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ewald_disp.cpp
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ewald_disp.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: Pieter in 't Veld (SNL), Stan Moore (SNL)
------------------------------------------------------------------------- */
#include <mpi.h>
#include <string.h>
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include "ewald_disp.h"
#include "math_vector.h"
#include "math_const.h"
#include "math_special.h"
#include "atom.h"
#include "comm.h"
#include "force.h"
#include "pair.h"
#include "domain.h"
#include "memory.h"
#include "error.h"
#include "update.h"
using namespace LAMMPS_NS;
using namespace MathConst;
using namespace MathSpecial;
#define SMALL 0.00001
enum{GEOMETRIC,ARITHMETIC,SIXTHPOWER}; // same as in pair.h
//#define DEBUG
/* ---------------------------------------------------------------------- */
EwaldDisp::EwaldDisp(LAMMPS *lmp, int narg, char **arg) : KSpace(lmp, narg, arg),
kenergy(NULL), kvirial(NULL), energy_self_peratom(NULL), virial_self_peratom(NULL),
ekr_local(NULL), hvec(NULL), kvec(NULL), B(NULL), cek_local(NULL), cek_global(NULL)
{
if (narg!=1) error->all(FLERR,"Illegal kspace_style ewald/n command");
ewaldflag = dispersionflag = dipoleflag = 1;
accuracy_relative = fabs(force->numeric(FLERR,arg[0]));
memset(function, 0, EWALD_NFUNCS*sizeof(int));
kenergy = kvirial = NULL;
cek_local = cek_global = NULL;
ekr_local = NULL;
hvec = NULL;
kvec = NULL;
B = NULL;
first_output = 0;
energy_self_peratom = NULL;
virial_self_peratom = NULL;
nmax = 0;
q2 = 0;
b2 = 0;
M2 = 0;
}
/* ---------------------------------------------------------------------- */
EwaldDisp::~EwaldDisp()
{
deallocate();
deallocate_peratom();
delete [] ekr_local;
delete [] B;
}
/* --------------------------------------------------------------------- */
void EwaldDisp::init()
{
nkvec = nkvec_max = nevec = nevec_max = 0;
nfunctions = nsums = sums = 0;
nbox = -1;
bytes = 0.0;
if (!comm->me) {
if (screen) fprintf(screen,"EwaldDisp initialization ...\n");
if (logfile) fprintf(logfile,"EwaldDisp initialization ...\n");
}
triclinic_check();
if (domain->dimension == 2)
error->all(FLERR,"Cannot use EwaldDisp with 2d simulation");
if (slabflag == 0 && domain->nonperiodic > 0)
error->all(FLERR,"Cannot use nonperiodic boundaries with EwaldDisp");
if (slabflag == 1) {
if (domain->xperiodic != 1 || domain->yperiodic != 1 ||
domain->boundary[2][0] != 1 || domain->boundary[2][1] != 1)
error->all(FLERR,"Incorrect boundaries with slab EwaldDisp");
}
scale = 1.0;
mumurd2e = force->qqrd2e;
dielectric = force->dielectric;
int tmp;
Pair *pair = force->pair;
int *ptr = pair ? (int *) pair->extract("ewald_order",tmp) : NULL;
double *cutoff = pair ? (double *) pair->extract("cut_coul",tmp) : NULL;
if (!(ptr||cutoff))
error->all(FLERR,"KSpace style is incompatible with Pair style");
int ewald_order = ptr ? *((int *) ptr) : 1<<1;
int ewald_mix = ptr ? *((int *) pair->extract("ewald_mix",tmp)) : GEOMETRIC;
memset(function, 0, EWALD_NFUNCS*sizeof(int));
for (int i=0; i<=EWALD_NORDER; ++i) // transcribe order
if (ewald_order&(1<<i)) { // from pair_style
int n[] = EWALD_NSUMS, k = 0;
switch (i) {
case 1:
k = 0; break;
case 3:
k = 3; break;
case 6:
if (ewald_mix==GEOMETRIC) { k = 1; break; }
else if (ewald_mix==ARITHMETIC) { k = 2; break; }
error->all(FLERR,
"Unsupported mixing rule in kspace_style ewald/disp");
default:
error->all(FLERR,"Unsupported order in kspace_style ewald/disp");
}
nfunctions += function[k] = 1;
nsums += n[k];
}
if (!gewaldflag) g_ewald = g_ewald_6 = 1.0;
pair->init(); // so B is defined
init_coeffs();
init_coeff_sums();
if (function[0]) qsum_qsq();
else qsqsum = qsum = 0.0;
natoms_original = atom->natoms;
if (!gewaldflag) g_ewald = g_ewald_6 = 0.0;
// turn off coulombic if no charge
if (function[0] && qsqsum == 0.0) {
function[0] = 0;
nfunctions -= 1;
nsums -= 1;
}
double bsbsum = 0.0;
M2 = 0.0;
if (function[1]) bsbsum = sum[1].x2;
if (function[2]) bsbsum = sum[2].x2;
if (function[3]) M2 = sum[9].x2;
if (function[3] && strcmp(update->unit_style,"electron") == 0)
error->all(FLERR,"Cannot (yet) use 'electron' units with dipoles");
if (qsqsum == 0.0 && bsbsum == 0.0 && M2 == 0.0)
error->all(FLERR,"Cannot use Ewald/disp solver "
"on system with no charge, dipole, or LJ particles");
if (fabs(qsum) > SMALL && comm->me == 0) {
char str[128];
sprintf(str,"System is not charge neutral, net charge = %g",qsum);
error->warning(FLERR,str);
}
if (!function[1] && !function[2]) dispersionflag = 0;
if (!function[3]) dipoleflag = 0;
pair_check();
// set accuracy (force units) from accuracy_relative or accuracy_absolute
if (accuracy_absolute >= 0.0) accuracy = accuracy_absolute;
else accuracy = accuracy_relative * two_charge_force;
// setup K-space resolution
q2 = qsqsum * force->qqrd2e;
M2 *= mumurd2e;
b2 = bsbsum; //Are these units right?
bigint natoms = atom->natoms;
if (!gewaldflag) {
if (function[0]) {
g_ewald = accuracy*sqrt(natoms*(*cutoff)*shape_det(domain->h)) / (2.0*q2);
if (g_ewald >= 1.0) g_ewald = (1.35 - 0.15*log(accuracy))/(*cutoff);
else g_ewald = sqrt(-log(g_ewald)) / (*cutoff);
} else if (function[3]) {
//Try Newton Solver
//Use old method to get guess
g_ewald = (1.35 - 0.15*log(accuracy))/ *cutoff;
double g_ewald_new =
NewtonSolve(g_ewald,(*cutoff),natoms,shape_det(domain->h),M2);
if (g_ewald_new > 0.0) g_ewald = g_ewald_new;
else error->warning(FLERR,"Ewald/disp Newton solver failed, "
"using old method to estimate g_ewald");
} else if (function[1] || function[2]) {
//Try Newton Solver
//Use old method to get guess
g_ewald = (1.35 - 0.15*log(accuracy))/ *cutoff;
double g_ewald_new =
NewtonSolve(g_ewald,(*cutoff),natoms,shape_det(domain->h),b2);
if (g_ewald_new > 0.0) g_ewald = g_ewald_new;
else error->warning(FLERR,"Ewald/disp Newton solver failed, "
"using old method to estimate g_ewald");
}
}
if (!comm->me) {
if (screen) fprintf(screen, " G vector = %g, accuracy = %g\n", g_ewald,accuracy);
if (logfile) fprintf(logfile, " G vector = %g accuracy = %g\n", g_ewald,accuracy);
}
g_ewald_6 = g_ewald;
deallocate_peratom();
peratom_allocate_flag = 0;
}
/* ----------------------------------------------------------------------
adjust EwaldDisp coeffs, called initially and whenever volume has changed
------------------------------------------------------------------------- */
void EwaldDisp::setup()
{
volume = shape_det(domain->h)*slab_volfactor;
memcpy(unit, domain->h_inv, sizeof(shape));
shape_scalar_mult(unit, 2.0*MY_PI);
unit[2] /= slab_volfactor;
// int nbox_old = nbox, nkvec_old = nkvec;
if (accuracy >= 1) {
nbox = 0;
error->all(FLERR,"KSpace accuracy too low");
}
bigint natoms = atom->natoms;
double err;
int kxmax = 1;
int kymax = 1;
int kzmax = 1;
err = rms(kxmax,domain->h[0],natoms,q2,b2,M2);
while (err > accuracy) {
kxmax++;
err = rms(kxmax,domain->h[0],natoms,q2,b2,M2);
}
err = rms(kymax,domain->h[1],natoms,q2,b2,M2);
while (err > accuracy) {
kymax++;
err = rms(kymax,domain->h[1],natoms,q2,b2,M2);
}
err = rms(kzmax,domain->h[2]*slab_volfactor,natoms,q2,b2,M2);
while (err > accuracy) {
kzmax++;
err = rms(kzmax,domain->h[2]*slab_volfactor,natoms,q2,b2,M2);
}
nbox = MAX(kxmax,kymax);
nbox = MAX(nbox,kzmax);
double gsqxmx = unit[0]*unit[0]*kxmax*kxmax;
double gsqymx = unit[1]*unit[1]*kymax*kymax;
double gsqzmx = unit[2]*unit[2]*kzmax*kzmax;
gsqmx = MAX(gsqxmx,gsqymx);
gsqmx = MAX(gsqmx,gsqzmx);
gsqmx *= 1.00001;
reallocate();
coefficients();
init_coeffs();
init_coeff_sums();
init_self();
if (!(first_output||comm->me)) {
first_output = 1;
if (screen) fprintf(screen,
" vectors: nbox = %d, nkvec = %d\n", nbox, nkvec);
if (logfile) fprintf(logfile,
" vectors: nbox = %d, nkvec = %d\n", nbox, nkvec);
}
}
/* ----------------------------------------------------------------------
compute RMS accuracy for a dimension
------------------------------------------------------------------------- */
double EwaldDisp::rms(int km, double prd, bigint natoms,
double q2, double b2, double M2)
{
double value = 0.0;
// Coulombic
double g2 = g_ewald*g_ewald;
value += 2.0*q2*g_ewald/prd *
sqrt(1.0/(MY_PI*km*natoms)) *
exp(-MY_PI*MY_PI*km*km/(g2*prd*prd));
// Lennard-Jones
double g7 = g2*g2*g2*g_ewald;
value += 4.0*b2*g7/3.0 *
sqrt(1.0/(MY_PI*natoms)) *
(exp(-MY_PI*MY_PI*km*km/(g2*prd*prd)) *
(MY_PI*km/(g_ewald*prd) + 1));
// dipole
value += 8.0*MY_PI*M2/volume*g_ewald *
sqrt(2.0*MY_PI*km*km*km/(15.0*natoms)) *
exp(-pow(MY_PI*km/(g_ewald*prd),2.0));
return value;
}
void EwaldDisp::reallocate()
{
int ix, iy, iz;
int nkvec_max = nkvec;
vector h;
nkvec = 0;
int *kflag = new int[(nbox+1)*(2*nbox+1)*(2*nbox+1)];
int *flag = kflag;
for (ix=0; ix<=nbox; ++ix)
for (iy=-nbox; iy<=nbox; ++iy)
for (iz=-nbox; iz<=nbox; ++iz)
if (!(ix||iy||iz)) *(flag++) = 0;
else if ((!ix)&&(iy<0)) *(flag++) = 0;
else if ((!(ix||iy))&&(iz<0)) *(flag++) = 0; // use symmetry
else {
h[0] = unit[0]*ix;
h[1] = unit[5]*ix+unit[1]*iy;
h[2] = unit[4]*ix+unit[3]*iy+unit[2]*iz;
if ((*(flag++) = h[0]*h[0]+h[1]*h[1]+h[2]*h[2]<=gsqmx)) ++nkvec;
}
if (nkvec>nkvec_max) {
deallocate(); // free memory
hvec = new hvector[nkvec]; // hvec
bytes += (nkvec-nkvec_max)*sizeof(hvector);
kvec = new kvector[nkvec]; // kvec
bytes += (nkvec-nkvec_max)*sizeof(kvector);
kenergy = new double[nkvec*nfunctions]; // kenergy
bytes += (nkvec-nkvec_max)*nfunctions*sizeof(double);
kvirial = new double[6*nkvec*nfunctions]; // kvirial
bytes += 6*(nkvec-nkvec_max)*nfunctions*sizeof(double);
cek_local = new complex[nkvec*nsums]; // cek_local
bytes += (nkvec-nkvec_max)*nsums*sizeof(complex);
cek_global = new complex[nkvec*nsums]; // cek_global
bytes += (nkvec-nkvec_max)*nsums*sizeof(complex);
nkvec_max = nkvec;
}
flag = kflag; // create index and
kvector *k = kvec; // wave vectors
hvector *hi = hvec;
for (ix=0; ix<=nbox; ++ix)
for (iy=-nbox; iy<=nbox; ++iy)
for (iz=-nbox; iz<=nbox; ++iz)
if (*(flag++)) {
hi->x = unit[0]*ix;
hi->y = unit[5]*ix+unit[1]*iy;
(hi++)->z = unit[4]*ix+unit[3]*iy+unit[2]*iz;
k->x = ix+nbox; k->y = iy+nbox; (k++)->z = iz+nbox; }
delete [] kflag;
}
/* ---------------------------------------------------------------------- */
void EwaldDisp::reallocate_atoms()
{
if (eflag_atom || vflag_atom)
if (atom->nmax > nmax) {
deallocate_peratom();
allocate_peratom();
nmax = atom->nmax;
}
if ((nevec = atom->nmax*(2*nbox+1))<=nevec_max) return;
delete [] ekr_local;
ekr_local = new cvector[nevec];
bytes += (nevec-nevec_max)*sizeof(cvector);
nevec_max = nevec;
}
/* ---------------------------------------------------------------------- */
void EwaldDisp::allocate_peratom()
{
memory->create(energy_self_peratom,
atom->nmax,EWALD_NFUNCS,"ewald/n:energy_self_peratom");
memory->create(virial_self_peratom,
atom->nmax,EWALD_NFUNCS,"ewald/n:virial_self_peratom");
}
/* ---------------------------------------------------------------------- */
void EwaldDisp::deallocate_peratom() // free memory
{
if (energy_self_peratom) {
memory->destroy(energy_self_peratom);
energy_self_peratom = NULL;
}
if (virial_self_peratom) {
memory->destroy(virial_self_peratom);
virial_self_peratom = NULL;
}
}
/* ---------------------------------------------------------------------- */
void EwaldDisp::deallocate() // free memory
{
delete [] hvec; hvec = NULL;
delete [] kvec; kvec = NULL;
delete [] kenergy; kenergy = NULL;
delete [] kvirial; kvirial = NULL;
delete [] cek_local; cek_local = NULL;
delete [] cek_global; cek_global = NULL;
}
/* ---------------------------------------------------------------------- */
void EwaldDisp::coefficients()
{
vector h;
hvector *hi = hvec, *nh;
double eta2 = 0.25/(g_ewald*g_ewald);
double b1, b2, expb2, h1, h2, c1, c2;
double *ke = kenergy, *kv = kvirial;
int func0 = function[0], func12 = function[1]||function[2],
func3 = function[3];
for (nh = (hi = hvec)+nkvec; hi<nh; ++hi) { // wave vectors
memcpy(h, hi, sizeof(vector));
expb2 = exp(-(b2 = (h2 = vec_dot(h, h))*eta2));
if (func0) { // qi*qj/r coeffs
*(ke++) = c1 = expb2/h2;
*(kv++) = c1-(c2 = 2.0*c1*(1.0+b2)/h2)*h[0]*h[0];
*(kv++) = c1-c2*h[1]*h[1]; // lammps convention
*(kv++) = c1-c2*h[2]*h[2]; // instead of voigt
*(kv++) = -c2*h[1]*h[0];
*(kv++) = -c2*h[2]*h[0];
*(kv++) = -c2*h[2]*h[1];
}
if (func12) { // -Bij/r^6 coeffs
b1 = sqrt(b2); // minus sign folded
h1 = sqrt(h2); // into constants
*(ke++) = c1 = -h1*h2*((c2=MY_PIS*erfc(b1))+(0.5/b2-1.0)*expb2/b1);
*(kv++) = c1-(c2 = 3.0*h1*(c2-expb2/b1))*h[0]*h[0];
*(kv++) = c1-c2*h[1]*h[1]; // lammps convention
*(kv++) = c1-c2*h[2]*h[2]; // instead of voigt
*(kv++) = -c2*h[1]*h[0];
*(kv++) = -c2*h[2]*h[0];
*(kv++) = -c2*h[2]*h[1];
}
if (func3) { // dipole coeffs
*(ke++) = c1 = expb2/h2;
*(kv++) = c1-(c2 = 2.0*c1*(1.0+b2)/h2)*h[0]*h[0];
*(kv++) = c1-c2*h[1]*h[1]; // lammps convention
*(kv++) = c1-c2*h[2]*h[2]; // instead of voigt
*(kv++) = -c2*h[1]*h[0];
*(kv++) = -c2*h[2]*h[0];
*(kv++) = -c2*h[2]*h[1];
}
}
}
/* ---------------------------------------------------------------------- */
void EwaldDisp::init_coeffs()
{
int tmp;
int n = atom->ntypes;
if (function[1]) { // geometric 1/r^6
double **b = (double **) force->pair->extract("B",tmp);
delete [] B;
B = new double[n+1];
B[0] = 0.0;
bytes += (n+1)*sizeof(double);
for (int i=1; i<=n; ++i) B[i] = sqrt(fabs(b[i][i]));
}
if (function[2]) { // arithmetic 1/r^6
double **epsilon = (double **) force->pair->extract("epsilon",tmp);
double **sigma = (double **) force->pair->extract("sigma",tmp);
double eps_i, sigma_i, sigma_n, *bi = B = new double[7*n+7];
double c[7] = {
1.0, sqrt(6.0), sqrt(15.0), sqrt(20.0), sqrt(15.0), sqrt(6.0), 1.0};
if (!(epsilon&&sigma))
error->all(
FLERR,"Epsilon or sigma reference not set by pair style in ewald/n");
for (int j=0; j<7; ++j)
*(bi++) = 0.0;
for (int i=1; i<=n; ++i) {
eps_i = sqrt(epsilon[i][i]);
sigma_i = sigma[i][i];
sigma_n = 1.0;
for (int j=0; j<7; ++j) {
*(bi++) = sigma_n*eps_i*c[j]; sigma_n *= sigma_i;
}
}
}
}
/* ---------------------------------------------------------------------- */
void EwaldDisp::init_coeff_sums()
{
if (sums) return; // calculated only once
sums = 1;
Sum sum_local[EWALD_MAX_NSUMS];
memset(sum_local, 0, EWALD_MAX_NSUMS*sizeof(Sum));
memset(sum, 0, EWALD_MAX_NSUMS*sizeof(Sum));
// now perform qsum and qsq via parent qsum_qsq()
sum_local[0].x = 0.0;
sum_local[0].x2 = 0.0;
//if (function[0]) { // 1/r
// double *q = atom->q, *qn = q+atom->nlocal;
// for (double *i=q; i<qn; ++i) {
// sum_local[0].x += i[0]; sum_local[0].x2 += i[0]*i[0]; }
//}
if (function[1]) { // geometric 1/r^6
int *type = atom->type, *ntype = type+atom->nlocal;
for (int *i=type; i<ntype; ++i) {
sum_local[1].x += B[i[0]]; sum_local[1].x2 += B[i[0]]*B[i[0]]; }
}
if (function[2]) { // arithmetic 1/r^6
double *bi;
int *type = atom->type, *ntype = type+atom->nlocal;
for (int *i=type; i<ntype; ++i) {
bi = B+7*i[0];
sum_local[2].x2 += bi[0]*bi[6];
for (int k=2; k<9; ++k) sum_local[k].x += *(bi++);
}
}
if (function[3]&&atom->mu) { // dipole
double *mu = atom->mu[0], *nmu = mu+4*atom->nlocal;
for (double *i = mu; i < nmu; i += 4)
sum_local[9].x2 += i[3]*i[3];
}
MPI_Allreduce(sum_local, sum, 2*EWALD_MAX_NSUMS, MPI_DOUBLE, MPI_SUM, world);
}
/* ---------------------------------------------------------------------- */
void EwaldDisp::init_self()
{
double g1 = g_ewald, g2 = g1*g1, g3 = g1*g2;
const double qscale = force->qqrd2e * scale;
memset(energy_self, 0, EWALD_NFUNCS*sizeof(double)); // self energy
memset(virial_self, 0, EWALD_NFUNCS*sizeof(double));
if (function[0]) { // 1/r
virial_self[0] = -0.5*MY_PI*qscale/(g2*volume)*qsum*qsum;
energy_self[0] = qsqsum*qscale*g1/MY_PIS-virial_self[0];
}
if (function[1]) { // geometric 1/r^6
virial_self[1] = MY_PI*MY_PIS*g3/(6.0*volume)*sum[1].x*sum[1].x;
energy_self[1] = -sum[1].x2*g3*g3/12.0+virial_self[1];
}
if (function[2]) { // arithmetic 1/r^6
virial_self[2] = MY_PI*MY_PIS*g3/(48.0*volume)*(sum[2].x*sum[8].x+
sum[3].x*sum[7].x+sum[4].x*sum[6].x+0.5*sum[5].x*sum[5].x);
energy_self[2] = -sum[2].x2*g3*g3/3.0+virial_self[2];
}
if (function[3]) { // dipole
virial_self[3] = 0; // in surface
energy_self[3] = sum[9].x2*mumurd2e*2.0*g3/3.0/MY_PIS-virial_self[3];
}
}
/* ---------------------------------------------------------------------- */
void EwaldDisp::init_self_peratom()
{
if (!(vflag_atom || eflag_atom)) return;
double g1 = g_ewald, g2 = g1*g1, g3 = g1*g2;
const double qscale = force->qqrd2e * scale;
double *energy = energy_self_peratom[0];
double *virial = virial_self_peratom[0];
int nlocal = atom->nlocal;
memset(energy, 0, EWALD_NFUNCS*nlocal*sizeof(double));
memset(virial, 0, EWALD_NFUNCS*nlocal*sizeof(double));
if (function[0]) { // 1/r
double *ei = energy;
double *vi = virial;
double ce = qscale*g1/MY_PIS;
double cv = -0.5*MY_PI*qscale/(g2*volume);
double *qi = atom->q, *qn = qi + nlocal;
for (; qi < qn; qi++, vi += EWALD_NFUNCS, ei += EWALD_NFUNCS) {
double q = *qi;
*vi = cv*q*qsum;
*ei = ce*q*q-vi[0];
}
}
if (function[1]) { // geometric 1/r^6
double *ei = energy+1;
double *vi = virial+1;
double ce = -g3*g3/12.0;
double cv = MY_PI*MY_PIS*g3/(6.0*volume);
int *typei = atom->type, *typen = typei + atom->nlocal;
for (; typei < typen; typei++, vi += EWALD_NFUNCS, ei += EWALD_NFUNCS) {
double b = B[*typei];
*vi = cv*b*sum[1].x;
*ei = ce*b*b+vi[0];
}
}
if (function[2]) { // arithmetic 1/r^6
double *bi;
double *ei = energy+2;
double *vi = virial+2;
double ce = -g3*g3/3.0;
double cv = 0.5*MY_PI*MY_PIS*g3/(48.0*volume);
int *typei = atom->type, *typen = typei + atom->nlocal;
for (; typei < typen; typei++, vi += EWALD_NFUNCS, ei += EWALD_NFUNCS) {
bi = B+7*typei[0]+7;
for (int k=2; k<9; ++k) *vi += cv*sum[k].x*(--bi)[0];
/* PJV 20120225:
should this be this instead? above implies an inverse dependence
seems to be the above way in original; i recall having tested
arithmetic mixing in the conception phase, but an extra test would
be prudent (pattern repeats in multiple functions below)
bi = B+7*typei[0];
for (int k=2; k<9; ++k) *vi += cv*sum[k].x*(bi++)[0];
*/
*ei = ce*bi[0]*bi[6]+vi[0];
}
}
if (function[3]&&atom->mu) { // dipole
double *ei = energy+3;
double *vi = virial+3;
double *imu = atom->mu[0], *nmu = imu+4*atom->nlocal;
double ce = mumurd2e*2.0*g3/3.0/MY_PIS;
for (; imu < nmu; imu += 4, vi += EWALD_NFUNCS, ei += EWALD_NFUNCS) {
*vi = 0; // in surface
*ei = ce*imu[3]*imu[3]-vi[0];
}
}
}
/* ----------------------------------------------------------------------
compute the EwaldDisp long-range force, energy, virial
------------------------------------------------------------------------- */
void EwaldDisp::compute(int eflag, int vflag)
{
if (!nbox) return;
// set energy/virial flags
// invoke allocate_peratom() if needed for first time
if (eflag || vflag) ev_setup(eflag,vflag);
else evflag = eflag_global = vflag_global = eflag_atom = vflag_atom = 0;
if (!peratom_allocate_flag && (eflag_atom || vflag_atom)) {
allocate_peratom();
peratom_allocate_flag = 1;
nmax = atom->nmax;
}
reallocate_atoms();
init_self_peratom();
compute_ek();
compute_force();
//compute_surface(); // assume conducting metal (tinfoil) boundary conditions
// update qsum and qsqsum, if atom count has changed and energy needed
if ((eflag_global || eflag_atom) && atom->natoms != natoms_original) {
if (function[0]) qsum_qsq();
natoms_original = atom->natoms;
}
compute_energy();
compute_energy_peratom();
compute_virial();
compute_virial_dipole();
compute_virial_peratom();
if (slabflag) compute_slabcorr();
}
void EwaldDisp::compute_ek()
{
cvector *ekr = ekr_local;
int lbytes = (2*nbox+1)*sizeof(cvector);
hvector *h = NULL;
kvector *k, *nk = kvec+nkvec;
cvector *z = new cvector[2*nbox+1];
cvector z1, *zx, *zy, *zz, *zn = z+2*nbox;
complex *cek, zxyz, zxy = COMPLEX_NULL, cx = COMPLEX_NULL;
vector mui;
double *x = atom->x[0], *xn = x+3*atom->nlocal, *q = atom->q, qi = 0.0;
double bi = 0.0, ci[7];
double *mu = atom->mu ? atom->mu[0] : NULL;
int i, kx, ky, n = nkvec*nsums, *type = atom->type, tri = domain->triclinic;
int func[EWALD_NFUNCS];
memcpy(func, function, EWALD_NFUNCS*sizeof(int));
memset(cek_local, 0, n*sizeof(complex)); // reset sums
while (x<xn) {
zx = (zy = (zz = z+nbox)+1)-2;
C_SET(zz->x, 1, 0); C_SET(zz->y, 1, 0); C_SET(zz->z, 1, 0); // z[0]
if (tri) { // triclinic z[1]
C_ANGLE(z1.x, unit[0]*x[0]+unit[5]*x[1]+unit[4]*x[2]);
C_ANGLE(z1.y, unit[1]*x[1]+unit[3]*x[2]);
C_ANGLE(z1.z, x[2]*unit[2]); x += 3;
}
else { // orthogonal z[1]
C_ANGLE(z1.x, *(x++)*unit[0]);
C_ANGLE(z1.y, *(x++)*unit[1]);
C_ANGLE(z1.z, *(x++)*unit[2]);
}
for (; zz<zn; --zx, ++zy, ++zz) { // set up z[k]=e^(ik.r)
C_RMULT(zy->x, zz->x, z1.x); // 3D k-vector
C_RMULT(zy->y, zz->y, z1.y); C_CONJ(zx->y, zy->y);
C_RMULT(zy->z, zz->z, z1.z); C_CONJ(zx->z, zy->z);
}
kx = ky = -1;
cek = cek_local;
if (func[0]) qi = *(q++);
if (func[1]) bi = B[*type];
if (func[2]) memcpy(ci, B+7*type[0], 7*sizeof(double));
if (func[3]) {
memcpy(mui, mu, sizeof(vector));
mu += 4;
h = hvec;
}
for (k=kvec; k<nk; ++k) { // compute rho(k)
if (ky!=k->y) { // based on order in
if (kx!=k->x) cx = z[kx = k->x].x; // reallocate
C_RMULT(zxy, z[ky = k->y].y, cx);
}
C_RMULT(zxyz, z[k->z].z, zxy);
if (func[0]) {
cek->re += zxyz.re*qi; (cek++)->im += zxyz.im*qi;
}
if (func[1]) {
cek->re += zxyz.re*bi; (cek++)->im += zxyz.im*bi;
}
if (func[2]) for (i=0; i<7; ++i) {
cek->re += zxyz.re*ci[i]; (cek++)->im += zxyz.im*ci[i];
}
if (func[3]) {
register double muk = mui[0]*h->x+mui[1]*h->y+mui[2]*h->z; ++h;
cek->re += zxyz.re*muk; (cek++)->im += zxyz.im*muk;
}
}
ekr = (cvector *) ((char *) memcpy(ekr, z, lbytes)+lbytes);
++type;
}
MPI_Allreduce(cek_local, cek_global, 2*n, MPI_DOUBLE, MPI_SUM, world);
delete [] z;
}
/* ---------------------------------------------------------------------- */
void EwaldDisp::compute_force()
{
kvector *k;
hvector *h, *nh;
cvector *z = ekr_local;
vector sum[EWALD_MAX_NSUMS], mui = COMPLEX_NULL;
complex *cek, zc, zx = COMPLEX_NULL, zxy = COMPLEX_NULL;
complex *cek_coul;
double *f = atom->f[0], *fn = f+3*atom->nlocal, *q = atom->q, *t = NULL;
double *mu = atom->mu ? atom->mu[0] : NULL;
const double qscale = force->qqrd2e * scale;
double *ke, c[EWALD_NFUNCS] = {
8.0*MY_PI*qscale/volume, 2.0*MY_PI*MY_PIS/(12.0*volume),
2.0*MY_PI*MY_PIS/(192.0*volume), 8.0*MY_PI*mumurd2e/volume};
int i, kx, ky, lbytes = (2*nbox+1)*sizeof(cvector), *type = atom->type;
int func[EWALD_NFUNCS];
if (atom->torque) t = atom->torque[0];
memcpy(func, function, EWALD_NFUNCS*sizeof(int));
memset(sum, 0, EWALD_MAX_NSUMS*sizeof(vector)); // fj = -dE/dr =
for (; f<fn; f+=3) { // -i*qj*fac*
k = kvec; // Sum[conj(d)-d]
kx = ky = -1; // d = k*conj(ekj)*ek
ke = kenergy;
cek = cek_global;
memset(sum, 0, EWALD_MAX_NSUMS*sizeof(vector));
if (func[3]) {
register double di = c[3];
mui[0] = di*(mu++)[0]; mui[1] = di*(mu++)[0]; mui[2] = di*(mu++)[0];
mu++;
}
for (nh = (h = hvec)+nkvec; h<nh; ++h, ++k) {
if (ky!=k->y) { // based on order in
if (kx!=k->x) zx = z[kx = k->x].x; // reallocate
C_RMULT(zxy, z[ky = k->y].y, zx);
}
C_CRMULT(zc, z[k->z].z, zxy);
if (func[0]) { // 1/r
register double im = *(ke++)*(zc.im*cek->re+cek->im*zc.re);
if (func[3]) cek_coul = cek;
++cek;
sum[0][0] += h->x*im; sum[0][1] += h->y*im; sum[0][2] += h->z*im;
}
if (func[1]) { // geometric 1/r^6
register double im = *(ke++)*(zc.im*cek->re+cek->im*zc.re); ++cek;
sum[1][0] += h->x*im; sum[1][1] += h->y*im; sum[1][2] += h->z*im;
}
if (func[2]) { // arithmetic 1/r^6
register double im, c = *(ke++);
for (i=2; i<9; ++i) {
im = c*(zc.im*cek->re+cek->im*zc.re); ++cek;
sum[i][0] += h->x*im; sum[i][1] += h->y*im; sum[i][2] += h->z*im;
}
}
if (func[3]) { // dipole
register double im = *(ke)*(zc.im*cek->re+
cek->im*zc.re)*(mui[0]*h->x+mui[1]*h->y+mui[2]*h->z);
register double im2 = *(ke)*(zc.re*cek->re-
cek->im*zc.im);
sum[9][0] += h->x*im; sum[9][1] += h->y*im; sum[9][2] += h->z*im;
t[0] += -mui[1]*h->z*im2 + mui[2]*h->y*im2; // torque
t[1] += -mui[2]*h->x*im2 + mui[0]*h->z*im2;
t[2] += -mui[0]*h->y*im2 + mui[1]*h->x*im2;
if (func[0]) { // charge-dipole
register double qi = *(q)*c[0];
im = - *(ke)*(zc.re*cek_coul->re -
cek_coul->im*zc.im)*(mui[0]*h->x+mui[1]*h->y+mui[2]*h->z);
im += *(ke)*(zc.re*cek->re - cek->im*zc.im)*qi;
sum[9][0] += h->x*im; sum[9][1] += h->y*im; sum[9][2] += h->z*im;
im2 = *(ke)*(zc.re*cek_coul->im + cek_coul->re*zc.im);
im2 += -*(ke)*(zc.re*cek->im - cek->im*zc.re);
t[0] += -mui[1]*h->z*im2 + mui[2]*h->y*im2; // torque
t[1] += -mui[2]*h->x*im2 + mui[0]*h->z*im2;
t[2] += -mui[0]*h->y*im2 + mui[1]*h->x*im2;
}
++cek;
ke++;
}
}
if (func[0]) { // 1/r
register double qi = *(q++)*c[0];
f[0] -= sum[0][0]*qi; f[1] -= sum[0][1]*qi; f[2] -= sum[0][2]*qi;
}
if (func[1]) { // geometric 1/r^6
register double bi = B[*type]*c[1];
f[0] -= sum[1][0]*bi; f[1] -= sum[1][1]*bi; f[2] -= sum[1][2]*bi;
}
if (func[2]) { // arithmetic 1/r^6
register double *bi = B+7*type[0]+7;
for (i=2; i<9; ++i) {
register double c2 = (--bi)[0]*c[2];
f[0] -= sum[i][0]*c2; f[1] -= sum[i][1]*c2; f[2] -= sum[i][2]*c2;
}
}
if (func[3]) { // dipole
f[0] -= sum[9][0]; f[1] -= sum[9][1]; f[2] -= sum[9][2];
}
z = (cvector *) ((char *) z+lbytes);
++type;
t += 3;
}
}
/* ---------------------------------------------------------------------- */
void EwaldDisp::compute_surface()
{
// assume conducting metal (tinfoil) boundary conditions, so this function is
// not called because dielectric at the boundary --> infinity, which makes all
// the terms here zero.
if (!function[3]) return;
if (!atom->mu) return;
vector sum_local = VECTOR_NULL, sum_total;
memset(sum_local, 0, sizeof(vector));
double *i, *n, *mu = atom->mu[0];
for (n = (i = mu) + 4*atom->nlocal; i < n; ++i) {
sum_local[0] += (i++)[0];
sum_local[1] += (i++)[0];
sum_local[2] += (i++)[0];
}
MPI_Allreduce(sum_local, sum_total, 3, MPI_DOUBLE, MPI_SUM, world);
virial_self[3] =
mumurd2e*(2.0*MY_PI*vec_dot(sum_total,sum_total)/(2.0*dielectric+1)/volume);
energy_self[3] -= virial_self[3];
if (!(vflag_atom || eflag_atom)) return;
double *ei = energy_self_peratom[0]+3;
double *vi = virial_self_peratom[0]+3;
double cv = 2.0*mumurd2e*MY_PI/(2.0*dielectric+1)/volume;
for (i = mu; i < n; i += 4, ei += EWALD_NFUNCS, vi += EWALD_NFUNCS) {
*vi = cv*(i[0]*sum_total[0]+i[1]*sum_total[1]+i[2]*sum_total[2]);
*ei -= *vi;
}
}
/* ---------------------------------------------------------------------- */
void EwaldDisp::compute_energy()
{
energy = 0.0;
if (!eflag_global) return;
complex *cek = cek_global;
complex *cek_coul;
double *ke = kenergy;
const double qscale = force->qqrd2e * scale;
double c[EWALD_NFUNCS] = {
4.0*MY_PI*qscale/volume, 2.0*MY_PI*MY_PIS/(24.0*volume),
2.0*MY_PI*MY_PIS/(192.0*volume), 4.0*MY_PI*mumurd2e/volume};
double sum[EWALD_NFUNCS];
int func[EWALD_NFUNCS];
memcpy(func, function, EWALD_NFUNCS*sizeof(int));
memset(sum, 0, EWALD_NFUNCS*sizeof(double)); // reset sums
for (int k=0; k<nkvec; ++k) { // sum over k vectors
if (func[0]) { // 1/r
sum[0] += *(ke++)*(cek->re*cek->re+cek->im*cek->im);
if (func[3]) cek_coul = cek;
++cek;
}
if (func[1]) { // geometric 1/r^6
sum[1] += *(ke++)*(cek->re*cek->re+cek->im*cek->im); ++cek; }
if (func[2]) { // arithmetic 1/r^6
register double r =
(cek[0].re*cek[6].re+cek[0].im*cek[6].im)+
(cek[1].re*cek[5].re+cek[1].im*cek[5].im)+
(cek[2].re*cek[4].re+cek[2].im*cek[4].im)+
0.5*(cek[3].re*cek[3].re+cek[3].im*cek[3].im); cek += 7;
sum[2] += *(ke++)*r;
}
if (func[3]) { // dipole
sum[3] += *(ke)*(cek->re*cek->re+cek->im*cek->im);
if (func[0]) { // charge-dipole
sum[3] += *(ke)*2.0*(cek->re*cek_coul->im - cek->im*cek_coul->re);
}
ke++;
++cek;
}
}
for (int k=0; k<EWALD_NFUNCS; ++k) energy += c[k]*sum[k]-energy_self[k];
}
/* ---------------------------------------------------------------------- */
void EwaldDisp::compute_energy_peratom()
{
if (!eflag_atom) return;
kvector *k;
hvector *h, *nh;
cvector *z = ekr_local;
vector mui = VECTOR_NULL;
double sum[EWALD_MAX_NSUMS];
complex *cek, zc = COMPLEX_NULL, zx = COMPLEX_NULL, zxy = COMPLEX_NULL;
complex *cek_coul;
double *q = atom->q;
double *eatomj = eatom;
double *mu = atom->mu ? atom->mu[0] : NULL;
const double qscale = force->qqrd2e * scale;
double *ke = kenergy;
double c[EWALD_NFUNCS] = {
4.0*MY_PI*qscale/volume, 2.0*MY_PI*MY_PIS/(24.0*volume),
2.0*MY_PI*MY_PIS/(192.0*volume), 4.0*MY_PI*mumurd2e/volume};
int i, kx, ky, lbytes = (2*nbox+1)*sizeof(cvector), *type = atom->type;
int func[EWALD_NFUNCS];
memcpy(func, function, EWALD_NFUNCS*sizeof(int));
for (int j = 0; j < atom->nlocal; j++, ++eatomj) {
k = kvec;
kx = ky = -1;
ke = kenergy;
cek = cek_global;
memset(sum, 0, EWALD_MAX_NSUMS*sizeof(double));
if (func[3]) {
register double di = c[3];
mui[0] = di*(mu++)[0]; mui[1] = di*(mu++)[0]; mui[2] = di*(mu++)[0];
mu++;
}
for (nh = (h = hvec)+nkvec; h<nh; ++h, ++k) {
if (ky!=k->y) { // based on order in
if (kx!=k->x) zx = z[kx = k->x].x; // reallocate
C_RMULT(zxy, z[ky = k->y].y, zx);
}
C_CRMULT(zc, z[k->z].z, zxy);
if (func[0]) { // 1/r
sum[0] += *(ke++)*(cek->re*zc.re - cek->im*zc.im);
if (func[3]) cek_coul = cek;
++cek;
}
if (func[1]) { // geometric 1/r^6
sum[1] += *(ke++)*(cek->re*zc.re - cek->im*zc.im); ++cek; }
if (func[2]) { // arithmetic 1/r^6
register double im, c = *(ke++);
for (i=2; i<9; ++i) {
im = c*(cek->re*zc.re - cek->im*zc.im); ++cek;
sum[i] += im;
}
}
if (func[3]) { // dipole
double muk = (mui[0]*h->x+mui[1]*h->y+mui[2]*h->z);
sum[9] += *(ke)*(cek->re*zc.re - cek->im*zc.im)*muk;
if (func[0]) { // charge-dipole
register double qj = *(q)*c[0];
sum[9] += *(ke)*(cek_coul->im*zc.re + cek_coul->re*zc.im)*muk;
sum[9] -= *(ke)*(cek->re*zc.im + cek->im*zc.re)*qj;
}
++cek;
ke++;
}
}
if (func[0]) { // 1/r
register double qj = *(q++)*c[0];
*eatomj += sum[0]*qj - energy_self_peratom[j][0];
}
if (func[1]) { // geometric 1/r^6
register double bj = B[*type]*c[1];
*eatomj += sum[1]*bj - energy_self_peratom[j][1];
}
if (func[2]) { // arithmetic 1/r^6
register double *bj = B+7*type[0]+7;
for (i=2; i<9; ++i) {
register double c2 = (--bj)[0]*c[2];
*eatomj += 0.5*sum[i]*c2;
}
*eatomj -= energy_self_peratom[j][2];
}
if (func[3]) { // dipole
*eatomj += sum[9] - energy_self_peratom[j][3];
}
z = (cvector *) ((char *) z+lbytes);
++type;
}
}
/* ---------------------------------------------------------------------- */
#define swap(a, b) { register double t = a; a= b; b = t; }
void EwaldDisp::compute_virial()
{
memset(virial, 0, sizeof(shape));
if (!vflag_global) return;
complex *cek = cek_global;
complex *cek_coul;
double *kv = kvirial;
const double qscale = force->qqrd2e * scale;
double c[EWALD_NFUNCS] = {
4.0*MY_PI*qscale/volume, 2.0*MY_PI*MY_PIS/(24.0*volume),
2.0*MY_PI*MY_PIS/(192.0*volume), 4.0*MY_PI*mumurd2e/volume};
shape sum[EWALD_NFUNCS];
int func[EWALD_NFUNCS];
memcpy(func, function, EWALD_NFUNCS*sizeof(int));
memset(sum, 0, EWALD_NFUNCS*sizeof(shape));
for (int k=0; k<nkvec; ++k) { // sum over k vectors
if (func[0]) { // 1/r
register double r = cek->re*cek->re+cek->im*cek->im;
if (func[3]) cek_coul = cek;
++cek;
sum[0][0] += *(kv++)*r; sum[0][1] += *(kv++)*r; sum[0][2] += *(kv++)*r;
sum[0][3] += *(kv++)*r; sum[0][4] += *(kv++)*r; sum[0][5] += *(kv++)*r;
}
if (func[1]) { // geometric 1/r^6
register double r = cek->re*cek->re+cek->im*cek->im; ++cek;
sum[1][0] += *(kv++)*r; sum[1][1] += *(kv++)*r; sum[1][2] += *(kv++)*r;
sum[1][3] += *(kv++)*r; sum[1][4] += *(kv++)*r; sum[1][5] += *(kv++)*r;
}
if (func[2]) { // arithmetic 1/r^6
register double r =
(cek[0].re*cek[6].re+cek[0].im*cek[6].im)+
(cek[1].re*cek[5].re+cek[1].im*cek[5].im)+
(cek[2].re*cek[4].re+cek[2].im*cek[4].im)+
0.5*(cek[3].re*cek[3].re+cek[3].im*cek[3].im); cek += 7;
sum[2][0] += *(kv++)*r; sum[2][1] += *(kv++)*r; sum[2][2] += *(kv++)*r;
sum[2][3] += *(kv++)*r; sum[2][4] += *(kv++)*r; sum[2][5] += *(kv++)*r;
}
if (func[3]) {
register double r = cek->re*cek->re+cek->im*cek->im;
sum[3][0] += *(kv++)*r; sum[3][1] += *(kv++)*r; sum[3][2] += *(kv++)*r;
sum[3][3] += *(kv++)*r; sum[3][4] += *(kv++)*r; sum[3][5] += *(kv++)*r;
if (func[0]) { // charge-dipole
kv -= 6;
register double r = 2.0*(cek->re*cek_coul->im - cek->im*cek_coul->re);
sum[3][0] += *(kv++)*r; sum[3][1] += *(kv++)*r; sum[3][2] += *(kv++)*r;
sum[3][3] += *(kv++)*r; sum[3][4] += *(kv++)*r; sum[3][5] += *(kv++)*r;
}
++cek;
}
}
for (int k=0; k<EWALD_NFUNCS; ++k)
if (func[k]) {
shape self = {virial_self[k], virial_self[k], virial_self[k], 0, 0, 0};
shape_scalar_mult(sum[k], c[k]);
shape_add(virial, sum[k]);
shape_subtr(virial, self);
}
}
/* ---------------------------------------------------------------------- */
void EwaldDisp::compute_virial_dipole()
{
if (!function[3]) return;
if (!vflag_atom && !vflag_global) return;
kvector *k;
hvector *h, *nh;
cvector *z = ekr_local;
vector mui = COMPLEX_NULL;
double sum[6];
double sum_total[6];
complex *cek, zc, zx = COMPLEX_NULL, zxy = COMPLEX_NULL;
complex *cek_coul;
double *mu = atom->mu ? atom->mu[0] : NULL;
double *vatomj = NULL;
if (vflag_atom && vatom) vatomj = vatom[0];
const double qscale = force->qqrd2e * scale;
double *ke, c[EWALD_NFUNCS] = {
8.0*MY_PI*qscale/volume, 2.0*MY_PI*MY_PIS/(12.0*volume),
2.0*MY_PI*MY_PIS/(192.0*volume), 8.0*MY_PI*mumurd2e/volume};
int i, kx, ky, lbytes = (2*nbox+1)*sizeof(cvector), *type = atom->type;
int func[EWALD_NFUNCS];
memcpy(func, function, EWALD_NFUNCS*sizeof(int));
memset(&sum[0], 0, 6*sizeof(double));
memset(&sum_total[0], 0, 6*sizeof(double));
for (int j = 0; j < atom->nlocal; j++) {
k = kvec;
kx = ky = -1;
ke = kenergy;
cek = cek_global;
memset(&sum[0], 0, 6*sizeof(double));
if (func[3]) {
register double di = c[3];
mui[0] = di*(mu++)[0]; mui[1] = di*(mu++)[0]; mui[2] = di*(mu++)[0];
mu++;
}
for (nh = (h = hvec)+nkvec; h<nh; ++h, ++k) {
if (ky!=k->y) { // based on order in
if (kx!=k->x) zx = z[kx = k->x].x; // reallocate
C_RMULT(zxy, z[ky = k->y].y, zx);
}
C_CRMULT(zc, z[k->z].z, zxy);
double im = 0.0;
if (func[0]) { // 1/r
ke++;
if (func[3]) cek_coul = cek;
++cek;
}
if (func[1]) { // geometric 1/r^6
ke++;
++cek;
}
if (func[2]) { // arithmetic 1/r^6
ke++;
for (i=2; i<9; ++i) {
++cek;
}
}
if (func[3]) { // dipole
im = *(ke)*(zc.re*cek->re - cek->im*zc.im);
if (func[0]) { // charge-dipole
im += *(ke)*(zc.im*cek_coul->re + cek_coul->im*zc.re);
}
sum[0] -= mui[0]*h->x*im;
sum[1] -= mui[1]*h->y*im;
sum[2] -= mui[2]*h->z*im;
sum[3] -= mui[0]*h->y*im;
sum[4] -= mui[0]*h->z*im;
sum[5] -= mui[1]*h->z*im;
++cek;
ke++;
}
}
if (vflag_global)
for (int n = 0; n < 6; n++)
sum_total[n] -= sum[n];
if (vflag_atom)
for (int n = 0; n < 6; n++)
vatomj[n] -= sum[n];
z = (cvector *) ((char *) z+lbytes);
++type;
if (vflag_atom) vatomj += 6;
}
if (vflag_global) {
MPI_Allreduce(&sum_total[0],&sum[0],6,MPI_DOUBLE,MPI_SUM,world);
for (int n = 0; n < 6; n++)
virial[n] += sum[n];
}
}
/* ---------------------------------------------------------------------- */
void EwaldDisp::compute_virial_peratom()
{
if (!vflag_atom) return;
kvector *k;
hvector *h, *nh;
cvector *z = ekr_local;
vector mui = VECTOR_NULL;
complex *cek, zc = COMPLEX_NULL, zx = COMPLEX_NULL, zxy = COMPLEX_NULL;
complex *cek_coul;
double *kv;
double *q = atom->q;
double *vatomj = vatom ? vatom[0] : NULL;
double *mu = atom->mu ? atom->mu[0] : NULL;
const double qscale = force->qqrd2e * scale;
double c[EWALD_NFUNCS] = {
4.0*MY_PI*qscale/volume, 2.0*MY_PI*MY_PIS/(24.0*volume),
2.0*MY_PI*MY_PIS/(192.0*volume), 4.0*MY_PI*mumurd2e/volume};
shape sum[EWALD_MAX_NSUMS];
int func[EWALD_NFUNCS];
memcpy(func, function, EWALD_NFUNCS*sizeof(int));
int i, kx, ky, lbytes = (2*nbox+1)*sizeof(cvector), *type = atom->type;
for (int j = 0; j < atom->nlocal; j++) {
k = kvec;
kx = ky = -1;
kv = kvirial;
cek = cek_global;
memset(sum, 0, EWALD_MAX_NSUMS*sizeof(shape));
if (func[3]) {
register double di = c[3];
mui[0] = di*(mu++)[0]; mui[1] = di*(mu++)[0]; mui[2] = di*(mu++)[0];
mu++;
}
for (nh = (h = hvec)+nkvec; h<nh; ++h, ++k) {
if (ky!=k->y) { // based on order in
if (kx!=k->x) zx = z[kx = k->x].x; // reallocate
C_RMULT(zxy, z[ky = k->y].y, zx);
}
C_CRMULT(zc, z[k->z].z, zxy);
if (func[0]) { // 1/r
if (func[3]) cek_coul = cek;
register double r = cek->re*zc.re - cek->im*zc.im; ++cek;
sum[0][0] += *(kv++)*r;
sum[0][1] += *(kv++)*r;
sum[0][2] += *(kv++)*r;
sum[0][3] += *(kv++)*r;
sum[0][4] += *(kv++)*r;
sum[0][5] += *(kv++)*r;
}
if (func[1]) { // geometric 1/r^6
register double r = cek->re*zc.re - cek->im*zc.im; ++cek;
sum[1][0] += *(kv++)*r;
sum[1][1] += *(kv++)*r;
sum[1][2] += *(kv++)*r;
sum[1][3] += *(kv++)*r;
sum[1][4] += *(kv++)*r;
sum[1][5] += *(kv++)*r;
}
if (func[2]) { // arithmetic 1/r^6
register double r;
for (i=2; i<9; ++i) {
r = cek->re*zc.re - cek->im*zc.im; ++cek;
sum[i][0] += *(kv++)*r;
sum[i][1] += *(kv++)*r;
sum[i][2] += *(kv++)*r;
sum[i][3] += *(kv++)*r;
sum[i][4] += *(kv++)*r;
sum[i][5] += *(kv++)*r;
kv -= 6;
}
kv += 6;
}
if (func[3]) { // dipole
double muk = (mui[0]*h->x+mui[1]*h->y+mui[2]*h->z);
register double
r = (cek->re*zc.re - cek->im*zc.im)*muk;
sum[9][0] += *(kv++)*r;
sum[9][1] += *(kv++)*r;
sum[9][2] += *(kv++)*r;
sum[9][3] += *(kv++)*r;
sum[9][4] += *(kv++)*r;
sum[9][5] += *(kv++)*r;
if (func[0]) { // charge-dipole
kv -= 6;
register double qj = *(q)*c[0];
r = (cek_coul->im*zc.re + cek_coul->re*zc.im)*muk;
r += -(cek->re*zc.im + cek->im*zc.re)*qj;
sum[9][0] += *(kv++)*r; sum[9][1] += *(kv++)*r; sum[9][2] += *(kv++)*r;
sum[9][3] += *(kv++)*r; sum[9][4] += *(kv++)*r; sum[9][5] += *(kv++)*r;
}
++cek;
}
}
if (func[0]) { // 1/r
register double qi = *(q++)*c[0];
for (int n = 0; n < 6; n++) vatomj[n] += sum[0][n]*qi;
}
if (func[1]) { // geometric 1/r^6
register double bi = B[*type]*c[1];
for (int n = 0; n < 6; n++) vatomj[n] += sum[1][n]*bi;
}
if (func[2]) { // arithmetic 1/r^6
register double *bj = B+7*type[0]+7;
for (i=2; i<9; ++i) {
register double c2 = (--bj)[0]*c[2];
for (int n = 0; n < 6; n++) vatomj[n] += 0.5*sum[i][n]*c2;
}
}
if (func[3]) { // dipole
for (int n = 0; n < 6; n++) vatomj[n] += sum[9][n];
}
for (int k=0; k<EWALD_NFUNCS; ++k) {
if (func[k]) {
for (int n = 0; n < 3; n++) vatomj[n] -= virial_self_peratom[j][k];
}
}
z = (cvector *) ((char *) z+lbytes);
++type;
vatomj += 6;
}
}
/* ----------------------------------------------------------------------
Slab-geometry correction term to dampen inter-slab interactions between
periodically repeating slabs. Yields good approximation to 2D Ewald if
adequate empty space is left between repeating slabs (J. Chem. Phys.
111, 3155). Slabs defined here to be parallel to the xy plane. Also
extended to non-neutral systems (J. Chem. Phys. 131, 094107).
------------------------------------------------------------------------- */
void EwaldDisp::compute_slabcorr()
{
// compute local contribution to global dipole moment
double *q = atom->q;
double **x = atom->x;
double zprd = domain->zprd;
int nlocal = atom->nlocal;
double dipole = 0.0;
for (int i = 0; i < nlocal; i++) dipole += q[i]*x[i][2];
if (function[3] && atom->mu) {
double **mu = atom->mu;
for (int i = 0; i < nlocal; i++) dipole += mu[i][2];
}
// sum local contributions to get global dipole moment
double dipole_all;
MPI_Allreduce(&dipole,&dipole_all,1,MPI_DOUBLE,MPI_SUM,world);
// need to make non-neutral systems and/or
// per-atom energy translationally invariant
double dipole_r2 = 0.0;
if (eflag_atom || fabs(qsum) > SMALL) {
if (function[3] && atom->mu)
error->all(FLERR,"Cannot (yet) use kspace slab correction with "
"long-range dipoles and non-neutral systems or per-atom energy");
for (int i = 0; i < nlocal; i++)
dipole_r2 += q[i]*x[i][2]*x[i][2];
// sum local contributions
double tmp;
MPI_Allreduce(&dipole_r2,&tmp,1,MPI_DOUBLE,MPI_SUM,world);
dipole_r2 = tmp;
}
// compute corrections
const double e_slabcorr = MY_2PI*(dipole_all*dipole_all -
qsum*dipole_r2 - qsum*qsum*zprd*zprd/12.0)/volume;
const double qscale = force->qqrd2e * scale;
if (eflag_global) energy += qscale * e_slabcorr;
// per-atom energy
if (eflag_atom) {
double efact = qscale * MY_2PI/volume;
for (int i = 0; i < nlocal; i++)
eatom[i] += efact * q[i]*(x[i][2]*dipole_all - 0.5*(dipole_r2 +
qsum*x[i][2]*x[i][2]) - qsum*zprd*zprd/12.0);
}
// add on force corrections
double ffact = qscale * (-4.0*MY_PI/volume);
double **f = atom->f;
for (int i = 0; i < nlocal; i++)
f[i][2] += ffact * q[i]*(dipole_all - qsum*x[i][2]);
// add on torque corrections
if (function[3] && atom->mu && atom->torque) {
double **mu = atom->mu;
double **torque = atom->torque;
for (int i = 0; i < nlocal; i++) {
torque[i][0] += ffact * dipole_all * mu[i][1];
torque[i][1] += -ffact * dipole_all * mu[i][0];
}
}
}
/* ----------------------------------------------------------------------
Newton solver used to find g_ewald for LJ systems
------------------------------------------------------------------------- */
double EwaldDisp::NewtonSolve(double x, double Rc,
bigint natoms, double vol, double b2)
{
double dx,tol;
int maxit;
maxit = 10000; //Maximum number of iterations
tol = 0.00001; //Convergence tolerance
//Begin algorithm
for (int i = 0; i < maxit; i++) {
dx = f(x,Rc,natoms,vol,b2) / derivf(x,Rc,natoms,vol,b2);
x = x - dx; //Update x
if (fabs(dx) < tol) return x;
if (x < 0 || x != x) // solver failed
return -1;
}
return -1;
}
/* ----------------------------------------------------------------------
Calculate f(x)
------------------------------------------------------------------------- */
double EwaldDisp::f(double x, double Rc, bigint natoms, double vol, double b2)
{
double a = Rc*x;
double f = 0.0;
if (function[3]) { // dipole
double rg2 = a*a;
double rg4 = rg2*rg2;
double rg6 = rg4*rg2;
double Cc = 4.0*rg4 + 6.0*rg2 + 3.0;
double Dc = 8.0*rg6 + 20.0*rg4 + 30.0*rg2 + 15.0;
f = (b2/(sqrt(vol*powint(x,4)*powint(Rc,9)*natoms)) *
sqrt(13.0/6.0*Cc*Cc + 2.0/15.0*Dc*Dc - 13.0/15.0*Cc*Dc) *
exp(-rg2)) - accuracy;
} else if (function[1] || function[2]) { // LJ
f = (4.0*MY_PI*b2*powint(x,4)/vol/sqrt((double)natoms)*erfc(a) *
(6.0*powint(a,-5) + 6.0*powint(a,-3) + 3.0/a + a) - accuracy);
}
return f;
}
/* ----------------------------------------------------------------------
Calculate numerical derivative f'(x)
------------------------------------------------------------------------- */
double EwaldDisp::derivf(double x, double Rc,
bigint natoms, double vol, double b2)
{
double h = 0.000001; //Derivative step-size
return (f(x + h,Rc,natoms,vol,b2) - f(x,Rc,natoms,vol,b2)) / h;
}

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