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radc.py
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radc.py
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# Copyright 2014-2019 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 time
import numpy as np
from pyscf import lib
from pyscf.lib import logger
from pyscf.adc import radc_ao2mo
from pyscf import __config__
def kernel(adc, nroots=1, guess=None, eris=None, verbose=None):
adc.method = adc.method.lower()
if adc.method not in ("adc(2)", "adc(2)-x", "adc(3)"):
raise NotImplementedError(adc.method)
cput0 = (time.clock(), time.time())
log = logger.Logger(adc.stdout, adc.verbose)
if adc.verbose >= logger.WARN:
adc.check_sanity()
adc.dump_flags()
if eris is None:
eris = radc_ao2mo.transform_integrals_incore(adc)
imds = adc.get_imds(eris)
matvec, diag = adc.gen_matvec(imds, eris)
guess = adc.get_init_guess(nroots, diag, ascending = True)
conv, E, U = lib.linalg_helper.davidson_nosym1(lambda xs : [matvec(x) for x in xs], guess, diag, nroots=nroots, verbose=log, tol=adc.conv_tol, max_cycle=adc.max_cycle, max_space=adc.max_space)
U = np.array(U)
T = adc.get_trans_moments()
spec_factors = adc.get_spec_factors(T, U, nroots)
nfalse = np.shape(conv)[0] - np.sum(conv)
if nfalse >= 1:
print ("*************************************************************")
print (" WARNING : ", "Davidson iterations for ",nfalse, "root(s) not converged")
print ("*************************************************************")
if adc.verbose >= logger.INFO:
if nroots == 1:
logger.info(adc, '%s root %d Energy (Eh) = %.8f Energy (eV) = %.8f Spec factors = %.8f conv = %s',
adc.method, 0, E, E*27.2114, spec_factors, conv)
else :
for n, en, pn, convn in zip(range(nroots), E, spec_factors, conv):
logger.info(adc, '%s root %d Energy (Eh) = %.8f Energy (eV) = %.8f Spec factors = %.8f conv = %s',
adc.method, n, en, en*27.2114, pn, convn)
log.timer('ADC', *cput0)
return E, U, spec_factors
def compute_amplitudes_energy(myadc, eris, verbose=None):
t1, t2 = myadc.compute_amplitudes(eris)
e_corr = myadc.compute_energy(t1, t2, eris)
return e_corr, t1, t2
def compute_amplitudes(myadc, eris):
if myadc.method not in ("adc(2)", "adc(2)-x", "adc(3)"):
raise NotImplementedError(myadc.method)
nocc = myadc._nocc
nvir = myadc._nvir
eris_oooo = eris.oooo
eris_ovoo = eris.ovoo
eris_ovov = eris.ovov
eris_oovv = eris.oovv
eris_ovvo = eris.ovvo
eris_ovvv = eris.ovvv
e = myadc.mo_energy
d_ij = e[:nocc][:,None] + e[:nocc]
d_ab = e[nocc:][:,None] + e[nocc:]
D2 = d_ij.reshape(-1,1) - d_ab.reshape(-1)
D2 = D2.reshape((nocc,nocc,nvir,nvir))
D1 = e[:nocc][:None].reshape(-1,1) - e[nocc:].reshape(-1)
D1 = D1.reshape((nocc,nvir))
# Compute first-order doubles t2 (tijab)
v2e_oovv = eris_ovov.transpose(0,2,1,3).copy()
t2_1 = v2e_oovv/D2
# Compute second-order singles t1 (tij)
t2_1_a = t2_1 - t2_1.transpose(1,0,2,3).copy()
eris_ovvv = radc_ao2mo.unpack_eri_1(eris.ovvv, nvir)
t1_2 = 0.5*lib.einsum('kdac,ikcd->ia',eris_ovvv,t2_1_a,optimize=True)
t1_2 -= 0.5*lib.einsum('kcad,ikcd->ia',eris_ovvv,t2_1_a,optimize=True)
t1_2 += lib.einsum('kdac,ikcd->ia',eris_ovvv,t2_1,optimize=True)
del eris_ovvv
t1_2 -= 0.5*lib.einsum('lcki,klac->ia',eris_ovoo,t2_1_a,optimize=True)
t1_2 -= 0.5*lib.einsum('kcli,lkac->ia',eris_ovoo,t2_1_a,optimize=True)
t1_2 -= lib.einsum('lcki,klac->ia',eris_ovoo,t2_1,optimize=True)
t1_2 = t1_2/D1
t2_2 = None
t1_3 = None
if (myadc.method == "adc(2)-x" or myadc.method == "adc(3)"):
# Compute second-order doubles t2 (tijab)
eris_oooo = eris.oooo
eris_ovvo = eris.ovvo
temp = t2_1.reshape(nocc*nocc,nvir*nvir)
eris_vvvv = eris.vvvv
t2_2 = np.dot(temp,eris_vvvv.T).reshape(nocc,nocc,nvir,nvir)
t2_2 += lib.einsum('kilj,klab->ijab',eris_oooo,t2_1,optimize=True)
t2_2 += lib.einsum('kcbj,kica->ijab',eris_ovvo,t2_1_a,optimize=True)
t2_2 += lib.einsum('kcbj,ikac->ijab',eris_ovvo,t2_1,optimize=True)
t2_2 -= lib.einsum('kjbc,ikac->ijab',eris_oovv,t2_1,optimize=True)
t2_2 -= lib.einsum('kibc,kjac->ijab',eris_oovv,t2_1,optimize=True)
t2_2 -= lib.einsum('kjac,ikcb->ijab',eris_oovv,t2_1,optimize=True)
t2_2 += lib.einsum('kcai,kjcb->ijab',eris_ovvo,t2_1_a,optimize=True)
t2_2 += lib.einsum('kcai,kjcb->ijab',eris_ovvo,t2_1,optimize=True)
t2_2 -= lib.einsum('kiac,kjcb->ijab',eris_oovv,t2_1,optimize=True)
t2_2 = t2_2/D2
if (myadc.method == "adc(3)"):
# Compute third-order singles (tij)
t2_2_a = t2_2 - t2_2.transpose(1,0,2,3).copy()
eris_ovoo = eris.ovoo
t1_3 = lib.einsum('d,ilad,ld->ia',e[nocc:],t2_1_a,t1_2,optimize=True)
t1_3 += lib.einsum('d,ilad,ld->ia',e[nocc:],t2_1,t1_2,optimize=True)
t1_3 -= lib.einsum('l,ilad,ld->ia',e[:nocc],t2_1_a, t1_2,optimize=True)
t1_3 -= lib.einsum('l,ilad,ld->ia',e[:nocc],t2_1,t1_2,optimize=True)
t1_3 += 0.5*lib.einsum('a,ilad,ld->ia',e[nocc:],t2_1_a, t1_2,optimize=True)
t1_3 += 0.5*lib.einsum('a,ilad,ld->ia',e[nocc:],t2_1,t1_2,optimize=True)
t1_3 -= 0.5*lib.einsum('i,ilad,ld->ia',e[:nocc],t2_1_a, t1_2,optimize=True)
t1_3 -= 0.5*lib.einsum('i,ilad,ld->ia',e[:nocc],t2_1,t1_2,optimize=True)
t1_3 += lib.einsum('ld,iald->ia',t1_2,eris_ovov,optimize=True)
t1_3 -= lib.einsum('ld,laid->ia',t1_2,eris_ovov,optimize=True)
t1_3 += lib.einsum('ld,iald->ia',t1_2,eris_ovov,optimize=True)
t1_3 += lib.einsum('ld,ldai->ia',t1_2,eris_ovvo ,optimize=True)
t1_3 -= lib.einsum('ld,liad->ia',t1_2,eris_oovv ,optimize=True)
t1_3 += lib.einsum('ld,ldai->ia',t1_2,eris_ovvo,optimize=True)
t1_3 -= 0.5*lib.einsum('lmad,mdli->ia',t2_2_a,eris_ovoo,optimize=True)
t1_3 += 0.5*lib.einsum('lmad,ldmi->ia',t2_2_a,eris_ovoo,optimize=True)
t1_3 -= lib.einsum('lmad,mdli->ia',t2_2,eris_ovoo,optimize=True)
eris_ovvv = radc_ao2mo.unpack_eri_1(eris.ovvv, nvir)
t1_3 += 0.5*lib.einsum('ilde,lead->ia',t2_2_a,eris_ovvv,optimize=True)
t1_3 -= 0.5*lib.einsum('ilde,ldae->ia',t2_2_a,eris_ovvv,optimize=True)
t1_3 -= lib.einsum('ildf,mefa,lmde->ia',t2_1_a, eris_ovvv, t2_1_a ,optimize=True)
t1_3 += lib.einsum('ildf,mafe,lmde->ia',t2_1_a, eris_ovvv, t2_1_a ,optimize=True)
t1_3 += lib.einsum('ilfd,mefa,mled->ia',t2_1,eris_ovvv, t2_1,optimize=True)
t1_3 -= lib.einsum('ilfd,mafe,mled->ia',t2_1,eris_ovvv, t2_1,optimize=True)
t1_3 += 0.5*lib.einsum('ilaf,mefd,lmde->ia',t2_1_a,eris_ovvv,t2_1_a,optimize=True)
t1_3 -= 0.5*lib.einsum('ilaf,mdfe,lmde->ia',t2_1_a,eris_ovvv,t2_1_a,optimize=True)
t1_3 += 0.5*lib.einsum('lmdf,iaef,lmde->ia',t2_1_a,eris_ovvv,t2_1_a,optimize=True)
t1_3 -= 0.5*lib.einsum('lmdf,ifea,lmde->ia',t2_1_a,eris_ovvv,t2_1_a,optimize=True)
t1_3 += lib.einsum('mlfd,iaef,mled->ia',t2_1,eris_ovvv,t2_1,optimize=True)
t1_3 -= lib.einsum('mlfd,ifea,mled->ia',t2_1,eris_ovvv,t2_1,optimize=True)
t1_3 -= 0.25*lib.einsum('lmef,iedf,lmad->ia',t2_1_a,eris_ovvv,t2_1_a,optimize=True)
t1_3 += 0.25*lib.einsum('lmef,ifde,lmad->ia',t2_1_a,eris_ovvv,t2_1_a,optimize=True)
t1_3 += 0.5*lib.einsum('ilaf,mefd,lmde->ia',t2_1,eris_ovvv,t2_1_a,optimize=True)
t1_3 -= 0.5*lib.einsum('ilaf,mdfe,lmde->ia',t2_1,eris_ovvv,t2_1_a,optimize=True)
t1_3 -= lib.einsum('ildf,mafe,mlde->ia',t2_1,eris_ovvv,t2_1,optimize=True)
t1_3 += lib.einsum('ilaf,mefd,mled->ia',t2_1,eris_ovvv,t2_1,optimize=True)
t1_3 += 0.5*lib.einsum('lmdf,iaef,lmde->ia',t2_1_a,eris_ovvv,t2_1_a,optimize=True)
t1_3 += lib.einsum('lmdf,iaef,lmde->ia',t2_1,eris_ovvv,t2_1,optimize=True)
t1_3 -= lib.einsum('lmef,iedf,lmad->ia',t2_1,eris_ovvv,t2_1,optimize=True)
t1_3 += lib.einsum('ilde,lead->ia',t2_2,eris_ovvv,optimize=True)
t1_3 -= lib.einsum('ildf,mefa,lmde->ia',t2_1_a,eris_ovvv, t2_1,optimize=True)
t1_3 += lib.einsum('ilfd,mefa,lmde->ia',t2_1,eris_ovvv,t2_1_a ,optimize=True)
t1_3 += lib.einsum('ilaf,mefd,lmde->ia',t2_1_a,eris_ovvv,t2_1,optimize=True)
del eris_ovvv
t1_3 += 0.25*lib.einsum('inde,lamn,lmde->ia',t2_1_a,eris_ovoo,t2_1_a,optimize=True)
t1_3 -= 0.25*lib.einsum('inde,maln,lmde->ia',t2_1_a,eris_ovoo,t2_1_a,optimize=True)
t1_3 += lib.einsum('inde,lamn,lmde->ia',t2_1,eris_ovoo,t2_1,optimize=True)
t1_3 += 0.5*lib.einsum('inad,lemn,lmde->ia',t2_1_a,eris_ovoo,t2_1_a,optimize=True)
t1_3 -= 0.5*lib.einsum('inad,meln,lmde->ia',t2_1_a,eris_ovoo,t2_1_a,optimize=True)
t1_3 -= 0.5 * lib.einsum('inad,lemn,mlde->ia',t2_1_a,eris_ovoo,t2_1,optimize=True)
t1_3 -= 0.5 * lib.einsum('inad,meln,lmde->ia',t2_1_a,eris_ovoo,t2_1,optimize=True)
t1_3 -= 0.5 *lib.einsum('inad,lemn,lmed->ia',t2_1,eris_ovoo,t2_1,optimize=True)
t1_3 -= 0.5*lib.einsum('inad,meln,mled->ia',t2_1,eris_ovoo,t2_1,optimize=True)
t1_3 += 0.5*lib.einsum('inad,lemn,lmde->ia',t2_1,eris_ovoo,t2_1_a,optimize=True)
t1_3 -= 0.5*lib.einsum('inad,meln,lmde->ia',t2_1,eris_ovoo,t2_1_a,optimize=True)
t1_3 -= 0.5*lib.einsum('lnde,ianm,lmde->ia',t2_1_a,eris_ovoo,t2_1_a,optimize=True)
t1_3 += 0.5*lib.einsum('lnde,naim,lmde->ia',t2_1_a,eris_ovoo,t2_1_a,optimize=True)
t1_3 -= lib.einsum('nled,ianm,mled->ia',t2_1,eris_ovoo,t2_1,optimize=True)
t1_3 += lib.einsum('nled,naim,mled->ia',t2_1,eris_ovoo,t2_1,optimize=True)
t1_3 -= 0.5*lib.einsum('lnde,ianm,lmde->ia',t2_1_a,eris_ovoo,t2_1_a,optimize=True)
t1_3 -= lib.einsum('lnde,ianm,lmde->ia',t2_1,eris_ovoo,t2_1,optimize=True)
t1_3 -= lib.einsum('lnde,ienm,lmad->ia',t2_1_a,eris_ovoo,t2_1_a,optimize=True)
t1_3 += lib.einsum('lnde,neim,lmad->ia',t2_1_a,eris_ovoo,t2_1_a,optimize=True)
t1_3 += lib.einsum('lnde,neim,lmad->ia',t2_1,eris_ovoo,t2_1_a,optimize=True)
t1_3 += lib.einsum('nled,ienm,mlad->ia',t2_1,eris_ovoo,t2_1,optimize=True)
t1_3 -= lib.einsum('nled,neim,mlad->ia',t2_1,eris_ovoo,t2_1,optimize=True)
t1_3 += lib.einsum('lned,ienm,lmad->ia',t2_1,eris_ovoo,t2_1,optimize=True)
t1_3 -= lib.einsum('lnde,neim,mlad->ia',t2_1_a,eris_ovoo,t2_1,optimize=True)
t1_3 = t1_3/D1
t1 = (t1_2, t1_3)
t2 = (t2_1, t2_2)
return t1, t2
def compute_energy(myadc, t1, t2, eris):
if myadc.method not in ("adc(2)", "adc(2)-x", "adc(3)"):
raise NotImplementedError(myadc.method)
nocc = myadc._nocc
nvir = myadc._nvir
eris_ovov = eris.ovov
t2_1 = t2[0]
#Compute MP2 correlation energy
e_mp2 = 0.5 * lib.einsum('ijab,iajb', t2_1, eris_ovov,optimize=True)
e_mp2 -= 0.5 * lib.einsum('ijab,ibja', t2_1, eris_ovov,optimize=True)
e_mp2 -= 0.5 * lib.einsum('jiab,iajb', t2_1, eris_ovov,optimize=True)
e_mp2 += 0.5 * lib.einsum('jiab,ibja', t2_1, eris_ovov,optimize=True)
e_mp2 += lib.einsum('ijab,iajb', t2_1, eris_ovov,optimize=True)
e_corr = e_mp2
if (myadc.method == "adc(3)"):
t2_1_a = t2_1 - t2_1.transpose(1,0,2,3).copy()
#Compute MP3 correlation energy
eris_oovv = eris.oovv
eris_ovvo = eris.ovvo
eris_oooo = eris.oooo
eris_vvvv = eris.vvvv
temp = t2_1_a.reshape(nocc*nocc,nvir*nvir)
temp_1_a = np.dot(temp,eris_vvvv.T).reshape(nocc,nocc,nvir,nvir)
temp_2 = t2_1.reshape(nocc*nocc,nvir*nvir)
temp_1_ab = np.dot(temp_2,eris_vvvv.T).reshape(nocc,nocc,nvir,nvir)
e_mp3 = lib.einsum('ijcd,ijcd',temp_1_ab, t2_1,optimize=True)
del temp_1_ab
temp = temp.reshape(nocc,nocc,nvir,nvir)
temp = np.ascontiguousarray(temp.transpose(0,1,3,2))
temp = temp.reshape(nocc*nocc,nvir*nvir)
temp_1_a -= np.dot(temp,eris_vvvv.T).reshape(nocc,nocc,nvir,nvir)
e_mp3 += 0.25 * lib.einsum('ijcd,ijcd',temp_1_a, t2_1_a,optimize=True)
del temp_1_a
temp_2_a = lib.einsum('ijab,klab', t2_1_a, t2_1_a,optimize=True)
e_mp3 += 0.25 * lib.einsum('ijkl,ikjl',temp_2_a, eris_oooo,optimize=True)
e_mp3 -= 0.25 * lib.einsum('ijkl,iljk',temp_2_a, eris_oooo,optimize=True)
del temp_2_a
temp_2 = lib.einsum('ijab,klab', t2_1, t2_1,optimize=True)
e_mp3 += lib.einsum('ijkl,ikjl',temp_2, eris_oooo,optimize=True)
del temp_2
temp_3_a = lib.einsum('ijab,ikcb->akcj', t2_1_a, t2_1_a,optimize=True)
temp_3_a += lib.einsum('jiab,kicb->akcj', t2_1, t2_1,optimize=True)
e_mp3 -= 2 * lib.einsum('akcj,kjac',temp_3_a, eris_oovv,optimize=True)
e_mp3 += 2 * lib.einsum('akcj,kcaj',temp_3_a, eris_ovvo,optimize=True)
del temp_3_a
temp_3 = lib.einsum('ijab,ikcb->akcj', t2_1, t2_1,optimize=True)
e_mp3 -= lib.einsum('akcj,kjac',temp_3, eris_oovv,optimize=True)
del temp_3
temp_3_1 = lib.einsum('jiba,kibc->akcj', t2_1, t2_1,optimize=True)
e_mp3 -= lib.einsum('akcj,kjac',temp_3_1, eris_oovv,optimize=True)
del temp_3_1
temp_3_2 = -lib.einsum('ijab,ikbc->akcj', t2_1_a, t2_1,optimize=True)
temp_3_2 -= lib.einsum('jiab,ikcb->akcj', t2_1, t2_1_a,optimize=True)
e_mp3 += lib.einsum('akcj,kcaj',temp_3_2, eris_ovvo,optimize=True)
del temp_3_2
temp_3_3 = -lib.einsum('ijba,ikcb->akcj', t2_1, t2_1_a,optimize=True)
temp_3_3 -= lib.einsum('ijab,kicb->akcj', t2_1_a, t2_1,optimize=True)
e_mp3 += lib.einsum('akcj,kcaj',temp_3_3, eris_ovvo,optimize=True)
del temp_3_3
e_corr += e_mp3
return e_corr
class RADC(lib.StreamObject):
'''Ground state calculations
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).
>>> mol = gto.M(atom = 'H 0 0 0; F 0 0 1.1', basis = 'ccpvdz')
>>> mf = scf.RHF(mol).run()
>>> myadc = adc.RADC(mf).run()
Saved results
e_corr : float
MPn correlation correction
e_tot : float
Total energy (HF + correlation)
t1, t2 :
T amplitudes t1[i,a], t2[i,j,a,b] (i,j in occ, a,b in virt)
'''
incore_complete = getattr(__config__, 'adc_radc_RADC_incore_complete', False)
def __init__(self, mf, frozen=0, mo_coeff=None, mo_occ=None):
from pyscf import gto
if 'dft' in str(mf.__module__):
raise NotImplementedError('DFT reference for UADC')
if mo_coeff is None: mo_coeff = mf.mo_coeff
if mo_occ is None: mo_occ = mf.mo_occ
self.mol = mf.mol
self._scf = mf
self.verbose = self.mol.verbose
self.stdout = self.mol.stdout
self.max_memory = mf.max_memory
self.max_space = getattr(__config__, 'adc_radc_RADC_max_space', 12)
self.max_cycle = getattr(__config__, 'adc_radc_RADC_max_cycle', 50)
self.conv_tol = getattr(__config__, 'adc_radc_RADC_conv_tol', 1e-12)
self.scf_energy = mf.e_tot
self.frozen = frozen
self.incore_complete = self.incore_complete or self.mol.incore_anyway
self.mo_coeff = mo_coeff
self.mo_occ = mo_occ
self.e_corr = None
self.e_tot = None
self.t1 = None
self.t2 = None
self._nocc = mf.mol.nelectron//2
self._nmo = mo_coeff.shape[1]
self._nvir = self._nmo - self._nocc
self.mo_energy = mf.mo_energy
self.chkfile = mf.chkfile
self.method = "adc(2)"
self.method_type = "ip"
keys = set(('conv_tol', 'e_corr', 'method', 'mo_coeff', 'mol', 'mo_energy', 'max_memory', 'scf_energy', 'e_tot', 't1', 'frozen', 'chkfile', 'max_space', 't2', 'mo_occ', 'max_cycle'))
self._keys = set(self.__dict__.keys()).union(keys)
compute_amplitudes = compute_amplitudes
compute_energy = compute_energy
def dump_flags(self, verbose=None):
logger.info(self, '')
logger.info(self, '******** %s ********', self.__class__)
logger.info(self, 'max_space = %d', self.max_space)
logger.info(self, 'max_cycle = %d', self.max_cycle)
logger.info(self, 'conv_tol = %s', self.conv_tol)
logger.info(self, 'max_memory %d MB (current use %d MB)',
self.max_memory, lib.current_memory()[0])
return self
def dump_flags_gs(self, verbose=None):
logger.info(self, '')
logger.info(self, '******** %s ********', self.__class__)
logger.info(self, 'max_memory %d MB (current use %d MB)',
self.max_memory, lib.current_memory()[0])
return self
def kernel_gs(self):
assert(self.mo_coeff is not None)
assert(self.mo_occ is not None)
self.method = self.method.lower()
if self.method not in ("adc(2)", "adc(2)-x", "adc(3)"):
raise NotImplementedError(self.method)
if self.verbose >= logger.WARN:
self.check_sanity()
self.dump_flags_gs()
eris = radc_ao2mo.transform_integrals_incore(self)
self.e_corr, self.t1, self.t2 = compute_amplitudes_energy(self, eris, verbose=self.verbose)
self.e_tot = self.scf_energy + self.e_corr
self._finalize()
return self.e_corr, self.t1, self.t2
def kernel(self, nroots=1, guess=None, eris=None):
assert(self.mo_coeff is not None)
assert(self.mo_occ is not None)
self.method = self.method.lower()
if self.method not in ("adc(2)", "adc(2)-x", "adc(3)"):
raise NotImplementedError(self.method)
if self.verbose >= logger.WARN:
self.check_sanity()
self.dump_flags_gs()
eris = radc_ao2mo.transform_integrals_incore(self)
self.e_corr, self.t1, self.t2 = compute_amplitudes_energy(self, eris, verbose=self.verbose)
self.e_tot = self.scf_energy + self.e_corr
self._finalize()
self.method_type = self.method_type.lower()
if(self.method_type == "ea"):
e_exc, v_exc, spec_fac = self.ea_adc(nroots=nroots, guess=guess, eris=eris)
elif(self.method_type == "ip"):
e_exc, v_exc, spec_fac = self.ip_adc(nroots=nroots, guess=guess, eris=eris)
else:
raise NotImplementedError(self.method_type)
return e_exc, v_exc, spec_fac
def _finalize(self):
'''Hook for dumping results and clearing up the object.'''
logger.note(self, 'E_corr = %.8f E_tot = %.8f',
self.e_corr, self.e_tot)
return self
def ea_adc(self, nroots=1, guess=None, eris=None):
return RADCEA(self).kernel(nroots, guess, eris)
def ip_adc(self, nroots=1, guess=None, eris=None):
return RADCIP(self).kernel(nroots, guess, eris)
def get_imds_ea(adc, eris=None):
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]
t2_1 = t2[0]
t2_1_a = t2_1 - t2_1.transpose(1,0,2,3).copy()
nocc = adc._nocc
nvir = adc._nvir
e_occ = adc.mo_energy[:nocc]
e_vir = adc.mo_energy[nocc:]
idn_occ = np.identity(nocc)
idn_vir = np.identity(nvir)
if eris is None:
eris = radc_ao2mo.transform_integrals_incore(adc)
eris_ovov = eris.ovov
# a-b block
# Zeroth-order terms
M_ab = lib.einsum('ab,a->ab', idn_vir, e_vir)
# Second-order terms
M_ab += lib.einsum('l,lmad,lmbd->ab',e_occ ,t2_1_a, t2_1_a,optimize=True)
M_ab += lib.einsum('l,lmad,lmbd->ab',e_occ,t2_1, t2_1,optimize=True)
M_ab += lib.einsum('l,mlad,mlbd->ab',e_occ,t2_1, t2_1,optimize=True)
M_ab -= 0.5 * lib.einsum('d,lmad,lmbd->ab',e_vir,t2_1_a, t2_1_a,optimize=True)
M_ab -= 0.5 * lib.einsum('d,lmad,lmbd->ab',e_vir,t2_1, t2_1,optimize=True)
M_ab -= 0.5 * lib.einsum('d,mlad,mlbd->ab',e_vir,t2_1, t2_1,optimize=True)
M_ab -= 0.25 * lib.einsum('a,lmad,lmbd->ab',e_vir,t2_1_a, t2_1_a,optimize=True)
M_ab -= 0.25 * lib.einsum('a,lmad,lmbd->ab',e_vir,t2_1, t2_1,optimize=True)
M_ab -= 0.25 * lib.einsum('a,mlad,mlbd->ab',e_vir,t2_1, t2_1,optimize=True)
M_ab -= 0.25 * lib.einsum('b,lmad,lmbd->ab',e_vir,t2_1_a, t2_1_a,optimize=True)
M_ab -= 0.25 * lib.einsum('b,lmad,lmbd->ab',e_vir,t2_1, t2_1,optimize=True)
M_ab -= 0.25 * lib.einsum('b,mlad,mlbd->ab',e_vir,t2_1, t2_1,optimize=True)
M_ab -= 0.5 * lib.einsum('lmad,lbmd->ab',t2_1_a, eris_ovov,optimize=True)
M_ab += 0.5 * lib.einsum('lmad,ldmb->ab',t2_1_a, eris_ovov,optimize=True)
M_ab -= lib.einsum('lmad,lbmd->ab',t2_1, eris_ovov,optimize=True)
M_ab -= 0.5 * lib.einsum('lmbd,lamd->ab',t2_1_a, eris_ovov,optimize=True)
M_ab += 0.5 * lib.einsum('lmbd,ldma->ab',t2_1_a, eris_ovov,optimize=True)
M_ab -= lib.einsum('lmbd,lamd->ab',t2_1, eris_ovov,optimize=True)
#Third-order terms
if(method =='adc(3)'):
t2_2 = t2[1]
t2_2_a = t2_2 - t2_2.transpose(1,0,2,3).copy()
eris_oovv = eris.oovv
eris_ovvo = eris.ovvo
eris_oooo = eris.oooo
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
M_ab -= 0.5 * lib.einsum('lmad,lbmd->ab',t2_2_a, eris_ovov,optimize=True)
M_ab += 0.5 * lib.einsum('lmad,ldmb->ab',t2_2_a, eris_ovov,optimize=True)
M_ab -= lib.einsum('lmad,lbmd->ab',t2_2, eris_ovov,optimize=True)
M_ab -= 0.5 * lib.einsum('lmbd,lamd->ab',t2_2_a,eris_ovov,optimize=True)
M_ab += 0.5 * lib.einsum('lmbd,ldma->ab',t2_2_a, eris_ovov,optimize=True)
M_ab -= lib.einsum('lmbd,lamd->ab',t2_2,eris_ovov,optimize=True)
M_ab += lib.einsum('l,lmbd,lmad->ab',e_occ, t2_1_a, t2_2_a, optimize=True)
M_ab += lib.einsum('l,lmbd,lmad->ab',e_occ, t2_1, t2_2, optimize=True)
M_ab += lib.einsum('l,mlbd,mlad->ab',e_occ, t2_1, t2_2, optimize=True)
M_ab += lib.einsum('l,lmad,lmbd->ab',e_occ, t2_1_a, t2_2_a, optimize=True)
M_ab += lib.einsum('l,lmad,lmbd->ab',e_occ, t2_1, t2_2, optimize=True)
M_ab += lib.einsum('l,mlad,mlbd->ab',e_occ, t2_1, t2_2, optimize=True)
M_ab -= 0.5*lib.einsum('d,lmbd,lmad->ab', e_vir, t2_1_a ,t2_2_a, optimize=True)
M_ab -= 0.5*lib.einsum('d,lmbd,lmad->ab', e_vir, t2_1 ,t2_2, optimize=True)
M_ab -= 0.5*lib.einsum('d,mlbd,mlad->ab', e_vir, t2_1 ,t2_2, optimize=True)
M_ab -= 0.5*lib.einsum('d,lmad,lmbd->ab', e_vir, t2_1_a, t2_2_a, optimize=True)
M_ab -= 0.5*lib.einsum('d,lmad,lmbd->ab', e_vir, t2_1, t2_2, optimize=True)
M_ab -= 0.5*lib.einsum('d,mlad,mlbd->ab', e_vir, t2_1, t2_2, optimize=True)
M_ab -= 0.25*lib.einsum('a,lmbd,lmad->ab',e_vir, t2_1_a, t2_2_a, optimize=True)
M_ab -= 0.25*lib.einsum('a,lmbd,lmad->ab',e_vir, t2_1, t2_2, optimize=True)
M_ab -= 0.25*lib.einsum('a,mlbd,mlad->ab',e_vir, t2_1, t2_2, optimize=True)
M_ab -= 0.25*lib.einsum('a,lmad,lmbd->ab',e_vir, t2_1_a, t2_2_a, optimize=True)
M_ab -= 0.25*lib.einsum('a,lmad,lmbd->ab',e_vir, t2_1, t2_2, optimize=True)
M_ab -= 0.25*lib.einsum('a,mlad,mlbd->ab',e_vir, t2_1, t2_2, optimize=True)
M_ab -= 0.25*lib.einsum('b,lmbd,lmad->ab',e_vir, t2_1_a, t2_2_a, optimize=True)
M_ab -= 0.25*lib.einsum('b,lmbd,lmad->ab',e_vir, t2_1, t2_2, optimize=True)
M_ab -= 0.25*lib.einsum('b,mlbd,mlad->ab',e_vir, t2_1, t2_2, optimize=True)
M_ab -= 0.25*lib.einsum('b,lmad,lmbd->ab',e_vir, t2_1_a, t2_2_a, optimize=True)
M_ab -= 0.25*lib.einsum('b,lmad,lmbd->ab',e_vir, t2_1, t2_2, optimize=True)
M_ab -= 0.25*lib.einsum('b,mlad,mlbd->ab',e_vir, t2_1, t2_2, optimize=True)
M_ab -= lib.einsum('lned,mlbd,nmae->ab',t2_1_a, t2_1_a, eris_oovv, optimize=True)
M_ab += lib.einsum('lned,mlbd,mane->ab',t2_1_a, t2_1_a, eris_ovov, optimize=True)
M_ab += lib.einsum('nled,mlbd,nmae->ab',t2_1, t2_1, eris_oovv, optimize=True)
M_ab -= lib.einsum('nled,mlbd,mane->ab',t2_1, t2_1, eris_ovov, optimize=True)
M_ab -= lib.einsum('lnde,mlbd,neam->ab',t2_1, t2_1_a, eris_ovvo, optimize=True)
M_ab += lib.einsum('lned,mlbd,neam->ab',t2_1_a, t2_1, eris_ovvo, optimize=True)
M_ab += lib.einsum('lned,lmbd,nmae->ab',t2_1, t2_1, eris_oovv, optimize=True)
M_ab -= lib.einsum('mled,lnad,nmeb->ab',t2_1_a, t2_1_a, eris_oovv, optimize=True)
M_ab += lib.einsum('mled,lnad,nbem->ab',t2_1_a, t2_1_a, eris_ovvo, optimize=True)
M_ab += lib.einsum('mled,nlad,nmeb->ab',t2_1, t2_1, eris_oovv, optimize=True)
M_ab -= lib.einsum('mled,nlad,nbem->ab',t2_1, t2_1, eris_ovvo, optimize=True)
M_ab += lib.einsum('lmed,lnad,nmeb->ab',t2_1, t2_1, eris_oovv, optimize=True)
M_ab -= lib.einsum('mled,nlad,nbem->ab',t2_1_a, t2_1, eris_ovvo, optimize=True)
M_ab += lib.einsum('lmde,lnad,nbem->ab',t2_1, t2_1_a, eris_ovvo, optimize=True)
M_ab -= lib.einsum('mlbd,lnae,nmde->ab',t2_1_a, t2_1_a, eris_oovv, optimize=True)
M_ab += lib.einsum('mlbd,lnae,nedm->ab',t2_1_a, t2_1_a, eris_ovvo, optimize=True)
M_ab += lib.einsum('lmbd,lnae,nmde->ab',t2_1, t2_1, eris_oovv, optimize=True)
M_ab -= lib.einsum('lmbd,lnae,nedm->ab',t2_1, t2_1, eris_ovvo, optimize=True)
M_ab += lib.einsum('mlbd,lnae,nedm->ab',t2_1_a, t2_1, eris_ovvo, optimize=True)
M_ab -= lib.einsum('lmbd,lnae,nedm->ab',t2_1, t2_1_a, eris_ovvo, optimize=True)
M_ab += lib.einsum('mlbd,nlae,nmde->ab',t2_1, t2_1, eris_oovv, optimize=True)
M_ab += 0.5*lib.einsum('lned,mled,nmab->ab',t2_1_a, t2_1_a, eris_oovv, optimize=True)
M_ab -= 0.5*lib.einsum('lned,mled,nbam->ab',t2_1_a, t2_1_a, eris_ovvo, optimize=True)
M_ab -= lib.einsum('nled,mled,nmab->ab',t2_1, t2_1, eris_oovv, optimize=True)
M_ab += lib.einsum('nled,mled,nbam->ab',t2_1, t2_1, eris_ovvo, optimize=True)
M_ab += 0.5*lib.einsum('lned,mled,nmab->ab',t2_1_a, t2_1_a, eris_oovv, optimize=True)
M_ab -= lib.einsum('lned,lmed,nmab->ab',t2_1, t2_1, eris_oovv, optimize=True)
M_ab -= 0.25*lib.einsum('mlbd,noad,nmol->ab',t2_1_a, t2_1_a, eris_oooo, optimize=True)
M_ab += 0.25*lib.einsum('mlbd,noad,nlom->ab',t2_1_a, t2_1_a, eris_oooo, optimize=True)
M_ab -= lib.einsum('mlbd,noad,nmol->ab',t2_1, t2_1, eris_oooo, optimize=True)
eris_vvvv = eris.vvvv
t2_1_a_r = t2_1_a.reshape(nocc*nocc,nvir*nvir)
t2_1_r = t2_1.reshape(nocc*nocc,nvir*nvir)
temp = np.dot(t2_1_a_r,eris_vvvv)
temp_n = np.dot(t2_1_r,eris_vvvv)
temp = temp.reshape(nocc,nocc,nvir,nvir)
temp_n = temp_n.reshape(nocc,nocc,nvir,nvir)
M_ab -= 0.25*lib.einsum('mlaf,mlbf->ab',t2_1_a, temp, optimize=True)
M_ab += 0.25*lib.einsum('mlaf,mlfb->ab',t2_1_a, temp, optimize=True)
M_ab -= lib.einsum('mlaf,mlbf->ab',t2_1, temp_n, optimize=True)
temp = np.dot(eris_vvvv,t2_1_a_r.T)
temp = temp.reshape(nvir,nvir,nocc,nocc)
M_ab += 0.25*lib.einsum('adlm,mlbd->ab',temp, t2_1_a, optimize=True)
eris_vvvv = eris_vvvv.reshape(nvir,nvir,nvir,nvir)
M_ab -= 0.25*lib.einsum('mlef,mlbd,adef->ab',t2_1_a, t2_1_a, eris_vvvv, optimize=True)
M_ab -= 0.5*lib.einsum('mldf,mled,aebf->ab',t2_1_a, t2_1_a, eris_vvvv, optimize=True)
M_ab += 0.5*lib.einsum('mldf,mled,aefb->ab',t2_1_a, t2_1_a, eris_vvvv, optimize=True)
M_ab += 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)
M_ab -= lib.einsum('mlef,mlbd,adef->ab',t2_1, t2_1, eris_vvvv, optimize=True)
M_ab -= 0.5*lib.einsum('mldf,mled,aebf->ab',t2_1_a, t2_1_a, eris_vvvv, optimize=True)
M_ab += lib.einsum('mldf,mlde,aebf->ab',t2_1, t2_1, eris_vvvv, optimize=True)
eris_vvvv = eris_vvvv.reshape(nvir*nvir,nvir*nvir)
return M_ab
def get_imds_ip(adc, eris=None):
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]
t2_1 = t2[0]
t2_1_a = t2_1 - t2_1.transpose(1,0,2,3).copy()
nocc = adc._nocc
nvir = adc._nvir
e_occ = adc.mo_energy[:nocc]
e_vir = adc.mo_energy[nocc:]
idn_occ = np.identity(nocc)
idn_vir = np.identity(nvir)
if eris is None:
eris = radc_ao2mo.transform_integrals_incore(adc)
eris_ovov = eris.ovov
# i-j block
# Zeroth-order terms
M_ij = lib.einsum('ij,j->ij', idn_occ ,e_occ)
# Second-order terms
M_ij += lib.einsum('d,ilde,jlde->ij',e_vir,t2_1_a, t2_1_a, optimize=True)
M_ij += lib.einsum('d,ilde,jlde->ij',e_vir,t2_1, t2_1, optimize=True)
M_ij += lib.einsum('d,iled,jled->ij',e_vir,t2_1, t2_1, optimize=True)
M_ij -= 0.5 * lib.einsum('l,ilde,jlde->ij',e_occ,t2_1_a, t2_1_a, optimize=True)
M_ij -= 0.5*lib.einsum('l,ilde,jlde->ij',e_occ,t2_1, t2_1, optimize=True)
M_ij -= 0.5*lib.einsum('l,ilde,jlde->ij',e_occ,t2_1, t2_1, optimize=True)
M_ij -= 0.25 * lib.einsum('i,ilde,jlde->ij',e_occ,t2_1_a, t2_1_a, optimize=True)
M_ij -= 0.25 * lib.einsum('i,ilde,jlde->ij',e_occ,t2_1, t2_1, optimize=True)
M_ij -= 0.25 * lib.einsum('i,ilde,jlde->ij',e_occ,t2_1, t2_1, optimize=True)
M_ij -= 0.25 * lib.einsum('j,ilde,jlde->ij',e_occ,t2_1_a, t2_1_a, optimize=True)
M_ij -= 0.25 * lib.einsum('j,ilde,jlde->ij',e_occ,t2_1, t2_1, optimize=True)
M_ij -= 0.25 * lib.einsum('j,ilde,jlde->ij',e_occ,t2_1, t2_1, optimize=True)
M_ij += 0.5 * lib.einsum('ilde,jdle->ij',t2_1_a, eris_ovov,optimize=True)
M_ij -= 0.5 * lib.einsum('ilde,jeld->ij',t2_1_a, eris_ovov,optimize=True)
M_ij += lib.einsum('ilde,jdle->ij',t2_1, eris_ovov,optimize=True)
M_ij += 0.5 * lib.einsum('jlde,idle->ij',t2_1_a, eris_ovov,optimize=True)
M_ij -= 0.5 * lib.einsum('jlde,ldie->ij',t2_1_a, eris_ovov,optimize=True)
M_ij += lib.einsum('jlde,idle->ij',t2_1, eris_ovov,optimize=True)
# Third-order terms
if (method == "adc(3)"):
t2_2 = t2[1]
t2_2_a = t2_2 - t2_2.transpose(1,0,2,3).copy()
eris_oovv = eris.oovv
eris_ovvo = eris.ovvo
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)
M_ij += 0.5* lib.einsum('ilde,jdle->ij',t2_2_a, eris_ovov,optimize=True)
M_ij -= 0.5* lib.einsum('ilde,jeld->ij',t2_2_a, eris_ovov,optimize=True)
M_ij += lib.einsum('ilde,jdle->ij',t2_2, eris_ovov,optimize=True)
M_ij += 0.5* lib.einsum('jlde,leid->ij',t2_2_a, eris_ovov,optimize=True)
M_ij -= 0.5* lib.einsum('jlde,ield->ij',t2_2_a, eris_ovov,optimize=True)
M_ij += lib.einsum('jlde,leid->ij',t2_2, eris_ovov,optimize=True)
M_ij += lib.einsum('d,ilde,jlde->ij',e_vir,t2_1_a, t2_2_a,optimize=True)
M_ij += lib.einsum('d,ilde,jlde->ij',e_vir,t2_1, t2_2,optimize=True)
M_ij += lib.einsum('d,iled,jled->ij',e_vir,t2_1, t2_2,optimize=True)
M_ij += lib.einsum('d,jlde,ilde->ij',e_vir,t2_1_a, t2_2_a,optimize=True)
M_ij += lib.einsum('d,jlde,ilde->ij',e_vir,t2_1, t2_2,optimize=True)
M_ij += lib.einsum('d,jled,iled->ij',e_vir,t2_1, t2_2,optimize=True)
M_ij -= 0.5 * lib.einsum('l,ilde,jlde->ij',e_occ,t2_1_a, t2_2_a,optimize=True)
M_ij -= 0.5*lib.einsum('l,ilde,jlde->ij',e_occ,t2_1, t2_2,optimize=True)
M_ij -= 0.5*lib.einsum('l,ilde,jlde->ij',e_occ,t2_1, t2_2,optimize=True)
M_ij -= 0.5 * lib.einsum('l,jlde,ilde->ij',e_occ,t2_1_a, t2_2_a,optimize=True)
M_ij -= 0.5*lib.einsum('l,jlde,ilde->ij',e_occ,t2_1, t2_2,optimize=True)
M_ij -= 0.5*lib.einsum('l,jlde,ilde->ij',e_occ,t2_1, t2_2,optimize=True)
M_ij -= 0.25 * lib.einsum('i,ilde,jlde->ij',e_occ,t2_1_a, t2_2_a,optimize=True)
M_ij -= 0.25 * lib.einsum('i,ilde,jlde->ij',e_occ,t2_1, t2_2,optimize=True)
M_ij -= 0.25 * lib.einsum('i,ilde,jlde->ij',e_occ,t2_1, t2_2,optimize=True)
M_ij -= 0.25 * lib.einsum('i,jlde,ilde->ij',e_occ,t2_1_a, t2_2_a,optimize=True)
M_ij -= 0.25 * lib.einsum('i,jlde,ilde->ij',e_occ,t2_1, t2_2,optimize=True)
M_ij -= 0.25 * lib.einsum('i,jlde,ilde->ij',e_occ,t2_1, t2_2,optimize=True)
M_ij -= 0.25 * lib.einsum('j,jlde,ilde->ij',e_occ,t2_1_a, t2_2_a,optimize=True)
M_ij -= 0.25 * lib.einsum('j,jlde,ilde->ij',e_occ,t2_1, t2_2,optimize=True)
M_ij -= 0.25 * lib.einsum('j,jlde,ilde->ij',e_occ,t2_1, t2_2,optimize=True)
M_ij -= 0.25 * lib.einsum('j,ilde,jlde->ij',e_occ,t2_1_a, t2_2_a,optimize=True)
M_ij -= 0.25 * lib.einsum('j,ilde,jlde->ij',e_occ,t2_1, t2_2,optimize=True)
M_ij -= 0.25 * lib.einsum('j,ilde,jlde->ij',e_occ,t2_1, t2_2,optimize=True)
M_ij -= lib.einsum('lmde,jldf,mefi->ij',t2_1_a, t2_1_a, eris_ovvo,optimize = True)
M_ij += lib.einsum('lmde,jldf,mife->ij',t2_1_a, t2_1_a, eris_oovv,optimize = True)
M_ij += lib.einsum('mled,jlfd,mefi->ij',t2_1, t2_1, eris_ovvo ,optimize = True)
M_ij -= lib.einsum('mled,jlfd,mife->ij',t2_1, t2_1, eris_oovv ,optimize = True)
M_ij -= lib.einsum('lmde,jldf,mefi->ij',t2_1, t2_1_a, eris_ovvo,optimize = True)
M_ij -= lib.einsum('mlde,jldf,mife->ij',t2_1, t2_1, eris_oovv ,optimize = True)
M_ij += lib.einsum('lmde,jlfd,mefi->ij',t2_1_a, t2_1, eris_ovvo ,optimize = True)
M_ij -= lib.einsum('lmde,ildf,mefj->ij',t2_1_a, t2_1_a, eris_ovvo ,optimize = True)
M_ij += lib.einsum('lmde,ildf,mjfe->ij',t2_1_a, t2_1_a, eris_oovv ,optimize = True)
M_ij += lib.einsum('mled,ilfd,mefj->ij',t2_1, t2_1, eris_ovvo ,optimize = True)
M_ij -= lib.einsum('mled,ilfd,mjfe->ij',t2_1, t2_1, eris_oovv ,optimize = True)
M_ij -= lib.einsum('lmde,ildf,mefj->ij',t2_1, t2_1_a, eris_ovvo,optimize = True)
M_ij -= lib.einsum('mlde,ildf,mjfe->ij',t2_1, t2_1, eris_oovv ,optimize = True)
M_ij += lib.einsum('lmde,ilfd,mefj->ij',t2_1_a, t2_1, eris_ovvo ,optimize = True)
M_ij += 0.25*lib.einsum('lmde,jnde,limn->ij',t2_1_a, t2_1_a,eris_oooo, optimize = True)
M_ij -= 0.25*lib.einsum('lmde,jnde,lnmi->ij',t2_1_a, t2_1_a,eris_oooo, optimize = True)
M_ij += lib.einsum('lmde,jnde,limn->ij',t2_1 ,t2_1, eris_oooo, optimize = True)
eris_vvvv = eris.vvvv
t2_1_a_r = t2_1_a.reshape(nocc*nocc,nvir*nvir)
t2_1_r = t2_1.reshape(nocc*nocc,nvir*nvir)
temp = np.dot(t2_1_a_r,eris_vvvv)
temp_n = np.dot(t2_1_r,eris_vvvv)
temp = temp.reshape(nocc,nocc,nvir,nvir)
temp_n = temp_n.reshape(nocc,nocc,nvir,nvir)
M_ij += 0.25*lib.einsum('ilde,jlde->ij',t2_1_a, temp, optimize = True)
M_ij -= 0.25*lib.einsum('ilde,jled->ij',t2_1_a, temp, optimize = True)
M_ij +=lib.einsum('ilde,jlde->ij',t2_1, temp_n, optimize = True)
M_ij += 0.25*lib.einsum('inde,lmde,jlnm->ij',t2_1_a, t2_1_a, eris_oooo, optimize = True)
M_ij -= 0.25*lib.einsum('inde,lmde,jmnl->ij',t2_1_a, t2_1_a, eris_oooo, optimize = True)
M_ij +=lib.einsum('inde,lmde,jlnm->ij',t2_1, t2_1, eris_oooo, optimize = True)
M_ij += 0.5*lib.einsum('lmdf,lmde,jief->ij',t2_1_a, t2_1_a, eris_oovv, optimize = True)
M_ij -= 0.5*lib.einsum('lmdf,lmde,jfei->ij',t2_1_a, t2_1_a, eris_ovvo, optimize = True)
M_ij +=lib.einsum('mlfd,mled,jief->ij',t2_1, t2_1, eris_oovv , optimize = True)
M_ij -=lib.einsum('mlfd,mled,jfei->ij',t2_1, t2_1, eris_ovvo , optimize = True)
M_ij +=lib.einsum('lmdf,lmde,jief->ij',t2_1, t2_1, eris_oovv , optimize = True)
M_ij +=0.5*lib.einsum('lmdf,lmde,jief->ij',t2_1_a, t2_1_a, eris_oovv , optimize = True)
M_ij -= lib.einsum('ilde,jmdf,lmfe->ij',t2_1_a, t2_1_a, eris_oovv, optimize = True)
M_ij += lib.einsum('ilde,jmdf,lefm->ij',t2_1_a, t2_1_a, eris_ovvo, optimize = True)
M_ij += lib.einsum('ilde,jmdf,lefm->ij',t2_1_a, t2_1, eris_ovvo, optimize = True)
M_ij += lib.einsum('ilde,jmdf,lefm->ij',t2_1, t2_1_a, eris_ovvo, optimize = True)
M_ij -= lib.einsum('ilde,jmdf,lmfe->ij',t2_1, t2_1, eris_oovv, optimize = True)
M_ij += lib.einsum('ilde,jmdf,lefm->ij',t2_1, t2_1, eris_ovvo, optimize = True)
M_ij -= lib.einsum('iled,jmfd,lmfe->ij',t2_1, t2_1, eris_oovv, optimize = True)
M_ij -= 0.5*lib.einsum('lnde,lmde,jinm->ij',t2_1_a, t2_1_a, eris_oooo, optimize = True)
M_ij += 0.5*lib.einsum('lnde,lmde,jmni->ij',t2_1_a, t2_1_a, eris_oooo, optimize = True)
M_ij -= lib.einsum('nled,mled,jinm->ij',t2_1, t2_1, eris_oooo, optimize = True)
M_ij += lib.einsum('nled,mled,jmni->ij',t2_1, t2_1, eris_oooo, optimize = True)
M_ij -= lib.einsum('lnde,lmde,jinm->ij',t2_1, t2_1, eris_oooo, optimize = True)
M_ij -= 0.5 * lib.einsum('lnde,lmde,jinm->ij',t2_1_a, t2_1_a, eris_oooo, optimize = True)
return M_ij
def ea_adc_diag(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
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:]
idn_occ = np.identity(nocc)
idn_vir = np.identity(nvir)
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
###### Additional terms for the preconditioner ####
if (method == "adc(2)-x" or method == "adc(3)"):
if eris is None:
eris = radc_ao2mo.transform_integrals_incore(adc)
eris_oovv = eris.oovv
eris_vvvv = eris.vvvv
eris_ovvo = eris.ovvo
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 -= np.ascontiguousarray(eris_ovvo.transpose(0,2,3,1))
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)
return diag
def ip_adc_diag(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
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:]
idn_occ = np.identity(nocc)
idn_vir = np.identity(nvir)
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 = radc_ao2mo.transform_integrals_incore(adc)
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 -= np.ascontiguousarray(eris_ovvo.transpose(0,2,3,1))
eris_ovov_p = eris_ovov_p.reshape(nocc*nvir, nocc*nvir)
temp = np.zeros((nocc, nocc, nvir))