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bf59c976f8532c072eb494407d3ac267d7fd6e16
lammps/src/MANYBODY/pair_vashishta.cpp
Anders Hafreager bf59c976f8 Added curly brackets and spaces for better code readability
2016-08-27 23:05:17 -04:00

750 lines
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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 author: Yongnan Xiong (HNU), xyn@hnu.edu.cn
Aidan Thompson (SNL)
Anders Hafreager (UiO), andershaf@gmail.com
------------------------------------------------------------------------- */
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include "pair_vashishta.h"
#include "atom.h"
#include "neighbor.h"
#include "neigh_request.h"
#include "force.h"
#include "comm.h"
#include "memory.h"
#include "neighbor.h"
#include "neigh_list.h"
#include "memory.h"
#include "error.h"
using namespace LAMMPS_NS;
#define MAXLINE 1024
#define DELTA 4
/* ---------------------------------------------------------------------- */
PairVashishta::PairVashishta(LAMMPS *lmp) : Pair(lmp)
{
single_enable = 0;
restartinfo = 0;
one_coeff = 1;
manybody_flag = 1;
nelements = 0;
elements = NULL;
nparams = maxparam = 0;
params = NULL;
elem2param = NULL;
map = NULL;
neigh3BodyMax = 0;
neigh3BodyCount = NULL;
neigh3Body = NULL;
useTable = false;
nTablebits = 12;
forceTable = NULL;
potentialTable = NULL;
}
/* ----------------------------------------------------------------------
check if allocated, since class can be destructed when incomplete
------------------------------------------------------------------------- */
PairVashishta::~PairVashishta()
{
if (elements)
for (int i = 0; i < nelements; i++) delete [] elements[i];
delete [] elements;
memory->destroy(params);
memory->destroy(elem2param);
memory->destroy(forceTable);
memory->destroy(potentialTable);
memory->destroy(neigh3BodyCount);
memory->destroy(neigh3Body);
if (allocated) {
memory->destroy(setflag);
memory->destroy(cutsq);
delete [] map;
}
}
void PairVashishta::modify_params(int narg, char **arg)
{
if (narg == 0) error->all(FLERR,"Illegal pair_modify command");
int iarg = 0;
while (iarg < narg) {
if (strcmp(arg[iarg],"table") == 0) {
if (iarg+2 > narg) error->all(FLERR,"Illegal pair_modify command");
nTablebits = force->inumeric(FLERR,arg[iarg+1]);
if (nTablebits > sizeof(float)*CHAR_BIT) {
error->all(FLERR,"Too many total bits for bitmapped lookup table");
}
if(nTablebits == 0) {
useTable = false;
} else {
useTable = true;
}
iarg += 2;
} else if (strcmp(arg[iarg],"tabinner") == 0) {
if (iarg+2 > narg) error->all(FLERR,"Illegal pair_modify command");
tabinner = force->numeric(FLERR,arg[iarg+1]);
iarg += 2;
}
}
createTable();
}
void PairVashishta::validateNeigh3Body() {
if (atom->nlocal > neigh3BodyMax) {
neigh3BodyMax = atom->nmax;
memory->destroy(neigh3BodyCount);
memory->destroy(neigh3Body);
memory->create(neigh3BodyCount,neigh3BodyMax, "pair:vashishta:neigh3BodyCount");
memory->create(neigh3Body,neigh3BodyMax, 1000, "pair:vashishta:neigh3Body"); // TODO: pick this number more wisely?
}
}
void PairVashishta::createTable()
{
int ntypes = atom->ntypes+1;
tabinnersq = tabinner*tabinner;
int ntable = 1;
for (int i = 0; i < nTablebits; i++) ntable *= 2;
deltaR2 = (cutmax*cutmax - tabinnersq) / (ntable-1);
oneOverDeltaR2 = 1.0/deltaR2;
memory->destroy(forceTable);
memory->destroy(potentialTable);
memory->create(forceTable,ntypes,ntypes,ntable+1,"pair:vashishta:forceTable");
memory->create(potentialTable,ntypes,ntypes,ntable+1,"pair:vashishta:potentialTable");
for (int ii = 0; ii < ntypes; ii++) {
int i = map[ii];
for (int jj = 0; jj < ntypes; jj++) {
int j = map[jj];
if (i < 0 || j < 0 || ii == 0 || jj == 0) {
for(int tableIndex=0; tableIndex<=ntable; tableIndex++) {
forceTable[ii][jj][tableIndex] = 0;
potentialTable[ii][jj][tableIndex] = 0;
}
} else {
int ijparam = elem2param[i][j][j];
for(int tableIndex=0; tableIndex<=ntable; tableIndex++) {
double rsq = tabinnersq + tableIndex*deltaR2;
double fpair, eng;
twobody(&params[ijparam], rsq, fpair, 1, eng, false /* Don't ask for tabulated since we are generating it now*/ );
forceTable[ii][jj][tableIndex] = fpair;
potentialTable[ii][jj][tableIndex] = eng;
}
}
}
}
}
/* ---------------------------------------------------------------------- */
void PairVashishta::compute(int eflag, int vflag)
{
validateNeigh3Body();
int i,j,k,ii,jj,kk,inum,jnum,jnumm1;
int itype,jtype,ktype,ijparam,ikparam,ijkparam;
tagint itag,jtag;
double xtmp,ytmp,ztmp,delx,dely,delz,evdwl,fpair;
double rsq,rsq1,rsq2;
double delr1[3],delr2[3],fj[3],fk[3];
int *ilist,*jlist,*numneigh,**firstneigh;
evdwl = 0.0;
if (eflag || vflag) ev_setup(eflag,vflag);
else evflag = vflag_fdotr = 0;
double **x = atom->x;
double **f = atom->f;
tagint *tag = atom->tag;
int *type = atom->type;
int nlocal = atom->nlocal;
int newton_pair = force->newton_pair;
inum = list->inum;
ilist = list->ilist;
numneigh = list->numneigh;
firstneigh = list->firstneigh;
// loop over full neighbor list of my atoms
for (ii = 0; ii < inum; ii++) {
i = ilist[ii];
itag = tag[i];
itype = map[type[i]];
xtmp = x[i][0];
ytmp = x[i][1];
ztmp = x[i][2];
neigh3BodyCount[i] = 0; // Reset the 3-body neighbor list
// two-body interactions, skip half of them
jlist = firstneigh[i];
jnum = numneigh[i];
for (jj = 0; jj < jnum; jj++) {
j = jlist[jj];
j &= NEIGHMASK;
jtag = tag[j];
jtype = map[type[j]];
delx = xtmp - x[j][0];
dely = ytmp - x[j][1];
delz = ztmp - x[j][2];
rsq = delx*delx + dely*dely + delz*delz;
ijparam = elem2param[itype][jtype][jtype];
if (rsq <= params[ijparam].cutsq2) {
neigh3Body[i][neigh3BodyCount[i]] = j;
neigh3BodyCount[i]++;
}
if (rsq > params[ijparam].cutsq) continue;
if (itag > jtag) {
if ((itag+jtag) % 2 == 0) continue;
} else if (itag < jtag) {
if ((itag+jtag) % 2 == 1) continue;
} else {
if (x[j][2] < ztmp) continue;
if (x[j][2] == ztmp && x[j][1] < ytmp) continue;
if (x[j][2] == ztmp && x[j][1] == ytmp && x[j][0] < xtmp) continue;
}
twobody(&params[ijparam],rsq,fpair,eflag,evdwl, useTable);
f[i][0] += delx*fpair;
f[i][1] += dely*fpair;
f[i][2] += delz*fpair;
f[j][0] -= delx*fpair;
f[j][1] -= dely*fpair;
f[j][2] -= delz*fpair;
if (evflag) ev_tally(i,j,nlocal,newton_pair,
evdwl,0.0,fpair,delx,dely,delz);
}
jlist = neigh3Body[i];
jnum = neigh3BodyCount[i];
jnumm1 = jnum - 1;
for (jj = 0; jj < jnumm1; jj++) {
j = jlist[jj];
j &= NEIGHMASK;
jtype = map[type[j]];
ijparam = elem2param[itype][jtype][jtype];
delr1[0] = x[j][0] - xtmp;
delr1[1] = x[j][1] - ytmp;
delr1[2] = x[j][2] - ztmp;
rsq1 = delr1[0]*delr1[0] + delr1[1]*delr1[1] + delr1[2]*delr1[2];
if (rsq1 >= params[ijparam].cutsq2) continue;
for (kk = jj+1; kk < jnum; kk++) {
k = jlist[kk];
k &= NEIGHMASK;
ktype = map[type[k]];
ikparam = elem2param[itype][ktype][ktype];
ijkparam = elem2param[itype][jtype][ktype];
delr2[0] = x[k][0] - xtmp;
delr2[1] = x[k][1] - ytmp;
delr2[2] = x[k][2] - ztmp;
rsq2 = delr2[0]*delr2[0] + delr2[1]*delr2[1] + delr2[2]*delr2[2];
if (rsq2 >= params[ikparam].cutsq2) continue;
threebody(&params[ijparam],&params[ikparam],&params[ijkparam],
rsq1,rsq2,delr1,delr2,fj,fk,eflag,evdwl);
f[i][0] -= fj[0] + fk[0];
f[i][1] -= fj[1] + fk[1];
f[i][2] -= fj[2] + fk[2];
f[j][0] += fj[0];
f[j][1] += fj[1];
f[j][2] += fj[2];
f[k][0] += fk[0];
f[k][1] += fk[1];
f[k][2] += fk[2];
if (evflag) ev_tally3(i,j,k,evdwl,0.0,fj,fk,delr1,delr2);
}
}
}
if (vflag_fdotr) virial_fdotr_compute();
}
/* ---------------------------------------------------------------------- */
void PairVashishta::allocate()
{
allocated = 1;
int n = atom->ntypes;
memory->create(setflag,n+1,n+1,"pair:setflag");
memory->create(cutsq,n+1,n+1,"pair:cutsq");
map = new int[n+1];
}
/* ----------------------------------------------------------------------
global settings
------------------------------------------------------------------------- */
void PairVashishta::settings(int narg, char **arg)
{
if (narg != 0) error->all(FLERR,"Illegal pair_style command");
}
/* ----------------------------------------------------------------------
set coeffs for one or more type pairs
------------------------------------------------------------------------- */
void PairVashishta::coeff(int narg, char **arg)
{
int i,j,n;
if (!allocated) allocate();
if (narg != 3 + atom->ntypes)
error->all(FLERR,"Incorrect args for pair coefficients");
// insure I,J args are * *
if (strcmp(arg[0],"*") != 0 || strcmp(arg[1],"*") != 0)
error->all(FLERR,"Incorrect args for pair coefficients");
// read args that map atom types to elements in potential file
// map[i] = which element the Ith atom type is, -1 if NULL
// nelements = # of unique elements
// elements = list of element names
if (elements) {
for (i = 0; i < nelements; i++) delete [] elements[i];
delete [] elements;
}
elements = new char*[atom->ntypes];
for (i = 0; i < atom->ntypes; i++) elements[i] = NULL;
nelements = 0;
for (i = 3; i < narg; i++) {
if (strcmp(arg[i],"NULL") == 0) {
map[i-2] = -1;
continue;
}
for (j = 0; j < nelements; j++)
if (strcmp(arg[i],elements[j]) == 0) break;
map[i-2] = j;
if (j == nelements) {
n = strlen(arg[i]) + 1;
elements[j] = new char[n];
strcpy(elements[j],arg[i]);
nelements++;
}
}
// read potential file and initialize potential parameters
read_file(arg[2]);
setup_params();
// 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 PairVashishta::init_style()
{
if (atom->tag_enable == 0)
error->all(FLERR,"Pair style Vashishta requires atom IDs");
if (force->newton_pair == 0)
error->all(FLERR,"Pair style Vashishta requires newton pair on");
// need a full neighbor list
int irequest = neighbor->request(this);
neighbor->requests[irequest]->half = 0;
neighbor->requests[irequest]->full = 1;
}
/* ----------------------------------------------------------------------
init for one type pair i,j and corresponding j,i
------------------------------------------------------------------------- */
double PairVashishta::init_one(int i, int j)
{
if (setflag[i][j] == 0) error->all(FLERR,"All pair coeffs are not set");
return cutmax;
}
/* ---------------------------------------------------------------------- */
void PairVashishta::read_file(char *file)
{
int params_per_line = 17;
char **words = new char*[params_per_line+1];
memory->sfree(params);
params = NULL;
nparams = maxparam = 0;
// open file on proc 0
FILE *fp;
if (comm->me == 0) {
fp = force->open_potential(file);
if (fp == NULL) {
char str[128];
sprintf(str,"Cannot open Vashishta potential file %s",file);
error->one(FLERR,str);
}
}
// read each set of params from potential file
// one set of params can span multiple lines
// store params if all 3 element tags are in element list
int n,nwords,ielement,jelement,kelement;
char line[MAXLINE],*ptr;
int eof = 0;
while (1) {
if (comm->me == 0) {
ptr = fgets(line,MAXLINE,fp);
if (ptr == NULL) {
eof = 1;
fclose(fp);
} else n = strlen(line) + 1;
}
MPI_Bcast(&eof,1,MPI_INT,0,world);
if (eof) break;
MPI_Bcast(&n,1,MPI_INT,0,world);
MPI_Bcast(line,n,MPI_CHAR,0,world);
// strip comment, skip line if blank
if ((ptr = strchr(line,'#'))) *ptr = '\0';
nwords = atom->count_words(line);
if (nwords == 0) continue;
// concatenate additional lines until have params_per_line words
while (nwords < params_per_line) {
n = strlen(line);
if (comm->me == 0) {
ptr = fgets(&line[n],MAXLINE-n,fp);
if (ptr == NULL) {
eof = 1;
fclose(fp);
} else n = strlen(line) + 1;
}
MPI_Bcast(&eof,1,MPI_INT,0,world);
if (eof) break;
MPI_Bcast(&n,1,MPI_INT,0,world);
MPI_Bcast(line,n,MPI_CHAR,0,world);
if ((ptr = strchr(line,'#'))) *ptr = '\0';
nwords = atom->count_words(line);
}
if (nwords != params_per_line)
error->all(FLERR,"Incorrect format in Vashishta potential file");
// words = ptrs to all words in line
nwords = 0;
words[nwords++] = strtok(line," \t\n\r\f");
while ((words[nwords++] = strtok(NULL," \t\n\r\f"))) continue;
// ielement,jelement,kelement = 1st args
// if all 3 args are in element list, then parse this line
// else skip to next entry in file
for (ielement = 0; ielement < nelements; ielement++)
if (strcmp(words[0],elements[ielement]) == 0) break;
if (ielement == nelements) continue;
for (jelement = 0; jelement < nelements; jelement++)
if (strcmp(words[1],elements[jelement]) == 0) break;
if (jelement == nelements) continue;
for (kelement = 0; kelement < nelements; kelement++)
if (strcmp(words[2],elements[kelement]) == 0) break;
if (kelement == nelements) continue;
// load up parameter settings and error check their values
if (nparams == maxparam) {
maxparam += DELTA;
params = (Param *) memory->srealloc(params,maxparam*sizeof(Param),
"pair:params");
}
params[nparams].ielement = ielement;
params[nparams].jelement = jelement;
params[nparams].kelement = kelement;
params[nparams].bigh = atof(words[3]);
params[nparams].eta = atof(words[4]);
params[nparams].zi = atof(words[5]);
params[nparams].zj = atof(words[6]);
params[nparams].lambda1 = atof(words[7]);
params[nparams].bigd = atof(words[8]);
params[nparams].lambda4 = atof(words[9]);
params[nparams].bigw = atof(words[10]);
params[nparams].cut = atof(words[11]);
params[nparams].bigb = atof(words[12]);
params[nparams].gamma = atof(words[13]);
params[nparams].r0 = atof(words[14]);
params[nparams].bigc = atof(words[15]);
params[nparams].costheta = atof(words[16]);
if (params[nparams].bigb < 0.0 || params[nparams].gamma < 0.0 ||
params[nparams].r0 < 0.0 || params[nparams].bigc < 0.0 ||
params[nparams].bigh < 0.0 || params[nparams].eta < 0.0 ||
params[nparams].lambda1 < 0.0 || params[nparams].bigd < 0.0 ||
params[nparams].lambda4 < 0.0 || params[nparams].bigw < 0.0 ||
params[nparams].cut < 0.0)
error->all(FLERR,"Illegal Vashishta parameter");
nparams++;
}
delete [] words;
}
/* ---------------------------------------------------------------------- */
void PairVashishta::setup_params()
{
int i,j,k,m,n;
// set elem2param for all triplet combinations
// must be a single exact match to lines read from file
// do not allow for ACB in place of ABC
memory->destroy(elem2param);
memory->create(elem2param,nelements,nelements,nelements,"pair:elem2param");
for (i = 0; i < nelements; i++)
for (j = 0; j < nelements; j++)
for (k = 0; k < nelements; k++) {
n = -1;
for (m = 0; m < nparams; m++) {
if (i == params[m].ielement && j == params[m].jelement &&
k == params[m].kelement) {
if (n >= 0) error->all(FLERR,"Potential file has duplicate entry");
n = m;
}
}
if (n < 0) error->all(FLERR,"Potential file is missing an entry");
elem2param[i][j][k] = n;
}
// compute parameter values derived from inputs
// set cutsq using shortcut to reduce neighbor list for accelerated
// calculations. cut must remain unchanged as it is a potential parameter
double tmp_par;
for (m = 0; m < nparams; m++) {
params[m].cutsq = params[m].cut * params[m].cut;
params[m].cutsq2 = params[m].r0 * params[m].r0;
tmp_par = params[m].lambda1;
params[m].lam1inv = (tmp_par == 0.0) ? 0.0 : 1.0/tmp_par;
tmp_par = params[m].lambda4;
params[m].lam4inv = (tmp_par == 0.0) ? 0.0 : 1.0/tmp_par;
params[m].zizj = params[m].zi*params[m].zj * force->qqr2e;
// note that bigd does not have 1/2 factor
params[m].mbigd = params[m].bigd;
params[m].heta = params[m].bigh*params[m].eta;
params[m].big2b = 2.0*params[m].bigb;
params[m].big6w = 6.0*params[m].bigw;
tmp_par = params[m].cut;
params[m].rcinv = (tmp_par == 0.0) ? 0.0 : 1.0/tmp_par;
params[m].rc2inv = params[m].rcinv*params[m].rcinv;
params[m].rc4inv = params[m].rc2inv*params[m].rc2inv;
params[m].rc6inv = params[m].rc2inv*params[m].rc4inv;
params[m].rceta = pow(params[m].rcinv,params[m].eta);
params[m].lam1rc = params[m].cut*params[m].lam1inv;
params[m].lam4rc = params[m].cut*params[m].lam4inv;
params[m].vrcc2 = params[m].zizj*params[m].rcinv *
exp(-params[m].lam1rc);
params[m].vrcc3 = params[m].mbigd*params[m].rc4inv *
exp(-params[m].lam4rc);
params[m].vrc = params[m].bigh*params[m].rceta +
params[m].vrcc2 - params[m].vrcc3 -
params[m].bigw*params[m].rc6inv;
params[m].dvrc =
params[m].vrcc3 * (4.0*params[m].rcinv+params[m].lam4inv)
+ params[m].big6w * params[m].rc6inv * params[m].rcinv
- params[m].heta * params[m].rceta*params[m].rcinv
- params[m].vrcc2 * (params[m].rcinv+params[m].lam1inv);
params[m].c0 = params[m].cut*params[m].dvrc - params[m].vrc;
}
// set cutmax to max of all params
cutmax = 0.0;
for (m = 0; m < nparams; m++) {
if (params[m].cut > cutmax) cutmax = params[m].cut;
if (params[m].r0 > cutmax) cutmax = params[m].r0;
}
createTable();
}
/* ---------------------------------------------------------------------- */
void PairVashishta::twobody(Param *param, double rsq, double &fforce,
int eflag, double &eng, bool tabulated)
{
if(tabulated) {
if (rsq < tabinnersq) {
sprintf(estr,"Pair distance < table inner cutoff: "
"ijtype %d %d dist %g",param->ielement+1,param->jelement+1,sqrt(rsq));
error->one(FLERR,estr);
}
int tableIndex = (rsq - tabinnersq)*oneOverDeltaR2;
double fraction = (rsq - tabinnersq)*oneOverDeltaR2 - tableIndex; // double - int will only keep the 0.xxxx part
double force0 = forceTable[param->ielement+1][param->jelement+1][tableIndex];
double force1 = forceTable[param->ielement+1][param->jelement+1][tableIndex+1];
fforce = (1.0 - fraction)*force0 + fraction*force1; // force is linearly interpolated between the two values
if(evflag) {
double energy0 = potentialTable[param->ielement+1][param->jelement+1][tableIndex];
double energy1 = potentialTable[param->ielement+1][param->jelement+1][tableIndex+1];
eng = (1.0 - fraction)*energy0 + fraction*energy1;
}
} else {
double r,rinvsq,r4inv,r6inv,reta,lam1r,lam4r,vc2,vc3;
r = sqrt(rsq);
rinvsq = 1.0/rsq;
r4inv = rinvsq*rinvsq;
r6inv = rinvsq*r4inv;
reta = pow(r,-param->eta);
lam1r = r*param->lam1inv;
lam4r = r*param->lam4inv;
vc2 = param->zizj * exp(-lam1r)/r;
vc3 = param->mbigd * r4inv*exp(-lam4r);
fforce = (param->dvrc*r
- (4.0*vc3 + lam4r*vc3+param->big6w*r6inv
- param->heta*reta - vc2 - lam1r*vc2)
) * rinvsq;
if (eflag) eng = param->bigh*reta
+ vc2 - vc3 - param->bigw*r6inv
- r*param->dvrc + param->c0;
}
}
/* ---------------------------------------------------------------------- */
void PairVashishta::threebody(Param *paramij, Param *paramik, Param *paramijk,
double rsq1, double rsq2,
double *delr1, double *delr2,
double *fj, double *fk, int eflag, double &eng)
{
double r1,rinvsq1,rainv1,gsrainv1,gsrainvsq1,expgsrainv1;
double r2,rinvsq2,rainv2,gsrainv2,gsrainvsq2,expgsrainv2;
double rinv12,cs,delcs,delcssq,facexp,facrad,frad1,frad2,pcsinv,pcsinvsq,pcs;
double facang,facang12,csfacang,csfac1,csfac2;
r1 = sqrt(rsq1);
rinvsq1 = 1.0/rsq1;
rainv1 = 1.0/(r1 - paramij->r0);
gsrainv1 = paramij->gamma * rainv1;
gsrainvsq1 = gsrainv1*rainv1/r1;
expgsrainv1 = exp(gsrainv1);
r2 = sqrt(rsq2);
rinvsq2 = 1.0/rsq2;
rainv2 = 1.0/(r2 - paramik->r0);
gsrainv2 = paramik->gamma * rainv2;
gsrainvsq2 = gsrainv2*rainv2/r2;
expgsrainv2 = exp(gsrainv2);
rinv12 = 1.0/(r1*r2);
cs = (delr1[0]*delr2[0] + delr1[1]*delr2[1] + delr1[2]*delr2[2]) * rinv12;
delcs = cs - paramijk->costheta;
delcssq = delcs*delcs;
pcsinv = paramijk->bigc*delcssq + 1.0;
pcsinvsq = pcsinv*pcsinv;
pcs = delcssq/pcsinv;
facexp = expgsrainv1*expgsrainv2;
facrad = paramijk->bigb * facexp * pcs;
frad1 = facrad*gsrainvsq1;
frad2 = facrad*gsrainvsq2;
facang = paramijk->big2b * facexp * delcs/pcsinvsq;
facang12 = rinv12*facang;
csfacang = cs*facang;
csfac1 = rinvsq1*csfacang;
fj[0] = delr1[0]*(frad1+csfac1)-delr2[0]*facang12;
fj[1] = delr1[1]*(frad1+csfac1)-delr2[1]*facang12;
fj[2] = delr1[2]*(frad1+csfac1)-delr2[2]*facang12;
csfac2 = rinvsq2*csfacang;
fk[0] = delr2[0]*(frad2+csfac2)-delr1[0]*facang12;
fk[1] = delr2[1]*(frad2+csfac2)-delr1[1]*facang12;
fk[2] = delr2[2]*(frad2+csfac2)-delr1[2]*facang12;
if (eflag) eng = facrad;
}
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