#!/usr/bin/env python
# Copyright 2014-2021 The PySCF Developers. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
'''
native implementation of DF-MP2/RI-MP2 with a UHF reference
'''
import numpy as np
import scipy
from pyscf import lib
from pyscf import scf
from pyscf import df
from pyscf.scf import ucphf
from pyscf.mp.dfmp2_native import DFRMP2, ints3c_cholesky, orbgrad_from_Gamma
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class DFUMP2(DFRMP2):
'''
native implementation of DF-MP2/RI-MP2 with a UHF reference
'''
def __init__(self, mf, frozen=None, auxbasis=None):
'''
Args:
mf : UHF instance
frozen : number of frozen orbitals or list of frozen orbitals
auxbasis : name of auxiliary basis set, otherwise determined automatically
'''
# UHF quantities are stored as numpy arrays
self.mo_coeff = np.array(mf.mo_coeff)
self.mo_energy = np.array(mf.mo_energy)
self.nocc = np.array([np.count_nonzero(mf.mo_occ[0]), np.count_nonzero(mf.mo_occ[1])])
# UHF MO coefficient matrix shape: (2, number of AOs, number of MOs)
self.nmo = self.mo_coeff.shape[2]
self.e_scf = mf.e_tot
self._scf = mf
# Process the frozen core option correctly as either an integer or two lists (alpha, beta).
# self.frozen_mask sets a flag for each orbital if it is frozen (True) or not (False).
# Only occupied orbitals can be frozen.
self.frozen_mask = np.zeros((2, self.nmo), dtype=bool)
if frozen is None:
pass
elif lib.isinteger(frozen):
if frozen > min(self.nocc):
raise ValueError('only occupied orbitals can be frozen')
self.frozen_mask[:, :frozen] = True
else:
try:
if len(frozen) != 2:
raise ValueError
for s in 0, 1:
if not lib.isintsequence(frozen[s]):
raise TypeError
except (TypeError, ValueError):
raise TypeError('frozen must be an integer or two integer lists')
if len(frozen[0]) != len(frozen[1]):
raise ValueError('frozen orbital lists not of equal length')
for s in 0, 1:
self.frozen_mask[s, frozen[s]] = True
# mask for occupied orbitals that are not frozen
self.occ_mask = np.zeros((2, self.nmo), dtype=bool)
for s in 0, 1:
self.occ_mask[s, :self.nocc[s]] = True
self.occ_mask[self.frozen_mask] = False
self.mol = mf.mol
if not auxbasis:
auxbasis = df.make_auxbasis(self.mol, mp2fit=True)
self.auxmol = df.make_auxmol(self.mol, auxbasis)
self.verbose = self.mol.verbose
self.stdout = self.mol.stdout
self.max_memory = self.mol.max_memory
# _intsfile will be a list with two elements for the alpha and beta integrals
self._intsfile = []
self.e_corr = None
# Spin component scaling factors
self.ps = 1.0
self.pt = 1.0
self.cphf_max_cycle = 100
self.cphf_tol = mf.conv_tol
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def dump_flags(self, logger=None):
'''
Prints selected information.
Args:
logger : Logger object
'''
if not logger:
logger = lib.logger.new_logger(self)
logger.info('')
logger.info('******** {0:s} ********'.format(repr(self.__class__)))
logger.info('nmo = {0:d}'.format(self.nmo))
logger.info('nocc = {0:d}, {1:d}'.format(self.nocc[0], self.nocc[1]))
nfrozen = np.count_nonzero(self.frozen_mask[0])
logger.info('no. of frozen = {0:d}'.format(nfrozen))
frozen_tmp = np.arange(self.nmo)[self.frozen_mask[0]]
logger.debug('frozen (alpha) = {0}'.format(frozen_tmp))
frozen_tmp = np.arange(self.nmo)[self.frozen_mask[1]]
logger.debug('frozen (beta) = {0}'.format(frozen_tmp))
logger.info('basis = {0:s}'.format(repr(self.mol.basis)))
logger.info('auxbasis = {0:s}'.format(repr(self.auxmol.basis)))
logger.info('max_memory = {0:.1f} MB (current use {1:.1f} MB)'.
format(self.max_memory, lib.current_memory()[0]))
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def calculate_energy(self):
'''
Calculates the MP2 correlation energy.
'''
if not self.has_ints:
self.calculate_integrals_()
logger = lib.logger.new_logger(self)
logger.info('')
logger.info('Calculating DF-MP2 energy')
self.e_corr = emp2_uhf(self._intsfile, self.mo_energy, self.frozen_mask,
logger, ps=self.ps, pt=self.pt)
logger.note('DF-MP2 correlation energy: {0:.14f}'.format(self.e_corr))
return self.e_corr
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def make_rdm1(self, relaxed=False, ao_repr=False):
'''
Calculates the MP2 1-RDM.
- The relaxed density matrix can be used to calculate properties of systems
for which MP2 is well-behaved.
- The unrelaxed density is less suited to calculate properties accurately,
but it can be used to calculate CASSCF starting orbitals.
Args:
relaxed : relaxed density if True, unrelaxed density if False
ao_repr : density in AO or in MO basis
Returns:
the 1-RDM
'''
logger = lib.logger.new_logger(self)
if relaxed:
logger.info('')
logger.info('DF-MP2 relaxed density calculation')
else:
logger.info('')
logger.info('DF-MP2 unrelaxed density calculation')
rdm1_mo = make_rdm1(self, relaxed, logger)
if ao_repr:
return lib.einsum('sxp,spq,syq->sxy', self.mo_coeff, rdm1_mo, self.mo_coeff)
else:
return rdm1_mo
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def make_natorbs(self, rdm1_mo=None, relaxed=False):
'''
Calculate natural orbitals.
Note: the most occupied orbitals come first (left)
and the least occupied orbitals last (right).
Args:
rdm1_mo : 1-RDM in MO basis
the function calculates a density matrix if none is provided
relaxed : calculated relaxed or unrelaxed density matrix
Returns:
natural occupation numbers, natural orbitals
'''
if rdm1_mo is None:
dm = self.make_rdm1(ao_repr=False, relaxed=relaxed)
elif isinstance(rdm1_mo, np.ndarray):
dm = rdm1_mo
else:
raise TypeError('rdm1_mo must be a 3-D array')
# Transform the beta component to the alpha basis and sum both together.
SAO = self.mol.intor_symmetric('int1e_ovlp')
Sab = lib.einsum('xp,xy,yq->pq', self.mo_coeff[0, :, :], SAO, self.mo_coeff[1, :, :])
rdm1_abas = dm[0, :, :] + lib.einsum('pr,rs,qs->pq', Sab, dm[1, :, :], Sab)
# Diagonalize the spin-traced 1-RDM in alpha basis to get the natural orbitals.
eigval, eigvec = np.linalg.eigh(rdm1_abas)
natocc = np.flip(eigval)
natorb = lib.dot(self.mo_coeff[0, :, :], np.fliplr(eigvec))
return natocc, natorb
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def calculate_integrals_(self):
'''
Calculates the three center integrals for MP2.
'''
if not isinstance(self._scf, scf.uhf.UHF):
raise TypeError('Class initialization with non-UHF object')
intsfile = []
logger = lib.logger.new_logger(self)
logger.info('')
logger.info('Calculating integrals')
for s in [0, 1]:
Co = self.mo_coeff[s][:, self.occ_mask[s]]
Cv = self.mo_coeff[s][:, self.nocc[s]:]
f = ints3c_cholesky(self.mol, self.auxmol, Co, Cv, self.max_memory, logger)
intsfile.append(f)
self._intsfile = intsfile
logger.info('Stored in files:\n{0:s}\n{1:s}'.
format(self._intsfile[0].filename, self._intsfile[1].filename))
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def delete(self):
'''
Delete the temporary file(s).
'''
self._intsfile = []
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def nuc_grad_method(self):
raise NotImplementedError
to_gpu = lib.to_gpu
MP2 = UMP2 = DFMP2 = DFUMP2
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class SCSDFUMP2(DFUMP2):
'''
UHF-DF-MP2 with spin-component scaling
S. Grimme, J. Chem. Phys. 118 (2003), 9095
https://doi.org/10.1063/1.1569242
'''
def __init__(self, mf, ps=6/5, pt=1/3, *args, **kwargs):
'''
mf : UHF instance
ps : opposite-spin (singlet) scaling factor
pt : same-spin (triplet) scaling factor
'''
super().__init__(mf, *args, **kwargs)
self.ps = ps
self.pt = pt
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def dump_flags(self, logger=None):
if not logger:
logger = lib.logger.new_logger(self)
super().dump_flags(logger=logger)
logger.info('pt(scs) = {0:.6f}'.format(self.pt))
logger.info('ps(scs) = {0:.6f}'.format(self.ps))
SCSMP2 = SCSUMP2 = SCSDFMP2 = SCSDFUMP2
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def emp2_uhf(intsfiles, mo_energy, frozen_mask, logger, ps=1.0, pt=1.0):
'''
Calculates the DF-MP2 energy with an UHF reference.
Args:
intsfiles : contains the three center integrals in MO basis
mo_energy : energies of the molecular orbitals
frozen_mask : boolean mask for frozen orbitals
logger : Logger instance
ps : SCS factor for opposite-spin contributions
pt : SCS factor for same-spin contributions
Returns:
the MP2 correlation energy
'''
ints_a = intsfiles[0]['ints_cholesky']
ints_b = intsfiles[1]['ints_cholesky']
nocc_act = np.array([ints_a.shape[0], ints_b.shape[0]])
nfrozen = np.count_nonzero(frozen_mask[0])
if np.count_nonzero(frozen_mask[1]) != nfrozen:
raise ValueError('number of frozen alpha and beta orbitals differs')
nocc = nocc_act + nfrozen
nvirt = np.array([ints_a.shape[2], ints_b.shape[2]])
logger.debug(' UHF-DF-MP2 energy routine')
logger.debug(' Occupied orbitals: {0:d}, {1:d}'.format(nocc[0], nocc[1]))
logger.debug(' Virtual orbitals: {0:d}, {1:d}'.format(nvirt[0], nvirt[1]))
logger.debug(' Frozen orbitals: {0:d}'.format(nfrozen))
logger.debug(' Integrals (alpha) from file: {0:s}'.format(intsfiles[0].filename))
logger.debug(' Integrals (beta) from file: {0:s}'.format(intsfiles[1].filename))
mo_energy_masked = mo_energy[~frozen_mask].reshape((2, -1))
energy_total = 0.0
# loop over spins to calculate same-spin energies
for s in 0, 1:
energy_contrib = 0.0
if s == 0:
logger.debug(' alpha-alpha pairs')
ints = ints_a
else:
logger.debug(' beta-beta pairs')
ints = ints_b
# precompute Eab[a, b] = mo_energy[a] + mo_energy[b] for the denominator
Eab = np.zeros((nvirt[s], nvirt[s]))
for a in range(nvirt[s]):
Eab[a, :] += mo_energy[s, nocc[s]+a]
Eab[:, a] += mo_energy[s, nocc[s]+a]
# loop over j < i
for i in range(nocc_act[s]):
ints3c_ia = ints[i, :, :]
for j in range(i):
ints3c_jb = ints[j, :, :]
Kab = lib.dot(ints3c_ia.T, ints3c_jb)
DE = mo_energy_masked[s, i] + mo_energy_masked[s, j] - Eab
Tab = (Kab - Kab.T) / DE
energy_contrib += pt * lib.einsum('ab,ab', Tab, Kab)
logger.debug(' E = {0:.14f}'.format(energy_contrib))
energy_total += energy_contrib
# opposite-spin energy
logger.debug(' alpha-beta pairs')
# precompute Eab[a, b] = mo_energy[a] + mo_energy[b] for the denominator
Eab = np.zeros((nvirt[0], nvirt[1]))
for a in range(nvirt[0]):
Eab[a, :] += mo_energy[0, nocc[0]+a]
for b in range(nvirt[1]):
Eab[:, b] += mo_energy[1, nocc[1]+b]
# loop over i(alpha), j(beta)
energy_contrib = 0.0
for i in range(nocc_act[0]):
ints3c_ia = ints_a[i, :, :]
for j in range(nocc_act[1]):
ints3c_jb = ints_b[j, :, :]
Kab = lib.dot(ints3c_ia.T, ints3c_jb)
DE = mo_energy_masked[0, i] + mo_energy_masked[1, j] - Eab
Tab = Kab / DE
energy_contrib += ps * lib.einsum('ab,ab', Tab, Kab)
logger.debug(' E = {0:.14f}'.format(energy_contrib))
energy_total += energy_contrib
logger.debug(' DF-MP2 correlation energy: {0:.14f}'.format(energy_total))
return energy_total
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def make_rdm1(mp2, relaxed, logger=None):
'''
Calculates the unrelaxed or relaxed MP2 density matrix.
Args:
mp2 : DFUMP2 instance
relaxed : relaxed density if True, unrelaxed density if False
logger : Logger instance
Returns:
the 1-RDM in MO basis
'''
if not mp2.has_ints:
mp2.calculate_integrals_()
# Calculate the unrelaxed 1-RDM.
if logger is None:
logger = lib.logger.new_logger(mp2)
rdm1, GammaFile = \
ump2_densities_contribs(mp2._intsfile, mp2.mo_energy, mp2.frozen_mask, mp2.max_memory,
logger, calcGamma=relaxed, auxmol=mp2.auxmol, ps=mp2.ps, pt=mp2.pt)
if relaxed:
Lvo = [None, None]
for s, sstr in [(0, 'alpha'), (1, 'beta')]:
# right-hand side for the CPHF equation
Gamma = GammaFile['Gamma_'+sstr]
Lvo[s], Lfo_s = \
orbgrad_from_Gamma(mp2.mol, mp2.auxmol, Gamma, mp2.mo_coeff[s], mp2.frozen_mask[s],
mp2.max_memory, logger)
# frozen core orbital relaxation contribution
frozen_list = np.arange(mp2.nmo)[mp2.frozen_mask[s]]
for fm, f in enumerate(frozen_list):
for i in np.arange(mp2.nmo)[mp2.occ_mask[s]]:
zfo = Lfo_s[fm, i] / (mp2.mo_energy[s, f] - mp2.mo_energy[s, i])
rdm1[s, f, i] += 0.5 * zfo
rdm1[s, i, f] += 0.5 * zfo
# Fock response
Lvo_a, Lvo_b = fock_response_uhf(mp2._scf, rdm1)
Lvo[0] -= Lvo_a
Lvo[1] -= Lvo_b
# solving the CPHF equations
minusLvo = [-Lvo[0], -Lvo[1]]
zvo = solve_cphf_uhf(mp2._scf, minusLvo, mp2.cphf_max_cycle, mp2.cphf_tol, logger)
# add the relaxation contribution to the density
for s in 0, 1:
rdm1[s, mp2.nocc[s]:, :mp2.nocc[s]] += 0.5 * zvo[s]
rdm1[s, :mp2.nocc[s], mp2.nocc[s]:] += 0.5 * zvo[s].T
# HF contribution
for s in 0, 1:
rdm1[s, :mp2.nocc[s], :mp2.nocc[s]] += np.eye(mp2.nocc[s])
return rdm1
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def ump2_densities_contribs(intsfiles, mo_energy, frozen_mask, max_memory, logger,
calcGamma=False, auxmol=None, ps=1.0, pt=1.0):
'''
Calculates the unrelaxed DF-MP2 density matrix contribution with a UHF reference.
Note: this is the difference density, i.e. without HF contribution.A
lso calculates the three-center two-particle density if requested.
Args:
intsfile : contains the three center integrals
mo_energy : molecular orbital energies
frozen_mask : boolean mask for frozen orbitals
max_memory : memory threshold in MB
logger : Logger instance
calcGamma : if True, calculate 3c2e density
auxmol : required if relaxed is True
ps : SCS factor for opposite-spin contributions
pt : SCS factor for same-spin contributions
Returns:
matrix containing the 1-RDM contribution, file with 3c2e density if requested
'''
ints = [intsfiles[s]['ints_cholesky'] for s in (0, 1)]
nocc_act = np.array([ints[s].shape[0] for s in (0, 1)])
naux = ints[0].shape[1]
if ints[1].shape[1] != naux:
raise ValueError('integrals have inconsistent aux dimensions')
nvirt = np.array([ints[s].shape[2] for s in (0, 1)])
nmo = mo_energy.shape[1]
nfrozen = np.count_nonzero(frozen_mask[0])
if np.count_nonzero(frozen_mask[0]) != nfrozen:
raise ValueError('unequal numbers of frozen orbitals for alpha and beta')
nocc = nfrozen + nocc_act
if np.any(nocc + nvirt != nmo):
raise ValueError('numbers of frozen, occupied and virtual orbitals inconsistent')
logger.debug(' Density matrix contributions for DF-MP2')
logger.debug(' Occupied orbitals: {0:d}, {1:d}'.format(nocc[0], nocc[1]))
logger.debug(' Virtual orbitals: {0:d}, {1:d}'.format(nvirt[0], nvirt[1]))
logger.debug(' Frozen orbitals: {0:d}'.format(nfrozen))
logger.debug(' Three center integrals (alpha) from file: {0:s}'.format(intsfiles[0].filename))
logger.debug(' Three center integrals (beta) from file: {0:s}'.format(intsfiles[1].filename))
GammaFile, LT = None, None
if calcGamma:
if not auxmol:
raise RuntimeError('auxmol needs to be specified for relaxed density computation')
# create temporary file to store the two-body density Gamma
GammaFile = lib.H5TmpFile(libver='latest')
GammaFile.create_dataset('Gamma_alpha', (nocc_act[0], naux, nvirt[0]), dtype='f8')
GammaFile.create_dataset('Gamma_beta', (nocc_act[1], naux, nvirt[1]), dtype='f8')
logger.debug(' Storing 3c2e density in file: {0:s}'.format(GammaFile.filename))
# We will need LT = L^T, where L L^T = V
LT = scipy.linalg.cholesky(auxmol.intor('int2c2e'), lower=False)
# We start forming P with contiguous frozen, occupied, virtual subblocks.
P = np.zeros((2, nmo, nmo))
mo_energy_masked = mo_energy[~frozen_mask].reshape(2, nmo-nfrozen)
# Loop over all the spin variants
for s1, s2 in [(0, 0), (0, 1), (1, 0), (1, 1)]:
with lib.H5TmpFile(libver='latest') as tfile:
tiset = \
tfile.create_dataset('amplitudes', (nocc_act[s2], nvirt[s1], nvirt[s2]), dtype='f8')
s1_str = ('alpha', 'beta')[s1]
s2_str = ('alpha', 'beta')[s2]
logger.debug(' {0:s}-{1:s} pairs'.format(s1_str, s2_str))
logger.debug(' Storing amplitudes in temporary file: {0:s}'.format(tfile.filename))
# Precompute Eab[a, b] = mo_energy[a] + mo_energy[b] for division with numpy.
Eab = np.zeros((nvirt[s1], nvirt[s2]))
for a in range(nvirt[s1]):
Eab[a, :] += mo_energy[s1, nocc[s1]+a]
for b in range(nvirt[s2]):
Eab[:, b] += mo_energy[s2, nocc[s2]+b]
# For each occupied spin orbital i, all amplitudes are calculated once and
# stored on disk. The occupied 1-RDM contribution is calculated in a batched
# algorithm. More memory -> more efficient I/O.
# The virtual contribution to the 1-RDM is calculated in memory.
for i in range(nocc_act[s1]):
ints3c_ia = ints[s1][i, :, :]
# Amplitudes T^ij_ab are calculated for a given orbital i with spin s1,
# and all j (s2), a (s1) and b (s2). These amplitudes are stored on disk.
for j in range(nocc_act[s2]):
ints3c_jb = ints[s2][j, :, :]
Kab = lib.dot(ints3c_ia.T, ints3c_jb)
DE = mo_energy_masked[s1, i] + mo_energy_masked[s2, j] - Eab
if s1 == s2:
numerator = Kab - Kab.T
prefactor = 0.5 * pt
else:
numerator = Kab
prefactor = ps
Tab = numerator / DE
tiset[j, :, :] = Tab
# virtual 1-RDM contribution
P[s1, nocc[s1]:, nocc[s1]:] += prefactor * lib.dot(Tab, Tab.T)
del ints3c_jb, Kab, DE, numerator, Tab
# Batches of amplitudes are read from disk to calculate the occupied
# 1-RDM contribution.
batchsize = int((max_memory - lib.current_memory()[0]) * 1e6 / (nocc_act[s2] * nvirt[s2] * 8))
batchsize = min(nvirt[s1], batchsize)
if batchsize < 1:
raise MemoryError('Insufficient memory (PYSCF_MAX_MEMORY).')
logger.debug2(' Batch size: {0:d} (of {1:d})'.format(batchsize, nvirt[s1]))
logger.debug2(' Pij formation - MO {0:d} ({1:s}), batch size {2:d} (of {3:d})'.
format(i, s1_str, batchsize, nvirt[s1]))
for astart in range(0, nvirt[s1], batchsize):
aend = min(astart+batchsize, nvirt[s1])
tbatch = tiset[:, astart:aend, :]
if s1 == s2:
prefactor = 0.5 * pt
else:
prefactor = ps
P[s2, nfrozen:nocc[s2], nfrozen:nocc[s2]] -= \
prefactor * lib.einsum('iab,jab->ij', tbatch, tbatch)
del tbatch
if calcGamma:
# This produces (P | Q)^-1 (Q | i a)
ints3cV1_ia = scipy.linalg.solve_triangular(LT, ints3c_ia, lower=False)
# Here, we construct Gamma for spin s2
Gamma = GammaFile['Gamma_'+s2_str]
# Read batches of amplitudes from disk and calculate the two-body density Gamma
size = nvirt[s1] * nvirt[s2] * 8 + naux * nvirt[s2] * 8
batchsize = int((max_memory - lib.current_memory()[0]) * 1e6 / size)
batchsize = min(nocc_act[s2], batchsize)
if batchsize < 1:
raise MemoryError('Insufficient memory (PYSCF_MAX_MEMORY).')
logger.debug2(' Gamma ({0:s}) formation - MO {1:d} ({2:s}), batch size {3:d} (of {4:d})'.
format(s2_str, i, s1_str, batchsize, nocc_act[s2]))
if s1 == s2:
prefactor = 2.0 * pt
else:
prefactor = 2.0 * ps
for jstart in range(0, nocc_act[s2], batchsize):
jend = min(jstart+batchsize, nocc_act[s2])
tbatch = tiset[jstart:jend, :, :]
# Here, we collect two-body density contributions for spin s2
Gbatch = Gamma[jstart:jend, :, :]
for jj in range(jend-jstart):
Tijab = tbatch[jj]
Gbatch[jj] += prefactor * lib.dot(ints3cV1_ia, Tijab)
Gamma[jstart:jend, :, :] = Gbatch
del tbatch, Gbatch
# now reorder P such that the frozen orbitals correspond to frozen_mask
for s in 0, 1:
idx_reordered = \
np.concatenate([np.arange(nmo)[frozen_mask[s]], np.arange(nmo)[~frozen_mask[s]]])
P[s][idx_reordered, :] = P[s].copy()
P[s][:, idx_reordered] = P[s].copy()
logger.debug(' Density matrix contributions calculation finished')
return P, GammaFile
[docs]
def fock_response_uhf(mf, dm, full=True):
'''
Calculate the unrestricted Fock response function for a given density matrix.
Args:
mf : UHF instance
dm : density matrix in MO basis
full : full MO density matrix if True, [virt. x occ., virt. x occ.] if False
Returns:
Fock response in MO basis. Shape: [virt. x occ., virt. x occ.]
'''
mo_coeff = mf.mo_coeff
mo_occ = mf.mo_occ
nao = mf.mol.nao
dmao = np.zeros((2, nao, nao))
for s in 0, 1:
if full:
dmao[s, :, :] = lib.einsum('xp,pq,yq->xy', mo_coeff[s], dm[s], mo_coeff[s])
else:
Ci = mo_coeff[s][:, mo_occ[s]>0]
Ca = mo_coeff[s][:, mo_occ[s]==0]
dmao[s, :, :] = lib.einsum('xa,ai,yi->xy', Ca, dm[s], Ci)
rao = mf.get_veff(dm=dmao+dmao.transpose((0, 2, 1)))
rvo = [None, None]
for s in 0, 1:
Ci = mo_coeff[s][:, mo_occ[s]>0]
Ca = mo_coeff[s][:, mo_occ[s]==0]
rvo[s] = lib.einsum('xa,xy,yi->ai', Ca, rao[s], Ci)
return rvo
[docs]
def solve_cphf_uhf(mf, Lvo, max_cycle, tol, logger):
'''
Solve the CPHF equations.
Args:
mf : a UHF object
Lvo : right-hand side the the response equation
max_cycle : number of iterations for the CPHF solver
tol : convergence tolerance for the CPHF solver
logger : Logger object
'''
logger.info('Solving the CPHF response equations')
logger.info('Max. iterations: {0:d}'.format(max_cycle))
logger.info('Convergence tolerance: {0:.3g}'.format(tol))
# Currently we need to make the CPHF solver somewhat more talkative to see anything at all.
cphf_verbose = logger.verbose
if logger.verbose == lib.logger.INFO:
cphf_verbose = lib.logger.DEBUG
nva, noa = Lvo[0].shape
nvb, nob = Lvo[1].shape
def fvind(zflat):
za = zflat[0, :noa*nva].reshape(nva, noa)
zb = zflat[0, -nob*nvb:].reshape(nvb, nob)
ra, rb = fock_response_uhf(mf, [za, zb], full=False)
rflat = np.hstack([ra.reshape((1, noa*nva)), rb.reshape((1, nob*nvb))])
return rflat
zvo = ucphf.solve(fvind, mf.mo_energy, mf.mo_occ, Lvo,
max_cycle=max_cycle, tol=tol, verbose=cphf_verbose)[0]
logger.info('CPHF iterations finished')
return zvo
if __name__ == '__main__':
from pyscf import gto
mol = gto.Mole()
mol.atom = [['O', (0., 0., 0.)],
['O', (1.21, 0., 0.)]]
mol.spin = 2
mol.basis = 'def2-SVP'
mol.verbose = lib.logger.INFO
mol.build()
mf = scf.UHF(mol)
mf.kernel()
with DFUMP2(mf) as pt:
pt.kernel()
natocc, _ = pt.make_natorbs()
print()
print(natocc)
