def _compute_multipole_potential_integrals(pe, site, order, moments):
if order > 2:
raise NotImplementedError("""Multipole potential integrals not
implemented for order > 2.""")
pe.mol.set_rinv_orig(site)
# TODO: only calculate up to requested order!
integral0 = pe.mol.intor("int1e_rinv")
integral1 = pe.mol.intor("int1e_iprinv") + pe.mol.intor("int1e_iprinv").transpose(0, 2, 1)
integral2 = pe.mol.intor("int1e_ipiprinv") + pe.mol.intor("int1e_ipiprinv").transpose(0, 2, 1) + 2.0 * pe.mol.intor("int1e_iprinvip")
# k = 2: 0,1,2,4,5,8 = XX, XY, XZ, YY, YZ, ZZ
# add the lower triangle to the upper triangle, i.e.,
# XY += YX : 1 + 3
# XZ += ZX : 2 + 6
# YZ += ZY : 5 + 7
# and divide by 2
integral2[1] += integral2[3]
integral2[2] += integral2[6]
integral2[5] += integral2[7]
integral2[1] *= 0.5
integral2[2] *= 0.5
integral2[5] *= 0.5
op = integral0 * moments[0] * cppe.prefactors(0)
if order > 0:
op += numpy.einsum('aij,a->ij', integral1,
moments[1] * cppe.prefactors(1))
if order > 1:
op += numpy.einsum('aij,a->ij',
integral2[[0, 1, 2, 4, 5, 8], :, :],
moments[2] * cppe.prefactors(2))
return op
def _compute_multipole_potential_integrals(self, sites, orders, moments):
orders = numpy.asarray(orders)
if numpy.any(orders > 2):
raise NotImplementedError("""Multipole potential integrals not
implemented for order > 2.""")
# order 0
fakemol = gto.fakemol_for_charges(sites)
integral0 = df.incore.aux_e2(self.mol, fakemol, intor='int3c2e')
moments_0 = numpy.array([m[0] for m in moments])
op = numpy.einsum('ijg,ga->ij', integral0,
moments_0 * cppe.prefactors(0))
# order 1
if numpy.any(orders >= 1):
idx = numpy.where(orders >= 1)[0]
fakemol = gto.fakemol_for_charges(sites[idx])
integral1 = df.incore.aux_e2(self.mol,
fakemol,
intor='int3c2e_ip1')
moments_1 = numpy.array([moments[i][1] for i in idx])
v = numpy.einsum('aijg,ga,a->ij', integral1, moments_1,
cppe.prefactors(1))
op += v + v.T
if numpy.any(orders >= 2):
idx = numpy.where(orders >= 2)[0]
fakemol = gto.fakemol_for_charges(sites[idx])
n_sites = idx.size
# moments_2 is the lower triangler of
# [[XX, XY, XZ], [YX, YY, YZ], [ZX, ZY, ZZ]] i.e.
# XX, XY, XZ, YY, YZ, ZZ = 0,1,2,4,5,8
# symmetrize it to the upper triangler part
# XX, YX, ZX, YY, ZY, ZZ = 0,3,6,4,7,8
m2 = numpy.einsum('ga,a->ga', [moments[i][2] for i in idx],
cppe.prefactors(2))
moments_2 = numpy.zeros((n_sites, 9))
moments_2[:, [0, 1, 2, 4, 5, 8]] = m2
moments_2[:, [0, 3, 6, 4, 7, 8]] += m2
moments_2 *= .5
integral2 = df.incore.aux_e2(self.mol,
fakemol,
intor='int3c2e_ipip1')
v = numpy.einsum('aijg,ga->ij', integral2, moments_2)
op += v + v.T
integral2 = df.incore.aux_e2(self.mol,
fakemol,
intor='int3c2e_ipvip1')
op += numpy.einsum('aijg,ga->ij', integral2, moments_2) * 2
return op
def build_electrostatics_operator(self):
n_bas = self.basisset.nbf()
self.V_es = np.zeros((n_bas, n_bas))
for site in self.cppe_state.potentials:
prefactors = []
for multipole in site.multipoles:
prefactors.extend(cppe.prefactors(multipole.k) * multipole.values)
integrals = self.mints.ao_multipole_potential(site.position, max_k=multipole.k)
self.V_es += sum(pref * intv.np for pref, intv in zip(prefactors, integrals))
def build_electrostatics_operator(self):
n_bas = self.basisset.nbf()
self.V_es = np.zeros((n_bas, n_bas))
# TODO: run this in one go...
for site in self.cppe_state.potentials:
prefactors = []
for multipole in site.multipoles:
prefactors.extend(cppe.prefactors(multipole.k) * multipole.values)
integrals = self.mints.ao_multipole_potential(order=multipole.k, origin=site.position)
self.V_es += sum(pref * intv.np for pref, intv in zip(prefactors, integrals))
def test_prefactors(self):
for k in range(3):
assert prefactors(k) == prefs[k]
