def _dip_nuc(mol: gto.Mole) -> np.ndarray:
"""
this function returns the nuclear contribution to the molecular dipole moment
"""
# coordinates and charges of nuclei
coords = mol.atom_coords()
charges = mol.atom_charges()
return contract('i,ix->ix', charges, coords)
def _e_nuc(mol: gto.Mole, mm_mol: Union[None, gto.Mole]) -> np.ndarray:
"""
this function returns the nuclear repulsion energy
"""
# coordinates and charges of nuclei
coords = mol.atom_coords()
charges = mol.atom_charges()
# internuclear distances (with self-repulsion removed)
dist = gto.inter_distance(mol)
dist[np.diag_indices_from(dist)] = 1e200
e_nuc = contract('i,ij,j->i', charges, 1. / dist, charges) * .5
# possible interaction with mm sites
if mm_mol is not None:
mm_coords = mm_mol.atom_coords()
mm_charges = mm_mol.atom_charges()
for j in range(mol.natm):
q2, r2 = charges[j], coords[j]
r = lib.norm(r2 - mm_coords, axis=1)
e_nuc[j] += q2 * np.sum(mm_charges / r)
return e_nuc
def _mm_pot(mol: gto.Mole, mm_mol: gto.Mole) -> np.ndarray:
"""
this function returns the full mm potential
(adapted from: qmmm/itrf.py:get_hcore() in PySCF)
"""
# settings
coords = mm_mol.atom_coords()
charges = mm_mol.atom_charges()
blksize = BLKSIZE
# integrals
intor = 'int3c2e_cart' if mol.cart else 'int3c2e_sph'
cintopt = gto.moleintor.make_cintopt(mol._atm, mol._bas,
mol._env, intor)
# compute interaction potential
mm_pot = 0
for i0, i1 in lib.prange(0, charges.size, blksize):
fakemol = gto.fakemol_for_charges(coords[i0:i1])
j3c = df.incore.aux_e2(mol, fakemol, intor=intor,
aosym='s2ij', cintopt=cintopt)
mm_pot += np.einsum('xk,k->x', j3c, -charges[i0:i1])
mm_pot = lib.unpack_tril(mm_pot)
return mm_pot
def _h_core(mol: gto.Mole, mm_mol: Union[None, gto.Mole]) -> Tuple[np.ndarray, np.ndarray, \
np.ndarray, Union[None, np.ndarray]]:
"""
this function returns the components of the core hamiltonian
"""
# kinetic integrals
kin = mol.intor_symmetric('int1e_kin')
# coordinates and charges of nuclei
coords = mol.atom_coords()
charges = mol.atom_charges()
# individual atomic potentials
sub_nuc = np.zeros([mol.natm, mol.nao_nr(), mol.nao_nr()], dtype=np.float64)
for k in range(mol.natm):
with mol.with_rinv_origin(coords[k]):
sub_nuc[k] = -1. * mol.intor('int1e_rinv') * charges[k]
# total nuclear potential
nuc = np.sum(sub_nuc, axis=0)
# possible mm potential
if mm_mol is not None:
mm_pot = _mm_pot(mol, mm_mol)
else:
mm_pot = None
return kin, nuc, sub_nuc, mm_pot