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pair_resquared.cpp
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pair_resquared.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 author: Mike Brown (SNL)
------------------------------------------------------------------------- */
#include "math.h"
#include "stdio.h"
#include "stdlib.h"
#include "string.h"
#include "pair_resquared.h"
#include "math_extra.h"
#include "atom.h"
#include "atom_vec.h"
#include "comm.h"
#include "force.h"
#include "neighbor.h"
#include "neigh_list.h"
#include "integrate.h"
#include "memory.h"
#include "error.h"
#define MIN(a,b) ((a) < (b) ? (a) : (b))
#define MAX(a,b) ((a) > (b) ? (a) : (b))
using namespace LAMMPS_NS;
enum{SPHERE_SPHERE,SPHERE_ELLIPSE,ELLIPSE_SPHERE,ELLIPSE_ELLIPSE};
/* ---------------------------------------------------------------------- */
PairRESquared::PairRESquared(LAMMPS *lmp) : Pair(lmp),
b_alpha(45.0/56.0),
cr60(pow(60.0,1.0/3.0))
{
single_enable = 0;
cr60 = pow(60.0,1.0/3.0);
b_alpha = 45.0/56.0;
solv_f_a = 3.0/(16.0*atan(1.0)*-36.0);
solv_f_r = 3.0/(16.0*atan(1.0)*2025.0);
}
/* ----------------------------------------------------------------------
free all arrays
------------------------------------------------------------------------- */
PairRESquared::~PairRESquared()
{
if (allocated) {
memory->destroy_2d_int_array(setflag);
memory->destroy_2d_double_array(cutsq);
memory->destroy_2d_int_array(form);
memory->destroy_2d_double_array(epsilon);
memory->destroy_2d_double_array(sigma);
memory->destroy_2d_double_array(shape2);
memory->destroy_2d_double_array(well);
memory->destroy_2d_double_array(cut);
memory->destroy_2d_double_array(lj1);
memory->destroy_2d_double_array(lj2);
memory->destroy_2d_double_array(lj3);
memory->destroy_2d_double_array(lj4);
memory->destroy_2d_double_array(offset);
delete [] lshape;
delete [] setwell;
}
}
/* ---------------------------------------------------------------------- */
void PairRESquared::compute(int eflag, int vflag)
{
int i,j,ii,jj,inum,jnum,itype,jtype;
double evdwl,one_eng,rsq,r2inv,r6inv,forcelj,factor_lj;
double fforce[3],ttor[3],rtor[3],r12[3];
int *ilist,*jlist,*numneigh,**firstneigh;
RE2Vars wi,wj;
evdwl = 0.0;
if (eflag || vflag) ev_setup(eflag,vflag);
else evflag = vflag_fdotr = 0;
double **x = atom->x;
double **f = atom->f;
double **tor = atom->torque;
int *type = atom->type;
int nlocal = atom->nlocal;
int nall = nlocal + atom->nghost;
double *special_lj = force->special_lj;
int newton_pair = force->newton_pair;
inum = list->inum;
ilist = list->ilist;
numneigh = list->numneigh;
firstneigh = list->firstneigh;
// loop over neighbors of my atoms
for (ii = 0; ii < inum; ii++) {
i = ilist[ii];
itype = type[i];
// not a LJ sphere
if (lshape[itype] != 0.0) precompute_i(i,wi);
jlist = firstneigh[i];
jnum = numneigh[i];
for (jj = 0; jj < jnum; jj++) {
j = jlist[jj];
if (j < nall) factor_lj = 1.0;
else {
factor_lj = special_lj[j/nall];
j %= nall;
}
// r12 = center to center vector
r12[0] = x[j][0]-x[i][0];
r12[1] = x[j][1]-x[i][1];
r12[2] = x[j][2]-x[i][2];
rsq = MathExtra::dot3(r12,r12);
jtype = type[j];
// compute if less than cutoff
if (rsq < cutsq[itype][jtype]) {
switch (form[itype][jtype]) {
case SPHERE_SPHERE:
r2inv = 1.0/rsq;
r6inv = r2inv*r2inv*r2inv;
forcelj = r6inv * (lj1[itype][jtype]*r6inv - lj2[itype][jtype]);
forcelj *= -r2inv;
if (eflag) one_eng =
r6inv*(r6inv*lj3[itype][jtype]-lj4[itype][jtype]) -
offset[itype][jtype];
fforce[0] = r12[0]*forcelj;
fforce[1] = r12[1]*forcelj;
fforce[2] = r12[2]*forcelj;
break;
case SPHERE_ELLIPSE:
precompute_i(j,wj);
if (newton_pair || j < nlocal) {
one_eng = resquared_lj(j,i,wj,r12,rsq,fforce,rtor,true);
tor[j][0] += rtor[0]*factor_lj;
tor[j][1] += rtor[1]*factor_lj;
tor[j][2] += rtor[2]*factor_lj;
} else
one_eng = resquared_lj(j,i,wj,r12,rsq,fforce,rtor,false);
break;
case ELLIPSE_SPHERE:
one_eng = resquared_lj(i,j,wi,r12,rsq,fforce,ttor,true);
tor[i][0] += ttor[0]*factor_lj;
tor[i][1] += ttor[1]*factor_lj;
tor[i][2] += ttor[2]*factor_lj;
break;
default:
precompute_i(j,wj);
one_eng = resquared_analytic(i,j,wi,wj,r12,rsq,fforce,ttor,rtor);
tor[i][0] += ttor[0]*factor_lj;
tor[i][1] += ttor[1]*factor_lj;
tor[i][2] += ttor[2]*factor_lj;
if (newton_pair || j < nlocal) {
tor[j][0] += rtor[0]*factor_lj;
tor[j][1] += rtor[1]*factor_lj;
tor[j][2] += rtor[2]*factor_lj;
}
break;
}
fforce[0] *= factor_lj;
fforce[1] *= factor_lj;
fforce[2] *= factor_lj;
f[i][0] += fforce[0];
f[i][1] += fforce[1];
f[i][2] += fforce[2];
if (newton_pair || j < nlocal) {
f[j][0] -= fforce[0];
f[j][1] -= fforce[1];
f[j][2] -= fforce[2];
}
if (eflag) evdwl = factor_lj*one_eng;
if (evflag) ev_tally_xyz(i,j,nlocal,newton_pair,
evdwl,0.0,fforce[0],fforce[1],fforce[2],
-r12[0],-r12[1],-r12[2]);
}
}
}
if (vflag_fdotr) virial_compute();
}
/* ----------------------------------------------------------------------
allocate all arrays
------------------------------------------------------------------------- */
void PairRESquared::allocate()
{
allocated = 1;
int n = atom->ntypes;
setflag = memory->create_2d_int_array(n+1,n+1,"pair:setflag");
for (int i = 1; i <= n; i++)
for (int j = i; j <= n; j++)
setflag[i][j] = 0;
cutsq = memory->create_2d_double_array(n+1,n+1,"pair:cutsq");
form = memory->create_2d_int_array(n+1,n+1,"pair:form");
epsilon = memory->create_2d_double_array(n+1,n+1,"pair:epsilon");
sigma = memory->create_2d_double_array(n+1,n+1,"pair:sigma");
shape2 = memory->create_2d_double_array(n+1,3,"pair:shape2");
well = memory->create_2d_double_array(n+1,3,"pair:well");
cut = memory->create_2d_double_array(n+1,n+1,"pair:cut");
lj1 = memory->create_2d_double_array(n+1,n+1,"pair:lj1");
lj2 = memory->create_2d_double_array(n+1,n+1,"pair:lj2");
lj3 = memory->create_2d_double_array(n+1,n+1,"pair:lj3");
lj4 = memory->create_2d_double_array(n+1,n+1,"pair:lj4");
offset = memory->create_2d_double_array(n+1,n+1,"pair:offset");
lshape = new double[n+1];
setwell = new int[n+1];
for (int i = 1; i <= n; i++) setwell[i] = 0;
}
/* ----------------------------------------------------------------------
global settings
------------------------------------------------------------------------- */
void PairRESquared::settings(int narg, char **arg)
{
if (narg != 1) error->all("Illegal pair_style command");
cut_global = force->numeric(arg[0]);
// reset cutoffs that have been explicitly set
if (allocated) {
int i,j;
for (i = 1; i <= atom->ntypes; i++)
for (j = i+1; j <= atom->ntypes; j++)
if (setflag[i][j]) cut[i][j] = cut_global;
}
}
/* ----------------------------------------------------------------------
set coeffs for one or more type pairs
------------------------------------------------------------------------- */
void PairRESquared::coeff(int narg, char **arg)
{
if (narg < 10 || narg > 11)
error->all("Incorrect args for pair coefficients");
if (!allocated) allocate();
int ilo,ihi,jlo,jhi;
force->bounds(arg[0],atom->ntypes,ilo,ihi);
force->bounds(arg[1],atom->ntypes,jlo,jhi);
double epsilon_one = force->numeric(arg[2]);
double sigma_one = force->numeric(arg[3]);
double eia_one = force->numeric(arg[4]);
double eib_one = force->numeric(arg[5]);
double eic_one = force->numeric(arg[6]);
double eja_one = force->numeric(arg[7]);
double ejb_one = force->numeric(arg[8]);
double ejc_one = force->numeric(arg[9]);
double cut_one = cut_global;
if (narg == 11) cut_one = force->numeric(arg[10]);
int count = 0;
for (int i = ilo; i <= ihi; i++) {
for (int j = MAX(jlo,i); j <= jhi; j++) {
epsilon[i][j] = epsilon_one;
sigma[i][j] = sigma_one;
cut[i][j] = cut_one;
if (eia_one != 0.0 || eib_one != 0.0 || eic_one != 0.0) {
well[i][0] = eia_one;
well[i][1] = eib_one;
well[i][2] = eic_one;
if (eia_one == 1.0 && eib_one == 1.0 && eic_one == 1.0) setwell[i] = 2;
else setwell[i] = 1;
}
if (eja_one != 0.0 || ejb_one != 0.0 || ejc_one != 0.0) {
well[j][0] = eja_one;
well[j][1] = ejb_one;
well[j][2] = ejc_one;
if (eja_one == 1.0 && ejb_one == 1.0 && ejc_one == 1.0) setwell[j] = 2;
else setwell[j] = 1;
}
setflag[i][j] = 1;
count++;
}
}
if (count == 0) error->all("Incorrect args for pair coefficients");
}
/* ----------------------------------------------------------------------
init specific to this pair style
------------------------------------------------------------------------- */
void PairRESquared::init_style()
{
if (!atom->quat_flag || !atom->torque_flag || !atom->avec->shape_type)
error->all("Pair resquared requires atom attributes quat, torque, shape");
if (atom->radius_flag)
error->all("Pair resquared cannot be used with atom attribute diameter");
int irequest = neighbor->request(this);
// per-type shape precalculations
for (int i = 1; i <= atom->ntypes; i++) {
if (setwell[i]) {
double *one = atom->shape[i];
shape2[i][0] = one[0]*one[0];
shape2[i][1] = one[1]*one[1];
shape2[i][2] = one[2]*one[2];
lshape[i] = one[0]*one[1]*one[2];
}
}
}
/* ----------------------------------------------------------------------
init for one type pair i,j and corresponding j,i
------------------------------------------------------------------------- */
double PairRESquared::init_one(int i, int j)
{
double **shape = atom->shape;
if (setwell[i] == 0 || setwell[j] == 0)
error->all("Pair resquared epsilon a,b,c coeffs are not all set");
int ishape = 0;
if (shape[i][0] != 0.0 && shape[i][1] != 0.0 && shape[i][2] != 0.0)
ishape = 1;
int jshape = 0;
if (shape[j][0] != 0.0 && shape[j][1] != 0.0 && shape[j][2] != 0.0)
jshape = 1;
if (ishape == 0 && jshape == 0) {
form[i][j] = SPHERE_SPHERE;
form[j][i] = SPHERE_SPHERE;
} else if (ishape == 0) {
form[i][j] = SPHERE_ELLIPSE;
form[j][i] = ELLIPSE_SPHERE;
} else if (jshape == 0) {
form[i][j] = ELLIPSE_SPHERE;
form[j][i] = SPHERE_ELLIPSE;
} else {
form[i][j] = ELLIPSE_ELLIPSE;
form[j][i] = ELLIPSE_ELLIPSE;
}
// allow mixing only for LJ spheres
if (setflag[i][j] == 0) {
if (setflag[j][i] == 0) {
if (ishape == 0 && jshape == 0) {
epsilon[i][j] = mix_energy(epsilon[i][i],epsilon[j][j],
sigma[i][i],sigma[j][j]);
sigma[i][j] = mix_distance(sigma[i][i],sigma[j][j]);
cut[i][j] = mix_distance(cut[i][i],cut[j][j]);
} else
error->all("Pair resquared epsilon and sigma coeffs are not all set");
}
epsilon[i][j] = epsilon[j][i];
sigma[i][j] = sigma[j][i];
cut[i][j] = cut[j][i];
}
lj1[i][j] = 48.0 * epsilon[i][j] * pow(sigma[i][j],12.0);
lj2[i][j] = 24.0 * epsilon[i][j] * pow(sigma[i][j],6.0);
lj3[i][j] = 4.0 * epsilon[i][j] * pow(sigma[i][j],12.0);
lj4[i][j] = 4.0 * epsilon[i][j] * pow(sigma[i][j],6.0);
if (offset_flag) {
double ratio = sigma[i][j] / cut[i][j];
offset[i][j] = 4.0 * epsilon[i][j] * (pow(ratio,12.0) - pow(ratio,6.0));
} else offset[i][j] = 0.0;
epsilon[j][i] = epsilon[i][j];
sigma[j][i] = sigma[i][j];
cut[j][i] = cut[i][j];
lj1[j][i] = lj1[i][j];
lj2[j][i] = lj2[i][j];
lj3[j][i] = lj3[i][j];
lj4[j][i] = lj4[i][j];
offset[j][i] = offset[i][j];
return cut[i][j];
}
/* ----------------------------------------------------------------------
proc 0 writes to restart file
------------------------------------------------------------------------- */
void PairRESquared::write_restart(FILE *fp)
{
write_restart_settings(fp);
int i,j;
for (i = 1; i <= atom->ntypes; i++) {
fwrite(&setwell[i],sizeof(int),1,fp);
if (setwell[i]) fwrite(&well[i][0],sizeof(double),3,fp);
for (j = i; j <= atom->ntypes; j++) {
fwrite(&setflag[i][j],sizeof(int),1,fp);
if (setflag[i][j]) {
fwrite(&epsilon[i][j],sizeof(double),1,fp);
fwrite(&sigma[i][j],sizeof(double),1,fp);
fwrite(&cut[i][j],sizeof(double),1,fp);
}
}
}
}
/* ----------------------------------------------------------------------
proc 0 reads from restart file, bcasts
------------------------------------------------------------------------- */
void PairRESquared::read_restart(FILE *fp)
{
read_restart_settings(fp);
allocate();
int i,j;
int me = comm->me;
for (i = 1; i <= atom->ntypes; i++) {
if (me == 0) fread(&setwell[i],sizeof(int),1,fp);
MPI_Bcast(&setwell[i],1,MPI_INT,0,world);
if (setwell[i]) {
if (me == 0) fread(&well[i][0],sizeof(double),3,fp);
MPI_Bcast(&well[i][0],3,MPI_DOUBLE,0,world);
}
for (j = i; j <= atom->ntypes; j++) {
if (me == 0) fread(&setflag[i][j],sizeof(int),1,fp);
MPI_Bcast(&setflag[i][j],1,MPI_INT,0,world);
if (setflag[i][j]) {
if (me == 0) {
fread(&epsilon[i][j],sizeof(double),1,fp);
fread(&sigma[i][j],sizeof(double),1,fp);
fread(&cut[i][j],sizeof(double),1,fp);
}
MPI_Bcast(&epsilon[i][j],1,MPI_DOUBLE,0,world);
MPI_Bcast(&sigma[i][j],1,MPI_DOUBLE,0,world);
MPI_Bcast(&cut[i][j],1,MPI_DOUBLE,0,world);
}
}
}
}
/* ----------------------------------------------------------------------
proc 0 writes to restart file
------------------------------------------------------------------------- */
void PairRESquared::write_restart_settings(FILE *fp)
{
fwrite(&cut_global,sizeof(double),1,fp);
fwrite(&mix_flag,sizeof(int),1,fp);
}
/* ----------------------------------------------------------------------
proc 0 reads from restart file, bcasts
------------------------------------------------------------------------- */
void PairRESquared::read_restart_settings(FILE *fp)
{
int me = comm->me;
if (me == 0) {
fread(&cut_global,sizeof(double),1,fp);
fread(&mix_flag,sizeof(int),1,fp);
}
MPI_Bcast(&cut_global,1,MPI_DOUBLE,0,world);
MPI_Bcast(&mix_flag,1,MPI_INT,0,world);
}
/* ----------------------------------------------------------------------
Precompute per-particle temporaries for RE-squared calculation
------------------------------------------------------------------------- */
void PairRESquared::precompute_i(const int i,RE2Vars &ws) {
double aTs[3][3]; // A1'*S1^2
MathExtra::quat_to_mat_trans(atom->quat[i],ws.A);
MathExtra::transpose_times_diag3(ws.A,well[atom->type[i]],ws.aTe);
MathExtra::transpose_times_diag3(ws.A,shape2[atom->type[i]],aTs);
MathExtra::diag_times3(shape2[atom->type[i]],ws.A,ws.sa);
MathExtra::times3(aTs,ws.A,ws.gamma);
MathExtra::rotation_generator_x(ws.A,ws.lA[0]);
MathExtra::rotation_generator_y(ws.A,ws.lA[1]);
MathExtra::rotation_generator_z(ws.A,ws.lA[2]);
for (int i=0; i<3; i++) {
MathExtra::times3(aTs,ws.lA[i],ws.lAtwo[i]);
MathExtra::transpose_times3(ws.lA[i],ws.sa,ws.lAsa[i]);
MathExtra::plus3(ws.lAsa[i],ws.lAtwo[i],ws.lAsa[i]);
}
}
/* ----------------------------------------------------------------------
Compute the derivative of the determinant of m, using m and the
derivative of m (m2)
------------------------------------------------------------------------- */
double PairRESquared::det_prime(const double m[3][3], const double m2[3][3])
{
double ans;
ans = m2[0][0]*m[1][1]*m[2][2] - m2[0][0]*m[1][2]*m[2][1] -
m[1][0]*m2[0][1]*m[2][2] + m[1][0]*m2[0][2]*m[2][1] +
m[2][0]*m2[0][1]*m[1][2] - m[2][0]*m2[0][2]*m[1][1] +
m[0][0]*m2[1][1]*m[2][2] - m[0][0]*m2[1][2]*m[2][1] -
m2[1][0]*m[0][1]*m[2][2] + m2[1][0]*m[0][2]*m[2][1] +
m[2][0]*m[0][1]*m2[1][2] - m[2][0]*m[0][2]*m2[1][1] +
m[0][0]*m[1][1]*m2[2][2] - m[0][0]*m[1][2]*m2[2][1] -
m[1][0]*m[0][1]*m2[2][2] + m[1][0]*m[0][2]*m2[2][1] +
m2[2][0]*m[0][1]*m[1][2] - m2[2][0]*m[0][2]*m[1][1];
return ans;
}
/* ----------------------------------------------------------------------
Compute the energy, force, torque for a pair (INTEGRATED-INTEGRATED)
------------------------------------------------------------------------- */
double PairRESquared::resquared_analytic(const int i, const int j,
const RE2Vars &wi, const RE2Vars &wj,
const double *r, const double rsq,
double *fforce, double *ttor,
double *rtor)
{
int *type = atom->type;
double **shape = atom->shape;
// pair computations for energy, force, torque
double z1[3],z2[3]; // A1*rhat # don't need to store
double v1[3],v2[3]; // inv(S1^2)*z1 # don't need to store
double sigma1,sigma2; // 1/sqrt(z1'*v1)
double sigma1p2,sigma2p2; // sigma1^2
double rnorm; // L2 norm of r
double rhat[3]; // r/rnorm
double s[3]; // inv(gamma1+gamma2)*rhat
double sigma12; // 1/sqrt(0.5*s'*rhat)
double H12[3][3]; // gamma1/sigma1+gamma2/sigma2
double dH; // det(H12)
double lambda; // dS1/sigma1p2+dS2/sigma2p2
double nu; // sqrt(dH/(sigma1+sigma2))
double w[3]; // inv(A1'*E1*A1+A2'*E2*A2)*rhat
double h12; // rnorm-sigma12;
double eta; // lambda/nu
double chi; // 2*rhat'*w
double sprod; // dS1*dS2
double sigh; // sigma/h12
double tprod; // eta*chi*sigh
double Ua,Ur; // attractive/repulsive parts of potential
// pair computations for force, torque
double sec; // sigma*eta*chi
double sigma1p3, sigma2p3; // sigma1^3
double vsigma1[3], vsigma2[3]; // sigma1^3*v1;
double sigma12p3; // sigma12^3
double gsigma1[3][3], gsigma2[3][3]; // -gamma1/sigma1^2
double tsig1sig2; // eta/(2*(sigma1+sigma2))
double tdH; // eta/(2*dH)
double teta1,teta2; // 2*eta/lambda*dS1/sigma1p3
double fourw[3]; // 4*w;
double spr[3]; // 0.5*sigma12^3*s
double hsec; // h12+[3,b_alpha]*sec
double dspu; // 1/h12 - 1/hsec + temp
double pbsu; // 3*sigma/hsec
double dspr; // 7/h12-1/hsec+temp
double pbsr; // b_alpha*sigma/hsec;
double u[3]; // (-rhat(i)*rhat+eye(:,i))/rnorm
double u1[3],u2[3]; // A1*u
double dsigma1,dsigma2; // u1'*vsigma1 (force) p'*vsigma1 (tor)
double dH12[3][3]; // dsigma1*gsigma1 + dsigma2*gsigma2
double ddH; // derivative of det(H12)
double deta,dchi,dh12; // derivatives of eta,chi,h12
double dUr,dUa; // derivatives of Ua,Ur
// pair computations for torque
double fwae[3]; // -fourw'*aTe
double p[3]; // lA*rhat
rnorm = sqrt(rsq);
rhat[0] = r[0]/rnorm;
rhat[1] = r[1]/rnorm;
rhat[2] = r[2]/rnorm;
// energy
double temp[3][3];
MathExtra::plus3(wi.gamma,wj.gamma,temp);
MathExtra::mldivide3(temp,rhat,s,error);
sigma12 = 1.0/sqrt(0.5*MathExtra::dot3(s,rhat));
MathExtra::times_column3(wi.A,rhat,z1);
MathExtra::times_column3(wj.A,rhat,z2);
v1[0] = z1[0]/shape2[type[i]][0];
v1[1] = z1[1]/shape2[type[i]][1];
v1[2] = z1[2]/shape2[type[i]][2];
v2[0] = z2[0]/shape2[type[j]][0];
v2[1] = z2[1]/shape2[type[j]][1];
v2[2] = z2[2]/shape2[type[j]][2];
sigma1 = 1.0/sqrt(MathExtra::dot3(z1,v1));
sigma2 = 1.0/sqrt(MathExtra::dot3(z2,v2));
H12[0][0] = wi.gamma[0][0]/sigma1+wj.gamma[0][0]/sigma2;
H12[0][1] = wi.gamma[0][1]/sigma1+wj.gamma[0][1]/sigma2;
H12[0][2] = wi.gamma[0][2]/sigma1+wj.gamma[0][2]/sigma2;
H12[1][0] = wi.gamma[1][0]/sigma1+wj.gamma[1][0]/sigma2;
H12[1][1] = wi.gamma[1][1]/sigma1+wj.gamma[1][1]/sigma2;
H12[1][2] = wi.gamma[1][2]/sigma1+wj.gamma[1][2]/sigma2;
H12[2][0] = wi.gamma[2][0]/sigma1+wj.gamma[2][0]/sigma2;
H12[2][1] = wi.gamma[2][1]/sigma1+wj.gamma[2][1]/sigma2;
H12[2][2] = wi.gamma[2][2]/sigma1+wj.gamma[2][2]/sigma2;
dH=MathExtra::det3(H12);
sigma1p2 = sigma1*sigma1;
sigma2p2 = sigma2*sigma2;
lambda = lshape[type[i]]/sigma1p2 + lshape[type[j]]/sigma2p2;
nu = sqrt(dH/(sigma1+sigma2));
MathExtra::times3(wi.aTe,wi.A,temp);
double temp2[3][3];
MathExtra::times3(wj.aTe,wj.A,temp2);
MathExtra::plus3(temp,temp2,temp);
MathExtra::mldivide3(temp,rhat,w,error);
h12 = rnorm-sigma12;
eta = lambda/nu;
chi = 2.0*MathExtra::dot3(rhat,w);
sprod = lshape[type[i]] * lshape[type[j]];
sigh = sigma[type[i]][type[j]]/h12;
tprod = eta*chi*sigh;
double stemp = h12/2.0;
Ua = (shape[type[i]][0]+stemp)*(shape[type[i]][1]+stemp)*
(shape[type[i]][2]+stemp)*(shape[type[j]][0]+stemp)*
(shape[type[j]][1]+stemp)*(shape[type[j]][2]+stemp);
Ua = (1.0+3.0*tprod)*sprod/Ua;
Ua = epsilon[type[i]][type[j]]*Ua/-36.0;
stemp = h12/cr60;
Ur = (shape[type[i]][0]+stemp)*(shape[type[i]][1]+stemp)*
(shape[type[i]][2]+stemp)*(shape[type[j]][0]+stemp)*
(shape[type[j]][1]+stemp)*(shape[type[j]][2]+stemp);
Ur = (1.0+b_alpha*tprod)*sprod/Ur;
Ur = epsilon[type[i]][type[j]]*Ur*pow(sigh,6.0)/2025.0;
// force
sec = sigma[type[i]][type[j]]*eta*chi;
sigma12p3 = pow(sigma12,3.0);
sigma1p3 = sigma1p2*sigma1;
sigma2p3 = sigma2p2*sigma2;
vsigma1[0] = -sigma1p3*v1[0];
vsigma1[1] = -sigma1p3*v1[1];
vsigma1[2] = -sigma1p3*v1[2];
vsigma2[0] = -sigma2p3*v2[0];
vsigma2[1] = -sigma2p3*v2[1];
vsigma2[2] = -sigma2p3*v2[2];
gsigma1[0][0] = -wi.gamma[0][0]/sigma1p2;
gsigma1[0][1] = -wi.gamma[0][1]/sigma1p2;
gsigma1[0][2] = -wi.gamma[0][2]/sigma1p2;
gsigma1[1][0] = -wi.gamma[1][0]/sigma1p2;
gsigma1[1][1] = -wi.gamma[1][1]/sigma1p2;
gsigma1[1][2] = -wi.gamma[1][2]/sigma1p2;
gsigma1[2][0] = -wi.gamma[2][0]/sigma1p2;
gsigma1[2][1] = -wi.gamma[2][1]/sigma1p2;
gsigma1[2][2] = -wi.gamma[2][2]/sigma1p2;
gsigma2[0][0] = -wj.gamma[0][0]/sigma2p2;
gsigma2[0][1] = -wj.gamma[0][1]/sigma2p2;
gsigma2[0][2] = -wj.gamma[0][2]/sigma2p2;
gsigma2[1][0] = -wj.gamma[1][0]/sigma2p2;
gsigma2[1][1] = -wj.gamma[1][1]/sigma2p2;
gsigma2[1][2] = -wj.gamma[1][2]/sigma2p2;
gsigma2[2][0] = -wj.gamma[2][0]/sigma2p2;
gsigma2[2][1] = -wj.gamma[2][1]/sigma2p2;
gsigma2[2][2] = -wj.gamma[2][2]/sigma2p2;
tsig1sig2 = eta/(2.0*(sigma1+sigma2));
tdH = eta/(2.0*dH);
teta1 = 2.0*eta/lambda;
teta2 = teta1*lshape[type[j]]/sigma2p3;
teta1 = teta1*lshape[type[i]]/sigma1p3;
fourw[0] = 4.0*w[0];
fourw[1] = 4.0*w[1];
fourw[2] = 4.0*w[2];
spr[0] = 0.5*sigma12p3*s[0];
spr[1] = 0.5*sigma12p3*s[1];
spr[2] = 0.5*sigma12p3*s[2];
stemp = 1.0/(shape[type[i]][0]*2.0+h12)+
1.0/(shape[type[i]][1]*2.0+h12)+
1.0/(shape[type[i]][2]*2.0+h12)+
1.0/(shape[type[j]][0]*2.0+h12)+
1.0/(shape[type[j]][1]*2.0+h12)+
1.0/(shape[type[j]][2]*2.0+h12);
hsec = h12+3.0*sec;
dspu = 1.0/h12-1.0/hsec+stemp;
pbsu = 3.0*sigma[type[i]][type[j]]/hsec;
stemp = 1.0/(shape[type[i]][0]*cr60+h12)+
1.0/(shape[type[i]][1]*cr60+h12)+
1.0/(shape[type[i]][2]*cr60+h12)+
1.0/(shape[type[j]][0]*cr60+h12)+
1.0/(shape[type[j]][1]*cr60+h12)+
1.0/(shape[type[j]][2]*cr60+h12);
hsec = h12+b_alpha*sec;
dspr = 7.0/h12-1.0/hsec+stemp;
pbsr = b_alpha*sigma[type[i]][type[j]]/hsec;
for (int i=0; i<3; i++) {
u[0] = -rhat[i]*rhat[0];
u[1] = -rhat[i]*rhat[1];
u[2] = -rhat[i]*rhat[2];
u[i] += 1.0;
u[0] /= rnorm;
u[1] /= rnorm;
u[2] /= rnorm;
MathExtra::times_column3(wi.A,u,u1);
MathExtra::times_column3(wj.A,u,u2);
dsigma1=MathExtra::dot3(u1,vsigma1);
dsigma2=MathExtra::dot3(u2,vsigma2);
dH12[0][0] = dsigma1*gsigma1[0][0]+dsigma2*gsigma2[0][0];
dH12[0][1] = dsigma1*gsigma1[0][1]+dsigma2*gsigma2[0][1];
dH12[0][2] = dsigma1*gsigma1[0][2]+dsigma2*gsigma2[0][2];
dH12[1][0] = dsigma1*gsigma1[1][0]+dsigma2*gsigma2[1][0];
dH12[1][1] = dsigma1*gsigma1[1][1]+dsigma2*gsigma2[1][1];
dH12[1][2] = dsigma1*gsigma1[1][2]+dsigma2*gsigma2[1][2];
dH12[2][0] = dsigma1*gsigma1[2][0]+dsigma2*gsigma2[2][0];
dH12[2][1] = dsigma1*gsigma1[2][1]+dsigma2*gsigma2[2][1];
dH12[2][2] = dsigma1*gsigma1[2][2]+dsigma2*gsigma2[2][2];
ddH = det_prime(H12,dH12);
deta = (dsigma1+dsigma2)*tsig1sig2;
deta -= ddH*tdH;
deta -= dsigma1*teta1+dsigma2*teta2;
dchi = MathExtra::dot3(u,fourw);
dh12 = rhat[i]+MathExtra::dot3(u,spr);
dUa = pbsu*(eta*dchi+deta*chi)-dh12*dspu;
dUr = pbsr*(eta*dchi+deta*chi)-dh12*dspr;
fforce[i]=dUr*Ur+dUa*Ua;
}
// torque on i
MathExtra::row_times3(fourw,wi.aTe,fwae);
for (int i=0; i<3; i++) {
MathExtra::times_column3(wi.lA[i],rhat,p);
dsigma1 = MathExtra::dot3(p,vsigma1);
dH12[0][0] = wi.lAsa[i][0][0]/sigma1+dsigma1*gsigma1[0][0];
dH12[0][1] = wi.lAsa[i][0][1]/sigma1+dsigma1*gsigma1[0][1];
dH12[0][2] = wi.lAsa[i][0][2]/sigma1+dsigma1*gsigma1[0][2];
dH12[1][0] = wi.lAsa[i][1][0]/sigma1+dsigma1*gsigma1[1][0];
dH12[1][1] = wi.lAsa[i][1][1]/sigma1+dsigma1*gsigma1[1][1];
dH12[1][2] = wi.lAsa[i][1][2]/sigma1+dsigma1*gsigma1[1][2];
dH12[2][0] = wi.lAsa[i][2][0]/sigma1+dsigma1*gsigma1[2][0];
dH12[2][1] = wi.lAsa[i][2][1]/sigma1+dsigma1*gsigma1[2][1];
dH12[2][2] = wi.lAsa[i][2][2]/sigma1+dsigma1*gsigma1[2][2];
ddH = det_prime(H12,dH12);
deta = tsig1sig2*dsigma1-tdH*ddH;
deta -= teta1*dsigma1;
double tempv[3];
MathExtra::times_column3(wi.lA[i],w,tempv);
dchi = -MathExtra::dot3(fwae,tempv);
MathExtra::times_column3(wi.lAtwo[i],spr,tempv);
dh12 = -MathExtra::dot3(s,tempv);
dUa = pbsu*(eta*dchi + deta*chi)-dh12*dspu;
dUr = pbsr*(eta*dchi + deta*chi)-dh12*dspr;
ttor[i] = -(dUa*Ua+dUr*Ur);
}
// torque on j
if (!(force->newton_pair || j < atom->nlocal))
return Ua+Ur;
MathExtra::row_times3(fourw,wj.aTe,fwae);
for (int i=0; i<3; i++) {
MathExtra::times_column3(wj.lA[i],rhat,p);
dsigma2 = MathExtra::dot3(p,vsigma2);
dH12[0][0] = wj.lAsa[i][0][0]/sigma2+dsigma2*gsigma2[0][0];
dH12[0][1] = wj.lAsa[i][0][1]/sigma2+dsigma2*gsigma2[0][1];
dH12[0][2] = wj.lAsa[i][0][2]/sigma2+dsigma2*gsigma2[0][2];
dH12[1][0] = wj.lAsa[i][1][0]/sigma2+dsigma2*gsigma2[1][0];
dH12[1][1] = wj.lAsa[i][1][1]/sigma2+dsigma2*gsigma2[1][1];
dH12[1][2] = wj.lAsa[i][1][2]/sigma2+dsigma2*gsigma2[1][2];
dH12[2][0] = wj.lAsa[i][2][0]/sigma2+dsigma2*gsigma2[2][0];
dH12[2][1] = wj.lAsa[i][2][1]/sigma2+dsigma2*gsigma2[2][1];
dH12[2][2] = wj.lAsa[i][2][2]/sigma2+dsigma2*gsigma2[2][2];
ddH = det_prime(H12,dH12);
deta = tsig1sig2*dsigma2-tdH*ddH;
deta -= teta2*dsigma2;
double tempv[3];
MathExtra::times_column3(wj.lA[i],w,tempv);
dchi = -MathExtra::dot3(fwae,tempv);
MathExtra::times_column3(wj.lAtwo[i],spr,tempv);
dh12 = -MathExtra::dot3(s,tempv);
dUa = pbsu*(eta*dchi + deta*chi)-dh12*dspu;
dUr = pbsr*(eta*dchi + deta*chi)-dh12*dspr;
rtor[i] = -(dUa*Ua+dUr*Ur);
}
return Ua+Ur;
}
/* ----------------------------------------------------------------------
Compute the energy, force, torque for a pair (INTEGRATED-LJ)
------------------------------------------------------------------------- */
double PairRESquared::resquared_lj(const int i, const int j,
const RE2Vars &wi, const double *r,
const double rsq, double *fforce,
double *ttor, bool calc_torque)
{
int *type = atom->type;
double **shape = atom->shape;
// pair computations for energy, force, torque
double rnorm; // L2 norm of r
double rhat[3]; // r/rnorm
double s[3]; // inv(gamma1)*rhat
double sigma12; // 1/sqrt(0.5*s'*rhat)
double w[3]; // inv(A1'*E1*A1+I)*rhat
double h12; // rnorm-sigma12;
double chi; // 2*rhat'*w
double sigh; // sigma/h12
double tprod; // chi*sigh
double Ua,Ur; // attractive/repulsive parts of potential
// pair computations for force, torque
double sec; // sigma*chi
double sigma12p3; // sigma12^3
double fourw[3]; // 4*w;
double spr[3]; // 0.5*sigma12^3*s
double hsec; // h12+[3,b_alpha]*sec
double dspu; // 1/h12 - 1/hsec + temp
double pbsu; // 3*sigma/hsec
double dspr; // 7/h12-1/hsec+temp
double pbsr; // b_alpha*sigma/hsec;
double u[3]; // (-rhat(i)*rhat+eye(:,i))/rnorm
double dchi,dh12; // derivatives of chi,h12
double dUr,dUa; // derivatives of Ua,Ur
double h12p3; // h12^3
// pair computations for torque
double fwae[3]; // -fourw'*aTe
double p[3]; // lA*rhat
// distance of closest approach correction
double aTs[3][3]; // A1'*S1^2
double gamma[3][3]; // A1'*S1^2*A
double lAtwo[3][3][3]; // A1'*S1^2*wi.lA
double scorrect[3];
double half_sigma=sigma[type[i]][type[j]] / 2.0;
scorrect[0] = shape[type[i]][0]+half_sigma;
scorrect[1] = shape[type[i]][1]+half_sigma;
scorrect[2] = shape[type[i]][2]+half_sigma;
scorrect[0] = scorrect[0] * scorrect[0] / 2.0;
scorrect[1] = scorrect[1] * scorrect[1] / 2.0;
scorrect[2] = scorrect[2] * scorrect[2] / 2.0;
MathExtra::transpose_times_diag3(wi.A,scorrect,aTs);
MathExtra::times3(aTs,wi.A,gamma);
for (int ii=0; ii<3; ii++)
MathExtra::times3(aTs,wi.lA[ii],lAtwo[ii]);
rnorm=sqrt(rsq);
rhat[0] = r[0]/rnorm;
rhat[1] = r[1]/rnorm;
rhat[2] = r[2]/rnorm;
// energy
MathExtra::mldivide3(gamma,rhat,s,error);
sigma12 = 1.0/sqrt(0.5*MathExtra::dot3(s,rhat));
double temp[3][3];
MathExtra::times3(wi.aTe,wi.A,temp);
temp[0][0] += 1.0;
temp[1][1] += 1.0;
temp[2][2] += 1.0;
MathExtra::mldivide3(temp,rhat,w,error);
h12 = rnorm-sigma12;
chi = 2.0*MathExtra::dot3(rhat,w);
sigh = sigma[type[i]][type[j]]/h12;
tprod = chi*sigh;
h12p3 = pow(h12,3.0);
double sigmap3 = pow(sigma[type[i]][type[j]],3.0);
double stemp = h12/2.0;
Ua = (shape[type[i]][0]+stemp)*(shape[type[i]][1]+stemp)*
(shape[type[i]][2]+stemp)*h12p3/8.0;
Ua = (1.0+3.0*tprod)*lshape[type[i]]/Ua;
Ua = epsilon[type[i]][type[j]]*Ua*sigmap3*solv_f_a;
stemp = h12/cr60;
Ur = (shape[type[i]][0]+stemp)*(shape[type[i]][1]+stemp)*
(shape[type[i]][2]+stemp)*h12p3/60.0;
Ur = (1.0+b_alpha*tprod)*lshape[type[i]]/Ur;
Ur = epsilon[type[i]][type[j]]*Ur*sigmap3*pow(sigh,6.0)*solv_f_r;
// force
sec = sigma[type[i]][type[j]]*chi;
sigma12p3 = pow(sigma12,3.0);
fourw[0] = 4.0*w[0];
fourw[1] = 4.0*w[1];
fourw[2] = 4.0*w[2];
spr[0] = 0.5*sigma12p3*s[0];
spr[1] = 0.5*sigma12p3*s[1];
spr[2] = 0.5*sigma12p3*s[2];
stemp = 1.0/(shape[type[i]][0]*2.0+h12)+
1.0/(shape[type[i]][1]*2.0+h12)+
1.0/(shape[type[i]][2]*2.0+h12)+
3.0/h12;
hsec = h12+3.0*sec;
dspu = 1.0/h12-1.0/hsec+stemp;
pbsu = 3.0*sigma[type[i]][type[j]]/hsec;
stemp = 1.0/(shape[type[i]][0]*cr60+h12)+
1.0/(shape[type[i]][1]*cr60+h12)+
1.0/(shape[type[i]][2]*cr60+h12)+
3.0/h12;
hsec = h12+b_alpha*sec;
dspr = 7.0/h12-1.0/hsec+stemp;
pbsr = b_alpha*sigma[type[i]][type[j]]/hsec;
for (int i=0; i<3; i++) {
u[0] = -rhat[i]*rhat[0];
u[1] = -rhat[i]*rhat[1];
u[2] = -rhat[i]*rhat[2];
u[i] += 1.0;
u[0] /= rnorm;
u[1] /= rnorm;
u[2] /= rnorm;
dchi = MathExtra::dot3(u,fourw);
dh12 = rhat[i]+MathExtra::dot3(u,spr);
dUa = pbsu*dchi-dh12*dspu;
dUr = pbsr*dchi-dh12*dspr;
fforce[i]=dUr*Ur+dUa*Ua;
}
// torque on i
if (calc_torque) {
MathExtra::row_times3(fourw,wi.aTe,fwae);
for (int i=0; i<3; i++) {
MathExtra::times_column3(wi.lA[i],rhat,p);
double tempv[3];
MathExtra::times_column3(wi.lA[i],w,tempv);
dchi = -MathExtra::dot3(fwae,tempv);
MathExtra::times_column3(lAtwo[i],spr,tempv);
dh12 = -MathExtra::dot3(s,tempv);
dUa = pbsu*dchi-dh12*dspu;
dUr = pbsr*dchi-dh12*dspr;
ttor[i] = -(dUa*Ua+dUr*Ur);
}
}
return Ua+Ur;
}

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