#!/usr/bin/env python
# Copyright 2014-2021 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.
'''
Restricted CCSD
Ref: Stanton et al., J. Chem. Phys. 94, 4334 (1990)
Ref: Hirata et al., J. Chem. Phys. 120, 2581 (2004)
'''
from functools import reduce
import numpy as np
from pyscf import lib
from pyscf import ao2mo
from pyscf.lib import logger
from pyscf.cc import ccsd
from pyscf.cc import rintermediates as imd
from pyscf.lib import linalg_helper
#einsum = np.einsum
einsum = lib.einsum
# note MO integrals are treated in chemist's notation
[docs]
def update_amps(cc, t1, t2, eris):
# Ref: Hirata et al., J. Chem. Phys. 120, 2581 (2004) Eqs.(35)-(36)
nocc, nvir = t1.shape
fock = eris.fock
fov = fock[:nocc,nocc:].copy()
foo = fock[:nocc,:nocc].copy()
fvv = fock[nocc:,nocc:].copy()
Foo = imd.cc_Foo(t1,t2,eris)
Fvv = imd.cc_Fvv(t1,t2,eris)
Fov = imd.cc_Fov(t1,t2,eris)
# Move energy terms to the other side
Foo -= np.diag(np.diag(foo))
Fvv -= np.diag(np.diag(fvv))
# T1 equation
t1new = np.asarray(fov).conj().copy()
t1new +=-2*einsum('kc,ka,ic->ia', fov, t1, t1)
t1new += einsum('ac,ic->ia', Fvv, t1)
t1new += -einsum('ki,ka->ia', Foo, t1)
t1new += 2*einsum('kc,kica->ia', Fov, t2)
t1new += -einsum('kc,ikca->ia', Fov, t2)
t1new += einsum('kc,ic,ka->ia', Fov, t1, t1)
t1new += 2*einsum('kcai,kc->ia', eris.ovvo, t1)
t1new += -einsum('kiac,kc->ia', eris.oovv, t1)
eris_ovvv = np.asarray(eris.ovvv)
t1new += 2*einsum('kdac,ikcd->ia', eris_ovvv, t2)
t1new += -einsum('kcad,ikcd->ia', eris_ovvv, t2)
t1new += 2*einsum('kdac,kd,ic->ia', eris_ovvv, t1, t1)
t1new += -einsum('kcad,kd,ic->ia', eris_ovvv, t1, t1)
t1new +=-2*einsum('kilc,klac->ia', eris.ooov, t2)
t1new += einsum('likc,klac->ia', eris.ooov, t2)
t1new +=-2*einsum('kilc,lc,ka->ia', eris.ooov, t1, t1)
t1new += einsum('likc,lc,ka->ia', eris.ooov, t1, t1)
# T2 equation
t2new = np.asarray(eris.ovov).conj().transpose(0,2,1,3).copy()
if cc.cc2:
Woooo2 = np.asarray(eris.oooo).transpose(0,2,1,3).copy()
Woooo2 += einsum('kilc,jc->klij', eris.ooov, t1)
Woooo2 += einsum('ljkc,ic->klij', eris.ooov, t1)
Woooo2 += einsum('kcld,ic,jd->klij', eris.ovov, t1, t1)
t2new += einsum('klij,ka,lb->ijab', Woooo2, t1, t1)
Wvvvv = einsum('kcbd,ka->abcd', eris_ovvv, -t1)
Wvvvv = Wvvvv + Wvvvv.transpose(1,0,3,2)
Wvvvv += np.asarray(eris.vvvv).transpose(0,2,1,3)
t2new += einsum('abcd,ic,jd->ijab', Wvvvv, t1, t1)
Lvv2 = fvv - einsum('kc,ka->ac', fov, t1)
Lvv2 -= np.diag(np.diag(fvv))
tmp = einsum('ac,ijcb->ijab', Lvv2, t2)
t2new += (tmp + tmp.transpose(1,0,3,2))
Loo2 = foo + einsum('kc,ic->ki', fov, t1)
Loo2 -= np.diag(np.diag(foo))
tmp = einsum('ki,kjab->ijab', Loo2, t2)
t2new -= (tmp + tmp.transpose(1,0,3,2))
else:
Loo = imd.Loo(t1, t2, eris)
Lvv = imd.Lvv(t1, t2, eris)
Loo -= np.diag(np.diag(foo))
Lvv -= np.diag(np.diag(fvv))
Woooo = imd.cc_Woooo(t1, t2, eris)
Wvoov = imd.cc_Wvoov(t1, t2, eris)
Wvovo = imd.cc_Wvovo(t1, t2, eris)
Wvvvv = imd.cc_Wvvvv(t1, t2, eris)
tau = t2 + einsum('ia,jb->ijab', t1, t1)
t2new += einsum('klij,klab->ijab', Woooo, tau)
t2new += einsum('abcd,ijcd->ijab', Wvvvv, tau)
tmp = einsum('ac,ijcb->ijab', Lvv, t2)
t2new += (tmp + tmp.transpose(1,0,3,2))
tmp = einsum('ki,kjab->ijab', Loo, t2)
t2new -= (tmp + tmp.transpose(1,0,3,2))
tmp = 2*einsum('akic,kjcb->ijab', Wvoov, t2)
tmp -= einsum('akci,kjcb->ijab', Wvovo, t2)
t2new += (tmp + tmp.transpose(1,0,3,2))
tmp = einsum('akic,kjbc->ijab', Wvoov, t2)
t2new -= (tmp + tmp.transpose(1,0,3,2))
tmp = einsum('bkci,kjac->ijab', Wvovo, t2)
t2new -= (tmp + tmp.transpose(1,0,3,2))
tmp2 = einsum('kibc,ka->abic', eris.oovv, -t1)
tmp2 += np.asarray(eris.ovvv).conj().transpose(1,3,0,2)
tmp = einsum('abic,jc->ijab', tmp2, t1)
t2new += (tmp + tmp.transpose(1,0,3,2))
tmp2 = einsum('kcai,jc->akij', eris.ovvo, t1)
tmp2 += np.asarray(eris.ooov).transpose(3,1,2,0).conj()
tmp = einsum('akij,kb->ijab', tmp2, t1)
t2new -= (tmp + tmp.transpose(1,0,3,2))
mo_e = eris.fock.diagonal().real
eia = mo_e[:nocc,None] - mo_e[None,nocc:]
eijab = lib.direct_sum('ia,jb->ijab',eia,eia)
t1new /= eia
t2new /= eijab
return t1new, t2new
[docs]
def energy(cc, t1, t2, eris):
nocc, nvir = t1.shape
fock = eris.fock
e = 2*einsum('ia,ia', fock[:nocc,nocc:], t1)
tau = einsum('ia,jb->ijab',t1,t1)
tau += t2
eris_ovov = np.asarray(eris.ovov)
e += 2*einsum('ijab,iajb', tau, eris_ovov)
e += -einsum('ijab,ibja', tau, eris_ovov)
return e.real
[docs]
class RCCSD(ccsd.CCSD):
_keys = set(['max_space'])
def __init__(self, mf, frozen=None, mo_coeff=None, mo_occ=None):
ccsd.CCSD.__init__(self, mf, frozen, mo_coeff, mo_occ)
self.max_space = 20
[docs]
def dump_flags(self, verbose=None):
ccsd.CCSD.dump_flags(self, verbose)
[docs]
def init_amps(self, eris):
nocc = self.nocc
mo_e = eris.fock.diagonal().real
eia = mo_e[:nocc,None] - mo_e[None,nocc:]
eijab = lib.direct_sum('ia,jb->ijab', eia, eia)
t1 = eris.fock[:nocc,nocc:].conj() / eia
eris_ovov = np.asarray(eris.ovov)
t2 = eris_ovov.transpose(0,2,1,3).conj() / eijab
self.emp2 = 2*einsum('ijab,iajb', t2, eris_ovov)
self.emp2 -= einsum('ijab,ibja', t2, eris_ovov)
lib.logger.info(self, 'Init t2, MP2 energy = %.15g', self.emp2)
return self.emp2, t1, t2
[docs]
def kernel(self, t1=None, t2=None, eris=None, mbpt2=False, cc2=False):
return self.ccsd(t1, t2, eris, mbpt2, cc2)
[docs]
def ccsd(self, t1=None, t2=None, eris=None, mbpt2=False, cc2=False):
'''Ground-state CCSD.
Kwargs:
mbpt2 : bool
Use one-shot MBPT2 approximation to CCSD.
cc2 : bool
Use CC2 approximation to CCSD.
'''
if mbpt2 and cc2:
raise RuntimeError('MBPT2 and CC2 are mutually exclusive approximations to the CCSD ground state.')
if eris is None: eris = self.ao2mo(self.mo_coeff)
self.e_hf = self.get_e_hf()
self.eris = eris
self.dump_flags()
if mbpt2:
cctyp = 'MBPT2'
self.e_corr, self.t1, self.t2 = self.init_amps(eris)
else:
if cc2:
cctyp = 'CC2'
self.cc2 = True
else:
cctyp = 'CCSD'
self.cc2 = False
self.converged, self.e_corr, self.t1, self.t2 = \
ccsd.kernel(self, eris, t1, t2, max_cycle=self.max_cycle,
tol=self.conv_tol, tolnormt=self.conv_tol_normt,
verbose=self.verbose)
if self.converged:
logger.info(self, '%s converged', cctyp)
else:
logger.info(self, '%s not converged', cctyp)
if self.e_hf == 0:
logger.note(self, 'E_corr = %.16g', self.e_corr)
else:
logger.note(self, 'E(%s) = %.16g E_corr = %.16g',
cctyp, self.e_tot, self.e_corr)
return self.e_corr, self.t1, self.t2
[docs]
def ao2mo(self, mo_coeff=None):
return _ChemistsERIs(self, mo_coeff)
energy = energy
update_amps = update_amps
[docs]
def nip(self):
nocc = self.nocc
nvir = self.nmo - nocc
self._nip = nocc + nocc*nocc*nvir
return self._nip
[docs]
def nea(self):
nocc = self.nocc
nvir = self.nmo - nocc
self._nea = nvir + nocc*nvir*nvir
return self._nea
[docs]
def nee(self):
nocc = self.nocc
nvir = self.nmo - nocc
self._nee = nocc*nvir + nocc*nocc*nvir*nvir
return self._nee
[docs]
def ipccsd(self, nroots=1, left=False, koopmans=False, guess=None, partition=None):
'''Calculate (N-1)-electron charged excitations via IP-EOM-CCSD.
Kwargs:
nroots : int
Number of roots (eigenvalues) requested
partition : bool or str
Use a matrix-partitioning for the doubles-doubles block.
Can be None, 'mp' (Moller-Plesset, i.e. orbital energies on the diagonal),
or 'full' (full diagonal elements).
koopmans : bool
Calculate Koopmans'-like (quasiparticle) excitations only, targeting via
overlap.
guess : list of ndarray
List of guess vectors to use for targeting via overlap.
'''
cput0 = (logger.process_clock(), logger.perf_counter())
log = logger.Logger(self.stdout, self.verbose)
size = self.nip()
nroots = min(nroots,size)
if partition:
partition = partition.lower()
assert partition in ['mp','full']
self.ip_partition = partition
if partition == 'full':
self._ipccsd_diag_matrix2 = self.vector_to_amplitudes_ip(self.ipccsd_diag())[1]
adiag = self.ipccsd_diag()
user_guess = False
if guess:
user_guess = True
assert len(guess) == nroots
for g in guess:
assert g.size == size
else:
guess = []
if koopmans:
for n in range(nroots):
g = np.zeros(size)
g[self.nocc-n-1] = 1.0
guess.append(g)
else:
idx = adiag.argsort()[:nroots]
for i in idx:
g = np.zeros(size)
g[i] = 1.0
guess.append(g)
def precond(r, e0, x0):
return r/(e0-adiag+1e-12)
if left:
matvec = self.lipccsd_matvec
else:
matvec = self.ipccsd_matvec
eig = linalg_helper.eig
if user_guess or koopmans:
def pickeig(w, v, nr, envs):
x0 = linalg_helper._gen_x0(envs['v'], envs['xs'])
idx = np.argmax( np.abs(np.dot(np.array(guess).conj(),np.array(x0).T)), axis=1 )
return lib.linalg_helper._eigs_cmplx2real(w, v, idx)
eip, evecs = eig(matvec, guess, precond, pick=pickeig,
tol=self.conv_tol, max_cycle=self.max_cycle,
max_space=self.max_space, nroots=nroots, verbose=self.verbose)
else:
eip, evecs = eig(matvec, guess, precond,
tol=self.conv_tol, max_cycle=self.max_cycle,
max_space=self.max_space, nroots=nroots, verbose=self.verbose)
self.eip = eip.real
if nroots == 1:
eip, evecs = [self.eip], [evecs]
for n, en, vn in zip(range(nroots), eip, evecs):
logger.info(self, 'IP root %d E = %.16g qpwt = %0.6g',
n, en, np.linalg.norm(vn[:self.nocc])**2)
log.timer('IP-CCSD', *cput0)
if nroots == 1:
return eip[0], evecs[0]
else:
return eip, evecs
[docs]
def ipccsd_matvec(self, vector):
# Ref: Nooijen and Snijders, J. Chem. Phys. 102, 1681 (1995) Eqs.(8)-(9)
if not getattr(self, 'imds', None):
self.imds = _IMDS(self)
if not self.imds.made_ip_imds:
self.imds.make_ip(self.ip_partition)
imds = self.imds
r1,r2 = self.vector_to_amplitudes_ip(vector)
# 1h-1h block
Hr1 = -einsum('ki,k->i',imds.Loo,r1)
#1h-2h1p block
Hr1 += 2*einsum('ld,ild->i',imds.Fov,r2)
Hr1 += -einsum('kd,kid->i',imds.Fov,r2)
Hr1 += -2*einsum('klid,kld->i',imds.Wooov,r2)
Hr1 += einsum('lkid,kld->i',imds.Wooov,r2)
# 2h1p-1h block
Hr2 = -einsum('kbij,k->ijb',imds.Wovoo,r1)
# 2h1p-2h1p block
if self.ip_partition == 'mp':
nocc, nvir = self.t1.shape
fock = self.eris.fock
foo = fock[:nocc,:nocc]
fvv = fock[nocc:,nocc:]
Hr2 += einsum('bd,ijd->ijb',fvv,r2)
Hr2 += -einsum('ki,kjb->ijb',foo,r2)
Hr2 += -einsum('lj,ilb->ijb',foo,r2)
elif self.ip_partition == 'full':
Hr2 += self._ipccsd_diag_matrix2*r2
else:
Hr2 += einsum('bd,ijd->ijb',imds.Lvv,r2)
Hr2 += -einsum('ki,kjb->ijb',imds.Loo,r2)
Hr2 += -einsum('lj,ilb->ijb',imds.Loo,r2)
Hr2 += einsum('klij,klb->ijb',imds.Woooo,r2)
Hr2 += 2*einsum('lbdj,ild->ijb',imds.Wovvo,r2)
Hr2 += -einsum('kbdj,kid->ijb',imds.Wovvo,r2)
Hr2 += -einsum('lbjd,ild->ijb',imds.Wovov,r2) #typo in Ref
Hr2 += -einsum('kbid,kjd->ijb',imds.Wovov,r2)
tmp = 2*einsum('lkdc,kld->c',imds.Woovv,r2)
tmp += -einsum('kldc,kld->c',imds.Woovv,r2)
Hr2 += -einsum('c,ijcb->ijb',tmp,self.t2)
vector = self.amplitudes_to_vector_ip(Hr1,Hr2)
return vector
[docs]
def lipccsd_matvec(self, vector):
if not getattr(self, 'imds', None):
self.imds = _IMDS(self)
if not self.imds.made_ip_imds:
self.imds.make_ip(self.ip_partition)
imds = self.imds
r1,r2 = self.vector_to_amplitudes_ip(vector)
# 1h-1h block
Hr1 = -einsum('ki,i->k',imds.Loo,r1)
#1h-2h1p block
Hr1 += -einsum('kbij,ijb->k',imds.Wovoo,r2)
# 2h1p-1h block
Hr2 = -einsum('kd,l->kld',imds.Fov,r1)
Hr2 += 2.*einsum('ld,k->kld',imds.Fov,r1)
Hr2 += -2.*einsum('klid,i->kld',imds.Wooov,r1)
Hr2 += einsum('lkid,i->kld',imds.Wooov,r1)
# 2h1p-2h1p block
if self.ip_partition == 'mp':
nocc, nvir = self.t1.shape
fock = self.eris.fock
foo = fock[:nocc,:nocc]
fvv = fock[nocc:,nocc:]
Hr2 += einsum('bd,klb->kld',fvv,r2)
Hr2 += -einsum('ki,ild->kld',foo,r2)
Hr2 += -einsum('lj,kjd->kld',foo,r2)
elif self.ip_partition == 'full':
Hr2 += self._ipccsd_diag_matrix2*r2
else:
Hr2 += einsum('bd,klb->kld',imds.Lvv,r2)
Hr2 += -einsum('ki,ild->kld',imds.Loo,r2)
Hr2 += -einsum('lj,kjd->kld',imds.Loo,r2)
Hr2 += 2.*einsum('lbdj,kjb->kld',imds.Wovvo,r2)
Hr2 += -einsum('kbdj,ljb->kld',imds.Wovvo,r2)
Hr2 += -einsum('lbjd,kjb->kld',imds.Wovov,r2)
Hr2 += einsum('klij,ijd->kld',imds.Woooo,r2)
Hr2 += -einsum('kbid,ilb->kld',imds.Wovov,r2)
tmp = einsum('ijcb,ijb->c',t2,r2)
Hr2 += einsum('kldc,c->kld',imds.Woovv,tmp)
Hr2 += -2.*einsum('lkdc,c->kld',imds.Woovv,tmp)
vector = self.amplitudes_to_vector_ip(Hr1,Hr2)
return vector
[docs]
def ipccsd_diag(self):
if not getattr(self, 'imds', None):
self.imds = _IMDS(self)
if not self.imds.made_ip_imds:
self.imds.make_ip(self.ip_partition)
imds = self.imds
t1, t2 = self.t1, self.t2
nocc, nvir = t1.shape
fock = self.eris.fock
foo = fock[:nocc,:nocc]
fvv = fock[nocc:,nocc:]
Hr1 = -np.diag(imds.Loo)
Hr2 = np.zeros((nocc,nocc,nvir), t1.dtype)
for i in range(nocc):
for j in range(nocc):
for b in range(nvir):
if self.ip_partition == 'mp':
Hr2[i,j,b] += fvv[b,b]
Hr2[i,j,b] += -foo[i,i]
Hr2[i,j,b] += -foo[j,j]
else:
Hr2[i,j,b] += imds.Lvv[b,b]
Hr2[i,j,b] += -imds.Loo[i,i]
Hr2[i,j,b] += -imds.Loo[j,j]
Hr2[i,j,b] += imds.Woooo[i,j,i,j]
Hr2[i,j,b] += 2*imds.Wovvo[j,b,b,j]
Hr2[i,j,b] += -imds.Wovvo[i,b,b,i]*(i==j)
Hr2[i,j,b] += -imds.Wovov[j,b,j,b]
Hr2[i,j,b] += -imds.Wovov[i,b,i,b]
Hr2[i,j,b] += -2*np.dot(imds.Woovv[j,i,b,:],t2[i,j,:,b])
Hr2[i,j,b] += np.dot(imds.Woovv[i,j,b,:],t2[i,j,:,b])
vector = self.amplitudes_to_vector_ip(Hr1,Hr2)
return vector
[docs]
def vector_to_amplitudes_ip(self,vector):
nocc = self.nocc
nvir = self.nmo - nocc
r1 = vector[:nocc].copy()
r2 = vector[nocc:].copy().reshape(nocc,nocc,nvir)
return [r1,r2]
[docs]
def amplitudes_to_vector_ip(self,r1,r2):
nocc = self.nocc
nvir = self.nmo - nocc
size = self.nip()
vector = np.zeros(size, r1.dtype)
vector[:nocc] = r1.copy()
vector[nocc:] = r2.copy().reshape(nocc*nocc*nvir)
return vector
[docs]
def ipccsd_star_contract(self, ipccsd_evals, ipccsd_evecs, lipccsd_evecs):
assert self.ip_partition is None
t2, eris = self.t2, self.eris
fock = eris.fock
nocc = self.nocc
nvir = self.nmo - nocc
#fov = fock[:nocc,nocc:]
foo = fock[:nocc,:nocc]
fvv = fock[nocc:,nocc:]
ovov = _cp(eris.ovov)
ovvv = _cp(eris.ovvv)
vovv = ovvv.conj().transpose(1,0,3,2)
oovv = _cp(eris.oovv)
ovvo = _cp(eris.ovvo)
ooov = _cp(eris.ooov)
vooo = ooov.conj().transpose(3,2,1,0)
oooo = _cp(eris.oooo)
eijkab = np.zeros((nocc,nocc,nocc,nvir,nvir))
for i,j,k in lib.cartesian_prod([range(nocc),range(nocc),range(nocc)]):
for a,b in lib.cartesian_prod([range(nvir),range(nvir)]):
eijkab[i,j,k,a,b] = foo[i,i] + foo[j,j] + foo[k,k] - fvv[a,a] - fvv[b,b]
ipccsd_evecs = np.array(ipccsd_evecs)
lipccsd_evecs = np.array(lipccsd_evecs)
e = []
for _eval, _evec, _levec in zip(ipccsd_evals, ipccsd_evecs, lipccsd_evecs):
l1,l2 = self.vector_to_amplitudes_ip(_levec)
r1,r2 = self.vector_to_amplitudes_ip(_evec)
ldotr = np.dot(l1.conj(),r1) + np.dot(l2.ravel(),r2.ravel())
l1 /= ldotr
l2 /= ldotr
l2 = 1./3*(l2 + 2.*l2.transpose(1,0,2))
_eijkab = eijkab + _eval
_eijkab = 1./_eijkab
lijkab = 0.5*einsum('iajb,k->ijkab', ovov, l1)
lijkab += einsum('iaeb,jke->ijkab', ovvv, l2)
lijkab += -einsum('kmjb,ima->ijkab', ooov, l2)
lijkab += -einsum('imjb,mka->ijkab', ooov, l2)
lijkab = lijkab + lijkab.transpose(1,0,2,4,3)
rijkab = -einsum('mkbe,m,ijae->ijkab', oovv, r1, t2)
rijkab -= einsum('mebj,m,ikae->ijkab', ovvo, r1, t2)
rijkab += einsum('mjnk,n,imab->ijkab', oooo, r1, t2)
rijkab += einsum('aibe,kje->ijkab', vovv, r2)
rijkab += -einsum('bjmk,mia->ijkab', vooo, r2)
rijkab += -einsum('bjmi,kma->ijkab', vooo, r2)
rijkab = rijkab + rijkab.transpose(1,0,2,4,3)
lijkab = 4.*lijkab \
- 2.*lijkab.transpose(1,0,2,3,4) \
- 2.*lijkab.transpose(2,1,0,3,4) \
- 2.*lijkab.transpose(0,2,1,3,4) \
+ 1.*lijkab.transpose(1,2,0,3,4) \
+ 1.*lijkab.transpose(2,0,1,3,4)
deltaE = 0.5*einsum('ijkab,ijkab,ijkab',lijkab,rijkab,_eijkab)
deltaE = deltaE.real
logger.note(self, "Exc. energy, delta energy = %16.12f, %16.12f",
_eval+deltaE, deltaE)
e.append(_eval+deltaE)
return e
[docs]
def eaccsd(self, nroots=1, left=False, koopmans=False, guess=None, partition=None):
'''Calculate (N+1)-electron charged excitations via EA-EOM-CCSD.
Kwargs:
See ipccd()
'''
cput0 = (logger.process_clock(), logger.perf_counter())
log = logger.Logger(self.stdout, self.verbose)
size = self.nea()
nroots = min(nroots,size)
if partition:
partition = partition.lower()
assert partition in ['mp','full']
self.ea_partition = partition
if partition == 'full':
self._eaccsd_diag_matrix2 = self.vector_to_amplitudes_ea(self.eaccsd_diag())[1]
adiag = self.eaccsd_diag()
user_guess = False
if guess:
user_guess = True
assert len(guess) == nroots
for g in guess:
assert g.size == size
else:
guess = []
if koopmans:
for n in range(nroots):
g = np.zeros(size)
g[n] = 1.0
guess.append(g)
else:
idx = adiag.argsort()[:nroots]
for i in idx:
g = np.zeros(size)
g[i] = 1.0
guess.append(g)
def precond(r, e0, x0):
return r/(e0-adiag+1e-12)
if left:
matvec = self.leaccsd_matvec
else:
matvec = self.eaccsd_matvec
eig = linalg_helper.eig
if user_guess or koopmans:
def pickeig(w, v, nr, envs):
x0 = linalg_helper._gen_x0(envs['v'], envs['xs'])
idx = np.argmax( np.abs(np.dot(np.array(guess).conj(),np.array(x0).T)), axis=1 )
return lib.linalg_helper._eigs_cmplx2real(w, v, idx)
eea, evecs = eig(matvec, guess, precond, pick=pickeig,
tol=self.conv_tol, max_cycle=self.max_cycle,
max_space=self.max_space, nroots=nroots, verbose=self.verbose)
else:
eea, evecs = eig(matvec, guess, precond,
tol=self.conv_tol, max_cycle=self.max_cycle,
max_space=self.max_space, nroots=nroots, verbose=self.verbose)
self.eea = eea.real
if nroots == 1:
eea, evecs = [self.eea], [evecs]
nvir = self.nmo - self.nocc
for n, en, vn in zip(range(nroots), eea, evecs):
logger.info(self, 'EA root %d E = %.16g qpwt = %0.6g',
n, en, np.linalg.norm(vn[:nvir])**2)
log.timer('EA-CCSD', *cput0)
if nroots == 1:
return eea[0], evecs[0]
else:
return eea, evecs
[docs]
def eaccsd_matvec(self,vector):
# Ref: Nooijen and Bartlett, J. Chem. Phys. 102, 3629 (1994) Eqs.(30)-(31)
if not getattr(self, 'imds', None):
self.imds = _IMDS(self)
if not self.imds.made_ea_imds:
self.imds.make_ea(self.ea_partition)
imds = self.imds
r1,r2 = self.vector_to_amplitudes_ea(vector)
# Eq. (30)
# 1p-1p block
Hr1 = einsum('ac,c->a',imds.Lvv,r1)
# 1p-2p1h block
Hr1 += einsum('ld,lad->a',2.*imds.Fov,r2)
Hr1 += einsum('ld,lda->a', -imds.Fov,r2)
Hr1 += 2*einsum('alcd,lcd->a',imds.Wvovv,r2)
Hr1 += -einsum('aldc,lcd->a',imds.Wvovv,r2)
# Eq. (31)
# 2p1h-1p block
Hr2 = einsum('abcj,c->jab',imds.Wvvvo,r1)
# 2p1h-2p1h block
if self.ea_partition == 'mp':
nocc, nvir = self.t1.shape
fock = self.eris.fock
foo = fock[:nocc,:nocc]
fvv = fock[nocc:,nocc:]
Hr2 += einsum('ac,jcb->jab',fvv,r2)
Hr2 += einsum('bd,jad->jab',fvv,r2)
Hr2 += -einsum('lj,lab->jab',foo,r2)
elif self.ea_partition == 'full':
Hr2 += self._eaccsd_diag_matrix2*r2
else:
Hr2 += einsum('ac,jcb->jab',imds.Lvv,r2)
Hr2 += einsum('bd,jad->jab',imds.Lvv,r2)
Hr2 += -einsum('lj,lab->jab',imds.Loo,r2)
Hr2 += 2*einsum('lbdj,lad->jab',imds.Wovvo,r2)
Hr2 += -einsum('lbjd,lad->jab',imds.Wovov,r2)
Hr2 += -einsum('lajc,lcb->jab',imds.Wovov,r2)
Hr2 += -einsum('lbcj,lca->jab',imds.Wovvo,r2)
nvir = self.nmo-self.nocc
for a in range(nvir):
Hr2[:,a,:] += einsum('bcd,jcd->jb',imds.Wvvvv[a],r2)
tmp = (2*einsum('klcd,lcd->k',imds.Woovv,r2)
-einsum('kldc,lcd->k',imds.Woovv,r2))
Hr2 += -einsum('k,kjab->jab',tmp,self.t2)
vector = self.amplitudes_to_vector_ea(Hr1,Hr2)
return vector
[docs]
def leaccsd_matvec(self,vector):
# Note this is not the same left EA equations used by Nooijen and Bartlett.
# Small changes were made so that the same type L2 basis was used for both the
# left EA and left IP equations. You will note more similarity for these
# equations to the left IP equations than for the left EA equations by Nooijen.
if not getattr(self, 'imds', None):
self.imds = _IMDS(self)
if not self.imds.made_ea_imds:
self.imds.make_ea(self.ea_partition)
imds = self.imds
r1,r2 = self.vector_to_amplitudes_ea(vector)
# Eq. (30)
# 1p-1p block
Hr1 = einsum('ac,a->c',imds.Lvv,r1)
# 1p-2p1h block
Hr1 += einsum('abcj,jab->c',imds.Wvvvo,r2)
# Eq. (31)
# 2p1h-1p block
Hr2 = 2.*einsum('c,ld->lcd',r1,imds.Fov)
Hr2 += -einsum('d,lc->lcd',r1,imds.Fov)
Hr2 += 2.*einsum('a,alcd->lcd',r1,imds.Wvovv)
Hr2 += -einsum('a,aldc->lcd',r1,imds.Wvovv)
# 2p1h-2p1h block
if self.ea_partition == 'mp':
nocc, nvir = self.t1.shape
fock = self.eris.fock
foo = fock[:nocc,:nocc]
fvv = fock[nocc:,nocc:]
Hr2 += einsum('lad,ac->lcd',r2,fvv)
Hr2 += einsum('lcb,bd->lcd',r2,fvv)
Hr2 += -einsum('jcd,lj->lcd',r2,foo)
elif self.ea_partition == 'full':
Hr2 += self._eaccsd_diag_matrix2*r2
else:
Hr2 += einsum('lad,ac->lcd',r2,imds.Lvv)
Hr2 += einsum('lcb,bd->lcd',r2,imds.Lvv)
Hr2 += -einsum('jcd,lj->lcd',r2,imds.Loo)
Hr2 += 2.*einsum('jcb,lbdj->lcd',r2,imds.Wovvo)
Hr2 += -einsum('jcb,lbjd->lcd',r2,imds.Wovov)
Hr2 += -einsum('lajc,jad->lcd',imds.Wovov,r2)
Hr2 += -einsum('lbcj,jdb->lcd',imds.Wovvo,r2)
nvir = self.nmo-self.nocc
for a in range(nvir):
Hr2 += einsum('lb,bcd->lcd',r2[:,a,:],imds.Wvvvv[a])
tmp = einsum('ijcb,ibc->j',t2,r2)
Hr2 += einsum('kjef,j->kef',imds.Woovv,tmp)
Hr2 += -2.*einsum('kjfe,j->kef',imds.Woovv,tmp)
vector = self.amplitudes_to_vector_ea(Hr1,Hr2)
return vector
[docs]
def eaccsd_diag(self):
if not getattr(self, 'imds', None):
self.imds = _IMDS(self)
if not self.imds.made_ea_imds:
self.imds.make_ea(self.ea_partition)
imds = self.imds
t1, t2 = self.t1, self.t2
nocc, nvir = t1.shape
fock = self.eris.fock
foo = fock[:nocc,:nocc]
fvv = fock[nocc:,nocc:]
Hr1 = np.diag(imds.Lvv)
Hr2 = np.zeros((nocc,nvir,nvir), t1.dtype)
for a in range(nvir):
if self.ea_partition != 'mp':
_Wvvvva = np.array(imds.Wvvvv[a])
for b in range(nvir):
for j in range(nocc):
if self.ea_partition == 'mp':
Hr2[j,a,b] += fvv[a,a]
Hr2[j,a,b] += fvv[b,b]
Hr2[j,a,b] += -foo[j,j]
else:
Hr2[j,a,b] += imds.Lvv[a,a]
Hr2[j,a,b] += imds.Lvv[b,b]
Hr2[j,a,b] += -imds.Loo[j,j]
Hr2[j,a,b] += 2*imds.Wovvo[j,b,b,j]
Hr2[j,a,b] += -imds.Wovov[j,b,j,b]
Hr2[j,a,b] += -imds.Wovov[j,a,j,a]
Hr2[j,a,b] += -imds.Wovvo[j,b,b,j]*(a==b)
Hr2[j,a,b] += _Wvvvva[b,a,b]
Hr2[j,a,b] += -2*np.dot(imds.Woovv[:,j,a,b],t2[:,j,a,b])
Hr2[j,a,b] += np.dot(imds.Woovv[:,j,b,a],t2[:,j,a,b])
vector = self.amplitudes_to_vector_ea(Hr1,Hr2)
return vector
[docs]
def vector_to_amplitudes_ea(self,vector):
nocc = self.nocc
nvir = self.nmo - nocc
r1 = vector[:nvir].copy()
r2 = vector[nvir:].copy().reshape(nocc,nvir,nvir)
return [r1,r2]
[docs]
def amplitudes_to_vector_ea(self,r1,r2):
nocc = self.nocc
nvir = self.nmo - nocc
size = self.nea()
vector = np.zeros(size, r1.dtype)
vector[:nvir] = r1.copy()
vector[nvir:] = r2.copy().reshape(nocc*nvir*nvir)
return vector
[docs]
def eaccsd_star_contract(self, eaccsd_evals, eaccsd_evecs, leaccsd_evecs):
assert self.ea_partition is None
t2, eris = self.t2, self.eris
fock = eris.fock
nocc = self.nocc
nvir = self.nmo - nocc
#fov = fock[:nocc,nocc:]
foo = fock[:nocc,:nocc]
fvv = fock[nocc:,nocc:]
ovov = _cp(eris.ovov)
ovvv = _cp(eris.ovvv)
vovv = ovvv.conj().transpose(1,0,3,2)
ooov = _cp(eris.ooov)
vooo = ooov.conj().transpose(3,2,1,0)
oovv = _cp(eris.oovv)
#oooo = _cp(eris.oooo)
vvvv = _cp(eris.vvvv)
ovvo = _cp(eris.ovvo)
eijabc = np.zeros((nocc,nocc,nvir,nvir,nvir))
for i,j in lib.cartesian_prod([range(nocc),range(nocc)]):
for a,b,c in lib.cartesian_prod([range(nvir),range(nvir),range(nvir)]):
eijabc[i,j,a,b,c] = foo[i,i] + foo[j,j] - fvv[a,a] - fvv[b,b] - fvv[c,c]
eaccsd_evecs = np.array(eaccsd_evecs)
leaccsd_evecs = np.array(leaccsd_evecs)
e = []
for _eval, _evec, _levec in zip(eaccsd_evals, eaccsd_evecs, leaccsd_evecs):
l1,l2 = self.vector_to_amplitudes_ea(_levec)
r1,r2 = self.vector_to_amplitudes_ea(_evec)
ldotr = np.dot(l1.conj(),r1) + np.dot(l2.ravel(),r2.ravel())
l1 /= ldotr
l2 /= ldotr
l2 = 1./3*(1.*l2 + 2.*l2.transpose(0,2,1))
r2 = r2.transpose(0,2,1)
_eijabc = eijabc + _eval
_eijabc = 1./_eijabc
lijabc = -0.5*einsum('c,iajb->ijabc', l1, ovov)
lijabc += einsum('jmia,mbc->ijabc', ooov, l2)
lijabc -= einsum('iaeb,jec->ijabc', ovvv, l2)
lijabc -= einsum('jbec,iae->ijabc', ovvv, l2)
lijabc = lijabc + lijabc.transpose(1,0,3,2,4)
rijabc = -einsum('becf,f,ijae->ijabc', vvvv, r1, t2)
rijabc += einsum('mjce,e,imab->ijabc', oovv, r1, t2)
rijabc += einsum('mebj,e,imac->ijabc', ovvo, r1, t2)
rijabc += einsum('aimj,mbc->ijabc', vooo, r2)
rijabc += -einsum('bjce,iae->ijabc', vovv, r2)
rijabc += -einsum('aibe,jec->ijabc', vovv, r2)
rijabc = rijabc + rijabc.transpose(1,0,3,2,4)
lijabc = 4.*lijabc \
- 2.*lijabc.transpose(0,1,3,2,4) \
- 2.*lijabc.transpose(0,1,4,3,2) \
- 2.*lijabc.transpose(0,1,2,4,3) \
+ 1.*lijabc.transpose(0,1,3,4,2) \
+ 1.*lijabc.transpose(0,1,4,2,3)
deltaE = 0.5*einsum('ijabc,ijabc,ijabc',lijabc,rijabc,_eijabc)
deltaE = deltaE.real
logger.note(self, "Exc. energy, delta energy = %16.12f, %16.12f",
_eval+deltaE, deltaE)
e.append(_eval+deltaE)
return e
[docs]
def eeccsd(self, nroots=1, koopmans=False, guess=None, partition=None):
'''Calculate N-electron neutral excitations via EE-EOM-CCSD.
Kwargs:
nroots : int
Number of roots (eigenvalues) requested
partition : bool or str
Use a matrix-partitioning for the doubles-doubles block.
Can be None, 'mp' (Moller-Plesset, i.e. orbital energies on the diagonal),
or 'full' (full diagonal elements).
koopmans : bool
Calculate Koopmans'-like (1p1h) excitations only, targeting via
overlap.
guess : list of ndarray
List of guess vectors to use for targeting via overlap.
'''
cput0 = (logger.process_clock(), logger.perf_counter())
log = logger.Logger(self.stdout, self.verbose)
size = self.nee()
nroots = min(nroots,size)
if partition:
partition = partition.lower()
assert partition in ['mp','full']
self.ee_partition = partition
if partition == 'full':
self._eeccsd_diag_matrix2 = self.vector_to_amplitudes_ee(self.eeccsd_diag())[1]
nvir = self.nmo - self.nocc
adiag = self.eeccsd_diag()
user_guess = False
if guess:
user_guess = True
assert len(guess) == nroots
for g in guess:
assert g.size == size
else:
guess = []
idx = adiag.argsort()
n = 0
for i in idx:
g = np.zeros(size)
g[i] = 1.0
if koopmans:
if np.linalg.norm(g[:self.nocc*nvir])**2 > 0.8:
guess.append(g)
n += 1
else:
guess.append(g)
n += 1
if n == nroots:
break
def precond(r, e0, x0):
return r/(e0-adiag+1e-12)
eig = linalg_helper.eig
if user_guess or koopmans:
def pickeig(w, v, nr, envs):
x0 = linalg_helper._gen_x0(envs['v'], envs['xs'])
idx = np.argmax( np.abs(np.dot(np.array(guess).conj(),np.array(x0).T)), axis=1 )
return lib.linalg_helper._eigs_cmplx2real(w, v, idx)
eee, evecs = eig(self.eeccsd_matvec, guess, precond, pick=pickeig,
tol=self.conv_tol, max_cycle=self.max_cycle,
max_space=self.max_space, nroots=nroots, verbose=self.verbose)
else:
eee, evecs = eig(self.eeccsd_matvec, guess, precond,
tol=self.conv_tol, max_cycle=self.max_cycle,
max_space=self.max_space, nroots=nroots, verbose=self.verbose)
self.eee = eee.real
if nroots == 1:
eee, evecs = [self.eee], [evecs]
for n, en, vn in zip(range(nroots), eee, evecs):
logger.info(self, 'EE root %d E = %.16g qpwt = %0.6g',
n, en, np.linalg.norm(vn[:self.nocc*nvir])**2)
log.timer('EE-CCSD', *cput0)
if nroots == 1:
return eee[0], evecs[0]
else:
return eee, evecs
[docs]
def eeccsd_matvec(self,vector):
raise NotImplementedError
[docs]
def eeccsd_diag(self):
raise NotImplementedError
[docs]
def vector_to_amplitudes_ee(self,vector):
nocc = self.nocc
nvir = self.nmo - nocc
r1 = vector[:nocc*nvir].copy().reshape((nocc,nvir))
r2 = vector[nocc*nvir:].copy().reshape((nocc,nocc,nvir,nvir))
return [r1,r2]
[docs]
def amplitudes_to_vector_ee(self,r1,r2):
nocc = self.nocc
nvir = self.nmo - nocc
size = self.nee()
vector = np.zeros(size, r1.dtype)
vector[:nocc*nvir] = r1.copy().reshape(nocc*nvir)
vector[nocc*nvir:] = r2.copy().reshape(nocc*nocc*nvir*nvir)
return vector
class _ChemistsERIs:
def __init__(self, cc, mo_coeff=None, method='incore',
ao2mofn=ao2mo.outcore.general_iofree):
if mo_coeff is None:
self.mo_coeff = mo_coeff = ccsd._mo_without_core(cc, cc.mo_coeff)
else:
self.mo_coeff = mo_coeff = ccsd._mo_without_core(cc, mo_coeff)
dm = cc._scf.make_rdm1(cc.mo_coeff, cc.mo_occ)
fockao = cc._scf.get_hcore() + cc._scf.get_veff(cc.mol, dm)
self.fock = reduce(np.dot, (mo_coeff.T, fockao, mo_coeff))
nocc = cc.nocc
nmo = cc.nmo
eri1 = ao2mo.incore.full(cc._scf._eri, mo_coeff)
eri1 = ao2mo.restore(1, eri1, nmo)
self.oooo = eri1[:nocc,:nocc,:nocc,:nocc].copy()
self.ooov = eri1[:nocc,:nocc,:nocc,nocc:].copy()
self.ovoo = eri1[:nocc,nocc:,:nocc,:nocc].copy()
self.ovov = eri1[:nocc,nocc:,:nocc,nocc:].copy()
self.oovv = eri1[:nocc,:nocc,nocc:,nocc:].copy()
self.ovvo = eri1[:nocc,nocc:,nocc:,:nocc].copy()
self.ovvv = eri1[:nocc,nocc:,nocc:,nocc:].copy()
self.vvvv = eri1[nocc:,nocc:,nocc:,nocc:].copy()
def get_ovvv(self, *slices):
'''To access a subblock of ovvv tensor'''
if slices:
return self.ovvv[slices]
else:
return self.ovvv
class _IMDS:
def __init__(self, cc):
self.verbose = cc.verbose
self.stdout = cc.stdout
self.t1 = cc.t1
self.t2 = cc.t2
self.eris = cc.eris
self.made_ip_imds = False
self.made_ea_imds = False
self._made_shared_2e = False
def _make_shared_1e(self):
cput0 = (logger.process_clock(), logger.perf_counter())
log = logger.Logger(self.stdout, self.verbose)
t1,t2,eris = self.t1, self.t2, self.eris
self.Loo = imd.Loo(t1,t2,eris)
self.Lvv = imd.Lvv(t1,t2,eris)
self.Fov = imd.cc_Fov(t1,t2,eris)
log.timer('EOM-CCSD shared one-electron intermediates', *cput0)
def _make_shared_2e(self):
cput0 = (logger.process_clock(), logger.perf_counter())
log = logger.Logger(self.stdout, self.verbose)
t1,t2,eris = self.t1, self.t2, self.eris
# 2 virtuals
self.Wovov = imd.Wovov(t1,t2,eris)
self.Wovvo = imd.Wovvo(t1,t2,eris)
self.Woovv = np.asarray(eris.ovov).transpose(0,2,1,3)
log.timer('EOM-CCSD shared two-electron intermediates', *cput0)
def make_ip(self, ip_partition=None):
self._make_shared_1e()
if self._made_shared_2e is False and ip_partition != 'mp':
self._make_shared_2e()
self._made_shared_2e = True
cput0 = (logger.process_clock(), logger.perf_counter())
log = logger.Logger(self.stdout, self.verbose)
t1,t2,eris = self.t1, self.t2, self.eris
# 0 or 1 virtuals
if ip_partition != 'mp':
self.Woooo = imd.Woooo(t1,t2,eris)
self.Wooov = imd.Wooov(t1,t2,eris)
self.Wovoo = imd.Wovoo(t1,t2,eris)
self.made_ip_imds = True
log.timer('EOM-CCSD IP intermediates', *cput0)
def make_ea(self, ea_partition=None):
self._make_shared_1e()
if self._made_shared_2e is False and ea_partition != 'mp':
self._make_shared_2e()
self._made_shared_2e = True
cput0 = (logger.process_clock(), logger.perf_counter())
log = logger.Logger(self.stdout, self.verbose)
t1,t2,eris = self.t1, self.t2, self.eris
# 3 or 4 virtuals
self.Wvovv = imd.Wvovv(t1,t2,eris)
if ea_partition == 'mp':
self.Wvvvo = imd.Wvvvo(t1,t2,eris)
else:
self.Wvvvv = imd.Wvvvv(t1,t2,eris)
self.Wvvvo = imd.Wvvvo(t1,t2,eris,self.Wvvvv)
self.made_ea_imds = True
log.timer('EOM-CCSD EA intermediates', *cput0)
def make_ee(self):
raise NotImplementedError
def _cp(a):
return np.array(a, copy=False, order='C')
if __name__ == '__main__':
from pyscf import scf
from pyscf import gto
mol = gto.M()
nocc, nvir = 5, 12
nmo = nocc + nvir
nmo_pair = nmo*(nmo+1)//2
mf = scf.RHF(mol)
np.random.seed(12)
mf._eri = np.random.random(nmo_pair*(nmo_pair+1)//2)
mf.mo_coeff = np.random.random((nmo,nmo))
mf.mo_energy = np.arange(0., nmo)
mf.mo_occ = np.zeros(nmo)
mf.mo_occ[:nocc] = 2
vhf = mf.get_veff(mol, mf.make_rdm1())
cinv = np.linalg.inv(mf.mo_coeff)
mf.get_hcore = lambda *args: (reduce(np.dot, (cinv.T*mf.mo_energy, cinv)) - vhf)
mycc = RCCSD(mf)
eris = mycc.ao2mo()
a = np.random.random((nmo,nmo)) * .1
eris.fock += a + a.T.conj()
t1 = np.random.random((nocc,nvir)) * .1
t2 = np.random.random((nocc,nocc,nvir,nvir)) * .1
t2 = t2 + t2.transpose(1,0,3,2)
mycc.cc2 = False
t1a, t2a = update_amps(mycc, t1, t2, eris)
print(lib.finger(t1a) - -106360.5276951083)
print(lib.finger(t2a) - 66540.100267798145)
mycc.cc2 = True
t1a, t2a = update_amps(mycc, t1, t2, eris)
print(lib.finger(t1a) - -106360.5276951083)
print(lib.finger(t2a) - -1517.9391800662809)
eri1 = np.random.random((nmo,nmo,nmo,nmo)) + np.random.random((nmo,nmo,nmo,nmo))*1j
eri1 = eri1.transpose(0,2,1,3)
eri1 = eri1 + eri1.transpose(1,0,3,2).conj()
eri1 = eri1 + eri1.transpose(2,3,0,1)
eri1 *= .1
eris.oooo = eri1[:nocc,:nocc,:nocc,:nocc].copy()
eris.ooov = eri1[:nocc,:nocc,:nocc,nocc:].copy()
eris.ovoo = eri1[:nocc,nocc:,:nocc,:nocc].copy()
eris.ovov = eri1[:nocc,nocc:,:nocc,nocc:].copy()
eris.oovv = eri1[:nocc,:nocc,nocc:,nocc:].copy()
eris.ovvo = eri1[:nocc,nocc:,nocc:,:nocc].copy()
eris.ovvv = eri1[:nocc,nocc:,nocc:,nocc:].copy()
eris.vvvv = eri1[nocc:,nocc:,nocc:,nocc:].copy()
a = np.random.random((nmo,nmo)) * .1j
eris.fock = eris.fock + a + a.T.conj()
t1 = t1 + np.random.random((nocc,nvir)) * .1j
t2 = t2 + np.random.random((nocc,nocc,nvir,nvir)) * .1j
t2 = t2 + t2.transpose(1,0,3,2)
mycc.cc2 = False
t1a, t2a = update_amps(mycc, t1, t2, eris)
print(lib.finger(t1a) - (-13.32050019680894-1.8825765910430254j))
print(lib.finger(t2a) - (9.2521062044785189+29.999480274811873j))
mycc.cc2 = True
t1a, t2a = update_amps(mycc, t1, t2, eris)
print(lib.finger(t1a) - (-13.32050019680894-1.8825765910430254j))
print(lib.finger(t2a) - (-0.056223856104895858+0.025472249329733986j))
mol = gto.Mole()
mol.atom = [
[8 , (0. , 0. , 0.)],
[1 , (0. , -0.757 , 0.587)],
[1 , (0. , 0.757 , 0.587)]]
mol.basis = 'cc-pvdz'
#mol.basis = '3-21G'
mol.verbose = 0
mol.spin = 0
mol.build()
mf = scf.RHF(mol).run(conv_tol=1e-14)
mycc = RCCSD(mf)
eris = mycc.ao2mo()
emp2, t1, t2 = mycc.init_amps(eris)
print(lib.finger(t2) - 0.044540097905897198)
np.random.seed(1)
t1 = np.random.random(t1.shape)*.1
t2 = np.random.random(t2.shape)*.1
t2 = t2 + t2.transpose(1,0,3,2)
t1, t2 = update_amps(mycc, t1, t2, eris)
print(lib.finger(t1) - 0.25118555558133576)
print(lib.finger(t2) - 0.02352137419932243)
ecc, t1, t2 = mycc.kernel()
print(ecc - -0.21334326214236796)
part = None
print("IP energies... (right eigenvector)")
e,v = mycc.ipccsd(nroots=3)
print(e[0] - 0.43356041409195489)
print(e[1] - 0.51876598058509493)
print(e[2] - 0.6782879569941862 )
print("IP energies... (left eigenvector)")
le,lv = mycc.ipccsd(nroots=3,left=True)
print(le[0] - 0.43356040428879794)
print(le[1] - 0.51876597800180335)
print(le[2] - 0.67828755013874864)
e = mycc.ipccsd_star_contract(e,v,lv)
print(e[0] - 0.43793202073189047)
print(e[1] - 0.52287073446559729)
print(e[2] - 0.67994597948852287)
print("EA energies... (right eigenvector)")
e,v = mycc.eaccsd(nroots=3)
print(e[0] - 0.16737886282063008)
print(e[1] - 0.24027622989542635)
print(e[2] - 0.51006796667905585)
print("EA energies... (left eigenvector)")
le,lv = mycc.eaccsd(nroots=3,left=True)
print(le[0] - 0.16737896537079733)
print(le[1] - 0.24027634198123343)
print(le[2] - 0.51006809015066612)
e = mycc.eaccsd_star_contract(e,v,lv)
print(e[0] - 0.16656250953550664)
print(e[1] - 0.23944144521387614)
print(e[2] - 0.41399436888830721)
# Note: Not implemented
#e,v = mycc.eeccsd(nroots=4)