def make_L1(pcmobj, r_vdw, ylm_1sph, fi):
# See JCTC, 9, 3637, Eq (18)
mol = pcmobj.mol
natm = mol.natm
lmax = pcmobj.lmax
eta = pcmobj.eta
nlm = (lmax + 1)**2
coords_1sph, weights_1sph = ddcosmo.make_grids_one_sphere(
pcmobj.lebedev_order)
ngrid_1sph = weights_1sph.size
atom_coords = mol.atom_coords()
ylm_1sph = ylm_1sph.reshape(nlm, ngrid_1sph)
Lmat = numpy.zeros((natm, 3, natm, nlm, natm, nlm))
fi1 = make_fi1(pcmobj, pcmobj.get_atomic_radii())
for ja in range(natm):
part_weights = weights_1sph.copy()
part_weights[fi[ja] > 1] /= fi[ja, fi[ja] > 1]
part_weights1 = numpy.zeros((natm, 3, ngrid_1sph))
tmp = part_weights[fi[ja] > 1] / fi[ja, fi[ja] > 1]
part_weights1[:, :, fi[ja] > 1] = -tmp * fi1[:, :, ja, fi[ja] > 1]
for ka in ddcosmo.atoms_with_vdw_overlap(ja, atom_coords, r_vdw):
vjk = r_vdw[ja] * coords_1sph + atom_coords[ja] - atom_coords[ka]
rv = lib.norm(vjk, axis=1)
tjk = rv / r_vdw[ka]
wjk0 = pcmobj.regularize_xt(tjk, eta, r_vdw[ka])
wjk1 = regularize_xt1(tjk, eta * r_vdw[ka])
sjk = vjk.T / rv
wjk1 = 1. / r_vdw[ka] * wjk1 * sjk
wjk01 = wjk0 * part_weights1
wjk0 *= part_weights
wjk1 *= part_weights
pol0 = sph.multipoles(vjk, lmax)
pol1 = multipoles1(vjk, lmax)
p1 = 0
for l in range(lmax + 1):
fac = 4 * numpy.pi / (l * 2 + 1) / r_vdw[ka]**(l + 1)
p0, p1 = p1, p1 + (l * 2 + 1)
a = numpy.einsum('xn,zn,mn->zxm', ylm_1sph, wjk1, pol0[l])
a += numpy.einsum('xn,n,zmn->zxm', ylm_1sph, wjk0, pol1[l])
Lmat[ja, :, ja, :, ka, p0:p1] += -fac * a
Lmat[ka, :, ja, :, ka, p0:p1] -= -fac * a
a = numpy.einsum('xn,azn,mn->azxm', ylm_1sph, wjk01, pol0[l])
Lmat[:, :, ja, :, ka, p0:p1] += -fac * a
return Lmat
def make_L1(pcmobj, r_vdw, ylm_1sph, fi):
# See JCTC, 9, 3637, Eq (18)
mol = pcmobj.mol
natm = mol.natm
lmax = pcmobj.lmax
eta = pcmobj.eta
nlm = (lmax+1)**2
coords_1sph, weights_1sph = ddcosmo.make_grids_one_sphere(pcmobj.lebedev_order)
ngrid_1sph = weights_1sph.size
atom_coords = mol.atom_coords()
ylm_1sph = ylm_1sph.reshape(nlm,ngrid_1sph)
Lmat = numpy.zeros((natm,3,natm,nlm,natm,nlm))
fi1 = make_fi1(pcmobj, pcmobj.get_atomic_radii())
for ja in range(natm):
part_weights = weights_1sph.copy()
part_weights[fi[ja]>1] /= fi[ja,fi[ja]>1]
part_weights1 = numpy.zeros((natm,3,ngrid_1sph))
tmp = part_weights[fi[ja]>1] / fi[ja,fi[ja]>1]
part_weights1[:,:,fi[ja]>1] = -tmp * fi1[:,:,ja,fi[ja]>1]
for ka in ddcosmo.atoms_with_vdw_overlap(ja, atom_coords, r_vdw):
vjk = r_vdw[ja] * coords_1sph + atom_coords[ja] - atom_coords[ka]
rv = lib.norm(vjk, axis=1)
tjk = rv / r_vdw[ka]
wjk0 = pcmobj.regularize_xt(tjk, eta, r_vdw[ka])
wjk1 = regularize_xt1(tjk, eta*r_vdw[ka])
sjk = vjk.T / rv
wjk1 = 1./r_vdw[ka] * wjk1 * sjk
wjk01 = wjk0 * part_weights1
wjk0 *= part_weights
wjk1 *= part_weights
pol0 = sph.multipoles(vjk, lmax)
pol1 = multipoles1(vjk, lmax)
p1 = 0
for l in range(lmax+1):
fac = 4*numpy.pi/(l*2+1) / r_vdw[ka]**(l+1)
p0, p1 = p1, p1 + (l*2+1)
a = numpy.einsum('xn,zn,mn->zxm', ylm_1sph, wjk1, pol0[l])
a+= numpy.einsum('xn,n,zmn->zxm', ylm_1sph, wjk0, pol1[l])
Lmat[ja,:,ja,:,ka,p0:p1] += -fac * a
Lmat[ka,:,ja,:,ka,p0:p1] -= -fac * a
a = numpy.einsum('xn,azn,mn->azxm', ylm_1sph, wjk01, pol0[l])
Lmat[:,:,ja,:,ka,p0:p1] += -fac * a
return Lmat
def make_fi1(pcmobj, r_vdw):
coords_1sph, weights_1sph = ddcosmo.make_grids_one_sphere(pcmobj.lebedev_order)
mol = pcmobj.mol
eta = pcmobj.eta
natm = mol.natm
atom_coords = mol.atom_coords()
ngrid_1sph = coords_1sph.shape[0]
fi1 = numpy.zeros((natm,3,natm,ngrid_1sph))
for ia in range(natm):
for ja in ddcosmo.atoms_with_vdw_overlap(ia, atom_coords, r_vdw):
v = r_vdw[ia]*coords_1sph + atom_coords[ia] - atom_coords[ja]
rv = lib.norm(v, axis=1)
t = rv / r_vdw[ja]
xt1 = regularize_xt1(t, eta*r_vdw[ja])
s_ij = v.T / rv
xt1 = 1./r_vdw[ja] * xt1 * s_ij
fi1[ia,:,ia] += xt1
fi1[ja,:,ia] -= xt1
fi = ddcosmo.make_fi(pcmobj, r_vdw)
fi1[:,:,fi<1e-20] = 0
return fi1
def make_fi1(pcmobj, r_vdw):
coords_1sph, weights_1sph = ddcosmo.make_grids_one_sphere(pcmobj.lebedev_order)
mol = pcmobj.mol
eta = pcmobj.eta
natm = mol.natm
atom_coords = mol.atom_coords()
ngrid_1sph = coords_1sph.shape[0]
fi1 = numpy.zeros((natm,3,natm,ngrid_1sph))
for ia in range(natm):
for ja in ddcosmo.atoms_with_vdw_overlap(ia, atom_coords, r_vdw):
v = r_vdw[ia]*coords_1sph + atom_coords[ia] - atom_coords[ja]
rv = lib.norm(v, axis=1)
t = rv / r_vdw[ja]
xt1 = regularize_xt1(t, eta*r_vdw[ja])
s_ij = v.T / rv
xt1 = 1./r_vdw[ja] * xt1 * s_ij
fi1[ia,:,ia] += xt1
fi1[ja,:,ia] -= xt1
fi = ddcosmo.make_fi(pcmobj, r_vdw)
fi1[:,:,fi<1e-20] = 0
return fi1
def make_A(pcmobj, r_vdw, ylm_1sph, ui):
# Part of A matrix defined in JCP, 144, 054101, Eq (43), (44)
mol = pcmobj.mol
natm = mol.natm
lmax = pcmobj.lmax
eta = pcmobj.eta
nlm = (lmax + 1)**2
coords_1sph, weights_1sph = ddcosmo.make_grids_one_sphere(
pcmobj.lebedev_order)
ngrid_1sph = weights_1sph.size
atom_coords = mol.atom_coords()
ylm_1sph = ylm_1sph.reshape(nlm, ngrid_1sph)
Amat = numpy.zeros((natm, nlm, natm, nlm))
for ja in range(natm):
# w_u = precontract w_n U_j
w_u = weights_1sph * ui[ja]
p1 = 0
for l in range(lmax + 1):
fac = 2 * numpy.pi / (l * 2 + 1)
p0, p1 = p1, p1 + (l * 2 + 1)
a = numpy.einsum('xn,n,mn->xm', ylm_1sph, w_u, ylm_1sph[p0:p1])
Amat[ja, :, ja, p0:p1] += -fac * a
for ka in ddcosmo.atoms_with_vdw_overlap(ja, atom_coords, r_vdw):
vjk = r_vdw[ja] * coords_1sph + atom_coords[ja] - atom_coords[ka]
rjk = lib.norm(vjk, axis=1)
pol = sph.multipoles(vjk, lmax)
p1 = 0
weights = w_u / rjk**(l * 2 + 1)
for l in range(lmax + 1):
fac = 4 * numpy.pi * l / (l * 2 + 1) * r_vdw[ka]**(l + 1)
p0, p1 = p1, p1 + (l * 2 + 1)
a = numpy.einsum('xn,n,mn->xm', ylm_1sph, weights, pol[l])
Amat[ja, :, ka, p0:p1] += -fac * a
return Amat
def make_A(pcmobj, r_vdw, ylm_1sph, ui):
# Part of A matrix defined in JCP, 144, 054101, Eq (43), (44)
mol = pcmobj.mol
natm = mol.natm
lmax = pcmobj.lmax
eta = pcmobj.eta
nlm = (lmax+1)**2
coords_1sph, weights_1sph = ddcosmo.make_grids_one_sphere(pcmobj.lebedev_order)
ngrid_1sph = weights_1sph.size
atom_coords = mol.atom_coords()
ylm_1sph = ylm_1sph.reshape(nlm,ngrid_1sph)
Amat = numpy.zeros((natm,nlm,natm,nlm))
for ja in range(natm):
# w_u = precontract w_n U_j
w_u = weights_1sph * ui[ja]
p1 = 0
for l in range(lmax+1):
fac = 2*numpy.pi/(l*2+1)
p0, p1 = p1, p1 + (l*2+1)
a = numpy.einsum('xn,n,mn->xm', ylm_1sph, w_u, ylm_1sph[p0:p1])
Amat[ja,:,ja,p0:p1] += -fac * a
for ka in ddcosmo.atoms_with_vdw_overlap(ja, atom_coords, r_vdw):
vjk = r_vdw[ja] * coords_1sph + atom_coords[ja] - atom_coords[ka]
rjk = lib.norm(vjk, axis=1)
pol = sph.multipoles(vjk, lmax)
p1 = 0
weights = w_u / rjk**(l*2+1)
for l in range(lmax+1):
fac = 4*numpy.pi*l/(l*2+1) * r_vdw[ka]**(l+1)
p0, p1 = p1, p1 + (l*2+1)
a = numpy.einsum('xn,n,mn->xm', ylm_1sph, weights, pol[l])
Amat[ja,:,ka,p0:p1] += -fac * a
return Amat
