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/* Copyright (c) 2019, 2021 MJ Rutter
*
* This program is free software; you can redistribute it and/or
* modify it under the terms of the GNU General Public License as
* published by the Free Software Foundation, either version 3
* of the Licence, or (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, see http://www.gnu.org/licenses/
*/
/* References:
*
* Slab correction: https://doi.org/10.1103/PhysRevB.46.16067
* Molecule in cube: https://doi.org/10.1103/PhysRevB.51.4014
* and https://doi.org/10.1103/PhysRevB.60.15476
* Molecule in tetragon: https://doi.org/10.1088/1361-648X/ab20e1
*/
#include<stdio.h>
#include<stdlib.h>
#include<math.h>
#include "c2xsf.h"
void fft3d(double *c, int *ngptar, int dir);
/* From charge.c */
double quadrupole(struct unit_cell *c, struct contents *m,
struct grid *g, double *ctr);
double quadrupole_ii(struct unit_cell *c, struct contents *m,
struct grid *g, double *ctr, int dir);
void dipole_calc(struct unit_cell *c, struct contents *m,
struct grid *g, double *dipole_ctr, double *dpole){
int i,j,ngx,ngy,ngz,ix,iy,iz;
int nn[3],ii[3];
double i_charge,i_dipole[3],e_charge,e_dipole[3],e_dipole_g[3],d[3];
double ed[3],scale,disp,*ptr,*ptr2,mag;
double *rgrid;
double theta;
i_charge=0;
d[0]=d[1]=d[2]=0;
for(i=0;i<m->n;i++){
i_charge+=m->atoms[i].chg;
for(j=0;j<3;j++){
/* force disp to range 0.5<=disp<=0.5 */
disp=fmod(m->atoms[i].frac[j]-dipole_ctr[j]+0.5,1.0);
if (disp<0) disp+=1;
disp-=0.5;
/* ignore ions split between +/- 0.5 */
if ((aeq(disp,0.5))||(aeq(disp,-0.5))) disp=0;
d[j]+=m->atoms[i].chg*disp;
}
}
/* Convert ionic dipole from fractional to absolute units */
for(i=0;i<3;i++){
i_dipole[i]=0;
for(j=0;j<3;j++)
i_dipole[i]+=d[j]*c->basis[j][i];
}
if (debug){
fprintf(stderr,"Ionic charge is %f\n",i_charge);
fprintf(stderr,"Ionic dipole is (%f,%f,%f)\n",
i_dipole[0],i_dipole[1],i_dipole[2]);
}
ptr=g->data;
if (!ptr) return;
e_charge=0;
ed[0]=ed[1]=ed[2]=0;
scale=c->vol/(g->size[0]*g->size[1]*g->size[2]);
for(ii[0]=0;ii[0]<g->size[0];ii[0]++){
for(ii[1]=0;ii[1]<g->size[1];ii[1]++){
for(ii[2]=0;ii[2]<g->size[2];ii[2]++){
e_charge-=scale*(*ptr);
for(i=0;i<3;i++){
disp=(double)ii[i]/g->size[i]-dipole_ctr[i]; /* BUG!!! */
/* force disp to range 0.5<=disp<=0.5 */
disp=fmod(disp+0.5,1.0);
if (disp<0) disp+=1;
disp-=0.5;
ed[i]-=disp*scale*(*ptr);
}
ptr++;
}
}
}
/* Convert electronic dipole from fractional to absolute units */
for(i=0;i<3;i++){
e_dipole[i]=0;
for(j=0;j<3;j++)
e_dipole[i]+=ed[j]*c->basis[j][i];
}
if (debug>1){
fprintf(stderr,"Electronic charge is %f\n",e_charge);
fprintf(stderr,"Electronic dipole is (%f,%f,%f)\n",
e_dipole[0],e_dipole[1],e_dipole[2]);
}
/* Try calculating the electronic dipole again in reciprocal space */
rgrid=malloc(2*g->size[0]*g->size[1]*g->size[2]*sizeof(double));
if(!rgrid) error_exit("Malloc error in dipole.c");
/* Copy real grid data to complex rgrid prior to FFT */
ptr=g->data;
ptr2=rgrid;
for(i=0;i<g->size[0]*g->size[1]*g->size[2];i++){
*(ptr2++)=*(ptr++);
*(ptr2++)=0;
}
/* FFT */
nn[0]=g->size[2];
nn[1]=g->size[1];
nn[2]=g->size[0];
fft3d(rgrid,nn,-1);
ngx=g->size[0];
ngy=g->size[1];
ngz=g->size[2];
ed[0]=ed[1]=ed[2]=0;
for(i=1;i<ngx;i++){
ix=i;
if (ix>ngx/2) ix=ix-ngx;
theta=2*M_PI*(dipole_ctr[0]-0.5)*ix;
ed[0]-=(rgrid[2*i*ngy*ngz]*sin(theta)+rgrid[2*i*ngy*ngz+1]*cos(theta))/ix;
// ed[0]+=(rgrid[2*i]*sin(theta)+rgrid[2*i+1]*cos(theta))/ix;
}
for(i=1;i<ngy;i++){
iy=i;
if (iy>ngy/2) iy=iy-ngy;
theta=2*M_PI*(dipole_ctr[1]-0.5)*iy;
ed[1]-=(rgrid[2*i*ngz]*sin(theta)+rgrid[2*i*ngz+1]*cos(theta))/iy;
// ed[1]+=(rgrid[2*i*ngx]*sin(theta)+rgrid[2*i*ngx+1]*cos(theta))/iy;
}
for(i=1;i<ngz;i++){
iz=i;
if (iz>ngz/2) iz=iz-ngz;
theta=2*M_PI*(dipole_ctr[2]-0.5)*iz;
ed[2]-=(rgrid[2*i]*sin(theta)+rgrid[2*i+1]*cos(theta))/iz;
}
for(i=0;i<3;i++) ed[i]*=scale/(2*M_PI);
if (debug>2) fprintf(stderr,"Ed: %f %f %f\n",ed[0],ed[1],ed[2]);
/* Convert electronic dipole from fractional to absolute units */
for(i=0;i<3;i++){
e_dipole_g[i]=0;
for(j=0;j<3;j++)
e_dipole_g[i]+=ed[j]*c->basis[j][i];
}
if (debug){
fprintf(stderr,"Elect (g) dipole is (%f,%f,%f)\n",
e_dipole_g[0],e_dipole_g[1],e_dipole_g[2]);
if (debug>1) fprintf(stderr,"g=0 change density is %f+%fi\n",
scale*rgrid[0],scale*rgrid[1]);
}
fprintf(stderr,"Total charge: %f\n",i_charge-scale*rgrid[0]);
if ((fabs(i_charge-scale*rgrid[0])>tol)&&
(!dict_get(m->dict,"dipole_no_charge_warn")))
fprintf(stderr,"Warning: total charge not zero\n");
fprintf(stderr,"Total dipole (eA): (");
for(i=0;i<3;i++) fprintf(stderr,"%f%s",i_dipole[i]+e_dipole_g[i],
(i==2)?"":",");
mag=0;
for(i=0;i<3;i++)
mag+=(i_dipole[i]+e_dipole_g[i])*(i_dipole[i]+e_dipole_g[i]);
mag=sqrt(mag);
fprintf(stderr,") magnitude %f\n",mag);
for(i=0;i<3;i++) dpole[i]=i_dipole[i]+e_dipole_g[i];
free(rgrid);
}
void dipole(struct unit_cell *c, struct contents *m,
struct grid *g, struct es *elect){
double dpole[3],mag,E,*dipole_ctr,v[3];
int i,dipole_slab_dir,c_dir;
double va,vc,dE,mag2,quad;
dipole_ctr=elect->dip_ctr;
fprintf(stderr,"Centre used for moments: (%f,%f,%f)\n",
dipole_ctr[0],dipole_ctr[1],dipole_ctr[2]);
dipole_calc(c,m,g,dipole_ctr,dpole);
if (debug){
fprintf(stderr,"Extra dipole field in V/A: (");
for(i=0;i<3;i++) fprintf(stderr,"%f%s",
(dpole[i])/(EPS0*c->vol),
(i==2)?"":",");
fprintf(stderr,")\n");
}
quad=quadrupole(c,m,g,dipole_ctr);
fprintf(stderr,"Trace of quadrupole tensor (eA^2): %f\n",quad);
for(i=0;i<3;i++){
quad=quadrupole_ii(c,m,g,dipole_ctr,i);
fprintf(stderr," quadrupole_%c%c (eA^2): %f\n",
i+'a',i+'a',quad);
}
if (!elect->dip_corr_dir) return; /* Report, don't correct */
dipole_slab_dir=-1;
if (elect->dip_corr_dir){
dipole_slab_dir=elect->dip_corr_dir[0]-'a';
}
if ((dipole_slab_dir>=0)&&(dipole_slab_dir<=2)){
/* Find unit vector corresponding to dipole slab axis */
for(i=0;i<3;i++)
v[i]=c->basis[dipole_slab_dir][i];
mag=0;
for(i=0;i<3;i++)
mag+=v[i]*v[i];
mag=sqrt(mag);
for(i=0;i<3;i++)
v[i]/=mag;
/* Now have unit vector, so dot with dipole */
mag=0;
for(i=0;i<3;i++)
mag+=v[i]*dpole[i];
E=0.5*mag*mag/(EPS0*c->vol);
fprintf(stderr,"Calculated dipole energy correction (%c axis): %f eV\n",
'a'+dipole_slab_dir,E);
if (elect->energy){
if ((elect->dip_corr==NULL)||(elect->dip_corr[0]=='N'))
fprintf(stderr,"Corrected energy %.6f + %.6f = %.6f eV\n",
*elect->energy,E,*elect->energy+E);
else
fprintf(stderr,"Reported energy of %.6f appears to include "
"a correction already\n",*elect->energy);
}
}
/* Molecules are harder */
if ((elect->dip_corr_dir)&&(*elect->dip_corr_dir=='m')){
double abc[6];
cart2abc(c,NULL,abc,NULL);
if ((aeq(abc[3],90))&&(aeq(abc[4],90))&&(aeq(abc[3],90))){
if ((aeq(abc[0],abc[1]))&&(aeq(abc[1],abc[2]))){
mag=0;
for(i=0;i<3;i++)
mag+=dpole[i]*dpole[i];
E=mag/(6*EPS0*c->vol);
fprintf(stderr,"Calculated dipole energy correction (molecule in cube):"
" %f eV\n",E);
if (elect->energy){
if ((elect->dip_corr==NULL)||(elect->dip_corr[0]=='N'))
fprintf(stderr,"Corrected energy %.6f + %.6f = %.6f eV\n",
*elect->energy,E,*elect->energy+E);
else
fprintf(stderr,"Reported energy of %.6f appears to include "
"a correction already\n",*elect->energy);
}
}
else{
c_dir=-1;
if (aeq(abc[0],abc[1])) c_dir=2;
if (aeq(abc[0],abc[2])) c_dir=1;
if (aeq(abc[1],abc[2])) c_dir=0;
if (c_dir!=-1){
/* Find unit vector corresponding to tetragonal c axis */
for(i=0;i<3;i++)
v[i]=c->basis[c_dir][i];
mag=0;
for(i=0;i<3;i++)
mag+=v[i]*v[i];
mag=sqrt(mag);
for(i=0;i<3;i++)
v[i]/=mag;
/* Now have unit vector, so dot with dipole */
mag=0;
for(i=0;i<3;i++)
mag+=v[i]*dpole[i];
/* Calculate also dipole magnitude */
mag2=0;
for(i=0;i<3;i++)
mag2+=dpole[i]*dpole[i];
mag2=sqrt(mag2);
if (mag2>1.05*fabs(mag))
fprintf(stderr,"Warning: only dipole moment parallel "
"to %c axis corrected\n",'a'+c_dir);
vc=abc[c_dir];
va=abc[0];
if (c_dir==0) va=abc[1];
E=((mag*mag)/(EPS0*va*va))*(1/(2*vc)-1/(3*va));
fprintf(stderr,
"Calculated dipole energy correction (%c axis):"
" %10.6f eV\n",
'a'+c_dir,E);
if (elect->energy){
if ((elect->dip_corr==NULL)||(elect->dip_corr[0]=='N'))
fprintf(stderr,"Corrected energy %14.6f + %10.6f = %14.6f eV\n",
*elect->energy,E,*elect->energy+E);
else
fprintf(stderr,"Reported energy of %.6f appears to include "
"a correction already\n",*elect->energy);
}
dE=-4*M_PI*mag*mag*(exp(-2*M_PI)-exp(-2*M_PI*vc/va))/(EPS0*va*va*va);
fprintf(stderr,"Additional correction if point dipole:"
" %14.6f eV\n",dE);
if (elect->energy){
fprintf(stderr,"Leading to corrected energy of:"
" %14.6f eV\n",
*elect->energy+E+dE);
}
}
else fprintf(stderr,"This version cannot "
"calculate dipole corrections for non-tetragonal cells.\n");
}
}
else
fprintf(stderr,"This version cannot "
"calculate dipole corrections for non-tetragonal cells.\n");
}
}
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