# 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 <abdelrahman.maa.ahmed@gmail.com>
# Alexander Sokolov <alexander.y.sokolov@gmail.com>
#
'''
Restricted algebraic diagrammatic construction
'''
import numpy as np
import pyscf.ao2mo as ao2mo
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 __config__
from pyscf import df
from pyscf import symm
[docs]
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]
ncvs = adc.ncvs
e_cvs = adc.mo_energy[:ncvs]
idn_cvs = np.identity(ncvs)
if eris is None:
eris = adc.transform_integrals()
eris_ovvo = eris.ovvo
# i-j block
# Zeroth-order terms
M_ij = lib.einsum('ij,j->ij', idn_cvs ,e_cvs)
# Second-order terms
t2_1 = t2[0][:]
t2_1_coee = t2_1[:ncvs,:,:,:].copy()
t2_1_ocee = t2_1[:,:ncvs,:,:].copy()
eris_ceeo = eris_ovvo[:ncvs,:,:,:].copy()
M_ij += 0.5 * 0.5 * lib.einsum('ilde,jdel->ij',t2_1_coee, eris_ceeo,optimize=True)
M_ij -= 0.5 * 0.5 * lib.einsum('lide,jdel->ij',t2_1_ocee, eris_ceeo,optimize=True)
M_ij -= 0.5 * 0.5 * lib.einsum('ilde,jedl->ij',t2_1_coee, eris_ceeo,optimize=True)
M_ij += 0.5 * 0.5 * lib.einsum('lide,jedl->ij',t2_1_ocee, eris_ceeo,optimize=True)
M_ij += 0.5 * lib.einsum('ilde,jdel->ij',t2_1_coee, eris_ceeo,optimize=True)
M_ij += 0.5 * 0.5 * lib.einsum('jlde,idel->ij',t2_1_coee, eris_ceeo,optimize=True)
M_ij -= 0.5 * 0.5 * lib.einsum('ljde,idel->ij',t2_1_ocee, eris_ceeo,optimize=True)
M_ij -= 0.5 * 0.5 * lib.einsum('jlde,iedl->ij',t2_1_coee, eris_ceeo,optimize=True)
M_ij += 0.5 * 0.5 * lib.einsum('ljde,iedl->ij',t2_1_ocee, eris_ceeo,optimize=True)
M_ij += 0.5 * lib.einsum('jlde,idel->ij',t2_1_coee, eris_ceeo,optimize=True)
del t2_1
cput0 = log.timer_debug1("Completed M_ij second-order terms ADC(2) calculation", *cput0)
# Third-order terms
if (method == "adc(3)"):
eris_oovv = eris.oovv
eris_ovoo = eris.ovoo
eris_oooo = eris.oooo
eris_oecc = eris_ovoo[:,:,:ncvs,:ncvs].copy()
eris_ceoc = eris_ovoo[:ncvs,:,:,:ncvs].copy()
eris_coee = eris_oovv[:ncvs,:,:,:].copy()
eris_ccee = eris_coee[:,:ncvs,:,:].copy()
eris_ceec = eris_ceeo[:,:,:,:ncvs].copy()
eris_cooo = eris_oooo[:ncvs,:,:,:].copy()
eris_cooc = eris_cooo[:,:,:,:ncvs].copy()
eris_ccoo = eris_cooo[:,:ncvs,:,:].copy()
M_ij += lib.einsum('ld,ldji->ij',t1_2, eris_oecc,optimize=True)
M_ij -= lib.einsum('ld,jdli->ij',t1_2, eris_ceoc,optimize=True)
M_ij += lib.einsum('ld,ldji->ij',t1_2, eris_oecc,optimize=True)
M_ij += lib.einsum('ld,ldij->ij',t1_2, eris_oecc,optimize=True)
M_ij -= lib.einsum('ld,idlj->ij',t1_2, eris_ceoc,optimize=True)
M_ij += lib.einsum('ld,ldij->ij',t1_2, eris_oecc,optimize=True)
t2_2 = t2[1][:]
t2_2_coee = t2_2[:ncvs,:,:,:].copy()
t2_2_ocee = t2_2[:,:ncvs,:,:].copy()
M_ij += 0.5 * 0.5* lib.einsum('ilde,jdel->ij',t2_2_coee, eris_ceeo,optimize=True)
M_ij -= 0.5 * 0.5* lib.einsum('lide,jdel->ij',t2_2_ocee, eris_ceeo,optimize=True)
M_ij -= 0.5 * 0.5* lib.einsum('ilde,jedl->ij',t2_2_coee, eris_ceeo,optimize=True)
M_ij += 0.5 * 0.5* lib.einsum('lide,jedl->ij',t2_2_ocee, eris_ceeo,optimize=True)
M_ij += 0.5 * lib.einsum('ilde,jdel->ij',t2_2_coee, eris_ceeo,optimize=True)
M_ij += 0.5 * 0.5* lib.einsum('jlde,idel->ij',t2_2_coee, eris_ceeo,optimize=True)
M_ij -= 0.5 * 0.5* lib.einsum('ljde,idel->ij',t2_2_ocee, eris_ceeo,optimize=True)
M_ij -= 0.5 * 0.5* lib.einsum('jlde,iedl->ij',t2_2_coee, eris_ceeo,optimize=True)
M_ij += 0.5 * 0.5* lib.einsum('ljde,iedl->ij',t2_2_ocee, eris_ceeo,optimize=True)
M_ij += 0.5 * lib.einsum('jlde,idel->ij',t2_2_coee, eris_ceeo,optimize=True)
t2_1 = t2[0][:]
log.timer_debug1("Starting the small integrals calculation")
temp_t2_v_1_oece = lib.einsum('lmde,jldf->mejf',t2_1, t2_1_coee,optimize=True)
temp_t2_v_1_ceoe = lib.einsum('lmde,jldf->mejf',t2_1_ocee, t2_1,optimize=True)
M_ij -= 0.5 * 2 * lib.einsum('mejf,ifem->ij',temp_t2_v_1_oece, eris_ceeo,optimize=True)
M_ij -= 0.5 * 2 * lib.einsum('jfme,ifem->ij',temp_t2_v_1_ceoe, eris_ceeo,optimize=True)
M_ij += 0.5 * lib.einsum('mejf,imfe->ij',temp_t2_v_1_oece, eris_coee,optimize=True)
M_ij += 0.5 * lib.einsum('jfme,imfe->ij',temp_t2_v_1_ceoe, eris_coee,optimize=True)
M_ij -= 0.5 * 2 * lib.einsum('meif,jfem->ij',temp_t2_v_1_oece, eris_ceeo ,optimize=True)
M_ij -= 0.5 * 2 * lib.einsum('ifme,jfem->ij',temp_t2_v_1_ceoe, eris_ceeo ,optimize=True)
M_ij += 0.5 * lib.einsum('meif,jmfe->ij',temp_t2_v_1_oece, eris_coee ,optimize=True)
M_ij += 0.5 * lib.einsum('ifme,jmfe->ij',temp_t2_v_1_ceoe, eris_coee ,optimize=True)
del temp_t2_v_1_oece
del temp_t2_v_1_ceoe
temp_t2_v_2 = lib.einsum('lmde,ljdf->mejf',t2_1, t2_1_ocee,optimize=True)
M_ij += 0.5 * 4 * lib.einsum('mejf,ifem->ij',temp_t2_v_2, eris_ceeo,optimize=True)
M_ij += 0.5 * 4 * lib.einsum('meif,jfem->ij',temp_t2_v_2, eris_ceeo,optimize=True)
M_ij -= 0.5 * 2 * lib.einsum('meif,jmfe->ij',temp_t2_v_2, eris_coee,optimize=True)
M_ij -= 0.5 * 2 * lib.einsum('mejf,imfe->ij',temp_t2_v_2, eris_coee,optimize=True)
del temp_t2_v_2
temp_t2_v_3 = lib.einsum('mlde,jldf->mejf',t2_1, t2_1_coee,optimize=True)
M_ij += 0.5 * lib.einsum('mejf,ifem->ij',temp_t2_v_3, eris_ceeo,optimize=True)
M_ij += 0.5 * lib.einsum('meif,jfem->ij',temp_t2_v_3, eris_ceeo,optimize=True)
M_ij -= 0.5 * 2 *lib.einsum('meif,jmfe->ij',temp_t2_v_3, eris_coee,optimize=True)
M_ij -= 0.5 * 2 * lib.einsum('mejf,imfe->ij',temp_t2_v_3, eris_coee,optimize=True)
del temp_t2_v_3
temp_t2_v_8 = lib.einsum('lmdf,lmde->fe',t2_1, t2_1,optimize=True)
M_ij += 3 *lib.einsum('fe,jief->ij',temp_t2_v_8, eris_ccee, optimize=True)
M_ij -= 1.5 *lib.einsum('fe,jfei->ij',temp_t2_v_8, eris_ceec, optimize=True)
M_ij += lib.einsum('ef,jief->ij',temp_t2_v_8, eris_ccee, optimize=True)
M_ij -= 0.5 * lib.einsum('ef,jfei->ij',temp_t2_v_8, eris_ceec, optimize=True)
del temp_t2_v_8
temp_t2_v_9 = lib.einsum('lmdf,mlde->fe',t2_1, t2_1,optimize=True)
M_ij -= 1.0 * lib.einsum('fe,jief->ij',temp_t2_v_9, eris_ccee, optimize=True)
M_ij -= 1.0 * lib.einsum('ef,jief->ij',temp_t2_v_9, eris_ccee, optimize=True)
M_ij += 0.5 * lib.einsum('fe,jfei->ij',temp_t2_v_9, eris_ceec, optimize=True)
M_ij += 0.5 * lib.einsum('ef,jfei->ij',temp_t2_v_9, eris_ceec, optimize=True)
del temp_t2_v_9
temp_t2_v_10 = lib.einsum('lnde,lmde->nm',t2_1, t2_1,optimize=True)
M_ij -= 3.0 * lib.einsum('nm,jinm->ij',temp_t2_v_10, eris_ccoo, optimize=True)
M_ij -= 1.0 * lib.einsum('mn,jinm->ij',temp_t2_v_10, eris_ccoo, optimize=True)
M_ij += 1.5 * lib.einsum('nm,jmni->ij',temp_t2_v_10, eris_cooc, optimize=True)
M_ij += 0.5 * lib.einsum('mn,jmni->ij',temp_t2_v_10, eris_cooc, optimize=True)
del temp_t2_v_10
temp_t2_v_11 = lib.einsum('lnde,mlde->nm',t2_1, t2_1,optimize=True)
M_ij += 1.0 * lib.einsum('nm,jinm->ij',temp_t2_v_11, eris_ccoo, optimize=True)
M_ij -= 0.5 * lib.einsum('nm,jmni->ij',temp_t2_v_11, eris_cooc, optimize=True)
M_ij -= 0.5 * lib.einsum('mn,jmni->ij',temp_t2_v_11, eris_cooc, optimize=True)
M_ij += 1.0 * lib.einsum('mn,jinm->ij',temp_t2_v_11, eris_ccoo, optimize=True)
del temp_t2_v_11
temp_t2_v_12_cooo = lib.einsum('inde,lmde->inlm',t2_1_coee, t2_1,optimize=True)
temp_t2_v_12_ooco = lib.einsum('inde,lmde->inlm',t2_1, t2_1_coee,optimize=True)
M_ij += 0.5 * 1.25 * lib.einsum('inlm,jlnm->ij',temp_t2_v_12_cooo, eris_cooo, optimize=True)
M_ij += 0.5 * 0.25 * lib.einsum('lmin,jlnm->ij',temp_t2_v_12_ooco, eris_cooo, optimize=True)
M_ij -= 0.5 * 0.25 * lib.einsum('inlm,jmnl->ij',temp_t2_v_12_cooo, eris_cooo, optimize=True)
M_ij -= 0.5 * 0.25 * lib.einsum('lmin,jmnl->ij',temp_t2_v_12_ooco, eris_cooo, optimize=True)
M_ij += 0.5 * 0.25 * lib.einsum('inlm,jlnm->ji',temp_t2_v_12_cooo, eris_cooo, optimize=True)
M_ij -= 0.5 * 0.25 * lib.einsum('inlm,jmnl->ji',temp_t2_v_12_cooo, eris_cooo, optimize=True)
M_ij += 0.5 * 1.00 * lib.einsum('inlm,jlmn->ji',temp_t2_v_12_cooo, eris_cooo, optimize=True)
M_ij -= 0.5 * 0.25 * lib.einsum('lmin,jmnl->ji',temp_t2_v_12_ooco, eris_cooo, optimize=True)
M_ij += 0.5 * 0.25 * lib.einsum('lmin,jlmn->ji',temp_t2_v_12_ooco, eris_cooo, optimize=True)
del temp_t2_v_12_cooo
del temp_t2_v_12_ooco
temp_t2_v_13_cooo = lib.einsum('inde,mlde->inml',t2_1_coee, t2_1,optimize=True)
temp_t2_v_13_ooco = lib.einsum('inde,mlde->inml',t2_1, t2_1_coee,optimize=True)
M_ij -= 0.5 * 0.25 * lib.einsum('inml,jlnm->ij',temp_t2_v_13_cooo, eris_cooo, optimize=True)
M_ij -= 0.5 * 0.25 * lib.einsum('mlin,jlnm->ij',temp_t2_v_13_ooco, eris_cooo, optimize=True)
M_ij += 0.5 * 0.25 * lib.einsum('inml,jmnl->ij',temp_t2_v_13_cooo, eris_cooo, optimize=True)
M_ij += 0.5 * 0.25 * lib.einsum('mlin,jmnl->ij',temp_t2_v_13_ooco, eris_cooo, optimize=True)
M_ij -= 0.5 * 0.25 * lib.einsum('inml,jlnm->ji',temp_t2_v_13_cooo, eris_cooo, optimize=True)
M_ij += 0.5 * 0.25 * lib.einsum('inml,jmnl->ji',temp_t2_v_13_cooo, eris_cooo, optimize=True)
M_ij -= 0.5 * 0.25 * lib.einsum('inml,jlmn->ji',temp_t2_v_13_cooo, eris_cooo, optimize=True)
M_ij += 0.5 * 0.25 * lib.einsum('inml,jmnl->ji',temp_t2_v_13_cooo, eris_cooo, optimize=True)
del temp_t2_v_13_cooo
del temp_t2_v_13_ooco
del t2_1
cput0 = log.timer_debug1("Completed CVS M_ij ADC(n) calculation", *cput0)
return M_ij
[docs]
def get_diag(adc,M_ij=None,eris=None):
if adc.method not in ("adc(2)", "adc(2)-x", "adc(3)"):
raise NotImplementedError(adc.method)
if M_ij is None:
M_ij = adc.get_imds()
nocc = adc._nocc
nvir = adc._nvir
ncvs = adc.ncvs
nval = nocc - ncvs
n_singles = ncvs
n_doubles_ecc = nvir * ncvs * ncvs
n_doubles_ecv = nvir * ncvs * nval
dim = n_singles + n_doubles_ecc + 2 * n_doubles_ecv
e_occ = adc.mo_energy[:nocc]
e_vir = adc.mo_energy[nocc:]
s1 = 0
f1 = n_singles
s2_ecc = f1
f2_ecc = s2_ecc + n_doubles_ecc
s2_ecv = f2_ecc
f2_ecv = s2_ecv + n_doubles_ecv
s2_evc = f2_ecv
f2_evc = s2_evc + n_doubles_ecv
d_ij = e_occ[:,None] + e_occ
d_a = e_vir[:,None]
D_n = -d_a + d_ij.reshape(-1)
D_aij = D_n.reshape(-1)
D_aij = D_n.reshape(nvir,nocc,nocc)
diag = np.zeros(dim)
# Compute precond in h1-h1 block
M_ij_diag = np.diagonal(M_ij)
diag[s1:f1] = M_ij_diag.copy()
# Compute precond in 2p1h-2p1h block
diag[s2_ecc:f2_ecc] = D_aij[:,:ncvs,:ncvs].reshape(-1)
diag[s2_ecv:f2_ecv] = D_aij[:,:ncvs,ncvs:].reshape(-1)
diag[s2_evc:f2_evc] = D_aij[:,ncvs:,:ncvs].reshape(-1)
diag = -diag
return diag
[docs]
def matvec(adc, M_ij=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
ncvs = adc.ncvs
nval = nocc - ncvs
n_singles = ncvs
n_doubles_ecc = nvir * ncvs * ncvs
n_doubles_ecv = nvir * ncvs * nval
dim = n_singles + n_doubles_ecc + 2 * n_doubles_ecv
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_ecc = f1
f2_ecc = s2_ecc + n_doubles_ecc
s2_ecv = f2_ecc
f2_ecv = s2_ecv + n_doubles_ecv
s2_evc = f2_ecv
f2_evc = s2_evc + n_doubles_ecv
d_ij = e_occ[:,None] + e_occ
d_a = e_vir[:,None]
D_n = -d_a + d_ij.reshape(-1)
D_aij = D_n.reshape(-1)
D_aij = D_n.reshape(nvir,nocc,nocc)
if M_ij is None:
M_ij = 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_ecc = r[s2_ecc:f2_ecc]
r2_ecv = r[s2_ecv:f2_ecv]
r2_evc = r[s2_evc:f2_evc]
r2_ecc = r2_ecc.reshape(nvir,ncvs,ncvs)
r2_ecv = r2_ecv.reshape(nvir,ncvs,nval)
r2_evc = r2_evc.reshape(nvir,nval,ncvs)
eris_ovoo = eris.ovoo
eris_cecc = eris_ovoo[:ncvs,:,:ncvs,:ncvs].copy()
eris_cecv = eris_ovoo[:ncvs,:,:ncvs,ncvs:].copy()
eris_vecc = eris_ovoo[ncvs:,:,:ncvs,:ncvs].copy()
del eris_ovoo
############ ADC(2) ij block ############################
s[s1:f1] = lib.einsum('IJ,J->I',M_ij,r1)
############ ADC(2) i - kja block #########################
s[s1:f1] += 2. * lib.einsum('jaki,ajk->i', eris_cecc, r2_ecc, optimize=True)
s[s1:f1] -= lib.einsum('kaji,ajk->i', eris_cecc, r2_ecc, optimize=True)
s[s1:f1] += 2. * lib.einsum('jaik,ajk->i', eris_cecv, r2_ecv, optimize=True)
s[s1:f1] -= lib.einsum('kaji,ajk->i', eris_vecc, r2_ecv, optimize=True)
s[s1:f1] += 2. * lib.einsum('jaki,ajk->i', eris_vecc, r2_evc, optimize=True)
s[s1:f1] -= lib.einsum('kaij,ajk->i', eris_cecv, r2_evc, optimize=True)
############## ADC(2) ajk - i block ############################
s[s2_ecc:f2_ecc] += lib.einsum('jaki,i->ajk', eris_cecc, r1, optimize=True).reshape(-1)
s[s2_ecv:f2_ecv] += lib.einsum('jaik,i->ajk', eris_cecv, r1, optimize=True).reshape(-1)
s[s2_evc:f2_evc] += lib.einsum('jaki,i->ajk', eris_vecc, r1, optimize=True).reshape(-1)
del eris_cecc, eris_cecv, eris_vecc
################ ADC(2) ajk - bil block ############################
temp_ecc = D_aij[:,:ncvs,:ncvs].reshape(-1)
s[s2_ecc:f2_ecc] += temp_ecc*r2_ecc.reshape(-1)
temp_ecv = D_aij[:,:ncvs,ncvs:].reshape(-1)
s[s2_ecv:f2_ecv] += temp_ecv*r2_ecv.reshape(-1)
temp_evc = D_aij[:,ncvs:,:ncvs].reshape(-1)
s[s2_evc:f2_evc] += temp_evc*r2_evc.reshape(-1)
############### ADC(3) ajk - bil block ############################
if (method == "adc(2)-x" or method == "adc(3)"):
eris_oooo = eris.oooo
eris_oovv = eris.oovv
eris_ovvo = eris.ovvo
eris_cccc = eris_oooo[:ncvs,:ncvs,:ncvs,:ncvs].copy()
eris_cccv = eris_oooo[:ncvs,:ncvs,:ncvs,ncvs:].copy()
eris_cvcv = eris_oooo[:ncvs,ncvs:,:ncvs,ncvs:].copy()
eris_ccvv = eris_oooo[:ncvs,:ncvs,ncvs:,ncvs:].copy()
eris_ceec = eris_ovvo[:ncvs,:,:,:ncvs].copy()
eris_ceev = eris_ovvo[:ncvs,:,:,ncvs:].copy()
eris_veev = eris_ovvo[ncvs:,:,:,ncvs:].copy()
eris_ccee = eris_oovv[:ncvs,:ncvs,:,:].copy()
eris_cvee = eris_oovv[:ncvs,ncvs:,:,:].copy()
eris_vvee = eris_oovv[ncvs:,ncvs:,:,:].copy()
del eris_oooo
del eris_oovv
del eris_ovvo
#eris_veev, eris_vvee
s[s2_ecv:f2_ecv] += lib.einsum('klba,bJl->aJk',eris_vvee,
r2_ecv,optimize=True).reshape(-1)
s[s2_evc:f2_evc] += lib.einsum('jlba,blK->ajK',eris_vvee,
r2_evc,optimize=True).reshape(-1)
del eris_vvee
s[s2_evc:f2_evc] += lib.einsum('jabl,bKl->ajK',eris_veev,
r2_ecv,optimize=True).reshape(-1)
s[s2_evc:f2_evc] -= 2*lib.einsum('jabl,blK->ajK',eris_veev,
r2_evc,optimize=True).reshape(-1)
del eris_veev
#eris_ceev, eris_cvee
s[s2_ecc:f2_ecc] += lib.einsum('Klba,bJl->aJK',eris_cvee,
r2_ecv,optimize=True).reshape(-1)
s[s2_ecc:f2_ecc] += lib.einsum('Jlba,blK->aJK',eris_cvee,
r2_evc,optimize=True).reshape(-1)
s[s2_ecv:f2_ecv] += lib.einsum('Lkba,bJL->aJk',eris_cvee,
r2_ecc,optimize=True).reshape(-1)
s[s2_evc:f2_evc] += lib.einsum('Ljba,bLK->ajK',eris_cvee,
r2_ecc,optimize=True).reshape(-1)
del eris_cvee
s[s2_ecc:f2_ecc] += lib.einsum('Jabl,bKl->aJK',eris_ceev,
r2_ecv,optimize=True).reshape(-1)
s[s2_ecc:f2_ecc] -= 2*lib.einsum('Jabl,blK->aJK',eris_ceev,
r2_evc,optimize=True).reshape(-1)
s[s2_evc:f2_evc] += lib.einsum('Lbaj,bKL->ajK',eris_ceev,
r2_ecc,optimize=True).reshape(-1)
s[s2_evc:f2_evc] -= 2*lib.einsum('Lbaj,bLK->ajK',eris_ceev,
r2_ecc,optimize=True).reshape(-1)
del eris_ceev
#eris_ceec, eris_ccee
s[s2_ecc:f2_ecc] += lib.einsum('KLba,bJL->aJK',eris_ccee,
r2_ecc,optimize=True).reshape(-1)
s[s2_ecc:f2_ecc] += lib.einsum('JLba,bLK->aJK',eris_ccee,
r2_ecc,optimize=True).reshape(-1)
s[s2_ecv:f2_ecv] += lib.einsum('JLba,bLk->aJk',eris_ccee,
r2_ecv,optimize=True).reshape(-1)
s[s2_evc:f2_evc] += lib.einsum('KLba,bjL->ajK',eris_ccee,
r2_evc,optimize=True).reshape(-1)
del eris_ccee
s[s2_ecc:f2_ecc] += lib.einsum('JabL,bKL->aJK',eris_ceec,
r2_ecc,optimize=True).reshape(-1)
s[s2_ecc:f2_ecc] -= 2*lib.einsum('JabL,bLK->aJK',eris_ceec,
r2_ecc,optimize=True).reshape(-1)
s[s2_ecv:f2_ecv] -= 2*lib.einsum('JabL,bLk->aJk',eris_ceec,
r2_ecv,optimize=True).reshape(-1)
s[s2_ecv:f2_ecv] += lib.einsum('JabL,bkL->aJk',eris_ceec,
r2_evc,optimize=True).reshape(-1)
del eris_ceec
#eris_cvcv, eris_ccvv
s[s2_ecv:f2_ecv] -= lib.einsum('JIkl,aIl->aJk',eris_ccvv,
r2_ecv,optimize=True).reshape(-1)
s[s2_evc:f2_evc] -= lib.einsum('KIjl,alI->ajK',eris_ccvv,
r2_evc,optimize=True).reshape(-1)
del eris_ccvv
s[s2_ecv:f2_ecv] -= lib.einsum('IkJl,alI->aJk',eris_cvcv,
r2_evc,optimize=True).reshape(-1)
s[s2_evc:f2_evc] -= lib.einsum('KlIj,aIl->ajK',eris_cvcv,
r2_ecv,optimize=True).reshape(-1)
del eris_cvcv
#eris_cccv
s[s2_ecc:f2_ecc] -= lib.einsum('KIJl,alI->aJK',eris_cccv,
r2_evc,optimize=True).reshape(-1)
s[s2_ecc:f2_ecc] -= lib.einsum('JIKl,aIl->aJK',eris_cccv,
r2_ecv,optimize=True).reshape(-1)
s[s2_ecv:f2_ecv] -= lib.einsum('JILk,aIL->aJk',eris_cccv,
r2_ecc,optimize=True).reshape(-1)
s[s2_evc:f2_evc] -= lib.einsum('KLIj,aIL->ajK',eris_cccv,
r2_ecc,optimize=True).reshape(-1)
del eris_cccv
#eris_cccc
s[s2_ecc:f2_ecc] -= lib.einsum('KLJI,aIL->aJK',eris_cccc,
r2_ecc,optimize=True).reshape(-1)
del eris_cccc
if (method == "adc(3)"):
eris_ovoo = eris.ovoo
t2_1 = adc.t2[0]
t2_1_ccee = t2_1[:ncvs,:ncvs,:,:].copy()
t2_1_cvee = t2_1[:ncvs,ncvs:,:,:].copy()
t2_1_vcee = t2_1[ncvs:,:ncvs,:,:].copy()
del t2_1
################ ADC(3) i - kja block and ajk - i ############################
eris_oecc = eris_ovoo[:,:,:ncvs,:ncvs].copy()
eris_oecv = eris_ovoo[:,:,:ncvs,ncvs:].copy()
eris_ceco = eris_ovoo[:ncvs,:,:ncvs,:].copy()
eris_cevo = eris_ovoo[:ncvs,:,ncvs:,:].copy()
temp_1_ecc = lib.einsum('ijbc,aij->abc',t2_1_ccee, r2_ecc, optimize=True)
temp_ecc = 0.25 * temp_1_ecc
temp_ecc -= 0.25 * lib.einsum('ijbc,aji->abc',t2_1_ccee, r2_ecc, optimize=True)
temp_ecc -= 0.25 * lib.einsum('jibc,aij->abc',t2_1_ccee, r2_ecc, optimize=True)
temp_ecc += 0.25 * lib.einsum('jibc,aji->abc',t2_1_ccee, r2_ecc, optimize=True)
temp_1_ecv = lib.einsum('ijbc,aij->abc',t2_1_cvee, r2_ecv, optimize=True)
temp_ecv = 0.25 * temp_1_ecv
temp_ecv -= 0.25 * lib.einsum('ijbc,aji->abc',t2_1_vcee, r2_ecv, optimize=True)
temp_ecv -= 0.25 * lib.einsum('jibc,aij->abc',t2_1_vcee, r2_ecv, optimize=True)
temp_ecv += 0.25 * lib.einsum('jibc,aji->abc',t2_1_cvee, r2_ecv, optimize=True)
temp_1_evc = lib.einsum('ijbc,aij->abc',t2_1_vcee, r2_evc, optimize=True)
temp_evc = 0.25 * temp_1_evc
temp_evc -= 0.25 * lib.einsum('ijbc,aji->abc',t2_1_cvee, r2_evc, optimize=True)
temp_evc -= 0.25 * lib.einsum('jibc,aij->abc',t2_1_cvee, r2_evc, optimize=True)
temp_evc += 0.25 * lib.einsum('jibc,aji->abc',t2_1_vcee, r2_evc, optimize=True)
if isinstance(eris.ovvv, type(None)):
chnk_size = radc_ao2mo.calculate_chunk_size(adc)
else:
chnk_size = nocc
a = 0
temp_singles = np.zeros((ncvs))
temp_doubles = np.zeros((nvir,nvir,nvir))
for p in range(0,ncvs,chnk_size):
if getattr(adc, 'with_df', None):
eris_ceee = dfadc.get_ovvv_df(
adc, eris.Lce, eris.Lee, p, chnk_size).reshape(-1,nvir,nvir,nvir)
else:
eris_ovvv = radc_ao2mo.unpack_eri_1(eris.ovvv, nvir)
eris_ceee = eris_ovvv[:ncvs,:,:,:].copy()
del eris_ovvv
k = eris_ceee.shape[0]
temp_singles[a:a+k] += lib.einsum('abc,icab->i',temp_ecc, eris_ceee, optimize=True)
temp_singles[a:a+k] -= lib.einsum('abc,ibac->i',temp_ecc, eris_ceee, optimize=True)
temp_singles[a:a+k] += lib.einsum('abc,icab->i',temp_ecv, eris_ceee, optimize=True)
temp_singles[a:a+k] -= lib.einsum('abc,ibac->i',temp_ecv, eris_ceee, optimize=True)
temp_singles[a:a+k] += lib.einsum('abc,icab->i',temp_evc, eris_ceee, optimize=True)
temp_singles[a:a+k] -= lib.einsum('abc,ibac->i',temp_evc, eris_ceee, optimize=True)
temp_singles[a:a+k] += lib.einsum('abc,icab->i',
temp_1_ecc, eris_ceee, optimize=True)
temp_singles[a:a+k] += lib.einsum('abc,icab->i',
temp_1_ecv, eris_ceee, optimize=True)
temp_singles[a:a+k] += lib.einsum('abc,icab->i',
temp_1_evc, eris_ceee, optimize=True)
temp_doubles = lib.einsum('i,icab->cba',r1[a:a+k],eris_ceee,optimize=True)
s[s1:f1] += temp_singles
s[s2_ecc:f2_ecc] += lib.einsum('cba,kjcb->ajk',
temp_doubles, t2_1_ccee, optimize=True).reshape(-1)
s[s2_ecv:f2_ecv] += lib.einsum('cba,kjcb->ajk',
temp_doubles, t2_1_vcee, optimize=True).reshape(-1)
s[s2_evc:f2_evc] += lib.einsum('cba,kjcb->ajk',
temp_doubles, t2_1_cvee, optimize=True).reshape(-1)
del eris_ceee, temp_singles, temp_doubles
a += k
# ADC(3) jka-i
temp_1_c_a = lib.einsum('I,lbIK->Kbl',r1,eris_oecc, optimize=True)
temp_1_c_b = -lib.einsum('I,IbKl->Kbl',r1,eris_ceco, optimize=True)
temp_1_c = temp_1_c_a + temp_1_c_b
temp_1_v_a = lib.einsum('I,lbIk->kbl',r1,eris_oecv, optimize=True)
temp_1_v_b = -lib.einsum('I,Ibkl->kbl',r1,eris_cevo, optimize=True)
temp_1_v = temp_1_v_a + temp_1_v_b
t2_1 = adc.t2[0]
t2_1_coee = t2_1[:ncvs,:,:,:].copy()
t2_1_ocee = t2_1[:,:ncvs,:,:].copy()
t2_1_voee = t2_1[ncvs:,:,:,:].copy()
t2_1_ovee = t2_1[:,ncvs:,:,:].copy()
del t2_1
temp_ecc = lib.einsum('Kbl,lJba->aJK',temp_1_c,t2_1_ocee,optimize=True)
temp_ecc += lib.einsum('Kbl,Jlab->aJK',temp_1_c_a,t2_1_coee,optimize=True)
temp_ecc -= lib.einsum('Kbl,lJab->aJK',temp_1_c_a,t2_1_ocee,optimize=True)
temp_ecc += lib.einsum('Jbl,Klba->aJK',temp_1_c_b,t2_1_coee,optimize=True)
temp_ecv = lib.einsum('kbl,lJba->aJk',temp_1_v,t2_1_ocee,optimize=True)
temp_ecv += lib.einsum('kbl,Jlab->aJk',temp_1_v_a,t2_1_coee,optimize=True)
temp_ecv -= lib.einsum('kbl,lJab->aJk',temp_1_v_a,t2_1_ocee,optimize=True)
temp_ecv += lib.einsum('Jbl,klba->aJk',temp_1_c_b,t2_1_voee,optimize=True)
temp_evc = lib.einsum('Kbl,ljba->ajK',temp_1_c,t2_1_ovee,optimize=True)
temp_evc += lib.einsum('Kbl,jlab->ajK',temp_1_c_a,t2_1_voee,optimize=True)
temp_evc -= lib.einsum('Kbl,ljab->ajK',temp_1_c_a,t2_1_ovee,optimize=True)
temp_evc += lib.einsum('jbl,Klba->ajK',temp_1_v_b,t2_1_coee,optimize=True)
s[s2_ecc:f2_ecc] += temp_ecc.reshape(-1)
s[s2_ecv:f2_ecv] += temp_ecv.reshape(-1)
s[s2_evc:f2_evc] += temp_evc.reshape(-1)
del temp_1_c_a, temp_1_c_b, temp_1_c , temp_1_v_a, temp_1_v_b, temp_1_v
# ADC(3) i-jka
temp_a = lib.einsum('Jlab,aJK->blK',t2_1_coee,r2_ecc,optimize=True)
temp_b = -lib.einsum('Jlab,aKJ->blK',t2_1_coee,r2_ecc,optimize=True)
temp_c = -lib.einsum('Jlba,aJK->blK',t2_1_coee,r2_ecc,optimize=True)
temp_d = lib.einsum('Jlba,aKJ->blK',t2_1_coee,r2_ecc,optimize=True)
temp_ecc = temp_a + temp_b + temp_c + temp_d
temp_1_ecc = -temp_a - temp_c
temp_2_ecc = -temp_a
temp_3_ecc = -temp_a - temp_b
temp_4_ecc = -temp_d
s[s1:f1] += lib.einsum('blK,lbIK->I',temp_ecc,eris_oecc,optimize=True)
s[s1:f1] -= lib.einsum('blK,IbKl->I',temp_ecc,eris_ceco,optimize=True)
s[s1:f1] -= lib.einsum('blJ,lbIJ->I',temp_1_ecc,eris_oecc,optimize=True)
s[s1:f1] -= lib.einsum('blJ,lbIJ->I',temp_2_ecc,eris_oecc,optimize=True)
s[s1:f1] += lib.einsum('blJ,IbJl->I',temp_2_ecc,eris_ceco,optimize=True)
s[s1:f1] -= lib.einsum('blJ,lbIJ->I',temp_3_ecc,eris_oecc,optimize=True)
s[s1:f1] += lib.einsum('blJ,IbJl->I',temp_4_ecc,eris_ceco,optimize=True)
del temp_a, temp_b, temp_c, temp_d, temp_ecc, temp_1_ecc, temp_2_ecc, temp_3_ecc, temp_4_ecc
temp_a = lib.einsum('Jlab,aJk->blk',t2_1_coee,r2_ecv,optimize=True)
temp_b = -lib.einsum('lJab,aJk->blk',t2_1_ocee,r2_ecv,optimize=True)
temp_c = -lib.einsum('Jlab,akJ->blk',t2_1_coee,r2_evc,optimize=True)
temp_d = lib.einsum('lJab,akJ->blk',t2_1_ocee,r2_evc,optimize=True)
temp_ecv = temp_a + temp_b + temp_c + temp_d
temp_1_ecv = -temp_a - temp_b
temp_2_ecv = -temp_a
temp_3_ecv = -temp_a - temp_c
temp_4_ecv = -lib.einsum('klba,aJk->blJ',t2_1_voee,r2_ecv,optimize=True)
s[s1:f1] += lib.einsum('blk,lbIk->I',temp_ecv,eris_oecv,optimize=True)
s[s1:f1] -= lib.einsum('blk,Ibkl->I',temp_ecv,eris_cevo,optimize=True)
s[s1:f1] -= lib.einsum('blj,lbIj->I',temp_1_ecv,eris_oecv,optimize=True)
s[s1:f1] -= lib.einsum('blj,lbIj->I',temp_2_ecv,eris_oecv,optimize=True)
s[s1:f1] += lib.einsum('blj,Ibjl->I',temp_2_ecv,eris_cevo,optimize=True)
s[s1:f1] -= lib.einsum('blj,lbIj->I',temp_3_ecv,eris_oecv,optimize=True)
s[s1:f1] += lib.einsum('blJ,IbJl->I',temp_4_ecv,eris_ceco,optimize=True)
del temp_a, temp_b, temp_c, temp_d, temp_ecv, temp_1_ecv, temp_2_ecv, temp_3_ecv, temp_4_ecv
temp_a = -lib.einsum('jlab,aKj->blK',t2_1_voee,r2_ecv,optimize=True)
temp_b = lib.einsum('ljab,aKj->blK',t2_1_ovee,r2_ecv,optimize=True)
temp_c = lib.einsum('jlab,ajK->blK',t2_1_voee,r2_evc,optimize=True)
temp_d = -lib.einsum('ljab,ajK->blK',t2_1_ovee,r2_evc,optimize=True)
temp_evc = temp_a + temp_b + temp_c + temp_d
temp_1_evc = -temp_c - temp_d
temp_2_evc = -temp_c
temp_3_evc = -temp_a - temp_c
temp_4_evc = -lib.einsum('Klba,ajK->blj',t2_1_coee,r2_evc,optimize=True)
s[s1:f1] += lib.einsum('blK,lbIK->I',temp_evc,eris_oecc,optimize=True)
s[s1:f1] -= lib.einsum('blK,IbKl->I',temp_evc,eris_ceco,optimize=True)
s[s1:f1] -= lib.einsum('blJ,lbIJ->I',temp_1_evc,eris_oecc,optimize=True)
s[s1:f1] -= lib.einsum('blJ,lbIJ->I',temp_2_evc,eris_oecc,optimize=True)
s[s1:f1] += lib.einsum('blJ,IbJl->I',temp_2_evc,eris_ceco,optimize=True)
s[s1:f1] -= lib.einsum('blJ,lbIJ->I',temp_3_evc,eris_oecc,optimize=True)
s[s1:f1] += lib.einsum('blj,Ibjl->I',temp_4_evc,eris_cevo,optimize=True)
del temp_a, temp_b, temp_c, temp_d, temp_evc, temp_1_evc, temp_2_evc, temp_3_evc, temp_4_evc
cput0 = log.timer_debug1("completed sigma vector calculation", *cput0)
s *= -1.0
return s
return sigma_
[docs]
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
[docs]
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
nocc = adc._nocc
nvir = adc._nvir
ncvs = adc.ncvs
nval = nocc - ncvs
t2_1 = adc.t2[0][:]
t2_1_coee = t2_1[:ncvs,:,:,:].copy()
if (adc.approx_trans_moments is False or adc.method == "adc(3)"):
t1_2 = adc.t1[0][:]
t1_2_ce = t1_2[:ncvs,:].copy()
n_singles = ncvs
n_doubles_ecc = nvir * ncvs * ncvs
n_doubles_ecv = nvir * ncvs * nval
dim = n_singles + n_doubles_ecc + 2 * n_doubles_ecv
idn_occ= np.identity(nocc)
s1 = 0
f1 = n_singles
s2_ecc = f1
f2_ecc = s2_ecc + n_doubles_ecc
s2_ecv = f2_ecc
f2_ecv = s2_ecv + n_doubles_ecv
s2_evc = f2_ecv
f2_evc = s2_evc + n_doubles_ecv
T = np.zeros((dim))
######## ADC(2) 1h part ############################################
if orb < nocc:
T[s1:f1] = idn_occ[orb, :ncvs]
T[s1:f1] += 0.25*lib.einsum('kdc,ikdc->i',t2_1[:,orb,:,:], t2_1_coee, optimize=True)
T[s1:f1] -= 0.25*lib.einsum('kcd,ikdc->i',t2_1[:,orb,:,:], t2_1_coee, optimize=True)
T[s1:f1] -= 0.25*lib.einsum('kdc,ikcd->i',t2_1[:,orb,:,:], t2_1_coee, optimize=True)
T[s1:f1] += 0.25*lib.einsum('kcd,ikcd->i',t2_1[:,orb,:,:], t2_1_coee, optimize=True)
T[s1:f1] -= 0.25*lib.einsum('kdc,ikdc->i',t2_1[orb,:,:,:], t2_1_coee, optimize=True)
T[s1:f1] -= 0.25*lib.einsum('kcd,ikcd->i',t2_1[orb,:,:,:], t2_1_coee, optimize=True)
else :
if (adc.approx_trans_moments is False or adc.method == "adc(3)"):
T[s1:f1] += t1_2_ce[:,(orb-nocc)]
######## ADC(2) 2h-1p part ############################################
t2_1_t = t2_1.transpose(2,3,1,0)
t2_1_t_eecc = t2_1_t[:,:,:ncvs,:ncvs].copy()
t2_1_t_eecv = t2_1_t[:,:,:ncvs,ncvs:].copy()
t2_1_t_eevc = t2_1_t[:,:,ncvs:,:ncvs].copy()
T[s2_ecc:f2_ecc] = t2_1_t_eecc[(orb-nocc),:,:,:].reshape(-1)
T[s2_ecv:f2_ecv] = t2_1_t_eecv[(orb-nocc),:,:,:].reshape(-1)
T[s2_evc:f2_evc] = t2_1_t_eevc[(orb-nocc),:,:,:].reshape(-1)
######## ADC(3) 2h-1p 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(2,3,1,0)
t2_2_t_eecc = t2_2_t[:,:,:ncvs,:ncvs].copy()
t2_2_t_eecv = t2_2_t[:,:,:ncvs,ncvs:].copy()
t2_2_t_eevc = t2_2_t[:,:,ncvs:,:ncvs].copy()
T[s2_ecc:f2_ecc] += t2_2_t_eecc[(orb-nocc),:,:,:].reshape(-1)
T[s2_ecv:f2_ecv] += t2_2_t_eecv[(orb-nocc),:,:,:].reshape(-1)
T[s2_evc:f2_evc] += t2_2_t_eevc[(orb-nocc),:,:,:].reshape(-1)
del t2_2, t2_2_t_eecc, t2_2_t_eecv, t2_2_t_eevc
######### ADC(3) 1h part ############################################
if(method=='adc(3)'):
t2_2 = adc.t2[1][:]
t2_2_coee = t2_2[:ncvs,:,:,:].copy()
if (adc.approx_trans_moments is False):
t1_3 = adc.t1[1]
t1_3_ce = t1_3[:ncvs,:].copy()
t2_1_ocee = t2_1[:,:ncvs,:,:].copy()
if orb < ncvs:
T[s1:f1] += 0.25*lib.einsum('kdc,ikdc->i',t2_1[:,orb,:,:], t2_2_coee, optimize=True)
T[s1:f1] -= 0.25*lib.einsum('kcd,ikdc->i',t2_1[:,orb,:,:], t2_2_coee, optimize=True)
T[s1:f1] -= 0.25*lib.einsum('kdc,ikcd->i',t2_1[:,orb,:,:], t2_2_coee, optimize=True)
T[s1:f1] += 0.25*lib.einsum('kcd,ikcd->i',t2_1[:,orb,:,:], t2_2_coee, optimize=True)
T[s1:f1] -= 0.25*lib.einsum('kdc,ikdc->i',t2_1[orb,:,:,:], t2_2_coee, optimize=True)
T[s1:f1] -= 0.25*lib.einsum('kcd,ikcd->i',t2_1[orb,:,:,:], t2_2_coee, optimize=True)
T[s1:f1] += 0.25*lib.einsum('ikdc,kdc->i',t2_1_coee, t2_2[:,orb,:,:],optimize=True)
T[s1:f1] -= 0.25*lib.einsum('ikcd,kdc->i',t2_1_coee, t2_2[:,orb,:,:],optimize=True)
T[s1:f1] -= 0.25*lib.einsum('ikdc,kcd->i',t2_1_coee, t2_2[:,orb,:,:],optimize=True)
T[s1:f1] += 0.25*lib.einsum('ikcd,kcd->i',t2_1_coee, t2_2[:,orb,:,:],optimize=True)
T[s1:f1] -= 0.25*lib.einsum('ikcd,kcd->i',t2_1_coee, t2_2[orb,:,:,:],optimize=True)
T[s1:f1] -= 0.25*lib.einsum('ikdc,kdc->i',t2_1_coee, t2_2[orb,:,:,:],optimize=True)
else:
T[s1:f1] += 0.5*lib.einsum('ikc,kc->i',t2_1_coee[:,:,(orb-nocc),:], t1_2,optimize=True)
T[s1:f1] -= 0.5*lib.einsum('kic,kc->i',t2_1_ocee[:,:,(orb-nocc),:], t1_2,optimize=True)
T[s1:f1] += 0.5*lib.einsum('ikc,kc->i',t2_1_coee[:,:,(orb-nocc),:], t1_2,optimize=True)
if (adc.approx_trans_moments is False):
T[s1:f1] += t1_3_ce[:,(orb-nocc)]
del t2_2
del t2_1
T_aaa_ecc = T[s2_ecc:f2_ecc].reshape(nvir,ncvs,ncvs).copy()
T_aaa_ecv = T[s2_ecv:f2_ecv].reshape(nvir,ncvs,nval).copy()
T_aaa_evc = T[s2_evc:f2_evc].reshape(nvir,nval,ncvs).copy()
T_aaa_ecc_asym = T_aaa_ecc - T_aaa_ecc.transpose(0,2,1)
T_aaa_ecv_asym = T_aaa_ecv - T_aaa_evc.transpose(0,2,1)
T_aaa_evc_asym = T_aaa_evc - T_aaa_ecv.transpose(0,2,1)
T[s2_ecc:f2_ecc] += T_aaa_ecc_asym.reshape(-1)
T[s2_ecv:f2_ecv] += T_aaa_ecv_asym.reshape(-1)
T[s2_evc:f2_evc] += T_aaa_evc_asym.reshape(-1)
return T
[docs]
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 \n',adc.method ,i)
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*************************************************************\n")
[docs]
def renormalize_eigenvectors(adc, nroots=1):
nocc = adc._nocc
nvir = adc._nvir
ncvs = adc.ncvs
nval = nocc - ncvs
n_singles = ncvs
n_doubles_ecc = nvir * ncvs * ncvs
n_doubles_ecv = nvir * ncvs * nval
f1 = n_singles
s2_ecc = f1
f2_ecc = s2_ecc + n_doubles_ecc
s2_ecv = f2_ecc
f2_ecv = s2_ecv + n_doubles_ecv
s2_evc = f2_ecv
f2_evc = s2_evc + n_doubles_ecv
U = adc.U
for I in range(U.shape[1]):
U1 = U[:n_singles,I]
U2_ecc = U[s2_ecc:f2_ecc,I].reshape(nvir,ncvs,ncvs)
U2_ecv = U[s2_ecv:f2_ecv,I].reshape(nvir,ncvs,nval)
U2_evc = U[s2_evc:f2_evc,I].reshape(nvir,nval,ncvs)
UdotU = np.dot(U1, U1)
UdotU += 2.*np.dot(U2_ecc.ravel(), U2_ecc.ravel()) - \
np.dot(U2_ecc.ravel(), U2_ecc.transpose(0,2,1).ravel())
UdotU += 2.*np.dot(U2_ecv.ravel(), U2_ecv.ravel()) - \
np.dot(U2_ecv.ravel(), U2_evc.transpose(0,2,1).ravel())
UdotU += 2.*np.dot(U2_evc.ravel(), U2_evc.ravel()) - \
np.dot(U2_evc.ravel(), U2_ecv.transpose(0,2,1).ravel())
U[:,I] /= np.sqrt(UdotU)
return U
[docs]
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
[docs]
def analyze(myadc):
#TODO: Implement eigenvector analysis for CVS-RADC
#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()
[docs]
def compute_dyson_mo(myadc):
X = myadc.X
if X is None:
nroots = myadc.U.shape[1]
P,X = myadc.get_properties(nroots)
nroots = X.shape[1]
dyson_mo = np.dot(myadc.mo_coeff,X)
return dyson_mo
[docs]
class RADCIPCVS(radc.RADC):
'''restricted ADC for IP-CVS energies and spectroscopic amplitudes
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.
method : string
nth-order ADC method. Options are : ADC(2), ADC(2)-X, ADC(3). Default is ADC(2).
conv_tol : float
Convergence threshold for Davidson iterations. Default is 1e-12.
max_cycle : int
Number of Davidson iterations. Default is 50.
max_space : int
Space size to hold trial vectors for Davidson iterative diagonalization. Default is 12.
Kwargs:
nroots : int
Number of roots (eigenvalues) requested. Default value is 1.
>>> myadc = adc.RADC(mf).run()
>>> myadcip = adc.RADC(myadc).run()
Saved results
e_ip : float or list of floats
IP energy (eigenvalue). For nroots = 1, it is a single float
number. If nroots > 1, it is a list of floats for the lowest
nroots eigenvalues.
v_ip : array
Eigenvectors for each IP transition.
p_ip : float
Spectroscopic amplitudes for each IP transition.
'''
_keys = set((
'tol_residual','conv_tol', 'e_corr', 'method', 'mo_coeff',
'mo_energy_b', 't1', 'mo_energy_a',
'max_space', 't2', 'max_cycle',
'nmo', 'transform_integrals', 'with_df', 'compute_properties',
'approx_trans_moments', 'E', 'U', 'P', 'X',
'evec_print_tol', 'spec_factor_print_tol', 'ncvs',
))
def __init__(self, adc):
self.mol = adc.mol
self.verbose = adc.verbose
self.stdout = adc.stdout
self.max_memory = adc.max_memory
self.max_space = adc.max_space
self.max_cycle = adc.max_cycle
self.conv_tol = adc.conv_tol
self.tol_residual = adc.tol_residual
self.t1 = adc.t1
self.t2 = adc.t2
self.imds = adc.imds
self.e_corr = adc.e_corr
self.method = adc.method
self.method_type = adc.method_type
self._scf = adc._scf
self._nocc = adc._nocc
self._nvir = adc._nvir
self._nmo = adc._nmo
self.mo_coeff = adc.mo_coeff
self.mo_energy = adc.mo_energy
self.nmo = adc._nmo
self.transform_integrals = adc.transform_integrals
self.with_df = adc.with_df
self.compute_properties = adc.compute_properties
self.approx_trans_moments = adc.approx_trans_moments
self.E = None
self.U = None
self.P = None
self.X = None
self.evec_print_tol = adc.evec_print_tol
self.spec_factor_print_tol = adc.spec_factor_print_tol
self.ncvs = adc.ncvs
kernel = radc.kernel
get_imds = get_imds
get_diag = get_diag
matvec = matvec
get_trans_moments = get_trans_moments
renormalize_eigenvectors = renormalize_eigenvectors
get_properties = get_properties
analyze_spec_factor = analyze_spec_factor
#analyze_eigenvector = analyze_eigenvector
analyze = analyze
compute_dyson_mo = compute_dyson_mo
[docs]
def get_init_guess(self, nroots=1, diag=None, ascending=True):
if diag is None :
diag = self.get_diag()
idx = None
if ascending:
idx = np.argsort(diag)
else:
idx = np.argsort(diag)[::-1]
guess = np.zeros((diag.shape[0], nroots))
min_shape = min(diag.shape[0], nroots)
guess[:min_shape,:min_shape] = np.identity(min_shape)
g = np.zeros((diag.shape[0], nroots))
g[idx] = guess.copy()
guess = []
for p in range(g.shape[1]):
guess.append(g[:,p])
return guess
[docs]
def gen_matvec(self, imds=None, eris=None):
if imds is None:
imds = self.get_imds(eris)
diag = self.get_diag(imds, eris)
matvec = self.matvec(imds, eris)
return matvec, diag