# 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: Samragni Banerjee <samragnibanerjee4@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]
nocc = adc._nocc
e_occ = adc.mo_energy[:nocc]
idn_occ = np.identity(nocc)
if eris is None:
eris = adc.transform_integrals()
eris_ovvo = eris.ovvo
M_ij = np.zeros((nocc,nocc))
# i-j block
# Zeroth-order terms
M_ij = lib.einsum('ij,j->ij', idn_occ ,e_occ)
# Second-order terms
t2_1 = t2[0][:]
M_ij += 0.5 * 0.5 * lib.einsum('ilde,jdel->ij',t2_1, eris_ovvo,optimize=True)
M_ij -= 0.5 * 0.5 * lib.einsum('lide,jdel->ij',t2_1, eris_ovvo,optimize=True)
M_ij -= 0.5 * 0.5 * lib.einsum('ilde,jedl->ij',t2_1, eris_ovvo,optimize=True)
M_ij += 0.5 * 0.5 * lib.einsum('lide,jedl->ij',t2_1, eris_ovvo,optimize=True)
M_ij += 0.5 * lib.einsum('ilde,jdel->ij',t2_1, eris_ovvo,optimize=True)
M_ij += 0.5 * 0.5 * lib.einsum('jlde,idel->ij',t2_1, eris_ovvo,optimize=True)
M_ij -= 0.5 * 0.5 * lib.einsum('ljde,idel->ij',t2_1, eris_ovvo,optimize=True)
M_ij -= 0.5 * 0.5 * lib.einsum('jlde,ldei->ij',t2_1, eris_ovvo,optimize=True)
M_ij += 0.5 * 0.5 * lib.einsum('ljde,ldei->ij',t2_1, eris_ovvo,optimize=True)
M_ij += 0.5 * lib.einsum('jlde,idel->ij',t2_1, eris_ovvo,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
M_ij += lib.einsum('ld,ldji->ij',t1_2, eris_ovoo,optimize=True)
M_ij -= lib.einsum('ld,jdli->ij',t1_2, eris_ovoo,optimize=True)
M_ij += lib.einsum('ld,ldji->ij',t1_2, eris_ovoo,optimize=True)
M_ij += lib.einsum('ld,ldij->ij',t1_2, eris_ovoo,optimize=True)
M_ij -= lib.einsum('ld,idlj->ij',t1_2, eris_ovoo,optimize=True)
M_ij += lib.einsum('ld,ldij->ij',t1_2, eris_ovoo,optimize=True)
t2_2 = t2[1][:]
M_ij += 0.5 * 0.5* lib.einsum('ilde,jdel->ij',t2_2, eris_ovvo,optimize=True)
M_ij -= 0.5 * 0.5* lib.einsum('lide,jdel->ij',t2_2, eris_ovvo,optimize=True)
M_ij -= 0.5 * 0.5* lib.einsum('ilde,jedl->ij',t2_2, eris_ovvo,optimize=True)
M_ij += 0.5 * 0.5* lib.einsum('lide,jedl->ij',t2_2, eris_ovvo,optimize=True)
M_ij += 0.5 * lib.einsum('ilde,jdel->ij',t2_2, eris_ovvo,optimize=True)
M_ij += 0.5 * 0.5* lib.einsum('jlde,ledi->ij',t2_2, eris_ovvo,optimize=True)
M_ij -= 0.5 * 0.5* lib.einsum('ljde,ledi->ij',t2_2, eris_ovvo,optimize=True)
M_ij -= 0.5 * 0.5* lib.einsum('jlde,iedl->ij',t2_2, eris_ovvo,optimize=True)
M_ij += 0.5 * 0.5* lib.einsum('ljde,iedl->ij',t2_2, eris_ovvo,optimize=True)
M_ij += 0.5 * lib.einsum('jlde,ledi->ij',t2_2, eris_ovvo,optimize=True)
t2_1 = t2[0][:]
log.timer_debug1("Starting the small integrals calculation")
temp_t2_v_1 = lib.einsum('lmde,jldf->mejf',t2_1, t2_1,optimize=True)
M_ij -= 0.5 * 2 * lib.einsum('mejf,mefi->ij',temp_t2_v_1, eris_ovvo,optimize=True)
M_ij -= 0.5 * 2 * lib.einsum('jfme,mefi->ij',temp_t2_v_1, eris_ovvo,optimize=True)
M_ij += 0.5 * lib.einsum('mejf,mife->ij',temp_t2_v_1, eris_oovv,optimize=True)
M_ij += 0.5 * lib.einsum('jfme,mife->ij',temp_t2_v_1, eris_oovv,optimize=True)
M_ij -= 0.5 * 2 * lib.einsum('meif,mefj->ij',temp_t2_v_1, eris_ovvo ,optimize=True)
M_ij -= 0.5 * 2 * lib.einsum('ifme,mefj->ij',temp_t2_v_1, eris_ovvo ,optimize=True)
M_ij += 0.5 * lib.einsum('meif,mjfe->ij',temp_t2_v_1, eris_oovv ,optimize=True)
M_ij += 0.5 * lib.einsum('ifme,mjfe->ij',temp_t2_v_1, eris_oovv ,optimize=True)
del temp_t2_v_1
temp_t2_v_2 = lib.einsum('lmde,ljdf->mejf',t2_1, t2_1,optimize=True)
M_ij += 0.5 * 4 * lib.einsum('mejf,mefi->ij',temp_t2_v_2, eris_ovvo,optimize=True)
M_ij += 0.5 * 4 * lib.einsum('meif,mefj->ij',temp_t2_v_2, eris_ovvo,optimize=True)
M_ij -= 0.5 * 2 * lib.einsum('meif,mjfe->ij',temp_t2_v_2, eris_oovv,optimize=True)
M_ij -= 0.5 * 2 * lib.einsum('mejf,mife->ij',temp_t2_v_2, eris_oovv,optimize=True)
del temp_t2_v_2
temp_t2_v_3 = lib.einsum('mlde,jldf->mejf',t2_1, t2_1,optimize=True)
M_ij += 0.5 * lib.einsum('mejf,mefi->ij',temp_t2_v_3, eris_ovvo,optimize=True)
M_ij += 0.5 * lib.einsum('meif,mefj->ij',temp_t2_v_3, eris_ovvo,optimize=True)
M_ij -= 0.5 * 2 *lib.einsum('meif,mjfe->ij',temp_t2_v_3, eris_oovv,optimize=True)
M_ij -= 0.5 * 2 * lib.einsum('mejf,mife->ij',temp_t2_v_3, eris_oovv,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_oovv, optimize=True)
M_ij -= 1.5 *lib.einsum('fe,jfei->ij',temp_t2_v_8, eris_ovvo, optimize=True)
M_ij += lib.einsum('ef,jief->ij',temp_t2_v_8, eris_oovv, optimize=True)
M_ij -= 0.5 * lib.einsum('ef,jfei->ij',temp_t2_v_8, eris_ovvo, 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_oovv, optimize=True)
M_ij -= 1.0 * lib.einsum('ef,jief->ij',temp_t2_v_9, eris_oovv, optimize=True)
M_ij += 0.5 * lib.einsum('fe,jfei->ij',temp_t2_v_9, eris_ovvo, optimize=True)
M_ij += 0.5 * lib.einsum('ef,jfei->ij',temp_t2_v_9, eris_ovvo, 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_oooo, optimize=True)
M_ij -= 1.0 * lib.einsum('mn,jinm->ij',temp_t2_v_10, eris_oooo, optimize=True)
M_ij += 1.5 * lib.einsum('nm,jmni->ij',temp_t2_v_10, eris_oooo, optimize=True)
M_ij += 0.5 * lib.einsum('mn,jmni->ij',temp_t2_v_10, eris_oooo, 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_oooo, optimize=True)
M_ij -= 0.5 * lib.einsum('nm,jmni->ij',temp_t2_v_11, eris_oooo, optimize=True)
M_ij -= 0.5 * lib.einsum('mn,jmni->ij',temp_t2_v_11, eris_oooo, optimize=True)
M_ij += 1.0 * lib.einsum('mn,jinm->ij',temp_t2_v_11, eris_oooo, optimize=True)
del temp_t2_v_11
temp_t2_v_12 = lib.einsum('inde,lmde->inlm',t2_1, t2_1,optimize=True)
M_ij += 0.5 * 1.25 * lib.einsum('inlm,jlnm->ij',temp_t2_v_12, eris_oooo, optimize=True)
M_ij += 0.5 * 0.25 * lib.einsum('lmin,jlnm->ij',temp_t2_v_12, eris_oooo, optimize=True)
M_ij -= 0.5 * 0.25 * lib.einsum('inlm,jmnl->ij',temp_t2_v_12, eris_oooo, optimize=True)
M_ij -= 0.5 * 0.25 * lib.einsum('lmin,jmnl->ij',temp_t2_v_12, eris_oooo, optimize=True)
M_ij += 0.5 * 0.25 * lib.einsum('inlm,jlnm->ji',temp_t2_v_12, eris_oooo, optimize=True)
M_ij -= 0.5 * 0.25 * lib.einsum('inlm,lnmj->ji',temp_t2_v_12, eris_oooo, optimize=True)
M_ij += 0.5 * 1.00 * lib.einsum('inlm,ljmn->ji',temp_t2_v_12, eris_oooo, optimize=True)
M_ij -= 0.5 * 0.25 * lib.einsum('lmin,lnmj->ji',temp_t2_v_12, eris_oooo, optimize=True)
M_ij += 0.5 * 0.25 * lib.einsum('lmin,ljmn->ji',temp_t2_v_12, eris_oooo, optimize=True)
del temp_t2_v_12
temp_t2_v_13 = lib.einsum('inde,mlde->inml',t2_1, t2_1,optimize=True)
M_ij -= 0.5 * 0.25 * lib.einsum('inml,jlnm->ij',temp_t2_v_13, eris_oooo, optimize=True)
M_ij -= 0.5 * 0.25 * lib.einsum('mlin,jlnm->ij',temp_t2_v_13, eris_oooo, optimize=True)
M_ij += 0.5 * 0.25 * lib.einsum('inml,jmnl->ij',temp_t2_v_13, eris_oooo, optimize=True)
M_ij += 0.5 * 0.25 * lib.einsum('mlin,jmnl->ij',temp_t2_v_13, eris_oooo, optimize=True)
M_ij -= 0.5 * 0.25 * lib.einsum('inml,jlnm->ji',temp_t2_v_13, eris_oooo, optimize=True)
M_ij += 0.5 * 0.25 * lib.einsum('inml,lnmj->ji',temp_t2_v_13, eris_oooo, optimize=True)
M_ij -= 0.5 * 0.25 * lib.einsum('inml,ljmn->ji',temp_t2_v_13, eris_oooo, optimize=True)
M_ij += 0.5 * 0.25 * lib.einsum('inml,lnmj->ji',temp_t2_v_13, eris_oooo, optimize=True)
del temp_t2_v_13
del t2_1
cput0 = log.timer_debug1("Completed M_ij ADC(n) calculation", *cput0)
return M_ij
[docs]
def get_diag(adc,M_ij=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_ij is None:
M_ij = adc.get_imds()
nocc = adc._nocc
nvir = adc._nvir
n_singles = nocc
n_doubles = nvir * nocc * nocc
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_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)
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:f2] = D_aij.copy()
# ###### Additional terms for the preconditioner ####
# if (method == "adc(2)-x" or method == "adc(3)"):
#
# if eris is None:
# eris = adc.transform_integrals()
#
# if isinstance(eris.vvvv, np.ndarray):
#
# eris_oooo = eris.oooo
# eris_oovv = eris.oovv
# eris_ovvo = eris.ovvo
#
# eris_oooo_p = np.ascontiguousarray(eris_oooo.transpose(0,2,1,3))
# eris_oooo_p = eris_oooo_p.reshape(nocc*nocc, nocc*nocc)
#
# temp = np.zeros((nvir, eris_oooo_p.shape[0]))
# temp[:] += np.diag(eris_oooo_p)
# 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((nocc, nocc, nvir))
# temp[:] += np.diagonal(eris_ovov_p).reshape(nocc, nvir)
# temp = np.ascontiguousarray(temp.transpose(2,1,0))
# 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((nocc, nocc, nvir))
# temp[:] += np.diagonal(eris_ovov_p).reshape(nocc, nvir)
# temp = np.ascontiguousarray(temp.transpose(2,0,1))
# diag[s2:f2] += temp.reshape(-1)
# else:
# raise Exception("Precond not available for out-of-core and density-fitted algo")
diag = -diag
log.timer_debug1("Completed ea_diag calculation")
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
n_singles = nocc
n_doubles = nvir * nocc * nocc
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_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)
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 = r[s2:f2]
r2 = r2.reshape(nvir,nocc,nocc)
eris_ovoo = 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_ovoo, r2, optimize=True)
s[s1:f1] -= lib.einsum('kaji,ajk->i', eris_ovoo, r2, optimize=True)
########## ###### ADC(2) ajk - i block ############################
temp = lib.einsum('jaki,i->ajk', eris_ovoo, r1, optimize=True).reshape(-1)
s[s2:f2] += temp.reshape(-1)
################# ADC(2) ajk - bil block ############################
s[s2:f2] += D_aij * r2.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
s[s2:f2] -= 0.5*lib.einsum('kijl,ali->ajk',eris_oooo, r2, optimize=True).reshape(-1)
s[s2:f2] -= 0.5*lib.einsum('klji,ail->ajk',eris_oooo ,r2, optimize=True).reshape(-1)
s[s2:f2] += 0.5*lib.einsum('klba,bjl->ajk',eris_oovv,r2,optimize=True).reshape(-1)
s[s2:f2] += 0.5*lib.einsum('jabl,bkl->ajk',eris_ovvo,r2,optimize=True).reshape(-1)
s[s2:f2] -= lib.einsum('jabl,blk->ajk',eris_ovvo,r2,optimize=True).reshape(-1)
s[s2:f2] += 0.5*lib.einsum('jlba,blk->ajk',eris_oovv,r2,optimize=True).reshape(-1)
s[s2:f2] += 0.5*lib.einsum('kiba,bji->ajk',eris_oovv,r2,optimize=True).reshape(-1)
s[s2:f2] += 0.5*lib.einsum('jiba,bik->ajk',eris_oovv,r2,optimize=True).reshape(-1)
s[s2:f2] -= lib.einsum('jabi,bik->ajk',eris_ovvo,r2,optimize=True).reshape(-1)
s[s2:f2] += 0.5*lib.einsum('jabi,bki->ajk',eris_ovvo,r2,optimize=True).reshape(-1)
if (method == "adc(3)"):
eris_ovoo = eris.ovoo
t2_1 = adc.t2[0]
################ ADC(3) i - kja block and ajk - i ############################
temp = 0.25 * lib.einsum('ijbc,aij->abc',t2_1, r2, optimize=True)
temp -= 0.25 * lib.einsum('ijbc,aji->abc',t2_1, r2, optimize=True)
temp -= 0.25 * lib.einsum('jibc,aij->abc',t2_1, r2, optimize=True)
temp += 0.25 * lib.einsum('jibc,aji->abc',t2_1, r2, optimize=True)
temp_1 = lib.einsum('kjcb,ajk->abc',t2_1,r2, optimize=True)
temp_singles = np.zeros((nocc))
temp_doubles = np.zeros((nvir,nvir,nvir))
if isinstance(eris.ovvv, type(None)):
chnk_size = radc_ao2mo.calculate_chunk_size(adc)
a = 0
for p in range(0,nocc,chnk_size):
eris_ovvv = dfadc.get_ovvv_df(
adc, eris.Lov, eris.Lvv, p, chnk_size).reshape(-1,nvir,nvir,nvir)
k = eris_ovvv.shape[0]
temp_singles[a:a+k] += lib.einsum('abc,icab->i',temp, eris_ovvv, optimize=True)
temp_singles[a:a+k] -= lib.einsum('abc,ibac->i',temp, eris_ovvv, optimize=True)
temp_singles[a:a+k] += lib.einsum('abc,icab->i',
temp_1, eris_ovvv, optimize=True)
temp_doubles = lib.einsum('i,icab->cba',r1[a:a+k],eris_ovvv,optimize=True)
s[s2:f2] += lib.einsum('cba,kjcb->ajk',temp_doubles,
t2_1, optimize=True).reshape(-1)
del eris_ovvv
del temp_doubles
a += k
else :
eris_ovvv = radc_ao2mo.unpack_eri_1(eris.ovvv, nvir)
temp_singles += lib.einsum('abc,icab->i',temp, eris_ovvv, optimize=True)
temp_singles -= lib.einsum('abc,ibac->i',temp, eris_ovvv, optimize=True)
temp_singles += lib.einsum('abc,icab->i',temp_1, eris_ovvv, optimize=True)
temp_doubles = lib.einsum('i,icab->cba',r1,eris_ovvv,optimize=True)
s[s2:f2] += lib.einsum('cba,kjcb->ajk',temp_doubles,
t2_1, optimize=True).reshape(-1)
del eris_ovvv
del temp_doubles
s[s1:f1] += temp_singles
temp = np.zeros_like(r2)
temp = lib.einsum('jlab,ajk->blk',t2_1,r2,optimize=True)
temp -= lib.einsum('jlab,akj->blk',t2_1,r2,optimize=True)
temp -= lib.einsum('ljab,ajk->blk',t2_1,r2,optimize=True)
temp += lib.einsum('ljab,akj->blk',t2_1,r2,optimize=True)
temp += lib.einsum('ljba,ajk->blk',t2_1,r2,optimize=True)
temp_1 = np.zeros_like(r2)
temp_1 = lib.einsum('jlab,ajk->blk',t2_1,r2,optimize=True)
temp_1 -= lib.einsum('jlab,akj->blk',t2_1,r2,optimize=True)
temp_1 += lib.einsum('jlab,ajk->blk',t2_1,r2,optimize=True)
temp_1 -= lib.einsum('ljab,ajk->blk',t2_1,r2,optimize=True)
temp_2 = lib.einsum('jlba,akj->blk',t2_1,r2, optimize=True)
s[s1:f1] += 0.5*lib.einsum('blk,lbik->i',temp,eris_ovoo,optimize=True)
s[s1:f1] -= 0.5*lib.einsum('blk,iblk->i',temp,eris_ovoo,optimize=True)
s[s1:f1] += 0.5*lib.einsum('blk,lbik->i',temp_1,eris_ovoo,optimize=True)
s[s1:f1] -= 0.5*lib.einsum('blk,iblk->i',temp_2,eris_ovoo,optimize=True)
del temp
del temp_1
del temp_2
temp = np.zeros_like(r2)
temp = -lib.einsum('klab,akj->blj',t2_1,r2,optimize=True)
temp += lib.einsum('klab,ajk->blj',t2_1,r2,optimize=True)
temp += lib.einsum('lkab,akj->blj',t2_1,r2,optimize=True)
temp -= lib.einsum('lkab,ajk->blj',t2_1,r2,optimize=True)
temp -= lib.einsum('lkba,akj->blj',t2_1,r2,optimize=True)
temp_1 = np.zeros_like(r2)
temp_1 = -2 * lib.einsum('klab,akj->blj',t2_1,r2,optimize=True)
temp_1 += lib.einsum('klab,ajk->blj',t2_1,r2,optimize=True)
temp_1 += lib.einsum('lkab,akj->blj',t2_1,r2,optimize=True)
temp_2 = -lib.einsum('klba,ajk->blj',t2_1,r2,optimize=True)
s[s1:f1] -= 0.5*lib.einsum('blj,lbij->i',temp,eris_ovoo,optimize=True)
s[s1:f1] += 0.5*lib.einsum('blj,iblj->i',temp,eris_ovoo,optimize=True)
s[s1:f1] -= 0.5*lib.einsum('blj,lbij->i',temp_1,eris_ovoo,optimize=True)
s[s1:f1] += 0.5*lib.einsum('blj,iblj->i',temp_2,eris_ovoo,optimize=True)
del temp
del temp_1
del temp_2
temp_1 = lib.einsum('i,lbik->kbl',r1,eris_ovoo)
temp_1 -= lib.einsum('i,iblk->kbl',r1,eris_ovoo)
temp_2 = lib.einsum('i,lbik->kbl',r1,eris_ovoo)
temp = lib.einsum('kbl,ljba->ajk',temp_1,t2_1,optimize=True)
temp += lib.einsum('kbl,jlab->ajk',temp_2,t2_1,optimize=True)
temp -= lib.einsum('kbl,ljab->ajk',temp_2,t2_1,optimize=True)
s[s2:f2] += temp.reshape(-1)
temp = -lib.einsum('i,iblj->jbl',r1,eris_ovoo,optimize=True)
temp_1 = -lib.einsum('jbl,klba->ajk',temp,t2_1,optimize=True)
s[s2:f2] -= temp_1.reshape(-1)
del temp
del temp_1
del temp_2
del t2_1
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
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 = nocc
n_doubles = nvir * nocc * nocc
dim = n_singles + n_doubles
idn_occ = np.identity(nocc)
s1 = 0
f1 = n_singles
s2 = f1
f2 = s2 + n_doubles
T = np.zeros((dim))
######## ADC(2) 1h part ############################################
if orb < nocc:
T[s1:f1] = idn_occ[orb, :]
T[s1:f1] += 0.25*lib.einsum('kdc,ikdc->i',t2_1[:,orb,:,:], t2_1, optimize=True)
T[s1:f1] -= 0.25*lib.einsum('kcd,ikdc->i',t2_1[:,orb,:,:], t2_1, optimize=True)
T[s1:f1] -= 0.25*lib.einsum('kdc,ikcd->i',t2_1[:,orb,:,:], t2_1, optimize=True)
T[s1:f1] += 0.25*lib.einsum('kcd,ikcd->i',t2_1[:,orb,:,:], t2_1, optimize=True)
T[s1:f1] -= 0.25*lib.einsum('kdc,ikdc->i',t2_1[orb,:,:,:], t2_1, optimize=True)
T[s1:f1] -= 0.25*lib.einsum('kcd,ikcd->i',t2_1[orb,:,:,:], t2_1, optimize=True)
else :
if (adc.approx_trans_moments is False or adc.method == "adc(3)"):
T[s1:f1] += t1_2[:,(orb-nocc)]
######### ADC(2) 2h-1p part ############################################
t2_1_t = t2_1.transpose(2,3,1,0)
T[s2:f2] += t2_1_t[(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)
T[s2:f2] += t2_2_t[(orb-nocc),:,:,:].reshape(-1)
del t2_2
######### ADC(3) 1h 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] += 0.25*lib.einsum('kdc,ikdc->i',t2_1[:,orb,:,:], t2_2, optimize=True)
T[s1:f1] -= 0.25*lib.einsum('kcd,ikdc->i',t2_1[:,orb,:,:], t2_2, optimize=True)
T[s1:f1] -= 0.25*lib.einsum('kdc,ikcd->i',t2_1[:,orb,:,:], t2_2, optimize=True)
T[s1:f1] += 0.25*lib.einsum('kcd,ikcd->i',t2_1[:,orb,:,:], t2_2, optimize=True)
T[s1:f1] -= 0.25*lib.einsum('kdc,ikdc->i',t2_1[orb,:,:,:], t2_2, optimize=True)
T[s1:f1] -= 0.25*lib.einsum('kcd,ikcd->i',t2_1[orb,:,:,:], t2_2, optimize=True)
T[s1:f1] += 0.25*lib.einsum('ikdc,kdc->i',t2_1, t2_2[:,orb,:,:],optimize=True)
T[s1:f1] -= 0.25*lib.einsum('ikcd,kdc->i',t2_1, t2_2[:,orb,:,:],optimize=True)
T[s1:f1] -= 0.25*lib.einsum('ikdc,kcd->i',t2_1, t2_2[:,orb,:,:],optimize=True)
T[s1:f1] += 0.25*lib.einsum('ikcd,kcd->i',t2_1, t2_2[:,orb,:,:],optimize=True)
T[s1:f1] -= 0.25*lib.einsum('ikcd,kcd->i',t2_1, t2_2[orb,:,:,:],optimize=True)
T[s1:f1] -= 0.25*lib.einsum('ikdc,kdc->i',t2_1, t2_2[orb,:,:,:],optimize=True)
else:
T[s1:f1] += 0.5 * lib.einsum('ikc,kc->i',t2_1[:,:,(orb-nocc),:], t1_2,optimize=True)
T[s1:f1] -= 0.5*lib.einsum('kic,kc->i',t2_1[:,:,(orb-nocc),:], t1_2,optimize=True)
T[s1:f1] += 0.5*lib.einsum('ikc,kc->i',t2_1[:,:,(orb-nocc),:], t1_2,optimize=True)
if (adc.approx_trans_moments is False):
T[s1:f1] += t1_3[:,(orb-nocc)]
del t2_2
del t2_1
T_aaa = T[n_singles:].reshape(nvir,nocc,nocc).copy()
T_aaa = T_aaa - T_aaa.transpose(0,2,1)
T[n_singles:] += T_aaa.reshape(-1)
return T
[docs]
def analyze_eigenvector(adc):
nocc = adc._nocc
nvir = adc._nvir
n_singles = nocc
evec_print_tol = adc.evec_print_tol
U = adc.U
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)
for I in range(U.shape[1]):
U1 = U[:n_singles,I]
U2 = U[n_singles:,I].reshape(nvir,nocc,nocc)
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:
i_idx = orb_idx + 1
singles_idx.append(i_idx)
singles_val.append(U_sorted[iter_num])
if orb_idx >= n_singles:
aij_idx = orb_idx - n_singles
ij_rem = aij_idx % (nocc*nocc)
a_idx = aij_idx//(nocc*nocc)
i_idx = ij_rem//nocc
j_idx = ij_rem % nocc
doubles_idx.append((a_idx + 1 + n_singles, i_idx + 1, j_idx + 1))
doubles_val.append(U_sorted[iter_num])
iter_num += 1
logger.info(adc, '%s | root %d | norm(1h) = %6.4f | norm(2h1p) = %6.4f ',
adc.method ,I, U1dotU1, U2dotU2)
if singles_val:
logger.info(adc, "\n1h block: ")
logger.info(adc, " i U(i)")
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, "\n2h1p block: ")
logger.info(adc, " i j a U(i,j,a)")
logger.info(adc, "-------------------------------")
for idx, print_doubles in enumerate(doubles_idx):
logger.info(adc, ' %4d %4d %4d %7.4f',
print_doubles[1], print_doubles[2], print_doubles[0], doubles_val[idx])
logger.info(adc, "\n*************************************************************\n")
[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
n_singles = nocc
U = adc.U
for I in range(U.shape[1]):
U1 = U[:n_singles,I]
U2 = U[n_singles:,I].reshape(nvir,nocc,nocc)
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
[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):
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]
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
[docs]
def make_rdm1_eigenvectors(adc, L, R):
L = np.array(L).ravel()
R = np.array(R).ravel()
t2_1 = adc.t2[0][:]
t1_2 = adc.t1[0][:]
nocc = adc._nocc
nvir = adc._nvir
nmo = nocc + nvir
n_singles = nocc
n_doubles = nvir * nocc * nocc
s1 = 0
f1 = n_singles
s2 = f1
f2 = s2 + n_doubles
rdm1 = np.zeros((nmo,nmo))
kd_oc = np.identity(nocc)
L1 = L[s1:f1]
L2 = L[s2:f2]
R1 = R[s1:f1]
R2 = R[s2:f2]
L2 = L2.reshape(nvir,nocc,nocc)
R2 = R2.reshape(nvir,nocc,nocc)
#####G^000#### block- ij
rdm1[:nocc,:nocc] = 2*np.einsum('ij,m,m->ij',kd_oc,L1,R1,optimize=True)
rdm1[:nocc,:nocc] -= np.einsum('i,j->ij',L1,R1,optimize=True)
rdm1[:nocc,:nocc] += 4*np.einsum('ij,etu,etu->ij',kd_oc,L2,R2,optimize=True)
rdm1[:nocc,:nocc] -= np.einsum('ij,etu,eut->ij',kd_oc,L2,R2,optimize=True)
rdm1[:nocc,:nocc] -= np.einsum('ij,eut,etu->ij',kd_oc,L2,R2,optimize=True)
rdm1[:nocc,:nocc] -= 4*np.einsum('eti,etj->ij',L2,R2,optimize=True)
rdm1[:nocc,:nocc] += np.einsum('eti,ejt->ij',L2,R2,optimize=True)
rdm1[:nocc,:nocc] += np.einsum('eit,etj->ij',L2,R2,optimize=True)
rdm1[:nocc,:nocc] -= 2*np.einsum('g,g,hjcd,hicd->ij', L1,R1,t2_1,t2_1,optimize=True)
rdm1[:nocc,:nocc] += 2*np.einsum('g,g,jhcd,hicd->ij', L1,R1,t2_1,t2_1,optimize=True)
rdm1[:nocc,:nocc] -= 2*np.einsum('g,g,jhcd,ihcd->ij', L1,R1,t2_1,t2_1,optimize=True)
rdm1[:nocc,:nocc] += 2*np.einsum('g,h,jgcd,ihcd->ij', L1,R1,t2_1,t2_1,optimize=True)
rdm1[:nocc,:nocc] -= np.einsum('g,h,gjcd,ihcd->ij', L1,R1,t2_1,t2_1,optimize=True)
temp_ij = np.einsum('g,j,ghcd,ihcd->ij',L1,R1,t2_1,t2_1,optimize=True)
temp_ij -= 0.25*np.einsum('g,j,hgcd,ihcd->ij',L1,R1,t2_1,t2_1,optimize=True)
temp_ij -= 0.25*np.einsum('g,j,ghcd,hicd->ij',L1,R1,t2_1,t2_1,optimize=True)
rdm1[:nocc,:nocc] += temp_ij
rdm1[:nocc,:nocc] += temp_ij.T
########## block- ab
rdm1[nocc:,nocc:] = np.einsum('atu,btu->ab', L2,R2,optimize=True)
rdm1[nocc:,nocc:] -= 0.5*np.einsum('aut,btu->ab', L2,R2,optimize=True)
rdm1[nocc:,nocc:] -= 0.5*np.einsum('atu,but->ab', L2,R2,optimize=True)
rdm1[nocc:,nocc:] += np.einsum('atu,btu->ab', L2,R2,optimize=True)
rdm1[nocc:,nocc:] += 4*np.einsum('g,g,hmbc,hmac->ab', L1,R1,t2_1,t2_1,optimize=True)
rdm1[nocc:,nocc:] -= np.einsum('g,g,mhbc,hmac->ab', L1,R1,t2_1,t2_1,optimize=True)
rdm1[nocc:,nocc:] -= np.einsum('g,g,hmbc,mhac->ab', L1,R1,t2_1,t2_1,optimize=True)
rdm1[nocc:,nocc:] -= 4*np.einsum('g,h,hmbc,gmac->ab', L1,R1,t2_1,t2_1,optimize=True)
rdm1[nocc:,nocc:] += np.einsum('g,h,mhbc,gmac->ab', L1,R1,t2_1,t2_1,optimize=True)
rdm1[nocc:,nocc:] += np.einsum('g,h,hmbc,mgac->ab', L1,R1,t2_1,t2_1,optimize=True)
########### block- ia
rdm1[:nocc,nocc:] = -np.einsum('n,ani->ia', R1,L2,optimize=True)
rdm1[:nocc,nocc:] += 2*np.einsum('n,ain->ia', R1,L2,optimize=True)
rdm1[:nocc,nocc:] -= 2*np.einsum('g,cgh,ihac->ia', L1,R2,t2_1,optimize=True)
rdm1[:nocc,nocc:] += np.einsum('g,cgh,hiac->ia', L1,R2,t2_1,optimize=True)
rdm1[:nocc,nocc:] += 4*np.einsum('g,chg,ihac->ia', L1,R2,t2_1,optimize=True)
rdm1[:nocc,nocc:] -= np.einsum('g,chg,hiac->ia', L1,R2,t2_1,optimize=True)
rdm1[:nocc,nocc:] -= np.einsum('g,cgh,ihac->ia', L1,R2,t2_1,optimize=True)
rdm1[:nocc,nocc:] += np.einsum('i,cgh,ghac->ia', L1,R2,t2_1,optimize=True)
rdm1[:nocc,nocc:] -= 2*np.einsum('i,chg,ghac->ia', L1,R2,t2_1,optimize=True)
rdm1[:nocc,nocc:] += np.einsum('g,g,ia->ia', L1,R1,t1_2,optimize=True)
rdm1[:nocc,nocc:] += np.einsum('g,g,ia->ia', L1,R1,t1_2,optimize=True)
rdm1[:nocc,nocc:] -= np.einsum('g,i,ga->ia', R1,L1,t1_2,optimize=True)
############ block- ai
rdm1[nocc:,:nocc] = rdm1[:nocc,nocc:].T
return rdm1
[docs]
class RADCIP(radc.RADC):
'''restricted ADC for IP 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',
))
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
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
make_rdm1 = make_rdm1
[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