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LazyMp.py
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LazyMp.py
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#!/usr/bin/env python3
## vi: tabstop=4 shiftwidth=4 softtabstop=4 expandtab
## ---------------------------------------------------------------------
##
## Copyright (C) 2019 by the adcc authors
##
## This file is part of adcc.
##
## adcc is free software: you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published
## by the Free Software Foundation, either version 3 of the License, or
## (at your option) any later version.
##
## adcc is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
## GNU General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with adcc. If not, see <http://www.gnu.org/licenses/>.
##
## ---------------------------------------------------------------------
import libadcc
import numpy as np
from .functions import direct_sum, evaluate, einsum
from .misc import cached_property, cached_member_function
from .ReferenceState import ReferenceState
from .OneParticleOperator import OneParticleOperator, product_trace
from .Intermediates import register_as_intermediate
from .timings import Timer, timed_member_call
from .MoSpaces import split_spaces
from . import block as b
class LazyMp:
def __init__(self, hf):
"""
Initialise the class dealing with the M/oller-Plesset ground state.
"""
if isinstance(hf, libadcc.HartreeFockSolution_i):
hf = ReferenceState(hf)
if not isinstance(hf, ReferenceState):
raise TypeError("hf needs to be a ReferenceState "
"or a HartreeFockSolution_i")
self.reference_state = hf
self.mospaces = hf.mospaces
self.timer = Timer()
self.has_core_occupied_space = hf.has_core_occupied_space
def __getattr__(self, attr):
# Shortcut some quantities, which are needed most often
if attr.startswith("t2") and len(attr) == 4: # t2oo, t2oc, t2cc
xxvv = b.__getattr__(attr[2:4] + "vv")
return self.t2(xxvv)
else:
raise AttributeError
@cached_member_function
def df(self, space):
"""Delta Fock matrix"""
hf = self.reference_state
s1, s2 = split_spaces(space)
fC = hf.fock(s1 + s1).diagonal()
fv = hf.fock(s2 + s2).diagonal()
return direct_sum("-i+a->ia", fC, fv)
@cached_member_function
def t2(self, space):
"""T2 amplitudes"""
hf = self.reference_state
sp = split_spaces(space)
assert all(s == b.v for s in sp[2:])
eia = self.df(sp[0] + b.v)
ejb = self.df(sp[1] + b.v)
return (
hf.eri(space) / direct_sum("ia+jb->ijab", eia, ejb).symmetrise((2, 3))
)
@cached_member_function
def td2(self, space):
"""Return the T^D_2 term"""
if space != b.oovv:
raise NotImplementedError("T^D_2 term not implemented "
f"for space {space}.")
t2erit = self.t2eri(b.oovv, b.ov).transpose((1, 0, 2, 3))
denom = direct_sum(
'ia,jb->ijab', self.df(b.ov), self.df(b.ov)
).symmetrise(0, 1)
return (
+ 4.0 * t2erit.antisymmetrise(2, 3).antisymmetrise(0, 1)
- 0.5 * self.t2eri(b.oovv, b.vv)
- 0.5 * self.t2eri(b.oovv, b.oo)
) / denom
@cached_member_function
def t2eri(self, space, contraction):
"""
Return the T2 tensor with ERI tensor contraction intermediates.
These are called pi1 to pi7 in libadc.
"""
hf = self.reference_state
key = space + contraction
expressions = {
# space + contraction
b.ooov + b.vv: ('ijbc,kabc->ijka', b.ovvv),
b.ooov + b.ov: ('ilab,lkjb->ijka', b.ooov),
b.oovv + b.oo: ('klab,ijkl->ijab', b.oooo),
b.oovv + b.ov: ('jkac,kbic->ijab', b.ovov),
b.oovv + b.vv: ('ijcd,abcd->ijab', b.vvvv),
b.ovvv + b.oo: ('jkbc,jkia->iabc', b.ooov),
b.ovvv + b.ov: ('ijbd,jcad->iabc', b.ovvv),
}
if key not in expressions:
raise NotImplementedError("t2eri intermediate not implemented "
f"for space '{space}' and contraction "
f"'{contraction}'.")
contraction_str, eri_block = expressions[key]
return einsum(contraction_str, self.t2oo, hf.eri(eri_block))
@cached_property
@timed_member_call(timer="timer")
def mp2_diffdm(self):
"""
Return the MP2 differensce density in the MO basis.
"""
hf = self.reference_state
ret = OneParticleOperator(self.mospaces, is_symmetric=True)
# NOTE: the following 3 blocks are equivalent to the cvs_p0 intermediates
# defined at the end of this file
ret[b.oo] = -0.5 * einsum("ikab,jkab->ij", self.t2oo, self.t2oo)
ret[b.ov] = -0.5 * (
+ einsum("ijbc,jabc->ia", self.t2oo, hf.ovvv)
+ einsum("jkib,jkab->ia", hf.ooov, self.t2oo)
) / self.df(b.ov)
ret[b.vv] = 0.5 * einsum("ijac,ijbc->ab", self.t2oo, self.t2oo)
if self.has_core_occupied_space:
# additional terms to "revert" CVS for ground state density
ret[b.oo] += -0.5 * einsum("iLab,jLab->ij", self.t2oc, self.t2oc)
ret[b.ov] += -0.5 * (
+ einsum("jMib,jMab->ia", hf.ocov, self.t2oc)
+ einsum("iLbc,Labc->ia", self.t2oc, hf.cvvv)
+ einsum("kLib,kLab->ia", hf.ocov, self.t2oc)
+ einsum("iMLb,LMab->ia", hf.occv, self.t2cc)
- einsum("iLMb,LMab->ia", hf.occv, self.t2cc)
) / self.df(b.ov)
ret[b.vv] += (
+ 0.5 * einsum("IJac,IJbc->ab", self.t2cc, self.t2cc)
+ 1.0 * einsum("kJac,kJbc->ab", self.t2oc, self.t2oc)
)
# compute extra CVS blocks
ret[b.cc] = -0.5 * (
+ einsum("kIab,kJab->IJ", self.t2oc, self.t2oc)
+ einsum('LIab,LJab->IJ', self.t2cc, self.t2cc)
)
ret[b.co] = -0.5 * (
+ einsum("kIab,kjab->Ij", self.t2oc, self.t2oo)
+ einsum("ILab,jLab->Ij", self.t2cc, self.t2oc)
)
ret[b.cv] = -0.5 * (
- einsum("jIbc,jabc->Ia", self.t2oc, hf.ovvv)
+ einsum("jkIb,jkab->Ia", hf.oocv, self.t2oo)
+ einsum("jMIb,jMab->Ia", hf.occv, self.t2oc)
+ einsum("ILbc,Labc->Ia", self.t2cc, hf.cvvv)
+ einsum("kLIb,kLab->Ia", hf.occv, self.t2oc)
+ einsum("LMIb,LMab->Ia", hf.cccv, self.t2cc)
) / self.df(b.cv)
ret.reference_state = self.reference_state
return evaluate(ret)
def density(self, level=2):
"""
Return the MP density in the MO basis with all corrections
up to the specified order of perturbation theory
"""
if level == 1:
return self.reference_state.density
elif level == 2:
return self.reference_state.density + self.mp2_diffdm
else:
raise NotImplementedError("Only densities for level 1 and 2"
" are implemented.")
def dipole_moment(self, level=2):
"""
Return the MP dipole moment at the specified level of
perturbation theory.
"""
if level == 1:
return self.reference_state.dipole_moment
elif level == 2:
return self.mp2_dipole_moment
else:
raise NotImplementedError("Only dipole moments for level 1 and 2"
" are implemented.")
@cached_member_function
def energy_correction(self, level=2):
"""Obtain the MP energy correction at a particular level"""
if level > 3:
raise NotImplementedError(f"MP({level}) energy correction "
"not implemented.")
if level < 2:
return 0.0
hf = self.reference_state
is_cvs = self.has_core_occupied_space
if level == 2 and not is_cvs:
terms = [(1.0, hf.oovv, self.t2oo)]
elif level == 2 and is_cvs:
terms = [(1.0, hf.oovv, self.t2oo),
(2.0, hf.ocvv, self.t2oc),
(1.0, hf.ccvv, self.t2cc)]
elif level == 3 and not is_cvs:
terms = [(1.0, hf.oovv, self.td2(b.oovv))]
elif level == 3 and is_cvs:
raise NotImplementedError("CVS-MP3 energy correction not implemented.")
return sum(
-0.25 * pref * eri.dot(t2)
for pref, eri, t2 in terms
)
def energy(self, level=2):
"""
Obtain the total energy (SCF energy plus all corrections)
at a particular level of perturbation theory.
"""
if level == 0:
# Sum of orbital energies ...
raise NotImplementedError("Total MP(0) energy not implemented.")
# Accumulator for all energy terms
energies = [self.reference_state.energy_scf]
for il in range(2, level + 1):
energies.append(self.energy_correction(il))
return sum(energies)
def to_qcvars(self, properties=False, recurse=False, maxlevel=2):
"""
Return a dictionary with property keys compatible to a Psi4 wavefunction
or a QCEngine Atomicresults object.
"""
qcvars = {}
for level in range(2, maxlevel + 1):
try:
mpcorr = self.energy_correction(level)
qcvars[f"MP{level} CORRELATION ENERGY"] = mpcorr
qcvars[f"MP{level} TOTAL ENERGY"] = self.energy(level)
except NotImplementedError:
pass
except ValueError:
pass
if properties:
for level in range(2, maxlevel + 1):
try:
qcvars["MP2 DIPOLE"] = self.dipole_moment(level)
except NotImplementedError:
pass
if recurse:
qcvars.update(self.reference_state.to_qcvars(properties, recurse))
return qcvars
@property
def mp2_density(self):
return self.density(2)
@cached_property
def mp2_dipole_moment(self):
refstate = self.reference_state
dipole_integrals = refstate.operators.electric_dipole
mp2corr = -np.array([product_trace(comp, self.mp2_diffdm)
for comp in dipole_integrals])
return refstate.dipole_moment + mp2corr
#
# Register cvs_p0 intermedites
#
@register_as_intermediate
def cvs_p0_oo(hf, mp, intermediates):
# NOTE: equal to mp2_diffdm if CVS applied for the density
return -0.5 * einsum("ikab,jkab->ij", mp.t2oo, mp.t2oo)
@register_as_intermediate
def cvs_p0_ov(hf, mp, intermediates):
# NOTE: equal to mp2_diffdm if CVS applied for the density
return -0.5 * (+ einsum("ijbc,jabc->ia", mp.t2oo, hf.ovvv)
+ einsum("jkib,jkab->ia", hf.ooov, mp.t2oo)) / mp.df(b.ov)
@register_as_intermediate
def cvs_p0_vv(hf, mp, intermediates):
# NOTE: equal to mp2_diffdm if CVS applied for the density
return 0.5 * einsum("ijac,ijbc->ab", mp.t2oo, mp.t2oo)