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ewald.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: Roy Pollock (LLNL), Paul Crozier (SNL)
------------------------------------------------------------------------- */
#include "mpi.h"
#include "stdlib.h"
#include "stdio.h"
#include "string.h"
#include "math.h"
#include "ewald.h"
#include "atom.h"
#include "comm.h"
#include "force.h"
#include "pair.h"
#include "domain.h"
#include "memory.h"
#include "error.h"
using namespace LAMMPS_NS;
#define SMALL 0.00001
#define MIN(a,b) ((a) < (b) ? (a) : (b))
#define MAX(a,b) ((a) > (b) ? (a) : (b))
/* ---------------------------------------------------------------------- */
Ewald::Ewald(LAMMPS *lmp, int narg, char **arg) : KSpace(lmp, narg, arg)
{
if (narg != 1) error->all("Illegal kspace_style ewald command");
precision = atof(arg[0]);
PI = 4.0*atan(1.0);
kmax = 0;
kxvecs = kyvecs = kzvecs = NULL;
ug = NULL;
eg = vg = NULL;
sfacrl = sfacim = sfacrl_all = sfacim_all = NULL;
nmax = 0;
ek = NULL;
cs = sn = NULL;
kcount = 0;
}
/* ----------------------------------------------------------------------
free all memory
------------------------------------------------------------------------- */
Ewald::~Ewald()
{
deallocate();
memory->destroy_2d_double_array(ek);
memory->destroy_3d_double_array(cs,-kmax_created);
memory->destroy_3d_double_array(sn,-kmax_created);
}
/* ---------------------------------------------------------------------- */
void Ewald::init()
{
if (comm->me == 0) {
if (screen) fprintf(screen,"Ewald initialization ...\n");
if (logfile) fprintf(logfile,"Ewald initialization ...\n");
}
// error check
if (domain->triclinic) error->all("Cannot use Ewald with triclinic box");
if (domain->dimension == 2)
error->all("Cannot use Ewald with 2d simulation");
if (!atom->q_flag) error->all("Kspace style requires atom attribute q");
if (slabflag == 0 && domain->nonperiodic > 0)
error->all("Cannot use nonperiodic boundaries with Ewald");
if (slabflag == 1) {
if (domain->xperiodic != 1 || domain->yperiodic != 1 ||
domain->boundary[2][0] != 1 || domain->boundary[2][1] != 1)
error->all("Incorrect boundaries with slab Ewald");
}
// extract short-range Coulombic cutoff from pair style
qqrd2e = force->qqrd2e;
scale = 1.0;
if (force->pair == NULL)
error->all("KSpace style is incompatible with Pair style");
int itmp;
double *p_cutoff = (double *) force->pair->extract("cut_coul",itmp);
if (p_cutoff == NULL)
error->all("KSpace style is incompatible with Pair style");
double cutoff = *p_cutoff;
qsum = qsqsum = 0.0;
for (int i = 0; i < atom->nlocal; i++) {
qsum += atom->q[i];
qsqsum += atom->q[i]*atom->q[i];
}
double tmp;
MPI_Allreduce(&qsum,&tmp,1,MPI_DOUBLE,MPI_SUM,world);
qsum = tmp;
MPI_Allreduce(&qsqsum,&tmp,1,MPI_DOUBLE,MPI_SUM,world);
qsqsum = tmp;
if (qsqsum == 0.0)
error->all("Cannot use kspace solver on system with no charge");
if (fabs(qsum) > SMALL && comm->me == 0) {
char str[128];
sprintf(str,"System is not charge neutral, net charge = %g",qsum);
error->warning(str);
}
// setup K-space resolution
if (!gewaldflag) g_ewald = (1.35 - 0.15*log(precision))/cutoff;
gsqmx = -4.0*g_ewald*g_ewald*log(precision);
if (comm->me == 0) {
if (screen) fprintf(screen," G vector = %g\n",g_ewald);
if (logfile) fprintf(logfile," G vector = %g\n",g_ewald);
}
// setup Ewald coefficients so can print stats
setup();
if (comm->me == 0) {
if (screen) fprintf(screen," vectors: actual 1d max = %d %d %d\n",
kcount,kmax,kmax3d);
if (logfile) fprintf(logfile," vectors: actual 1d max = %d %d %d\n",
kcount,kmax,kmax3d);
}
}
/* ----------------------------------------------------------------------
adjust Ewald coeffs, called initially and whenever volume has changed
------------------------------------------------------------------------- */
void Ewald::setup()
{
// volume-dependent factors
double xprd = domain->xprd;
double yprd = domain->yprd;
double zprd = domain->zprd;
// adjustment of z dimension for 2d slab Ewald
// 3d Ewald just uses zprd since slab_volfactor = 1.0
double zprd_slab = zprd*slab_volfactor;
volume = xprd * yprd * zprd_slab;
unitk[0] = 2.0*PI/xprd;
unitk[1] = 2.0*PI/yprd;
unitk[2] = 2.0*PI/zprd_slab;
// determine kmax
// function of current box size, precision, G_ewald (short-range cutoff)
int nkxmx = static_cast<int> ((g_ewald*xprd/PI) * sqrt(-log(precision)));
int nkymx = static_cast<int> ((g_ewald*yprd/PI) * sqrt(-log(precision)));
int nkzmx =
static_cast<int> ((g_ewald*zprd_slab/PI) * sqrt(-log(precision)));
int kmax_old = kmax;
kmax = MAX(nkxmx,nkymx);
kmax = MAX(kmax,nkzmx);
kmax3d = 4*kmax*kmax*kmax + 6*kmax*kmax + 3*kmax;
// if size has grown, reallocate k-dependent and nlocal-dependent arrays
if (kmax > kmax_old) {
deallocate();
allocate();
memory->destroy_2d_double_array(ek);
memory->destroy_3d_double_array(cs,-kmax_created);
memory->destroy_3d_double_array(sn,-kmax_created);
nmax = atom->nmax;
ek = memory->create_2d_double_array(nmax,3,"ewald:ek");
cs = memory->create_3d_double_array(-kmax,kmax,3,nmax,"ewald:cs");
sn = memory->create_3d_double_array(-kmax,kmax,3,nmax,"ewald:sn");
kmax_created = kmax;
}
// pre-compute Ewald coefficients
coeffs();
}
/* ----------------------------------------------------------------------
compute the Ewald long-range force, energy, virial
------------------------------------------------------------------------- */
void Ewald::compute(int eflag, int vflag)
{
int i,k,n;
energy = 0.0;
if (vflag) for (n = 0; n < 6; n++) virial[n] = 0.0;
// extend size of per-atom arrays if necessary
if (atom->nlocal > nmax) {
memory->destroy_2d_double_array(ek);
memory->destroy_3d_double_array(cs,-kmax_created);
memory->destroy_3d_double_array(sn,-kmax_created);
nmax = atom->nmax;
ek = memory->create_2d_double_array(nmax,3,"ewald:ek");
cs = memory->create_3d_double_array(-kmax,kmax,3,nmax,"ewald:cs");
sn = memory->create_3d_double_array(-kmax,kmax,3,nmax,"ewald:sn");
kmax_created = kmax;
}
// partial structure factors on each processor
// total structure factor by summing over procs
eik_dot_r();
MPI_Allreduce(sfacrl,sfacrl_all,kcount,MPI_DOUBLE,MPI_SUM,world);
MPI_Allreduce(sfacim,sfacim_all,kcount,MPI_DOUBLE,MPI_SUM,world);
// K-space portion of electric field
// double loop over K-vectors and local atoms
double **f = atom->f;
double *q = atom->q;
int nlocal = atom->nlocal;
int kx,ky,kz;
double cypz,sypz,exprl,expim,partial;
for (i = 0; i < nlocal; i++) {
ek[i][0] = 0.0;
ek[i][1] = 0.0;
ek[i][2] = 0.0;
}
for (k = 0; k < kcount; k++) {
kx = kxvecs[k];
ky = kyvecs[k];
kz = kzvecs[k];
for (i = 0; i < nlocal; i++) {
cypz = cs[ky][1][i]*cs[kz][2][i] - sn[ky][1][i]*sn[kz][2][i];
sypz = sn[ky][1][i]*cs[kz][2][i] + cs[ky][1][i]*sn[kz][2][i];
exprl = cs[kx][0][i]*cypz - sn[kx][0][i]*sypz;
expim = sn[kx][0][i]*cypz + cs[kx][0][i]*sypz;
partial = expim*sfacrl_all[k] - exprl*sfacim_all[k];
ek[i][0] += partial*eg[k][0];
ek[i][1] += partial*eg[k][1];
ek[i][2] += partial*eg[k][2];
}
}
// convert E-field to force
for (i = 0; i < nlocal; i++) {
f[i][0] += qqrd2e*scale * q[i]*ek[i][0];
f[i][1] += qqrd2e*scale * q[i]*ek[i][1];
f[i][2] += qqrd2e*scale * q[i]*ek[i][2];
}
// energy if requested
if (eflag) {
for (k = 0; k < kcount; k++)
energy += ug[k] * (sfacrl_all[k]*sfacrl_all[k] +
sfacim_all[k]*sfacim_all[k]);
PI = 4.0*atan(1.0);
energy -= g_ewald*qsqsum/1.772453851 +
0.5*PI*qsum*qsum / (g_ewald*g_ewald*volume);
energy *= qqrd2e*scale;
}
// virial if requested
if (vflag) {
double uk;
for (k = 0; k < kcount; k++) {
uk = ug[k] * (sfacrl_all[k]*sfacrl_all[k] + sfacim_all[k]*sfacim_all[k]);
for (n = 0; n < 6; n++) virial[n] += uk*vg[k][n];
}
for (n = 0; n < 6; n++) virial[n] *= qqrd2e*scale;
}
if (slabflag) slabcorr(eflag);
}
/* ---------------------------------------------------------------------- */
void Ewald::eik_dot_r()
{
int i,k,l,m,n,ic;
double cstr1,sstr1,cstr2,sstr2,cstr3,sstr3,cstr4,sstr4;
double sqk,clpm,slpm;
double **x = atom->x;
double *q = atom->q;
int nlocal = atom->nlocal;
n = 0;
// (k,0,0), (0,l,0), (0,0,m)
for (ic = 0; ic < 3; ic++) {
sqk = unitk[ic]*unitk[ic];
if (sqk <= gsqmx) {
cstr1 = 0.0;
sstr1 = 0.0;
for (i = 0; i < nlocal; i++) {
cs[0][ic][i] = 1.0;
sn[0][ic][i] = 0.0;
cs[1][ic][i] = cos(unitk[ic]*x[i][ic]);
sn[1][ic][i] = sin(unitk[ic]*x[i][ic]);
cs[-1][ic][i] = cs[1][ic][i];
sn[-1][ic][i] = -sn[1][ic][i];
cstr1 += q[i]*cs[1][ic][i];
sstr1 += q[i]*sn[1][ic][i];
}
sfacrl[n] = cstr1;
sfacim[n++] = sstr1;
}
}
for (m = 2; m <= kmax; m++) {
for (ic = 0; ic < 3; ic++) {
sqk = m*unitk[ic] * m*unitk[ic];
if (sqk <= gsqmx) {
cstr1 = 0.0;
sstr1 = 0.0;
for (i = 0; i < nlocal; i++) {
cs[m][ic][i] = cs[m-1][ic][i]*cs[1][ic][i] -
sn[m-1][ic][i]*sn[1][ic][i];
sn[m][ic][i] = sn[m-1][ic][i]*cs[1][ic][i] +
cs[m-1][ic][i]*sn[1][ic][i];
cs[-m][ic][i] = cs[m][ic][i];
sn[-m][ic][i] = -sn[m][ic][i];
cstr1 += q[i]*cs[m][ic][i];
sstr1 += q[i]*sn[m][ic][i];
}
sfacrl[n] = cstr1;
sfacim[n++] = sstr1;
}
}
}
// 1 = (k,l,0), 2 = (k,-l,0)
for (k = 1; k <= kmax; k++) {
for (l = 1; l <= kmax; l++) {
sqk = (k*unitk[0] * k*unitk[0]) + (l*unitk[1] * l*unitk[1]);
if (sqk <= gsqmx) {
cstr1 = 0.0;
sstr1 = 0.0;
cstr2 = 0.0;
sstr2 = 0.0;
for (i = 0; i < nlocal; i++) {
cstr1 += q[i]*(cs[k][0][i]*cs[l][1][i] - sn[k][0][i]*sn[l][1][i]);
sstr1 += q[i]*(sn[k][0][i]*cs[l][1][i] + cs[k][0][i]*sn[l][1][i]);
cstr2 += q[i]*(cs[k][0][i]*cs[l][1][i] + sn[k][0][i]*sn[l][1][i]);
sstr2 += q[i]*(sn[k][0][i]*cs[l][1][i] - cs[k][0][i]*sn[l][1][i]);
}
sfacrl[n] = cstr1;
sfacim[n++] = sstr1;
sfacrl[n] = cstr2;
sfacim[n++] = sstr2;
}
}
}
// 1 = (0,l,m), 2 = (0,l,-m)
for (l = 1; l <= kmax; l++) {
for (m = 1; m <= kmax; m++) {
sqk = (l*unitk[1] * l*unitk[1]) + (m*unitk[2] * m*unitk[2]);
if (sqk <= gsqmx) {
cstr1 = 0.0;
sstr1 = 0.0;
cstr2 = 0.0;
sstr2 = 0.0;
for (i = 0; i < nlocal; i++) {
cstr1 += q[i]*(cs[l][1][i]*cs[m][2][i] - sn[l][1][i]*sn[m][2][i]);
sstr1 += q[i]*(sn[l][1][i]*cs[m][2][i] + cs[l][1][i]*sn[m][2][i]);
cstr2 += q[i]*(cs[l][1][i]*cs[m][2][i] + sn[l][1][i]*sn[m][2][i]);
sstr2 += q[i]*(sn[l][1][i]*cs[m][2][i] - cs[l][1][i]*sn[m][2][i]);
}
sfacrl[n] = cstr1;
sfacim[n++] = sstr1;
sfacrl[n] = cstr2;
sfacim[n++] = sstr2;
}
}
}
// 1 = (k,0,m), 2 = (k,0,-m)
for (k = 1; k <= kmax; k++) {
for (m = 1; m <= kmax; m++) {
sqk = (k*unitk[0] * k*unitk[0]) + (m*unitk[2] * m*unitk[2]);
if (sqk <= gsqmx) {
cstr1 = 0.0;
sstr1 = 0.0;
cstr2 = 0.0;
sstr2 = 0.0;
for (i = 0; i < nlocal; i++) {
cstr1 += q[i]*(cs[k][0][i]*cs[m][2][i] - sn[k][0][i]*sn[m][2][i]);
sstr1 += q[i]*(sn[k][0][i]*cs[m][2][i] + cs[k][0][i]*sn[m][2][i]);
cstr2 += q[i]*(cs[k][0][i]*cs[m][2][i] + sn[k][0][i]*sn[m][2][i]);
sstr2 += q[i]*(sn[k][0][i]*cs[m][2][i] - cs[k][0][i]*sn[m][2][i]);
}
sfacrl[n] = cstr1;
sfacim[n++] = sstr1;
sfacrl[n] = cstr2;
sfacim[n++] = sstr2;
}
}
}
// 1 = (k,l,m), 2 = (k,-l,m), 3 = (k,l,-m), 4 = (k,-l,-m)
for (k = 1; k <= kmax; k++) {
for (l = 1; l <= kmax; l++) {
for (m = 1; m <= kmax; m++) {
sqk = (k*unitk[0] * k*unitk[0]) + (l*unitk[1] * l*unitk[1]) +
(m*unitk[2] * m*unitk[2]);
if (sqk <= gsqmx) {
cstr1 = 0.0;
sstr1 = 0.0;
cstr2 = 0.0;
sstr2 = 0.0;
cstr3 = 0.0;
sstr3 = 0.0;
cstr4 = 0.0;
sstr4 = 0.0;
for (i = 0; i < nlocal; i++) {
clpm = cs[l][1][i]*cs[m][2][i] - sn[l][1][i]*sn[m][2][i];
slpm = sn[l][1][i]*cs[m][2][i] + cs[l][1][i]*sn[m][2][i];
cstr1 += q[i]*(cs[k][0][i]*clpm - sn[k][0][i]*slpm);
sstr1 += q[i]*(sn[k][0][i]*clpm + cs[k][0][i]*slpm);
clpm = cs[l][1][i]*cs[m][2][i] + sn[l][1][i]*sn[m][2][i];
slpm = -sn[l][1][i]*cs[m][2][i] + cs[l][1][i]*sn[m][2][i];
cstr2 += q[i]*(cs[k][0][i]*clpm - sn[k][0][i]*slpm);
sstr2 += q[i]*(sn[k][0][i]*clpm + cs[k][0][i]*slpm);
clpm = cs[l][1][i]*cs[m][2][i] + sn[l][1][i]*sn[m][2][i];
slpm = sn[l][1][i]*cs[m][2][i] - cs[l][1][i]*sn[m][2][i];
cstr3 += q[i]*(cs[k][0][i]*clpm - sn[k][0][i]*slpm);
sstr3 += q[i]*(sn[k][0][i]*clpm + cs[k][0][i]*slpm);
clpm = cs[l][1][i]*cs[m][2][i] - sn[l][1][i]*sn[m][2][i];
slpm = -sn[l][1][i]*cs[m][2][i] - cs[l][1][i]*sn[m][2][i];
cstr4 += q[i]*(cs[k][0][i]*clpm - sn[k][0][i]*slpm);
sstr4 += q[i]*(sn[k][0][i]*clpm + cs[k][0][i]*slpm);
}
sfacrl[n] = cstr1;
sfacim[n++] = sstr1;
sfacrl[n] = cstr2;
sfacim[n++] = sstr2;
sfacrl[n] = cstr3;
sfacim[n++] = sstr3;
sfacrl[n] = cstr4;
sfacim[n++] = sstr4;
}
}
}
}
}
/* ----------------------------------------------------------------------
pre-compute coefficients for each Ewald K-vector
------------------------------------------------------------------------- */
void Ewald::coeffs()
{
int k,l,m;
double sqk,vterm;
double unitkx = unitk[0];
double unitky = unitk[1];
double unitkz = unitk[2];
double g_ewald_sq_inv = 1.0 / (g_ewald*g_ewald);
double preu = 4.0*PI/volume;
kcount = 0;
// (k,0,0), (0,l,0), (0,0,m)
for (m = 1; m <= kmax; m++) {
sqk = (m*unitkx) * (m*unitkx);
if (sqk <= gsqmx) {
kxvecs[kcount] = m;
kyvecs[kcount] = 0;
kzvecs[kcount] = 0;
ug[kcount] = preu*exp(-0.25*sqk*g_ewald_sq_inv)/sqk;
eg[kcount][0] = 2.0*unitkx*m*ug[kcount];
eg[kcount][1] = 0.0;
eg[kcount][2] = 0.0;
vterm = -2.0*(1.0/sqk + 0.25*g_ewald_sq_inv);
vg[kcount][0] = 1.0 + vterm*(unitkx*m)*(unitkx*m);
vg[kcount][1] = 1.0;
vg[kcount][2] = 1.0;
vg[kcount][3] = 0.0;
vg[kcount][4] = 0.0;
vg[kcount][5] = 0.0;
kcount++;
}
sqk = (m*unitky) * (m*unitky);
if (sqk <= gsqmx) {
kxvecs[kcount] = 0;
kyvecs[kcount] = m;
kzvecs[kcount] = 0;
ug[kcount] = preu*exp(-0.25*sqk*g_ewald_sq_inv)/sqk;
eg[kcount][0] = 0.0;
eg[kcount][1] = 2.0*unitky*m*ug[kcount];
eg[kcount][2] = 0.0;
vterm = -2.0*(1.0/sqk + 0.25*g_ewald_sq_inv);
vg[kcount][0] = 1.0;
vg[kcount][1] = 1.0 + vterm*(unitky*m)*(unitky*m);
vg[kcount][2] = 1.0;
vg[kcount][3] = 0.0;
vg[kcount][4] = 0.0;
vg[kcount][5] = 0.0;
kcount++;
}
sqk = (m*unitkz) * (m*unitkz);
if (sqk <= gsqmx) {
kxvecs[kcount] = 0;
kyvecs[kcount] = 0;
kzvecs[kcount] = m;
ug[kcount] = preu*exp(-0.25*sqk*g_ewald_sq_inv)/sqk;
eg[kcount][0] = 0.0;
eg[kcount][1] = 0.0;
eg[kcount][2] = 2.0*unitkz*m*ug[kcount];
vterm = -2.0*(1.0/sqk + 0.25*g_ewald_sq_inv);
vg[kcount][0] = 1.0;
vg[kcount][1] = 1.0;
vg[kcount][2] = 1.0 + vterm*(unitkz*m)*(unitkz*m);
vg[kcount][3] = 0.0;
vg[kcount][4] = 0.0;
vg[kcount][5] = 0.0;
kcount++;
}
}
// 1 = (k,l,0), 2 = (k,-l,0)
for (k = 1; k <= kmax; k++) {
for (l = 1; l <= kmax; l++) {
sqk = (unitkx*k) * (unitkx*k) + (unitky*l) * (unitky*l);
if (sqk <= gsqmx) {
kxvecs[kcount] = k;
kyvecs[kcount] = l;
kzvecs[kcount] = 0;
ug[kcount] = preu*exp(-0.25*sqk*g_ewald_sq_inv)/sqk;
eg[kcount][0] = 2.0*unitkx*k*ug[kcount];
eg[kcount][1] = 2.0*unitky*l*ug[kcount];
eg[kcount][2] = 0.0;
vterm = -2.0*(1.0/sqk + 0.25*g_ewald_sq_inv);
vg[kcount][0] = 1.0 + vterm*(unitkx*k)*(unitkx*k);
vg[kcount][1] = 1.0 + vterm*(unitky*l)*(unitky*l);
vg[kcount][2] = 1.0;
vg[kcount][3] = vterm*unitkx*k*unitky*l;
vg[kcount][4] = 0.0;
vg[kcount][5] = 0.0;
kcount++;
kxvecs[kcount] = k;
kyvecs[kcount] = -l;
kzvecs[kcount] = 0;
ug[kcount] = preu*exp(-0.25*sqk*g_ewald_sq_inv)/sqk;
eg[kcount][0] = 2.0*unitkx*k*ug[kcount];
eg[kcount][1] = -2.0*unitky*l*ug[kcount];
eg[kcount][2] = 0.0;
vg[kcount][0] = 1.0 + vterm*(unitkx*k)*(unitkx*k);
vg[kcount][1] = 1.0 + vterm*(unitky*l)*(unitky*l);
vg[kcount][2] = 1.0;
vg[kcount][3] = -vterm*unitkx*k*unitky*l;
vg[kcount][4] = 0.0;
vg[kcount][5] = 0.0;
kcount++;;
}
}
}
// 1 = (0,l,m), 2 = (0,l,-m)
for (l = 1; l <= kmax; l++) {
for (m = 1; m <= kmax; m++) {
sqk = (unitky*l) * (unitky*l) + (unitkz*m) * (unitkz*m);
if (sqk <= gsqmx) {
kxvecs[kcount] = 0;
kyvecs[kcount] = l;
kzvecs[kcount] = m;
ug[kcount] = preu*exp(-0.25*sqk*g_ewald_sq_inv)/sqk;
eg[kcount][0] = 0.0;
eg[kcount][1] = 2.0*unitky*l*ug[kcount];
eg[kcount][2] = 2.0*unitkz*m*ug[kcount];
vterm = -2.0*(1.0/sqk + 0.25*g_ewald_sq_inv);
vg[kcount][0] = 1.0;
vg[kcount][1] = 1.0 + vterm*(unitky*l)*(unitky*l);
vg[kcount][2] = 1.0 + vterm*(unitkz*m)*(unitkz*m);
vg[kcount][3] = 0.0;
vg[kcount][4] = 0.0;
vg[kcount][5] = vterm*unitky*l*unitkz*m;
kcount++;
kxvecs[kcount] = 0;
kyvecs[kcount] = l;
kzvecs[kcount] = -m;
ug[kcount] = preu*exp(-0.25*sqk*g_ewald_sq_inv)/sqk;
eg[kcount][0] = 0.0;
eg[kcount][1] = 2.0*unitky*l*ug[kcount];
eg[kcount][2] = -2.0*unitkz*m*ug[kcount];
vg[kcount][0] = 1.0;
vg[kcount][1] = 1.0 + vterm*(unitky*l)*(unitky*l);
vg[kcount][2] = 1.0 + vterm*(unitkz*m)*(unitkz*m);
vg[kcount][3] = 0.0;
vg[kcount][4] = 0.0;
vg[kcount][5] = -vterm*unitky*l*unitkz*m;
kcount++;
}
}
}
// 1 = (k,0,m), 2 = (k,0,-m)
for (k = 1; k <= kmax; k++) {
for (m = 1; m <= kmax; m++) {
sqk = (unitkx*k) * (unitkx*k) + (unitkz*m) * (unitkz*m);
if (sqk <= gsqmx) {
kxvecs[kcount] = k;
kyvecs[kcount] = 0;
kzvecs[kcount] = m;
ug[kcount] = preu*exp(-0.25*sqk*g_ewald_sq_inv)/sqk;
eg[kcount][0] = 2.0*unitkx*k*ug[kcount];
eg[kcount][1] = 0.0;
eg[kcount][2] = 2.0*unitkz*m*ug[kcount];
vterm = -2.0*(1.0/sqk + 0.25*g_ewald_sq_inv);
vg[kcount][0] = 1.0 + vterm*(unitkx*k)*(unitkx*k);
vg[kcount][1] = 1.0;
vg[kcount][2] = 1.0 + vterm*(unitkz*m)*(unitkz*m);
vg[kcount][3] = 0.0;
vg[kcount][4] = vterm*unitkx*k*unitkz*m;
vg[kcount][5] = 0.0;
kcount++;
kxvecs[kcount] = k;
kyvecs[kcount] = 0;
kzvecs[kcount] = -m;
ug[kcount] = preu*exp(-0.25*sqk*g_ewald_sq_inv)/sqk;
eg[kcount][0] = 2.0*unitkx*k*ug[kcount];
eg[kcount][1] = 0.0;
eg[kcount][2] = -2.0*unitkz*m*ug[kcount];
vg[kcount][0] = 1.0 + vterm*(unitkx*k)*(unitkx*k);
vg[kcount][1] = 1.0;
vg[kcount][2] = 1.0 + vterm*(unitkz*m)*(unitkz*m);
vg[kcount][3] = 0.0;
vg[kcount][4] = -vterm*unitkx*k*unitkz*m;
vg[kcount][5] = 0.0;
kcount++;
}
}
}
// 1 = (k,l,m), 2 = (k,-l,m), 3 = (k,l,-m), 4 = (k,-l,-m)
for (k = 1; k <= kmax; k++) {
for (l = 1; l <= kmax; l++) {
for (m = 1; m <= kmax; m++) {
sqk = (unitkx*k) * (unitkx*k) + (unitky*l) * (unitky*l) +
(unitkz*m) * (unitkz*m);
if (sqk <= gsqmx) {
kxvecs[kcount] = k;
kyvecs[kcount] = l;
kzvecs[kcount] = m;
ug[kcount] = preu*exp(-0.25*sqk*g_ewald_sq_inv)/sqk;
eg[kcount][0] = 2.0*unitkx*k*ug[kcount];
eg[kcount][1] = 2.0*unitky*l*ug[kcount];
eg[kcount][2] = 2.0*unitkz*m*ug[kcount];
vterm = -2.0*(1.0/sqk + 0.25*g_ewald_sq_inv);
vg[kcount][0] = 1.0 + vterm*(unitkx*k)*(unitkx*k);
vg[kcount][1] = 1.0 + vterm*(unitky*l)*(unitky*l);
vg[kcount][2] = 1.0 + vterm*(unitkz*m)*(unitkz*m);
vg[kcount][3] = vterm*unitkx*k*unitky*l;
vg[kcount][4] = vterm*unitkx*k*unitkz*m;
vg[kcount][5] = vterm*unitky*l*unitkz*m;
kcount++;
kxvecs[kcount] = k;
kyvecs[kcount] = -l;
kzvecs[kcount] = m;
ug[kcount] = preu*exp(-0.25*sqk*g_ewald_sq_inv)/sqk;
eg[kcount][0] = 2.0*unitkx*k*ug[kcount];
eg[kcount][1] = -2.0*unitky*l*ug[kcount];
eg[kcount][2] = 2.0*unitkz*m*ug[kcount];
vg[kcount][0] = 1.0 + vterm*(unitkx*k)*(unitkx*k);
vg[kcount][1] = 1.0 + vterm*(unitky*l)*(unitky*l);
vg[kcount][2] = 1.0 + vterm*(unitkz*m)*(unitkz*m);
vg[kcount][3] = -vterm*unitkx*k*unitky*l;
vg[kcount][4] = vterm*unitkx*k*unitkz*m;
vg[kcount][5] = -vterm*unitky*l*unitkz*m;
kcount++;
kxvecs[kcount] = k;
kyvecs[kcount] = l;
kzvecs[kcount] = -m;
ug[kcount] = preu*exp(-0.25*sqk*g_ewald_sq_inv)/sqk;
eg[kcount][0] = 2.0*unitkx*k*ug[kcount];
eg[kcount][1] = 2.0*unitky*l*ug[kcount];
eg[kcount][2] = -2.0*unitkz*m*ug[kcount];
vg[kcount][0] = 1.0 + vterm*(unitkx*k)*(unitkx*k);
vg[kcount][1] = 1.0 + vterm*(unitky*l)*(unitky*l);
vg[kcount][2] = 1.0 + vterm*(unitkz*m)*(unitkz*m);
vg[kcount][3] = vterm*unitkx*k*unitky*l;
vg[kcount][4] = -vterm*unitkx*k*unitkz*m;
vg[kcount][5] = -vterm*unitky*l*unitkz*m;
kcount++;
kxvecs[kcount] = k;
kyvecs[kcount] = -l;
kzvecs[kcount] = -m;
ug[kcount] = preu*exp(-0.25*sqk*g_ewald_sq_inv)/sqk;
eg[kcount][0] = 2.0*unitkx*k*ug[kcount];
eg[kcount][1] = -2.0*unitky*l*ug[kcount];
eg[kcount][2] = -2.0*unitkz*m*ug[kcount];
vg[kcount][0] = 1.0 + vterm*(unitkx*k)*(unitkx*k);
vg[kcount][1] = 1.0 + vterm*(unitky*l)*(unitky*l);
vg[kcount][2] = 1.0 + vterm*(unitkz*m)*(unitkz*m);
vg[kcount][3] = -vterm*unitkx*k*unitky*l;
vg[kcount][4] = -vterm*unitkx*k*unitkz*m;
vg[kcount][5] = vterm*unitky*l*unitkz*m;
kcount++;;
}
}
}
}
}
/* ----------------------------------------------------------------------
allocate memory that depends on # of K-vectors
------------------------------------------------------------------------- */
void Ewald::allocate()
{
kxvecs = new int[kmax3d];
kyvecs = new int[kmax3d];
kzvecs = new int[kmax3d];
ug = new double[kmax3d];
eg = memory->create_2d_double_array(kmax3d,3,"ewald:eg");
vg = memory->create_2d_double_array(kmax3d,6,"ewald:vg");
sfacrl = new double[kmax3d];
sfacim = new double[kmax3d];
sfacrl_all = new double[kmax3d];
sfacim_all = new double[kmax3d];
}
/* ----------------------------------------------------------------------
deallocate memory that depends on # of K-vectors
------------------------------------------------------------------------- */
void Ewald::deallocate()
{
delete [] kxvecs;
delete [] kyvecs;
delete [] kzvecs;
delete [] ug;
memory->destroy_2d_double_array(eg);
memory->destroy_2d_double_array(vg);
delete [] sfacrl;
delete [] sfacim;
delete [] sfacrl_all;
delete [] sfacim_all;
}
/* ----------------------------------------------------------------------
Slab-geometry correction term to dampen inter-slab interactions between
periodically repeating slabs. Yields good approximation to 2-D 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.
------------------------------------------------------------------------- */
void Ewald::slabcorr(int eflag)
{
// compute local contribution to global dipole moment
double *q = atom->q;
double **x = atom->x;
int nlocal = atom->nlocal;
double dipole = 0.0;
for (int i = 0; i < nlocal; i++) dipole += q[i]*x[i][2];
// sum local contributions to get global dipole moment
double dipole_all;
MPI_Allreduce(&dipole,&dipole_all,1,MPI_DOUBLE,MPI_SUM,world);
// compute corrections
double e_slabcorr = 2.0*PI*dipole_all*dipole_all/volume;
if (eflag) energy += qqrd2e*scale * e_slabcorr;
// add on force corrections
double ffact = -4.0*PI*dipole_all/volume;
double **f = atom->f;
for (int i = 0; i < nlocal; i++) f[i][2] += qqrd2e*scale * q[i]*ffact;
}
/* ----------------------------------------------------------------------
memory usage of local arrays
------------------------------------------------------------------------- */
double Ewald::memory_usage()
{
double bytes = 3 * kmax3d * sizeof(int);
bytes += (1 + 3 + 6) * kmax3d * sizeof(double);
bytes += 4 * kmax3d * sizeof(double);
bytes += nmax*3 * sizeof(double);
bytes += 2 * (2*kmax+1)*3*nmax * sizeof(double);
return bytes;
}

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