/*
* 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
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 double
disp_overlap(struct efp *efp, size_t fr_i_idx, size_t fr_j_idx,
size_t pt_i_idx, size_t pt_j_idx, double s_ij, six_t ds_ij,
double sum, const struct swf *swf)
{
const struct frag *fr_i = efp->frags + fr_i_idx;
const struct frag *fr_j = efp->frags + fr_j_idx;
const struct dynamic_polarizable_pt *pt_i =
fr_i->dynamic_polarizable_pts + pt_i_idx;
const struct dynamic_polarizable_pt *pt_j =
fr_j->dynamic_polarizable_pts + pt_j_idx;
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 r = vec_len(&dr);
double r2 = r * r;
double r6 = r2 * r2 * r2;
double ln_s = 0.0;
double damp = 1.0;
if (fabs(s_ij) > 1.0e-5) {
ln_s = log(fabs(s_ij));
damp = 1.0 - s_ij * s_ij * (1.0 - 2.0 * ln_s + 2.0 * ln_s * ln_s);
}
double energy = -4.0 / 3.0 * sum * damp / r6;
if (efp->do_gradient) {
vec_t force, torque_i, torque_j;
double t1 = -8.0 * sum / r6 / r2 * damp;
double t2 = -16.0 / 3.0 * sum / r6 * ln_s * ln_s * s_ij;
vec_t dr_i = vec_sub(CVEC(pt_i->x), CVEC(fr_i->x));
vec_t dr_j = vec_sub(CVEC(pt_j->x), CVEC(fr_j->x));
force.x = (t1 * dr.x - t2 * ds_ij.x) * swf->swf;
force.y = (t1 * dr.y - t2 * ds_ij.y) * swf->swf;
force.z = (t1 * dr.z - t2 * ds_ij.z) * swf->swf;
torque_i.x = swf->swf * (t1 * (dr.z * dr_i.y - dr.y * dr_i.z) +
t2 * ds_ij.a);
torque_i.y = swf->swf * (t1 * (dr.x * dr_i.z - dr.z * dr_i.x) +
t2 * ds_ij.b);
torque_i.z = swf->swf * (t1 * (dr.y * dr_i.x - dr.x * dr_i.y) +
t2 * ds_ij.c);
torque_j.x = swf->swf * (t1 * (dr.z * dr_j.y - dr.y * dr_j.z) +
t2 * (ds_ij.z * swf->dr.y - ds_ij.y * swf->dr.z) +
t2 * ds_ij.a);
torque_j.y = swf->swf * (t1 * (dr.x * dr_j.z - dr.z * dr_j.x) +
t2 * (ds_ij.x * swf->dr.z - ds_ij.z * swf->dr.x) +
t2 * ds_ij.b);
torque_j.z = swf->swf * (t1 * (dr.y * dr_j.x - dr.x * dr_j.y) +
t2 * (ds_ij.y * swf->dr.x - ds_ij.x * swf->dr.y) +
t2 * ds_ij.c);
six_atomic_add_xyz(efp->grad + fr_i_idx, &force);
six_atomic_add_abc(efp->grad + fr_i_idx, &torque_i);
six_atomic_sub_xyz(efp->grad + fr_j_idx, &force);
six_atomic_sub_abc(efp->grad + fr_j_idx, &torque_j);
efp_add_stress(&swf->dr, &force, &efp->stress);
}
return energy;
}
