def IX_intermediates(mycc, t1, t2, l1, l2, d1=None, d2=None, eris=None):
if d1 is None:
doo, dov, dvo, dvv = ccsd_t_rdm.gamma1_intermediates(mycc, t1, t2, l1, l2, eris)
else:
doo, dov, dvo, dvv = d1
if d2 is None:
# Note gamma2 are in Chemist's notation
d2 = ccsd_t_rdm.gamma2_intermediates(mycc, t1, t2, l1, l2, eris)
else:
dovov, dvvvv, doooo, doovv, dovvo, dvvov, dovvv, dooov = d2
if dovvv is None:
dovvv = dvvov.transpose(2,3,0,1)
elif dvvov is None:
dvvov = dovvv.transpose(2,3,0,1)
nocc, nvir = t1.shape
eris_ovvv = _ccsd.unpack_tril(_cp(eris.ovvv).reshape(nocc*nvir,-1))
eris_ovvv = eris_ovvv.reshape(nocc,nvir,nvir,nvir)
eris_vvvv = pyscf.ao2mo.restore(1, _cp(eris.vvvv), nvir)
dvvvv = pyscf.ao2mo.restore(1, _cp(dvvvv), nvir)
# Note Ioo is not hermitian
Ioo =(numpy.einsum('jakb,iakb->ij', dovov, eris.ovov)
+ numpy.einsum('kbja,iakb->ij', dovov, eris.ovov))
Ioo +=(numpy.einsum('jabk,iakb->ij', dovvo, eris.ovov)
+ numpy.einsum('kbaj,iakb->ij', dovvo, eris.ovov)
+ numpy.einsum('jkab,ikab->ij', doovv, eris.oovv)
+ numpy.einsum('kjba,ikab->ij', doovv, eris.oovv))
Ioo +=(numpy.einsum('jmlk,imlk->ij', doooo, eris.oooo) * 2
+ numpy.einsum('mjkl,imlk->ij', doooo, eris.oooo) * 2)
Ioo +=(numpy.einsum('jlka,ilka->ij', dooov, eris.ooov)
+ numpy.einsum('klja,klia->ij', dooov, eris.ooov))
Ioo += numpy.einsum('abjc,icab->ij', dvvov, eris_ovvv)
Ioo += numpy.einsum('ljka,lika->ij', dooov, eris.ooov)
Ioo *= -1
# Note Ivv is not hermitian
Ivv =(numpy.einsum('ibjc,iajc->ab', dovov, eris.ovov)
+ numpy.einsum('jcib,iajc->ab', dovov, eris.ovov))
Ivv +=(numpy.einsum('jcbi,iajc->ab', dovvo, eris.ovov)
+ numpy.einsum('ibcj,iajc->ab', dovvo, eris.ovov)
+ numpy.einsum('jibc,jiac->ab', doovv, eris.oovv)
+ numpy.einsum('ijcb,jiac->ab', doovv, eris.oovv))
Ivv +=(numpy.einsum('bced,aced->ab', dvvvv, eris_vvvv) * 2
+ numpy.einsum('cbde,aced->ab', dvvvv, eris_vvvv) * 2)
Ivv +=(numpy.einsum('dbic,icda->ab', dvvov, eris_ovvv)
+ numpy.einsum('dcib,iadc->ab', dvvov, eris_ovvv))
Ivv += numpy.einsum('bcid,idac->ab', dvvov, eris_ovvv)
Ivv += numpy.einsum('jikb,jika->ab', dooov, eris.ooov)
Ivv *= -1
Ivo =(numpy.einsum('kajb,kijb->ai', dovov, eris.ooov)
+ numpy.einsum('kbja,jikb->ai', dovov, eris.ooov))
Ivo +=(numpy.einsum('acbd,icbd->ai', dvvvv, eris_ovvv) * 2
+ numpy.einsum('cadb,icbd->ai', dvvvv, eris_ovvv) * 2)
Ivo +=(numpy.einsum('jbak,jbik->ai', dovvo, eris.ovoo)
+ numpy.einsum('kabj,jbik->ai', dovvo, eris.ovoo)
+ numpy.einsum('jkab,jkib->ai', doovv, eris.ooov)
+ numpy.einsum('kjba,jkib->ai', doovv, eris.ooov))
Ivo +=(numpy.einsum('dajc,idjc->ai', dvvov, eris.ovov)
+ numpy.einsum('dcja,jidc->ai', dvvov, eris.oovv))
Ivo += numpy.einsum('abjc,ibjc->ai', dvvov, eris.ovov)
Ivo += numpy.einsum('jlka,jlki->ai', dooov, eris.oooo)
Ivo *= -1
Xvo =(numpy.einsum('kj,kjia->ai', doo, eris.ooov) * 2
+ numpy.einsum('kj,kjia->ai', doo, eris.ooov) * 2
- numpy.einsum('kj,kija->ai', doo, eris.ooov)
- numpy.einsum('kj,ijka->ai', doo, eris.ooov))
Xvo +=(numpy.einsum('cb,iacb->ai', dvv, eris_ovvv) * 2
+ numpy.einsum('cb,iacb->ai', dvv, eris_ovvv) * 2
- numpy.einsum('cb,icab->ai', dvv, eris_ovvv)
- numpy.einsum('cb,ibca->ai', dvv, eris_ovvv))
Xvo +=(numpy.einsum('icjb,jbac->ai', dovov, eris_ovvv)
+ numpy.einsum('jcib,jcab->ai', dovov, eris_ovvv))
Xvo +=(numpy.einsum('iklj,ljka->ai', doooo, eris.ooov) * 2
+ numpy.einsum('kijl,ljka->ai', doooo, eris.ooov) * 2)
Xvo +=(numpy.einsum('ibcj,jcab->ai', dovvo, eris_ovvv)
+ numpy.einsum('jcbi,jcab->ai', dovvo, eris_ovvv)
+ numpy.einsum('ijcb,jacb->ai', doovv, eris_ovvv)
+ numpy.einsum('jibc,jacb->ai', doovv, eris_ovvv))
Xvo +=(numpy.einsum('ijkb,jakb->ai', dooov, eris.ovov)
+ numpy.einsum('kjib,kjab->ai', dooov, eris.oovv))
Xvo += numpy.einsum('dbic,dbac->ai', dvvov, eris_vvvv)
Xvo += numpy.einsum('jikb,jakb->ai', dooov, eris.ovov)
Xvo += Ivo
return Ioo, Ivv, Ivo, Xvo
def IX_intermediates(mycc, t1, t2, l1, l2, d1=None, d2=None, eris=None):
if d1 is None:
doo, dov, dvo, dvv = ccsd_t_rdm.gamma1_intermediates(
mycc, t1, t2, l1, l2, eris)
else:
doo, dov, dvo, dvv = d1
if d2 is None:
# Note gamma2 are in Chemist's notation
d2 = ccsd_t_rdm.gamma2_intermediates(mycc, t1, t2, l1, l2, eris)
else:
dovov, dvvvv, doooo, doovv, dovvo, dvvov, dovvv, dooov = d2
if dovvv is None:
dovvv = dvvov.transpose(2, 3, 0, 1)
elif dvvov is None:
dvvov = dovvv.transpose(2, 3, 0, 1)
nocc, nvir = t1.shape
eris_ovvv = lib.unpack_tril(_cp(eris.ovvv).reshape(nocc * nvir, -1))
eris_ovvv = eris_ovvv.reshape(nocc, nvir, nvir, nvir)
eris_vvvv = pyscf.ao2mo.restore(1, _cp(eris.vvvv), nvir)
dvvvv = pyscf.ao2mo.restore(1, _cp(dvvvv), nvir)
# Note Ioo is not hermitian
Ioo = (numpy.einsum('jakb,iakb->ij', dovov, eris.ovov) +
numpy.einsum('kbja,iakb->ij', dovov, eris.ovov))
Ioo += (numpy.einsum('jabk,iakb->ij', dovvo, eris.ovov) +
numpy.einsum('kbaj,iakb->ij', dovvo, eris.ovov) +
numpy.einsum('jkab,ikab->ij', doovv, eris.oovv) +
numpy.einsum('kjba,ikab->ij', doovv, eris.oovv))
Ioo += (numpy.einsum('jmlk,imlk->ij', doooo, eris.oooo) * 2 +
numpy.einsum('mjkl,imlk->ij', doooo, eris.oooo) * 2)
Ioo += (numpy.einsum('jlka,ilka->ij', dooov, eris.ooov) +
numpy.einsum('klja,klia->ij', dooov, eris.ooov))
Ioo += numpy.einsum('abjc,icab->ij', dvvov, eris_ovvv)
Ioo += numpy.einsum('ljka,lika->ij', dooov, eris.ooov)
Ioo *= -1
# Note Ivv is not hermitian
Ivv = (numpy.einsum('ibjc,iajc->ab', dovov, eris.ovov) +
numpy.einsum('jcib,iajc->ab', dovov, eris.ovov))
Ivv += (numpy.einsum('jcbi,iajc->ab', dovvo, eris.ovov) +
numpy.einsum('ibcj,iajc->ab', dovvo, eris.ovov) +
numpy.einsum('jibc,jiac->ab', doovv, eris.oovv) +
numpy.einsum('ijcb,jiac->ab', doovv, eris.oovv))
Ivv += (numpy.einsum('bced,aced->ab', dvvvv, eris_vvvv) * 2 +
numpy.einsum('cbde,aced->ab', dvvvv, eris_vvvv) * 2)
Ivv += (numpy.einsum('dbic,icda->ab', dvvov, eris_ovvv) +
numpy.einsum('dcib,iadc->ab', dvvov, eris_ovvv))
Ivv += numpy.einsum('bcid,idac->ab', dvvov, eris_ovvv)
Ivv += numpy.einsum('jikb,jika->ab', dooov, eris.ooov)
Ivv *= -1
Ivo = (numpy.einsum('kajb,kijb->ai', dovov, eris.ooov) +
numpy.einsum('kbja,jikb->ai', dovov, eris.ooov))
Ivo += (numpy.einsum('acbd,icbd->ai', dvvvv, eris_ovvv) * 2 +
numpy.einsum('cadb,icbd->ai', dvvvv, eris_ovvv) * 2)
Ivo += (numpy.einsum('jbak,jbik->ai', dovvo, eris.ovoo) +
numpy.einsum('kabj,jbik->ai', dovvo, eris.ovoo) +
numpy.einsum('jkab,jkib->ai', doovv, eris.ooov) +
numpy.einsum('kjba,jkib->ai', doovv, eris.ooov))
Ivo += (numpy.einsum('dajc,idjc->ai', dvvov, eris.ovov) +
numpy.einsum('dcja,jidc->ai', dvvov, eris.oovv))
Ivo += numpy.einsum('abjc,ibjc->ai', dvvov, eris.ovov)
Ivo += numpy.einsum('jlka,jlki->ai', dooov, eris.oooo)
Ivo *= -1
Xvo = (numpy.einsum('kj,kjia->ai', doo, eris.ooov) * 2 +
numpy.einsum('kj,kjia->ai', doo, eris.ooov) * 2 -
numpy.einsum('kj,kija->ai', doo, eris.ooov) -
numpy.einsum('kj,ijka->ai', doo, eris.ooov))
Xvo += (numpy.einsum('cb,iacb->ai', dvv, eris_ovvv) * 2 +
numpy.einsum('cb,iacb->ai', dvv, eris_ovvv) * 2 -
numpy.einsum('cb,icab->ai', dvv, eris_ovvv) -
numpy.einsum('cb,ibca->ai', dvv, eris_ovvv))
Xvo += (numpy.einsum('icjb,jbac->ai', dovov, eris_ovvv) +
numpy.einsum('jcib,jcab->ai', dovov, eris_ovvv))
Xvo += (numpy.einsum('iklj,ljka->ai', doooo, eris.ooov) * 2 +
numpy.einsum('kijl,ljka->ai', doooo, eris.ooov) * 2)
Xvo += (numpy.einsum('ibcj,jcab->ai', dovvo, eris_ovvv) +
numpy.einsum('jcbi,jcab->ai', dovvo, eris_ovvv) +
numpy.einsum('ijcb,jacb->ai', doovv, eris_ovvv) +
numpy.einsum('jibc,jacb->ai', doovv, eris_ovvv))
Xvo += (numpy.einsum('ijkb,jakb->ai', dooov, eris.ovov) +
numpy.einsum('kjib,kjab->ai', dooov, eris.oovv))
Xvo += numpy.einsum('dbic,dbac->ai', dvvov, eris_vvvv)
Xvo += numpy.einsum('jikb,jakb->ai', dooov, eris.ovov)
Xvo += Ivo
return Ioo, Ivv, Ivo, Xvo
def kernel(mycc, t1=None, t2=None, l1=None, l2=None, eris=None, atmlst=None,
mf_grad=None, verbose=logger.INFO):
if t1 is None: t1 = mycc.t1
if t2 is None: t2 = mycc.t2
if l1 is None: l1 = mycc.l1
if l2 is None: l2 = mycc.l2
if eris is None: eris = ccsd._ERIS(mycc)
if mf_grad is None:
mf_grad = pyscf.grad.RHF(mycc._scf)
log = logger.Logger(mycc.stdout, mycc.verbose)
time0 = time.clock(), time.time()
mol = mycc.mol
moidx = numpy.ones(mycc.mo_energy.size, dtype=numpy.bool)
if isinstance(mycc.frozen, (int, numpy.integer)):
raise NotImplementedError('frozen orbital ccsd_grad')
moidx[:mycc.frozen] = False
else:
moidx[mycc.frozen] = False
mo_coeff = mycc.mo_coeff[:,moidx] #FIXME: ensure mycc.mo_coeff is canonical orbital
mo_energy = mycc.mo_energy[moidx]
nocc, nvir = t1.shape
nao, nmo = mo_coeff.shape
nao_pair = nao * (nao+1) // 2
log.debug('Build ccsd rdm1 intermediates')
d1 = ccsd_t_rdm.gamma1_intermediates(mycc, t1, t2, l1, l2, eris)
doo, dov, dvo, dvv = d1
time1 = log.timer('rdm1 intermediates', *time0)
log.debug('Build ccsd rdm2 intermediates')
d2 = ccsd_t_rdm.gamma2_intermediates(mycc, t1, t2, l1, l2, eris)
time1 = log.timer('rdm2 intermediates', *time1)
log.debug('Build ccsd response_rdm1')
Ioo, Ivv, Ivo, Xvo = IX_intermediates(mycc, t1, t2, l1, l2, d1, d2, eris)
time1 = log.timer('response_rdm1 intermediates', *time1)
dm1mo = ccsd_grad.response_dm1(mycc, t1, t2, l1, l2, eris, (Ioo, Ivv, Ivo, Xvo))
dm1mo[:nocc,:nocc] = doo * 2
dm1mo[nocc:,nocc:] = dvv * 2
dm1ao = reduce(numpy.dot, (mo_coeff, dm1mo, mo_coeff.T))
im1 = numpy.zeros_like(dm1mo)
im1[:nocc,:nocc] = Ioo
im1[nocc:,nocc:] = Ivv
im1[nocc:,:nocc] = Ivo
im1[:nocc,nocc:] = Ivo.T
im1 = reduce(numpy.dot, (mo_coeff, im1, mo_coeff.T))
time1 = log.timer('response_rdm1', *time1)
log.debug('symmetrized rdm2 and MO->AO transformation')
dm2ao = ccsd_grad._rdm2_mo2ao(mycc, d2, dm1mo, mo_coeff)
time1 = log.timer('MO->AO transformation', *time1)
#TODO: pass hf_grad object to compute h1 and s1
log.debug('h1 and JK1')
h1 = mf_grad.get_hcore(mol)
s1 = mf_grad.get_ovlp(mol)
zeta = numpy.empty((nmo,nmo))
zeta[:nocc,:nocc] = (mo_energy[:nocc].reshape(-1,1) + mo_energy[:nocc]) * .5
zeta[nocc:,nocc:] = (mo_energy[nocc:].reshape(-1,1) + mo_energy[nocc:]) * .5
zeta[nocc:,:nocc] = mo_energy[:nocc]
zeta[:nocc,nocc:] = mo_energy[:nocc].reshape(-1,1)
zeta = reduce(numpy.dot, (mo_coeff, zeta*dm1mo, mo_coeff.T))
p1 = numpy.dot(mo_coeff[:,:nocc], mo_coeff[:,:nocc].T)
vhf4sij = reduce(numpy.dot, (p1, mycc._scf.get_veff(mol, dm1ao+dm1ao.T), p1))
time1 = log.timer('h1 and JK1', *time1)
# Hartree-Fock part contribution
hf_dm1 = mycc._scf.make_rdm1(mycc.mo_coeff, mycc.mo_occ)
dm1ao += hf_dm1
zeta += mf_grad.make_rdm1e(mycc.mo_energy, mycc.mo_coeff, mycc.mo_occ)
if atmlst is None:
atmlst = range(mol.natm)
offsetdic = mol.offset_nr_by_atom()
de = numpy.zeros((len(atmlst),3))
for k, ia in enumerate(atmlst):
shl0, shl1, p0, p1 = offsetdic[ia]
# s[1] dot I, note matrix im1 is not hermitian
de[k] =(numpy.einsum('xij,ij->x', s1[:,p0:p1], im1[p0:p1])
+ numpy.einsum('xji,ij->x', s1[:,p0:p1], im1[:,p0:p1]))
# h[1] \dot DM, *2 for +c.c., contribute to f1
vrinv = mf_grad._grad_rinv(mol, ia)
de[k] +=(numpy.einsum('xij,ij->x', h1[:,p0:p1], dm1ao[p0:p1] )
+ numpy.einsum('xji,ij->x', h1[:,p0:p1], dm1ao[:,p0:p1]))
de[k] +=(numpy.einsum('xij,ij->x', vrinv, dm1ao)
+ numpy.einsum('xji,ij->x', vrinv, dm1ao))
# -s[1]*e \dot DM, contribute to f1
de[k] -=(numpy.einsum('xij,ij->x', s1[:,p0:p1], zeta[p0:p1] )
+ numpy.einsum('xji,ij->x', s1[:,p0:p1], zeta[:,p0:p1]))
# -vhf[s_ij[1]], contribute to f1, *2 for s1+s1.T
de[k] -= numpy.einsum('xij,ij->x', s1[:,p0:p1], vhf4sij[p0:p1]) * 2
# 2e AO integrals dot 2pdm
eri1 = gto.moleintor.getints('cint2e_ip1_sph', mol._atm, mol._bas,
mol._env, numpy.arange(shl0,shl1), comp=3,
aosym='s2kl').reshape(3,p1-p0,nao,-1)
dm2buf = ccsd_grad._load_block_tril(dm2ao, p0, p1)
de[k] -= numpy.einsum('xijk,ijk->x', eri1, dm2buf) * 2
for i in range(3):
#:tmp = _ccsd.unpack_tril(eri1[i].reshape(-1,nao_pair))
#:vj = numpy.einsum('ijkl,kl->ij', tmp, hf_dm1)
#:vk = numpy.einsum('ijkl,jk->il', tmp, hf_dm1)
vj, vk = ccsd_grad.hf_get_jk_incore(eri1[i], hf_dm1)
de[k,i] -=(numpy.einsum('ij,ij->', vj, hf_dm1[p0:p1])
- numpy.einsum('ij,ij->', vk, hf_dm1[p0:p1])*.5) * 2
eri1 = dm2buf = None
log.debug('grad of atom %d %s = %s', ia, mol.atom_symbol(ia), de[k])
time1 = log.timer('grad of atom %d'%ia, *time1)
log.note('CCSD gradinets')
log.note('==============')
log.note(' x y z')
for k, ia in enumerate(atmlst):
log.note('%d %s %15.9f %15.9f %15.9f', ia, mol.atom_symbol(ia),
de[k,0], de[k,1], de[k,2])
log.timer('CCSD gradients', *time0)
return de
def kernel(mycc,
t1=None,
t2=None,
l1=None,
l2=None,
eris=None,
atmlst=None,
mf_grad=None,
verbose=logger.INFO):
if t1 is None: t1 = mycc.t1
if t2 is None: t2 = mycc.t2
if l1 is None: l1 = mycc.l1
if l2 is None: l2 = mycc.l2
if eris is None: eris = ccsd._ERIS(mycc)
if mf_grad is None:
mf_grad = pyscf.grad.RHF(mycc._scf)
log = logger.Logger(mycc.stdout, mycc.verbose)
time0 = time.clock(), time.time()
mol = mycc.mol
moidx = numpy.ones(mycc.mo_energy.size, dtype=numpy.bool)
if isinstance(mycc.frozen, (int, numpy.integer)):
raise NotImplementedError('frozen orbital ccsd_grad')
moidx[:mycc.frozen] = False
else:
moidx[mycc.frozen] = False
mo_coeff = mycc.mo_coeff[:,
moidx] #FIXME: ensure mycc.mo_coeff is canonical orbital
mo_energy = mycc.mo_energy[moidx]
nocc, nvir = t1.shape
nao, nmo = mo_coeff.shape
nao_pair = nao * (nao + 1) // 2
log.debug('Build ccsd rdm1 intermediates')
d1 = ccsd_t_rdm.gamma1_intermediates(mycc, t1, t2, l1, l2, eris)
doo, dov, dvo, dvv = d1
time1 = log.timer('rdm1 intermediates', *time0)
log.debug('Build ccsd rdm2 intermediates')
d2 = ccsd_t_rdm.gamma2_intermediates(mycc, t1, t2, l1, l2, eris)
time1 = log.timer('rdm2 intermediates', *time1)
log.debug('Build ccsd response_rdm1')
Ioo, Ivv, Ivo, Xvo = IX_intermediates(mycc, t1, t2, l1, l2, d1, d2, eris)
time1 = log.timer('response_rdm1 intermediates', *time1)
dm1mo = ccsd_grad.response_dm1(mycc, t1, t2, l1, l2, eris,
(Ioo, Ivv, Ivo, Xvo))
dm1mo[:nocc, :nocc] = doo * 2
dm1mo[nocc:, nocc:] = dvv * 2
dm1ao = reduce(numpy.dot, (mo_coeff, dm1mo, mo_coeff.T))
im1 = numpy.zeros_like(dm1mo)
im1[:nocc, :nocc] = Ioo
im1[nocc:, nocc:] = Ivv
im1[nocc:, :nocc] = Ivo
im1[:nocc, nocc:] = Ivo.T
im1 = reduce(numpy.dot, (mo_coeff, im1, mo_coeff.T))
time1 = log.timer('response_rdm1', *time1)
log.debug('symmetrized rdm2 and MO->AO transformation')
dm2ao = ccsd_grad._rdm2_mo2ao(mycc, d2, dm1mo, mo_coeff)
time1 = log.timer('MO->AO transformation', *time1)
#TODO: pass hf_grad object to compute h1 and s1
log.debug('h1 and JK1')
h1 = mf_grad.get_hcore(mol)
s1 = mf_grad.get_ovlp(mol)
zeta = numpy.empty((nmo, nmo))
zeta[:nocc, :nocc] = (mo_energy[:nocc].reshape(-1, 1) +
mo_energy[:nocc]) * .5
zeta[nocc:,
nocc:] = (mo_energy[nocc:].reshape(-1, 1) + mo_energy[nocc:]) * .5
zeta[nocc:, :nocc] = mo_energy[:nocc]
zeta[:nocc, nocc:] = mo_energy[:nocc].reshape(-1, 1)
zeta = reduce(numpy.dot, (mo_coeff, zeta * dm1mo, mo_coeff.T))
p1 = numpy.dot(mo_coeff[:, :nocc], mo_coeff[:, :nocc].T)
vhf4sij = reduce(numpy.dot,
(p1, mycc._scf.get_veff(mol, dm1ao + dm1ao.T), p1))
time1 = log.timer('h1 and JK1', *time1)
# Hartree-Fock part contribution
hf_dm1 = mycc._scf.make_rdm1(mycc.mo_coeff, mycc.mo_occ)
dm1ao += hf_dm1
zeta += mf_grad.make_rdm1e(mycc.mo_energy, mycc.mo_coeff, mycc.mo_occ)
if atmlst is None:
atmlst = range(mol.natm)
offsetdic = mol.offset_nr_by_atom()
de = numpy.zeros((len(atmlst), 3))
for k, ia in enumerate(atmlst):
shl0, shl1, p0, p1 = offsetdic[ia]
# s[1] dot I, note matrix im1 is not hermitian
de[k] = (numpy.einsum('xij,ij->x', s1[:, p0:p1], im1[p0:p1]) +
numpy.einsum('xji,ij->x', s1[:, p0:p1], im1[:, p0:p1]))
# h[1] \dot DM, *2 for +c.c., contribute to f1
vrinv = mf_grad._grad_rinv(mol, ia)
de[k] += (numpy.einsum('xij,ij->x', h1[:, p0:p1], dm1ao[p0:p1]) +
numpy.einsum('xji,ij->x', h1[:, p0:p1], dm1ao[:, p0:p1]))
de[k] += (numpy.einsum('xij,ij->x', vrinv, dm1ao) +
numpy.einsum('xji,ij->x', vrinv, dm1ao))
# -s[1]*e \dot DM, contribute to f1
de[k] -= (numpy.einsum('xij,ij->x', s1[:, p0:p1], zeta[p0:p1]) +
numpy.einsum('xji,ij->x', s1[:, p0:p1], zeta[:, p0:p1]))
# -vhf[s_ij[1]], contribute to f1, *2 for s1+s1.T
de[k] -= numpy.einsum('xij,ij->x', s1[:, p0:p1], vhf4sij[p0:p1]) * 2
# 2e AO integrals dot 2pdm
eri1 = mol.intor('cint2e_ip1_sph',
comp=3,
aosym='s2kl',
shls_slice=(shl0, shl1, 0, mol.nbas, 0, mol.nbas, 0,
mol.nbas))
eri1 = eri1.reshape(3, p1 - p0, nao, -1)
dm2buf = ccsd_grad._load_block_tril(dm2ao, p0, p1)
de[k] -= numpy.einsum('xijk,ijk->x', eri1, dm2buf) * 2
for i in range(3):
#:tmp = lib.unpack_tril(eri1[i].reshape(-1,nao_pair))
#:vj = numpy.einsum('ijkl,kl->ij', tmp, hf_dm1)
#:vk = numpy.einsum('ijkl,jk->il', tmp, hf_dm1)
vj, vk = ccsd_grad.hf_get_jk_incore(eri1[i], hf_dm1)
de[k, i] -= (numpy.einsum('ij,ij->', vj, hf_dm1[p0:p1]) -
numpy.einsum('ij,ij->', vk, hf_dm1[p0:p1]) * .5) * 2
eri1 = dm2buf = None
log.debug('grad of atom %d %s = %s', ia, mol.atom_symbol(ia), de[k])
time1 = log.timer('grad of atom %d' % ia, *time1)
log.note('CCSD gradinets')
log.note('==============')
log.note(' x y z')
for k, ia in enumerate(atmlst):
log.note('%d %s %15.9f %15.9f %15.9f', ia, mol.atom_symbol(ia),
de[k, 0], de[k, 1], de[k, 2])
log.timer('CCSD gradients', *time0)
return de
