def _gamma2_intermediates(mycc, t1, t2, l1, l2, eris=None):
dovov, dvvvv, doooo, doovv, dovvo, dvvov, dovvv, dooov = \
gccsd_rdm._gamma2_intermediates(mycc, t1, t2, l1, l2)
if eris is None: eris = mycc.ao2mo()
nocc, nvir = t1.shape
bcei = numpy.asarray(eris.ovvv).conj().transpose(3, 2, 1, 0)
majk = numpy.asarray(eris.ooov).conj().transpose(2, 3, 0, 1)
bcjk = numpy.asarray(eris.oovv).conj().transpose(2, 3, 0, 1)
mo_e = eris.fock.diagonal().real
eia = mo_e[:nocc, None] - mo_e[nocc:]
d3 = lib.direct_sum('ia+jb+kc->ijkabc', eia, eia, eia)
t3c = (numpy.einsum('jkae,bcei->ijkabc', t2, bcei) -
numpy.einsum('imbc,majk->ijkabc', t2, majk))
t3c = t3c - t3c.transpose(0, 1, 2, 4, 3, 5) - t3c.transpose(
0, 1, 2, 5, 4, 3)
t3c = t3c - t3c.transpose(1, 0, 2, 3, 4, 5) - t3c.transpose(
2, 1, 0, 3, 4, 5)
t3c /= d3
t3d = numpy.einsum('ia,bcjk->ijkabc', t1, bcjk)
t3d += numpy.einsum('ai,jkbc->ijkabc', eris.fock[nocc:, :nocc], t2)
t3d = t3d - t3d.transpose(0, 1, 2, 4, 3, 5) - t3d.transpose(
0, 1, 2, 5, 4, 3)
t3d = t3d - t3d.transpose(1, 0, 2, 3, 4, 5) - t3d.transpose(
2, 1, 0, 3, 4, 5)
t3d /= d3
goovv = numpy.einsum('kc,ijkabc->ijab', t1.conj(), t3c).conj() * (1. / 4)
dovov += goovv.transpose(0, 2, 1, 3) - goovv.transpose(0, 3, 1, 2)
m3 = t3c * 2 + t3d
# *(1/8) instead of (1/4) because ooov appears 4 times in the 2pdm tensor due
# to symmetrization, and its contribution is scaled by 1/2 in Tr(H,2pdm)
gooov = numpy.einsum('imbc,ijkabc->jkma', t2, m3.conj()) * (1. / 8)
dooov -= gooov.transpose(0, 2, 1, 3) - gooov.transpose(1, 2, 0, 3)
govvv = numpy.einsum('jkae,ijkabc->iecb', t2, m3.conj()) * (1. / 8)
dovvv += govvv.transpose(0, 2, 1, 3) - govvv.transpose(0, 3, 1, 2)
return dovov, dvvvv, doooo, doovv, dovvo, dvvov, dovvv, dooov
def make_rdm2(mycc, t1, t2, l1, l2, ao_repr=False, with_dm1=True):
r'''
Two-particle density matrix in the molecular spin-orbital representation
dm2[p,q,r,s] = <p^\dagger r^\dagger s q>
where p,q,r,s are spin-orbitals. p,q correspond to one particle and r,s
correspond to another particle. The contraction between ERIs (in
Chemist's notation) and rdm2 is
E = einsum('pqrs,pqrs', eri, rdm2)
'''
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 l1 is None:
l1, l2 = mycc.solve_lambda(t1, t2)
d1 = _gamma1_intermediates(mycc, t1, t2, l1, l2)
# ZHC TODO
# use MPI for distributed intermediates
t1, t2 = mycc.gather_amplitudes(t1, t2)
l1, l2 = mycc.gather_lambda(l1, l2)
if rank == 0:
d2 = gccsd_rdm._gamma2_intermediates(mycc, t1, t2, l1, l2)
rdm2 = gccsd_rdm._make_rdm2(mycc,
d1,
d2,
with_dm1=with_dm1,
with_frozen=True,
ao_repr=ao_repr)
else:
rdm2 = None
return rdm2
def _gamma2_intermediates(mycc, t1, t2, l1, l2, eris=None):
dovov, dvvvv, doooo, doovv, dovvo, dvvov, dovvv, dooov = \
gccsd_rdm._gamma2_intermediates(mycc, t1, t2, l1, l2)
if eris is None: eris = mycc.ao2mo()
nocc, nvir = t1.shape
bcei = numpy.asarray(eris.ovvv).conj().transpose(3,2,1,0)
majk = numpy.asarray(eris.ooov).conj().transpose(2,3,0,1)
bcjk = numpy.asarray(eris.oovv).conj().transpose(2,3,0,1)
mo_e = eris.mo_energy
eia = mo_e[:nocc,None] - mo_e[nocc:]
d3 = lib.direct_sum('ia+jb+kc->ijkabc', eia, eia, eia)
t3c =(numpy.einsum('jkae,bcei->ijkabc', t2, bcei)
- numpy.einsum('imbc,majk->ijkabc', t2, majk))
t3c = t3c - t3c.transpose(0,1,2,4,3,5) - t3c.transpose(0,1,2,5,4,3)
t3c = t3c - t3c.transpose(1,0,2,3,4,5) - t3c.transpose(2,1,0,3,4,5)
t3c /= d3
t3d = numpy.einsum('ia,bcjk->ijkabc', t1, bcjk)
t3d += numpy.einsum('ai,jkbc->ijkabc', eris.fock[nocc:,:nocc], t2)
t3d = t3d - t3d.transpose(0,1,2,4,3,5) - t3d.transpose(0,1,2,5,4,3)
t3d = t3d - t3d.transpose(1,0,2,3,4,5) - t3d.transpose(2,1,0,3,4,5)
t3d /= d3
goovv = numpy.einsum('kc,ijkabc->ijab', t1.conj(), t3c).conj() * (1./4)
dovov += goovv.transpose(0,2,1,3) - goovv.transpose(0,3,1,2)
m3 = t3c * 2 + t3d
# *(1/8) instead of (1/4) because ooov appears 4 times in the 2pdm tensor due
# to symmetrization, and its contribution is scaled by 1/2 in Tr(H,2pdm)
gooov = numpy.einsum('imbc,ijkabc->jkma', t2, m3.conj()) * (1./8)
dooov -= gooov.transpose(0,2,1,3) - gooov.transpose(1,2,0,3)
govvv = numpy.einsum('jkae,ijkabc->iecb', t2, m3.conj()) * (1./8)
dovvv += govvv.transpose(0,2,1,3) - govvv.transpose(0,3,1,2)
return dovov, dvvvv, doooo, doovv, dovvo, dvvov, dovvv, dooov