgets(s,MAXLINE,fp);
sscanf(s,"%d %d",&nr,&nBOt);
fclose(fp);
npairs=bop_types*(bop_types+1)/2;
}
MPI_Bcast(&nr,1,MPI_INT,0,world);
MPI_Bcast(&nBOt,1,MPI_INT,0,world);
MPI_Bcast(&bop_types,1,MPI_INT,0,world);
MPI_Bcast(&npairs,1,MPI_INT,0,world);
memory->create(pi_a,npairs,"BOP:pi_a");
memory->create(pro_delta,bop_types,"BOP:pro_delta");
memory->create(pi_delta,npairs,"BOP:pi_delta");
memory->create(pi_p,bop_types,"BOP:pi_p");
memory->create(pi_c,npairs,"BOP:pi_c");
memory->create(r1,npairs,"BOP:r1");
memory->create(pro,bop_types,"BOP:pro");
memory->create(sigma_delta,npairs,"BOP:sigma_delta");
memory->create(sigma_c,npairs,"BOP:sigma_c");
memory->create(sigma_a,npairs,"BOP:sigma_a");
memory->create(sigma_g0,bop_types
,bop_types,bop_types,"BOP:sigma_g0");
memory->create(sigma_g1,bop_types
,bop_types,bop_types,"BOP:sigma_g1");
memory->create(sigma_g2,bop_types
,bop_types,bop_types,"BOP:sigma_g2");
memory->create(sigma_f,npairs,"BOP:sigma_f");
memory->create(sigma_k,npairs,"BOP:sigma_k");
memory->create(small3,npairs,"BOP:small3");
allocate();
if (me == 0) {
FILE *fp = open_potential(filename);
if (fp == NULL) {
char str[128];
sprintf(str,"Cannot open BOP potential file %s",filename);
error->one(FLERR,str);
}
for(i=0;i<bop_types+2;i++) {
fgets(s,MAXLINE,fp);
}
fgets(s,MAXLINE,fp);
sscanf(s,"%lf%lf%lf%lf%lf%lf%lf",&small1,&small2,&small3g
,&small4,&small5,&small6,&small7);
for(i=0;i<bop_types;i++) {
fgets(s,MAXLINE,fp);
sscanf(s,"%lf",&pi_p[i]);
}
cutmax=0;
for(i=0;i<npairs;i++) {
fgets(s,MAXLINE,fp);
sscanf(s,"%lf",&rcut[i]);
if(rcut[i]>cutmax)
cutmax=rcut[i];
fgets(s,MAXLINE,fp);
sscanf(s,"%lf%lf%lf%lf",&sigma_c[i],&sigma_a[i],&pi_c[i],&pi_a[i]);
fgets(s,MAXLINE,fp);
sscanf(s,"%lf%lf",&sigma_delta[i],&pi_delta[i]);
fgets(s,MAXLINE,fp);
sscanf(s,"%lf%lf%lf",&sigma_f[i],&sigma_k[i],&small3[i]);
}
for(i=0;i<bop_types;i++)
for(j=0;j<bop_types;j++)
for(k=0;k<bop_types;k++) {
fgets(s,MAXLINE,fp);
sscanf(s,"%lf%lf%lf",&sigma_g0[i][j][k],&sigma_g1[i][j][k],&sigma_g2[i][j][k]);
}
for(i=0;i<npairs;i++) {
for(j=0;j<nr;j++) {
fgets(s,MAXLINE,fp);
sscanf(s,"%lf%lf%lf%lf%lf",&pRepul[i][j],&pRepul[i][j+1]
,&pRepul[i][j+2],&pRepul[i][j+3],&pRepul[i][j+4]);
j+=4;
}
}
for(i=0;i<npairs;i++) {
for(j=0;j<nr;j++) {
fgets(s,MAXLINE,fp);
sscanf(s,"%lf%lf%lf%lf%lf",&pBetaS[i][j],&pBetaS[i][j+1]
,&pBetaS[i][j+2],&pBetaS[i][j+3],&pBetaS[i][j+4]);
j+=4;
}
}
for(i=0;i<npairs;i++) {
for(j=0;j<nr;j++) {
fgets(s,MAXLINE,fp);
sscanf(s,"%lf%lf%lf%lf%lf",&pBetaP[i][j],&pBetaP[i][j+1]
,&pBetaP[i][j+2],&pBetaP[i][j+3],&pBetaP[i][j+4]);
j+=4;
}
}
for(i=0;i<npairs;i++) {
for(j=0;j<nBOt;j++) {
fgets(s,MAXLINE,fp);
sscanf(s,"%lf%lf%lf%lf%lf",&FsigBO[i][j],&FsigBO[i][j+1]
,&FsigBO[i][j+2],&FsigBO[i][j+3],&FsigBO[i][j+4]);
j+=4;
}
}
for(i=0;i<bop_types;i++) {
fgets(s,MAXLINE,fp);
sscanf(s,"%lf",&pro_delta[i]);
}
for(i=0;i<bop_types;i++) {
fgets(s,MAXLINE,fp);
sscanf(s,"%lf",&pro[i]);
}
for(i=0;i<npairs;i++) {
dr[i]=rcut[i]/((double)nr-1.0);
rdr[i]=1.0/dr[i];
}
dBO=1.0/((double)nBOt-1.0);
rdBO=1.0/(double)dBO;
for(i=0;i<npairs;i++) {
pBetaS1[i][0]=pBetaS[i][1]-pBetaS[i][0];
pBetaS1[i][1]=0.5*(pBetaS[i][2]-pBetaS[i][0]);
pBetaS1[i][nr-2]=0.5*(pBetaS[i][nr-1]-pBetaS[i][nr-3]);
pBetaS1[i][nr-1]=pBetaS[i][nr-1]-pBetaS[i][nr-2];
pBetaP1[i][0]=pBetaP[i][1]-pBetaP[i][0];
pBetaP1[i][1]=0.5*(pBetaP[i][2]-pBetaP[i][0]);
pBetaP1[i][nr-2]=0.5*(pBetaP[i][nr-1]-pBetaP[i][nr-3]);
pBetaP1[i][nr-1]=pBetaP[i][nr-1]-pBetaP[i][nr-2];
pRepul1[i][0]=pRepul[i][1]-pRepul[i][0];
pRepul1[i][1]=0.5*(pRepul[i][2]-pRepul[i][0]);
pRepul1[i][nr-2]=0.5*(pRepul[i][nr-1]-pRepul[i][nr-3]);
pRepul1[i][nr-1]=pRepul[i][nr-1]-pRepul[i][nr-2];
FsigBO1[i][0]=FsigBO[i][1]-FsigBO[i][0];
FsigBO1[i][1]=0.5*(FsigBO[i][2]-FsigBO[i][0]);
FsigBO1[i][nBOt-2]=0.5*(FsigBO[i][nBOt-1]-FsigBO[i][nBOt-3]);
FsigBO1[i][nBOt-1]=FsigBO[i][nBOt-1]-FsigBO[i][nBOt-2];
for(k=2;k<nr-2;k++) {
pBetaS1[i][k]=((pBetaS[i][k-2]-pBetaS[i][k+2])
+8.0*(pBetaS[i][k+1]-pBetaS[i][k-1]))/12.0;
pBetaP1[i][k]=((pBetaP[i][k-2]-pBetaP[i][k+2])
+8.0*(pBetaP[i][k+1]-pBetaP[i][k-1]))/12.0;
pRepul1[i][k]=((pRepul[i][k-2]-pRepul[i][k+2])
+8.0*(pRepul[i][k+1]-pRepul[i][k-1]))/12.0;
}
for(k=2;k<nr-2;k++) {
FsigBO1[i][k]=((FsigBO[i][k-2]-FsigBO[i][k+2])
+8.0*(FsigBO[i][k+1]-FsigBO[i][k-1]))/12.0;
}
for(k=0;k<nr-1;k++) {
pBetaS2[i][k]=3.0*(pBetaS[i][k+1]-pBetaS[i][k])
-2.0*pBetaS1[i][k]-pBetaS1[i][k+1];
pBetaS3[i][k]=pBetaS1[i][k]+pBetaS1[i][k+1]
-2.0*(pBetaS[i][k+1]-pBetaS[i][k]);
pBetaP2[i][k]=3.0*(pBetaP[i][k+1]-pBetaP[i][k])
-2.0*pBetaP1[i][k]-pBetaP1[i][k+1];
pBetaP3[i][k]=pBetaP1[i][k]+pBetaP1[i][k+1]
-2.0*(pBetaP[i][k+1]-pBetaP[i][k]);
pRepul2[i][k]=3.0*(pRepul[i][k+1]-pRepul[i][k])
-2.0*pRepul1[i][k]-pRepul1[i][k+1];
pRepul3[i][k]=pRepul1[i][k]+pRepul1[i][k+1]
-2.0*(pRepul[i][k+1]-pRepul[i][k]);
}
for(k=0;k<nBOt-1;k++) {
FsigBO2[i][k]=3.0*(FsigBO[i][k+1]-FsigBO[i][k])
-2.0*FsigBO1[i][k]-FsigBO1[i][k+1];
FsigBO3[i][k]=FsigBO1[i][k]+FsigBO1[i][k+1]
-2.0*(FsigBO[i][k+1]-FsigBO[i][k]);
}
pBetaS2[i][nr-1]=0.0;
pBetaS3[i][nr-1]=0.0;
pBetaP2[i][nr-1]=0.0;
pBetaP3[i][nr-1]=0.0;
pRepul2[i][nr-1]=0.0;
pRepul3[i][nr-1]=0.0;
FsigBO2[i][nBOt-1]=0.0;
FsigBO3[i][nBOt-1]=0.0;
for(k=0;k<nr;k++) {
pBetaS4[i][k]=pBetaS1[i][k]/dr[i];
pBetaS5[i][k]=2.0*pBetaS2[i][k]/dr[i];
pBetaS6[i][k]=3.0*pBetaS3[i][k]/dr[i];
pBetaP4[i][k]=pBetaP1[i][k]/dr[i];
pBetaP5[i][k]=2.0*pBetaP2[i][k]/dr[i];
pBetaP6[i][k]=3.0*pBetaP3[i][k]/dr[i];
pRepul4[i][k]=pRepul1[i][k]/dr[i];
pRepul5[i][k]=2.0*pRepul2[i][k]/dr[i];
pRepul6[i][k]=3.0*pRepul3[i][k]/dr[i];
}
for(k=0;k<nBOt;k++) {
FsigBO4[i][k]=FsigBO1[i][k]/dBO;
FsigBO5[i][k]=2.0*FsigBO2[i][k]/dBO;
FsigBO6[i][k]=3.0*FsigBO3[i][k]/dBO;
}
}
fclose(fp);
}
MPI_Bcast(&rdBO,1,MPI_DOUBLE,0,world);
MPI_Bcast(&dBO,1,MPI_DOUBLE,0,world);
MPI_Bcast(&bop_types,1,MPI_INT,0,world);
MPI_Bcast(&small1,1,MPI_DOUBLE,0,world);
MPI_Bcast(&small2,1,MPI_DOUBLE,0,world);
MPI_Bcast(&small3g,1,MPI_DOUBLE,0,world);
MPI_Bcast(&small4,1,MPI_DOUBLE,0,world);
MPI_Bcast(&small5,1,MPI_DOUBLE,0,world);
MPI_Bcast(&small6,1,MPI_DOUBLE,0,world);
MPI_Bcast(&small7,1,MPI_DOUBLE,0,world);
MPI_Bcast(&pro[0],bop_types,MPI_DOUBLE,0,world);
MPI_Bcast(&pro_delta[0],bop_types,MPI_DOUBLE,0,world);
MPI_Bcast(&pi_p[0],bop_types,MPI_DOUBLE,0,world);
MPI_Bcast(&r1[0],npairs,MPI_DOUBLE,0,world);
MPI_Bcast(&rcut[0],npairs,MPI_DOUBLE,0,world);
MPI_Bcast(&cutmax,1,MPI_DOUBLE,0,world);
MPI_Bcast(&sigma_a[0],npairs,MPI_DOUBLE,0,world);
MPI_Bcast(&sigma_c[0],npairs,MPI_DOUBLE,0,world);
MPI_Bcast(&sigma_delta[0],npairs,MPI_DOUBLE,0,world);
MPI_Bcast(&pi_a[0],npairs,MPI_DOUBLE,0,world);
MPI_Bcast(&pi_c[0],npairs,MPI_DOUBLE,0,world);
MPI_Bcast(&pi_delta[0],npairs,MPI_DOUBLE,0,world);
MPI_Bcast(&sigma_f[0],npairs,MPI_DOUBLE,0,world);
MPI_Bcast(&sigma_k[0],npairs,MPI_DOUBLE,0,world);
MPI_Bcast(&small3[0],npairs,MPI_DOUBLE,0,world);
MPI_Bcast(&sigma_g0[0][0][0],bop_types*bop_types*bop_types,MPI_DOUBLE,0,world);
MPI_Bcast(&sigma_g1[0][0][0],bop_types*bop_types*bop_types,MPI_DOUBLE,0,world);
MPI_Bcast(&sigma_g2[0][0][0],bop_types*bop_types*bop_types,MPI_DOUBLE,0,world);
MPI_Bcast(&dr[0],npairs,MPI_DOUBLE,0,world);
MPI_Bcast(&rdr[0],npairs,MPI_DOUBLE,0,world);
MPI_Bcast(&pBetaS[0][0],npairs*nr,MPI_DOUBLE,0,world);
MPI_Bcast(&pBetaS1[0][0],npairs*nr,MPI_DOUBLE,0,world);
MPI_Bcast(&pBetaS2[0][0],npairs*nr,MPI_DOUBLE,0,world);
MPI_Bcast(&pBetaS3[0][0],npairs*nr,MPI_DOUBLE,0,world);
MPI_Bcast(&pBetaS4[0][0],npairs*nr,MPI_DOUBLE,0,world);
MPI_Bcast(&pBetaS5[0][0],npairs*nr,MPI_DOUBLE,0,world);
MPI_Bcast(&pBetaS6[0][0],npairs*nr,MPI_DOUBLE,0,world);
MPI_Bcast(&pBetaP[0][0],npairs*nr,MPI_DOUBLE,0,world);
MPI_Bcast(&pBetaP1[0][0],npairs*nr,MPI_DOUBLE,0,world);
MPI_Bcast(&pBetaP2[0][0],npairs*nr,MPI_DOUBLE,0,world);
MPI_Bcast(&pBetaP3[0][0],npairs*nr,MPI_DOUBLE,0,world);
MPI_Bcast(&pBetaP4[0][0],npairs*nr,MPI_DOUBLE,0,world);
MPI_Bcast(&pBetaP5[0][0],npairs*nr,MPI_DOUBLE,0,world);
MPI_Bcast(&pBetaP6[0][0],npairs*nr,MPI_DOUBLE,0,world);
MPI_Bcast(&pRepul[0][0],npairs*nr,MPI_DOUBLE,0,world);
MPI_Bcast(&pRepul1[0][0],npairs*nr,MPI_DOUBLE,0,world);
MPI_Bcast(&pRepul2[0][0],npairs*nr,MPI_DOUBLE,0,world);
MPI_Bcast(&pRepul3[0][0],npairs*nr,MPI_DOUBLE,0,world);
MPI_Bcast(&pRepul4[0][0],npairs*nr,MPI_DOUBLE,0,world);
MPI_Bcast(&pRepul5[0][0],npairs*nr,MPI_DOUBLE,0,world);
MPI_Bcast(&pRepul6[0][0],npairs*nr,MPI_DOUBLE,0,world);
MPI_Bcast(&FsigBO[0][0],npairs*nBOt,MPI_DOUBLE,0,world);
MPI_Bcast(&FsigBO1[0][0],npairs*nBOt,MPI_DOUBLE,0,world);
MPI_Bcast(&FsigBO2[0][0],npairs*nBOt,MPI_DOUBLE,0,world);
MPI_Bcast(&FsigBO3[0][0],npairs*nBOt,MPI_DOUBLE,0,world);
MPI_Bcast(&FsigBO4[0][0],npairs*nBOt,MPI_DOUBLE,0,world);
MPI_Bcast(&FsigBO5[0][0],npairs*nBOt,MPI_DOUBLE,0,world);
MPI_Bcast(&FsigBO6[0][0],npairs*nBOt,MPI_DOUBLE,0,world);
}
/* ---------------------------------------------------------------------- */
void PairBOP::setPbetaS()
{
int i,j,k;
double r,value,dvalue;
for(i=0;i<npairs;i++) {
for(j=0;j<nr;j++) {
r=(double)j*dr[i];
if(r<rcore)
r=rcore;
if(ncutoff==3) {
if(r>=rcut[i])
pBetaS[i][j]=0.0;
else if(r<=r1[i]) {
value=betaSfunc(i,r);
dvalue=dBetaSfunc(i,r,value,1.0);
pBetaS[i][j]=value;
}
else {
value=betaSfunc(i,r1[i]);
dvalue=dBetaSfunc(i,r1[i],value,1.0);
pBetaS[i][j]=-(r-rcut[i])*(r-rcut[i])*(value*(2.0*r-3.0*r1[i]+rcut[i])
-dvalue*(r-r1[i])*(r1[i]-rcut[i]))/((r1[i]-rcut[i])
*(r1[i]-rcut[i])*(r1[i]-rcut[i]));
}
}
else {
if(r>=rcut[i])
pBetaS[i][j]=0.0;
else {
value=betaSfunc(i,r);
dvalue=dBetaSfunc(i,r,value,0.0);
pBetaS[i][j]=value*cutoff(r1[i],rcut[i],ncutoff,r);
}
}
}
pBetaS[i][nr-1]=0.0;
pBetaS1[i][0]=pBetaS[i][1]-pBetaS[i][0];
pBetaS1[i][1]=0.5*(pBetaS[i][2]-pBetaS[i][0]);
pBetaS1[i][nr-2]=0.5*(pBetaS[i][nr-1]-pBetaS[i][nr-3]);
pBetaS1[i][nr-1]=pBetaS[i][nr-1]-pBetaS[i][nr-2];
for(k=2;k<nr-2;k++) {
pBetaS1[i][k]=((pBetaS[i][k-2]-pBetaS[i][k+2])+8.0*(pBetaS[i][k+1]
-pBetaS[i][k-1]))/12.0;
}
for(k=0;k<nr-1;k++) {
pBetaS2[i][k]=3.0*(pBetaS[i][k+1]-pBetaS[i][k])-2.0*pBetaS1[i][k]-pBetaS1[i][k+1];
pBetaS3[i][k]=pBetaS1[i][k]+pBetaS1[i][k+1]-2.0*(pBetaS[i][k+1]-pBetaS[i][k]);
}
pBetaS2[i][nr-1]=0.0;
pBetaS3[i][nr-1]=0.0;
for(k=0;k<nr;k++) {
pBetaS4[i][k]=pBetaS1[i][k]/dr[i];
pBetaS5[i][k]=2.0*pBetaS2[i][k]/dr[i];
pBetaS6[i][k]=3.0*pBetaS3[i][k]/dr[i];
}
}
}
/* ---------------------------------------------------------------------- */
void PairBOP::setPbetaP()
{
int i,j,k;
double r,value,dvalue;
for(i=0;i<npairs;i++) {
for(j=0;j<nr;j++) {
r=(double)j*dr[i];
if(r<rcore)
r=rcore;
if(ncutoff==3) {
if(r>=rcut[i])
pBetaP[i][j]=0.0;
else if(r<=r1[i]) {
value=betaPfunc(i,r);
dvalue=dBetaPfunc(i,r,value,0.0);
pBetaP[i][j]=value;
}
else {
value=betaPfunc(i,r1[i]);
dvalue=dBetaPfunc(i,r1[i],value,1.0);
pBetaP[i][j]=-(r-rcut[i])*(r-rcut[i])*(value*(2.0*r-3.0*r1[i]
+rcut[i])-dvalue*(r-r1[1])*(r1[i]-rcut[i]))/((r1[i]-rcut[i])
*(r1[i]-rcut[i])*(r1[i]-rcut[i]));
}
}
else {
if(r>=rcut[i])
pBetaP[i][j]=0.0;
else {
value=betaPfunc(i,r);
dvalue=dBetaPfunc(i,r,value,0.0);
pBetaP[i][j]=value*cutoff(r1[i],rcut[i],ncutoff,r);
}
}
}
pBetaP[i][nr-1]=0.0;
pBetaP1[i][0]=pBetaP[i][1]-pBetaP[i][0];
pBetaP1[i][1]=0.5*(pBetaP[i][2]-pBetaP[i][0]);
pBetaP1[i][nr-2]=0.5*(pBetaP[i][nr-1]-pBetaP[i][nr-3]);
pBetaP1[i][nr-1]=pBetaP[i][nr-1]-pBetaP[i][nr-2];
for(k=2;k<nr-2;k++)
pBetaP1[i][k]=((pBetaP[i][k-2]-pBetaP[i][k+2])+8.0*(pBetaP[i][k+1]
-pBetaP[i][k-1]))/12.0;
for(k=0;k<nr-1;k++) {
pBetaP2[i][k]=3.0*(pBetaP[i][k+1]-pBetaP[i][k])-2.0*pBetaP1[i][k]-pBetaP1[i][k+1];
pBetaP3[i][k]=pBetaP1[i][k]+pBetaP1[i][k+1]-2.0*(pBetaP[i][k+1]-pBetaP[i][k]);
}
pBetaP2[i][nr-1]=0.0;
pBetaP3[i][nr-1]=0.0;
for(k=0;k<nr;k++) {
pBetaP4[i][k]=pBetaP1[i][k]/dr[i];
pBetaP5[i][k]=2.0*pBetaP2[i][k]/dr[i];
pBetaP6[i][k]=3.0*pBetaP3[i][k]/dr[i];
}
}
}
/* ---------------------------------------------------------------------- */
void PairBOP::setPrepul()
{
int i,j,k;
double r,value,dvalue;
for(i=0;i<npairs;i++) {
for(j=0;j<nr;j++) {
r=(double)j*dr[i];
if(r<rcore)
r=rcore;
if(ncutoff==3) {
if(r>=rcut[i])
pRepul[i][j]=0.0;
else if(r<=r1[i]) {
value=repulfunc(i,r);
dvalue=dRepulfunc(i,r,value,0.0);
pRepul[i][j]=value;
}
else {
value=repulfunc(i,r1[i]);
dvalue=dRepulfunc(i,r1[i],value,1.0);
pRepul[i][j]=-(r-rcut[i])*(r-rcut[i])*(value*(2.0*r-3.0*r1[i]+rcut[i])
-dvalue*(r-r1[i])*(r1[i]-rcut[i]))/((r1[i]-rcut[i])
*(r1[i]-rcut[i])*(r1[i]-rcut[i]));
}
}
else {
if(r>=rcut[i])
pRepul[i][j]=0.0;
else {
value=repulfunc(i,r);
dvalue=dRepulfunc(i,r,value,0.0);
pRepul[i][j]=value*cutoff(r1[i],rcut[i],ncutoff,r);
}
}
}
pRepul[i][nr-1]=0.0;
pRepul1[i][0]=pRepul[i][1]-pRepul[i][0];
pRepul1[i][1]=0.5*(pRepul[i][2]-pRepul[i][0]);
pRepul1[i][nr-2]=0.5*(pRepul[i][nr-1]-pRepul[i][nr-3]);
pRepul1[i][nr-1]=pRepul[i][nr-1]-pRepul[i][nr-2];
for(k=2;k<nr-2;k++)
pRepul1[i][k]=((pRepul[i][k-2]-pRepul[i][k+2])+8.0*(pRepul[i][k+1]
-pRepul[i][k-1]))/12.0;
for(k=0;k<nr-1;k++) {
pRepul2[i][k]=3.0*(pRepul[i][k+1]-pRepul[i][k])-2.0*pRepul1[i][k]-pRepul1[i][k+1];
pRepul3[i][k]=pRepul1[i][k]+pRepul1[i][k+1]-2.0*(pRepul[i][k+1]-pRepul[i][k]);
}
pRepul2[i][nr-1]=0.0;
pRepul3[i][nr-1]=0.0;
for(k=0;k<nr;k++) {
pRepul4[i][k]=pRepul1[i][k]/dr[i];
pRepul5[i][k]=2.0*pRepul2[i][k]/dr[i];
pRepul6[i][k]=3.0*pRepul3[i][k]/dr[i];
}
}
}
/* ---------------------------------------------------------------------- */
double PairBOP::betaSfunc(int i,double r)
{
double temp_value;
if(nfunc==1) {
temp_value=pow(sigma_r0[i]/r,sigma_n[i])*exp(sigma_n[i]*pow(sigma_r0[i]
/sigma_rc[i],sigma_nc[i])-sigma_n[i]*pow(r/sigma_rc[i],sigma_nc[i]));
temp_value=sigma_beta0[i]*temp_value;
}
if(nfunc==2)
temp_value=sigma_beta0[i]*exp(-sigma_n[i]*r);
if(nfunc==3)
temp_value=sigma_beta0[i]/pow(r,sigma_n[i]);
return(temp_value);
}
/* ---------------------------------------------------------------------- */
double PairBOP::dBetaSfunc(int i,double r,double value,double dmore)
{
double temp_dvalue;
if(nfunc==1)
if(dmore==1.0)
temp_dvalue=-sigma_n[i]*value/r*(1.0+sigma_nc[i]
*pow(r/sigma_rc[i],sigma_nc[i]));
if(nfunc==2)
if(dmore==1.0)
temp_dvalue=-sigma_n[i]*value;
if(nfunc==3)
if(dmore==1.0)
temp_dvalue=-sigma_n[i]*value/r;
return(temp_dvalue);
}
/* ---------------------------------------------------------------------- */
double PairBOP::betaPfunc(int i,double r)
{
double temp_value;
if(nfunc==1) {
temp_value=pow(pi_r0[i]/r,pi_n[i])*exp(pi_n[i]*pow(pi_r0[i]
/pi_rc[i],pi_nc[i])-pi_n[i]*pow(r/pi_rc[i],pi_nc[i]));
temp_value=pi_beta0[i]*temp_value;
}
if(nfunc==2)
temp_value=pi_beta0[i]*exp(-pi_n[i]*r);
if(nfunc==3)
temp_value=pi_beta0[i]/pow(r,pi_n[i]);
return(temp_value);
}
/* ---------------------------------------------------------------------- */
double PairBOP::dBetaPfunc(int i,double r,double value,double dmore)
{
double temp_dvalue;
if(nfunc==1)
if(dmore==1.0)
temp_dvalue=-pi_n[i]*value/r*(1.0+pi_nc[i]*pow(r/pi_rc[i],pi_nc[i]));
if(nfunc==2)
if(dmore==1.0)
temp_dvalue=-pi_n[i]*value;
if(nfunc==3)
if(dmore==1.0)
temp_dvalue=-pi_n[i]*value/r;
return(temp_dvalue);
}
/* ---------------------------------------------------------------------- */
double PairBOP::repulfunc(int i,double r)
{
double temp_value;
if(nfunc==1) {
temp_value=pow(phi_r0[i]/r,phi_m[i])*exp(phi_m[i]*pow(phi_r0[i]/phi_rc[i]
,phi_nc[i])-phi_m[i]*pow(r/phi_rc[i],phi_nc[i]));
temp_value=phi0[i]*temp_value;
}
if(nfunc==2)
temp_value=phi0[i]*exp(-phi_m[i]*r);
if(nfunc==3)
temp_value=phi0[i]/pow(r,phi_m[i]);
return(temp_value);
}
/* ---------------------------------------------------------------------- */
double PairBOP::dRepulfunc(int i,double r,double value,double dmore)
{
double temp_dvalue;
if(nfunc==1)
if(dmore==1.0)
temp_dvalue=-phi_m[i]*value/r*(1.0+phi_nc[i]*pow(r/phi_rc[i],phi_nc[i]));
if(nfunc==2)
if(dmore==1.0)
temp_dvalue=-phi_m[i]*value;
if(nfunc==3)
if(dmore==1.0)
temp_dvalue=-phi_m[i]*value/r;
return(temp_dvalue);
}
/* ---------------------------------------------------------------------- */
void PairBOP::setSign()
{
int i,j,k;
double y0,tmp,xBO,fth,cs,bigF;
double epsilon,fsigma1,slope,sat;
dBO=1.0/(nBOt-1.0);
rdBO=1.0/dBO;
for(i=0;i<npairs;i++) {
for(j=0;j<nBOt;j++) {
xBO=(double)j*dBO;
if(which==1.0) {
fth=0.0;
if(xBO>alpha)
fth=4.0/3.0*(xBO-alpha);
if(sigma_f[i]<=fth)
FsigBO[i][j]=2.0*sigma_f[i];
else if(sigma_f[i]>=1.0-fth)
FsigBO[i][j]=2.0*(1.0-sigma_f[i]);
else {
cs=0.0;
if(xBO<alpha)
cs=32.0*(alpha-xBO);
bigF=(sigma_f[i]*(1.0-sigma_f[i])-fth*(1.0-fth))/square(1.0-2.0*fth);
FsigBO[i][j]=2.0*fth+2.0*bigF*(1.0-2.0*fth)*(1.0+bigF*(1.0-cs*bigF));
}
}
else if(which==2.0) {
epsilon=0.0000000001;
fsigma1=sigma_f[i];
if(fsigma1>0.5)
fsigma1=1.0-fsigma1;
y0=alpha1*pow(fsigma1,beta1)*pow(0.5-fsigma1,gamma1);
slope=(1.0-exp(-alpha2*pow(fsigma1,beta2)))/(1.0-exp(-alpha2*pow(0.5,beta2)));
sat=alpha3*fsigma1+beta3;
tmp=y0+slope*xBO+sat;
FsigBO[i][j]=(tmp-sqrt(tmp*tmp-4.0*(-epsilon*sqrt(1.0+slope*slope)
+y0*sat+slope*sat*xBO)))/2.0;
}
}
FsigBO1[i][0]=FsigBO[i][1]-FsigBO[i][0];
FsigBO1[i][1]=0.5*(FsigBO[i][2]-FsigBO[i][0]);
FsigBO1[i][nBOt-2]=0.5*(FsigBO[i][nBOt-1]-FsigBO[i][nBOt-3]);
FsigBO1[i][nBOt-1]=FsigBO[i][nBOt-1]-FsigBO[i][nBOt-2];
for(k=2;k<nBOt-2;k++)
FsigBO1[i][k]=((FsigBO[i][k-2]-FsigBO[i][k+2])+8.0*(FsigBO[i][k+1]
-FsigBO[i][k-1]))/12.0;
for(k=0;k<nBOt-1;k++) {
FsigBO2[i][k]=3.0*(FsigBO[i][k+1]-FsigBO[i][k])-2.0*FsigBO1[i][k]-FsigBO1[i][k+1];
FsigBO3[i][k]=FsigBO1[i][k]+FsigBO1[i][k+1]-2.0*(FsigBO[i][k+1]-FsigBO[i][k]);
}
FsigBO2[i][nBOt-1]=0.0;
FsigBO3[i][nBOt-1]=0.0;
for(k=0;k<nBOt;k++) {
FsigBO4[i][k]=FsigBO1[i][k]/dBO;
FsigBO5[i][k]=2.0*FsigBO2[i][k]/dBO;
FsigBO6[i][k]=3.0*FsigBO3[i][k]/dBO;
}
}
}
/* ---------------------------------------------------------------------- */
double PairBOP::cutoff(double rp,double vrcut,int mode,double r)
{
double tmp,tmp_beta,tmp_alpha,cut_store;
if(mode==1) {
tmp=(rsmall-rbig)*(r-rp)/(vrcut-rp)+rbig;
cut_store=(erfc(tmp)-erfc(rsmall))/(erfc(rbig)-erfc(rsmall));
}
else {
tmp_beta=log(log(rbig)/log(rsmall))/log(rp/vrcut);
tmp_alpha=-log(rbig)/pow(rp,tmp_beta);
cut_store=(exp(-tmp_alpha*pow(r,tmp_beta))-exp(-tmp_alpha*pow(vrcut
,tmp_beta)))/(exp(-tmp_alpha*pow(rp,tmp_beta))-exp(-tmp_alpha
*pow(vrcut,tmp_beta)));
}
return(cut_store);
}
/* ----------------------------------------------------------------------
memory usage of local atom-based arrays
------------------------------------------------------------------------- */
double PairBOP::memory_usage()
{
int nlocal,nghost,nall;
int n = atom->ntypes;
nlocal = atom->nlocal;
nghost = atom->nghost;
nall = nlocal + nghost;
double bytes = 0.0;
// rcut
bytes += npairs * sizeof (double);
// dr
bytes += npairs * sizeof (double);
// rdr
bytes += npairs * sizeof (double);
// setflag
bytes += (n+1) * (n+1) * sizeof (int);
// cutsq
bytes += (n+1) * (n+1) * sizeof (double);
// cutghost
bytes += (n+1) * (n+1) * sizeof (double);
// cutghost
bytes += (n+1) * (n+1) * sizeof (double);
// pBetaS
bytes += npairs * nr * sizeof (double);
// pBetaS1
bytes += npairs * nr * sizeof (double);
// pBetaS2
bytes += npairs * nr * sizeof (double);
// pBetaS3
bytes += npairs * nr * sizeof (double);
// pBetaS4
bytes += npairs * nr * sizeof (double);
// pBetaS5
bytes += npairs * nr * sizeof (double);
// pBetaS6
bytes += npairs * nr * sizeof (double);
// pBetaP
bytes += npairs * nr * sizeof (double);
// pBetaP1
bytes += npairs * nr * sizeof (double);
// pBetaP2
bytes += npairs * nr * sizeof (double);
// pBetaP3
bytes += npairs * nr * sizeof (double);
// pBetaP4
bytes += npairs * nr * sizeof (double);
// pBetaP5
bytes += npairs * nr * sizeof (double);
// pBetaP6
bytes += npairs * nr * sizeof (double);
// pRepul
bytes += npairs * nr * sizeof (double);
// pRepul1
bytes += npairs * nr * sizeof (double);
// pRepul2
bytes += npairs * nr * sizeof (double);
// pRepul3
bytes += npairs * nr * sizeof (double);
// pRepul4
bytes += npairs * nr * sizeof (double);
// pRepul5
bytes += npairs * nr * sizeof (double);
// pRepul6
bytes += npairs * nr * sizeof (double);
// FsigBO
bytes += npairs * nr * sizeof (double);
// FsigBO1
bytes += npairs * nr * sizeof (double);
// FsigBO2
bytes += npairs * nr * sizeof (double);
// FsigBO3
bytes += npairs * nr * sizeof (double);
// FsigBO4
bytes += npairs * nr * sizeof (double);
// FsigBO5
bytes += npairs * nr * sizeof (double);
// FsigBO6
bytes += npairs * nr * sizeof (double);
// itypeSigBk
bytes += neigh_total *neigh_ct* sizeof(int);
// nSigBk
bytes += neigh_total * sizeof(int);
// sigB
bytes += neigh_total * sizeof(int);
// sigB1
bytes += neigh_total * sizeof(int);
// nPiBk
bytes += neigh_total * sizeof(int);
// piB
bytes += neigh_total * sizeof(int);
// itypePiBk
bytes += neigh_total *neigh_ct* sizeof(int);
// BOP_index
bytes += nall * sizeof(double);
if(otfly==0) {
// cosAng
bytes += cos_total* sizeof(double);
// dcAng
bytes += cos_total * 3 * 2 * sizeof(double);
// disij
bytes += neigh_total * 3 * sizeof(double);
// rij
bytes += neigh_total * sizeof(double);
// betaS
bytes += neigh_total * sizeof(double);
// dBetaS
bytes += neigh_total * sizeof(double);
// betaP
bytes += neigh_total * sizeof(double);
// dBetaP
bytes += neigh_total * sizeof(double);
// repul
bytes += neigh_total * sizeof(double);
// dRepul
bytes += neigh_total * sizeof(double);
// cos_index
bytes += nall * sizeof(double);
}
// pi_a
bytes += npairs * sizeof(double);
// pro_delta
bytes += npairs * sizeof(double);
// pi_delta
bytes += npairs * sizeof(double);
// pi_p
bytes += npairs * sizeof(double);
// pi_c
bytes += npairs * sizeof(double);
// sigma_r0
bytes += npairs * sizeof(double);
// pi_r0
bytes += npairs * sizeof(double);
// phi_r0
bytes += npairs * sizeof(double);
// sigma_rc
bytes += npairs * sizeof(double);
// pi_rc
bytes += npairs * sizeof(double);
// pi_a
bytes += npairs * sizeof(double);
// pro_delta
bytes += npairs * sizeof(double);
// pi_delta
bytes += npairs * sizeof(double);
// pi_p
bytes += npairs * sizeof(double);
// pi_c
bytes += npairs * sizeof(double);
// sigma_r0
bytes += npairs * sizeof(double);
// pi_r0
bytes += npairs * sizeof(double);
// phi_r0
bytes += npairs * sizeof(double);
// sigma_rc
bytes += npairs * sizeof(double);
// pi_rc
bytes += npairs * sizeof(double);
// phi_rc
bytes += npairs * sizeof(double);
// r1
bytes += npairs * sizeof(double);
// sigma_beta0
bytes += npairs * sizeof(double);
// pi_beta0
bytes += npairs * sizeof(double);
// phi0
bytes += npairs * sizeof(double);
// sigma_n
bytes += npairs * sizeof(double);
// pi_n
bytes += npairs * sizeof(double);
// phi_m
bytes += npairs * sizeof(double);
// sigma_nc
bytes += npairs * sizeof(double);
// pi_nc
bytes += npairs * sizeof(double);
// phi_nc
bytes += npairs * sizeof(double);
// pro
bytes += npairs * sizeof(double);
// sigma_delta
bytes += npairs * sizeof(double);
// sigma_c
bytes += npairs * sizeof(double);
// sigma_a
bytes += npairs * sizeof(double);
// sigma_g0
bytes += bop_types * bop_types *bop_types * sizeof(double);
// sigma_g1
bytes += bop_types * bop_types *bop_types * sizeof(double);
// sigma_g2
bytes += bop_types * bop_types *bop_types * sizeof(double);
// sigma_g3
bytes += bop_types * bop_types *bop_types * sizeof(double);
// sigma_g4
bytes += bop_types * bop_types *bop_types * sizeof(double);
// sigma_f
bytes += npairs * sizeof(double);
// sigma_k
bytes += npairs * sizeof(double);
// small3
bytes += npairs * sizeof(double);
// bt_pi
bytes += maxneigh*(maxneigh/2) *sizeof(B_PI);
// bt_sigma
bytes += maxneigh*(maxneigh/2) *sizeof(B_SG);
return bytes;
}
/* ---------------------------------------------------------------------- */
void PairBOP::memory_theta_create()
{
int nlocal,nghost,nall;
nlocal = atom->nlocal;
nghost = atom->nghost;
nall = nlocal + nghost;
if(maxneigh<8)
neigh_ct=(maxneigh-1)*(maxneigh-1)*(maxneigh-1);
else
neigh_ct=(maxneigh-1)*(maxneigh-1);
memory->create(itypeSigBk,neigh_total
,neigh_ct,"itypeSigBk");
memory->create(nSigBk,neigh_total,"nSigBk");
memory->create(sigB,neigh_total,"sigB");
memory->create(sigB1,neigh_total,"sigB1");
memory->create(itypePiBk,neigh_total
,neigh_ct,"itypePiBk");
memory->create(nPiBk,neigh_total,"nPiBk");
memory->create(piB,neigh_total,"piB");
memory->create(neigh_flag,neigh_total,"neigh_flag");
if(otfly==0) {
memory->create(cosAng,cos_total,"BOP:cosAng");
memory->create(dcAng,cos_total*2,3,2,"BOP:dcAng");
memory->create(disij,3,neigh_total,"disij");
memory->create(rij,neigh_total,"rij");
memory->create(betaS,neigh_total,"betaS");
memory->create(dBetaS,neigh_total,"dBetaS");
memory->create(betaP,neigh_total,"betaP");
memory->create(dBetaP,neigh_total,"dBetaP");
memory->create(repul,neigh_total,"repul");
memory->create(dRepul,neigh_total,"dRepul");
}
update_list=1;
}
/* ---------------------------------------------------------------------- */
void PairBOP::memory_theta_grow()
{
int nlocal,nghost,nall;
nlocal = atom->nlocal;
nghost = atom->nghost;
nall = nlocal + nghost;
if(maxneigh<8)
neigh_ct=(maxneigh-1)*(maxneigh-1)*(maxneigh-1);
else
neigh_ct=(maxneigh-1)*(maxneigh-1);
memory->grow(itypeSigBk,neigh_total
,neigh_ct,"itypeSigBk");
memory->grow(nSigBk,neigh_total,"nSigBk");
memory->grow(sigB,neigh_total,"sigB");
memory->grow(sigB1,neigh_total,"sigB1");
memory->grow(itypePiBk,neigh_total
,neigh_ct,"itypePiBk");
memory->grow(nPiBk,neigh_total,"nPiBk");
memory->grow(piB,neigh_total,"piB");
memory->grow(neigh_flag,neigh_total,"neigh_flag");
if(otfly==0) {
memory->grow(cosAng,cos_total,"BOP:cosAng");
memory->grow(dcAng,cos_total*2,3,2,"BOP:dcAng");
memory->grow(disij,3,neigh_total,"disij");
memory->grow(rij,neigh_total,"rij");
memory->grow(betaS,neigh_total,"betaS");
memory->grow(dBetaS,neigh_total,"dBetaS");
memory->grow(betaP,neigh_total,"betaP");
memory->grow(dBetaP,neigh_total,"dBetaP");
memory->grow(repul,neigh_total,"repul");
memory->grow(dRepul,neigh_total,"dRepul");
}
update_list=1;
}
/* ---------------------------------------------------------------------- */
void PairBOP::memory_theta_destroy()
{
memory->destroy(itypeSigBk);
memory->destroy(nSigBk);
memory->destroy(sigB);
memory->destroy(sigB1);
memory->destroy(itypePiBk);
memory->destroy(nPiBk);
memory->destroy(piB);
memory->destroy(neigh_flag);
if(otfly==0) {
memory->destroy(cosAng);
memory->destroy(dcAng);
memory->destroy(disij);
memory->destroy(rij);
memory->destroy(betaS);
memory->destroy(dBetaS);
memory->destroy(betaP);
memory->destroy(dBetaP);
memory->destroy(repul);
memory->destroy(dRepul);
}
update_list=0;
}
/* ---------------------------------------------------------------------- */
void PairBOP::create_pi(int n_tot)
{
bt_pi = (B_PI *) memory->smalloc(n_tot*sizeof(B_PI),"BOP:bt_pi");
allocate_pi=1;
}
void PairBOP::create_sigma(int n_tot)
{
bt_sg = (B_SG *) memory->smalloc(n_tot*sizeof(B_SG),"BOP:bt_sg");
allocate_sigma=1;
}
void PairBOP::destroy_pi()
{
memory->destroy(bt_pi);
allocate_pi=0;
}
void PairBOP::destroy_sigma()
{
memory->destroy(bt_sg);
allocate_sigma=0;
}
/* ---------------------------------------------------------------------- */
void PairBOP::grow_pi(int n1, int n2)
{
int i,j;
B_PI *bt_temp;
bt_temp = (B_PI *) memory->smalloc(n1*sizeof(B_PI),"BOP:b_temp");
for(i=0;i<n1;i++) {
bt_temp[i].temp = bt_pi[i].temp;
bt_temp[i].i = bt_pi[i].i;
bt_temp[i].j = bt_pi[i].j;
for(j=0;j<3;j++) {
bt_temp[i].dAA[j] = bt_pi[i].dAA[j];
bt_temp[i].dBB[j] = bt_pi[i].dBB[j];
bt_temp[i].dPiB[j] = bt_pi[i].dPiB[j];
}
}
memory->destroy(bt_pi);
bt_pi=NULL;
bt_pi = (B_PI *) memory->smalloc(n2*sizeof(B_PI),"BOP:bt_pi");
for(i=0;i<n1;i++) {
bt_pi[i].temp = bt_temp[i].temp;
bt_pi[i].i = bt_temp[i].i;
bt_pi[i].j = bt_temp[i].j;
for(j=0;j<3;j++) {
bt_pi[i].dAA[j] = bt_temp[i].dAA[j];
bt_pi[i].dBB[j] = bt_temp[i].dBB[j];
bt_pi[i].dPiB[j] = bt_temp[i].dPiB[j];
}
}
for(i=n1;i<n2;i++) {
bt_pi[i].i = -1;
bt_pi[i].j = -1;
for(j=0;j<3;j++) {
bt_pi[i].dAA[j] = 0.0;
bt_pi[i].dBB[j] = 0.0;
bt_pi[i].dPiB[j] = 0.0;
}
}
memory->destroy(bt_temp);
}
/* ---------------------------------------------------------------------- */
void PairBOP::grow_sigma(int n1,int n2)
{
int i,j;
B_SG *bt_temp;
bt_temp = (B_SG *) memory->smalloc(n1*sizeof(B_SG),"BOP:bt_temp");
for(i=0;i<n1;i++) {
bt_temp[i].temp = bt_sg[i].temp;
bt_temp[i].i = bt_sg[i].i;
bt_temp[i].j = bt_sg[i].j;
for(j=0;j<3;j++) {
bt_temp[i].dAA[j] = bt_sg[i].dAA[j];
bt_temp[i].dBB[j] = bt_sg[i].dBB[j];
bt_temp[i].dCC[j] = bt_sg[i].dCC[j];
bt_temp[i].dDD[j] = bt_sg[i].dDD[j];
bt_temp[i].dEE[j] = bt_sg[i].dEE[j];
bt_temp[i].dEE1[j] = bt_sg[i].dEE1[j];
bt_temp[i].dFF[j] = bt_sg[i].dFF[j];
bt_temp[i].dAAC[j] = bt_sg[i].dAAC[j];
bt_temp[i].dBBC[j] = bt_sg[i].dBBC[j];
bt_temp[i].dCCC[j] = bt_sg[i].dCCC[j];
bt_temp[i].dDDC[j] = bt_sg[i].dDDC[j];
bt_temp[i].dEEC[j] = bt_sg[i].dEEC[j];
bt_temp[i].dFFC[j] = bt_sg[i].dFFC[j];
bt_temp[i].dGGC[j] = bt_sg[i].dGGC[j];
bt_temp[i].dUT[j] = bt_sg[i].dUT[j];
bt_temp[i].dSigB1[j] = bt_sg[i].dSigB1[j];
bt_temp[i].dSigB[j] = bt_sg[i].dSigB[j];
}
}
memory->destroy(bt_sg);
bt_sg=NULL;
bt_sg = (B_SG *) memory->smalloc(n2*sizeof(B_SG),"BOP:bt_sg");
for(i=0;i<n1;i++) {
bt_sg[i].temp = bt_temp[i].temp;
bt_sg[i].i = bt_temp[i].i;
bt_sg[i].j = bt_temp[i].j;
for(j=0;j<3;j++) {
bt_sg[i].dAA[j] = bt_temp[i].dAA[j];
bt_sg[i].dBB[j] = bt_temp[i].dBB[j];
bt_sg[i].dCC[j] = bt_temp[i].dCC[j];
bt_sg[i].dDD[j] = bt_temp[i].dDD[j];
bt_sg[i].dEE[j] = bt_temp[i].dEE[j];
bt_sg[i].dEE1[j] = bt_temp[i].dEE1[j];
bt_sg[i].dFF[j] = bt_temp[i].dFF[j];
bt_sg[i].dAAC[j] = bt_temp[i].dAAC[j];
bt_sg[i].dBBC[j] = bt_temp[i].dBBC[j];
bt_sg[i].dCCC[j] = bt_temp[i].dCCC[j];
bt_sg[i].dDDC[j] = bt_temp[i].dDDC[j];
bt_sg[i].dEEC[j] = bt_temp[i].dEEC[j];
bt_sg[i].dFFC[j] = bt_temp[i].dFFC[j];
bt_sg[i].dGGC[j] = bt_temp[i].dGGC[j];
bt_sg[i].dUT[j] = bt_temp[i].dUT[j];
bt_sg[i].dSigB1[j] = bt_temp[i].dSigB1[j];
bt_sg[i].dSigB[j] = bt_temp[i].dSigB[j];
}
}
for(i=n1;i<n2;i++) {
bt_sg[i].i = -1;
bt_sg[i].j = -1;
for(j=0;j<3;j++) {
bt_sg[i].dAA[j] = 0.0;
bt_sg[i].dBB[j] = 0.0;
bt_sg[i].dCC[j] = 0.0;
bt_sg[i].dDD[j] = 0.0;
bt_sg[i].dEE[j] = 0.0;
bt_sg[i].dEE1[j] = 0.0;
bt_sg[i].dFF[j] = 0.0;
bt_sg[i].dAAC[j] = 0.0;
bt_sg[i].dBBC[j] = 0.0;
bt_sg[i].dCCC[j] = 0.0;
bt_sg[i].dDDC[j] = 0.0;
bt_sg[i].dEEC[j] = 0.0;
bt_sg[i].dFFC[j] = 0.0;
bt_sg[i].dGGC[j] = 0.0;
bt_sg[i].dUT[j] = 0.0;
bt_sg[i].dSigB1[j] = 0.0;
bt_sg[i].dSigB[j] = 0.0;
}
}
memory->destroy(bt_temp);
}

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