def test_h2o_rdm(self):
mol = mol_s2
mf = mf_s2
mycc = uccsd.UCCSD(mf)
mycc.frozen = 2
ecc, t1, t2 = mycc.kernel()
l1, l2 = mycc.solve_lambda()
dm1a, dm1b = mycc.make_rdm1(t1, t2, l1, l2)
dm2aa, dm2ab, dm2bb = mycc.make_rdm2(t1, t2, l1, l2)
mo_a = mf.mo_coeff[0]
mo_b = mf.mo_coeff[1]
nmoa = mo_a.shape[1]
nmob = mo_b.shape[1]
eriaa = ao2mo.kernel(mf._eri, mo_a, compact=False).reshape([nmoa] * 4)
eribb = ao2mo.kernel(mf._eri, mo_b, compact=False).reshape([nmob] * 4)
eriab = ao2mo.kernel(mf._eri, (mo_a, mo_a, mo_b, mo_b), compact=False)
eriab = eriab.reshape([nmoa, nmoa, nmob, nmob])
hcore = mf.get_hcore()
h1a = reduce(numpy.dot, (mo_a.T.conj(), hcore, mo_a))
h1b = reduce(numpy.dot, (mo_b.T.conj(), hcore, mo_b))
e1 = numpy.einsum('ij,ji', h1a, dm1a)
e1 += numpy.einsum('ij,ji', h1b, dm1b)
e1 += numpy.einsum('ijkl,ijkl', eriaa, dm2aa) * .5
e1 += numpy.einsum('ijkl,ijkl', eriab, dm2ab)
e1 += numpy.einsum('ijkl,ijkl', eribb, dm2bb) * .5
e1 += mol.energy_nuc()
self.assertAlmostEqual(e1, mycc.e_tot, 7)
d1 = uccsd_rdm._gamma1_intermediates(mycc, mycc.t1, mycc.t2, mycc.l1,
mycc.l2)
mycc.max_memory = 0
d2 = uccsd_rdm._gamma2_intermediates(mycc, mycc.t1, mycc.t2, mycc.l1,
mycc.l2, True)
dm2 = uccsd_rdm._make_rdm2(mycc,
d1,
d2,
with_dm1=True,
with_frozen=True)
e1 = numpy.einsum('ij,ji', h1a, dm1a)
e1 += numpy.einsum('ij,ji', h1b, dm1b)
e1 += numpy.einsum('ijkl,ijkl', eriaa, dm2[0]) * .5
e1 += numpy.einsum('ijkl,ijkl', eriab, dm2[1])
e1 += numpy.einsum('ijkl,ijkl', eribb, dm2[2]) * .5
e1 += mol.energy_nuc()
self.assertAlmostEqual(e1, mycc.e_tot, 7)
def test_h2o_rdm(self):
mol = mol_s2
mf = mf_s2
mycc = uccsd.UCCSD(mf)
mycc.frozen = 2
ecc, t1, t2 = mycc.kernel()
l1, l2 = mycc.solve_lambda()
dm1a,dm1b = mycc.make_rdm1(t1, t2, l1, l2)
dm2aa,dm2ab,dm2bb = mycc.make_rdm2(t1, t2, l1, l2)
mo_a = mf.mo_coeff[0]
mo_b = mf.mo_coeff[1]
nmoa = mo_a.shape[1]
nmob = mo_b.shape[1]
eriaa = ao2mo.kernel(mf._eri, mo_a, compact=False).reshape([nmoa]*4)
eribb = ao2mo.kernel(mf._eri, mo_b, compact=False).reshape([nmob]*4)
eriab = ao2mo.kernel(mf._eri, (mo_a,mo_a,mo_b,mo_b), compact=False)
eriab = eriab.reshape([nmoa,nmoa,nmob,nmob])
hcore = mf.get_hcore()
h1a = reduce(numpy.dot, (mo_a.T.conj(), hcore, mo_a))
h1b = reduce(numpy.dot, (mo_b.T.conj(), hcore, mo_b))
e1 = numpy.einsum('ij,ji', h1a, dm1a)
e1+= numpy.einsum('ij,ji', h1b, dm1b)
e1+= numpy.einsum('ijkl,ijkl', eriaa, dm2aa) * .5
e1+= numpy.einsum('ijkl,ijkl', eriab, dm2ab)
e1+= numpy.einsum('ijkl,ijkl', eribb, dm2bb) * .5
e1+= mol.energy_nuc()
self.assertAlmostEqual(e1, mycc.e_tot, 7)
d1 = uccsd_rdm._gamma1_intermediates(mycc, mycc.t1, mycc.t2, mycc.l1, mycc.l2)
mycc.max_memory = 0
d2 = uccsd_rdm._gamma2_intermediates(mycc, mycc.t1, mycc.t2, mycc.l1, mycc.l2, True)
dm2 = uccsd_rdm._make_rdm2(mycc, d1, d2, with_dm1=True, with_frozen=True)
e1 = numpy.einsum('ij,ji', h1a, dm1a)
e1+= numpy.einsum('ij,ji', h1b, dm1b)
e1+= numpy.einsum('ijkl,ijkl', eriaa, dm2[0]) * .5
e1+= numpy.einsum('ijkl,ijkl', eriab, dm2[1])
e1+= numpy.einsum('ijkl,ijkl', eribb, dm2[2]) * .5
e1+= mol.energy_nuc()
self.assertAlmostEqual(e1, mycc.e_tot, 7)
def _gamma1_intermediates(mycc, t1, t2, l1, l2, eris=None, for_grad=False):
d1 = uccsd_rdm._gamma1_intermediates(mycc, t1, t2, l1, l2)
if eris is None: eris = mycc.ao2mo()
t1a, t1b = t1
t2aa, t2ab, t2bb = t2
nocca, noccb, nvira, nvirb = t2ab.shape
nmoa = eris.focka.shape[0]
nmob = eris.fockb.shape[0]
mo_ea = eris.focka.diagonal().real
mo_eb = eris.fockb.diagonal().real
eia = mo_ea[:nocca, None] - mo_ea[nocca:]
eIA = mo_eb[:noccb, None] - mo_eb[noccb:]
fvo = eris.focka[nocca:, :nocca]
fVO = eris.fockb[noccb:, :noccb]
# aaa
d3 = lib.direct_sum('ia+jb+kc->ijkabc', eia, eia, eia)
w = numpy.einsum('ijae,kceb->ijkabc', t2aa,
numpy.asarray(eris.get_ovvv()).conj())
w -= numpy.einsum('mkbc,iajm->ijkabc', t2aa,
numpy.asarray(eris.ovoo.conj()))
v = numpy.einsum('jbkc,ia->ijkabc', numpy.asarray(eris.ovov).conj(), t1a)
v += numpy.einsum('jkbc,ai->ijkabc', t2aa, fvo) * .5
rw = p6(r6(w)) / d3
wvd = p6(w + v) / d3
goo = numpy.einsum('iklabc,jklabc->ij', wvd.conj(), rw) * .125
gvv = numpy.einsum('ijkacd,ijkbcd->ab', wvd, rw.conj()) * .125
gvo = numpy.einsum('jkbc,ijkabc->ai', t2aa.conj(), rw) * .125
# bbb
d3 = lib.direct_sum('ia+jb+kc->ijkabc', eIA, eIA, eIA)
w = numpy.einsum('ijae,kceb->ijkabc', t2bb,
numpy.asarray(eris.get_OVVV()).conj())
w -= numpy.einsum('imab,kcjm->ijkabc', t2bb,
numpy.asarray(eris.OVOO.conj()))
v = numpy.einsum('jbkc,ia->ijkabc', numpy.asarray(eris.OVOV).conj(), t1b)
v += numpy.einsum('jkbc,ai->ijkabc', t2bb, fVO) * .5
rw = p6(r6(w)) / d3
wvd = p6(w + v) / d3
gOO = numpy.einsum('iklabc,jklabc->ij', wvd.conj(), rw) * .125
gVV = numpy.einsum('ijkacd,ijkbcd->ab', wvd, rw.conj()) * .125
gVO = numpy.einsum('jkbc,ijkabc->ai', t2bb.conj(), rw) * .125
# baa
d3 = lib.direct_sum('ia+jb+kc->ijkabc', eIA, eia, eia)
w = numpy.einsum('jIeA,kceb->IjkAbc', t2ab,
numpy.asarray(eris.get_ovvv()).conj()) * 2
w += numpy.einsum('jIbE,kcEA->IjkAbc', t2ab,
numpy.asarray(eris.get_ovVV()).conj()) * 2
w += numpy.einsum('jkbe,IAec->IjkAbc', t2aa,
numpy.asarray(eris.get_OVvv()).conj())
w -= numpy.einsum('mIbA,kcjm->IjkAbc', t2ab,
numpy.asarray(eris.ovoo).conj()) * 2
w -= numpy.einsum('jMbA,kcIM->IjkAbc', t2ab,
numpy.asarray(eris.ovOO).conj()) * 2
w -= numpy.einsum('jmbc,IAkm->IjkAbc', t2aa,
numpy.asarray(eris.OVoo).conj())
v = numpy.einsum('jbkc,IA->IjkAbc', numpy.asarray(eris.ovov).conj(), t1b)
v += numpy.einsum('kcIA,jb->IjkAbc', numpy.asarray(eris.ovOV).conj(), t1a)
v += numpy.einsum('kcIA,jb->IjkAbc', numpy.asarray(eris.ovOV).conj(), t1a)
v += numpy.einsum('jkbc,AI->IjkAbc', t2aa, fVO) * .5
v += numpy.einsum('kIcA,bj->IjkAbc', t2ab, fvo) * 2
rw = r4(w) / d3
wvd = (w + v) / d3
goo += numpy.einsum('kilabc,kjlabc->ij', wvd.conj(), rw) * .25
goo += numpy.einsum('kliabc,kljabc->ij', wvd.conj(), rw) * .25
gOO += numpy.einsum('iklabc,jklabc->ij', wvd.conj(), rw) * .25
gvv += numpy.einsum('ijkcad,ijkcbd->ab', wvd, rw.conj()) * .25
gvv += numpy.einsum('ijkcda,ijkcdb->ab', wvd, rw.conj()) * .25
gVV += numpy.einsum('ijkacd,ijkbcd->ab', wvd, rw.conj()) * .25
gvo += numpy.einsum('kica,ijkabc->bj', t2ab.conj(), rw) * .5
gVO += numpy.einsum('jkbc,ijkabc->ai', t2aa.conj(), rw) * .125
# bba
d3 = lib.direct_sum('ia+jb+kc->ijkabc', eia, eIA, eIA)
w = numpy.einsum('ijae,kceb->ijkabc', t2ab,
numpy.asarray(eris.get_OVVV()).conj()) * 2
w += numpy.einsum('ijeb,kcea->ijkabc', t2ab,
numpy.asarray(eris.get_OVvv()).conj()) * 2
w += numpy.einsum('jkbe,iaec->ijkabc', t2bb,
numpy.asarray(eris.get_ovVV()).conj())
w -= numpy.einsum('imab,kcjm->ijkabc', t2ab,
numpy.asarray(eris.OVOO).conj()) * 2
w -= numpy.einsum('mjab,kcim->ijkabc', t2ab,
numpy.asarray(eris.OVoo).conj()) * 2
w -= numpy.einsum('jmbc,iakm->ijkabc', t2bb,
numpy.asarray(eris.ovOO).conj())
v = numpy.einsum('jbkc,ia->ijkabc', numpy.asarray(eris.OVOV).conj(), t1a)
v += numpy.einsum('iakc,jb->ijkabc', numpy.asarray(eris.ovOV).conj(), t1b)
v += numpy.einsum('iakc,jb->ijkabc', numpy.asarray(eris.ovOV).conj(), t1b)
v += numpy.einsum('JKBC,ai->iJKaBC', t2bb, fvo) * .5
v += numpy.einsum('iKaC,BJ->iJKaBC', t2ab, fVO) * 2
rw = r4(w) / d3
wvd = (w + v) / d3
goo += numpy.einsum('iklabc,jklabc->ij', wvd.conj(), rw) * .25
gOO += numpy.einsum('kilabc,kjlabc->ij', wvd.conj(), rw) * .25
gOO += numpy.einsum('kliabc,kljabc->ij', wvd.conj(), rw) * .25
gvv += numpy.einsum('ijkacd,ijkbcd->ab', wvd, rw.conj()) * .25
gVV += numpy.einsum('ijkcad,ijkcbd->ab', wvd, rw.conj()) * .25
gVV += numpy.einsum('ijkcda,ijkcdb->ab', wvd, rw.conj()) * .25
gVO += numpy.einsum('ikac,ijkabc->bj', t2ab.conj(), rw) * .5
gvo += numpy.einsum('jkbc,ijkabc->ai', t2bb.conj(), rw) * .125
doo, dOO = d1[0]
dov, dOV = d1[1]
dvo, dVO = d1[2]
dvv, dVV = d1[3]
if for_grad:
doo -= goo
dOO -= gOO
dvv += gvv
dVV += gVV
else:
doo[numpy.diag_indices(nocca)] -= goo.diagonal()
dOO[numpy.diag_indices(noccb)] -= gOO.diagonal()
dvv[numpy.diag_indices(nvira)] += gvv.diagonal()
dVV[numpy.diag_indices(nvirb)] += gVV.diagonal()
dvo += gvo
dVO += gVO
return d1
def _gamma1_intermediates(mycc, t1, t2, l1, l2, eris=None, for_grad=False):
d1 = uccsd_rdm._gamma1_intermediates(mycc, t1, t2, l1, l2)
if eris is None: eris = mycc.ao2mo()
t1a, t1b = t1
t2aa, t2ab, t2bb = t2
nocca, noccb, nvira, nvirb = t2ab.shape
nmoa = eris.focka.shape[0]
nmob = eris.fockb.shape[0]
mo_ea, mo_eb = eris.mo_energy
eia = mo_ea[:nocca,None] - mo_ea[nocca:]
eIA = mo_eb[:noccb,None] - mo_eb[noccb:]
fvo = eris.focka[nocca:,:nocca]
fVO = eris.fockb[noccb:,:noccb]
# aaa
d3 = lib.direct_sum('ia+jb+kc->ijkabc', eia, eia, eia)
w = numpy.einsum('ijae,kceb->ijkabc', t2aa, numpy.asarray(eris.get_ovvv()).conj())
w-= numpy.einsum('mkbc,iajm->ijkabc', t2aa, numpy.asarray(eris.ovoo.conj()))
v = numpy.einsum('jbkc,ia->ijkabc', numpy.asarray(eris.ovov).conj(), t1a)
v+= numpy.einsum('jkbc,ai->ijkabc', t2aa, fvo) * .5
rw = p6(r6(w)) / d3
wvd = p6(w + v) / d3
goo = numpy.einsum('iklabc,jklabc->ij', wvd.conj(), rw) * .125
gvv = numpy.einsum('ijkacd,ijkbcd->ab', wvd, rw.conj()) * .125
gvo = numpy.einsum('jkbc,ijkabc->ai', t2aa.conj(), rw) * .125
# bbb
d3 = lib.direct_sum('ia+jb+kc->ijkabc', eIA, eIA, eIA)
w = numpy.einsum('ijae,kceb->ijkabc', t2bb, numpy.asarray(eris.get_OVVV()).conj())
w-= numpy.einsum('imab,kcjm->ijkabc', t2bb, numpy.asarray(eris.OVOO.conj()))
v = numpy.einsum('jbkc,ia->ijkabc', numpy.asarray(eris.OVOV).conj(), t1b)
v+= numpy.einsum('jkbc,ai->ijkabc', t2bb, fVO) * .5
rw = p6(r6(w)) / d3
wvd = p6(w + v) / d3
gOO = numpy.einsum('iklabc,jklabc->ij', wvd.conj(), rw) * .125
gVV = numpy.einsum('ijkacd,ijkbcd->ab', wvd, rw.conj()) * .125
gVO = numpy.einsum('jkbc,ijkabc->ai', t2bb.conj(), rw) * .125
# baa
d3 = lib.direct_sum('ia+jb+kc->ijkabc', eIA, eia, eia)
w = numpy.einsum('jIeA,kceb->IjkAbc', t2ab, numpy.asarray(eris.get_ovvv()).conj()) * 2
w += numpy.einsum('jIbE,kcEA->IjkAbc', t2ab, numpy.asarray(eris.get_ovVV()).conj()) * 2
w += numpy.einsum('jkbe,IAec->IjkAbc', t2aa, numpy.asarray(eris.get_OVvv()).conj())
w -= numpy.einsum('mIbA,kcjm->IjkAbc', t2ab, numpy.asarray(eris.ovoo).conj()) * 2
w -= numpy.einsum('jMbA,kcIM->IjkAbc', t2ab, numpy.asarray(eris.ovOO).conj()) * 2
w -= numpy.einsum('jmbc,IAkm->IjkAbc', t2aa, numpy.asarray(eris.OVoo).conj())
v = numpy.einsum('jbkc,IA->IjkAbc', numpy.asarray(eris.ovov).conj(), t1b)
v += numpy.einsum('kcIA,jb->IjkAbc', numpy.asarray(eris.ovOV).conj(), t1a)
v += numpy.einsum('kcIA,jb->IjkAbc', numpy.asarray(eris.ovOV).conj(), t1a)
v += numpy.einsum('jkbc,AI->IjkAbc', t2aa, fVO) * .5
v += numpy.einsum('kIcA,bj->IjkAbc', t2ab, fvo) * 2
rw = r4(w) / d3
wvd = (w + v) / d3
goo += numpy.einsum('kilabc,kjlabc->ij', wvd.conj(), rw) * .25
goo += numpy.einsum('kliabc,kljabc->ij', wvd.conj(), rw) * .25
gOO += numpy.einsum('iklabc,jklabc->ij', wvd.conj(), rw) * .25
gvv += numpy.einsum('ijkcad,ijkcbd->ab', wvd, rw.conj()) * .25
gvv += numpy.einsum('ijkcda,ijkcdb->ab', wvd, rw.conj()) * .25
gVV += numpy.einsum('ijkacd,ijkbcd->ab', wvd, rw.conj()) * .25
gvo += numpy.einsum('kica,ijkabc->bj', t2ab.conj(), rw) * .5
gVO += numpy.einsum('jkbc,ijkabc->ai', t2aa.conj(), rw) * .125
# bba
d3 = lib.direct_sum('ia+jb+kc->ijkabc', eia, eIA, eIA)
w = numpy.einsum('ijae,kceb->ijkabc', t2ab, numpy.asarray(eris.get_OVVV()).conj()) * 2
w += numpy.einsum('ijeb,kcea->ijkabc', t2ab, numpy.asarray(eris.get_OVvv()).conj()) * 2
w += numpy.einsum('jkbe,iaec->ijkabc', t2bb, numpy.asarray(eris.get_ovVV()).conj())
w -= numpy.einsum('imab,kcjm->ijkabc', t2ab, numpy.asarray(eris.OVOO).conj()) * 2
w -= numpy.einsum('mjab,kcim->ijkabc', t2ab, numpy.asarray(eris.OVoo).conj()) * 2
w -= numpy.einsum('jmbc,iakm->ijkabc', t2bb, numpy.asarray(eris.ovOO).conj())
v = numpy.einsum('jbkc,ia->ijkabc', numpy.asarray(eris.OVOV).conj(), t1a)
v += numpy.einsum('iakc,jb->ijkabc', numpy.asarray(eris.ovOV).conj(), t1b)
v += numpy.einsum('iakc,jb->ijkabc', numpy.asarray(eris.ovOV).conj(), t1b)
v += numpy.einsum('JKBC,ai->iJKaBC', t2bb, fvo) * .5
v += numpy.einsum('iKaC,BJ->iJKaBC', t2ab, fVO) * 2
rw = r4(w) / d3
wvd = (w + v) / d3
goo += numpy.einsum('iklabc,jklabc->ij', wvd.conj(), rw) * .25
gOO += numpy.einsum('kilabc,kjlabc->ij', wvd.conj(), rw) * .25
gOO += numpy.einsum('kliabc,kljabc->ij', wvd.conj(), rw) * .25
gvv += numpy.einsum('ijkacd,ijkbcd->ab', wvd, rw.conj()) * .25
gVV += numpy.einsum('ijkcad,ijkcbd->ab', wvd, rw.conj()) * .25
gVV += numpy.einsum('ijkcda,ijkcdb->ab', wvd, rw.conj()) * .25
gVO += numpy.einsum('ikac,ijkabc->bj', t2ab.conj(), rw) * .5
gvo += numpy.einsum('jkbc,ijkabc->ai', t2bb.conj(), rw) * .125
doo, dOO = d1[0]
dov, dOV = d1[1]
dvo, dVO = d1[2]
dvv, dVV = d1[3]
if for_grad:
doo -= goo
dOO -= gOO
dvv += gvv
dVV += gVV
else:
doo[numpy.diag_indices(nocca)] -= goo.diagonal()
dOO[numpy.diag_indices(noccb)] -= gOO.diagonal()
dvv[numpy.diag_indices(nvira)] += gvv.diagonal()
dVV[numpy.diag_indices(nvirb)] += gVV.diagonal()
dvo += gvo
dVO += gVO
return d1
def grad_elec(cc_grad, t1=None, t2=None, l1=None, l2=None, eris=None, atmlst=None,
d1=None, d2=None, verbose=logger.INFO):
mycc = cc_grad.base
if eris is not None:
if (abs(eris.focka - numpy.diag(eris.focka.diagonal())).max() > 1e-3 or
abs(eris.fockb - numpy.diag(eris.fockb.diagonal())).max() > 1e-3):
raise RuntimeError('UCCSD gradients does not support NHF (non-canonical HF)')
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
log = logger.new_logger(mycc, verbose)
time0 = time.clock(), time.time()
log.debug('Build uccsd rdm1 intermediates')
if d1 is None:
d1 = uccsd_rdm._gamma1_intermediates(mycc, t1, t2, l1, l2)
time1 = log.timer_debug1('rdm1 intermediates', *time0)
log.debug('Build uccsd rdm2 intermediates')
fdm2 = lib.H5TmpFile()
if d2 is None:
d2 = uccsd_rdm._gamma2_outcore(mycc, t1, t2, l1, l2, fdm2, True)
time1 = log.timer_debug1('rdm2 intermediates', *time1)
mol = cc_grad.mol
mo_a, mo_b = mycc.mo_coeff
mo_ea, mo_eb = mycc._scf.mo_energy
nao, nmoa = mo_a.shape
nmob = mo_b.shape[1]
nocca = numpy.count_nonzero(mycc.mo_occ[0] > 0)
noccb = numpy.count_nonzero(mycc.mo_occ[1] > 0)
nvira = nmoa - nocca
nvirb = nmob - noccb
with_frozen = not (mycc.frozen is None or mycc.frozen is 0)
moidx = mycc.get_frozen_mask()
OA_a, VA_a, OF_a, VF_a = ccsd_grad._index_frozen_active(moidx[0], mycc.mo_occ[0])
OA_b, VA_b, OF_b, VF_b = ccsd_grad._index_frozen_active(moidx[1], mycc.mo_occ[1])
log.debug('symmetrized rdm2 and MO->AO transformation')
# Roughly, dm2*2 is computed in _rdm2_mo2ao
mo_active = (mo_a[:,numpy.hstack((OA_a,VA_a))],
mo_b[:,numpy.hstack((OA_b,VA_b))])
_rdm2_mo2ao(mycc, d2, mo_active, fdm2) # transform the active orbitals
time1 = log.timer_debug1('MO->AO transformation', *time1)
hf_dm1a, hf_dm1b = mycc._scf.make_rdm1(mycc.mo_coeff, mycc.mo_occ)
hf_dm1 = hf_dm1a + hf_dm1b
if atmlst is None:
atmlst = range(mol.natm)
offsetdic = mol.offset_nr_by_atom()
diagidx = numpy.arange(nao)
diagidx = diagidx*(diagidx+1)//2 + diagidx
de = numpy.zeros((len(atmlst),3))
Imata = numpy.zeros((nao,nao))
Imatb = numpy.zeros((nao,nao))
vhf1 = fdm2.create_dataset('vhf1', (len(atmlst),2,3,nao,nao), 'f8')
# 2e AO integrals dot 2pdm
max_memory = max(0, mycc.max_memory - lib.current_memory()[0])
blksize = max(1, int(max_memory*.9e6/8/(nao**3*2.5)))
for k, ia in enumerate(atmlst):
shl0, shl1, p0, p1 = offsetdic[ia]
ip1 = p0
vhf = numpy.zeros((2,3,nao,nao))
for b0, b1, nf in ccsd_grad._shell_prange(mol, shl0, shl1, blksize):
ip0, ip1 = ip1, ip1 + nf
dm2bufa = ccsd_grad._load_block_tril(fdm2['dm2aa+ab'], ip0, ip1, nao)
dm2bufb = ccsd_grad._load_block_tril(fdm2['dm2bb+ab'], ip0, ip1, nao)
dm2bufa[:,:,diagidx] *= .5
dm2bufb[:,:,diagidx] *= .5
shls_slice = (b0,b1,0,mol.nbas,0,mol.nbas,0,mol.nbas)
eri0 = mol.intor('int2e', aosym='s2kl', shls_slice=shls_slice)
Imata += lib.einsum('ipx,iqx->pq', eri0.reshape(nf,nao,-1), dm2bufa)
Imatb += lib.einsum('ipx,iqx->pq', eri0.reshape(nf,nao,-1), dm2bufb)
eri0 = None
eri1 = mol.intor('int2e_ip1', comp=3, aosym='s2kl',
shls_slice=shls_slice).reshape(3,nf,nao,-1)
de[k] -= numpy.einsum('xijk,ijk->x', eri1, dm2bufa) * 2
de[k] -= numpy.einsum('xijk,ijk->x', eri1, dm2bufb) * 2
dm2bufa = dm2bufb = None
# HF part
for i in range(3):
eri1tmp = lib.unpack_tril(eri1[i].reshape(nf*nao,-1))
eri1tmp = eri1tmp.reshape(nf,nao,nao,nao)
vhf[:,i] += numpy.einsum('ijkl,ij->kl', eri1tmp, hf_dm1[ip0:ip1])
vhf[0,i] -= numpy.einsum('ijkl,il->kj', eri1tmp, hf_dm1a[ip0:ip1])
vhf[1,i] -= numpy.einsum('ijkl,il->kj', eri1tmp, hf_dm1b[ip0:ip1])
vhf[:,i,ip0:ip1] += numpy.einsum('ijkl,kl->ij', eri1tmp, hf_dm1)
vhf[0,i,ip0:ip1] -= numpy.einsum('ijkl,jk->il', eri1tmp, hf_dm1a)
vhf[1,i,ip0:ip1] -= numpy.einsum('ijkl,jk->il', eri1tmp, hf_dm1b)
eri1 = eri1tmp = None
vhf1[k] = vhf
log.debug('2e-part grad of atom %d %s = %s', ia, mol.atom_symbol(ia), de[k])
time1 = log.timer_debug1('2e-part grad of atom %d'%ia, *time1)
s0 = mycc._scf.get_ovlp()
Imata = reduce(numpy.dot, (mo_a.T, Imata, s0, mo_a)) * -1
Imatb = reduce(numpy.dot, (mo_b.T, Imatb, s0, mo_b)) * -1
dm1a = numpy.zeros((nmoa,nmoa))
dm1b = numpy.zeros((nmob,nmob))
doo, dOO = d1[0]
dov, dOV = d1[1]
dvo, dVO = d1[2]
dvv, dVV = d1[3]
if with_frozen:
dco = Imata[OF_a[:,None],OA_a] / (mo_ea[OF_a,None] - mo_ea[OA_a])
dfv = Imata[VF_a[:,None],VA_a] / (mo_ea[VF_a,None] - mo_ea[VA_a])
dm1a[OA_a[:,None],OA_a] = (doo + doo.T) * .5
dm1a[OF_a[:,None],OA_a] = dco
dm1a[OA_a[:,None],OF_a] = dco.T
dm1a[VA_a[:,None],VA_a] = (dvv + dvv.T) * .5
dm1a[VF_a[:,None],VA_a] = dfv
dm1a[VA_a[:,None],VF_a] = dfv.T
dco = Imatb[OF_b[:,None],OA_b] / (mo_eb[OF_b,None] - mo_eb[OA_b])
dfv = Imatb[VF_b[:,None],VA_b] / (mo_eb[VF_b,None] - mo_eb[VA_b])
dm1b[OA_b[:,None],OA_b] = (dOO + dOO.T) * .5
dm1b[OF_b[:,None],OA_b] = dco
dm1b[OA_b[:,None],OF_b] = dco.T
dm1b[VA_b[:,None],VA_b] = (dVV + dVV.T) * .5
dm1b[VF_b[:,None],VA_b] = dfv
dm1b[VA_b[:,None],VF_b] = dfv.T
else:
dm1a[:nocca,:nocca] = (doo + doo.T) * .5
dm1a[nocca:,nocca:] = (dvv + dvv.T) * .5
dm1b[:noccb,:noccb] = (dOO + dOO.T) * .5
dm1b[noccb:,noccb:] = (dVV + dVV.T) * .5
dm1 = (reduce(numpy.dot, (mo_a, dm1a, mo_a.T)),
reduce(numpy.dot, (mo_b, dm1b, mo_b.T)))
vhf = mycc._scf.get_veff(mycc.mol, dm1)
Xvo = reduce(numpy.dot, (mo_a[:,nocca:].T, vhf[0], mo_a[:,:nocca]))
XVO = reduce(numpy.dot, (mo_b[:,noccb:].T, vhf[1], mo_b[:,:noccb]))
Xvo+= Imata[:nocca,nocca:].T - Imata[nocca:,:nocca]
XVO+= Imatb[:noccb,noccb:].T - Imatb[noccb:,:noccb]
dm1_resp = _response_dm1(mycc, (Xvo,XVO), eris)
dm1a += dm1_resp[0]
dm1b += dm1_resp[1]
time1 = log.timer_debug1('response_rdm1 intermediates', *time1)
Imata[nocca:,:nocca] = Imata[:nocca,nocca:].T
Imatb[noccb:,:noccb] = Imatb[:noccb,noccb:].T
im1 = reduce(numpy.dot, (mo_a, Imata, mo_a.T))
im1+= reduce(numpy.dot, (mo_b, Imatb, mo_b.T))
time1 = log.timer_debug1('response_rdm1', *time1)
log.debug('h1 and JK1')
# Initialize hcore_deriv with the underlying SCF object because some
# extensions (e.g. QM/MM, solvent) modifies the SCF object only.
mf_grad = cc_grad.base._scf.nuc_grad_method()
hcore_deriv = mf_grad.hcore_generator(mol)
s1 = mf_grad.get_ovlp(mol)
zeta = (mo_ea[:,None] + mo_ea) * .5
zeta[nocca:,:nocca] = mo_ea[:nocca]
zeta[:nocca,nocca:] = mo_ea[:nocca].reshape(-1,1)
zeta_a = reduce(numpy.dot, (mo_a, zeta*dm1a, mo_a.T))
zeta = (mo_eb[:,None] + mo_eb) * .5
zeta[noccb:,:noccb] = mo_eb[:noccb]
zeta[:noccb,noccb:] = mo_eb[:noccb].reshape(-1,1)
zeta_b = reduce(numpy.dot, (mo_b, zeta*dm1b, mo_b.T))
dm1 = (reduce(numpy.dot, (mo_a, dm1a, mo_a.T)),
reduce(numpy.dot, (mo_b, dm1b, mo_b.T)))
vhf_s1occ = mycc._scf.get_veff(mol, (dm1[0]+dm1[0].T, dm1[1]+dm1[1].T))
p1a = numpy.dot(mo_a[:,:nocca], mo_a[:,:nocca].T)
p1b = numpy.dot(mo_b[:,:noccb], mo_b[:,:noccb].T)
vhf_s1occ = (reduce(numpy.dot, (p1a, vhf_s1occ[0], p1a)) +
reduce(numpy.dot, (p1b, vhf_s1occ[1], p1b))) * .5
time1 = log.timer_debug1('h1 and JK1', *time1)
# Hartree-Fock part contribution
dm1pa = hf_dm1a + dm1[0]*2
dm1pb = hf_dm1b + dm1[1]*2
dm1 = dm1[0] + dm1[1] + hf_dm1
zeta_a += rhf_grad.make_rdm1e(mo_ea, mo_a, mycc.mo_occ[0])
zeta_b += rhf_grad.make_rdm1e(mo_eb, mo_b, mycc.mo_occ[1])
zeta = zeta_a + zeta_b
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])
de[k] += numpy.einsum('xji,ij->x', s1[:,p0:p1], im1[:,p0:p1])
# h[1] \dot DM, contribute to f1
h1ao = hcore_deriv(ia)
de[k] += numpy.einsum('xij,ji->x', h1ao, dm1)
# -s[1]*e \dot DM, contribute to f1
de[k] -= numpy.einsum('xij,ij->x', s1[:,p0:p1], zeta[p0:p1] )
de[k] -= 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], vhf_s1occ[p0:p1]) * 2
de[k] -= numpy.einsum('xij,ij->x', vhf1[k,0], dm1pa)
de[k] -= numpy.einsum('xij,ij->x', vhf1[k,1], dm1pb)
log.timer('%s gradients' % mycc.__class__.__name__, *time0)
return de
def kernel(mycc, t1=None, t2=None, l1=None, l2=None, eris=None, atmlst=None,
mf_grad=None, d1=None, d2=None, verbose=logger.INFO):
if eris is not None:
if (abs(eris.focka - numpy.diag(eris.focka.diagonal())).max() > 1e-3 or
abs(eris.fockb - numpy.diag(eris.fockb.diagonal())).max() > 1e-3):
raise RuntimeError('UCCSD gradients does not support NHF (non-canonical HF)')
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 mf_grad is None: mf_grad = mycc._scf.nuc_grad_method()
log = logger.new_logger(mycc, verbose)
time0 = time.clock(), time.time()
log.debug('Build uccsd rdm1 intermediates')
if d1 is None:
d1 = uccsd_rdm._gamma1_intermediates(mycc, t1, t2, l1, l2)
time1 = log.timer_debug1('rdm1 intermediates', *time0)
log.debug('Build uccsd rdm2 intermediates')
fdm2 = lib.H5TmpFile()
if d2 is None:
d2 = uccsd_rdm._gamma2_outcore(mycc, t1, t2, l1, l2, fdm2, True)
time1 = log.timer_debug1('rdm2 intermediates', *time1)
mol = mycc.mol
mo_a, mo_b = mycc.mo_coeff
mo_ea, mo_eb = mycc._scf.mo_energy
nao, nmoa = mo_a.shape
nmob = mo_b.shape[1]
nocca = numpy.count_nonzero(mycc.mo_occ[0] > 0)
noccb = numpy.count_nonzero(mycc.mo_occ[1] > 0)
nvira = nmoa - nocca
nvirb = nmob - noccb
with_frozen = not (mycc.frozen is None or mycc.frozen is 0)
moidx = mycc.get_frozen_mask()
OA_a, VA_a, OF_a, VF_a = ccsd_grad._index_frozen_active(moidx[0], mycc.mo_occ[0])
OA_b, VA_b, OF_b, VF_b = ccsd_grad._index_frozen_active(moidx[1], mycc.mo_occ[1])
log.debug('symmetrized rdm2 and MO->AO transformation')
# Roughly, dm2*2 is computed in _rdm2_mo2ao
mo_active = (mo_a[:,numpy.hstack((OA_a,VA_a))],
mo_b[:,numpy.hstack((OA_b,VA_b))])
_rdm2_mo2ao(mycc, d2, mo_active, fdm2) # transform the active orbitals
time1 = log.timer_debug1('MO->AO transformation', *time1)
hf_dm1a, hf_dm1b = mycc._scf.make_rdm1(mycc.mo_coeff, mycc.mo_occ)
hf_dm1 = hf_dm1a + hf_dm1b
if atmlst is None:
atmlst = range(mol.natm)
offsetdic = mol.offset_nr_by_atom()
diagidx = numpy.arange(nao)
diagidx = diagidx*(diagidx+1)//2 + diagidx
de = numpy.zeros((len(atmlst),3))
Imata = numpy.zeros((nao,nao))
Imatb = numpy.zeros((nao,nao))
vhf1 = fdm2.create_dataset('vhf1', (len(atmlst),2,3,nao,nao), 'f8')
# 2e AO integrals dot 2pdm
max_memory = max(0, mycc.max_memory - lib.current_memory()[0])
blksize = max(1, int(max_memory*.9e6/8/(nao**3*2.5)))
for k, ia in enumerate(atmlst):
shl0, shl1, p0, p1 = offsetdic[ia]
ip1 = p0
vhf = numpy.zeros((2,3,nao,nao))
for b0, b1, nf in ccsd_grad._shell_prange(mol, shl0, shl1, blksize):
ip0, ip1 = ip1, ip1 + nf
dm2bufa = ccsd_grad._load_block_tril(fdm2['dm2aa+ab'], ip0, ip1, nao)
dm2bufb = ccsd_grad._load_block_tril(fdm2['dm2bb+ab'], ip0, ip1, nao)
dm2bufa[:,:,diagidx] *= .5
dm2bufb[:,:,diagidx] *= .5
shls_slice = (b0,b1,0,mol.nbas,0,mol.nbas,0,mol.nbas)
eri0 = mol.intor('int2e', aosym='s2kl', shls_slice=shls_slice)
Imata += lib.einsum('ipx,iqx->pq', eri0.reshape(nf,nao,-1), dm2bufa)
Imatb += lib.einsum('ipx,iqx->pq', eri0.reshape(nf,nao,-1), dm2bufb)
eri0 = None
eri1 = mol.intor('int2e_ip1', comp=3, aosym='s2kl',
shls_slice=shls_slice).reshape(3,nf,nao,-1)
de[k] -= numpy.einsum('xijk,ijk->x', eri1, dm2bufa) * 2
de[k] -= numpy.einsum('xijk,ijk->x', eri1, dm2bufb) * 2
dm2bufa = dm2bufb = None
# HF part
for i in range(3):
eri1tmp = lib.unpack_tril(eri1[i].reshape(nf*nao,-1))
eri1tmp = eri1tmp.reshape(nf,nao,nao,nao)
vhf[:,i] += numpy.einsum('ijkl,ij->kl', eri1tmp, hf_dm1[ip0:ip1])
vhf[0,i] -= numpy.einsum('ijkl,il->kj', eri1tmp, hf_dm1a[ip0:ip1])
vhf[1,i] -= numpy.einsum('ijkl,il->kj', eri1tmp, hf_dm1b[ip0:ip1])
vhf[:,i,ip0:ip1] += numpy.einsum('ijkl,kl->ij', eri1tmp, hf_dm1)
vhf[0,i,ip0:ip1] -= numpy.einsum('ijkl,jk->il', eri1tmp, hf_dm1a)
vhf[1,i,ip0:ip1] -= numpy.einsum('ijkl,jk->il', eri1tmp, hf_dm1b)
eri1 = eri1tmp = None
vhf1[k] = vhf
log.debug('2e-part grad of atom %d %s = %s', ia, mol.atom_symbol(ia), de[k])
time1 = log.timer_debug1('2e-part grad of atom %d'%ia, *time1)
s0 = mycc._scf.get_ovlp()
Imata = reduce(numpy.dot, (mo_a.T, Imata, s0, mo_a)) * -1
Imatb = reduce(numpy.dot, (mo_b.T, Imatb, s0, mo_b)) * -1
dm1a = numpy.zeros((nmoa,nmoa))
dm1b = numpy.zeros((nmob,nmob))
doo, dOO = d1[0]
dov, dOV = d1[1]
dvo, dVO = d1[2]
dvv, dVV = d1[3]
if with_frozen:
dco = Imata[OF_a[:,None],OA_a] / (mo_ea[OF_a,None] - mo_ea[OA_a])
dfv = Imata[VF_a[:,None],VA_a] / (mo_ea[VF_a,None] - mo_ea[VA_a])
dm1a[OA_a[:,None],OA_a] = (doo + doo.T) * .5
dm1a[OF_a[:,None],OA_a] = dco
dm1a[OA_a[:,None],OF_a] = dco.T
dm1a[VA_a[:,None],VA_a] = (dvv + dvv.T) * .5
dm1a[VF_a[:,None],VA_a] = dfv
dm1a[VA_a[:,None],VF_a] = dfv.T
dco = Imatb[OF_b[:,None],OA_b] / (mo_eb[OF_b,None] - mo_eb[OA_b])
dfv = Imatb[VF_b[:,None],VA_b] / (mo_eb[VF_b,None] - mo_eb[VA_b])
dm1b[OA_b[:,None],OA_b] = (dOO + dOO.T) * .5
dm1b[OF_b[:,None],OA_b] = dco
dm1b[OA_b[:,None],OF_b] = dco.T
dm1b[VA_b[:,None],VA_b] = (dVV + dVV.T) * .5
dm1b[VF_b[:,None],VA_b] = dfv
dm1b[VA_b[:,None],VF_b] = dfv.T
else:
dm1a[:nocca,:nocca] = (doo + doo.T) * .5
dm1a[nocca:,nocca:] = (dvv + dvv.T) * .5
dm1b[:noccb,:noccb] = (dOO + dOO.T) * .5
dm1b[noccb:,noccb:] = (dVV + dVV.T) * .5
dm1 = (reduce(numpy.dot, (mo_a, dm1a, mo_a.T)),
reduce(numpy.dot, (mo_b, dm1b, mo_b.T)))
vhf = mycc._scf.get_veff(mycc.mol, dm1)
Xvo = reduce(numpy.dot, (mo_a[:,nocca:].T, vhf[0], mo_a[:,:nocca]))
XVO = reduce(numpy.dot, (mo_b[:,noccb:].T, vhf[1], mo_b[:,:noccb]))
Xvo+= Imata[:nocca,nocca:].T - Imata[nocca:,:nocca]
XVO+= Imatb[:noccb,noccb:].T - Imatb[noccb:,:noccb]
dm1_resp = _response_dm1(mycc, (Xvo,XVO), eris)
dm1a += dm1_resp[0]
dm1b += dm1_resp[1]
time1 = log.timer_debug1('response_rdm1 intermediates', *time1)
Imata[nocca:,:nocca] = Imata[:nocca,nocca:].T
Imatb[noccb:,:noccb] = Imatb[:noccb,noccb:].T
im1 = reduce(numpy.dot, (mo_a, Imata, mo_a.T))
im1+= reduce(numpy.dot, (mo_b, Imatb, mo_b.T))
time1 = log.timer_debug1('response_rdm1', *time1)
log.debug('h1 and JK1')
hcore_deriv = mf_grad.hcore_generator(mol)
s1 = mf_grad.get_ovlp(mol)
zeta = (mo_ea[:,None] + mo_ea) * .5
zeta[nocca:,:nocca] = mo_ea[:nocca]
zeta[:nocca,nocca:] = mo_ea[:nocca].reshape(-1,1)
zeta_a = reduce(numpy.dot, (mo_a, zeta*dm1a, mo_a.T))
zeta = (mo_eb[:,None] + mo_eb) * .5
zeta[noccb:,:noccb] = mo_eb[:noccb]
zeta[:noccb,noccb:] = mo_eb[:noccb].reshape(-1,1)
zeta_b = reduce(numpy.dot, (mo_b, zeta*dm1b, mo_b.T))
dm1 = (reduce(numpy.dot, (mo_a, dm1a, mo_a.T)),
reduce(numpy.dot, (mo_b, dm1b, mo_b.T)))
vhf_s1occ = mycc._scf.get_veff(mol, (dm1[0]+dm1[0].T, dm1[1]+dm1[1].T))
p1a = numpy.dot(mo_a[:,:nocca], mo_a[:,:nocca].T)
p1b = numpy.dot(mo_b[:,:noccb], mo_b[:,:noccb].T)
vhf_s1occ = (reduce(numpy.dot, (p1a, vhf_s1occ[0], p1a)) +
reduce(numpy.dot, (p1b, vhf_s1occ[1], p1b))) * .5
time1 = log.timer_debug1('h1 and JK1', *time1)
# Hartree-Fock part contribution
dm1pa = hf_dm1a + dm1[0]*2
dm1pb = hf_dm1b + dm1[1]*2
dm1 = dm1[0] + dm1[1] + hf_dm1
zeta_a += rhf_grad.make_rdm1e(mo_ea, mo_a, mycc.mo_occ[0])
zeta_b += rhf_grad.make_rdm1e(mo_eb, mo_b, mycc.mo_occ[1])
zeta = zeta_a + zeta_b
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])
de[k] += numpy.einsum('xji,ij->x', s1[:,p0:p1], im1[:,p0:p1])
# h[1] \dot DM, contribute to f1
h1ao = hcore_deriv(ia)
de[k] += numpy.einsum('xij,ji->x', h1ao, dm1)
# -s[1]*e \dot DM, contribute to f1
de[k] -= numpy.einsum('xij,ij->x', s1[:,p0:p1], zeta[p0:p1] )
de[k] -= 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], vhf_s1occ[p0:p1]) * 2
de[k] -= numpy.einsum('xij,ij->x', vhf1[k,0], dm1pa)
de[k] -= numpy.einsum('xij,ij->x', vhf1[k,1], dm1pb)
de += mf_grad.grad_nuc(mol)
log.timer('%s gradients' % mycc.__class__.__name__, *time0)
return de