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state2state_transition_dm.py
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state2state_transition_dm.py
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#!/usr/bin/env python3
## vi: tabstop=4 shiftwidth=4 softtabstop=4 expandtab
## ---------------------------------------------------------------------
##
## Copyright (C) 2018 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 adcc import block as b
from adcc.AdcMethod import AdcMethod
from adcc.functions import einsum
from adcc.AmplitudeVector import AmplitudeVector
from adcc.OneParticleOperator import OneParticleOperator
from .util import check_singles_amplitudes, check_doubles_amplitudes
import libadcc
def s2s_tdm_adc0(mp, amplitude_l, amplitude_r, intermediates):
check_singles_amplitudes([b.o, b.v], amplitude_l, amplitude_r)
ul1 = amplitude_l["s"]
ur1 = amplitude_r["s"]
dm = OneParticleOperator(mp, is_symmetric=False)
dm[b.oo] = -einsum('ja,ia->ij', ul1, ur1)
dm[b.vv] = einsum('ia,ib->ab', ul1, ur1)
return dm
def s2s_tdm_adc2(mp, amplitude_l, amplitude_r, intermediates):
check_doubles_amplitudes([b.o, b.o, b.v, b.v], amplitude_l, amplitude_r)
dm = s2s_tdm_adc0(mp, amplitude_l, amplitude_r, intermediates)
ul1, ul2 = amplitude_l["s"], amplitude_l["d"]
ur1, ur2 = amplitude_r["s"], amplitude_r["d"]
t2 = mp.t2(b.oovv)
p0_ov = mp.mp2_diffdm[b.ov]
p0_oo = mp.mp2_diffdm[b.oo]
p0_vv = mp.mp2_diffdm[b.vv]
p1_oo = dm[b.oo].evaluate() # ADC(1) tdm
p1_vv = dm[b.vv].evaluate() # ADC(1) tdm
# ADC(2) ISR intermediate (TODO Move to intermediates)
rul1 = einsum('ijab,jb->ia', t2, ul1).evaluate()
rur1 = einsum('ijab,jb->ia', t2, ur1).evaluate()
dm[b.oo] = (
p1_oo - 2.0 * einsum('ikab,jkab->ij', ur2, ul2)
+ 0.5 * einsum('ik,kj->ij', p1_oo, p0_oo)
+ 0.5 * einsum('ik,kj->ij', p0_oo, p1_oo)
- 0.5 * einsum('ikcd,lk,jlcd->ij', t2, p1_oo, t2)
+ 1.0 * einsum('ikcd,jkcb,db->ij', t2, t2, p1_vv)
- 0.5 * einsum('ia,jkac,kc->ij', ur1, t2, rul1)
- 0.5 * einsum('ikac,kc,ja->ij', t2, rur1, ul1)
- 1.0 * einsum('ia,ja->ij', rul1, rur1)
)
dm[b.vv] = (
p1_vv + 2.0 * einsum('ijac,ijbc->ab', ul2, ur2)
- 0.5 * einsum("ac,cb->ab", p1_vv, p0_vv)
- 0.5 * einsum("ac,cb->ab", p0_vv, p1_vv)
- 0.5 * einsum("klbc,klad,cd->ab", t2, t2, p1_vv)
+ 1.0 * einsum("klbc,jk,jlac->ab", t2, p1_oo, t2)
+ 0.5 * einsum("ikac,kc,ib->ab", t2, rul1, ur1)
+ 0.5 * einsum("ia,ikbc,kc->ab", ul1, t2, rur1)
+ 1.0 * einsum("ia,ib->ab", rur1, rul1)
)
p1_ov = -2.0 * einsum("jb,ijab->ia", ul1, ur2).evaluate()
p1_vo = -2.0 * einsum("ijab,jb->ai", ul2, ur1).evaluate()
dm[b.ov] = (
p1_ov
- einsum("ijab,bj->ia", t2, p1_vo)
- einsum("ib,ba->ia", p0_ov, p1_vv)
+ einsum("ij,ja->ia", p1_oo, p0_ov)
- einsum("ib,klca,klcb->ia", ur1, t2, ul2)
- einsum("ikcd,jkcd,ja->ia", t2, ul2, ur1)
)
dm[b.vo] = (
p1_vo
- einsum("ijab,jb->ai", t2, p1_ov)
- einsum("ib,ab->ai", p0_ov, p1_vv)
+ einsum("ji,ja->ai", p1_oo, p0_ov)
- einsum("ib,klca,klcb->ai", ul1, t2, ur2)
- einsum("ikcd,jkcd,ja->ai", t2, ur2, ul1)
)
return dm
# Ref: https://doi.org/10.1080/00268976.2013.859313
DISPATCH = {"adc0": s2s_tdm_adc0,
"adc1": s2s_tdm_adc0, # same as ADC(0)
"adc2": s2s_tdm_adc2,
"adc2x": s2s_tdm_adc2, # same as ADC(2)
}
def state2state_transition_dm(method, ground_state, amplitude_from,
amplitude_to, intermediates=None):
"""
Compute the state to state transition density matrix
state in the MO basis using the intermediate-states representation.
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_from : AmplitudeVector
The amplitude vector of the state to start from
amplitude_to : AmplitudeVector
The amplitude vector of the state to excite to
intermediates : AdcIntermediates
Intermediates from the ADC calculation to reuse
"""
if not isinstance(method, AdcMethod):
method = AdcMethod(method)
if not isinstance(ground_state, libadcc.LazyMp):
raise TypeError("ground_state should be a LazyMp object.")
if not isinstance(amplitude_from, AmplitudeVector):
raise TypeError("amplitude_from should be an AmplitudeVector object.")
if not isinstance(amplitude_to, AmplitudeVector):
raise TypeError("amplitude_to should be an AmplitudeVector object.")
if intermediates is None:
intermediates = libadcc.AdcIntermediates(ground_state)
if method.name not in DISPATCH:
raise NotImplementedError("state2state_transition_dm is not implemented "
f"for {method.name}.")
else:
# final state is on the bra side/left (complex conjugate)
# see ref https://doi.org/10.1080/00268976.2013.859313, appendix A2
ret = DISPATCH[method.name](ground_state, amplitude_to, amplitude_from,
intermediates)
return ret.evaluate()