/*
* Reference:
*
* Ivana Adamovic, Mark Gordon
*
* Dynamic polarizability, dispersion coefficient C6 and dispersion energy in
* the effective fragment potential method
*
* Mol. Phys. 103, 379 (2005)
*/
double
efp_frag_frag_disp(struct efp *efp, size_t frag_i, size_t frag_j,
const double *s, const six_t *ds)
{
double energy = 0.0;
struct frag *fr_i = efp->frags + frag_i;
struct frag *fr_j = efp->frags + frag_j;
size_t n_disp_i = fr_i->n_dynamic_polarizable_pts;
size_t n_disp_j = fr_j->n_dynamic_polarizable_pts;
struct swf swf = efp_make_swf(efp, fr_i, fr_j);
for (size_t ii = 0, idx = 0; ii < n_disp_i; ii++)
for (size_t jj = 0; jj < n_disp_j; jj++, idx++)
energy += point_point_disp(efp, frag_i, frag_j, ii, jj,
s[idx], ds[idx], &swf);
vec_t force = {
swf.dswf.x * energy,
swf.dswf.y * energy,
swf.dswf.z * energy
};
six_atomic_add_xyz(efp->grad + frag_i, &force);
six_atomic_sub_xyz(efp->grad + frag_j, &force);
efp_add_stress(&swf.dr, &force, &efp->stress);
return energy * swf.swf;
}
static void
get_induced_dipole_field(struct efp *efp, size_t frag_idx,
struct polarizable_pt *pt,
vec_t *field, vec_t *field_conj)
{
struct frag *fr_i = efp->frags + frag_idx;
*field = vec_zero;
*field_conj = vec_zero;
for (size_t j = 0; j < efp->n_frag; j++) {
if (j == frag_idx || efp_skip_frag_pair(efp, frag_idx, j))
continue;
struct frag *fr_j = efp->frags + j;
struct swf swf = efp_make_swf(efp, fr_i, fr_j);
for (size_t jj = 0; jj < fr_j->n_polarizable_pts; jj++) {
struct polarizable_pt *pt_j = fr_j->polarizable_pts + jj;
size_t idx = fr_j->polarizable_offset + jj;
vec_t dr = {
pt->x - pt_j->x + swf.cell.x,
pt->y - pt_j->y + swf.cell.y,
pt->z - pt_j->z + swf.cell.z
};
double r = vec_len(&dr);
double r3 = r * r * r;
double r5 = r3 * r * r;
double t1 = vec_dot(&efp->indip[idx], &dr);
double t2 = vec_dot(&efp->indipconj[idx], &dr);
double p1 = 1.0;
if (efp->opts.pol_damp == EFP_POL_DAMP_TT)
p1 = efp_get_pol_damp_tt(r, fr_i->pol_damp, fr_j->pol_damp);
field->x -= swf.swf * p1 * (efp->indip[idx].x / r3 -
3.0 * t1 * dr.x / r5);
field->y -= swf.swf * p1 * (efp->indip[idx].y / r3 -
3.0 * t1 * dr.y / r5);
field->z -= swf.swf * p1 * (efp->indip[idx].z / r3 -
3.0 * t1 * dr.z / r5);
field_conj->x -= swf.swf * p1 * (efp->indipconj[idx].x / r3 -
3.0 * t2 * dr.x / r5);
field_conj->y -= swf.swf * p1 * (efp->indipconj[idx].y / r3 -
3.0 * t2 * dr.y / r5);
field_conj->z -= swf.swf * p1 * (efp->indipconj[idx].z / r3 -
3.0 * t2 * dr.z / r5);
}
}
}
static mat_t
get_int_mat(const struct efp *efp, size_t i, size_t j, size_t ii, size_t jj)
{
mat_t m;
const struct frag *fr_i = efp->frags + i;
const struct frag *fr_j = efp->frags + j;
const struct polarizable_pt *pt_i = fr_i->polarizable_pts + ii;
const struct polarizable_pt *pt_j = fr_j->polarizable_pts + jj;
struct swf swf = efp_make_swf(efp, fr_i, fr_j);
vec_t dr = {
pt_j->x - pt_i->x - swf.cell.x,
pt_j->y - pt_i->y - swf.cell.y,
pt_j->z - pt_i->z - swf.cell.z
};
double p1 = 1.0;
double r = vec_len(&dr);
double r3 = r * r * r;
double r5 = r3 * r * r;
if (efp->opts.pol_damp == EFP_POL_DAMP_TT)
p1 = efp_get_pol_damp_tt(r, fr_i->pol_damp, fr_j->pol_damp);
m.xx = swf.swf * p1 * (3.0 * dr.x * dr.x / r5 - 1.0 / r3);
m.xy = swf.swf * p1 * 3.0 * dr.x * dr.y / r5;
m.xz = swf.swf * p1 * 3.0 * dr.x * dr.z / r5;
m.yx = swf.swf * p1 * 3.0 * dr.y * dr.x / r5;
m.yy = swf.swf * p1 * (3.0 * dr.y * dr.y / r5 - 1.0 / r3);
m.yz = swf.swf * p1 * 3.0 * dr.y * dr.z / r5;
m.zx = swf.swf * p1 * 3.0 * dr.z * dr.x / r5;
m.zy = swf.swf * p1 * 3.0 * dr.z * dr.y / r5;
m.zz = swf.swf * p1 * (3.0 * dr.z * dr.z / r5 - 1.0 / r3);
return m;
}
EFP_EXPORT enum efp_result
efp_get_electric_field(struct efp *efp, size_t frag_idx, const double *xyz, double *field)
{
assert(efp);
assert(frag_idx < efp->n_frag);
assert(xyz);
assert(field);
const struct frag *frag = efp->frags + frag_idx;
vec_t elec_field = vec_zero;
for (size_t i = 0; i < efp->n_frag; i++) {
if (i == frag_idx || efp_skip_frag_pair(efp, i, frag_idx))
continue;
const struct frag *fr_i = efp->frags + i;
struct swf swf = efp_make_swf(efp, fr_i, frag);
/* field due to nuclei */
for (size_t j = 0; j < fr_i->n_atoms; j++) {
const struct efp_atom *at = fr_i->atoms + j;
vec_t dr = {
xyz[0] - at->x - swf.cell.x,
xyz[1] - at->y - swf.cell.y,
xyz[2] - at->z - swf.cell.z
};
double r = vec_len(&dr);
double r3 = r * r * r;
elec_field.x += swf.swf * at->znuc * dr.x / r3;
elec_field.y += swf.swf * at->znuc * dr.y / r3;
elec_field.z += swf.swf * at->znuc * dr.z / r3;
}
/* field due to multipoles */
for (size_t j = 0; j < fr_i->n_multipole_pts; j++) {
const struct multipole_pt *mpt = fr_i->multipole_pts + j;
vec_t mult_field = get_multipole_field((const vec_t *)xyz, mpt, &swf);
elec_field.x += mult_field.x;
elec_field.y += mult_field.y;
elec_field.z += mult_field.z;
}
/* field due to induced dipoles */
for (size_t j = 0; j < fr_i->n_polarizable_pts; j++) {
struct polarizable_pt *pt_i = fr_i->polarizable_pts + j;
size_t idx = fr_i->polarizable_offset + j;
vec_t dr = {
xyz[0] - pt_i->x - swf.cell.x,
xyz[1] - pt_i->y - swf.cell.y,
xyz[2] - pt_i->z - swf.cell.z
};
double r = vec_len(&dr);
double r3 = r * r * r;
double r5 = r3 * r * r;
double t1 = vec_dot(&efp->indip[idx], &dr);
elec_field.x -= swf.swf * (efp->indip[idx].x / r3 -
3.0 * t1 * dr.x / r5);
elec_field.y -= swf.swf * (efp->indip[idx].y / r3 -
3.0 * t1 * dr.y / r5);
elec_field.z -= swf.swf * (efp->indip[idx].z / r3 -
3.0 * t1 * dr.z / r5);
}
}
if (efp->opts.terms & EFP_TERM_AI_POL) {
/* field due to nuclei from ab initio subsystem */
for (size_t i = 0; i < efp->n_ptc; i++) {
vec_t dr = vec_sub((const vec_t *)xyz, efp->ptc_xyz + i);
double r = vec_len(&dr);
double r3 = r * r * r;
elec_field.x += efp->ptc[i] * dr.x / r3;
elec_field.y += efp->ptc[i] * dr.y / r3;
elec_field.z += efp->ptc[i] * dr.z / r3;
}
}
*((vec_t *)field) = elec_field;
return (EFP_RESULT_SUCCESS);
}
static void
compute_grad_point(struct efp *efp, size_t frag_idx, size_t pt_idx)
{
const struct frag *fr_i = efp->frags + frag_idx;
const struct polarizable_pt *pt_i = fr_i->polarizable_pts + pt_idx;
size_t idx_i = fr_i->polarizable_offset + pt_idx;
vec_t dipole_i = {
0.5 * (efp->indip[idx_i].x + efp->indipconj[idx_i].x),
0.5 * (efp->indip[idx_i].y + efp->indipconj[idx_i].y),
0.5 * (efp->indip[idx_i].z + efp->indipconj[idx_i].z)
};
for (size_t j = 0; j < efp->n_frag; j++) {
if (j == frag_idx || efp_skip_frag_pair(efp, frag_idx, j))
continue;
struct frag *fr_j = efp->frags + j;
struct swf swf = efp_make_swf(efp, fr_i, fr_j);
/* energy without switching applied */
double energy = 0.0;
/* induced dipole - nuclei */
for (size_t k = 0; k < fr_j->n_atoms; k++) {
struct efp_atom *at_j = fr_j->atoms + k;
vec_t dr = {
at_j->x - pt_i->x - swf.cell.x,
at_j->y - pt_i->y - swf.cell.y,
at_j->z - pt_i->z - swf.cell.z
};
double p1 = 1.0, p2 = 0.0;
if (efp->opts.pol_damp == EFP_POL_DAMP_TT) {
double r = vec_len(&dr);
p1 = efp_get_pol_damp_tt(r, fr_i->pol_damp,
fr_j->pol_damp);
p2 = efp_get_pol_damp_tt_grad(r, fr_i->pol_damp,
fr_j->pol_damp);
}
vec_t force, add_i, add_j;
double e = -efp_charge_dipole_energy(at_j->znuc, &dipole_i, &dr);
efp_charge_dipole_grad(at_j->znuc, &dipole_i, &dr,
&force, &add_j, &add_i);
vec_negate(&force);
vec_scale(&force, p1);
vec_scale(&add_i, p1);
vec_scale(&add_j, p1);
force.x += p2 * e * dr.x;
force.y += p2 * e * dr.y;
force.z += p2 * e * dr.z;
vec_scale(&force, swf.swf);
vec_scale(&add_i, swf.swf);
vec_scale(&add_j, swf.swf);
efp_add_force(efp->grad + frag_idx, CVEC(fr_i->x),
CVEC(pt_i->x), &force, &add_i);
efp_sub_force(efp->grad + j, CVEC(fr_j->x),
CVEC(at_j->x), &force, &add_j);
efp_add_stress(&swf.dr, &force, &efp->stress);
energy += p1 * e;
}
/* induced dipole - multipoles */
for (size_t k = 0; k < fr_j->n_multipole_pts; k++) {
struct multipole_pt *pt_j = fr_j->multipole_pts + k;
vec_t dr = {
pt_j->x - pt_i->x - swf.cell.x,
pt_j->y - pt_i->y - swf.cell.y,
pt_j->z - pt_i->z - swf.cell.z
};
double p1 = 1.0, p2 = 0.0;
if (efp->opts.pol_damp == EFP_POL_DAMP_TT) {
double r = vec_len(&dr);
p1 = efp_get_pol_damp_tt(r, fr_i->pol_damp,
fr_j->pol_damp);
p2 = efp_get_pol_damp_tt_grad(r, fr_i->pol_damp,
fr_j->pol_damp);
}
double e = 0.0;
vec_t force_, add_i_, add_j_;
vec_t force = vec_zero, add_i = vec_zero, add_j = vec_zero;
/* induced dipole - charge */
e -= efp_charge_dipole_energy(pt_j->monopole, &dipole_i, &dr);
efp_charge_dipole_grad(pt_j->monopole, &dipole_i, &dr,
&force_, &add_j_, &add_i_);
vec_negate(&force_);
add_3(&force, &force_, &add_i, &add_i_, &add_j, &add_j_);
/* induced dipole - dipole */
e += efp_dipole_dipole_energy(&dipole_i, &pt_j->dipole, &dr);
efp_dipole_dipole_grad(&dipole_i, &pt_j->dipole, &dr,
&force_, &add_i_, &add_j_);
vec_negate(&add_j_);
add_3(&force, &force_, &add_i, &add_i_, &add_j, &add_j_);
/* induced dipole - quadrupole */
e += efp_dipole_quadrupole_energy(&dipole_i, pt_j->quadrupole, &dr);
efp_dipole_quadrupole_grad(&dipole_i, pt_j->quadrupole, &dr,
&force_, &add_i_, &add_j_);
add_3(&force, &force_, &add_i, &add_i_, &add_j, &add_j_);
/* induced dipole - octupole interactions are ignored */
vec_scale(&force, p1);
vec_scale(&add_i, p1);
vec_scale(&add_j, p1);
force.x += p2 * e * dr.x;
force.y += p2 * e * dr.y;
force.z += p2 * e * dr.z;
vec_scale(&force, swf.swf);
vec_scale(&add_i, swf.swf);
vec_scale(&add_j, swf.swf);
efp_add_force(efp->grad + frag_idx, CVEC(fr_i->x),
CVEC(pt_i->x), &force, &add_i);
efp_sub_force(efp->grad + j, CVEC(fr_j->x),
CVEC(pt_j->x), &force, &add_j);
efp_add_stress(&swf.dr, &force, &efp->stress);
energy += p1 * e;
}
/* induced dipole - induced dipoles */
for (size_t jj = 0; jj < fr_j->n_polarizable_pts; jj++) {
struct polarizable_pt *pt_j = fr_j->polarizable_pts + jj;
size_t idx_j = fr_j->polarizable_offset + jj;
vec_t dr = {
pt_j->x - pt_i->x - swf.cell.x,
pt_j->y - pt_i->y - swf.cell.y,
pt_j->z - pt_i->z - swf.cell.z
};
vec_t half_dipole_i = {
0.5 * efp->indip[idx_i].x,
0.5 * efp->indip[idx_i].y,
0.5 * efp->indip[idx_i].z
};
double p1 = 1.0, p2 = 0.0;
if (efp->opts.pol_damp == EFP_POL_DAMP_TT) {
double r = vec_len(&dr);
p1 = efp_get_pol_damp_tt(r, fr_i->pol_damp,
fr_j->pol_damp);
p2 = efp_get_pol_damp_tt_grad(r, fr_i->pol_damp,
fr_j->pol_damp);
}
vec_t force, add_i, add_j;
double e = efp_dipole_dipole_energy(&half_dipole_i,
&efp->indipconj[idx_j], &dr);
efp_dipole_dipole_grad(&half_dipole_i, &efp->indipconj[idx_j],
&dr, &force, &add_i, &add_j);
vec_negate(&add_j);
vec_scale(&force, p1);
vec_scale(&add_i, p1);
vec_scale(&add_j, p1);
force.x += p2 * e * dr.x;
force.y += p2 * e * dr.y;
force.z += p2 * e * dr.z;
vec_scale(&force, swf.swf);
vec_scale(&add_i, swf.swf);
vec_scale(&add_j, swf.swf);
efp_add_force(efp->grad + frag_idx, CVEC(fr_i->x),
CVEC(pt_i->x), &force, &add_i);
efp_sub_force(efp->grad + j, CVEC(fr_j->x),
CVEC(pt_j->x), &force, &add_j);
efp_add_stress(&swf.dr, &force, &efp->stress);
energy += p1 * e;
}
vec_t force = {
swf.dswf.x * energy,
swf.dswf.y * energy,
swf.dswf.z * energy
};
six_atomic_add_xyz(efp->grad + frag_idx, &force);
six_atomic_sub_xyz(efp->grad + j, &force);
efp_add_stress(&swf.dr, &force, &efp->stress);
}
/* induced dipole - ab initio nuclei */
if (efp->opts.terms & EFP_TERM_AI_POL) {
for (size_t j = 0; j < efp->n_ptc; j++) {
vec_t dr = vec_sub(efp->ptc_xyz + j, CVEC(pt_i->x));
vec_t force, add_i, add_j;
efp_charge_dipole_grad(efp->ptc[j], &dipole_i, &dr,
&force, &add_j, &add_i);
vec_negate(&add_i);
vec_atomic_add(efp->ptc_grad + j, &force);
efp_sub_force(efp->grad + frag_idx, CVEC(fr_i->x),
CVEC(pt_i->x), &force, &add_i);
}
}
}
static vec_t
get_elec_field(const struct efp *efp, size_t frag_idx, size_t pt_idx)
{
const struct frag *fr_j = efp->frags + frag_idx;
const struct polarizable_pt *pt = fr_j->polarizable_pts + pt_idx;
vec_t elec_field = vec_zero;
for (size_t i = 0; i < efp->n_frag; i++) {
if (i == frag_idx || efp_skip_frag_pair(efp, i, frag_idx))
continue;
const struct frag *fr_i = efp->frags + i;
struct swf swf = efp_make_swf(efp, fr_i, fr_j);
/* field due to nuclei */
for (size_t j = 0; j < fr_i->n_atoms; j++) {
const struct efp_atom *at = fr_i->atoms + j;
vec_t dr = {
pt->x - at->x - swf.cell.x,
pt->y - at->y - swf.cell.y,
pt->z - at->z - swf.cell.z
};
double r = vec_len(&dr);
double r3 = r * r * r;
double p1 = 1.0;
if (efp->opts.pol_damp == EFP_POL_DAMP_TT)
p1 = efp_get_pol_damp_tt(r, fr_i->pol_damp, fr_j->pol_damp);
elec_field.x += swf.swf * at->znuc * dr.x / r3 * p1;
elec_field.y += swf.swf * at->znuc * dr.y / r3 * p1;
elec_field.z += swf.swf * at->znuc * dr.z / r3 * p1;
}
/* field due to multipoles */
for (size_t j = 0; j < fr_i->n_multipole_pts; j++) {
const struct multipole_pt *mult_pt = fr_i->multipole_pts + j;
vec_t mult_field = get_multipole_field(CVEC(pt->x), mult_pt, &swf);
vec_t dr = {
pt->x - mult_pt->x - swf.cell.x,
pt->y - mult_pt->y - swf.cell.y,
pt->z - mult_pt->z - swf.cell.z
};
double r = vec_len(&dr);
double p1 = 1.0;
if (efp->opts.pol_damp == EFP_POL_DAMP_TT)
p1 = efp_get_pol_damp_tt(r, fr_i->pol_damp, fr_j->pol_damp);
elec_field.x += mult_field.x * p1;
elec_field.y += mult_field.y * p1;
elec_field.z += mult_field.z * p1;
}
}
if (efp->opts.terms & EFP_TERM_AI_POL) {
/* field due to nuclei from ab initio subsystem */
for (size_t i = 0; i < efp->n_ptc; i++) {
vec_t dr = vec_sub(CVEC(pt->x), efp->ptc_xyz + i);
double r = vec_len(&dr);
double r3 = r * r * r;
elec_field.x += efp->ptc[i] * dr.x / r3;
elec_field.y += efp->ptc[i] * dr.y / r3;
elec_field.z += efp->ptc[i] * dr.z / r3;
}
}
return (elec_field);
}
