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Copy pathradc_ea.py
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1616 lines (1312 loc) · 75.2 KB
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# Copyright 2014-2022 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: Abdelrahman Ahmed <>
# Samragni Banerjee <samragnibanerjee4@gmail.com>
# James Serna <jamcar456@gmail.com>
# Terrence Stahl <>
# Ning-Yuan Chen <cny003@outlook.com>
# Alexander Sokolov <alexander.y.sokolov@gmail.com>
'''
Restricted algebraic diagrammatic construction
'''
import numpy as np
from pyscf import lib
from pyscf.lib import logger
from pyscf.adc import radc
from pyscf.adc import radc_ao2mo
from pyscf.adc import dfadc
from pyscf import symm
from pyscf.data.nist import HARTREE2EV
def get_imds(adc, eris=None):
cput0 = (logger.process_clock(), logger.perf_counter())
log = logger.Logger(adc.stdout, adc.verbose)
if adc.method not in ("adc(2)", "adc(2)-x", "adc(3)"):
raise NotImplementedError(adc.method)
method = adc.method
t1 = adc.t1
t2 = adc.t2
t1_2 = t1[0]
eris_ovvo = eris.ovvo
nocc = adc._nocc
nvir = adc._nvir
e_vir = adc.mo_energy[nocc:].copy()
idn_vir = np.identity(nvir)
if eris is None:
eris = adc.transform_integrals()
# a-b block
# Zeroth-order terms
M_ab = lib.einsum('ab,a->ab', idn_vir, e_vir)
# Second-order terms
t2_1 = t2[0][:]
M_ab -= 1.5 * 0.5 * lib.einsum('lmad,lbdm->ab',t2_1, eris_ovvo,optimize=True)
M_ab += 0.5 * 0.5 * lib.einsum('mlad,lbdm->ab',t2_1, eris_ovvo,optimize=True)
M_ab += 0.5 * 0.5 * lib.einsum('lmad,ldbm->ab',t2_1, eris_ovvo,optimize=True)
M_ab -= 0.5 * 0.5 * lib.einsum('mlad,ldbm->ab',t2_1, eris_ovvo,optimize=True)
#M_ab -= 0.5 * lib.einsum('lmad,lbdm->ab',t2_1, eris_ovvo,optimize=True)
M_ab -= 1.5 * 0.5 * lib.einsum('lmbd,ladm->ab',t2_1, eris_ovvo,optimize=True)
M_ab += 0.5 * 0.5 * lib.einsum('mlbd,ladm->ab',t2_1, eris_ovvo,optimize=True)
M_ab += 0.5 * 0.5 * lib.einsum('lmbd,ldam->ab',t2_1, eris_ovvo,optimize=True)
M_ab -= 0.5 * 0.5 * lib.einsum('mlbd,ldam->ab',t2_1, eris_ovvo,optimize=True)
#M_ab -= 0.5 * lib.einsum('lmbd,ladm->ab',t2_1, eris_ovvo,optimize=True)
del t2_1
cput0 = log.timer_debug1("Completed M_ab second-order terms ADC(2) calculation", *cput0)
#Third-order terms
if (method =='adc(3)'):
eris_oovv = eris.oovv
if eris.ovvv is None:
chnk_size = radc_ao2mo.calculate_chunk_size(adc)
for a,b in lib.prange(0,nocc,chnk_size):
eris_ovvv = dfadc.get_ovvv_df(adc, eris.Lov, eris.Lvv,
a, chnk_size).reshape(-1,nvir,nvir,nvir)
M_ab += 4. * lib.einsum('ld,ldab->ab',t1_2[a:b], eris_ovvv,optimize=True)
M_ab -= lib.einsum('ld,lbad->ab',t1_2[a:b], eris_ovvv,optimize=True)
M_ab -= lib.einsum('ld,ladb->ab',t1_2[a:b], eris_ovvv,optimize=True)
del eris_ovvv
else :
eris_ovvv = radc_ao2mo.unpack_eri_1(eris.ovvv, nvir)
M_ab += 4. * lib.einsum('ld,ldab->ab',t1_2, eris_ovvv,optimize=True)
M_ab -= lib.einsum('ld,lbad->ab',t1_2, eris_ovvv,optimize=True)
M_ab -= lib.einsum('ld,ladb->ab',t1_2, eris_ovvv,optimize=True)
del eris_ovvv
cput0 = log.timer_debug1("Completed M_ab ovvv ADC(3) calculation", *cput0)
t2_2 = t2[1][:]
M_ab -= 0.5 * 0.5 * lib.einsum('lmad,lbdm->ab',t2_2, eris_ovvo,optimize=True)
M_ab += 0.5 * 0.5 * lib.einsum('mlad,lbdm->ab',t2_2, eris_ovvo,optimize=True)
M_ab += 0.5 * 0.5 * lib.einsum('lmad,ldbm->ab',t2_2, eris_ovvo,optimize=True)
M_ab -= 0.5 * 0.5 * lib.einsum('mlad,ldbm->ab',t2_2, eris_ovvo,optimize=True)
M_ab -= 0.5 * lib.einsum('lmad,lbdm->ab',t2_2, eris_ovvo,optimize=True)
M_ab -= 0.5 * 0.5 * lib.einsum('lmbd,ladm->ab',t2_2,eris_ovvo,optimize=True)
M_ab += 0.5 * 0.5 * lib.einsum('mlbd,ladm->ab',t2_2,eris_ovvo,optimize=True)
M_ab += 0.5 * 0.5 * lib.einsum('lmbd,ldam->ab',t2_2, eris_ovvo,optimize=True)
M_ab -= 0.5 * 0.5 * lib.einsum('mlbd,ldam->ab',t2_2, eris_ovvo,optimize=True)
M_ab -= 0.5 * 1.0 * lib.einsum('lmbd,ladm->ab',t2_2,eris_ovvo,optimize=True)
t2_1 = t2[0][:]
log.timer_debug1("Starting the small integrals calculation")
temp_t2_v_1 = lib.einsum('lned,mlbd->nemb',t2_1, t2_1,optimize=True)
M_ab -= 0.5 * lib.einsum('nemb,nmae->ab',temp_t2_v_1, eris_oovv, optimize=True)
M_ab -= 0.5 * lib.einsum('mbne,nmae->ab',temp_t2_v_1, eris_oovv, optimize=True)
M_ab += 0.5 * lib.einsum('nemb,maen->ab',temp_t2_v_1, eris_ovvo, optimize=True)
M_ab += 0.5 * lib.einsum('mbne,maen->ab',temp_t2_v_1, eris_ovvo, optimize=True)
M_ab += 0.5 * lib.einsum('nemb,neam->ab',temp_t2_v_1, eris_ovvo, optimize=True)
M_ab -= 0.5 * lib.einsum('name,nmeb->ab',temp_t2_v_1, eris_oovv, optimize=True)
M_ab -= 0.5 * lib.einsum('mena,nmeb->ab',temp_t2_v_1, eris_oovv, optimize=True)
M_ab += 0.5 * 2. * lib.einsum('name,nbem->ab',temp_t2_v_1, eris_ovvo, optimize=True)
M_ab += 0.5 * 2. * lib.einsum('mena,nbem->ab',temp_t2_v_1, eris_ovvo, optimize=True)
M_ab += 0.5 * lib.einsum('nbme,mean->ab',temp_t2_v_1, eris_ovvo, optimize=True)
del temp_t2_v_1
temp_t2_v_2 = lib.einsum('nled,mlbd->nemb',t2_1, t2_1,optimize=True)
M_ab += 0.5 * 2. * lib.einsum('nemb,nmae->ab',temp_t2_v_2, eris_oovv, optimize=True)
M_ab -= 0.5 * 4. * lib.einsum('nemb,maen->ab',temp_t2_v_2, eris_ovvo, optimize=True)
M_ab += 0.5 * 2. * lib.einsum('mena,nmeb->ab',temp_t2_v_2, eris_oovv, optimize=True)
M_ab -= 0.5 * 4. * lib.einsum('mena,nbem->ab',temp_t2_v_2, eris_ovvo, optimize=True)
del temp_t2_v_2
temp_t2_v_3 = lib.einsum('lned,lmbd->nemb',t2_1, t2_1,optimize=True)
M_ab -= 0.5 * lib.einsum('nemb,maen->ab',temp_t2_v_3, eris_ovvo, optimize=True)
M_ab += 0.5 * 2. * lib.einsum('nemb,nmae->ab',temp_t2_v_3, eris_oovv, optimize=True)
M_ab += 0.5 * 2. * lib.einsum('mena,nmeb->ab',temp_t2_v_3, eris_oovv, optimize=True)
M_ab -= 0.5 * lib.einsum('mena,nbem->ab',temp_t2_v_3, eris_ovvo, optimize=True)
del temp_t2_v_3
temp_t2_v_8 = lib.einsum('lned,mled->mn',t2_1, t2_1,optimize=True)
M_ab += 2.* lib.einsum('mn,nmab->ab',temp_t2_v_8, eris_oovv, optimize=True)
M_ab -= lib.einsum('mn,nbam->ab', temp_t2_v_8, eris_ovvo, optimize=True)
del temp_t2_v_8
temp_t2_v_9 = lib.einsum('nled,mled->mn',t2_1, t2_1,optimize=True)
M_ab -= 4.* lib.einsum('mn,nmab->ab',temp_t2_v_9, eris_oovv, optimize=True)
M_ab += 2. * lib.einsum('mn,nbam->ab',temp_t2_v_9, eris_ovvo, optimize=True)
del temp_t2_v_9
log.timer_debug1("Completed M_ab ADC(3) small integrals calculation")
log.timer_debug1("Starting M_ab vvvv ADC(3) calculation")
if isinstance(eris.vvvv, np.ndarray):
temp_t2 = adc.imds.t2_1_vvvv
M_ab -= 0.5 * 0.25*lib.einsum('mlaf,mlbf->ab',t2_1, temp_t2, optimize=True)
M_ab += 0.5 * 0.25*lib.einsum('mlaf,lmbf->ab',t2_1, temp_t2, optimize=True)
M_ab += 0.5 * 0.25*lib.einsum('lmaf,mlbf->ab',t2_1, temp_t2, optimize=True)
M_ab -= 0.5 * 0.25*lib.einsum('lmaf,lmbf->ab',t2_1, temp_t2, optimize=True)
M_ab += 0.5 * 0.25*lib.einsum('mlaf,mlfb->ab',t2_1, temp_t2, optimize=True)
M_ab -= 0.5 * 0.25*lib.einsum('mlaf,lmfb->ab',t2_1, temp_t2, optimize=True)
M_ab -= 0.5 * 0.25*lib.einsum('lmaf,mlfb->ab',t2_1, temp_t2, optimize=True)
M_ab += 0.5 * 0.25*lib.einsum('lmaf,lmfb->ab',t2_1, temp_t2, optimize=True)
M_ab -= 0.5 * lib.einsum('mlaf,mlbf->ab',t2_1, temp_t2, optimize=True)
M_ab -= 0.5 * 0.25*lib.einsum('mlad,mlbd->ab', temp_t2, t2_1, optimize=True)
M_ab += 0.5 * 0.25*lib.einsum('mlad,lmbd->ab', temp_t2, t2_1, optimize=True)
M_ab += 0.5 * 0.25*lib.einsum('lmad,mlbd->ab', temp_t2, t2_1, optimize=True)
M_ab -= 0.5 * 0.25*lib.einsum('lmad,lmbd->ab', temp_t2, t2_1, optimize=True)
M_ab -= 0.5 * lib.einsum('mlad,mlbd->ab', temp_t2, t2_1, optimize=True)
M_ab += 0.5 * 0.25*lib.einsum('lmad,mlbd->ab',temp_t2, t2_1, optimize=True)
M_ab -= 0.5 * 0.25*lib.einsum('lmad,lmbd->ab',temp_t2, t2_1, optimize=True)
M_ab -= 0.5 * 0.25*lib.einsum('mlad,mlbd->ab',temp_t2, t2_1, optimize=True)
M_ab += 0.5 * 0.25*lib.einsum('mlad,lmbd->ab',temp_t2, t2_1, optimize=True)
del temp_t2
eris_vvvv = eris.vvvv
eris_vvvv = eris_vvvv.reshape(nvir,nvir,nvir,nvir)
M_ab -= lib.einsum('mldf,mled,aebf->ab',t2_1, t2_1, eris_vvvv, optimize=True)
M_ab += lib.einsum('mldf,lmed,aebf->ab',t2_1, t2_1, eris_vvvv, optimize=True)
M_ab += lib.einsum('lmdf,mled,aebf->ab',t2_1, t2_1, eris_vvvv, optimize=True)
M_ab -= lib.einsum('lmdf,lmed,aebf->ab',t2_1, t2_1, eris_vvvv, optimize=True)
M_ab += 0.5*lib.einsum('mldf,mled,aefb->ab',t2_1, t2_1, eris_vvvv, optimize=True)
M_ab -= 0.5*lib.einsum('mldf,lmed,aefb->ab',t2_1, t2_1, eris_vvvv, optimize=True)
M_ab -= 0.5*lib.einsum('lmdf,mled,aefb->ab',t2_1, t2_1, eris_vvvv, optimize=True)
M_ab += 0.5*lib.einsum('lmdf,lmed,aefb->ab',t2_1, t2_1, eris_vvvv, optimize=True)
M_ab += 2.*lib.einsum('mlfd,mled,aebf->ab',t2_1, t2_1, eris_vvvv, optimize=True)
M_ab -= lib.einsum('mlfd,mled,aefb->ab',t2_1, t2_1, eris_vvvv, optimize=True)
eris_vvvv = eris_vvvv.reshape(nvir*nvir,nvir*nvir)
else:
temp_t2_vvvv = adc.imds.t2_1_vvvv[:]
M_ab -= 0.5 * 0.25*lib.einsum('mlaf,mlbf->ab',t2_1, temp_t2_vvvv, optimize=True)
M_ab += 0.5 * 0.25*lib.einsum('mlaf,lmbf->ab',t2_1, temp_t2_vvvv, optimize=True)
M_ab += 0.5 * 0.25*lib.einsum('lmaf,mlbf->ab',t2_1, temp_t2_vvvv, optimize=True)
M_ab -= 0.5 * 0.25*lib.einsum('lmaf,lmbf->ab',t2_1, temp_t2_vvvv, optimize=True)
M_ab += 0.5 * 0.25*lib.einsum('mlaf,mlfb->ab',t2_1, temp_t2_vvvv, optimize=True)
M_ab -= 0.5 * 0.25*lib.einsum('mlaf,lmfb->ab',t2_1, temp_t2_vvvv, optimize=True)
M_ab -= 0.5 * 0.25*lib.einsum('lmaf,mlfb->ab',t2_1, temp_t2_vvvv, optimize=True)
M_ab += 0.5 * 0.25*lib.einsum('lmaf,lmfb->ab',t2_1, temp_t2_vvvv, optimize=True)
M_ab -= 0.5 * lib.einsum('mlaf,mlbf->ab',t2_1, temp_t2_vvvv, optimize=True)
M_ab += 0.5 * 0.25*lib.einsum('lmad,mlbd->ab',temp_t2_vvvv, t2_1, optimize=True)
M_ab -= 0.5 * 0.25*lib.einsum('lmad,lmbd->ab',temp_t2_vvvv, t2_1, optimize=True)
M_ab -= 0.5 * 0.25*lib.einsum('mlad,mlbd->ab',temp_t2_vvvv, t2_1, optimize=True)
M_ab += 0.5 * 0.25*lib.einsum('mlad,lmbd->ab',temp_t2_vvvv, t2_1, optimize=True)
M_ab -= 0.5 * 0.25*lib.einsum('mlad,mlbd->ab', temp_t2_vvvv, t2_1, optimize=True)
M_ab += 0.5 * 0.25*lib.einsum('mlad,lmbd->ab', temp_t2_vvvv, t2_1, optimize=True)
M_ab += 0.5 * 0.25*lib.einsum('lmad,mlbd->ab', temp_t2_vvvv, t2_1, optimize=True)
M_ab -= 0.5 * 0.25*lib.einsum('lmad,lmbd->ab', temp_t2_vvvv, t2_1, optimize=True)
M_ab -= 0.5 * lib.einsum('mlad,mlbd->ab', temp_t2_vvvv, t2_1, optimize=True)
del temp_t2_vvvv
chnk_size = radc_ao2mo.calculate_chunk_size(adc)
temp = np.zeros((nvir,nvir))
if isinstance(eris.vvvv, list):
a = 0
for dataset in eris.vvvv:
k = dataset.shape[0]
eris_vvvv = dataset[:].reshape(-1,nvir,nvir,nvir)
temp[a:a+k] -= lib.einsum('mldf,mled,aebf->ab',t2_1,
t2_1, eris_vvvv, optimize=True)
temp[a:a+k] += lib.einsum('mldf,lmed,aebf->ab',t2_1,
t2_1, eris_vvvv, optimize=True)
temp[a:a+k] += lib.einsum('lmdf,mled,aebf->ab',t2_1,
t2_1, eris_vvvv, optimize=True)
temp[a:a+k] -= lib.einsum('lmdf,lmed,aebf->ab',t2_1,
t2_1, eris_vvvv, optimize=True)
temp[a:a+k] += 0.5*lib.einsum('mldf,mled,aefb->ab',
t2_1, t2_1, eris_vvvv, optimize=True)
temp[a:a+k] -= 0.5*lib.einsum('mldf,lmed,aefb->ab',
t2_1, t2_1, eris_vvvv, optimize=True)
temp[a:a+k] -= 0.5*lib.einsum('lmdf,mled,aefb->ab',
t2_1, t2_1, eris_vvvv, optimize=True)
temp[a:a+k] += 0.5*lib.einsum('lmdf,lmed,aefb->ab',
t2_1, t2_1, eris_vvvv, optimize=True)
temp[a:a+k] += 2.*lib.einsum('mlfd,mled,aebf->ab',
t2_1, t2_1, eris_vvvv, optimize=True)
temp[a:a+k] -= lib.einsum('mlfd,mled,aefb->ab',t2_1,
t2_1, eris_vvvv, optimize=True)
del eris_vvvv
a += k
else :
for a,b in lib.prange(0,nvir,chnk_size):
vvvv = dfadc.get_vvvv_df(adc, eris.Lvv, a, chnk_size).reshape(-1,nvir,nvir,nvir)
temp[a:b] -= lib.einsum('mldf,mled,aebf->ab',t2_1, t2_1, vvvv, optimize=True)
temp[a:b] += lib.einsum('mldf,lmed,aebf->ab',t2_1, t2_1, vvvv, optimize=True)
temp[a:b] += lib.einsum('lmdf,mled,aebf->ab',t2_1, t2_1, vvvv, optimize=True)
temp[a:b] -= lib.einsum('lmdf,lmed,aebf->ab',t2_1, t2_1, vvvv, optimize=True)
temp[a:b] += 0.5*lib.einsum('mldf,mled,aefb->ab',
t2_1, t2_1, vvvv, optimize=True)
temp[a:b] -= 0.5*lib.einsum('mldf,lmed,aefb->ab',
t2_1, t2_1, vvvv, optimize=True)
temp[a:b] -= 0.5*lib.einsum('lmdf,mled,aefb->ab',
t2_1, t2_1, vvvv, optimize=True)
temp[a:b] += 0.5*lib.einsum('lmdf,lmed,aefb->ab',
t2_1, t2_1, vvvv, optimize=True)
temp[a:b] += 2.*lib.einsum('mlfd,mled,aebf->ab',
t2_1, t2_1, vvvv, optimize=True)
temp[a:b] -= lib.einsum('mlfd,mled,aefb->ab',t2_1, t2_1, vvvv, optimize=True)
del vvvv
M_ab += temp
del temp
del t2_1
cput0 = log.timer_debug1("Completed M_ab ADC(3) calculation", *cput0)
return M_ab
def get_diag(adc,M_ab=None,eris=None):
log = logger.Logger(adc.stdout, adc.verbose)
if adc.method not in ("adc(2)", "adc(2)-x", "adc(3)"):
raise NotImplementedError(adc.method)
if M_ab is None:
M_ab = adc.get_imds()
nocc = adc._nocc
nvir = adc._nvir
n_singles = nvir
n_doubles = nocc * nvir * nvir
dim = n_singles + n_doubles
e_occ = adc.mo_energy[:nocc]
e_vir = adc.mo_energy[nocc:]
s1 = 0
f1 = n_singles
s2 = f1
f2 = s2 + n_doubles
d_ab = e_vir[:,None] + e_vir
d_i = e_occ[:,None]
D_n = -d_i + d_ab.reshape(-1)
D_iab = D_n.reshape(-1)
diag = np.zeros(dim)
# Compute precond in p1-p1 block
M_ab_diag = np.diagonal(M_ab)
diag[s1:f1] = M_ab_diag.copy()
# Compute precond in 2p1h-2p1h block
diag[s2:f2] = D_iab.copy()
del D_iab
# ###### Additional terms for the preconditioner ####
#
# if (method == "adc(2)-x" or method == "adc(3)"):
#
# if eris is None:
# eris = adc.transform_integrals()
#
# #TODO Implement this for out-of-core and density-fitted algorithms
# if isinstance(eris.vvvv, np.ndarray):
#
# eris_oovv = eris.oovv
# eris_ovvo = eris.ovvo
# eris_vvvv = eris.vvvv
#
# temp = np.zeros((nocc, eris_vvvv.shape[0]))
# temp[:] += np.diag(eris_vvvv)
# diag[s2:f2] += temp.reshape(-1)
#
# eris_ovov_p = np.ascontiguousarray(eris_oovv[:].transpose(0,2,1,3))
# eris_ovov_p = eris_ovov_p.reshape(nocc*nvir, nocc*nvir)
#
# temp = np.zeros((nvir, nocc, nvir))
# temp[:] += np.diagonal(eris_ovov_p).reshape(nocc, nvir)
# temp = np.ascontiguousarray(temp.transpose(1,0,2))
# diag[s2:f2] += -temp.reshape(-1)
#
# eris_ovov_p = np.ascontiguousarray(eris_oovv[:].transpose(0,2,1,3))
# eris_ovov_p = eris_ovov_p.reshape(nocc*nvir, nocc*nvir)
#
# temp = np.zeros((nvir, nocc, nvir))
# temp[:] += np.diagonal(eris_ovov_p).reshape(nocc, nvir)
# temp = np.ascontiguousarray(temp.transpose(1,2,0))
# diag[s2:f2] += -temp.reshape(-1)
# else:
# raise Exception("Precond not available for out-of-core and density-fitted algo")
log.timer_debug1("Completed ea_diag calculation")
return diag
def matvec(adc, M_ab=None, eris=None):
if adc.method not in ("adc(2)", "adc(2)-x", "adc(3)"):
raise NotImplementedError(adc.method)
method = adc.method
nocc = adc._nocc
nvir = adc._nvir
n_singles = nvir
n_doubles = nocc * nvir * nvir
dim = n_singles + n_doubles
e_occ = adc.mo_energy[:nocc]
e_vir = adc.mo_energy[nocc:]
if eris is None:
eris = adc.transform_integrals()
s1 = 0
f1 = n_singles
s2 = f1
f2 = s2 + n_doubles
d_ab = e_vir[:,None] + e_vir
d_i = e_occ[:,None]
D_n = -d_i + d_ab.reshape(-1)
D_iab = D_n.reshape(-1)
if M_ab is None:
M_ab = adc.get_imds()
#Calculate sigma vector
def sigma_(r):
cput0 = (logger.process_clock(), logger.perf_counter())
log = logger.Logger(adc.stdout, adc.verbose)
s = np.zeros(dim)
r1 = r[s1:f1]
r2 = r[s2:f2]
r2 = r2.reshape(nocc,nvir,nvir)
############ ADC(2) ab block ############################
s[s1:f1] = lib.einsum('ab,b->a',M_ab,r1)
############## ADC(2) a - ibc and ibc - a coupling blocks #########################
temp_doubles = np.zeros((nocc,nvir,nvir))
if eris.ovvv is None:
chnk_size = radc_ao2mo.calculate_chunk_size(adc)
for a,b in lib.prange(0,nocc,chnk_size):
eris_ovvv = dfadc.get_ovvv_df(adc, eris.Lov, eris.Lvv,
a, chnk_size).reshape(-1,nvir,nvir,nvir)
s[s1:f1] += 2. * lib.einsum('icab,ibc->a', eris_ovvv, r2[a:b], optimize=True)
s[s1:f1] -= lib.einsum('ibac,ibc->a', eris_ovvv, r2[a:b], optimize=True)
temp_doubles[a:b] += lib.einsum('icab,a->ibc', eris_ovvv, r1, optimize=True)
del eris_ovvv
else :
eris_ovvv = radc_ao2mo.unpack_eri_1(eris.ovvv, nvir)
s[s1:f1] += 2. * lib.einsum('icab,ibc->a', eris_ovvv, r2, optimize=True)
s[s1:f1] -= lib.einsum('ibac,ibc->a', eris_ovvv, r2, optimize=True)
temp_doubles += lib.einsum('icab,a->ibc', eris_ovvv, r1, optimize=True)
del eris_ovvv
s[s2:f2] += temp_doubles.reshape(-1)
################ ADC(2) iab - jcd block ############################
s[s2:f2] += D_iab * r2.reshape(-1)
############### ADC(3) iab - jcd block ############################
if (method == "adc(2)-x" or method == "adc(3)"):
eris_oovv = eris.oovv
eris_ovvo = eris.ovvo
r2 = r2.reshape(nocc, nvir, nvir)
if isinstance(eris.vvvv, np.ndarray):
r_bab_t = r2.reshape(nocc,-1)
eris_vvvv = eris.vvvv
s[s2:f2] += np.dot(r_bab_t,eris_vvvv.T).reshape(-1)
elif isinstance(eris.vvvv, list):
s[s2:f2] += contract_r_vvvv(adc,r2,eris.vvvv)
else :
s[s2:f2] += contract_r_vvvv(adc,r2,eris.Lvv)
s[s2:f2] -= 0.5*lib.einsum('jzyi,jzx->ixy',eris_ovvo,r2,optimize=True).reshape(-1)
s[s2:f2] += lib.einsum('jzyi,jxz->ixy',eris_ovvo,r2,optimize=True).reshape(-1)
s[s2:f2] -= 0.5*lib.einsum('jiyz,jxz->ixy',eris_oovv,r2,optimize=True).reshape(-1)
s[s2:f2] -= 0.5*lib.einsum('jixz,jzy->ixy',eris_oovv,r2,optimize=True).reshape(-1)
s[s2:f2] -= 0.5*lib.einsum('jixw,jwy->ixy',eris_oovv,r2,optimize=True).reshape(-1)
s[s2:f2] -= 0.5*lib.einsum('jiyw,jxw->ixy',eris_oovv,r2,optimize=True).reshape(-1)
s[s2:f2] += lib.einsum('jwyi,jxw->ixy',eris_ovvo,r2,optimize=True).reshape(-1)
s[s2:f2] -= 0.5*lib.einsum('jwyi,jwx->ixy',eris_ovvo,r2,optimize=True).reshape(-1)
if (method == "adc(3)"):
eris_ovoo = eris.ovoo
############### ADC(3) a - ibc block and ibc-a coupling blocks ########################
t2_1 = adc.t2[0][:]
temp = 0.25 * lib.einsum('lmab,jab->lmj',t2_1,r2)
temp -= 0.25 * lib.einsum('lmab,jba->lmj',t2_1,r2)
temp -= 0.25 * lib.einsum('mlab,jab->lmj',t2_1,r2)
temp += 0.25 * lib.einsum('mlab,jba->lmj',t2_1,r2)
s[s1:f1] += lib.einsum('lmj,lamj->a',temp, eris_ovoo, optimize=True)
s[s1:f1] -= lib.einsum('lmj,malj->a',temp, eris_ovoo, optimize=True)
del temp
temp_1 = -lib.einsum('lmzw,jzw->jlm',t2_1,r2)
s[s1:f1] -= lib.einsum('jlm,lamj->a',temp_1, eris_ovoo, optimize=True)
temp_s_a = lib.einsum('jlwd,jzw->lzd',t2_1,r2,optimize=True)
temp_s_a -= lib.einsum('jlwd,jwz->lzd',t2_1,r2,optimize=True)
temp_s_a -= lib.einsum('ljwd,jzw->lzd',t2_1,r2,optimize=True)
temp_s_a += lib.einsum('ljwd,jwz->lzd',t2_1,r2,optimize=True)
temp_s_a += lib.einsum('ljdw,jzw->lzd',t2_1,r2,optimize=True)
temp_s_a_1 = -lib.einsum('jlzd,jwz->lwd',t2_1,r2,optimize=True)
temp_s_a_1 += lib.einsum('jlzd,jzw->lwd',t2_1,r2,optimize=True)
temp_s_a_1 += lib.einsum('ljzd,jwz->lwd',t2_1,r2,optimize=True)
temp_s_a_1 -= lib.einsum('ljzd,jzw->lwd',t2_1,r2,optimize=True)
temp_s_a_1 += -lib.einsum('ljdz,jwz->lwd',t2_1,r2,optimize=True)
temp_t2_r2_1 = lib.einsum('jlwd,jzw->lzd',t2_1,r2,optimize=True)
temp_t2_r2_1 -= lib.einsum('jlwd,jwz->lzd',t2_1,r2,optimize=True)
temp_t2_r2_1 += lib.einsum('jlwd,jzw->lzd',t2_1,r2,optimize=True)
temp_t2_r2_1 -= lib.einsum('ljwd,jzw->lzd',t2_1,r2,optimize=True)
temp_t2_r2_2 = -lib.einsum('jlzd,jwz->lwd',t2_1,r2,optimize=True)
temp_t2_r2_2 += lib.einsum('jlzd,jzw->lwd',t2_1,r2,optimize=True)
temp_t2_r2_2 -= lib.einsum('jlzd,jwz->lwd',t2_1,r2,optimize=True)
temp_t2_r2_2 += lib.einsum('ljzd,jwz->lwd',t2_1,r2,optimize=True)
temp_t2_r2_3 = -lib.einsum('ljzd,jzw->lwd',t2_1,r2,optimize=True)
temp_a = t2_1.transpose(0,3,1,2).copy()
temp_b = temp_a.reshape(nocc*nvir,nocc*nvir)
r2_t = r2.reshape(nocc*nvir,-1)
temp_c = np.dot(temp_b,r2_t).reshape(nocc,nvir,nvir)
temp_t2_r2_4 = temp_c.transpose(0,2,1).copy()
del t2_1
temp = np.zeros((nocc,nvir,nvir))
temp_1_1 = np.zeros((nocc,nvir,nvir))
temp_2_1 = np.zeros((nocc,nvir,nvir))
if eris.ovvv is None:
chnk_size = radc_ao2mo.calculate_chunk_size(adc)
for a,b in lib.prange(0,nocc,chnk_size):
eris_ovvv = dfadc.get_ovvv_df(
adc, eris.Lov, eris.Lvv, a, chnk_size).reshape(-1,nvir,nvir,nvir)
temp_1_1[a:b] = lib.einsum('ldxb,b->lxd', eris_ovvv,r1,optimize=True)
temp_1_1[a:b] -= lib.einsum('lbxd,b->lxd', eris_ovvv,r1,optimize=True)
temp_2_1[a:b] = lib.einsum('ldxb,b->lxd', eris_ovvv,r1,optimize=True)
s[s1:f1] += 0.5*lib.einsum('lzd,ldza->a',temp_s_a[a:b],
eris_ovvv,optimize=True)
s[s1:f1] -= 0.5*lib.einsum('lzd,lazd->a',temp_s_a[a:b],
eris_ovvv,optimize=True)
s[s1:f1] -= 0.5*lib.einsum('lwd,ldwa->a',
temp_s_a_1[a:b],eris_ovvv,optimize=True)
s[s1:f1] += 0.5*lib.einsum('lwd,lawd->a',
temp_s_a_1[a:b],eris_ovvv,optimize=True)
s[s1:f1] += 0.5*lib.einsum('lzd,ldza->a',
temp_t2_r2_1[a:b],eris_ovvv,optimize=True)
s[s1:f1] -= 0.5*lib.einsum('lwd,ldwa->a',
temp_t2_r2_2[a:b],eris_ovvv,optimize=True)
s[s1:f1] += 0.5*lib.einsum('lwd,lawd->a',
temp_t2_r2_3[a:b],eris_ovvv,optimize=True)
s[s1:f1] -= 0.5*lib.einsum('lzd,lazd->a',
temp_t2_r2_4[a:b],eris_ovvv,optimize=True)
temp[a:b] -= lib.einsum('lbyd,b->lyd',eris_ovvv,r1,optimize=True)
del eris_ovvv
else :
eris_ovvv = radc_ao2mo.unpack_eri_1(eris.ovvv, nvir)
temp_1_1 = lib.einsum('ldxb,b->lxd', eris_ovvv,r1,optimize=True)
temp_1_1 -= lib.einsum('lbxd,b->lxd', eris_ovvv,r1,optimize=True)
temp_2_1 = lib.einsum('ldxb,b->lxd', eris_ovvv,r1,optimize=True)
s[s1:f1] += 0.5*lib.einsum('lzd,ldza->a',temp_s_a,eris_ovvv,optimize=True)
s[s1:f1] -= 0.5*lib.einsum('lzd,lazd->a',temp_s_a,eris_ovvv,optimize=True)
s[s1:f1] -= 0.5*lib.einsum('lwd,ldwa->a',temp_s_a_1,eris_ovvv,optimize=True)
s[s1:f1] += 0.5*lib.einsum('lwd,lawd->a',temp_s_a_1,eris_ovvv,optimize=True)
s[s1:f1] += 0.5*lib.einsum('lzd,ldza->a',temp_t2_r2_1,eris_ovvv,optimize=True)
s[s1:f1] -= 0.5*lib.einsum('lwd,ldwa->a',temp_t2_r2_2,eris_ovvv,optimize=True)
s[s1:f1] += 0.5*lib.einsum('lwd,lawd->a',temp_t2_r2_3,eris_ovvv,optimize=True)
s[s1:f1] -= 0.5*lib.einsum('lzd,lazd->a',temp_t2_r2_4,eris_ovvv,optimize=True)
temp -= lib.einsum('lbyd,b->lyd',eris_ovvv,r1,optimize=True)
del eris_ovvv
t2_1 = adc.t2[0][:]
temp_1 = -lib.einsum('lyd,lixd->ixy',temp,t2_1,optimize=True)
s[s2:f2] -= temp_1.reshape(-1)
del temp_s_a
del temp_s_a_1
del temp_t2_r2_1
del temp_t2_r2_2
del temp_t2_r2_3
del temp_t2_r2_4
temp_1 = lib.einsum('b,lbmi->lmi',r1,eris_ovoo)
s[s2:f2] += lib.einsum('lmi,lmxy->ixy',temp_1, t2_1, optimize=True).reshape(-1)
temp = lib.einsum('lxd,lidy->ixy',temp_1_1,t2_1,optimize=True)
temp += lib.einsum('lxd,ilyd->ixy',temp_2_1,t2_1,optimize=True)
temp -= lib.einsum('lxd,ildy->ixy',temp_2_1,t2_1,optimize=True)
s[s2:f2] += temp.reshape(-1)
del t2_1
del temp
del temp_1
del temp_1_1
del temp_2_1
cput0 = log.timer_debug1("completed sigma vector calculation", *cput0)
return s
return sigma_
def get_trans_moments(adc):
nmo = adc.nmo
T = []
for orb in range(nmo):
T_a = get_trans_moments_orbital(adc,orb)
T.append(T_a)
T = np.array(T)
return T
def get_trans_moments_orbital(adc, orb):
if adc.method not in ("adc(2)", "adc(2)-x", "adc(3)"):
raise NotImplementedError(adc.method)
method = adc.method
t2_1 = adc.t2[0][:]
if (adc.approx_trans_moments is False or adc.method == "adc(3)"):
t1_2 = adc.t1[0][:]
nocc = adc._nocc
nvir = adc._nvir
n_singles = nvir
n_doubles = nocc * nvir * nvir
dim = n_singles + n_doubles
idn_vir = np.identity(nvir)
s1 = 0
f1 = n_singles
s2 = f1
f2 = s2 + n_doubles
T = np.zeros(dim)
######## ADC(2) part ############################################
if orb < nocc:
if (adc.approx_trans_moments is False or adc.method == "adc(3)"):
T[s1:f1] = -t1_2[orb,:]
t2_1_t = -t2_1.transpose(1,0,2,3)
T[s2:f2] += t2_1_t[:,orb,:,:].reshape(-1)
else:
T[s1:f1] += idn_vir[(orb-nocc), :]
T[s1:f1] -= 0.25*lib.einsum('klc,klac->a',t2_1[:,:,(orb-nocc),:], t2_1, optimize=True)
T[s1:f1] -= 0.25*lib.einsum('lkc,lkac->a',t2_1[:,:,(orb-nocc),:], t2_1, optimize=True)
T[s1:f1] -= 0.25*lib.einsum('klc,klac->a',t2_1[:,:,(orb-nocc),:], t2_1, optimize=True)
T[s1:f1] += 0.25*lib.einsum('lkc,klac->a',t2_1[:,:,(orb-nocc),:], t2_1, optimize=True)
T[s1:f1] += 0.25*lib.einsum('klc,lkac->a',t2_1[:,:,(orb-nocc),:], t2_1, optimize=True)
T[s1:f1] -= 0.25*lib.einsum('lkc,lkac->a',t2_1[:,:,(orb-nocc),:], t2_1, optimize=True)
######### ADC(3) 2p-1h part ############################################
if (adc.method == "adc(2)-x" and adc.approx_trans_moments is False) or (adc.method == "adc(3)"):
t2_2 = adc.t2[1][:]
if orb < nocc:
t2_2_t = -t2_2.transpose(1,0,2,3)
T[s2:f2] += t2_2_t[:,orb,:,:].reshape(-1)
########### ADC(3) 1p part ############################################
if (method=='adc(3)'):
t2_2 = adc.t2[1][:]
if (adc.approx_trans_moments is False):
t1_3 = adc.t1[1]
if orb < nocc:
T[s1:f1] += 0.5*lib.einsum('kac,ck->a',t2_1[:,orb,:,:], t1_2.T,optimize=True)
T[s1:f1] -= 0.5*lib.einsum('kac,ck->a',t2_1[orb,:,:,:], t1_2.T,optimize=True)
T[s1:f1] -= 0.5*lib.einsum('kac,ck->a',t2_1[orb,:,:,:], t1_2.T,optimize=True)
if (adc.approx_trans_moments is False):
T[s1:f1] -= t1_3[orb,:]
else:
T[s1:f1] -= 0.25*lib.einsum('klc,klac->a',t2_1[:,:,(orb-nocc),:], t2_2, optimize=True)
T[s1:f1] -= 0.25*lib.einsum('lkc,lkac->a',t2_1[:,:,(orb-nocc),:], t2_2, optimize=True)
T[s1:f1] -= 0.25*lib.einsum('klac,klc->a',t2_1, t2_2[:,:,(orb-nocc),:],optimize=True)
T[s1:f1] -= 0.25*lib.einsum('lkac,lkc->a',t2_1, t2_2[:,:,(orb-nocc),:],optimize=True)
T[s1:f1] -= 0.25*lib.einsum('klc,klac->a',t2_1[:,:,(orb-nocc),:], t2_2, optimize=True)
T[s1:f1] += 0.25*lib.einsum('klc,lkac->a',t2_1[:,:,(orb-nocc),:], t2_2, optimize=True)
T[s1:f1] += 0.25*lib.einsum('lkc,klac->a',t2_1[:,:,(orb-nocc),:], t2_2, optimize=True)
T[s1:f1] -= 0.25*lib.einsum('lkc,lkac->a',t2_1[:,:,(orb-nocc),:], t2_2, optimize=True)
T[s1:f1] -= 0.25*lib.einsum('klac,klc->a',t2_1, t2_2[:,:,(orb-nocc),:],optimize=True)
T[s1:f1] += 0.25*lib.einsum('klac,lkc->a',t2_1, t2_2[:,:,(orb-nocc),:],optimize=True)
T[s1:f1] += 0.25*lib.einsum('lkac,klc->a',t2_1, t2_2[:,:,(orb-nocc),:],optimize=True)
T[s1:f1] -= 0.25*lib.einsum('lkac,lkc->a',t2_1, t2_2[:,:,(orb-nocc),:],optimize=True)
del t2_2
del t2_1
T_aaa = T[n_singles:].reshape(nocc,nvir,nvir).copy()
T_aaa = T_aaa - T_aaa.transpose(0,2,1)
T[n_singles:] += T_aaa.reshape(-1)
return T
def analyze_eigenvector(adc):
nocc = adc._nocc
nvir = adc._nvir
evec_print_tol = adc.evec_print_tol
logger.info(adc, "Number of occupied orbitals = %d", nocc)
logger.info(adc, "Number of virtual orbitals = %d", nvir)
logger.info(adc, "Print eigenvector elements > %f\n", evec_print_tol)
n_singles = nvir
U = adc.U
for I in range(U.shape[1]):
U1 = U[:n_singles,I]
U2 = U[n_singles:,I].reshape(nocc,nvir,nvir)
U1dotU1 = np.dot(U1, U1)
U2dotU2 = 2.*np.dot(U2.ravel(), U2.ravel()) - \
np.dot(U2.ravel(), U2.transpose(0,2,1).ravel())
U_sq = U[:,I].copy()**2
ind_idx = np.argsort(-U_sq)
U_sq = U_sq[ind_idx]
U_sorted = U[ind_idx,I].copy()
U_sorted = U_sorted[U_sq > evec_print_tol**2]
ind_idx = ind_idx[U_sq > evec_print_tol**2]
singles_idx = []
doubles_idx = []
singles_val = []
doubles_val = []
iter_num = 0
for orb_idx in ind_idx:
if orb_idx < n_singles:
a_idx = orb_idx + 1 + nocc
singles_idx.append(a_idx)
singles_val.append(U_sorted[iter_num])
if orb_idx >= n_singles:
iab_idx = orb_idx - n_singles
ab_rem = iab_idx % (nvir*nvir)
i_idx = iab_idx //(nvir*nvir)
a_idx = ab_rem//nvir
b_idx = ab_rem % nvir
doubles_idx.append((i_idx + 1, a_idx + 1 + nocc, b_idx + 1 + nocc))
doubles_val.append(U_sorted[iter_num])
iter_num += 1
logger.info(adc, '%s | root %d | Energy (eV) = %12.8f | norm(1p) = %6.4f | norm(1h2p) = %6.4f ',
adc.method, I, adc.E[I]*HARTREE2EV, U1dotU1, U2dotU2)
if singles_val:
logger.info(adc, "\n1p block: ")
logger.info(adc, " a U(a)")
logger.info(adc, "------------------")
for idx, print_singles in enumerate(singles_idx):
logger.info(adc, ' %4d %7.4f', print_singles, singles_val[idx])
if doubles_val:
logger.info(adc, "\n1h2p block: ")
logger.info(adc, " i a b U(i,a,b)")
logger.info(adc, "-------------------------------")
for idx, print_doubles in enumerate(doubles_idx):
logger.info(adc, ' %4d %4d %4d %7.4f',
print_doubles[0], print_doubles[1], print_doubles[2], doubles_val[idx])
logger.info(adc,
"***************************************************************************************\n")
def analyze_spec_factor(adc):
X = adc.X
X_2 = (X.copy()**2)*2
thresh = adc.spec_factor_print_tol
logger.info(adc, "Print spectroscopic factors > %E\n", adc.spec_factor_print_tol)
for i in range(X_2.shape[1]):
sort = np.argsort(-X_2[:,i])
X_2_row = X_2[:,i]
X_2_row = X_2_row[sort]
if not adc.mol.symmetry:
sym = np.repeat(['A'], X_2_row.shape[0])
else:
sym = [symm.irrep_id2name(adc.mol.groupname, x) for x in adc._scf.mo_coeff.orbsym]
sym = np.array(sym)
sym = sym[sort]
spec_Contribution = X_2_row[X_2_row > thresh]
index_mo = sort[X_2_row > thresh]+1
if np.sum(spec_Contribution) == 0.0:
continue
logger.info(adc, '%s | root %d | Energy (eV) = %12.8f \n',
adc.method, i, adc.E[i]*HARTREE2EV)
logger.info(adc, " HF MO Spec. Contribution Orbital symmetry")
logger.info(adc, "-----------------------------------------------------------")
for c in range(index_mo.shape[0]):
logger.info(adc, ' %3.d %10.8f %s',
index_mo[c], spec_Contribution[c], sym[c])
logger.info(adc, '\nPartial spec. factor sum = %10.8f', np.sum(spec_Contribution))
logger.info(adc,
"***********************************************************\n")
def renormalize_eigenvectors(adc, nroots=1):
nocc = adc._nocc
nvir = adc._nvir
n_singles = nvir
U = adc.U
for I in range(U.shape[1]):
U1 = U[:n_singles,I]
U2 = U[n_singles:,I].reshape(nocc,nvir,nvir)
UdotU = np.dot(U1, U1) + 2.*np.dot(U2.ravel(), U2.ravel()) - \
np.dot(U2.ravel(), U2.transpose(0,2,1).ravel())
U[:,I] /= np.sqrt(UdotU)
return U
def get_properties(adc, nroots=1):
#Transition moments
T = adc.get_trans_moments()
#Spectroscopic amplitudes
U = adc.renormalize_eigenvectors(nroots)
X = np.dot(T, U).reshape(-1, nroots)
#Spectroscopic factors
P = 2.0*lib.einsum("pi,pi->i", X, X)
return P,X
def analyze(myadc):
header = ("\n*************************************************************"
"\n Eigenvector analysis summary"
"\n*************************************************************")
logger.info(myadc, header)
myadc.analyze_eigenvector()
if myadc.compute_properties:
header = ("\n*************************************************************"
"\n Spectroscopic factors analysis summary"
"\n*************************************************************")
logger.info(myadc, header)
myadc.analyze_spec_factor()
def make_rdm1(adc):
cput0 = (logger.process_clock(), logger.perf_counter())
log = logger.Logger(adc.stdout, adc.verbose)
nroots = adc.U.shape[1]
U = adc.renormalize_eigenvectors(nroots)
list_rdm1 = []
for i in range(U.shape[1]):
rdm1 = make_rdm1_eigenvectors(adc, U[:,i], U[:,i])
list_rdm1.append(rdm1)
cput0 = log.timer_debug1("completed OPDM calculation", *cput0)
return list_rdm1
def make_rdm1_eigenvectors(adc, L, R):
# Using SQA EA
L = np.array(L).ravel()
R = np.array(R).ravel()
t1_ccee = adc.t2[0][:]
nocc = adc._nocc
nvir = adc._nvir
nmo = nocc + nvir
n_singles = nvir
n_doubles = nvir * nvir * nocc
if adc.t1[0] is not None:
t2_ce = adc.t1[0]
else:
t2_ce = np.zeros((nocc, nvir))
occ_list = range(nocc)
s1 = 0
f1 = n_singles
s2 = f1
f2 = s2 + n_doubles
rdm1 = np.zeros((nmo,nmo))
L1 = L[s1:f1]
L2 = L[s2:f2]
R1 = R[s1:f1]
R2 = R[s2:f2]
L2 = L2.reshape(nocc,nvir,nvir)
R2 = R2.reshape(nocc,nvir,nvir)
einsum = lib.einsum
einsum_type = True
############# block- ij
### 000 ###
rdm1[occ_list, occ_list] += 2 * einsum('a,a->', L1, R1, optimize = einsum_type)
### 101 ###
rdm1[:nocc, :nocc] -= 2 * einsum('Jab,Iab->IJ', L2, R2, optimize = einsum_type)
rdm1[:nocc, :nocc] += 1 * einsum('Jab,Iba->IJ', L2, R2, optimize = einsum_type)
rdm1[occ_list, occ_list] += 4 * einsum('iab,iab->', L2, R2, optimize = einsum_type)
rdm1[occ_list, occ_list] -= 2 * einsum('iab,iba->', L2, R2, optimize = einsum_type)
### 020 ###
rdm1[:nocc, :nocc] -= 2 * einsum('a,a,Iibc,Jibc->IJ', L1, R1,
t1_ccee, t1_ccee, optimize = einsum_type)
rdm1[:nocc, :nocc] += einsum('a,a,Iibc,Jicb->IJ', L1, R1, t1_ccee,
t1_ccee, optimize = einsum_type)
rdm1[:nocc, :nocc] += 2 * einsum('a,b,Iiac,Jibc->IJ', L1, R1,
t1_ccee, t1_ccee, optimize = einsum_type)
rdm1[:nocc, :nocc] -= einsum('a,b,Iiac,Jicb->IJ', L1, R1, t1_ccee,
t1_ccee, optimize = einsum_type)
rdm1[:nocc, :nocc] -= einsum('a,b,Iica,Jibc->IJ', L1, R1, t1_ccee,
t1_ccee, optimize = einsum_type)
rdm1[:nocc, :nocc] += einsum('a,b,Iica,Jicb->IJ', L1, R1, t1_ccee,
t1_ccee, optimize = einsum_type)
rdm1[:nocc, :nocc] -= 2 * einsum('a,a,Iibc,Jibc->IJ', L1, R1,
t1_ccee, t1_ccee, optimize = einsum_type)
rdm1[:nocc, :nocc] += einsum('a,a,Iibc,Jicb->IJ', L1, R1, t1_ccee,
t1_ccee, optimize = einsum_type)
rdm1[:nocc, :nocc] += einsum('a,b,Iica,Jicb->IJ', L1, R1, t1_ccee,
t1_ccee, optimize = einsum_type)
############# block- ab
### 000 ###
rdm1[nocc:, nocc:] += einsum('B,A->AB', L1, R1, optimize = einsum_type)
### 020 ###
rdm1[nocc:, nocc:] -= einsum('A,a,ijab,ijBb->AB', L1, R1, t1_ccee,
t1_ccee, optimize = einsum_type)
rdm1[nocc:, nocc:] += 1/2 * einsum('A,a,ijab,jiBb->AB', L1,
R1, t1_ccee, t1_ccee, optimize = einsum_type)
rdm1[nocc:, nocc:] -= einsum('a,B,ijab,ijAb->AB', L1, R1, t1_ccee,
t1_ccee, optimize = einsum_type)