def casci_grad_with_ccsd_solver(mc,
mo_coeff=None,
ci=None,
atmlst=None,
mf_grad=None,
verbose=None):
if mo_coeff is None: mo_coeff = mc._scf.mo_coeff
if ci is None: ci = mc.ci
if mf_grad is None: mf_grad = mc._scf.nuc_grad_method()
mol = mc.mol
ncore = mc.ncore
ncas = mc.ncas
nocc = ncore + ncas
nelecas = mc.nelecas
nao, nmo = mo_coeff.shape
nao_pair = nao * (nao + 1) // 2
mo_occ = mo_coeff[:, :nocc]
mo_core = mo_coeff[:, :ncore]
mo_cas = mo_coeff[:, ncore:nocc]
casdm1, casdm2 = mc.fcisolver.make_rdm12(mc.ci, ncas, nelecas)
no = mc.nelecas[0]
for i in range(no):
casdm1[i, i] -= 2
for i in range(no):
for j in range(no):
casdm2[i, i, j, j] -= 4
casdm2[i, j, j, i] += 2
for i in range(no):
casdm2[i, i, :, :] -= casdm1 * 2
casdm2[:, :, i, i] -= casdm1 * 2
casdm2[:, i, i, :] += casdm1
casdm2[i, :, :, i] += casdm1
mc.mo_occ = mc._scf.mo_occ
mask = numpy.zeros(nmo, dtype=bool)
mask[ncore:nocc] = True
mc.frozen = numpy.where(~mask)[0]
mc.get_frozen_mask = lambda *args: mask
d1 = (casdm1[:no, :no] * .5, casdm1[:no, no:] * .5, casdm1[no:, :no] * .5,
casdm1[no:, no:] * .5)
casdm2 = (casdm2 + casdm2.transpose(1, 0, 2, 3)) * .5
vvvv = casdm2[no:, no:, no:, no:]
d2 = (casdm2[:no, no:, :no, no:] * .5, ao2mo.restore(4, vvvv, ncas - no) *
.25, casdm2[:no, :no, :no, :no] * .25,
casdm2[:no, :no, no:, no:] * .5, casdm2[:no, no:, no:, :no] * .5,
casdm2, casdm2[:no, no:, no:, no:], casdm2[:no, :no, :no, no:])
mc.mo_coeff = mo_coeff
t1 = t2 = l1 = l2 = ci
de = ccsd_grad.grad_elec(mc.Gradients(), t1, t2, l1, l2, None, atmlst, d1,
d2, verbose)
de += rhf_grad.grad_nuc(mol)
return de
def test_casscf_grad(self):
mc = mcscf.CASSCF(mf, 4, 4).run()
g1 = casscf_grad.kernel(mc)
self.assertAlmostEqual(lib.finger(g1), -0.065094188906156134, 7)
g1ref = grad_elec(mc, mf.nuc_grad_method())
g1ref += rhf_grad.grad_nuc(mol)
self.assertAlmostEqual(abs(g1 - g1ref).max(), 0, 9)
mcs = mc.as_scanner()
pmol = mol.copy()
e1 = mcs(pmol.set_geom_('N 0 0 0; N 0 0 1.201; H 1 1 0; H 1 1 1.2'))
e2 = mcs(pmol.set_geom_('N 0 0 0; N 0 0 1.199; H 1 1 0; H 1 1 1.2'))
self.assertAlmostEqual(g1[1, 2], (e1 - e2) / 0.002 * lib.param.BOHR, 4)
def test_casscf_grad(self):
mc = mcscf.CASSCF(mf, 4, 4).run()
g1 = casscf_grad.kernel(mc)
self.assertAlmostEqual(lib.finger(g1), -0.065094188906156134, 7)
g1ref = grad_elec(mc, mf.nuc_grad_method())
g1ref += rhf_grad.grad_nuc(mol)
self.assertAlmostEqual(abs(g1-g1ref).max(), 0, 9)
mcs = mc.as_scanner()
pmol = mol.copy()
e1 = mcs(pmol.set_geom_('N 0 0 0; N 0 0 1.201; H 1 1 0; H 1 1 1.2'))
e2 = mcs(pmol.set_geom_('N 0 0 0; N 0 0 1.199; H 1 1 0; H 1 1 1.2'))
self.assertAlmostEqual(g1[1,2], (e1-e2)/0.002*lib.param.BOHR, 4)
def kernel(mc,
mo_coeff=None,
ci=None,
atmlst=None,
mf_grad=None,
verbose=None):
if mo_coeff is None: mo_coeff = mc._scf.mo_coeff
if ci is None: ci = mc.ci
if mf_grad is None: mf_grad = mc._scf.nuc_grad_method()
assert (isinstance(ci, numpy.ndarray))
mol = mc.mol
ncore = mc.ncore
ncas = mc.ncas
nocc = ncore + ncas
nelecas = mc.nelecas
nao, nmo = mo_coeff.shape
nao_pair = nao * (nao + 1) // 2
mo_energy = mc._scf.mo_energy
mo_occ = mo_coeff[:, :nocc]
mo_core = mo_coeff[:, :ncore]
mo_cas = mo_coeff[:, ncore:nocc]
neleca, nelecb = mol.nelec
assert (neleca == nelecb)
orbo = mo_coeff[:, :neleca]
orbv = mo_coeff[:, neleca:]
casdm1, casdm2 = mc.fcisolver.make_rdm12(ci, ncas, nelecas)
dm_core = numpy.dot(mo_core, mo_core.T) * 2
dm_cas = reduce(numpy.dot, (mo_cas, casdm1, mo_cas.T))
aapa = ao2mo.kernel(mol, (mo_cas, mo_cas, mo_coeff, mo_cas), compact=False)
aapa = aapa.reshape(ncas, ncas, nmo, ncas)
vj, vk = mc._scf.get_jk(mol, (dm_core, dm_cas))
h1 = mc.get_hcore()
vhf_c = vj[0] - vk[0] * .5
vhf_a = vj[1] - vk[1] * .5
# Imat = h1_{pi} gamma1_{iq} + h2_{pijk} gamma_{iqkj}
Imat = numpy.zeros((nmo, nmo))
Imat[:, :nocc] = reduce(numpy.dot,
(mo_coeff.T, h1 + vhf_c + vhf_a, mo_occ)) * 2
Imat[:, ncore:nocc] = reduce(numpy.dot,
(mo_coeff.T, h1 + vhf_c, mo_cas, casdm1))
Imat[:, ncore:nocc] += lib.einsum('uviw,vuwt->it', aapa, casdm2)
aapa = vj = vk = vhf_c = vhf_a = h1 = None
ee = mo_energy[:, None] - mo_energy
zvec = numpy.zeros_like(Imat)
zvec[:ncore,
ncore:neleca] = Imat[:ncore, ncore:neleca] / -ee[:ncore, ncore:neleca]
zvec[ncore:neleca, :ncore] = Imat[
ncore:neleca, :ncore] / -ee[ncore:neleca, :ncore]
zvec[nocc:,
neleca:nocc] = Imat[nocc:, neleca:nocc] / -ee[nocc:, neleca:nocc]
zvec[neleca:nocc,
nocc:] = Imat[neleca:nocc, nocc:] / -ee[neleca:nocc, nocc:]
zvec_ao = reduce(numpy.dot, (mo_coeff, zvec + zvec.T, mo_coeff.T))
vhf = mc._scf.get_veff(mol, zvec_ao) * 2
xvo = reduce(numpy.dot, (orbv.T, vhf, orbo))
xvo += Imat[neleca:, :neleca] - Imat[:neleca, neleca:].T
def fvind(x):
x = x.reshape(xvo.shape)
dm = reduce(numpy.dot, (orbv, x, orbo.T))
v = mc._scf.get_veff(mol, dm + dm.T)
v = reduce(numpy.dot, (orbv.T, v, orbo))
return v * 2
dm1resp = cphf.solve(fvind, mo_energy, mc._scf.mo_occ, xvo,
max_cycle=30)[0]
zvec[neleca:, :neleca] = dm1resp
zeta = numpy.einsum('ij,j->ij', zvec, mo_energy)
zeta = reduce(numpy.dot, (mo_coeff, zeta, mo_coeff.T))
zvec_ao = reduce(numpy.dot, (mo_coeff, zvec + zvec.T, mo_coeff.T))
p1 = numpy.dot(mo_coeff[:, :neleca], mo_coeff[:, :neleca].T)
vhf_s1occ = reduce(numpy.dot, (p1, mc._scf.get_veff(mol, zvec_ao), p1))
Imat[:ncore, ncore:neleca] = 0
Imat[ncore:neleca, :ncore] = 0
Imat[nocc:, neleca:nocc] = 0
Imat[neleca:nocc, nocc:] = 0
Imat[neleca:, :neleca] = Imat[:neleca, neleca:].T
im1 = reduce(numpy.dot, (mo_coeff, Imat, mo_coeff.T))
casci_dm1 = dm_core + dm_cas
hf_dm1 = mc._scf.make_rdm1(mo_coeff, mc._scf.mo_occ)
hcore_deriv = mf_grad.hcore_generator(mol)
s1 = mf_grad.get_ovlp(mol)
diag_idx = numpy.arange(nao)
diag_idx = diag_idx * (diag_idx + 1) // 2 + diag_idx
casdm2_cc = casdm2 + casdm2.transpose(0, 1, 3, 2)
dm2buf = ao2mo._ao2mo.nr_e2(casdm2_cc.reshape(ncas**2, ncas**2), mo_cas.T,
(0, nao, 0, nao)).reshape(ncas**2, nao, nao)
dm2buf = lib.pack_tril(dm2buf)
dm2buf[:, diag_idx] *= .5
dm2buf = dm2buf.reshape(ncas, ncas, nao_pair)
casdm2 = casdm2_cc = None
if atmlst is None:
atmlst = range(mol.natm)
aoslices = mol.aoslice_by_atom()
de = numpy.zeros((len(atmlst), 3))
max_memory = mc.max_memory - lib.current_memory()[0]
blksize = int(max_memory * .9e6 / 8 /
((aoslices[:, 3] - aoslices[:, 2]).max() * nao_pair))
blksize = min(nao, max(2, blksize))
for k, ia in enumerate(atmlst):
shl0, shl1, p0, p1 = aoslices[ia]
h1ao = hcore_deriv(ia)
de[k] += numpy.einsum('xij,ij->x', h1ao, casci_dm1)
de[k] += numpy.einsum('xij,ij->x', h1ao, zvec_ao)
vhf1 = numpy.zeros((3, nao, nao))
q1 = 0
for b0, b1, nf in _shell_prange(mol, 0, mol.nbas, blksize):
q0, q1 = q1, q1 + nf
dm2_ao = lib.einsum('ijw,pi,qj->pqw', dm2buf, mo_cas[p0:p1],
mo_cas[q0:q1])
shls_slice = (shl0, shl1, b0, b1, 0, mol.nbas, 0, mol.nbas)
eri1 = mol.intor('int2e_ip1',
comp=3,
aosym='s2kl',
shls_slice=shls_slice).reshape(
3, p1 - p0, nf, nao_pair)
de[k] -= numpy.einsum('xijw,ijw->x', eri1, dm2_ao) * 2
for i in range(3):
eri1tmp = lib.unpack_tril(eri1[i].reshape((p1 - p0) * nf, -1))
eri1tmp = eri1tmp.reshape(p1 - p0, nf, nao, nao)
de[k, i] -= numpy.einsum('ijkl,ij,kl', eri1tmp,
hf_dm1[p0:p1, q0:q1], zvec_ao) * 2
de[k, i] -= numpy.einsum('ijkl,kl,ij', eri1tmp, hf_dm1,
zvec_ao[p0:p1, q0:q1]) * 2
de[k, i] += numpy.einsum('ijkl,il,kj', eri1tmp, hf_dm1[p0:p1],
zvec_ao[q0:q1])
de[k, i] += numpy.einsum('ijkl,jk,il', eri1tmp, hf_dm1[q0:q1],
zvec_ao[p0:p1])
#:vhf1c, vhf1a = mf_grad.get_veff(mol, (dm_core, dm_cas))
#:de[k] += numpy.einsum('xij,ij->x', vhf1c[:,p0:p1], casci_dm1[p0:p1]) * 2
#:de[k] += numpy.einsum('xij,ij->x', vhf1a[:,p0:p1], dm_core[p0:p1]) * 2
de[k, i] -= numpy.einsum('ijkl,lk,ij', eri1tmp, dm_core[q0:q1],
casci_dm1[p0:p1]) * 2
de[k, i] += numpy.einsum('ijkl,jk,il', eri1tmp, dm_core[q0:q1],
casci_dm1[p0:p1])
de[k, i] -= numpy.einsum('ijkl,lk,ij', eri1tmp, dm_cas[q0:q1],
dm_core[p0:p1]) * 2
de[k, i] += numpy.einsum('ijkl,jk,il', eri1tmp, dm_cas[q0:q1],
dm_core[p0:p1])
eri1 = eri1tmp = None
de[k] -= numpy.einsum('xij,ij->x', s1[:, p0:p1], im1[p0:p1])
de[k] -= numpy.einsum('xij,ji->x', s1[:, p0:p1], im1[:, p0:p1])
de[k] -= numpy.einsum('xij,ij->x', s1[:, p0:p1], zeta[p0:p1]) * 2
de[k] -= numpy.einsum('xij,ji->x', s1[:, p0:p1], zeta[:, p0:p1]) * 2
de[k] -= numpy.einsum('xij,ij->x', s1[:, p0:p1], vhf_s1occ[p0:p1]) * 2
de[k] -= numpy.einsum('xij,ji->x', s1[:, p0:p1], vhf_s1occ[:,
p0:p1]) * 2
de += rhf_grad.grad_nuc(mol, atmlst)
return de
def kernel(mc,
mo_coeff=None,
ci=None,
atmlst=None,
mf_grad=None,
verbose=None):
if mo_coeff is None: mo_coeff = mc.mo_coeff
if ci is None: ci = mc.ci
if mf_grad is None: mf_grad = mc._scf.nuc_grad_method()
if mc.frozen is not None:
raise NotImplementedError
mol = mc.mol
ncore = mc.ncore
ncas = mc.ncas
nocc = ncore + ncas
nelecas = mc.nelecas
nao, nmo = mo_coeff.shape
nao_pair = nao * (nao + 1) // 2
mo_occ = mo_coeff[:, :nocc]
mo_core = mo_coeff[:, :ncore]
mo_cas = mo_coeff[:, ncore:nocc]
casdm1, casdm2 = mc.fcisolver.make_rdm12(ci, ncas, nelecas)
# gfock = Generalized Fock, Adv. Chem. Phys., 69, 63
dm_core = numpy.dot(mo_core, mo_core.T) * 2
dm_cas = reduce(numpy.dot, (mo_cas, casdm1, mo_cas.T))
aapa = ao2mo.kernel(mol, (mo_cas, mo_cas, mo_occ, mo_cas), compact=False)
aapa = aapa.reshape(ncas, ncas, nocc, ncas)
vj, vk = mc._scf.get_jk(mol, (dm_core, dm_cas))
h1 = mc.get_hcore()
vhf_c = vj[0] - vk[0] * .5
vhf_a = vj[1] - vk[1] * .5
gfock = reduce(numpy.dot, (mo_occ.T, h1 + vhf_c + vhf_a, mo_occ)) * 2
gfock[:, ncore:nocc] = reduce(numpy.dot,
(mo_occ.T, h1 + vhf_c, mo_cas, casdm1))
gfock[:, ncore:nocc] += numpy.einsum('uviw,vuwt->it', aapa, casdm2)
dme0 = reduce(numpy.dot, (mo_occ, (gfock + gfock.T) * .5, mo_occ.T))
aapa = vj = vk = vhf_c = vhf_a = h1 = gfock = None
dm1 = dm_core + dm_cas
vhf1c, vhf1a = mf_grad.get_veff(mol, (dm_core, dm_cas))
hcore_deriv = mf_grad.hcore_generator(mol)
s1 = mf_grad.get_ovlp(mol)
diag_idx = numpy.arange(nao)
diag_idx = diag_idx * (diag_idx + 1) // 2 + diag_idx
casdm2_cc = casdm2 + casdm2.transpose(0, 1, 3, 2)
dm2buf = ao2mo._ao2mo.nr_e2(casdm2_cc.reshape(ncas**2, ncas**2), mo_cas.T,
(0, nao, 0, nao)).reshape(ncas**2, nao, nao)
dm2buf = lib.pack_tril(dm2buf)
dm2buf[:, diag_idx] *= .5
dm2buf = dm2buf.reshape(ncas, ncas, nao_pair)
casdm2 = casdm2_cc = None
if atmlst is None:
atmlst = range(mol.natm)
aoslices = mol.aoslice_by_atom()
de = numpy.zeros((len(atmlst), 3))
max_memory = mc.max_memory - lib.current_memory()[0]
blksize = int(max_memory * .9e6 / 8 /
((aoslices[:, 3] - aoslices[:, 2]).max() * nao_pair))
blksize = min(nao, max(2, blksize))
for k, ia in enumerate(atmlst):
shl0, shl1, p0, p1 = aoslices[ia]
h1ao = hcore_deriv(ia)
de[k] += numpy.einsum('xij,ij->x', h1ao, dm1)
de[k] -= numpy.einsum('xij,ij->x', s1[:, p0:p1], dme0[p0:p1]) * 2
q1 = 0
for b0, b1, nf in _shell_prange(mol, 0, mol.nbas, blksize):
q0, q1 = q1, q1 + nf
dm2_ao = lib.einsum('ijw,pi,qj->pqw', dm2buf, mo_cas[p0:p1],
mo_cas[q0:q1])
shls_slice = (shl0, shl1, b0, b1, 0, mol.nbas, 0, mol.nbas)
eri1 = mol.intor('int2e_ip1',
comp=3,
aosym='s2kl',
shls_slice=shls_slice).reshape(
3, p1 - p0, nf, nao_pair)
de[k] -= numpy.einsum('xijw,ijw->x', eri1, dm2_ao) * 2
eri1 = None
de[k] += numpy.einsum('xij,ij->x', vhf1c[:, p0:p1], dm1[p0:p1]) * 2
de[k] += numpy.einsum('xij,ij->x', vhf1a[:, p0:p1], dm_core[p0:p1]) * 2
de += rhf_grad.grad_nuc(mol, atmlst)
return de
def kernel(mc,
mo_coeff=None,
ci=None,
atmlst=None,
mf_grad=None,
verbose=None):
if mo_coeff is None: mo_coeff = mc._scf.mo_coeff
if ci is None: ci = mc.ci
if mf_grad is None: mf_grad = mc._scf.nuc_grad_method()
mol = mc.mol
ncore = mc.ncore
ncas = mc.ncas
nocc = ncore + ncas
nelecas = mc.nelecas
nao, nmo = mo_coeff.shape
nao_pair = nao * (nao + 1) // 2
mo_energy = mc._scf.mo_energy
hcore_deriv = mf_grad.hcore_generator(mol)
s1 = mf_grad.get_ovlp(mol)
mo_occ = mo_coeff[:, :nocc]
mo_core = mo_coeff[:, :ncore]
mo_cas = mo_coeff[:, ncore:nocc]
casdm1, casdm2 = mc.fcisolver.make_rdm12(mc.ci, ncas, nelecas)
# gfock = Generalized Fock, Adv. Chem. Phys., 69, 63
dm_core = numpy.dot(mo_core, mo_core.T) * 2
dm_cas = reduce(numpy.dot, (mo_cas, casdm1, mo_cas.T))
aapa = ao2mo.kernel(mol, (mo_cas, mo_cas, mo_occ, mo_cas), compact=False)
aapa = aapa.reshape(ncas, ncas, nocc, ncas)
vj, vk = mc._scf.get_jk(mol, (dm_core, dm_cas))
h1 = mc.get_hcore()
vhf_c = vj[0] - vk[0] * .5
vhf_a = vj[1] - vk[1] * .5
gfock = reduce(numpy.dot, (mo_occ.T, h1 + vhf_c + vhf_a, mo_occ)) * 2
gfock[:, ncore:nocc] = reduce(numpy.dot,
(mo_occ.T, h1 + vhf_c, mo_cas, casdm1))
gfock[:, ncore:nocc] += numpy.einsum('uviw,vuwt->it', aapa, casdm2)
dme0 = reduce(numpy.dot, (mo_occ, (gfock + gfock.T) * .5, mo_occ.T))
aapa = vj = vk = vhf_c = vhf_a = h1 = gfock = None
dm1 = dm_core + dm_cas
vhf1c, vhf1a = mf_grad.get_veff(mol, (dm_core, dm_cas))
diag_idx = numpy.arange(nao)
diag_idx = diag_idx * (diag_idx + 1) // 2 + diag_idx
casdm2_cc = casdm2 + casdm2.transpose(0, 1, 3, 2)
dm2buf = ao2mo._ao2mo.nr_e2(casdm2_cc.reshape(ncas**2, ncas**2), mo_cas.T,
(0, nao, 0, nao)).reshape(ncas**2, nao, nao)
dm2buf = lib.pack_tril(dm2buf)
dm2buf[:, diag_idx] *= .5
dm2buf = dm2buf.reshape(ncas, ncas, nao_pair)
#casdm2 = casdm2_cc = None
atmlst = range(mol.natm)
aoslices = mol.aoslice_by_atom()
de = numpy.zeros((len(atmlst), 3))
max_memory = mc.max_memory - lib.current_memory()[0]
blksize = int(max_memory * .9e6 / 8 /
((aoslices[:, 3] - aoslices[:, 2]).max() * nao_pair))
blksize = min(nao, max(2, blksize))
for k, ia in enumerate(atmlst):
shl0, shl1, p0, p1 = aoslices[ia]
h1ao = hcore_deriv(ia)
de[k] += numpy.einsum('xij,ij->x', h1ao, dm1)
#de[k] -= numpy.einsum('xij,ij->x', s1[:,p0:p1], dme0[p0:p1]) * 2
q1 = 0
for b0, b1, nf in _shell_prange(mol, 0, mol.nbas, blksize):
q0, q1 = q1, q1 + nf
dm2_ao = lib.einsum('ijw,pi,qj->pqw', dm2buf, mo_cas[p0:p1],
mo_cas[q0:q1])
shls_slice = (shl0, shl1, b0, b1, 0, mol.nbas, 0, mol.nbas)
eri1 = mol.intor('int2e_ip1',
comp=3,
aosym='s2kl',
shls_slice=shls_slice).reshape(
3, p1 - p0, nf, nao_pair)
de[k] -= numpy.einsum('xijw,ijw->x', eri1, dm2_ao) * 2
eri1 = None
de[k] += numpy.einsum('xij,ij->x', vhf1c[:, p0:p1], dm1[p0:p1]) * 2
de[k] += numpy.einsum('xij,ij->x', vhf1a[:, p0:p1], dm_core[p0:p1]) * 2
dm2 = numpy.zeros((nmo, nmo, nmo, nmo))
for i in range(ncore):
for j in range(ncore):
dm2[i, i, j, j] += 4
dm2[i, j, j, i] -= 2
dm2[i, i, ncore:nocc, ncore:nocc] = casdm1 * 2
dm2[ncore:nocc, ncore:nocc, i, i] = casdm1 * 2
dm2[i, ncore:nocc, ncore:nocc, i] = -casdm1
dm2[ncore:nocc, i, i, ncore:nocc] = -casdm1
dm2[ncore:nocc, ncore:nocc, ncore:nocc, ncore:nocc] = casdm2
eri0 = ao2mo.restore(1, ao2mo.full(mc._scf._eri, mo_coeff), nmo)
Imat = numpy.einsum('pjkl,qjkl->pq', eri0, dm2)
dm1 = numpy.zeros((nmo, nmo))
for i in range(ncore):
dm1[i, i] = 2
dm1[ncore:nocc, ncore:nocc] = casdm1
neleca, nelecb = mol.nelec
h1 = -(mol.intor('int1e_ipkin', comp=3) + mol.intor('int1e_ipnuc', comp=3))
s1 = -mol.intor('int1e_ipovlp', comp=3)
eri1 = mol.intor('int2e_ip1', comp=3).reshape(3, nao, nao, nao, nao)
eri1 = numpy.einsum('xipkl,pj->xijkl', eri1, mo_coeff)
eri1 = numpy.einsum('xijpl,pk->xijkl', eri1, mo_coeff)
eri1 = numpy.einsum('xijkp,pl->xijkl', eri1, mo_coeff)
h0 = reduce(numpy.dot, (mo_coeff.T, mc._scf.get_hcore(), mo_coeff))
g0 = ao2mo.restore(1, ao2mo.full(mol, mo_coeff), nmo)
def hess():
nocc = mol.nelectron // 2
nvir = nmo - nocc
eri_mo = g0
eai = lib.direct_sum('a-i->ai', mo_energy[nocc:], mo_energy[:nocc])
h = eri_mo[nocc:, :nocc, nocc:, :nocc] * 4
h -= numpy.einsum('cdlk->ckdl', eri_mo[nocc:, nocc:, :nocc, :nocc])
h -= numpy.einsum('cldk->ckdl', eri_mo[nocc:, :nocc, nocc:, :nocc])
for a in range(nvir):
for i in range(nocc):
h[a, i, a, i] += eai[a, i]
return -h.reshape(nocc * nvir, -1)
hh = hess()
ee = mo_energy[:, None] - mo_energy
for k, (sh0, sh1, p0, p1) in enumerate(mol.offset_nr_by_atom()):
mol.set_rinv_origin(mol.atom_coord(k))
vrinv = -mol.atom_charge(k) * mol.intor('int1e_iprinv', comp=3)
# 2e AO integrals dot 2pdm
for i in range(3):
g1 = numpy.einsum('pjkl,pi->ijkl', eri1[i, p0:p1], mo_coeff[p0:p1])
g1 = g1 + g1.transpose(1, 0, 2, 3)
g1 = g1 + g1.transpose(2, 3, 0, 1)
g1 *= -1
hx = (numpy.einsum('pq,pi,qj->ij', h1[i, p0:p1], mo_coeff[p0:p1],
mo_coeff) +
reduce(numpy.dot, (mo_coeff.T, vrinv[i], mo_coeff)))
hx = hx + hx.T
sx = numpy.einsum('pq,pi,qj->ij', s1[i, p0:p1], mo_coeff[p0:p1],
mo_coeff)
sx = sx + sx.T
fij = (hx[:neleca, :neleca] - numpy.einsum(
'ij,j->ij', sx[:neleca, :neleca], mo_energy[:neleca]) -
numpy.einsum('kl,ijlk->ij', sx[:neleca, :neleca],
g0[:neleca, :neleca, :neleca, :neleca]) * 2 +
numpy.einsum('kl,iklj->ij', sx[:neleca, :neleca],
g0[:neleca, :neleca, :neleca, :neleca]) +
numpy.einsum('ijkk->ij',
g1[:neleca, :neleca, :neleca, :neleca]) * 2 -
numpy.einsum('ikkj->ij',
g1[:neleca, :neleca, :neleca, :neleca]))
fab = (hx[neleca:, neleca:] - numpy.einsum(
'ij,j->ij', sx[neleca:, neleca:], mo_energy[neleca:]) -
numpy.einsum('kl,ijlk->ij', sx[:neleca, :neleca],
g0[neleca:, neleca:, :neleca, :neleca]) * 2 +
numpy.einsum('kl,iklj->ij', sx[:neleca, :neleca],
g0[neleca:, :neleca, :neleca, neleca:]) +
numpy.einsum('ijkk->ij',
g1[neleca:, neleca:, :neleca, :neleca]) * 2 -
numpy.einsum('ikkj->ij', g1[neleca:, :neleca, :neleca,
neleca:]))
fai = (hx[neleca:, :neleca] - numpy.einsum(
'ai,i->ai', sx[neleca:, :neleca], mo_energy[:neleca]) -
numpy.einsum('kl,ijlk->ij', sx[:neleca, :neleca],
g0[neleca:, :neleca, :neleca, :neleca]) * 2 +
numpy.einsum('kl,iklj->ij', sx[:neleca, :neleca],
g0[neleca:, :neleca, :neleca, :neleca]) +
numpy.einsum('ijkk->ij',
g1[neleca:, :neleca, :neleca, :neleca]) * 2 -
numpy.einsum('ikkj->ij',
g1[neleca:, :neleca, :neleca, :neleca]))
c1 = numpy.zeros((nmo, nmo))
c1[:neleca, :neleca] = -.5 * sx[:neleca, :neleca]
c1[neleca:, neleca:] = -.5 * sx[neleca:, neleca:]
cvo1 = numpy.linalg.solve(hh, fai.ravel()).reshape(-1, neleca)
cov1 = -(sx[neleca:, :neleca] + cvo1).T
c1[neleca:, :neleca] = cvo1
c1[:neleca, neleca:] = cov1
v1 = numpy.einsum('pqai,ai->pq', g0[:, :, neleca:, :neleca],
cvo1) * 4
v1 -= numpy.einsum('paiq,ai->pq', g0[:, neleca:, :neleca, :], cvo1)
v1 -= numpy.einsum('piaq,ai->pq', g0[:, :neleca, neleca:, :], cvo1)
fij += v1[:neleca, :neleca]
fab += v1[neleca:, neleca:]
c1[:ncore,
ncore:neleca] = -fij[:ncore, ncore:] / ee[:ncore, ncore:neleca]
c1[ncore:neleca, :ncore] = -fij[ncore:, :ncore] / ee[
ncore:neleca, :ncore]
m = nocc - neleca
c1[nocc:, neleca:nocc] = -fab[m:, :m] / ee[nocc:, neleca:nocc]
c1[neleca:nocc, nocc:] = -fab[:m, m:] / ee[neleca:nocc, nocc:]
h0c1 = h0.dot(c1)
h0c1 = h0c1 + h0c1.T
g0c1 = numpy.einsum('pjkl,pi->ijkl', g0, c1)
g0c1 = g0c1 + g0c1.transpose(1, 0, 2, 3)
g0c1 = g0c1 + g0c1.transpose(2, 3, 0, 1)
de[k, i] += numpy.einsum('ij,ji', h0c1, dm1)
de[k, i] += numpy.einsum('ijkl,jilk', g0c1, dm2) * .5
de += rhf_grad.grad_nuc(mol)
return de
def kernel(mp, t2, atmlst=None, mf_grad=None, verbose=logger.INFO):
if mf_grad is None: mf_grad = mp._scf.nuc_grad_method()
log = logger.new_logger(mp, verbose)
time0 = time.clock(), time.time()
log.debug('Build ump2 rdm1 intermediates')
d1 = ump2._gamma1_intermediates(mp, t2)
time1 = log.timer_debug1('rdm1 intermediates', *time0)
log.debug('Build ump2 rdm2 intermediates')
mol = mp.mol
with_frozen = not (mp.frozen is None or mp.frozen is 0)
moidx = mp.get_frozen_mask()
OA_a, VA_a, OF_a, VF_a = mp2_grad._index_frozen_active(
moidx[0], mp.mo_occ[0])
OA_b, VA_b, OF_b, VF_b = mp2_grad._index_frozen_active(
moidx[1], mp.mo_occ[1])
orboa = mp.mo_coeff[0][:, OA_a]
orbva = mp.mo_coeff[0][:, VA_a]
orbob = mp.mo_coeff[1][:, OA_b]
orbvb = mp.mo_coeff[1][:, VA_b]
nao, nocca = orboa.shape
nvira = orbva.shape[1]
noccb = orbob.shape[1]
nvirb = orbvb.shape[1]
# Partially transform MP2 density matrix and hold it in memory
# The rest transformation are applied during the contraction to ERI integrals
t2aa, t2ab, t2bb = t2
part_dm2aa = _ao2mo.nr_e2(t2aa.reshape(nocca**2, nvira**2),
numpy.asarray(orbva.T,
order='F'), (0, nao, 0, nao), 's1',
's1').reshape(nocca, nocca, nao, nao)
part_dm2bb = _ao2mo.nr_e2(t2bb.reshape(noccb**2, nvirb**2),
numpy.asarray(orbvb.T,
order='F'), (0, nao, 0, nao), 's1',
's1').reshape(noccb, noccb, nao, nao)
part_dm2ab = lib.einsum('ijab,pa,qb->ipqj', t2ab, orbva, orbvb)
part_dm2aa = (part_dm2aa.transpose(0, 2, 3, 1) -
part_dm2aa.transpose(0, 3, 2, 1)) * .5
part_dm2bb = (part_dm2bb.transpose(0, 2, 3, 1) -
part_dm2bb.transpose(0, 3, 2, 1)) * .5
hf_dm1a, hf_dm1b = mp._scf.make_rdm1(mp.mo_coeff, mp.mo_occ)
hf_dm1 = hf_dm1a + hf_dm1b
if atmlst is None:
atmlst = range(mol.natm)
offsetdic = mol.offset_nr_by_atom()
diagidx = numpy.arange(nao)
diagidx = diagidx * (diagidx + 1) // 2 + diagidx
de = numpy.zeros((len(atmlst), 3))
Imata = numpy.zeros((nao, nao))
Imatb = numpy.zeros((nao, nao))
fdm2 = lib.H5TmpFile()
vhf1 = fdm2.create_dataset('vhf1', (len(atmlst), 2, 3, nao, nao), 'f8')
# 2e AO integrals dot 2pdm
max_memory = max(0, mp.max_memory - lib.current_memory()[0])
blksize = max(1, int(max_memory * .9e6 / 8 / (nao**3 * 2.5)))
for k, ia in enumerate(atmlst):
shl0, shl1, p0, p1 = offsetdic[ia]
ip1 = p0
vhf = numpy.zeros((2, 3, nao, nao))
for b0, b1, nf in mp2_grad._shell_prange(mol, shl0, shl1, blksize):
ip0, ip1 = ip1, ip1 + nf
dm2bufa = lib.einsum('pi,iqrj->pqrj', orboa[ip0:ip1], part_dm2aa)
dm2bufa += lib.einsum('qi,iprj->pqrj', orboa, part_dm2aa[:,
ip0:ip1])
dm2bufa = lib.einsum('pqrj,sj->pqrs', dm2bufa, orboa)
tmp = lib.einsum('pi,iqrj->pqrj', orboa[ip0:ip1], part_dm2ab)
tmp += lib.einsum('qi,iprj->pqrj', orboa, part_dm2ab[:, ip0:ip1])
dm2bufa += lib.einsum('pqrj,sj->pqrs', tmp, orbob)
tmp = None
dm2bufa = dm2bufa + dm2bufa.transpose(0, 1, 3, 2)
dm2bufa = lib.pack_tril(dm2bufa.reshape(-1, nao,
nao)).reshape(nf, nao, -1)
dm2bufa[:, :, diagidx] *= .5
dm2bufb = lib.einsum('pi,iqrj->pqrj', orbob[ip0:ip1], part_dm2bb)
dm2bufb += lib.einsum('qi,iprj->pqrj', orbob, part_dm2bb[:,
ip0:ip1])
dm2bufb = lib.einsum('pqrj,sj->pqrs', dm2bufb, orbob)
tmp = lib.einsum('iqrj,sj->iqrs', part_dm2ab, orbob[ip0:ip1])
tmp += lib.einsum('iqrj,sj->iqsr', part_dm2ab[:, :, ip0:ip1],
orbob)
dm2bufb += lib.einsum('pi,iqrs->srpq', orboa, tmp)
tmp = None
dm2bufb = dm2bufb + dm2bufb.transpose(0, 1, 3, 2)
dm2bufb = lib.pack_tril(dm2bufb.reshape(-1, nao,
nao)).reshape(nf, nao, -1)
dm2bufb[:, :, diagidx] *= .5
shls_slice = (b0, b1, 0, mol.nbas, 0, mol.nbas, 0, mol.nbas)
eri0 = mol.intor('int2e', aosym='s2kl', shls_slice=shls_slice)
Imata += lib.einsum('ipx,iqx->pq', eri0.reshape(nf, nao, -1),
dm2bufa)
Imatb += lib.einsum('ipx,iqx->pq', eri0.reshape(nf, nao, -1),
dm2bufb)
eri0 = None
eri1 = mol.intor('int2e_ip1',
comp=3,
aosym='s2kl',
shls_slice=shls_slice).reshape(3, nf, nao, -1)
de[k] -= numpy.einsum('xijk,ijk->x', eri1, dm2bufa) * 2
de[k] -= numpy.einsum('xijk,ijk->x', eri1, dm2bufb) * 2
dm2bufa = dm2bufb = None
# HF part
for i in range(3):
eri1tmp = lib.unpack_tril(eri1[i].reshape(nf * nao, -1))
eri1tmp = eri1tmp.reshape(nf, nao, nao, nao)
vhf[:, i] += numpy.einsum('ijkl,ij->kl', eri1tmp,
hf_dm1[ip0:ip1])
vhf[0, i] -= numpy.einsum('ijkl,il->kj', eri1tmp,
hf_dm1a[ip0:ip1])
vhf[1, i] -= numpy.einsum('ijkl,il->kj', eri1tmp,
hf_dm1b[ip0:ip1])
vhf[:, i, ip0:ip1] += numpy.einsum('ijkl,kl->ij', eri1tmp,
hf_dm1)
vhf[0, i, ip0:ip1] -= numpy.einsum('ijkl,jk->il', eri1tmp,
hf_dm1a)
vhf[1, i, ip0:ip1] -= numpy.einsum('ijkl,jk->il', eri1tmp,
hf_dm1b)
eri1 = eri1tmp = None
vhf1[k] = vhf
log.debug('2e-part grad of atom %d %s = %s', ia, mol.atom_symbol(ia),
de[k])
time1 = log.timer_debug1('2e-part grad of atom %d' % ia, *time1)
# Recompute nocc, nvir to include the frozen orbitals and make contraction for
# the 1-particle quantities, see also the kernel function in uccsd_grad module.
mo_a, mo_b = mp.mo_coeff
mo_ea, mo_eb = mp._scf.mo_energy
nao, nmoa = mo_a.shape
nmob = mo_b.shape[1]
nocca = numpy.count_nonzero(mp.mo_occ[0] > 0)
noccb = numpy.count_nonzero(mp.mo_occ[1] > 0)
s0 = mp._scf.get_ovlp()
Imata = reduce(numpy.dot, (mo_a.T, Imata, s0, mo_a)) * -1
Imatb = reduce(numpy.dot, (mo_b.T, Imatb, s0, mo_b)) * -1
dm1a = numpy.zeros((nmoa, nmoa))
dm1b = numpy.zeros((nmob, nmob))
doo, dOO = d1[0]
dvv, dVV = d1[1]
if with_frozen:
dco = Imata[OF_a[:, None], OA_a] / (mo_ea[OF_a, None] - mo_ea[OA_a])
dfv = Imata[VF_a[:, None], VA_a] / (mo_ea[VF_a, None] - mo_ea[VA_a])
dm1a[OA_a[:, None], OA_a] = (doo + doo.T) * .5
dm1a[OF_a[:, None], OA_a] = dco
dm1a[OA_a[:, None], OF_a] = dco.T
dm1a[VA_a[:, None], VA_a] = (dvv + dvv.T) * .5
dm1a[VF_a[:, None], VA_a] = dfv
dm1a[VA_a[:, None], VF_a] = dfv.T
dco = Imatb[OF_b[:, None], OA_b] / (mo_eb[OF_b, None] - mo_eb[OA_b])
dfv = Imatb[VF_b[:, None], VA_b] / (mo_eb[VF_b, None] - mo_eb[VA_b])
dm1b[OA_b[:, None], OA_b] = (dOO + dOO.T) * .5
dm1b[OF_b[:, None], OA_b] = dco
dm1b[OA_b[:, None], OF_b] = dco.T
dm1b[VA_b[:, None], VA_b] = (dVV + dVV.T) * .5
dm1b[VF_b[:, None], VA_b] = dfv
dm1b[VA_b[:, None], VF_b] = dfv.T
else:
dm1a[:nocca, :nocca] = (doo + doo.T) * .5
dm1a[nocca:, nocca:] = (dvv + dvv.T) * .5
dm1b[:noccb, :noccb] = (dOO + dOO.T) * .5
dm1b[noccb:, noccb:] = (dVV + dVV.T) * .5
dm1 = (reduce(numpy.dot,
(mo_a, dm1a, mo_a.T)), reduce(numpy.dot,
(mo_b, dm1b, mo_b.T)))
vhf = mp._scf.get_veff(mp.mol, dm1)
Xvo = reduce(numpy.dot, (mo_a[:, nocca:].T, vhf[0], mo_a[:, :nocca]))
XVO = reduce(numpy.dot, (mo_b[:, noccb:].T, vhf[1], mo_b[:, :noccb]))
Xvo += Imata[:nocca, nocca:].T - Imata[nocca:, :nocca]
XVO += Imatb[:noccb, noccb:].T - Imatb[noccb:, :noccb]
dm1_resp = _response_dm1(mp, (Xvo, XVO))
dm1a += dm1_resp[0]
dm1b += dm1_resp[1]
time1 = log.timer_debug1('response_rdm1 intermediates', *time1)
Imata[nocca:, :nocca] = Imata[:nocca, nocca:].T
Imatb[noccb:, :noccb] = Imatb[:noccb, noccb:].T
im1 = reduce(numpy.dot, (mo_a, Imata, mo_a.T))
im1 += reduce(numpy.dot, (mo_b, Imatb, mo_b.T))
time1 = log.timer_debug1('response_rdm1', *time1)
log.debug('h1 and JK1')
hcore_deriv = mf_grad.hcore_generator(mol)
s1 = mf_grad.get_ovlp(mol)
zeta = (mo_ea[:, None] + mo_ea) * .5
zeta[nocca:, :nocca] = mo_ea[:nocca]
zeta[:nocca, nocca:] = mo_ea[:nocca].reshape(-1, 1)
zeta_a = reduce(numpy.dot, (mo_a, zeta * dm1a, mo_a.T))
zeta = (mo_eb[:, None] + mo_eb) * .5
zeta[noccb:, :noccb] = mo_eb[:noccb]
zeta[:noccb, noccb:] = mo_eb[:noccb].reshape(-1, 1)
zeta_b = reduce(numpy.dot, (mo_b, zeta * dm1b, mo_b.T))
dm1 = (reduce(numpy.dot,
(mo_a, dm1a, mo_a.T)), reduce(numpy.dot,
(mo_b, dm1b, mo_b.T)))
vhf_s1occ = mp._scf.get_veff(mol, (dm1[0] + dm1[0].T, dm1[1] + dm1[1].T))
p1a = numpy.dot(mo_a[:, :nocca], mo_a[:, :nocca].T)
p1b = numpy.dot(mo_b[:, :noccb], mo_b[:, :noccb].T)
vhf_s1occ = (reduce(numpy.dot, (p1a, vhf_s1occ[0], p1a)) +
reduce(numpy.dot, (p1b, vhf_s1occ[1], p1b))) * .5
time1 = log.timer_debug1('h1 and JK1', *time1)
# Hartree-Fock part contribution
dm1pa = hf_dm1a + dm1[0] * 2
dm1pb = hf_dm1b + dm1[1] * 2
dm1 = dm1[0] + dm1[1] + hf_dm1
zeta_a += rhf_grad.make_rdm1e(mo_ea, mo_a, mp.mo_occ[0])
zeta_b += rhf_grad.make_rdm1e(mo_eb, mo_b, mp.mo_occ[1])
zeta = zeta_a + zeta_b
for k, ia in enumerate(atmlst):
shl0, shl1, p0, p1 = offsetdic[ia]
# s[1] dot I, note matrix im1 is not hermitian
de[k] += numpy.einsum('xij,ij->x', s1[:, p0:p1], im1[p0:p1])
de[k] += numpy.einsum('xji,ij->x', s1[:, p0:p1], im1[:, p0:p1])
# h[1] \dot DM, contribute to f1
h1ao = hcore_deriv(ia)
de[k] += numpy.einsum('xij,ji->x', h1ao, dm1)
# -s[1]*e \dot DM, contribute to f1
de[k] -= numpy.einsum('xij,ij->x', s1[:, p0:p1], zeta[p0:p1])
de[k] -= numpy.einsum('xji,ij->x', s1[:, p0:p1], zeta[:, p0:p1])
# -vhf[s_ij[1]], contribute to f1, *2 for s1+s1.T
de[k] -= numpy.einsum('xij,ij->x', s1[:, p0:p1], vhf_s1occ[p0:p1]) * 2
de[k] -= numpy.einsum('xij,ij->x', vhf1[k, 0], dm1pa)
de[k] -= numpy.einsum('xij,ij->x', vhf1[k, 1], dm1pb)
de += rhf_grad.grad_nuc(mol)
log.timer('%s gradients' % mp.__class__.__name__, *time0)
return de
def kernel(mycc,
t1=None,
t2=None,
l1=None,
l2=None,
eris=None,
atmlst=None,
mf_grad=None,
d1=None,
d2=None,
verbose=logger.INFO):
if eris is not None:
if abs(eris.fock - numpy.diag(eris.fock.diagonal())).max() > 1e-3:
raise RuntimeError(
'CCSD gradients does not support NHF (non-canonical HF)')
if t1 is None: t1 = mycc.t1
if t2 is None: t2 = mycc.t2
if l1 is None: l1 = mycc.l1
if l2 is None: l2 = mycc.l2
if mf_grad is None: mf_grad = mycc._scf.nuc_grad_method()
log = logger.new_logger(mycc, verbose)
time0 = time.clock(), time.time()
log.debug('Build ccsd rdm1 intermediates')
if d1 is None:
d1 = ccsd_rdm._gamma1_intermediates(mycc, t1, t2, l1, l2)
doo, dov, dvo, dvv = d1
time1 = log.timer_debug1('rdm1 intermediates', *time0)
log.debug('Build ccsd rdm2 intermediates')
fdm2 = lib.H5TmpFile()
if d2 is None:
d2 = ccsd_rdm._gamma2_outcore(mycc, t1, t2, l1, l2, fdm2, True)
time1 = log.timer_debug1('rdm2 intermediates', *time1)
mol = mycc.mol
mo_coeff = mycc.mo_coeff
mo_energy = mycc._scf.mo_energy
nao, nmo = mo_coeff.shape
nocc = numpy.count_nonzero(mycc.mo_occ > 0)
with_frozen = not (mycc.frozen is None or mycc.frozen is 0)
OA, VA, OF, VF = _index_frozen_active(mycc.get_frozen_mask(), mycc.mo_occ)
log.debug('symmetrized rdm2 and MO->AO transformation')
# Roughly, dm2*2 is computed in _rdm2_mo2ao
mo_active = mo_coeff[:, numpy.hstack((OA, VA))]
_rdm2_mo2ao(mycc, d2, mo_active, fdm2) # transform the active orbitals
time1 = log.timer_debug1('MO->AO transformation', *time1)
hf_dm1 = mycc._scf.make_rdm1(mycc.mo_coeff, mycc.mo_occ)
if atmlst is None:
atmlst = range(mol.natm)
offsetdic = mol.offset_nr_by_atom()
diagidx = numpy.arange(nao)
diagidx = diagidx * (diagidx + 1) // 2 + diagidx
de = numpy.zeros((len(atmlst), 3))
Imat = numpy.zeros((nao, nao))
vhf1 = fdm2.create_dataset('vhf1', (len(atmlst), 3, nao, nao), 'f8')
# 2e AO integrals dot 2pdm
max_memory = max(0, mycc.max_memory - lib.current_memory()[0])
blksize = max(1, int(max_memory * .9e6 / 8 / (nao**3 * 2.5)))
for k, ia in enumerate(atmlst):
shl0, shl1, p0, p1 = offsetdic[ia]
ip1 = p0
vhf = numpy.zeros((3, nao, nao))
for b0, b1, nf in _shell_prange(mol, shl0, shl1, blksize):
ip0, ip1 = ip1, ip1 + nf
dm2buf = _load_block_tril(fdm2['dm2'], ip0, ip1, nao)
dm2buf[:, :, diagidx] *= .5
shls_slice = (b0, b1, 0, mol.nbas, 0, mol.nbas, 0, mol.nbas)
eri0 = mol.intor('int2e', aosym='s2kl', shls_slice=shls_slice)
Imat += lib.einsum('ipx,iqx->pq', eri0.reshape(nf, nao, -1),
dm2buf)
eri0 = None
eri1 = mol.intor('int2e_ip1',
comp=3,
aosym='s2kl',
shls_slice=shls_slice).reshape(3, nf, nao, -1)
de[k] -= numpy.einsum('xijk,ijk->x', eri1, dm2buf) * 2
dm2buf = None
# HF part
for i in range(3):
eri1tmp = lib.unpack_tril(eri1[i].reshape(nf * nao, -1))
eri1tmp = eri1tmp.reshape(nf, nao, nao, nao)
vhf[i] += numpy.einsum('ijkl,ij->kl', eri1tmp, hf_dm1[ip0:ip1])
vhf[i] -= numpy.einsum('ijkl,il->kj', eri1tmp,
hf_dm1[ip0:ip1]) * .5
vhf[i, ip0:ip1] += numpy.einsum('ijkl,kl->ij', eri1tmp, hf_dm1)
vhf[i, ip0:ip1] -= numpy.einsum('ijkl,jk->il', eri1tmp,
hf_dm1) * .5
eri1 = eri1tmp = None
vhf1[k] = vhf
log.debug('2e-part grad of atom %d %s = %s', ia, mol.atom_symbol(ia),
de[k])
time1 = log.timer_debug1('2e-part grad of atom %d' % ia, *time1)
Imat = reduce(numpy.dot,
(mo_coeff.T, Imat, mycc._scf.get_ovlp(), mo_coeff)) * -1
dm1mo = numpy.zeros((nmo, nmo))
if with_frozen:
dco = Imat[OF[:, None], OA] / (mo_energy[OF, None] - mo_energy[OA])
dfv = Imat[VF[:, None], VA] / (mo_energy[VF, None] - mo_energy[VA])
dm1mo[OA[:, None], OA] = doo + doo.T
dm1mo[OF[:, None], OA] = dco
dm1mo[OA[:, None], OF] = dco.T
dm1mo[VA[:, None], VA] = dvv + dvv.T
dm1mo[VF[:, None], VA] = dfv
dm1mo[VA[:, None], VF] = dfv.T
else:
dm1mo[:nocc, :nocc] = doo + doo.T
dm1mo[nocc:, nocc:] = dvv + dvv.T
dm1 = reduce(numpy.dot, (mo_coeff, dm1mo, mo_coeff.T))
vhf = mycc._scf.get_veff(mycc.mol, dm1) * 2
Xvo = reduce(numpy.dot, (mo_coeff[:, nocc:].T, vhf, mo_coeff[:, :nocc]))
Xvo += Imat[:nocc, nocc:].T - Imat[nocc:, :nocc]
dm1mo += _response_dm1(mycc, Xvo, eris)
time1 = log.timer_debug1('response_rdm1 intermediates', *time1)
Imat[nocc:, :nocc] = Imat[:nocc, nocc:].T
im1 = reduce(numpy.dot, (mo_coeff, Imat, mo_coeff.T))
time1 = log.timer_debug1('response_rdm1', *time1)
log.debug('h1 and JK1')
hcore_deriv = mf_grad.hcore_generator(mol)
s1 = mf_grad.get_ovlp(mol)
zeta = lib.direct_sum('i+j->ij', mo_energy, mo_energy) * .5
zeta[nocc:, :nocc] = mo_energy[:nocc]
zeta[:nocc, nocc:] = mo_energy[:nocc].reshape(-1, 1)
zeta = reduce(numpy.dot, (mo_coeff, zeta * dm1mo, mo_coeff.T))
dm1 = reduce(numpy.dot, (mo_coeff, dm1mo, mo_coeff.T))
p1 = numpy.dot(mo_coeff[:, :nocc], mo_coeff[:, :nocc].T)
vhf_s1occ = reduce(numpy.dot,
(p1, mycc._scf.get_veff(mol, dm1 + dm1.T), p1))
time1 = log.timer_debug1('h1 and JK1', *time1)
# Hartree-Fock part contribution
dm1p = hf_dm1 + dm1 * 2
dm1 += hf_dm1
zeta += mf_grad.make_rdm1e(mo_energy, mo_coeff, mycc.mo_occ)
for k, ia in enumerate(atmlst):
shl0, shl1, p0, p1 = offsetdic[ia]
# s[1] dot I, note matrix im1 is not hermitian
de[k] += numpy.einsum('xij,ij->x', s1[:, p0:p1], im1[p0:p1])
de[k] += numpy.einsum('xji,ij->x', s1[:, p0:p1], im1[:, p0:p1])
# h[1] \dot DM, contribute to f1
h1ao = hcore_deriv(ia)
de[k] += numpy.einsum('xij,ji->x', h1ao, dm1)
# -s[1]*e \dot DM, contribute to f1
de[k] -= numpy.einsum('xij,ij->x', s1[:, p0:p1], zeta[p0:p1])
de[k] -= numpy.einsum('xji,ij->x', s1[:, p0:p1], zeta[:, p0:p1])
# -vhf[s_ij[1]], contribute to f1, *2 for s1+s1.T
de[k] -= numpy.einsum('xij,ij->x', s1[:, p0:p1], vhf_s1occ[p0:p1]) * 2
de[k] -= numpy.einsum('xij,ij->x', vhf1[k], dm1p)
de += rhf_grad.grad_nuc(mol, atmlst)
log.timer('%s gradients' % mycc.__class__.__name__, *time0)
return de
def kernel(mc, mo_coeff=None, ci=None, atmlst=None, mf_grad=None,
verbose=None):
if mo_coeff is None: mo_coeff = mc._scf.mo_coeff
if ci is None: ci = mc.ci
if mf_grad is None: mf_grad = mc._scf.nuc_grad_method()
mol = mc.mol
ncore = mc.ncore
ncas = mc.ncas
nocc = ncore + ncas
nelecas = mc.nelecas
nao, nmo = mo_coeff.shape
nao_pair = nao * (nao+1) // 2
mo_energy = mc._scf.mo_energy
hcore_deriv = mf_grad.hcore_generator(mol)
s1 = mf_grad.get_ovlp(mol)
mo_occ = mo_coeff[:,:nocc]
mo_core = mo_coeff[:,:ncore]
mo_cas = mo_coeff[:,ncore:nocc]
casdm1, casdm2 = mc.fcisolver.make_rdm12(mc.ci, ncas, nelecas)
# gfock = Generalized Fock, Adv. Chem. Phys., 69, 63
dm_core = numpy.dot(mo_core, mo_core.T) * 2
dm_cas = reduce(numpy.dot, (mo_cas, casdm1, mo_cas.T))
aapa = ao2mo.kernel(mol, (mo_cas, mo_cas, mo_occ, mo_cas), compact=False)
aapa = aapa.reshape(ncas,ncas,nocc,ncas)
vj, vk = mc._scf.get_jk(mol, (dm_core, dm_cas))
h1 = mc.get_hcore()
vhf_c = vj[0] - vk[0] * .5
vhf_a = vj[1] - vk[1] * .5
gfock = reduce(numpy.dot, (mo_occ.T, h1 + vhf_c + vhf_a, mo_occ)) * 2
gfock[:,ncore:nocc] = reduce(numpy.dot, (mo_occ.T, h1 + vhf_c, mo_cas, casdm1))
gfock[:,ncore:nocc] += numpy.einsum('uviw,vuwt->it', aapa, casdm2)
dme0 = reduce(numpy.dot, (mo_occ, (gfock+gfock.T)*.5, mo_occ.T))
aapa = vj = vk = vhf_c = vhf_a = h1 = gfock = None
dm1 = dm_core + dm_cas
vhf1c, vhf1a = mf_grad.get_veff(mol, (dm_core, dm_cas))
diag_idx = numpy.arange(nao)
diag_idx = diag_idx * (diag_idx+1) // 2 + diag_idx
casdm2_cc = casdm2 + casdm2.transpose(0,1,3,2)
dm2buf = ao2mo._ao2mo.nr_e2(casdm2_cc.reshape(ncas**2,ncas**2), mo_cas.T,
(0, nao, 0, nao)).reshape(ncas**2,nao,nao)
dm2buf = lib.pack_tril(dm2buf)
dm2buf[:,diag_idx] *= .5
dm2buf = dm2buf.reshape(ncas,ncas,nao_pair)
#casdm2 = casdm2_cc = None
atmlst = range(mol.natm)
aoslices = mol.aoslice_by_atom()
de = numpy.zeros((len(atmlst),3))
max_memory = mc.max_memory - lib.current_memory()[0]
blksize = int(max_memory*.9e6/8 / ((aoslices[:,3]-aoslices[:,2]).max()*nao_pair))
blksize = min(nao, max(2, blksize))
for k, ia in enumerate(atmlst):
shl0, shl1, p0, p1 = aoslices[ia]
h1ao = hcore_deriv(ia)
de[k] += numpy.einsum('xij,ij->x', h1ao, dm1)
#de[k] -= numpy.einsum('xij,ij->x', s1[:,p0:p1], dme0[p0:p1]) * 2
q1 = 0
for b0, b1, nf in _shell_prange(mol, 0, mol.nbas, blksize):
q0, q1 = q1, q1 + nf
dm2_ao = lib.einsum('ijw,pi,qj->pqw', dm2buf, mo_cas[p0:p1], mo_cas[q0:q1])
shls_slice = (shl0,shl1,b0,b1,0,mol.nbas,0,mol.nbas)
eri1 = mol.intor('int2e_ip1', comp=3, aosym='s2kl',
shls_slice=shls_slice).reshape(3,p1-p0,nf,nao_pair)
de[k] -= numpy.einsum('xijw,ijw->x', eri1, dm2_ao) * 2
eri1 = None
de[k] += numpy.einsum('xij,ij->x', vhf1c[:,p0:p1], dm1[p0:p1]) * 2
de[k] += numpy.einsum('xij,ij->x', vhf1a[:,p0:p1], dm_core[p0:p1]) * 2
dm2 = numpy.zeros((nmo,nmo,nmo,nmo))
for i in range(ncore):
for j in range(ncore):
dm2[i,i,j,j] += 4
dm2[i,j,j,i] -= 2
dm2[i,i,ncore:nocc,ncore:nocc] = casdm1 * 2
dm2[ncore:nocc,ncore:nocc,i,i] = casdm1 * 2
dm2[i,ncore:nocc,ncore:nocc,i] =-casdm1
dm2[ncore:nocc,i,i,ncore:nocc] =-casdm1
dm2[ncore:nocc,ncore:nocc,ncore:nocc,ncore:nocc] = casdm2
eri0 = ao2mo.restore(1, ao2mo.full(mc._scf._eri, mo_coeff), nmo)
Imat = numpy.einsum('pjkl,qjkl->pq', eri0, dm2)
dm1 = numpy.zeros((nmo,nmo))
for i in range(ncore):
dm1[i,i] = 2
dm1[ncore:nocc,ncore:nocc] = casdm1
neleca, nelecb = mol.nelec
h1 =-(mol.intor('int1e_ipkin', comp=3)
+mol.intor('int1e_ipnuc', comp=3))
s1 =-mol.intor('int1e_ipovlp', comp=3)
eri1 = mol.intor('int2e_ip1', comp=3).reshape(3,nao,nao,nao,nao)
eri1 = numpy.einsum('xipkl,pj->xijkl', eri1, mo_coeff)
eri1 = numpy.einsum('xijpl,pk->xijkl', eri1, mo_coeff)
eri1 = numpy.einsum('xijkp,pl->xijkl', eri1, mo_coeff)
h0 = reduce(numpy.dot, (mo_coeff.T, mc._scf.get_hcore(), mo_coeff))
g0 = ao2mo.restore(1, ao2mo.full(mol, mo_coeff), nmo)
def hess():
nocc = mol.nelectron//2
nvir = nmo - nocc
eri_mo = g0
eai = lib.direct_sum('a-i->ai', mo_energy[nocc:], mo_energy[:nocc])
h = eri_mo[nocc:,:nocc,nocc:,:nocc] * 4
h-= numpy.einsum('cdlk->ckdl', eri_mo[nocc:,nocc:,:nocc,:nocc])
h-= numpy.einsum('cldk->ckdl', eri_mo[nocc:,:nocc,nocc:,:nocc])
for a in range(nvir):
for i in range(nocc):
h[a,i,a,i] += eai[a,i]
return -h.reshape(nocc*nvir,-1)
hh = hess()
ee = mo_energy[:,None] - mo_energy
for k,(sh0, sh1, p0, p1) in enumerate(mol.offset_nr_by_atom()):
mol.set_rinv_origin(mol.atom_coord(k))
vrinv = -mol.atom_charge(k) * mol.intor('int1e_iprinv', comp=3)
# 2e AO integrals dot 2pdm
for i in range(3):
g1 = numpy.einsum('pjkl,pi->ijkl', eri1[i,p0:p1], mo_coeff[p0:p1])
g1 = g1 + g1.transpose(1,0,2,3)
g1 = g1 + g1.transpose(2,3,0,1)
g1 *= -1
hx =(numpy.einsum('pq,pi,qj->ij', h1[i,p0:p1], mo_coeff[p0:p1], mo_coeff)
+ reduce(numpy.dot, (mo_coeff.T, vrinv[i], mo_coeff)))
hx = hx + hx.T
sx = numpy.einsum('pq,pi,qj->ij', s1[i,p0:p1], mo_coeff[p0:p1], mo_coeff)
sx = sx + sx.T
fij =(hx[:neleca,:neleca]
- numpy.einsum('ij,j->ij', sx[:neleca,:neleca], mo_energy[:neleca])
- numpy.einsum('kl,ijlk->ij', sx[:neleca,:neleca],
g0[:neleca,:neleca,:neleca,:neleca]) * 2
+ numpy.einsum('kl,iklj->ij', sx[:neleca,:neleca],
g0[:neleca,:neleca,:neleca,:neleca])
+ numpy.einsum('ijkk->ij', g1[:neleca,:neleca,:neleca,:neleca]) * 2
- numpy.einsum('ikkj->ij', g1[:neleca,:neleca,:neleca,:neleca]))
fab =(hx[neleca:,neleca:]
- numpy.einsum('ij,j->ij', sx[neleca:,neleca:], mo_energy[neleca:])
- numpy.einsum('kl,ijlk->ij', sx[:neleca,:neleca],
g0[neleca:,neleca:,:neleca,:neleca]) * 2
+ numpy.einsum('kl,iklj->ij', sx[:neleca,:neleca],
g0[neleca:,:neleca,:neleca,neleca:])
+ numpy.einsum('ijkk->ij', g1[neleca:,neleca:,:neleca,:neleca]) * 2
- numpy.einsum('ikkj->ij', g1[neleca:,:neleca,:neleca,neleca:]))
fai =(hx[neleca:,:neleca]
- numpy.einsum('ai,i->ai', sx[neleca:,:neleca], mo_energy[:neleca])
- numpy.einsum('kl,ijlk->ij', sx[:neleca,:neleca],
g0[neleca:,:neleca,:neleca,:neleca]) * 2
+ numpy.einsum('kl,iklj->ij', sx[:neleca,:neleca],
g0[neleca:,:neleca,:neleca,:neleca])
+ numpy.einsum('ijkk->ij', g1[neleca:,:neleca,:neleca,:neleca]) * 2
- numpy.einsum('ikkj->ij', g1[neleca:,:neleca,:neleca,:neleca]))
c1 = numpy.zeros((nmo,nmo))
c1[:neleca,:neleca] = -.5 * sx[:neleca,:neleca]
c1[neleca:,neleca:] = -.5 * sx[neleca:,neleca:]
cvo1 = numpy.linalg.solve(hh, fai.ravel()).reshape(-1,neleca)
cov1 = -(sx[neleca:,:neleca] + cvo1).T
c1[neleca:,:neleca] = cvo1
c1[:neleca,neleca:] = cov1
v1 = numpy.einsum('pqai,ai->pq', g0[:,:,neleca:,:neleca], cvo1) * 4
v1-= numpy.einsum('paiq,ai->pq', g0[:,neleca:,:neleca,:], cvo1)
v1-= numpy.einsum('piaq,ai->pq', g0[:,:neleca,neleca:,:], cvo1)
fij += v1[:neleca,:neleca]
fab += v1[neleca:,neleca:]
c1[:ncore,ncore:neleca] = -fij[:ncore,ncore:] / ee[:ncore,ncore:neleca]
c1[ncore:neleca,:ncore] = -fij[ncore:,:ncore] / ee[ncore:neleca,:ncore]
m = nocc - neleca
c1[nocc:,neleca:nocc] = -fab[m:,:m] / ee[nocc:,neleca:nocc]
c1[neleca:nocc,nocc:] = -fab[:m,m:] / ee[neleca:nocc,nocc:]
h0c1 = h0.dot(c1)
h0c1 = h0c1 + h0c1.T
g0c1 = numpy.einsum('pjkl,pi->ijkl', g0, c1)
g0c1 = g0c1 + g0c1.transpose(1,0,2,3)
g0c1 = g0c1 + g0c1.transpose(2,3,0,1)
de[k,i] += numpy.einsum('ij,ji', h0c1, dm1)
de[k,i] += numpy.einsum('ijkl,jilk', g0c1, dm2)*.5
de += rhf_grad.grad_nuc(mol)
return de
def kernel(mp, t2, atmlst=None, mf_grad=None, verbose=logger.INFO):
if mf_grad is None: mf_grad = mp._scf.nuc_grad_method()
log = logger.new_logger(mp, verbose)
time0 = time.clock(), time.time()
log.debug('Build mp2 rdm1 intermediates')
d1 = mp2._gamma1_intermediates(mp, t2)
doo, dvv = d1
time1 = log.timer_debug1('rdm1 intermediates', *time0)
# Set nocc, nvir for half-transformation of 2pdm. Frozen orbitals are exculded.
# nocc, nvir should be updated to include the frozen orbitals when proceeding
# the 1-particle quantities later.
mol = mp.mol
with_frozen = not (mp.frozen is None or mp.frozen is 0)
OA, VA, OF, VF = _index_frozen_active(mp.get_frozen_mask(), mp.mo_occ)
orbo = mp.mo_coeff[:,OA]
orbv = mp.mo_coeff[:,VA]
nao, nocc = orbo.shape
nvir = orbv.shape[1]
# Partially transform MP2 density matrix and hold it in memory
# The rest transformation are applied during the contraction to ERI integrals
part_dm2 = _ao2mo.nr_e2(t2.reshape(nocc**2,nvir**2),
numpy.asarray(orbv.T, order='F'), (0,nao,0,nao),
's1', 's1').reshape(nocc,nocc,nao,nao)
part_dm2 = (part_dm2.transpose(0,2,3,1) * 4 -
part_dm2.transpose(0,3,2,1) * 2)
hf_dm1 = mp._scf.make_rdm1(mp.mo_coeff, mp.mo_occ)
if atmlst is None:
atmlst = range(mol.natm)
offsetdic = mol.offset_nr_by_atom()
diagidx = numpy.arange(nao)
diagidx = diagidx*(diagidx+1)//2 + diagidx
de = numpy.zeros((len(atmlst),3))
Imat = numpy.zeros((nao,nao))
fdm2 = lib.H5TmpFile()
vhf1 = fdm2.create_dataset('vhf1', (len(atmlst),3,nao,nao), 'f8')
# 2e AO integrals dot 2pdm
max_memory = max(0, mp.max_memory - lib.current_memory()[0])
blksize = max(1, int(max_memory*.9e6/8/(nao**3*2.5)))
Imat1 = 0
Imat2 = 0
for k, ia in enumerate(atmlst):
shl0, shl1, p0, p1 = offsetdic[ia]
ip1 = p0
vhf = numpy.zeros((3,nao,nao))
for b0, b1, nf in _shell_prange(mol, shl0, shl1, blksize):
ip0, ip1 = ip1, ip1 + nf
dm2buf = lib.einsum('pi,iqrj->pqrj', orbo[ip0:ip1], part_dm2)
dm2buf+= lib.einsum('qi,iprj->pqrj', orbo, part_dm2[:,ip0:ip1])
dm2buf = lib.einsum('pqrj,sj->pqrs', dm2buf, orbo)
dm2buf = dm2buf + dm2buf.transpose(0,1,3,2)
dm2buf = lib.pack_tril(dm2buf.reshape(-1,nao,nao)).reshape(nf,nao,-1)
dm2buf[:,:,diagidx] *= .5
shls_slice = (b0,b1,0,mol.nbas,0,mol.nbas,0,mol.nbas)
eri0 = mol.intor('int2e', aosym='s2kl', shls_slice=shls_slice)
Imat += lib.einsum('ipx,iqx->pq', eri0.reshape(nf,nao,-1), dm2buf)
eri0 = None
eri1 = mol.intor('int2e_ip1', comp=3, aosym='s2kl',
shls_slice=shls_slice).reshape(3,nf,nao,-1)
de[k] -= numpy.einsum('xijk,ijk->x', eri1, dm2buf) * 2
dm2buf = None
# HF part
for i in range(3):
eri1tmp = lib.unpack_tril(eri1[i]).reshape(nf*nao,-1)
eri1tmp = eri1tmp.reshape(nf,nao,nao,nao)
vhf[i] += numpy.einsum('ijkl,ij->kl', eri1tmp, hf_dm1[ip0:ip1])
vhf[i] -= numpy.einsum('ijkl,il->kj', eri1tmp, hf_dm1[ip0:ip1]) * .5
vhf[i,ip0:ip1] += numpy.einsum('ijkl,kl->ij', eri1tmp, hf_dm1)
vhf[i,ip0:ip1] -= numpy.einsum('ijkl,jk->il', eri1tmp, hf_dm1) * .5
eri1 = eri1tmp = None
vhf1[k] = vhf
log.debug('2e-part grad of atom %d %s = %s', ia, mol.atom_symbol(ia), de[k])
time1 = log.timer_debug1('2e-part grad of atom %d'%ia, *time1)
# Recompute nocc, nvir to include the frozen orbitals and make contraction for
# the 1-particle quantities, see also the kernel function in ccsd_grad module.
mo_coeff = mp.mo_coeff
mo_energy = mp._scf.mo_energy
nao, nmo = mo_coeff.shape
nocc = numpy.count_nonzero(mp.mo_occ > 0)
Imat = reduce(numpy.dot, (mo_coeff.T, Imat, mp._scf.get_ovlp(), mo_coeff)) * -1
dm1mo = numpy.zeros((nmo,nmo))
if with_frozen:
dco = Imat[OF[:,None],OA] / (mo_energy[OF,None] - mo_energy[OA])
dfv = Imat[VF[:,None],VA] / (mo_energy[VF,None] - mo_energy[VA])
dm1mo[OA[:,None],OA] = doo + doo.T
dm1mo[OF[:,None],OA] = dco
dm1mo[OA[:,None],OF] = dco.T
dm1mo[VA[:,None],VA] = dvv + dvv.T
dm1mo[VF[:,None],VA] = dfv
dm1mo[VA[:,None],VF] = dfv.T
else:
dm1mo[:nocc,:nocc] = doo + doo.T
dm1mo[nocc:,nocc:] = dvv + dvv.T
dm1 = reduce(numpy.dot, (mo_coeff, dm1mo, mo_coeff.T))
vhf = mp._scf.get_veff(mp.mol, dm1) * 2
Xvo = reduce(numpy.dot, (mo_coeff[:,nocc:].T, vhf, mo_coeff[:,:nocc]))
Xvo+= Imat[:nocc,nocc:].T - Imat[nocc:,:nocc]
dm1mo += _response_dm1(mp, Xvo)
time1 = log.timer_debug1('response_rdm1 intermediates', *time1)
Imat[nocc:,:nocc] = Imat[:nocc,nocc:].T
im1 = reduce(numpy.dot, (mo_coeff, Imat, mo_coeff.T))
time1 = log.timer_debug1('response_rdm1', *time1)
log.debug('h1 and JK1')
hcore_deriv = mf_grad.hcore_generator(mol)
s1 = mf_grad.get_ovlp(mol)
zeta = lib.direct_sum('i+j->ij', mo_energy, mo_energy) * .5
zeta[nocc:,:nocc] = mo_energy[:nocc]
zeta[:nocc,nocc:] = mo_energy[:nocc].reshape(-1,1)
zeta = reduce(numpy.dot, (mo_coeff, zeta*dm1mo, mo_coeff.T))
dm1 = reduce(numpy.dot, (mo_coeff, dm1mo, mo_coeff.T))
p1 = numpy.dot(mo_coeff[:,:nocc], mo_coeff[:,:nocc].T)
vhf_s1occ = reduce(numpy.dot, (p1, mp._scf.get_veff(mol, dm1+dm1.T), p1))
time1 = log.timer_debug1('h1 and JK1', *time1)
# Hartree-Fock part contribution
dm1p = hf_dm1 + dm1*2
dm1 += hf_dm1
zeta += mf_grad.make_rdm1e(mo_energy, mo_coeff, mp.mo_occ)
for k, ia in enumerate(atmlst):
shl0, shl1, p0, p1 = offsetdic[ia]
# s[1] dot I, note matrix im1 is not hermitian
de[k] += numpy.einsum('xij,ij->x', s1[:,p0:p1], im1[p0:p1])
de[k] += numpy.einsum('xji,ij->x', s1[:,p0:p1], im1[:,p0:p1])
# h[1] \dot DM, contribute to f1
h1ao = hcore_deriv(ia)
de[k] += numpy.einsum('xij,ji->x', h1ao, dm1)
# -s[1]*e \dot DM, contribute to f1
de[k] -= numpy.einsum('xij,ij->x', s1[:,p0:p1], zeta[p0:p1] )
de[k] -= numpy.einsum('xji,ij->x', s1[:,p0:p1], zeta[:,p0:p1])
# -vhf[s_ij[1]], contribute to f1, *2 for s1+s1.T
de[k] -= numpy.einsum('xij,ij->x', s1[:,p0:p1], vhf_s1occ[p0:p1]) * 2
de[k] -= numpy.einsum('xij,ij->x', vhf1[k], dm1p)
de += rhf_grad.grad_nuc(mol)
log.timer('%s gradients' % mp.__class__.__name__, *time0)
return de
def kernel(mycc,
t1=None,
t2=None,
l1=None,
l2=None,
eris=None,
atmlst=None,
mf_grad=None,
d1=None,
d2=None,
verbose=logger.INFO):
if eris is not None:
if (abs(eris.focka - numpy.diag(eris.focka.diagonal())).max() > 1e-3
or abs(eris.fockb - numpy.diag(eris.fockb.diagonal())).max() >
1e-3):
raise RuntimeError(
'UCCSD gradients does not support NHF (non-canonical HF)')
if t1 is None: t1 = mycc.t1
if t2 is None: t2 = mycc.t2
if l1 is None: l1 = mycc.l1
if l2 is None: l2 = mycc.l2
if mf_grad is None: mf_grad = mycc._scf.nuc_grad_method()
log = logger.new_logger(mycc, verbose)
time0 = time.clock(), time.time()
log.debug('Build uccsd rdm1 intermediates')
if d1 is None:
d1 = uccsd_rdm._gamma1_intermediates(mycc, t1, t2, l1, l2)
time1 = log.timer_debug1('rdm1 intermediates', *time0)
log.debug('Build uccsd rdm2 intermediates')
fdm2 = lib.H5TmpFile()
if d2 is None:
d2 = uccsd_rdm._gamma2_outcore(mycc, t1, t2, l1, l2, fdm2, True)
time1 = log.timer_debug1('rdm2 intermediates', *time1)
mol = mycc.mol
mo_a, mo_b = mycc.mo_coeff
mo_ea, mo_eb = mycc._scf.mo_energy
nao, nmoa = mo_a.shape
nmob = mo_b.shape[1]
nocca = numpy.count_nonzero(mycc.mo_occ[0] > 0)
noccb = numpy.count_nonzero(mycc.mo_occ[1] > 0)
nvira = nmoa - nocca
nvirb = nmob - noccb
with_frozen = not (mycc.frozen is None or mycc.frozen is 0)
moidx = mycc.get_frozen_mask()
OA_a, VA_a, OF_a, VF_a = ccsd_grad._index_frozen_active(
moidx[0], mycc.mo_occ[0])
OA_b, VA_b, OF_b, VF_b = ccsd_grad._index_frozen_active(
moidx[1], mycc.mo_occ[1])
log.debug('symmetrized rdm2 and MO->AO transformation')
# Roughly, dm2*2 is computed in _rdm2_mo2ao
mo_active = (mo_a[:, numpy.hstack((OA_a, VA_a))], mo_b[:,
numpy.hstack(
(OA_b, VA_b))])
_rdm2_mo2ao(mycc, d2, mo_active, fdm2) # transform the active orbitals
time1 = log.timer_debug1('MO->AO transformation', *time1)
hf_dm1a, hf_dm1b = mycc._scf.make_rdm1(mycc.mo_coeff, mycc.mo_occ)
hf_dm1 = hf_dm1a + hf_dm1b
if atmlst is None:
atmlst = range(mol.natm)
offsetdic = mol.offset_nr_by_atom()
diagidx = numpy.arange(nao)
diagidx = diagidx * (diagidx + 1) // 2 + diagidx
de = numpy.zeros((len(atmlst), 3))
Imata = numpy.zeros((nao, nao))
Imatb = numpy.zeros((nao, nao))
vhf1 = fdm2.create_dataset('vhf1', (len(atmlst), 2, 3, nao, nao), 'f8')
# 2e AO integrals dot 2pdm
max_memory = max(0, mycc.max_memory - lib.current_memory()[0])
blksize = max(1, int(max_memory * .9e6 / 8 / (nao**3 * 2.5)))
for k, ia in enumerate(atmlst):
shl0, shl1, p0, p1 = offsetdic[ia]
ip1 = p0
vhf = numpy.zeros((2, 3, nao, nao))
for b0, b1, nf in ccsd_grad._shell_prange(mol, shl0, shl1, blksize):
ip0, ip1 = ip1, ip1 + nf
dm2bufa = ccsd_grad._load_block_tril(fdm2['dm2aa+ab'], ip0, ip1,
nao)
dm2bufb = ccsd_grad._load_block_tril(fdm2['dm2bb+ab'], ip0, ip1,
nao)
dm2bufa[:, :, diagidx] *= .5
dm2bufb[:, :, diagidx] *= .5
shls_slice = (b0, b1, 0, mol.nbas, 0, mol.nbas, 0, mol.nbas)
eri0 = mol.intor('int2e', aosym='s2kl', shls_slice=shls_slice)
Imata += lib.einsum('ipx,iqx->pq', eri0.reshape(nf, nao, -1),
dm2bufa)
Imatb += lib.einsum('ipx,iqx->pq', eri0.reshape(nf, nao, -1),
dm2bufb)
eri0 = None
eri1 = mol.intor('int2e_ip1',
comp=3,
aosym='s2kl',
shls_slice=shls_slice).reshape(3, nf, nao, -1)
de[k] -= numpy.einsum('xijk,ijk->x', eri1, dm2bufa) * 2
de[k] -= numpy.einsum('xijk,ijk->x', eri1, dm2bufb) * 2
dm2bufa = dm2bufb = None
# HF part
for i in range(3):
eri1tmp = lib.unpack_tril(eri1[i].reshape(nf * nao, -1))
eri1tmp = eri1tmp.reshape(nf, nao, nao, nao)
vhf[:, i] += numpy.einsum('ijkl,ij->kl', eri1tmp,
hf_dm1[ip0:ip1])
vhf[0, i] -= numpy.einsum('ijkl,il->kj', eri1tmp,
hf_dm1a[ip0:ip1])
vhf[1, i] -= numpy.einsum('ijkl,il->kj', eri1tmp,
hf_dm1b[ip0:ip1])
vhf[:, i, ip0:ip1] += numpy.einsum('ijkl,kl->ij', eri1tmp,
hf_dm1)
vhf[0, i, ip0:ip1] -= numpy.einsum('ijkl,jk->il', eri1tmp,
hf_dm1a)
vhf[1, i, ip0:ip1] -= numpy.einsum('ijkl,jk->il', eri1tmp,
hf_dm1b)
eri1 = eri1tmp = None
vhf1[k] = vhf
log.debug('2e-part grad of atom %d %s = %s', ia, mol.atom_symbol(ia),
de[k])
time1 = log.timer_debug1('2e-part grad of atom %d' % ia, *time1)
s0 = mycc._scf.get_ovlp()
Imata = reduce(numpy.dot, (mo_a.T, Imata, s0, mo_a)) * -1
Imatb = reduce(numpy.dot, (mo_b.T, Imatb, s0, mo_b)) * -1
dm1a = numpy.zeros((nmoa, nmoa))
dm1b = numpy.zeros((nmob, nmob))
doo, dOO = d1[0]
dov, dOV = d1[1]
dvo, dVO = d1[2]
dvv, dVV = d1[3]
if with_frozen:
dco = Imata[OF_a[:, None], OA_a] / (mo_ea[OF_a, None] - mo_ea[OA_a])
dfv = Imata[VF_a[:, None], VA_a] / (mo_ea[VF_a, None] - mo_ea[VA_a])
dm1a[OA_a[:, None], OA_a] = (doo + doo.T) * .5
dm1a[OF_a[:, None], OA_a] = dco
dm1a[OA_a[:, None], OF_a] = dco.T
dm1a[VA_a[:, None], VA_a] = (dvv + dvv.T) * .5
dm1a[VF_a[:, None], VA_a] = dfv
dm1a[VA_a[:, None], VF_a] = dfv.T
dco = Imatb[OF_b[:, None], OA_b] / (mo_eb[OF_b, None] - mo_eb[OA_b])
dfv = Imatb[VF_b[:, None], VA_b] / (mo_eb[VF_b, None] - mo_eb[VA_b])
dm1b[OA_b[:, None], OA_b] = (dOO + dOO.T) * .5
dm1b[OF_b[:, None], OA_b] = dco
dm1b[OA_b[:, None], OF_b] = dco.T
dm1b[VA_b[:, None], VA_b] = (dVV + dVV.T) * .5
dm1b[VF_b[:, None], VA_b] = dfv
dm1b[VA_b[:, None], VF_b] = dfv.T
else:
dm1a[:nocca, :nocca] = (doo + doo.T) * .5
dm1a[nocca:, nocca:] = (dvv + dvv.T) * .5
dm1b[:noccb, :noccb] = (dOO + dOO.T) * .5
dm1b[noccb:, noccb:] = (dVV + dVV.T) * .5
dm1 = (reduce(numpy.dot,
(mo_a, dm1a, mo_a.T)), reduce(numpy.dot,
(mo_b, dm1b, mo_b.T)))
vhf = mycc._scf.get_veff(mycc.mol, dm1)
Xvo = reduce(numpy.dot, (mo_a[:, nocca:].T, vhf[0], mo_a[:, :nocca]))
XVO = reduce(numpy.dot, (mo_b[:, noccb:].T, vhf[1], mo_b[:, :noccb]))
Xvo += Imata[:nocca, nocca:].T - Imata[nocca:, :nocca]
XVO += Imatb[:noccb, noccb:].T - Imatb[noccb:, :noccb]
dm1_resp = _response_dm1(mycc, (Xvo, XVO), eris)
dm1a += dm1_resp[0]
dm1b += dm1_resp[1]
time1 = log.timer_debug1('response_rdm1 intermediates', *time1)
Imata[nocca:, :nocca] = Imata[:nocca, nocca:].T
Imatb[noccb:, :noccb] = Imatb[:noccb, noccb:].T
im1 = reduce(numpy.dot, (mo_a, Imata, mo_a.T))
im1 += reduce(numpy.dot, (mo_b, Imatb, mo_b.T))
time1 = log.timer_debug1('response_rdm1', *time1)
log.debug('h1 and JK1')
hcore_deriv = mf_grad.hcore_generator(mol)
s1 = mf_grad.get_ovlp(mol)
zeta = (mo_ea[:, None] + mo_ea) * .5
zeta[nocca:, :nocca] = mo_ea[:nocca]
zeta[:nocca, nocca:] = mo_ea[:nocca].reshape(-1, 1)
zeta_a = reduce(numpy.dot, (mo_a, zeta * dm1a, mo_a.T))
zeta = (mo_eb[:, None] + mo_eb) * .5
zeta[noccb:, :noccb] = mo_eb[:noccb]
zeta[:noccb, noccb:] = mo_eb[:noccb].reshape(-1, 1)
zeta_b = reduce(numpy.dot, (mo_b, zeta * dm1b, mo_b.T))
dm1 = (reduce(numpy.dot,
(mo_a, dm1a, mo_a.T)), reduce(numpy.dot,
(mo_b, dm1b, mo_b.T)))
vhf_s1occ = mycc._scf.get_veff(mol, (dm1[0] + dm1[0].T, dm1[1] + dm1[1].T))
p1a = numpy.dot(mo_a[:, :nocca], mo_a[:, :nocca].T)
p1b = numpy.dot(mo_b[:, :noccb], mo_b[:, :noccb].T)
vhf_s1occ = (reduce(numpy.dot, (p1a, vhf_s1occ[0], p1a)) +
reduce(numpy.dot, (p1b, vhf_s1occ[1], p1b))) * .5
time1 = log.timer_debug1('h1 and JK1', *time1)
# Hartree-Fock part contribution
dm1pa = hf_dm1a + dm1[0] * 2
dm1pb = hf_dm1b + dm1[1] * 2
dm1 = dm1[0] + dm1[1] + hf_dm1
zeta_a += rhf_grad.make_rdm1e(mo_ea, mo_a, mycc.mo_occ[0])
zeta_b += rhf_grad.make_rdm1e(mo_eb, mo_b, mycc.mo_occ[1])
zeta = zeta_a + zeta_b
for k, ia in enumerate(atmlst):
shl0, shl1, p0, p1 = offsetdic[ia]
# s[1] dot I, note matrix im1 is not hermitian
de[k] += numpy.einsum('xij,ij->x', s1[:, p0:p1], im1[p0:p1])
de[k] += numpy.einsum('xji,ij->x', s1[:, p0:p1], im1[:, p0:p1])
# h[1] \dot DM, contribute to f1
h1ao = hcore_deriv(ia)
de[k] += numpy.einsum('xij,ji->x', h1ao, dm1)
# -s[1]*e \dot DM, contribute to f1
de[k] -= numpy.einsum('xij,ij->x', s1[:, p0:p1], zeta[p0:p1])
de[k] -= numpy.einsum('xji,ij->x', s1[:, p0:p1], zeta[:, p0:p1])
# -vhf[s_ij[1]], contribute to f1, *2 for s1+s1.T
de[k] -= numpy.einsum('xij,ij->x', s1[:, p0:p1], vhf_s1occ[p0:p1]) * 2
de[k] -= numpy.einsum('xij,ij->x', vhf1[k, 0], dm1pa)
de[k] -= numpy.einsum('xij,ij->x', vhf1[k, 1], dm1pb)
de += rhf_grad.grad_nuc(mol)
log.timer('%s gradients' % mycc.__class__.__name__, *time0)
return de