# Copyright 2014-2020 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.
#
# Author: Oliver J. Backhouse <olbackhouse@gmail.com>
# George H. Booth <george.booth@kcl.ac.uk>
#
'''
Auxiliary second-order Green's function perturbation theory for
arbitrary moment consistency
'''
import numpy as np
from pyscf import lib
from pyscf.lib import logger
from pyscf import __config__
from pyscf.agf2 import ragf2
from pyscf.agf2 import aux_space as aux
[docs]
def build_se_part(agf2, eri, gf_occ, gf_vir, os_factor=1.0, ss_factor=1.0):
''' Builds either the auxiliaries of the occupied self-energy,
or virtual if :attr:`gf_occ` and :attr:`gf_vir` are swapped.
Args:
eri : _ChemistsERIs
Electronic repulsion integrals
gf_occ : GreensFunction
Occupied Green's function
gf_vir : GreensFunction
Virtual Green's function
Kwargs:
os_factor : float
Opposite-spin factor for spin-component-scaled (SCS)
calculations. Default 1.0
ss_factor : float
Same-spin factor for spin-component-scaled (SCS)
calculations. Default 1.0
Returns:
:class:`SelfEnergy`
'''
cput0 = (logger.process_clock(), logger.perf_counter())
log = logger.Logger(agf2.stdout, agf2.verbose)
assert type(gf_occ) is aux.GreensFunction
assert type(gf_vir) is aux.GreensFunction
nmo = agf2.nmo
nocc = gf_occ.naux
nvir = gf_vir.naux
naux = nocc * nocc * nvir
tol = agf2.weight_tol
if not (agf2.frozen is None or agf2.frozen == 0):
mask = ragf2.get_frozen_mask(agf2)
nmo -= np.sum(~mask)
e = np.zeros((naux))
v = np.zeros((nmo, naux))
fpos = np.sqrt(0.5 * os_factor)
fneg = np.sqrt(0.5 * os_factor + ss_factor)
fdia = np.sqrt(os_factor)
eja = lib.direct_sum('j,a->ja', gf_occ.energy, -gf_vir.energy)
coeffs = (gf_occ.coupling, gf_occ.coupling, gf_vir.coupling)
qeri = _make_qmo_eris_incore(agf2, eri, coeffs)
p1 = 0
for i in range(nocc):
xija = qeri[:,i,:i].reshape(nmo, -1)
xjia = qeri[:,:i,i].reshape(nmo, -1)
xiia = qeri[:,i,i].reshape(nmo, -1)
eija = gf_occ.energy[i] + eja[:i+1]
p0, p1 = p1, p1 + i*nvir
e[p0:p1] = eija[:i].ravel()
v[:,p0:p1] = fneg * (xija - xjia)
p0, p1 = p1, p1 + i*nvir
e[p0:p1] = eija[:i].ravel()
v[:,p0:p1] = fpos * (xija + xjia)
p0, p1 = p1, p1 + nvir
e[p0:p1] = eija[i].ravel()
v[:,p0:p1] = fdia * xiia
se = aux.SelfEnergy(e, v, chempot=gf_occ.chempot)
se.remove_uncoupled(tol=tol)
if not (agf2.frozen is None or agf2.frozen == 0):
coupling = np.zeros((agf2.nmo, se.naux))
coupling[mask] = se.coupling
se = aux.SelfEnergy(se.energy, coupling, chempot=se.chempot)
log.timer('se part', *cput0)
return se
[docs]
class RAGF2(ragf2.RAGF2):
''' Restricted AGF2 with canonical HF reference for arbitrary
moment consistency
Attributes:
nmom : tuple of int
Compression level of the Green's function and
self-energy, respectively
verbose : int
Print level. Default value equals to :class:`Mole.verbose`
max_memory : float or int
Allowed memory in MB. Default value equals to :class:`Mole.max_memory`
conv_tol : float
Convergence threshold for AGF2 energy. Default value is 1e-7
conv_tol_rdm1 : float
Convergence threshold for first-order reduced density matrix.
Default value is 1e-8.
conv_tol_nelec : float
Convergence threshold for the number of electrons. Default
value is 1e-6.
max_cycle : int
Maximum number of AGF2 iterations. Default value is 50.
max_cycle_outer : int
Maximum number of outer Fock loop iterations. Default
value is 20.
max_cycle_inner : int
Maximum number of inner Fock loop iterations. Default
value is 50.
weight_tol : float
Threshold in spectral weight of auxiliaries to be considered
zero. Default 1e-11.
fock_diis_space : int
DIIS space size for Fock loop iterations. Default value is 6.
fock_diis_min_space :
Minimum space of DIIS. Default value is 1.
os_factor : float
Opposite-spin factor for spin-component-scaled (SCS)
calculations. Default 1.0
ss_factor : float
Same-spin factor for spin-component-scaled (SCS)
calculations. Default 1.0
damping : float
Damping factor for the self-energy. Default value is 0.0
Saved results
e_corr : float
AGF2 correlation energy
e_tot : float
Total energy (HF + correlation)
e_1b : float
One-body part of :attr:`e_tot`
e_2b : float
Two-body part of :attr:`e_tot`
e_init : float
Initial correlation energy (truncated MP2)
converged : bool
Whether convergence was successful
se : SelfEnergy
Auxiliaries of the self-energy
gf : GreensFunction
Auxiliaries of the Green's function
'''
_keys = set(['nmom'])
def __init__(self, mf, nmom=(None,0), frozen=None, mo_energy=None, mo_coeff=None, mo_occ=None):
ragf2.RAGF2.__init__(self, mf, frozen=frozen, mo_energy=mo_energy,
mo_coeff=mo_coeff, mo_occ=mo_occ)
self.nmom = nmom
build_se_part = build_se_part
[docs]
def build_se(self, eri=None, gf=None, os_factor=None, ss_factor=None, se_prev=None):
''' Builds the auxiliaries of the self-energy.
Args:
eri : _ChemistsERIs
Electronic repulsion integrals
gf : GreensFunction
Auxiliaries of the Green's function
Kwargs:
os_factor : float
Opposite-spin factor for spin-component-scaled (SCS)
calculations. Default 1.0
ss_factor : float
Same-spin factor for spin-component-scaled (SCS)
calculations. Default 1.0
se_prev : SelfEnergy
Previous self-energy for damping. Default value is None
Returns:
:class:`SelfEnergy`
'''
if eri is None: eri = self.ao2mo()
if gf is None: gf = self.gf
if gf is None: gf = self.init_gf()
fock = None
if self.nmom[0] is not None:
fock = self.get_fock(eri=eri, gf=gf)
if os_factor is None: os_factor = self.os_factor
if ss_factor is None: ss_factor = self.ss_factor
facs = dict(os_factor=os_factor, ss_factor=ss_factor)
gf_occ = gf.get_occupied()
gf_vir = gf.get_virtual()
se_occ = self.build_se_part(eri, gf_occ, gf_vir, **facs)
se_occ = se_occ.compress(n=(None, self.nmom[1]))
se_vir = self.build_se_part(eri, gf_vir, gf_occ, **facs)
se_vir = se_vir.compress(n=(None, self.nmom[1]))
se = aux.combine(se_vir, se_occ)
se = se.compress(phys=fock, n=(self.nmom[0], None))
if se_prev is not None and self.damping != 0.0:
se.coupling *= np.sqrt(1.0-self.damping)
se_prev.coupling *= np.sqrt(self.damping)
se = aux.combine(se, se_prev)
se = se.compress(n=self.nmom)
return se
[docs]
def dump_flags(self, verbose=None):
ragf2.RAGF2.dump_flags(self, verbose=verbose)
logger.info(self, 'nmom = %s', repr(self.nmom))
return self
[docs]
def run_diis(self, se, diis=None):
return se
class _ChemistsERIs(ragf2._ChemistsERIs):
pass
_make_qmo_eris_incore = ragf2._make_qmo_eris_incore
if __name__ == '__main__':
from pyscf import gto, scf, mp
mol = gto.M(atom='O 0 0 0; H 0 0 1; H 0 1 0', basis='cc-pvdz', verbose=3)
rhf = scf.RHF(mol)
rhf.conv_tol = 1e-11
rhf.run()
agf2 = RAGF2(rhf, nmom=(None,0))
agf2.run()
agf2 = ragf2.RAGF2(rhf)
agf2.run()