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state_diffdm.py
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state_diffdm.py
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#!/usr/bin/env python3
## vi: tabstop=4 shiftwidth=4 softtabstop=4 expandtab
## ---------------------------------------------------------------------
##
## Copyright (C) 2020 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/>.
##
## ---------------------------------------------------------------------
from math import sqrt
from adcc import block as b
from adcc.LazyMp import LazyMp
from adcc.AdcMethod import AdcMethod
from adcc.functions import einsum
from adcc.Intermediates import Intermediates
from adcc.AmplitudeVector import AmplitudeVector
from adcc.OneParticleOperator import OneParticleOperator
from .util import check_doubles_amplitudes, check_singles_amplitudes
def diffdm_adc0(mp, amplitude, intermediates):
# C is either c(ore) or o(ccupied)
C = b.c if mp.has_core_occupied_space else b.o
check_singles_amplitudes([C, b.v], amplitude)
u1 = amplitude.ph
dm = OneParticleOperator(mp, is_symmetric=True)
dm[C + C] = -einsum("ia,ja->ij", u1, u1)
dm.vv = einsum("ia,ib->ab", u1, u1)
return dm
def diffdm_adc2(mp, amplitude, intermediates):
dm = diffdm_adc0(mp, amplitude, intermediates) # Get ADC(1) result
check_doubles_amplitudes([b.o, b.o, b.v, b.v], amplitude)
u1, u2 = amplitude.ph, amplitude.pphh
t2 = mp.t2(b.oovv)
p0 = mp.mp2_diffdm
p1_oo = dm.oo.evaluate() # ADC(1) diffdm
p1_vv = dm.vv.evaluate() # ADC(1) diffdm
# Zeroth order doubles contributions
p2_oo = -einsum("ikab,jkab->ij", u2, u2)
p2_vv = einsum("ijac,ijbc->ab", u2, u2)
p2_ov = -2 * einsum("jb,ijab->ia", u1, u2).evaluate()
# ADC(2) ISR intermediate (TODO Move to intermediates)
ru1 = einsum("ijab,jb->ia", t2, u1).evaluate()
# Compute second-order contributions to the density matrix
dm.oo = ( # adc2_p_oo
p1_oo + 2 * p2_oo - einsum("ia,ja->ij", ru1, ru1) + (
+ einsum("ik,kj->ij", p1_oo, p0.oo)
- einsum("ikcd,jkcd->ij", t2,
+ 0.5 * einsum("lk,jlcd->jkcd", p1_oo, t2)
- einsum("jkcb,db->jkcd", t2, p1_vv))
- einsum("ia,jkac,kc->ij", u1, t2, ru1)
).symmetrise()
)
dm.vv = ( # adc2_p_vv
p1_vv + 2 * p2_vv + einsum("ia,ib->ab", ru1, ru1) - (
+ einsum("ac,cb->ab", p1_vv, p0.vv)
+ einsum("klbc,klac->ab", t2,
+ 0.5 * einsum("klad,cd->klac", t2, p1_vv)
- einsum("jk,jlac->klac", p1_oo, t2))
- einsum("ikac,kc,ib->ab", t2, ru1, u1)
).symmetrise()
)
dm.ov = ( # adc2_p_ov
+ p2_ov
- einsum("ijab,jb->ia", t2, p2_ov)
- einsum("ib,ba->ia", p0.ov, p1_vv)
+ einsum("ij,ja->ia", p1_oo, p0.ov)
- einsum("ib,klca,klcb->ia", u1, t2, u2)
- einsum("ikcd,jkcd,ja->ia", t2, u2, u1)
)
return dm
def diffdm_cvs_adc2(mp, amplitude, intermediates):
dm = diffdm_adc0(mp, amplitude, intermediates) # Get ADC(1) result
check_doubles_amplitudes([b.o, b.c, b.v, b.v], amplitude)
u1, u2 = amplitude.ph, amplitude.pphh
t2 = mp.t2(b.oovv)
p0 = intermediates.cvs_p0
p1_vv = dm.vv.evaluate() # ADC(1) diffdm
# Zeroth order doubles contributions
p2_ov = -sqrt(2) * einsum("jb,ijab->ia", u1, u2)
p2_vo = -sqrt(2) * einsum("ijab,jb->ai", u2, u1)
p2_oo = -einsum("ljab,kjab->kl", u2, u2)
p2_vv = 2 * einsum("ijac,ijbc->ab", u2, u2)
# Second order contributions
# cvs_adc2_dp_oo
dm.oo = p2_oo + einsum("ab,ikac,jkbc->ij", p1_vv, t2, t2)
dm.ov = p2_ov + ( # cvs_adc2_dp_ov
- einsum("ka,ab->kb", p0.ov, p1_vv)
- einsum("lkdb,dl->kb", t2, p2_vo)
+ 1 / sqrt(2) * einsum("ib,klad,liad->kb", u1, t2, u2)
)
dm.vv = p1_vv + p2_vv - 0.5 * ( # cvs_adc2_dp_vv
+ einsum("cb,ac->ab", p1_vv, p0.vv)
+ einsum("cb,ac->ab", p0.vv, p1_vv)
+ einsum("ijbc,ijad,cd->ab", t2, t2, p1_vv)
)
# Add 2nd order correction to CVS-ADC(1) diffdm
dm.cc -= einsum("kIab,kJab->IJ", u2, u2)
return dm
# dict controlling the dispatch of the state_diffdm function
DISPATCH = {
"adc0": diffdm_adc0,
"adc1": diffdm_adc0, # same as ADC(0)
"adc2": diffdm_adc2,
"adc2x": diffdm_adc2,
"cvs-adc0": diffdm_adc0,
"cvs-adc1": diffdm_adc0, # same as ADC(0)
"cvs-adc2": diffdm_cvs_adc2,
"cvs-adc2x": diffdm_cvs_adc2,
}
def state_diffdm(method, ground_state, amplitude, intermediates=None):
"""
Compute the one-particle difference density matrix of an excited state
in the MO basis.
Parameters
----------
method : str, AdcMethod
The method to use for the computation (e.g. "adc2")
ground_state : LazyMp
The ground state upon which the excitation was based
amplitude : AmplitudeVector
The amplitude vector
intermediates : adcc.Intermediates
Intermediates from the ADC calculation to reuse
"""
if not isinstance(method, AdcMethod):
method = AdcMethod(method)
if not isinstance(ground_state, LazyMp):
raise TypeError("ground_state should be a LazyMp object.")
if not isinstance(amplitude, AmplitudeVector):
raise TypeError("amplitude should be an AmplitudeVector object.")
if intermediates is None:
intermediates = Intermediates(ground_state)
if method.name not in DISPATCH:
raise NotImplementedError("state_diffdm is not implemented "
f"for {method.name}.")
else:
ret = DISPATCH[method.name](ground_state, amplitude, intermediates)
return ret.evaluate()