def make_rdm2(self, t1=None, t2=None, l1=None, l2=None):
'''2-particle density matrix in MO space'''
from pyscf.cc import ccsd_rdm
if t1 is None: t1 = self.t1
if t2 is None: t2 = self.t2
if l1 is None: l1 = self.l1
if l2 is None: l2 = self.l2
if l1 is None: l1, l2 = self.solve_lambda(t1, t2)[1:]
return ccsd_rdm.make_rdm2(self, t1, t2, l1, l2)
def make_rdm2(self, t1=None, t2=None, l1=None, l2=None):
'''2-particle density matrix in MO space'''
from pyscf.cc import ccsd_rdm
if t1 is None: t1 = self.t1
if t2 is None: t2 = self.t2
if l1 is None: l1 = self.l1
if l2 is None: l2 = self.l2
if l1 is None: l1, l2 = self.solve_lambda(t1, t2)[1:]
return ccsd_rdm.make_rdm2(self, t1, t2, l1, l2)
def make_rdm2(self, t1=None, t2=None, l1=None, l2=None):
'''2-particle density matrix in MO space. The density matrix is
stored in physicist notation
dm2[p,q,r,s] = <p^+ q^+ s r>
'''
from pyscf.cc import ccsd_rdm
if t1 is None: t1 = self.t1
if t2 is None: t2 = self.t2
if l1 is None: l1 = self.l1
if l2 is None: l2 = self.l2
if l1 is None: l1, l2 = self.solve_lambda(t1, t2)
return ccsd_rdm.make_rdm2(self, t1, t2, l1, l2)
def make_rdm2(self, t1=None, t2=None, l1=None, l2=None):
'''2-particle density matrix in MO space. The density matrix is
stored in physicist notation
dm2[p,q,r,s] = <p^+ q^+ s r>
'''
from pyscf.cc import ccsd_rdm
if t1 is None: t1 = self.t1
if t2 is None: t2 = self.t2
if l1 is None: l1 = self.l1
if l2 is None: l2 = self.l2
if l1 is None: l1, l2 = self.solve_lambda(t1, t2)
return ccsd_rdm.make_rdm2(self, t1, t2, l1, l2)
def make_rdm2(self, t1=None, t2=None, l1=None, l2=None, ao_repr=False):
'''2-particle density matrix in MO space. The density matrix is
stored as
dm2[p,r,q,s] = <p^+ q^+ s r>
'''
if t2 is None: t2 = self.t2
if l2 is None: l2 = self.l2
if l2 is None: l2 = self.solve_lambda(t2)
nocc = self.nocc
nvir = self.nmo - nocc
l1 = t1 = numpy.zeros((nocc, nvir))
return ccsd_rdm.make_rdm2(self, t1, t2, l1, l2, ao_repr=ao_repr)
mol.basis = "cc-pvdz"
mol.build()
rhf = scf.RHF(mol)
rhf.conv_tol = 1e-16
rhf.scf()
mcc = ccsd.CCSD(rhf)
mcc.conv_tol = 1e-12
ecc, t1, t2 = mcc.kernel()
nmo = rhf.mo_energy.size
fock0 = numpy.diag(rhf.mo_energy)
nocc = mol.nelectron // 2
nvir = nmo - nocc
eris = mcc.ao2mo()
conv, l1, l2 = kernel(mcc, eris, t1, t2, tol=1e-8)
print(numpy.linalg.norm(l1) - 0.0132626841292)
print(numpy.linalg.norm(l2) - 0.212575609057)
from pyscf.cc import ccsd_rdm
dm1 = ccsd_rdm.make_rdm1(mcc, t1, t2, l1, l2)
dm2 = ccsd_rdm.make_rdm2(mcc, t1, t2, l1, l2)
h1 = reduce(numpy.dot, (rhf.mo_coeff.T, rhf.get_hcore(), rhf.mo_coeff))
eri = ao2mo.full(rhf._eri, rhf.mo_coeff)
eri = ao2mo.restore(1, eri, nmo).reshape((nmo,) * 4)
e1 = numpy.einsum("pq,pq", h1, dm1)
e2 = numpy.einsum("pqrs,pqrs", eri, dm2) * 0.5
print(e1 + e2 + mol.energy_nuc() - rhf.e_tot - ecc)
def test_rdm_trace(self):
mycc = rccsd.RCCSD(mf)
numpy.random.seed(2)
nocc = 5
nmo = 12
nvir = nmo - nocc
eri0 = numpy.random.random((nmo, nmo, nmo, nmo))
eri0 = ao2mo.restore(1, ao2mo.restore(8, eri0, nmo), nmo)
fock0 = numpy.random.random((nmo, nmo))
fock0 = fock0 + fock0.T + numpy.diag(range(nmo)) * 2
t1 = numpy.random.random((nocc, nvir))
t2 = numpy.random.random((nocc, nocc, nvir, nvir))
t2 = t2 + t2.transpose(1, 0, 3, 2)
l1 = numpy.random.random((nocc, nvir))
l2 = numpy.random.random((nocc, nocc, nvir, nvir))
l2 = l2 + l2.transpose(1, 0, 3, 2)
h1 = fock0 - (numpy.einsum('kkpq->pq', eri0[:nocc, :nocc]) * 2 -
numpy.einsum('pkkq->pq', eri0[:, :nocc, :nocc]))
eris = lambda: None
eris.oooo = eri0[:nocc, :nocc, :nocc, :nocc].copy()
eris.ooov = eri0[:nocc, :nocc, :nocc, nocc:].copy()
eris.ovoo = eri0[:nocc, nocc:, :nocc, :nocc].copy()
eris.oovv = eri0[:nocc, :nocc, nocc:, nocc:].copy()
eris.ovov = eri0[:nocc, nocc:, :nocc, nocc:].copy()
eris.ovvo = eri0[:nocc, nocc:, nocc:, :nocc].copy()
eris.ovvv = eri0[:nocc, nocc:, nocc:, nocc:].copy()
eris.vvvv = eri0[nocc:, nocc:, nocc:, nocc:].copy()
eris.fock = fock0
doo, dov, dvo, dvv = ccsd_rdm._gamma1_intermediates(
mycc, t1, t2, l1, l2)
self.assertAlmostEqual(
(numpy.einsum('ij,ij', doo, fock0[:nocc, :nocc])) * 2,
-20166.329861034799, 8)
self.assertAlmostEqual(
(numpy.einsum('ab,ab', dvv, fock0[nocc:, nocc:])) * 2,
58078.964019246778, 8)
self.assertAlmostEqual(
(numpy.einsum('ai,ia', dvo, fock0[:nocc, nocc:])) * 2,
-74994.356886784764, 8)
self.assertAlmostEqual(
(numpy.einsum('ia,ai', dov, fock0[nocc:, :nocc])) * 2,
34.010188025702391, 9)
fdm2 = lib.H5TmpFile()
dovov, dvvvv, doooo, doovv, dovvo, dvvov, dovvv, dooov = \
ccsd_rdm._gamma2_outcore(mycc, t1, t2, l1, l2, fdm2, True)
self.assertAlmostEqual(lib.finger(numpy.array(dovov)),
-14384.907042073517, 9)
self.assertAlmostEqual(lib.finger(numpy.array(dvvvv)),
-25.374007033024839, 9)
self.assertAlmostEqual(lib.finger(numpy.array(doooo)),
60.114594698129963, 9)
self.assertAlmostEqual(lib.finger(numpy.array(doovv)),
-79.176348067958401, 9)
self.assertAlmostEqual(lib.finger(numpy.array(dovvo)),
9.864134457251815, 9)
self.assertAlmostEqual(lib.finger(numpy.array(dovvv)),
-421.90333700061342, 9)
self.assertAlmostEqual(lib.finger(numpy.array(dooov)),
-592.66863759586136, 9)
fdm2 = None
dovov, dvvvv, doooo, doovv, dovvo, dvvov, dovvv, dooov = \
ccsd_rdm._gamma2_intermediates(mycc, t1, t2, l1, l2)
self.assertAlmostEqual(lib.finger(numpy.array(dovov)),
-14384.907042073517, 9)
self.assertAlmostEqual(lib.finger(numpy.array(dvvvv)),
45.872344902116758, 9)
self.assertAlmostEqual(lib.finger(numpy.array(doooo)),
60.114594698129963, 9)
self.assertAlmostEqual(lib.finger(numpy.array(doovv)),
-79.176348067958401, 9)
self.assertAlmostEqual(lib.finger(numpy.array(dovvo)),
9.864134457251815, 9)
self.assertAlmostEqual(lib.finger(numpy.array(dovvv)),
-421.90333700061342, 9)
self.assertAlmostEqual(lib.finger(numpy.array(dooov)),
-592.66863759586136, 9)
self.assertAlmostEqual(
numpy.einsum('kilj,kilj', doooo, eris.oooo) * 2, 15939.9007625418,
7)
self.assertAlmostEqual(
numpy.einsum('acbd,acbd', dvvvv, eris.vvvv) * 2, 37581.823919588,
7)
self.assertAlmostEqual(
numpy.einsum('jkia,jkia', dooov, eris.ooov) * 2, 128470.009687716,
7)
self.assertAlmostEqual(
numpy.einsum('icba,icba', dovvv, eris.ovvv) * 2, -166794.225195056,
7)
self.assertAlmostEqual(
numpy.einsum('iajb,iajb', dovov, eris.ovov) * 2, -719279.812916893,
7)
self.assertAlmostEqual(
numpy.einsum('jbai,jbia', dovvo, eris.ovov) * 2 +
numpy.einsum('jiab,jiba', doovv, eris.oovv) * 2, -53634.0012286654,
7)
dm1 = ccsd_rdm.make_rdm1(mycc, t1, t2, l1, l2)
dm2 = ccsd_rdm.make_rdm2(mycc, t1, t2, l1, l2)
e2 = (
numpy.einsum('ijkl,ijkl', doooo, eris.oooo) * 2 +
numpy.einsum('acbd,acbd', dvvvv, eris.vvvv) * 2 +
numpy.einsum('jkia,jkia', dooov, eris.ooov) * 2 +
numpy.einsum('icba,icba', dovvv, eris.ovvv) * 2 +
numpy.einsum('iajb,iajb', dovov, eris.ovov) * 2 +
numpy.einsum('jbai,jbia', dovvo, eris.ovov) * 2 +
numpy.einsum('ijab,ijab', doovv, eris.oovv) * 2 +
numpy.einsum('ij,ij', doo, fock0[:nocc, :nocc]) * 2 +
numpy.einsum('ai,ia', dvo, fock0[:nocc, nocc:]) * 2 +
numpy.einsum('ia,ai', dov, fock0[nocc:, :nocc]) * 2 +
numpy.einsum('ab,ab', dvv, fock0[nocc:, nocc:]) * 2 +
fock0[:nocc].trace() * 2 - numpy.einsum(
'kkpq->pq', eri0[:nocc, :nocc, :nocc, :nocc]).trace() * 2 +
numpy.einsum('pkkq->pq', eri0[:nocc, :nocc, :nocc, :nocc]).trace())
self.assertAlmostEqual(e2, -794721.197459942, 8)
self.assertAlmostEqual(
numpy.einsum('pqrs,pqrs', dm2, eri0) * .5 +
numpy.einsum('pq,qp', dm1, h1), e2, 9)
self.assertAlmostEqual(
abs(dm2 - dm2.transpose(1, 0, 3, 2)).max(), 0, 9)
self.assertAlmostEqual(
abs(dm2 - dm2.transpose(2, 3, 0, 1)).max(), 0, 9)
d1 = numpy.einsum('kkpq->qp', dm2) / 9
self.assertAlmostEqual(abs(d1 - dm1).max(), 0, 9)
mol.basis = 'cc-pvdz'
mol.build()
rhf = scf.RHF(mol)
rhf.conv_tol = 1e-16
rhf.scf()
mcc = ccsd.CCSD(rhf)
mcc.conv_tol = 1e-12
ecc, t1, t2 = mcc.kernel()
nmo = rhf.mo_energy.size
fock0 = numpy.diag(rhf.mo_energy)
nocc = mol.nelectron // 2
nvir = nmo - nocc
eris = mcc.ao2mo()
conv, l1, l2 = kernel(mcc, eris, t1, t2, tol=1e-8)
print(numpy.linalg.norm(l1) - 0.0132626841292)
print(numpy.linalg.norm(l2) - 0.212575609057)
from pyscf.cc import ccsd_rdm
dm1 = ccsd_rdm.make_rdm1(mcc, t1, t2, l1, l2)
dm2 = ccsd_rdm.make_rdm2(mcc, t1, t2, l1, l2)
h1 = reduce(numpy.dot, (rhf.mo_coeff.T, rhf.get_hcore(), rhf.mo_coeff))
eri = pyscf.ao2mo.full(rhf._eri, rhf.mo_coeff)
eri = pyscf.ao2mo.restore(1, eri, nmo).reshape((nmo, ) * 4)
e1 = numpy.einsum('pq,pq', h1, dm1)
e2 = numpy.einsum('pqrs,pqrs', eri, dm2) * .5
print(e1 + e2 + mol.energy_nuc() - rhf.e_tot - ecc)
def test_rdm_trace(self):
mycc = rccsd.RCCSD(mf)
numpy.random.seed(2)
nocc = 5
nmo = 12
nvir = nmo - nocc
eri0 = numpy.random.random((nmo,nmo,nmo,nmo))
eri0 = ao2mo.restore(1, ao2mo.restore(8, eri0, nmo), nmo)
fock0 = numpy.random.random((nmo,nmo))
fock0 = fock0 + fock0.T + numpy.diag(range(nmo))*2
t1 = numpy.random.random((nocc,nvir))
t2 = numpy.random.random((nocc,nocc,nvir,nvir))
t2 = t2 + t2.transpose(1,0,3,2)
l1 = numpy.random.random((nocc,nvir))
l2 = numpy.random.random((nocc,nocc,nvir,nvir))
l2 = l2 + l2.transpose(1,0,3,2)
h1 = fock0 - (numpy.einsum('kkpq->pq', eri0[:nocc,:nocc])*2
- numpy.einsum('pkkq->pq', eri0[:,:nocc,:nocc]))
eris = lambda:None
eris.oooo = eri0[:nocc,:nocc,:nocc,:nocc].copy()
eris.ooov = eri0[:nocc,:nocc,:nocc,nocc:].copy()
eris.ovoo = eri0[:nocc,nocc:,:nocc,:nocc].copy()
eris.oovv = eri0[:nocc,:nocc,nocc:,nocc:].copy()
eris.ovov = eri0[:nocc,nocc:,:nocc,nocc:].copy()
eris.ovvo = eri0[:nocc,nocc:,nocc:,:nocc].copy()
eris.ovvv = eri0[:nocc,nocc:,nocc:,nocc:].copy()
eris.vvvv = eri0[nocc:,nocc:,nocc:,nocc:].copy()
eris.fock = fock0
doo, dov, dvo, dvv = ccsd_rdm._gamma1_intermediates(mycc, t1, t2, l1, l2)
self.assertAlmostEqual((numpy.einsum('ij,ij', doo, fock0[:nocc,:nocc]))*2, -20166.329861034799, 8)
self.assertAlmostEqual((numpy.einsum('ab,ab', dvv, fock0[nocc:,nocc:]))*2, 58078.964019246778, 8)
self.assertAlmostEqual((numpy.einsum('ai,ia', dvo, fock0[:nocc,nocc:]))*2, -74994.356886784764, 8)
self.assertAlmostEqual((numpy.einsum('ia,ai', dov, fock0[nocc:,:nocc]))*2, 34.010188025702391, 9)
fdm2 = lib.H5TmpFile()
dovov, dvvvv, doooo, doovv, dovvo, dvvov, dovvv, dooov = \
ccsd_rdm._gamma2_outcore(mycc, t1, t2, l1, l2, fdm2, True)
self.assertAlmostEqual(lib.finger(numpy.array(dovov)), -14384.907042073517, 9)
self.assertAlmostEqual(lib.finger(numpy.array(dvvvv)), -25.374007033024839, 9)
self.assertAlmostEqual(lib.finger(numpy.array(doooo)), 60.114594698129963, 9)
self.assertAlmostEqual(lib.finger(numpy.array(doovv)), -79.176348067958401, 9)
self.assertAlmostEqual(lib.finger(numpy.array(dovvo)), 9.864134457251815, 9)
self.assertAlmostEqual(lib.finger(numpy.array(dovvv)), -421.90333700061342, 9)
self.assertAlmostEqual(lib.finger(numpy.array(dooov)), -592.66863759586136, 9)
fdm2 = None
dovov, dvvvv, doooo, doovv, dovvo, dvvov, dovvv, dooov = \
ccsd_rdm._gamma2_intermediates(mycc, t1, t2, l1, l2)
self.assertAlmostEqual(lib.finger(numpy.array(dovov)), -14384.907042073517, 9)
self.assertAlmostEqual(lib.finger(numpy.array(dvvvv)), 45.872344902116758, 9)
self.assertAlmostEqual(lib.finger(numpy.array(doooo)), 60.114594698129963, 9)
self.assertAlmostEqual(lib.finger(numpy.array(doovv)), -79.176348067958401, 9)
self.assertAlmostEqual(lib.finger(numpy.array(dovvo)), 9.864134457251815, 9)
self.assertAlmostEqual(lib.finger(numpy.array(dovvv)), -421.90333700061342, 9)
self.assertAlmostEqual(lib.finger(numpy.array(dooov)), -592.66863759586136, 9)
self.assertAlmostEqual(numpy.einsum('kilj,kilj', doooo, eris.oooo)*2, 15939.9007625418, 7)
self.assertAlmostEqual(numpy.einsum('acbd,acbd', dvvvv, eris.vvvv)*2, 37581.823919588 , 7)
self.assertAlmostEqual(numpy.einsum('jkia,jkia', dooov, eris.ooov)*2, 128470.009687716, 7)
self.assertAlmostEqual(numpy.einsum('icba,icba', dovvv, eris.ovvv)*2,-166794.225195056, 7)
self.assertAlmostEqual(numpy.einsum('iajb,iajb', dovov, eris.ovov)*2,-719279.812916893, 7)
self.assertAlmostEqual(numpy.einsum('jbai,jbia', dovvo, eris.ovov)*2+
numpy.einsum('jiab,jiba', doovv, eris.oovv)*2,-53634.0012286654, 7)
dm1 = ccsd_rdm.make_rdm1(mycc, t1, t2, l1, l2)
dm2 = ccsd_rdm.make_rdm2(mycc, t1, t2, l1, l2)
e2 =(numpy.einsum('ijkl,ijkl', doooo, eris.oooo)*2
+numpy.einsum('acbd,acbd', dvvvv, eris.vvvv)*2
+numpy.einsum('jkia,jkia', dooov, eris.ooov)*2
+numpy.einsum('icba,icba', dovvv, eris.ovvv)*2
+numpy.einsum('iajb,iajb', dovov, eris.ovov)*2
+numpy.einsum('jbai,jbia', dovvo, eris.ovov)*2
+numpy.einsum('ijab,ijab', doovv, eris.oovv)*2
+numpy.einsum('ij,ij', doo, fock0[:nocc,:nocc])*2
+numpy.einsum('ai,ia', dvo, fock0[:nocc,nocc:])*2
+numpy.einsum('ia,ai', dov, fock0[nocc:,:nocc])*2
+numpy.einsum('ab,ab', dvv, fock0[nocc:,nocc:])*2
+fock0[:nocc].trace()*2
-numpy.einsum('kkpq->pq', eri0[:nocc,:nocc,:nocc,:nocc]).trace()*2
+numpy.einsum('pkkq->pq', eri0[:nocc,:nocc,:nocc,:nocc]).trace())
self.assertAlmostEqual(e2, -794721.197459942, 8)
self.assertAlmostEqual(numpy.einsum('pqrs,pqrs', dm2, eri0)*.5 +
numpy.einsum('pq,qp', dm1, h1), e2, 9)
self.assertAlmostEqual(abs(dm2-dm2.transpose(1,0,3,2)).max(), 0, 9)
self.assertAlmostEqual(abs(dm2-dm2.transpose(2,3,0,1)).max(), 0, 9)
d1 = numpy.einsum('kkpq->qp', dm2) / 9
self.assertAlmostEqual(abs(d1-dm1).max(), 0, 9)
