def cc_Wovvo(t1,t2,eris):
eris_ovvo = - _cp(eris.ovov).transpose(0,1,3,2)
eris_oovo = - _cp(eris.ooov).transpose(0,1,3,2)
Wmbej = eris_ovvo.copy()
Wmbej += einsum('jf,mbef->mbej',t1,eris.ovvv)
Wmbej += -einsum('nb,mnej->mbej',t1,eris_oovo)
Wmbej += -0.5*einsum('jnfb,mnef->mbej',t2,eris.oovv)
Wmbej += -einsum('jf,nb,mnef->mbej',t1,t1,eris.oovv)
return Wmbej
def cc_Wovvo(t1, t2, eris):
eris_ovvo = -_cp(eris.ovov).transpose(0, 1, 3, 2)
eris_oovo = -_cp(eris.ooov).transpose(0, 1, 3, 2)
Wmbej = eris_ovvo.copy()
Wmbej += einsum('jf,mbef->mbej', t1, eris.ovvv)
Wmbej += -einsum('nb,mnej->mbej', t1, eris_oovo)
Wmbej += -0.5 * einsum('jnfb,mnef->mbej', t2, eris.oovv)
Wmbej += -einsum('jf,nb,mnef->mbej', t1, t1, eris.oovv)
return Wmbej
def init_amps(self, eris):
time0 = time.clock(), time.time()
mo_e = eris.fock.diagonal()
nocc = self.nocc()
nvir = mo_e.size - nocc
t1 = np.zeros((nocc,nvir), eris.dtype)
#eia = mo_e[:nocc,None] - mo_e[None,nocc:]
#t1 = eris.fock[:nocc,nocc:] / eia
t2 = np.zeros((nocc,nocc,nvir,nvir), eris.dtype)
self.emp2 = 0
foo = eris.fock[:nocc,:nocc]
fvv = eris.fock[nocc:,nocc:]
eia = np.zeros((nocc,nvir))
eijab = np.zeros((nocc,nocc,nvir,nvir))
for i in range(nocc):
for a in range(nvir):
eia[i,a] = (foo[i,i] - fvv[a,a]).real
for j in range(nocc):
for b in range(nvir):
eijab[i,j,a,b] = ( foo[i,i] + foo[j,j]
- fvv[a,a] - fvv[b,b] ).real
t2[i,j,a,b] = eris.oovv[i,j,a,b]/eijab[i,j,a,b]
eris_oovv = _cp(eris.oovv)
self.emp2 = 0.25*einsum('ijab,ijab',t2,eris_oovv.conj()).real
logger.info(self, 'Init t2, MP2 energy = %.15g', self.emp2)
logger.timer(self, 'init mp2', *time0)
return self.emp2, t1, t2
def Wvvvo(t1,t2,eris):
eris_ovvo = - _cp(eris.ovov).transpose(0,1,3,2)
eris_vvvo = - _cp(eris.ovvv).transpose(2,3,1,0).conj()
eris_oovo = - _cp(eris.ooov).transpose(0,1,3,2)
tmp1 = einsum('mbef,miaf->abei',eris.ovvv,t2)
tmp2 = ( einsum('ma,mbei->abei',t1,eris_ovvo)
- einsum('ma,nibf,mnef->abei',t1,t2,eris.oovv) )
FFov = Fov(t1,t2,eris)
WWvvvv = Wvvvv(t1,t2,eris)
tau = make_tau(t2,t1,t1)
Wabei = ( eris_vvvo - einsum('me,miab->abei',FFov,t2)
+ einsum('if,abef->abei',t1,WWvvvv)
+ 0.5 * einsum('mnei,mnab->abei',eris_oovo,tau)
- tmp1 + tmp1.transpose(1,0,2,3)
- tmp2 + tmp2.transpose(1,0,2,3) )
return Wabei
def cc_Wvvvv(t1,t2,eris):
eris_vovv = _cp(eris.ovvv).transpose(1,0,3,2)
tau = make_tau(t2,t1,t1)
tmp = einsum('mb,amef->abef',t1,eris_vovv)
Wabef = eris.vvvv - tmp + tmp.transpose(1,0,2,3)
Wabef += 0.25*einsum('mnab,mnef->abef',tau,eris.oovv)
return Wabef
def Wvvvo_incore(t1, t2, eris):
eris_ovvo = -_cp(eris.ovov).transpose(0, 1, 3, 2)
eris_vvvo = -_cp(eris.ovvv).transpose(2, 3, 1, 0).conj()
eris_oovo = -_cp(eris.ooov).transpose(0, 1, 3, 2)
tmp1 = einsum('mbef,miaf->abei', eris.ovvv, t2)
tmp2 = (einsum('ma,mbei->abei', t1, eris_ovvo) -
einsum('ma,nibf,mnef->abei', t1, t2, eris.oovv))
FFov = Fov(t1, t2, eris)
#TODO: Wasteful to create Wvvvv twice (now cc_Wvvvv three times!)
WWvvvv = Wvvvv(t1, t2, eris)
tau = make_tau(t2, t1, t1)
Wabei = (eris_vvvo - einsum('me,miab->abei', FFov, t2) +
einsum('if,abef->abei', t1, WWvvvv) +
0.5 * einsum('mnei,mnab->abei', eris_oovo, tau) - tmp1 +
tmp1.transpose(1, 0, 2, 3) - tmp2 + tmp2.transpose(1, 0, 2, 3))
return Wabei
def Wvvvo_incore(t1,t2,eris):
eris_ovvo = - _cp(eris.ovov).transpose(0,1,3,2)
eris_vvvo = - _cp(eris.ovvv).transpose(2,3,1,0).conj()
eris_oovo = - _cp(eris.ooov).transpose(0,1,3,2)
tmp1 = einsum('mbef,miaf->abei',eris.ovvv,t2)
tmp2 = ( einsum('ma,mbei->abei',t1,eris_ovvo)
- einsum('ma,nibf,mnef->abei',t1,t2,eris.oovv) )
FFov = Fov(t1,t2,eris)
#TODO: Wasteful to create Wvvvv twice (now cc_Wvvvv three times!)
WWvvvv = Wvvvv(t1,t2,eris)
tau = make_tau(t2,t1,t1)
Wabei = ( eris_vvvo - einsum('me,miab->abei',FFov,t2)
+ einsum('if,abef->abei',t1,WWvvvv)
+ 0.5 * einsum('mnei,mnab->abei',eris_oovo,tau)
- tmp1 + tmp1.transpose(1,0,2,3)
- tmp2 + tmp2.transpose(1,0,2,3) )
return Wabei
def cc_Fvv(t1, t2, eris):
nocc, nvir = t1.shape
fov = eris.fock[:nocc, nocc:]
fvv = eris.fock[nocc:, nocc:]
eris_vovv = _cp(eris.ovvv).transpose(1, 0, 3, 2)
tau_tilde = make_tau(t2, t1, t1, fac=0.5)
Fae = (fvv - 0.5 * einsum('me,ma->ae', fov, t1) +
einsum('mf,amef->ae', t1, eris_vovv) -
0.5 * einsum('mnaf,mnef->ae', tau_tilde, eris.oovv))
return Fae
def cc_Fvv(t1,t2,eris):
nocc, nvir = t1.shape
fov = eris.fock[:nocc,nocc:]
fvv = eris.fock[nocc:,nocc:]
eris_vovv = _cp(eris.ovvv).transpose(1,0,3,2)
tau_tilde = make_tau(t2,t1,t1,fac=0.5)
Fae = ( fvv - 0.5*einsum('me,ma->ae',fov,t1)
+ einsum('mf,amef->ae',t1,eris_vovv)
- 0.5*einsum('mnaf,mnef->ae',tau_tilde,eris.oovv) )
return Fae
def Wvvvo(t1, t2, eris):
eris_ovvo = -_cp(eris.ovov).transpose(0, 1, 3, 2)
eris_vvvo = -_cp(eris.ovvv).transpose(2, 3, 1, 0).conj()
eris_oovo = -_cp(eris.ooov).transpose(0, 1, 3, 2)
tmp1 = einsum('mbef,miaf->abei', eris.ovvv, t2)
tmp2 = (einsum('ma,mbei->abei', t1, eris_ovvo) -
einsum('ma,nibf,mnef->abei', t1, t2, eris.oovv))
FFov = Fov(t1, t2, eris)
tau = make_tau(t2, t1, t1)
Wabei = eris_vvvo
Wabei += -einsum('me,miab->abei', FFov, t2)
Wabei += 0.5 * einsum('mnei,mnab->abei', eris_oovo, tau)
Wabei += -tmp1 + tmp1.transpose(1, 0, 2, 3)
Wabei += -tmp2 + tmp2.transpose(1, 0, 2, 3)
nocc, nvir = t1.shape
#TODO: Wasteful to create Wvvvv twice (now cc_Wvvvv three times!)
_Wvvvv = Wvvvv(t1, t2, eris)
for a in range(nvir):
Wabei[a] += einsum('if,bef->bei', t1, _Wvvvv[a])
return Wabei
def energy(cc, t1, t2, eris):
nocc, nvir = t1.shape
fock = eris.fock
e = einsum('ia,ia', fock[:nocc,nocc:], t1)
t1t1 = einsum('ia,jb->ijab',t1,t1)
tau = t2 + 2*t1t1
eris_oovv = _cp(eris.oovv)
e += 0.25 * np.dot(tau.flatten(), eris_oovv.flatten())
#e += (0.25*np.einsum('ijab,ijab',t2,eris_oovv)
# + 0.5*np.einsum('ia,jb,ijab',t1,t1,eris_oovv))
return e.real
def Wvvvo(t1,t2,eris):
eris_ovvo = - _cp(eris.ovov).transpose(0,1,3,2)
eris_vvvo = - _cp(eris.ovvv).transpose(2,3,1,0).conj()
eris_oovo = - _cp(eris.ooov).transpose(0,1,3,2)
tmp1 = einsum('mbef,miaf->abei',eris.ovvv,t2)
tmp2 = ( einsum('ma,mbei->abei',t1,eris_ovvo)
- einsum('ma,nibf,mnef->abei',t1,t2,eris.oovv) )
FFov = Fov(t1,t2,eris)
tau = make_tau(t2,t1,t1)
Wabei = eris_vvvo
Wabei += -einsum('me,miab->abei',FFov,t2)
Wabei += 0.5 * einsum('mnei,mnab->abei',eris_oovo,tau)
Wabei += -tmp1 + tmp1.transpose(1,0,2,3)
Wabei += -tmp2 + tmp2.transpose(1,0,2,3)
nocc,nvir = t1.shape
#TODO: Wasteful to create Wvvvv twice (now cc_Wvvvv three times!)
_Wvvvv = Wvvvv(t1,t2,eris)
for a in range(nvir):
Wabei[a] += einsum('if,bef->bei',t1,_Wvvvv[a])
return Wabei
def Wovoo(t1, t2, eris):
eris_ovvo = -_cp(eris.ovov).transpose(0, 1, 3, 2)
tmp1 = einsum('mnie,jnbe->mbij', eris.ooov, t2)
tmp2 = (einsum('ie,mbej->mbij', t1, eris_ovvo) -
einsum('ie,njbf,mnef->mbij', t1, t2, eris.oovv))
FFov = Fov(t1, t2, eris)
WWoooo = Woooo(t1, t2, eris)
tau = make_tau(t2, t1, t1)
Wmbij = (eris.ovoo - einsum('me,ijbe->mbij', FFov, t2) -
einsum('nb,mnij->mbij', t1, WWoooo) +
0.5 * einsum('mbef,ijef->mbij', eris.ovvv, tau) + tmp1 -
tmp1.transpose(0, 1, 3, 2) + tmp2 - tmp2.transpose(0, 1, 3, 2))
return Wmbij
def Wovoo(t1,t2,eris):
eris_ovvo = - _cp(eris.ovov).transpose(0,1,3,2)
tmp1 = einsum('mnie,jnbe->mbij',eris.ooov,t2)
tmp2 = ( einsum('ie,mbej->mbij',t1,eris_ovvo)
- einsum('ie,njbf,mnef->mbij',t1,t2,eris.oovv) )
FFov = Fov(t1,t2,eris)
WWoooo = Woooo(t1,t2,eris)
tau = make_tau(t2,t1,t1)
Wmbij = ( eris.ovoo - einsum('me,ijbe->mbij',FFov,t2)
- einsum('nb,mnij->mbij',t1,WWoooo)
+ 0.5 * einsum('mbef,ijef->mbij',eris.ovvv,tau)
+ tmp1 - tmp1.transpose(0,1,3,2)
+ tmp2 - tmp2.transpose(0,1,3,2) )
return Wmbij
def Wvovv(t1, t2, eris):
eris_vovv = -_cp(eris.ovvv).transpose(1, 0, 2, 3)
Wamef = eris_vovv - einsum('na,nmef->amef', t1, eris.oovv)
return Wamef
def Wvovv(t1,t2,eris):
eris_vovv = - _cp(eris.ovvv).transpose(1,0,2,3)
Wamef = eris_vovv - einsum('na,nmef->amef',t1,eris.oovv)
return Wamef
def update_amps(cc, t1, t2, eris, max_memory=2000):
time0 = time.clock(), time.time()
log = logger.Logger(cc.stdout, cc.verbose)
nocc, nvir = t1.shape
#nov = nocc*nvir
fock = eris.fock
#t1new = numpy.zeros_like(t1)
#t2new = numpy.zeros_like(t2)
fov = fock[:nocc,nocc:]
foo = fock[:nocc,:nocc]
fvv = fock[nocc:,nocc:]
mo_e = eris.fock.diagonal()
eia = mo_e[:nocc,None] - mo_e[None,nocc:]
eijab = lib.direct_sum('ia,jb->ijab',eia,eia)
tau = imd.make_tau(t2,t1,t1)
Fvv = imd.cc_Fvv(t1,t2,eris)
Foo = imd.cc_Foo(t1,t2,eris)
Fov = imd.cc_Fov(t1,t2,eris)
Woooo = imd.cc_Woooo(t1,t2,eris)
Wvvvv = imd.cc_Wvvvv(t1,t2,eris)
Wovvo = imd.cc_Wovvo(t1,t2,eris)
# Move energy terms to the other side
Fvv -= fvv
Foo -= foo
# eris might be an HDF5 Dataset, so _cp to ndarray
eris_oovo = - _cp(eris.ooov).transpose(0,1,3,2)
eris_ovvo = - _cp(eris.ovov).transpose(0,1,3,2)
eris_vvvo = - _cp(eris.ovvv).transpose(2,3,1,0).conj()
# T1 equation
# TODO: Does this need a conj()? Usually zero w/ canonical HF.
t1new = fov.copy()
t1new += einsum('ie,ae->ia',t1,Fvv)
t1new += -einsum('ma,mi->ia',t1,Foo)
t1new += einsum('imae,me->ia',t2,Fov)
t1new += -einsum('nf,naif->ia',t1,eris.ovov)
t1new += -0.5*einsum('imef,maef->ia',t2,eris.ovvv)
t1new += -0.5*einsum('mnae,nmei->ia',t2,eris_oovo)
# T2 equation
# For conj(), see Hirata and Bartlett, Eq. (36)
t2new = np.array(eris.oovv, copy=True).conj()
Ftmp = Fvv - 0.5*einsum('mb,me->be',t1,Fov)
tmp = einsum('ijae,be->ijab',t2,Ftmp)
t2new += (tmp - tmp.transpose(0,1,3,2))
Ftmp = Foo + 0.5*einsum('je,me->mj',t1,Fov)
tmp = einsum('imab,mj->ijab',t2,Ftmp)
t2new -= (tmp - tmp.transpose(1,0,2,3))
t2new += ( 0.5*einsum('mnab,mnij->ijab',tau,Woooo)
+ 0.5*einsum('ijef,abef->ijab',tau,Wvvvv) )
tmp = einsum('imae,mbej->ijab',t2,Wovvo)
tmp -= einsum('ie,ma,mbej->ijab',t1,t1,eris_ovvo)
t2new += ( tmp - tmp.transpose(0,1,3,2)
- tmp.transpose(1,0,2,3) + tmp.transpose(1,0,3,2) )
tmp = einsum('ie,abej->ijab',t1,eris_vvvo)
t2new += (tmp - tmp.transpose(1,0,2,3))
tmp = einsum('ma,mbij->ijab',t1,eris.ovoo)
t2new -= (tmp - tmp.transpose(0,1,3,2))
t1new /= eia
t2new /= eijab
time0 = log.timer_debug1('update t1 t2', *time0)
return t1new, t2new