void CINTOpt_setij(CINTOpt *opt, FINT *ng,
FINT *atm, FINT natm,
FINT *bas, FINT nbas, double *env)
{
FINT i, j, ip, jp, io, jo, off;
if (opt->prim_offset == NULL) {
opt->prim_offset = (FINT *)malloc(sizeof(FINT) * nbas);
opt->tot_prim = 0;
for (i = 0; i < nbas; i++) {
opt->prim_offset[i] = opt->tot_prim;
opt->tot_prim += bas(NPRIM_OF, i);
}
}
FINT ijkl_inc;
if ((ng[IINC]+ng[JINC]) > (ng[KINC]+ng[LINC])) {
ijkl_inc = ng[IINC] + ng[JINC];
} else {
ijkl_inc = ng[KINC] + ng[LINC];
}
FINT iprim, ictr, jprim, jctr, il, jl;
double eij, aij, rr, maxci, maxcj, rirj_g4d;
double *ai, *aj, *ri, *rj, *ci, *cj;
double *expij, *rij;
FINT *cceij;
opt->expij = (double **)malloc(sizeof(double *) * opt->tot_prim);
opt->rij = (double **)malloc(sizeof(double *) * opt->tot_prim);
opt->cceij = (FINT **)malloc(sizeof(FINT *) * opt->tot_prim);
for (i = 0; i < nbas; i++) {
ri = env + atm(PTR_COORD,bas(ATOM_OF,i));
ai = env + bas(PTR_EXP,i);
io = opt->prim_offset[i];
iprim = bas(NPRIM_OF,i);
ictr = bas(NCTR_OF,i);
ci = env + bas(PTR_COEFF,i);
// For derivative/dipole operator, the l-value in g2e is virtually increased
il = bas(ANG_OF,i);
for (ip = 0; ip < bas(NPRIM_OF,i); ip++) {
maxci = max_pgto_coeff(ci, iprim, ictr, ip);
maxci = maxci / CINTgto_norm(bas(ANG_OF,i), ai[ip]);
expij = (double *)malloc(sizeof(double)*opt->tot_prim);
rij = (double *)malloc(sizeof(double)*opt->tot_prim*3);
cceij = (FINT *)malloc(sizeof(FINT) * opt->tot_prim);
opt->expij[io+ip] = expij;
opt->rij[io+ip] = rij;
opt->cceij[io+ip] = cceij;
for (j = 0; j < nbas; j++) {
rj = env + atm(PTR_COORD,bas(ATOM_OF,j));
aj = env + bas(PTR_EXP,j);
jo = opt->prim_offset[j];
jprim = bas(NPRIM_OF,j);
jctr = bas(NCTR_OF,j);
cj = env + bas(PTR_COEFF,j);
jl = bas(ANG_OF,j);
rr = (ri[0]-rj[0])*(ri[0]-rj[0])
+ (ri[1]-rj[1])*(ri[1]-rj[1])
+ (ri[2]-rj[2])*(ri[2]-rj[2]);
for (jp = 0; jp < bas(NPRIM_OF,j); jp++) {
maxcj = max_pgto_coeff(cj, jprim, jctr, jp);
maxcj = maxcj / CINTgto_norm(bas(ANG_OF,j), aj[jp]);
aij = ai[ip] + aj[jp];
off = jo + jp;
eij = rr * ai[ip] * aj[jp] / aij;
expij[off] = exp(-eij);
rij[off*3+0] = (ai[ip]*ri[0] + aj[jp]*rj[0]) / aij;
rij[off*3+1] = (ai[ip]*ri[1] + aj[jp]*rj[1]) / aij;
rij[off*3+2] = (ai[ip]*ri[2] + aj[jp]*rj[2]) / aij;
if (maxci*maxcj == 0) {
cceij[off] = 750;
} else if (rr > 1e-12) {
/* value estimation based on g0_2e_2d and g0_xx2d_4d,
* value/exp(-eij) ~< (il+jl+2)!*(aij/2)^(il+jl)*(ri_or_rj-rij)^(ij+jl)*rirj^max(il,jl)
* ~< (il+jl+2)!*(aij/2)^(il+jl)*|rirj|^((il+jl)+max(il,jl))
* But in practice, |rirj|^((il+jl)/2) is large enough to cover all other factors */
rirj_g4d = pow(rr+0.5, (il+jl+ijkl_inc+1)/2);
cceij[off] = eij - log(maxci*maxcj*rirj_g4d);
} else {
/* If basis on the same center, include the (ss|ss)^{1/2} contribution
* (ss|ss) = 2\sqrt{aij/pi} */
cceij[off] = -log(maxci*maxcj) - log(aij)/4;
}
}
}
}
}
}
void CINTOpt_setij(CINTOpt *opt, FINT *ng,
const FINT *atm, const FINT natm,
const FINT *bas, const FINT nbas, const double *env)
{
FINT i, j, ip, jp, io, jo, off;
if (!opt->prim_offset) {
opt->prim_offset = (FINT *)malloc(sizeof(FINT) * nbas);
opt->tot_prim = 0;
for (i = 0; i < nbas; i++) {
opt->prim_offset[i] = opt->tot_prim;
opt->tot_prim += bas(NPRIM_OF, i);
}
}
FINT ik_inc, jl_inc;
if ((ng[IINC]+ng[JINC]) > (ng[KINC]+ng[LINC])) {
ik_inc = ng[IINC];
jl_inc = ng[JINC];
} else {
ik_inc = ng[KINC];
jl_inc = ng[LINC];
}
FINT iprim, ictr, jprim, jctr, il, jl;
double eij, aij, rr, maxci, maxcj, rirj_g4d;
const double *ai, *aj, *ri, *rj, *ci, *cj;
double *expij, *rij;
FINT *cceij;
opt->expij = (double **)malloc(sizeof(double *) * opt->tot_prim);
opt->rij = (double **)malloc(sizeof(double *) * opt->tot_prim);
opt->cceij = (FINT **)malloc(sizeof(FINT *) * opt->tot_prim);
for (i = 0; i < nbas; i++) {
ri = env + atm(PTR_COORD,bas(ATOM_OF,i));
ai = env + bas(PTR_EXP,i);
io = opt->prim_offset[i];
iprim = bas(NPRIM_OF,i);
ictr = bas(NCTR_OF,i);
ci = env + bas(PTR_COEFF,i);
// For derivative/dipole operator, the l-value in g2e is virtually increased
il = bas(ANG_OF,i) + ik_inc;
for (ip = 0; ip < bas(NPRIM_OF,i); ip++) {
maxci = max_pgto_coeff(ci, iprim, ictr, ip);
maxci = maxci / CINTgto_norm(il, ai[ip]);
expij = (double *)malloc(sizeof(double)*opt->tot_prim);
rij = (double *)malloc(sizeof(double)*opt->tot_prim*3);
cceij = (FINT *)malloc(sizeof(FINT) * opt->tot_prim);
opt->expij[io+ip] = expij;
opt->rij[io+ip] = rij;
opt->cceij[io+ip] = cceij;
for (j = 0; j < nbas; j++) {
rj = env + atm(PTR_COORD,bas(ATOM_OF,j));
aj = env + bas(PTR_EXP,j);
jo = opt->prim_offset[j];
jprim = bas(NPRIM_OF,j);
jctr = bas(NCTR_OF,j);
cj = env + bas(PTR_COEFF,j);
jl = bas(ANG_OF,j) + jl_inc;
rr = (ri[0]-rj[0])*(ri[0]-rj[0])
+ (ri[1]-rj[1])*(ri[1]-rj[1])
+ (ri[2]-rj[2])*(ri[2]-rj[2]);
for (jp = 0; jp < bas(NPRIM_OF,j); jp++) {
maxcj = max_pgto_coeff(cj, jprim, jctr, jp);
maxcj = maxcj/CINTgto_norm(jl, aj[jp]);
aij = ai[ip] + aj[jp];
off = jo + jp;
eij = rr * ai[ip] * aj[jp] / aij;
expij[off] = exp(-eij);
rij[off*3+0] = (ai[ip]*ri[0] + aj[jp]*rj[0]) / aij;
rij[off*3+1] = (ai[ip]*ri[1] + aj[jp]*rj[1]) / aij;
rij[off*3+2] = (ai[ip]*ri[2] + aj[jp]*rj[2]) / aij;
/* estimation of the value, based on g0_2e_2d and g0_xx2d_4d,
* value ~< exp(-eij)*(il+jl+2)!*(aij/2)^(il+jl)*(ri_or_rj-rij)^(ij+jl)*rirj^max(il,jl)
* ~< * exp(-eij)*(il+jl+2)!*(aij/2)^(il+jl)*rirj^((il+jl)+max(il,jl))
* But in practice, rirj^((il+jl)/2) is usually large enough to cover all other factors */
/* rr+1 to prevent log() diverge when i,j on same center */
rirj_g4d = pow((rr+1), (il+jl+1)/2);
/*cceij[off] =-log(expij[off]*maxci*maxcj*rirj_g4d);
when eij is big, expij == 0, singular value in cceij */
cceij[off] = eij - log(maxci*maxcj*rirj_g4d);
}
}
}
}
}