# 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
unrestricted references
'''
import time
import numpy as np
from pyscf import lib
from pyscf.lib import logger
from pyscf import __config__
from pyscf import ao2mo
from pyscf.scf import _vhf
from pyscf.agf2 import ragf2, _agf2, mpi_helper
from pyscf.agf2 import aux_space as aux
from pyscf.agf2.chempot import binsearch_chempot, minimize_chempot
from pyscf.mp.ump2 import get_frozen_mask as _get_frozen_mask
BLKMIN = getattr(__config__, 'agf2_blkmin', 1)
[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,
for a single spin.
Args:
eri : _ChemistsERIs
Electronic repulsion integrals
gf_occ : tuple of GreensFunction
Occupied Green's function for each spin
gf_vir : tuple of GreensFunction
Virtual Green's function for each spin
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[0]) is aux.GreensFunction
assert type(gf_occ[1]) is aux.GreensFunction
assert type(gf_vir[0]) is aux.GreensFunction
assert type(gf_vir[1]) is aux.GreensFunction
nmo = eri.nmo
noa, nob = gf_occ[0].naux, gf_occ[1].naux
nva, nvb = gf_vir[0].naux, gf_vir[1].naux
tol = agf2.weight_tol
facs = dict(os_factor=os_factor, ss_factor=ss_factor)
ci_a, ei_a = gf_occ[0].coupling, gf_occ[0].energy
ci_b, ei_b = gf_occ[1].coupling, gf_occ[1].energy
ca_a, ea_a = gf_vir[0].coupling, gf_vir[0].energy
ca_b, ea_b = gf_vir[1].coupling, gf_vir[1].energy
mem_incore = (nmo[0]*noa*(noa*nva+nob*nvb)) * 8/1e6
mem_now = lib.current_memory()[0]
if (mem_incore+mem_now < agf2.max_memory) or agf2.incore_complete:
qeri = _make_qmo_eris_incore(agf2, eri, (ci_a, ci_a, ca_a), (ci_b, ci_b, ca_b), spin=0)
else:
qeri = _make_qmo_eris_outcore(agf2, eri, (ci_a, ci_a, ca_a), (ci_b, ci_b, ca_b), spin=0)
if isinstance(qeri[0], np.ndarray):
vv, vev = _agf2.build_mats_uagf2_incore(qeri, (ei_a, ei_b), (ea_a, ea_b), **facs)
else:
vv, vev = _agf2.build_mats_uagf2_outcore(qeri, (ei_a, ei_b), (ea_a, ea_b), **facs)
e, c = _agf2.cholesky_build(vv, vev)
se_a = aux.SelfEnergy(e, c, chempot=gf_occ[0].chempot)
se_a.remove_uncoupled(tol=tol)
if not (agf2.frozen is None or agf2.frozen == 0):
mask = get_frozen_mask(agf2)
coupling = np.zeros((nmo[0], se_a.naux))
coupling[mask[0]] = se_a.coupling
se_a = aux.SelfEnergy(se_a.energy, coupling, chempot=se_a.chempot)
cput0 = log.timer('se part (alpha)', *cput0)
mem_incore = (nmo[1]*nob*(nob*nvb+noa*nva)) * 8/1e6
mem_now = lib.current_memory()[0]
if (mem_incore+mem_now < agf2.max_memory) or agf2.incore_complete:
qeri = _make_qmo_eris_incore(agf2, eri, (ci_a, ci_a, ca_a), (ci_b, ci_b, ca_b), spin=1)
else:
qeri = _make_qmo_eris_outcore(agf2, eri, (ci_a, ci_a, ca_a), (ci_b, ci_b, ca_b), spin=1)
if isinstance(qeri[0], np.ndarray):
vv, vev = _agf2.build_mats_uagf2_incore(qeri, (ei_b, ei_a), (ea_b, ea_a), **facs)
else:
vv, vev = _agf2.build_mats_uagf2_outcore(qeri, (ei_b, ei_a), (ea_b, ea_a), **facs)
e, c = _agf2.cholesky_build(vv, vev)
se_b = aux.SelfEnergy(e, c, chempot=gf_occ[1].chempot)
se_b.remove_uncoupled(tol=tol)
if not (agf2.frozen is None or agf2.frozen == 0):
mask = get_frozen_mask(agf2)
coupling = np.zeros((nmo[1], se_b.naux))
coupling[mask[1]] = se_b.coupling
se_b = aux.SelfEnergy(se_b.energy, coupling, chempot=se_b.chempot)
cput0 = log.timer('se part (beta)', *cput0)
return (se_a, se_b)
[docs]
def get_fock(agf2, eri, gf=None, rdm1=None):
''' Computes the physical space Fock matrix in MO basis. If :attr:`rdm1`
is not supplied, it is built from :attr:`gf`, which defaults to
the mean-field Green's function.
Args:
eri : _ChemistsERIs
Electronic repulsion integrals
Kwargs:
gf : GreensFunction
Auxiliaries of the Green's function
rdm1 : 2D array
Reduced density matrix
Returns:
ndarray of physical space Fock matrix
'''
if rdm1 is None:
rdm1 = agf2.make_rdm1(gf)
vj_aa, vk_aa = agf2.get_jk(eri.eri_aa, rdm1=rdm1[0])
vj_bb, vk_bb = agf2.get_jk(eri.eri_bb, rdm1=rdm1[1])
vj_ab = agf2.get_jk(eri.eri_ab, rdm1=rdm1[1], with_k=False)[0]
vj_ba = agf2.get_jk(eri.eri_ba, rdm1=rdm1[0], with_k=False)[0]
fock_a = eri.h1e[0] + vj_aa + vj_ab - vk_aa
fock_b = eri.h1e[1] + vj_bb + vj_ba - vk_bb
fock = (fock_a, fock_b)
return fock
[docs]
def fock_loop(agf2, eri, gf, se):
''' Self-consistent loop for the density matrix via the HF self-
consistent field.
Args:
eri : _ChemistsERIs
Electronic repulsion integrals
gf : tuple of GreensFunction
Auxiliaries of the Green's function for each spin
se : tuple of SelfEnergy
Auxiliaries of the self-energy for each spin
Returns:
:class:`SelfEnergy`, :class:`GreensFunction` and a boolean
indicating whether convergence was successful.
'''
assert type(gf[0]) is aux.GreensFunction
assert type(gf[1]) is aux.GreensFunction
assert type(se[0]) is aux.SelfEnergy
assert type(se[1]) is aux.SelfEnergy
cput0 = cput1 = (logger.process_clock(), logger.perf_counter())
log = logger.Logger(agf2.stdout, agf2.verbose)
diis = lib.diis.DIIS(agf2)
diis.space = agf2.fock_diis_space
diis.min_space = agf2.fock_diis_min_space
focka, fockb = agf2.get_fock(eri, gf)
sea, seb = se
gfa, gfb = gf
nalph, nbeta = agf2.nocc
nmoa, nmob = eri.nmo
nauxa, nauxb = sea.naux, seb.naux
nqmoa, nqmob = nauxa+nmoa, nauxb+nmob
bufa, bufb = np.zeros((nqmoa, nqmoa)), np.zeros((nqmob, nqmob))
rdm1a_prev = 0
rdm1b_prev = 0
converged = False
opts = dict(tol=agf2.conv_tol_nelec, maxiter=agf2.max_cycle_inner)
for niter1 in range(1, agf2.max_cycle_outer+1):
sea, opt = minimize_chempot(sea, focka, nalph, x0=sea.chempot,
occupancy=1, **opts)
seb, opt = minimize_chempot(seb, fockb, nbeta, x0=seb.chempot,
occupancy=1, **opts)
for niter2 in range(1, agf2.max_cycle_inner+1):
wa, va = sea.eig(focka, chempot=0.0, out=bufa)
wb, vb = seb.eig(fockb, chempot=0.0, out=bufb)
sea.chempot, nerra = \
binsearch_chempot((wa, va), nmoa, nalph, occupancy=1)
seb.chempot, nerrb = \
binsearch_chempot((wb, vb), nmob, nbeta, occupancy=1)
nerr = max(nerra, nerrb)
wa, va = sea.eig(focka, out=bufa)
wb, vb = seb.eig(fockb, out=bufb)
gfa = aux.GreensFunction(wa, va[:nmoa], chempot=sea.chempot)
gfb = aux.GreensFunction(wb, vb[:nmob], chempot=seb.chempot)
gf = (gfa, gfb)
focka, fockb = agf2.get_fock(eri, gf)
rdm1a, rdm1b = agf2.make_rdm1(gf)
focka, fockb = diis.update(np.array((focka, fockb)), xerr=None)
if niter2 > 1:
derra = np.max(np.absolute(rdm1a - rdm1a_prev))
derrb = np.max(np.absolute(rdm1b - rdm1b_prev))
derr = max(derra, derrb)
if derr < agf2.conv_tol_rdm1:
break
rdm1a_prev = rdm1a.copy()
rdm1b_prev = rdm1b.copy()
log.debug1('fock loop %d cycles = %d dN = %.3g |ddm| = %.3g',
niter1, niter2, nerr, derr)
cput1 = log.timer_debug1('fock loop %d'%niter1, *cput1)
if derr < agf2.conv_tol_rdm1 and abs(nerr) < agf2.conv_tol_nelec:
converged = True
break
se = (sea, seb)
log.info('fock converged = %s' % converged)
log.info(' alpha: chempot = %.9g dN = %.3g |ddm| = %.3g',
sea.chempot, nerra, derra)
log.info(' beta: chempot = %.9g dN = %.3g |ddm| = %.3g',
seb.chempot, nerrb, derrb)
log.timer('fock loop', *cput0)
return gf, se, converged
[docs]
def energy_1body(agf2, eri, gf):
''' Calculates the one-body energy according to the UHF form.
Args:
eri : _ChemistsERIs
Electronic repulsion integrals
gf : tuple of GreensFunction
Auxiliaries of the Green's function for each spin
Returns:
One-body energy
'''
assert type(gf[0]) is aux.GreensFunction
assert type(gf[1]) is aux.GreensFunction
rdm1 = agf2.make_rdm1(gf)
fock = agf2.get_fock(eri, gf)
e1b_a = 0.5 * np.sum(rdm1[0] * (eri.h1e[0] + fock[0]))
e1b_b = 0.5 * np.sum(rdm1[1] * (eri.h1e[1] + fock[1]))
e1b = e1b_a + e1b_b
e1b += agf2.energy_nuc()
return e1b
[docs]
def energy_2body(agf2, gf, se):
''' Calculates the two-body energy using analytically integrated
Galitskii-Migdal formula. The formula is symmetric and only
one side needs to be calculated.
Args:
gf : tuple of GreensFunction
Auxiliaries of the Green's function for each spin
se : tuple of SelfEnergy
Auxiliaries of the self-energy for each spin
Returns:
Two-body energy
'''
e2b_a = ragf2.energy_2body(agf2, gf[0], se[0])
e2b_b = ragf2.energy_2body(agf2, gf[1], se[1])
e2b = (e2b_a + e2b_b) * 0.5
return e2b
[docs]
def energy_mp2(agf2, gf, se):
''' Calculates the two-body energy using analytically integrated
Galitskii-Migdal formula for an MP2 self-energy. Per the
definition of one- and two-body partitioning in the Dyson
equation, this result is half of :func:`energy_2body`.
Args:
gf : tuple of GreensFunction
Auxiliaries of the Green's function for each spin
se : tuple of SelfEnergy
Auxiliaries of the self-energy for each spin
Returns:
MP2 energy
'''
emp2_a = ragf2.energy_mp2(agf2, gf[0], se[0])
emp2_b = ragf2.energy_mp2(agf2, gf[1], se[1])
emp2 = (emp2_a + emp2_b) * 0.5
return emp2
[docs]
class UAGF2(ragf2.RAGF2):
''' Unrestricted AGF2 with canonical HF reference
Attributes:
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`
incore_complete : bool
Avoid all I/O. Default is False.
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.
diis : bool or lib.diis.DIIS
Whether to use DIIS, can also be a lib.diis.DIIS object. Default
value is True.
diis_space : int
DIIS space size. Default value is 8.
diis_min_space : int
Minimum space of DIIS. Default value is 1.
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 : tuple of SelfEnergy
Auxiliaries of the self-energy for each spin
gf : tuple of GreensFunction
Auxiliaries of the Green's function for each spin
'''
energy_1body = energy_1body
energy_2body = energy_2body
fock_loop = fock_loop
build_se_part = build_se_part
[docs]
def ao2mo(self, mo_coeff=None):
''' Get the electronic repulsion integrals in MO basis.
'''
nmo = max(self.nmo)
mem_incore = ((nmo*(nmo+1)//2)**2) * 8/1e6
mem_now = lib.current_memory()[0]
if (self._scf._eri is not None and
(mem_incore+mem_now < self.max_memory or self.incore_complete)):
eri = _make_mo_eris_incore(self, mo_coeff)
else:
logger.warn(self, 'MO eris are outcore - this may be very '
'slow for agf2. increasing max_memory or '
'using density fitting is recommended.')
eri = _make_mo_eris_outcore(self, mo_coeff)
return eri
[docs]
def make_rdm1(self, gf=None):
''' Compute the one-body reduced density matrix in MO basis.
Kwargs:
gf : tuple of GreensFunction
Auxiliaries of the Green's functions for each spin
Returns:
tuple of ndarray of density matrices
'''
if gf is None: gf = self.gf
if gf is None: gf = self.init_gf()
rdm1_a = gf[0].make_rdm1(occupancy=1)
rdm1_b = gf[1].make_rdm1(occupancy=1)
return (rdm1_a, rdm1_b)
[docs]
def get_fock(self, eri=None, gf=None, rdm1=None):
''' Computes the physical space Fock matrix in MO basis.
'''
if eri is None: eri = self.ao2mo()
if gf is None: gf = self.gf
return get_fock(self, eri, gf=gf, rdm1=rdm1)
[docs]
def energy_mp2(self, mo_energy=None, se=None):
if mo_energy is None: mo_energy = self.mo_energy
if se is None: se = self.build_se(gf=self.gf)
self.e_init = energy_mp2(self, mo_energy, se)
return self.e_init
[docs]
def init_gf(self, frozen=False):
''' Builds the Hartree-Fock Green's function.
Returns:
tuple of :class:`GreensFunction`, tuple of :class:`SelfEnergy`
'''
nmoa, nmob = self.nmo
nocca, noccb = self.nocc
energy = self.mo_energy
coupling = (np.eye(nmoa), np.eye(nmob))
focka = np.diag(energy[0])
fockb = np.diag(energy[1])
cpt_a = binsearch_chempot(focka, nmoa, nocca, occupancy=1)[0]
cpt_b = binsearch_chempot(fockb, nmob, noccb, occupancy=1)[1]
if frozen:
mask = get_frozen_mask(self)
energy = (energy[0][mask[0]], energy[1][mask[1]])
coupling = (coupling[0][:,mask[0]], coupling[1][:,mask[1]])
gf_a = aux.GreensFunction(energy[0], coupling[0], chempot=cpt_a)
gf_b = aux.GreensFunction(energy[1], coupling[1], chempot=cpt_b)
gf = (gf_a, gf_b)
return gf
[docs]
def build_gf(self, eri=None, gf=None, se=None):
''' Builds the auxiliaries of the Green's functions by solving
the Dyson equation for each spin.
Kwargs:
eri : _ChemistsERIs
Electronic repulsion integrals
gf : tuple of GreensFunction
Auxiliaries of the Green's function for each spin
se : tuple of SelfEnergy
Auxiliaries of the self-energy for each spin
Returns:
tuple of :class:`GreensFunction`
'''
if eri is None: eri = self.ao2mo()
if gf is None: gf = self.gf
if gf is None: gf = self.init_gf()
if se is None: se = self.build_se(eri, gf)
focka, fockb = self.get_fock(eri, gf)
gf_a = se[0].get_greens_function(focka)
gf_b = se[1].get_greens_function(fockb)
return (gf_a, gf_b)
[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 : tuple of 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
tuple of :class:`SelfEnergy`
'''
if eri is None: eri = self.ao2mo()
if gf is None: gf = self.gf
if gf is None: gf = self.init_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[0].get_occupied(), gf[1].get_occupied())
gf_vir = (gf[0].get_virtual(), gf[1].get_virtual())
se_occ = self.build_se_part(eri, gf_occ, gf_vir, **facs)
se_vir = self.build_se_part(eri, gf_vir, gf_occ, **facs)
se_a = aux.combine(se_occ[0], se_vir[0])
se_b = aux.combine(se_occ[1], se_vir[1])
if se_prev is not None and self.damping != 0.0:
se_a_prev, se_b_prev = se_prev
se_a.coupling *= np.sqrt(1.0-self.damping)
se_b.coupling *= np.sqrt(1.0-self.damping)
se_a_prev.coupling *= np.sqrt(self.damping)
se_b_prev.coupling *= np.sqrt(self.damping)
se_a = aux.combine(se_a, se_a_prev)
se_b = aux.combine(se_b, se_b_prev)
se_a = se_a.compress(n=(None,0))
se_b = se_b.compress(n=(None,0))
return (se_a, se_b)
[docs]
def run_diis(self, se, diis=None):
''' Runs the direct inversion of the iterative subspace for the
self-energy.
Args:
se : SelfEnergy
Auxiliaries of the self-energy
diis : lib.diis.DIIS
DIIS object
Returns:
tuple of :class:`SelfEnergy`
'''
if diis is None:
return se
se_occ_a, se_occ_b = (se[0].get_occupied(), se[1].get_occupied())
se_vir_a, se_vir_b = (se[0].get_virtual(), se[1].get_virtual())
vv_occ_a = np.dot(se_occ_a.coupling, se_occ_a.coupling.T)
vv_occ_b = np.dot(se_occ_b.coupling, se_occ_b.coupling.T)
vv_vir_a = np.dot(se_vir_a.coupling, se_vir_a.coupling.T)
vv_vir_b = np.dot(se_vir_b.coupling, se_vir_b.coupling.T)
vev_occ_a = np.dot(se_occ_a.coupling * se_occ_a.energy[None], se_occ_a.coupling.T)
vev_occ_b = np.dot(se_occ_b.coupling * se_occ_b.energy[None], se_occ_b.coupling.T)
vev_vir_a = np.dot(se_vir_a.coupling * se_vir_a.energy[None], se_vir_a.coupling.T)
vev_vir_b = np.dot(se_vir_b.coupling * se_vir_b.energy[None], se_vir_b.coupling.T)
dat = np.array([vv_occ_a, vv_vir_a, vev_occ_a, vev_vir_a,
vv_occ_b, vv_vir_b, vev_occ_b, vev_vir_b])
dat = diis.update(dat)
vv_occ_a, vv_vir_a, vev_occ_a, vev_vir_a, \
vv_occ_b, vv_vir_b, vev_occ_b, vev_vir_b = dat
se_occ_a = aux.SelfEnergy(*_agf2.cholesky_build(vv_occ_a, vev_occ_a), chempot=se[0].chempot)
se_vir_a = aux.SelfEnergy(*_agf2.cholesky_build(vv_vir_a, vev_vir_a), chempot=se[0].chempot)
se_occ_b = aux.SelfEnergy(*_agf2.cholesky_build(vv_occ_b, vev_occ_b), chempot=se[1].chempot)
se_vir_b = aux.SelfEnergy(*_agf2.cholesky_build(vv_vir_b, vev_vir_b), chempot=se[1].chempot)
se = (aux.combine(se_occ_a, se_vir_a), aux.combine(se_occ_b, se_vir_b))
return se
[docs]
def density_fit(self, auxbasis=None, with_df=None):
from pyscf.agf2 import dfuagf2
myagf2 = dfuagf2.DFUAGF2(self._scf)
myagf2.__dict__.update(self.__dict__)
if with_df is not None:
myagf2.with_df = with_df
if auxbasis is not None and myagf2.with_df.auxbasis != auxbasis:
myagf2.with_df = myagf2.with_df.copy()
myagf2.with_df.auxbasis = auxbasis
return myagf2
[docs]
def get_ip(self, gf, nroots=5):
gf_occ = (gf[0].get_occupied(), gf[1].get_occupied())
spin = np.array([0,]*gf_occ[0].naux + [1,]*gf_occ[1].naux)
e_ip = np.concatenate([gf_occ[0].energy, gf_occ[1].energy], axis=0)
v_ip = np.concatenate([gf_occ[0].coupling, gf_occ[1].coupling], axis=1)
mask = np.argsort(e_ip)
spin = list(spin[mask][-nroots:])[::-1]
e_ip = list(-e_ip[mask][-nroots:])[::-1]
v_ip = list(v_ip[:,mask][:,-nroots:].T)[::-1]
return e_ip, v_ip, spin
[docs]
def ipagf2(self, nroots=5):
e_ip, v_ip, spin = self.get_ip(self.gf, nroots=nroots)
for n, en, vn, sn in zip(range(nroots), e_ip, v_ip, spin):
qpwt = np.linalg.norm(vn)**2
tag = ['alpha', 'beta'][sn]
logger.note(self, 'IP energy level %d E = %.16g QP weight = %0.6g (%s)', n, en, qpwt, tag)
if nroots == 1:
return e_ip[0], v_ip[0]
else:
return e_ip, v_ip
[docs]
def get_ea(self, gf, nroots=5):
gf_vir = (gf[0].get_virtual(), gf[1].get_virtual())
spin = np.array([0,]*gf_vir[0].naux + [1,]*gf_vir[1].naux)
e_ea = np.concatenate([gf_vir[0].energy, gf_vir[1].energy], axis=0)
v_ea = np.concatenate([gf_vir[0].coupling, gf_vir[1].coupling], axis=1)
mask = np.argsort(e_ea)
spin = list(spin[mask][:nroots])
e_ea = list(e_ea[mask][:nroots])
v_ea = list(v_ea[:,mask][:,:nroots].T)
return e_ea, v_ea, spin
[docs]
def eaagf2(self, nroots=5):
e_ea, v_ea, spin = self.get_ea(self.gf, nroots=nroots)
for n, en, vn, sn in zip(range(nroots), e_ea, v_ea, spin):
qpwt = np.linalg.norm(vn)**2
tag = ['alpha', 'beta'][sn]
logger.note(self, 'EA energy level %d E = %.16g QP weight = %0.6g (%s)', n, en, qpwt, tag)
if nroots == 1:
return e_ea[0], v_ea[0]
else:
return e_ea, v_ea
@property
def nocc(self):
if self._nocc is None:
self._nocc = (np.sum(self.mo_occ[0] > 0), np.sum(self.mo_occ[1] > 0))
return self._nocc
@nocc.setter
def nocc(self, val):
self._nocc = val
@property
def nmo(self):
if self._nmo is None:
self._nmo = (self.mo_occ[0].size, self.mo_occ[1].size)
return self._nmo
@nmo.setter
def nmo(self, val):
self._nmo = val
@property
def qmo_energy(self):
return (self.gf[0].energy, self.gf[1].energy)
@property
def qmo_coeff(self):
''' Gives the couplings in AO basis '''
return (np.dot(self.mo_coeff[0], self.gf[0].coupling),
np.dot(self.mo_coeff[1], self.gf[1].coupling))
@property
def qmo_occ(self):
coeff_a = self.gf[0].get_occupied().coupling
coeff_b = self.gf[1].get_occupied().coupling
occ_a = np.linalg.norm(coeff_a, axis=0) ** 2
occ_b = np.linalg.norm(coeff_b, axis=0) ** 2
vir_a = np.zeros_like(self.gf[0].get_virtual().energy)
vir_b = np.zeros_like(self.gf[1].get_virtual().energy)
qmo_occ_a = np.concatenate([occ_a, vir_a])
qmo_occ_b = np.concatenate([occ_b, vir_b])
return qmo_occ_a, qmo_occ_b
[docs]
def get_frozen_mask(agf2):
with lib.temporary_env(agf2, _nocc=None, _nmo=None):
return _get_frozen_mask(agf2)
class _ChemistsERIs:
''' (pq|rs)
MO integrals stored in s4 symmetry, we only need QMO integrals
in low-symmetry tensors and s4 is highest supported by _vhf
'''
def __init__(self, mol=None):
self.mol = mol
self.mo_coeff = None
self.nocc = None
self.nmo = None
self.fock = None
self.h1e = None
self.eri = None
self.e_hf = None
def _common_init_(self, agf2, mo_coeff=None):
if mo_coeff is None:
mo_coeff = agf2.mo_coeff
self.mo_coeff = mo_coeff
dm = agf2._scf.make_rdm1(agf2.mo_coeff, agf2.mo_occ)
h1e_ao = agf2._scf.get_hcore()
vhf = agf2._scf.get_veff(agf2.mol, dm)
fock_ao = agf2._scf.get_fock(vhf=vhf, dm=dm)
self.h1e = (np.dot(np.dot(mo_coeff[0].conj().T, h1e_ao), mo_coeff[0]),
np.dot(np.dot(mo_coeff[1].conj().T, h1e_ao), mo_coeff[1]))
self.fock = (np.dot(np.dot(mo_coeff[0].conj().T, fock_ao[0]), mo_coeff[0]),
np.dot(np.dot(mo_coeff[1].conj().T, fock_ao[1]), mo_coeff[1]))
self.h1e = (mpi_helper.bcast(self.h1e[0]), mpi_helper.bcast(self.h1e[1]))
self.fock = (mpi_helper.bcast(self.fock[0]), mpi_helper.bcast(self.fock[1]))
self.e_hf = mpi_helper.bcast(agf2._scf.e_tot)
self.nmo = agf2.nmo
nocca, noccb = self.nocc = agf2.nocc
self.mol = agf2.mol
mo_e = (self.fock[0].diagonal(), self.fock[1].diagonal())
gap_a = abs(mo_e[0][:nocca,None] - mo_e[0][None,nocca:]).min()
gap_b = abs(mo_e[1][:noccb,None] - mo_e[1][None,noccb:]).min()
gap = min(gap_a, gap_b)
if gap < 1e-5:
logger.warn(agf2, 'HOMO-LUMO gap %s may be too small for AGF2', gap)
return self
def _make_mo_eris_incore(agf2, mo_coeff=None):
''' Returns _ChemistsERIs
'''
cput0 = (logger.process_clock(), logger.perf_counter())
log = logger.Logger(agf2.stdout, agf2.verbose)
eris = _ChemistsERIs()
eris._common_init_(agf2, mo_coeff)
moa, mob = eris.mo_coeff
nmoa, nmob = eris.nmo
eri_aa = ao2mo.incore.full(agf2._scf._eri, moa, verbose=log)
eri_bb = ao2mo.incore.full(agf2._scf._eri, mob, verbose=log)
eri_aa = ao2mo.addons.restore('s4', eri_aa, nmoa)
eri_bb = ao2mo.addons.restore('s4', eri_bb, nmob)
eri_ab = ao2mo.incore.general(agf2._scf._eri, (moa,moa,mob,mob), verbose=log)
assert eri_ab.shape == (nmoa*(nmob+1)//2, nmob*(nmob+1)//2)
eri_ba = np.transpose(eri_ab)
eris.eri_aa = eri_aa
eris.eri_ab = eri_ab
eris.eri_ba = eri_ba
eris.eri_bb = eri_bb
eris.eri = ((eri_aa, eri_ab), (eri_ba, eri_bb))
log.timer('MO integral transformation', *cput0)
return eris
def _make_mo_eris_outcore(agf2, mo_coeff=None):
''' Returns _ChemistsERIs
'''
log = logger.Logger(agf2.stdout, agf2.verbose)
eris = _ChemistsERIs()
eris._common_init_(agf2, mo_coeff)
mol = agf2.mol
moa = np.asarray(eris.mo_coeff[0], order='F')
mob = np.asarray(eris.mo_coeff[1], order='F')
nmoa, nmob = eris.nmo
eris.feri = lib.H5TmpFile()
ao2mo.outcore.full(mol, moa, eris.feri, dataname='mo/aa')
ao2mo.outcore.full(mol, mob, eris.feri, dataname='mo/bb')
ao2mo.outcore.general(mol, (moa,moa,mob,mob), eris.feri, dataname='mo/ab', verbose=log)
ao2mo.outcore.general(mol, (mob,mob,moa,moa), eris.feri, dataname='mo/ba', verbose=log)
eris.eri_aa = eris.feri['mo/aa']
eris.eri_ab = eris.feri['mo/ab']
eris.eri_ba = eris.feri['mo/ba']
eris.eri_bb = eris.feri['mo/bb']
eris.eri = ((eris.eri_aa, eris.eri_ab), (eris.eri_ba, eris.eri_bb))
return eris
def _make_qmo_eris_incore(agf2, eri, coeffs_a, coeffs_b, spin=None):
''' Returns nested tuple of ndarray
spin = None: ((aaaa, aabb), (bbaa, bbbb))
spin = 0: (aaaa, aabb)
spin = 1: (bbbb, bbaa)
'''
cput0 = (logger.process_clock(), logger.perf_counter())
log = logger.Logger(agf2.stdout, agf2.verbose)
nmo = eri.nmo
nmoa, nmob = nmo
cxa = np.eye(nmoa)
cxb = np.eye(nmob)
if not (agf2.frozen is None or agf2.frozen == 0):
mask = get_frozen_mask(agf2)
cxa = cxa[:,mask[0]]
cxb = cxb[:,mask[1]]
# npaira, npairb = nmoa*(nmoa+1)//2, nmob*(nmob+1)//2
cia, cja, caa = coeffs_a
cib, cjb, cab = coeffs_b
nia, nja, naa = [x.shape[1] for x in coeffs_a]
nib, njb, nab = [x.shape[1] for x in coeffs_b]
if spin is None or spin == 0:
c_aa = (cxa, cia, cja, caa)
c_ab = (cxa, cia, cjb, cab)
qeri_aa = ao2mo.incore.general(eri.eri_aa, c_aa, compact=False, verbose=log)
qeri_ab = ao2mo.incore.general(eri.eri_ab, c_ab, compact=False, verbose=log)
qeri_aa = qeri_aa.reshape(cxa.shape[1], nia, nja, naa)
qeri_ab = qeri_ab.reshape(cxa.shape[1], nia, njb, nab)
if spin is None or spin == 1:
c_bb = (cxb, cib, cjb, cab)
c_ba = (cxb, cib, cja, caa)
qeri_bb = ao2mo.incore.general(eri.eri_bb, c_bb, compact=False, verbose=log)
qeri_ba = ao2mo.incore.general(eri.eri_ba, c_ba, compact=False, verbose=log)
qeri_bb = qeri_bb.reshape(cxb.shape[1], nib, njb, nab)
qeri_ba = qeri_ba.reshape(cxb.shape[1], nib, nja, naa)
if spin is None:
qeri = ((qeri_aa, qeri_ab), (qeri_ba, qeri_bb))
elif spin == 0:
qeri = (qeri_aa, qeri_ab)
elif spin == 1:
qeri = (qeri_bb, qeri_ba)
log.timer('QMO integral transformation', *cput0)
return qeri
def _make_qmo_eris_outcore(agf2, eri, coeffs_a, coeffs_b, spin=None):
''' Returns nested tuple of H5 dataset
spin = None: ((aaaa, aabb), (bbaa, bbbb))
spin = 0: (aaaa, aabb)
spin = 1: (bbbb, bbaa)
'''
cput0 = (logger.process_clock(), logger.perf_counter())
log = logger.Logger(agf2.stdout, agf2.verbose)
nmo = eri.nmo
nmoa, nmob = nmo
mask = get_frozen_mask(agf2)
frozena = np.sum(~mask[0])
frozenb = np.sum(~mask[1])
# npaira, npairb = nmoa*(nmoa+1)//2, nmob*(nmob+1)//2
cia, cja, caa = coeffs_a
cib, cjb, cab = coeffs_b
nia, nja, naa = [x.shape[1] for x in coeffs_a]
nib, njb, nab = [x.shape[1] for x in coeffs_b]
# possible to have incore MO, outcore QMO
if getattr(eri, 'feri', None) is None:
eri.feri = lib.H5TmpFile()
else:
for key in ['aa', 'ab', 'ba', 'bb']:
if 'qmo/%s'%key in eri.feri:
del eri.feri['qmo/%s'%key]
if spin is None or spin == 0:
eri.feri.create_dataset('qmo/aa', (nmoa-frozena, nia, nja, naa), 'f8')
eri.feri.create_dataset('qmo/ab', (nmoa-frozena, nia, njb, nab), 'f8')
blksize = _agf2.get_blksize(agf2.max_memory, (nmoa**3, nmoa*nja*naa),
(nmoa*nmob**2, nmoa*njb*nab))
blksize = min(nmoa, max(BLKMIN, blksize))
log.debug1('blksize (uagf2._make_qmo_eris_outcore) = %d', blksize)
tril2sq = lib.square_mat_in_trilu_indices(nmoa)
q1 = 0
for p0, p1 in lib.prange(0, nmoa, blksize):
if not np.any(mask[0][p0:p1]):
# block is fully frozen
continue
inds = np.arange(p0, p1)[mask[0][p0:p1]]
q0, q1 = q1, q1 + len(inds)
idx = list(np.concatenate(tril2sq[inds]))
# aa
buf = eri.eri_aa[idx] # (blk, nmoa, npaira)
buf = buf.reshape((q1-q0)*nmoa, -1) # (blk*nmoa, npaira)
jasym_aa, nja_aa, cja_aa, sja_aa = ao2mo.incore._conc_mos(cja, caa)
buf = ao2mo._ao2mo.nr_e2(buf, cja_aa, sja_aa, 's2kl', 's1')
buf = buf.reshape(q1-q0, nmoa, nja, naa)
buf = lib.einsum('xpja,pi->xija', buf, cia)
eri.feri['qmo/aa'][q0:q1] = np.asarray(buf, order='C')
# ab
buf = eri.eri_ab[idx] # (blk, nmoa, npairb)
buf = buf.reshape((q1-q0)*nmob, -1) # (blk*nmoa, npairb)
jasym_ab, nja_ab, cja_ab, sja_ab = ao2mo.incore._conc_mos(cjb, cab)
buf = ao2mo._ao2mo.nr_e2(buf, cja_ab, sja_ab, 's2kl', 's1')
buf = buf.reshape(q1-q0, nmoa, njb, nab)
buf = lib.einsum('xpja,pi->xija', buf, cia)
eri.feri['qmo/ab'][q0:q1] = np.asarray(buf, order='C')
if spin is None or spin == 1:
eri.feri.create_dataset('qmo/ba', (nmob-frozenb, nib, nja, naa), 'f8')
eri.feri.create_dataset('qmo/bb', (nmob-frozenb, nib, njb, nab), 'f8')
max_memory = agf2.max_memory - lib.current_memory()[0]
blksize = int((max_memory/8e-6) / max(nmob**3+nmob*njb*nab,
nmob*nmoa**2*nja*naa))
blksize = min(nmob, max(BLKMIN, blksize))
log.debug1('blksize (uagf2._make_qmo_eris_outcore) = %d', blksize)
tril2sq = lib.square_mat_in_trilu_indices(nmob)
q1 = 0
for p0, p1 in lib.prange(0, nmob, blksize):
if not np.any(mask[1][p0:p1]):
# block is fully frozen
continue
inds = np.arange(p0, p1)[mask[1][p0:p1]]
q0, q1 = q1, q1 + len(inds)
idx = list(np.concatenate(tril2sq[inds]))
# ba
buf = eri.eri_ba[idx] # (blk, nmob, npaira)
buf = buf.reshape((q1-q0)*nmob, -1) # (blk*nmob, npaira)
jasym_ba, nja_ba, cja_ba, sja_ba = ao2mo.incore._conc_mos(cja, caa)
buf = ao2mo._ao2mo.nr_e2(buf, cja_ba, sja_ba, 's2kl', 's1')
buf = buf.reshape(q1-q0, nmob, nja, naa)
buf = lib.einsum('xpja,pi->xija', buf, cib)
eri.feri['qmo/ba'][q0:q1] = np.asarray(buf, order='C')
# bb
buf = eri.eri_bb[idx] # (blk, nmob, npairb)
buf = buf.reshape((q1-q0)*nmob, -1) # (blk*nmob, npairb)
jasym_bb, nja_bb, cja_bb, sja_bb = ao2mo.incore._conc_mos(cjb, cab)
buf = ao2mo._ao2mo.nr_e2(buf, cja_bb, sja_bb, 's2kl', 's1')
buf = buf.reshape(q1-q0, nmob, njb, nab)
buf = lib.einsum('xpja,pi->xija', buf, cib)
eri.feri['qmo/bb'][q0:q1] = np.asarray(buf, order='C')
if spin is None:
qeri = ((eri.feri['qmo/aa'], eri.feri['qmo/ab']),
(eri.feri['qmo/ba'], eri.feri['qmo/bb']))
elif spin == 0:
qeri = (eri.feri['qmo/aa'], eri.feri['qmo/ab'])
elif spin == 1:
qeri = (eri.feri['qmo/bb'], eri.feri['qmo/ba'])
log.timer('QMO integral transformation', *cput0)
return qeri
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', charge=-1, spin=1, verbose=3)
uhf = scf.UHF(mol)
uhf.conv_tol = 1e-11
uhf.run()
uagf2 = UAGF2(uhf, frozen=0)
uagf2.run()
uagf2.ipagf2(nroots=5)
uagf2.eaagf2(nroots=5)
uagf2 = uagf2.density_fit()
uagf2.run()