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 += mf_grad.grad_nuc(mol)
log.timer('%s gradients' % mp.__class__.__name__, *time0)
return de
def grad_elec(mp_grad, t2, atmlst=None, verbose=logger.INFO):
mp = mp_grad.base
log = logger.new_logger(mp, verbose)
time0 = logger.process_clock(), logger.perf_counter()
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_grad.mol
with_frozen = not ((mp.frozen is None) or
(isinstance(mp.frozen,
(int, numpy.integer)) and mp.frozen == 0) or
(len(mp.frozen) == 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)))
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')
# Initialize hcore_deriv with the underlying SCF object because some
# extensions (e.g. QM/MM, solvent) modifies the SCF object only.
mf_grad = mp_grad.base._scf.nuc_grad_method()
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 += rhf_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)
log.timer('%s gradients' % mp.__class__.__name__, *time0)
return de
def make_rdm1_with_orbital_response(mp):
import time
from pyscf import lib
from pyscf.grad.mp2 import _response_dm1, _index_frozen_active, _shell_prange
from pyscf.mp import mp2
from pyscf.ao2mo import _ao2mo
log = lib.logger.new_logger(mp)
time0 = time.clock(), time.time()
mol = mp.mol
log.debug('Build mp2 rdm1 intermediates')
d1 = mp2._gamma1_intermediates(mp, mp.t2)
doo, dvv = d1
time1 = log.timer_debug1('rdm1 intermediates', *time0)
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(mp.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)
offsetdic = mol.offset_nr_by_atom()
diagidx = numpy.arange(nao)
diagidx = diagidx * (diagidx + 1) // 2 + diagidx
Imat = numpy.zeros((nao, nao))
# 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 ia in range(mol.natm):
shl0, shl1, p0, p1 = offsetdic[ia]
ip1 = p0
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
dm2buf = None
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)
# Transform to AO basis
dm1 = reduce(numpy.dot, (mo_coeff, dm1mo, mo_coeff.T))
dm1 += mp._scf.make_rdm1(mp.mo_coeff, mp.mo_occ)
return dm1