def make_rdm2(myci, civec=None, nmo=None, nocc=None):
r'''
Two-particle spin density matrices dm2aa, dm2ab, dm2bb in MO basis
dm2aa[p,q,r,s] = <q_alpha^\dagger s_alpha^\dagger r_alpha p_alpha>
dm2ab[p,q,r,s] = <q_alpha^\dagger s_beta^\dagger r_beta p_alpha>
dm2bb[p,q,r,s] = <q_beta^\dagger s_beta^\dagger r_beta p_beta>
(p,q correspond to one particle and r,s correspond to another particle)
Two-particle density matrix should be contracted to integrals with the
pattern below to compute energy
E = numpy.einsum('pqrs,pqrs', eri_aa, dm2_aa)
E+= numpy.einsum('pqrs,pqrs', eri_ab, dm2_ab)
E+= numpy.einsum('pqrs,rspq', eri_ba, dm2_ab)
E+= numpy.einsum('pqrs,pqrs', eri_bb, dm2_bb)
where eri_aa[p,q,r,s] = (p_alpha q_alpha | r_alpha s_alpha )
eri_ab[p,q,r,s] = ( p_alpha q_alpha | r_beta s_beta )
eri_ba[p,q,r,s] = ( p_beta q_beta | r_alpha s_alpha )
eri_bb[p,q,r,s] = ( p_beta q_beta | r_beta s_beta )
'''
if civec is None: civec = myci.ci
if nmo is None: nmo = myci.nmo
if nocc is None: nocc = myci.nocc
d1 = _gamma1_intermediates(myci, civec, nmo, nocc)
d2 = _gamma2_intermediates(myci, civec, nmo, nocc)
return uccsd_rdm._make_rdm2(myci, d1, d2, with_dm1=True, with_frozen=True)
def make_rdm2(myci, civec=None, nmo=None, nocc=None):
r'''
Two-particle spin density matrices dm2aa, dm2ab, dm2bb in MO basis
dm2aa[p,q,r,s] = <q_alpha^\dagger s_alpha^\dagger r_alpha p_alpha>
dm2ab[p,q,r,s] = <q_alpha^\dagger s_beta^\dagger r_beta p_alpha>
dm2bb[p,q,r,s] = <q_beta^\dagger s_beta^\dagger r_beta p_beta>
(p,q correspond to one particle and r,s correspond to another particle)
Two-particle density matrix should be contracted to integrals with the
pattern below to compute energy
E = numpy.einsum('pqrs,pqrs', eri_aa, dm2_aa)
E+= numpy.einsum('pqrs,pqrs', eri_ab, dm2_ab)
E+= numpy.einsum('pqrs,rspq', eri_ba, dm2_ab)
E+= numpy.einsum('pqrs,pqrs', eri_bb, dm2_bb)
where eri_aa[p,q,r,s] = (p_alpha q_alpha | r_alpha s_alpha )
eri_ab[p,q,r,s] = ( p_alpha q_alpha | r_beta s_beta )
eri_ba[p,q,r,s] = ( p_beta q_beta | r_alpha s_alpha )
eri_bb[p,q,r,s] = ( p_beta q_beta | r_beta s_beta )
'''
if civec is None: civec = myci.ci
if nmo is None: nmo = myci.nmo
if nocc is None: nocc = myci.nocc
d1 = _gamma1_intermediates(myci, civec, nmo, nocc)
d2 = _gamma2_intermediates(myci, civec, nmo, nocc)
return uccsd_rdm._make_rdm2(myci, d1, d2, with_dm1=True, with_frozen=True)
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 make_rdm2(mycc, t1, t2, l1, l2, eris=None):
d1 = _gamma1_intermediates(mycc, t1, t2, l1, l2, eris)
d2 = _gamma2_intermediates(mycc, t1, t2, l1, l2, eris)
return uccsd_rdm._make_rdm2(mycc, d1, d2, True, True)
def make_rdm2(mycc, t1, t2, l1, l2, eris=None):
d1 = _gamma1_intermediates(mycc, t1, t2, l1, l2, eris)
d2 = _gamma2_intermediates(mycc, t1, t2, l1, l2, eris)
return uccsd_rdm._make_rdm2(mycc, d1, d2, True, True)
