def check_frozen(frozen):
myci = ci.GCISD(mf)
myci.frozen = frozen
myci.nroots = 3
myci.kernel()
nocc = myci.nocc
nmo = myci.nmo
nfroz = len(frozen)
try:
ket_id = 1
fciket = gcisd.to_fcivec(myci.ci[ket_id], mol.nelectron, orbspin, myci.frozen)
except RuntimeError:
ket_id = 2
fciket = gcisd.to_fcivec(myci.ci[ket_id], mol.nelectron, orbspin, myci.frozen)
# spin-forbidden transition
cidm1 = myci.trans_rdm1(myci.ci[0], myci.ci[1], nmo, nocc)
self.assertAlmostEqual(abs(cidm1[idxa[:,None],idxa]).max(), 0, 7)
self.assertAlmostEqual(abs(cidm1[idxb[:,None],idxb]).max(), 0, 7)
cibra = (myci.ci[0] + myci.ci[ket_id]) * numpy.sqrt(.5)
fcibra = gcisd.to_fcivec(cibra, mol.nelectron, orbspin, myci.frozen)
fcidm1 = fci.direct_spin1.trans_rdm1s(fcibra, fciket, nmo_1c, mol.nelectron)
cidm1 = myci.trans_rdm1(cibra, myci.ci[ket_id], nmo, nocc)
self.assertAlmostEqual(abs(fcidm1[0]-cidm1[idxa[:,None],idxa]).max(), 0, 12)
self.assertAlmostEqual(abs(fcidm1[1]-cidm1[idxb[:,None],idxb]).max(), 0, 12)
def test_rdm_h4(self):
mol = gto.Mole()
mol.verbose = 7
mol.output = '/dev/null'
mol.atom = [
['O', ( 0., 0. , 0. )],
['H', ( 0., -0.757, 0.587)],
['H', ( 0., 0.757 , 0.587)],]
mol.spin = 2
mol.basis = 'sto-3g'
mol.build()
mf = scf.RHF(mol).run(conv_tol=1e-14)
myci = ci.GCISD(mf)
eris = myci.ao2mo()
ecisd, civec = myci.kernel(eris=eris)
self.assertAlmostEqual(ecisd, -0.035165114624046617, 8)
nmo = eris.mo_coeff.shape[1]
rdm1 = myci.make_rdm1(civec, nmo, mol.nelectron)
rdm2 = myci.make_rdm2(civec, nmo, mol.nelectron)
mo = eris.mo_coeff[:7] + eris.mo_coeff[7:]
eri = ao2mo.kernel(mf._eri, mo, compact=False).reshape([nmo]*4)
eri[eris.orbspin[:,None]!=eris.orbspin,:,:] = 0
eri[:,:,eris.orbspin[:,None]!=eris.orbspin] = 0
h1e = reduce(numpy.dot, (mo.T, mf.get_hcore(), mo))
h1e[eris.orbspin[:,None]!=eris.orbspin] = 0
e2 = (numpy.einsum('ij,ji', h1e, rdm1) +
numpy.einsum('ijkl,ijkl', eri, rdm2) * .5)
e2 += mol.energy_nuc()
self.assertAlmostEqual(myci.e_tot, e2, 9)
dm1 = numpy.einsum('ijkk->ji', rdm2)/(mol.nelectron-1)
self.assertAlmostEqual(abs(rdm1 - dm1).max(), 0, 9)
def test_multi_roots(self):
mol = gto.Mole()
mol.verbose = 0
mol.atom = [
['H', ( 1.,-1. , 0. )],
['H', ( 0.,-1. ,-1. )],
['H', ( 1.,-0.5 , 0. )],
['H', ( 0.,-1. , 1. )],
]
mol.basis = '3-21g'
mol.build()
mf = scf.GHF(mol).run()
myci = ci.GCISD(mf)
myci.nroots = 3
myci.run()
self.assertAlmostEqual(myci.e_tot[2], -1.9802158893844912, 8)
def test_ao_direct(self):
mol = gto.Mole()
mol.verbose = 0
mol.atom = [
['O', ( 0., 0. , 0. )],
['H', ( 0., -0.757, 0.587)],
['H', ( 0., 0.757 , 0.587)],]
mol.spin = 2
mol.basis = 'ccpvdz'
mol.build()
mf = scf.RHF(mol).run(conv_tol=1e-14)
myci = ci.GCISD(mf)
myci.max_memory = .1
myci.frozen = [2,3,4,5]
myci.direct = True
ecisd, civec = myci.kernel()
self.assertAlmostEqual(ecisd, -0.048829195509732602, 8)
def test_contract(self):
'''cross check with UCISD'''
mol = gto.M()
mol.nelectron = 6
nocc, nvir = mol.nelectron // 2, 4
nmo = nocc + nvir
nmo_pair = nmo * (nmo + 1) // 2
mf = scf.UHF(mol)
numpy.random.seed(12)
mf._eri = numpy.random.random(nmo_pair * (nmo_pair + 1) // 2) * .2
mf.mo_coeff = numpy.random.random((2, nmo, nmo))
mf.mo_energy = [numpy.arange(0., nmo)] * 2
mf.mo_occ = numpy.zeros((2, nmo))
mf.mo_occ[:, :nocc] = 1
h1 = numpy.random.random((nmo, nmo)) * .1
h1 = h1 + h1.T + numpy.diag(numpy.arange(nmo))
mf.get_hcore = lambda *args: h1
mf1 = scf.addons.convert_to_ghf(mf)
mf1.get_hcore = lambda *args: scipy.linalg.block_diag(h1, h1)
gci = ci.GCISD(mf1)
c2 = numpy.random.random(
(nocc * 2, nocc * 2, nvir * 2, nvir * 2)) * .1 - .1
c2 = c2 - c2.transpose(0, 1, 3, 2)
c2 = c2 - c2.transpose(1, 0, 2, 3)
c1 = numpy.random.random((nocc * 2, nvir * 2)) * .1
c0 = .5
civec = gci.amplitudes_to_cisdvec(c0, c1, c2)
civecref = gci.contract(civec, gci.ao2mo())
c0ref, c1ref, c2ref = gci.cisdvec_to_amplitudes(civecref)
c1ref = gci.spin2spatial(c1ref)
c2ref = gci.spin2spatial(c2ref)
c1 = gci.spin2spatial(c1)
c2 = gci.spin2spatial(c2)
myci = ci.UCISD(mf)
civec = myci.amplitudes_to_cisdvec(c0, c1, c2)
cinew = myci.contract(civec, myci.ao2mo())
c0new, c1new, c2new = myci.cisdvec_to_amplitudes(cinew)
self.assertAlmostEqual(abs(c0new - c0ref).max(), 0, 12)
self.assertAlmostEqual(abs(c1new[0] - c1ref[0]).max(), 0, 12)
self.assertAlmostEqual(abs(c1new[1] - c1ref[1]).max(), 0, 12)
self.assertAlmostEqual(abs(c2new[0] - c2ref[0]).max(), 0, 12)
self.assertAlmostEqual(abs(c2new[1] - c2ref[1]).max(), 0, 12)
self.assertAlmostEqual(abs(c2new[2] - c2ref[2]).max(), 0, 12)
self.assertAlmostEqual(lib.finger(cinew), -102.17887236599671, 9)
def test_trans_rdm1(self):
numpy.random.seed(1)
norb = 4
nocc = 2
nvir = norb - nocc
c2 = numpy.random.random((nocc, nocc, nvir, nvir))
c2 = c2 + c2.transpose(1, 0, 3, 2)
cibra = numpy.hstack(
(numpy.random.random(1 + nocc * nvir), c2.ravel()))
c2 = numpy.random.random((nocc, nocc, nvir, nvir))
c2 = c2 + c2.transpose(1, 0, 3, 2)
ciket = numpy.hstack(
(numpy.random.random(1 + nocc * nvir), c2.ravel()))
cibra /= ci.cisd.dot(cibra, cibra, norb, nocc)**.5
ciket /= ci.cisd.dot(ciket, ciket, norb, nocc)**.5
fcibra = ci.cisd.to_fcivec(cibra, norb, nocc * 2)
fciket = ci.cisd.to_fcivec(ciket, norb, nocc * 2)
fcidm1 = fci.direct_spin1.trans_rdm1s(fcibra, fciket, norb, nocc * 2)
myci1 = ci.GCISD(scf.GHF(gto.M()))
myci1.nmo = norb = 8
myci1.nocc = nocc = 4
orbspin = numpy.zeros(norb, dtype=int)
orbspin[1::2] = 1
myci1.mo_coeff = lib.tag_array(numpy.eye(norb), orbspin=orbspin)
myci1.mo_occ = numpy.zeros(norb)
myci1.mo_occ[:nocc] = 1
cibra = myci1.from_rcisdvec(cibra, (nocc // 2, nocc // 2), orbspin)
ciket = myci1.from_rcisdvec(ciket)
cidm1 = myci1.trans_rdm1(cibra, ciket, norb, nocc)
self.assertAlmostEqual(abs(cidm1[0::2, 0::2] - fcidm1[0]).max(), 0, 12)
self.assertAlmostEqual(abs(cidm1[1::2, 1::2] - fcidm1[1]).max(), 0, 12)
cibra = myci1.to_ucisdvec(cibra, orbspin)
ciket = myci1.to_ucisdvec(ciket)
myci2 = ci.UCISD(scf.UHF(gto.M()))
cidm1 = myci2.trans_rdm1(cibra, ciket, (norb // 2, norb // 2),
(nocc // 2, nocc // 2))
self.assertAlmostEqual(abs(cidm1[0] - fcidm1[0]).max(), 0, 12)
self.assertAlmostEqual(abs(cidm1[1] - fcidm1[1]).max(), 0, 12)
def test_h4_a(self):
'''Compare to FCI'''
mol = gto.Mole()
mol.verbose = 0
mol.atom = [
['H', ( 1.,-1. , 0. )],
['H', ( 0.,-1. ,-1. )],
['H', ( 1.,-0.5 , 0. )],
['H', ( 0.,-1. , 1. )],
]
mol.charge = -2
mol.spin = 2
mol.basis = '3-21g'
mol.build()
mf = scf.UHF(mol).run(conv_tol=1e-14)
ehf0 = mf.e_tot - mol.energy_nuc()
gmf = scf.addons.convert_to_ghf(mf)
myci = ci.GCISD(gmf)
eris = myci.ao2mo()
numpy.random.seed(12)
nocca, noccb = mol.nelec
nmo = mol.nao_nr()
nvira = nmo - nocca
nvirb = nmo - noccb
#cisdvec = myci.get_init_guess(eris)[1]
c1a = .1 * numpy.random.random((nocca,nvira))
c1b = .1 * numpy.random.random((noccb,nvirb))
c2aa = .1 * numpy.random.random((nocca,nocca,nvira,nvira))
c2bb = .1 * numpy.random.random((noccb,noccb,nvirb,nvirb))
c2ab = .1 * numpy.random.random((nocca,noccb,nvira,nvirb))
c1 = myci.spatial2spin((c1a, c1b))
c2 = myci.spatial2spin((c2aa, c2ab, c2bb))
cisdvec = myci.amplitudes_to_cisdvec(1., c1, c2)
self.assertEqual(cisdvec.size, myci.vector_size())
hcisd0 = myci.contract(cisdvec, eris)
eri_aa = ao2mo.kernel(mf._eri, mf.mo_coeff[0])
eri_bb = ao2mo.kernel(mf._eri, mf.mo_coeff[1])
eri_ab = ao2mo.kernel(mf._eri, [mf.mo_coeff[0], mf.mo_coeff[0],
mf.mo_coeff[1], mf.mo_coeff[1]])
h1a = reduce(numpy.dot, (mf.mo_coeff[0].T, mf.get_hcore(), mf.mo_coeff[0]))
h1b = reduce(numpy.dot, (mf.mo_coeff[1].T, mf.get_hcore(), mf.mo_coeff[1]))
h2e = fci.direct_uhf.absorb_h1e((h1a,h1b), (eri_aa,eri_ab,eri_bb),
h1a.shape[0], mol.nelec, .5)
fcivec = myci.to_fcivec(cisdvec, mol.nelectron, eris.orbspin)
hci1 = fci.direct_uhf.contract_2e(h2e, fcivec, h1a.shape[0], mol.nelec)
hci1 -= ehf0 * fcivec
hcisd1 = myci.from_fcivec(hci1, mol.nelectron, eris.orbspin)
self.assertAlmostEqual(abs(hcisd1-hcisd0).max(), 0, 9)
hdiag0 = myci.make_diagonal(eris)
hdiag0 = myci.to_fcivec(hdiag0, mol.nelectron, eris.orbspin).ravel()
hdiag0 = myci.from_fcivec(hdiag0, mol.nelectron, eris.orbspin).ravel()
hdiag1 = fci.direct_uhf.make_hdiag((h1a,h1b), (eri_aa,eri_ab,eri_bb),
h1a.shape[0], mol.nelec)
hdiag1 = myci.from_fcivec(hdiag1, mol.nelectron, eris.orbspin).ravel()
self.assertAlmostEqual(abs(abs(hdiag0)-abs(hdiag1)).max(), 0, 9)
ecisd = myci.kernel()[0]
efci = fci.direct_uhf.kernel((h1a,h1b), (eri_aa,eri_ab,eri_bb),
h1a.shape[0], mol.nelec)[0]
self.assertAlmostEqual(ecisd, -0.037067274690894436, 9)
self.assertTrue(myci.e_tot-mol.energy_nuc() - efci < 0.002)
def test_h4(self):
mol = gto.Mole()
mol.verbose = 0
mol.atom = [
['H', ( 1.,-1. , 0. )],
['H', ( 0.,-1. ,-1. )],
['H', ( 1.,-0.5 , 0. )],
['H', ( 0.,-1. , 1. )],
]
mol.charge = 2
mol.spin = 2
mol.basis = '3-21g'
mol.build()
mf = scf.GHF(mol).run(conv_tol=1e-14)
myci = ci.GCISD(mf)
myci.kernel()
self.assertAlmostEqual(myci.e_tot, -0.86423570617209888, 8)
mf = scf.RHF(mol).run(conv_tol=1e-14)
myci = ci.GCISD(mf)
myci.kernel()
self.assertAlmostEqual(myci.e_tot, -0.86423570617209888, 8)
mol = gto.Mole()
mol.verbose = 0
mol.atom = [
['H', ( 1.,-1. , 0. )],
['H', ( 0.,-1. ,-1. )],
['H', ( 1.,-0.5 , 0. )],
['H', ( 0.,-1. , 1. )],
]
mol.charge = 2
mol.spin = 0
mol.basis = '3-21g'
mol.build()
mf = scf.UHF(mol).run(conv_tol=1e-14)
myci = ci.GCISD(mf)
myci.kernel()
self.assertAlmostEqual(myci.e_tot, -0.86423570617209888, 8)
mf = scf.UHF(mol).run(conv_tol=1e-14)
gmf = scf.addons.convert_to_ghf(mf)
ehf0 = mf.e_tot - mol.energy_nuc()
myci = gcisd.GCISD(gmf)
eris = myci.ao2mo()
ecisd = myci.kernel(eris=eris)[0]
eri_aa = ao2mo.kernel(mf._eri, mf.mo_coeff[0])
eri_bb = ao2mo.kernel(mf._eri, mf.mo_coeff[1])
eri_ab = ao2mo.kernel(mf._eri, [mf.mo_coeff[0], mf.mo_coeff[0],
mf.mo_coeff[1], mf.mo_coeff[1]])
h1a = reduce(numpy.dot, (mf.mo_coeff[0].T, mf.get_hcore(), mf.mo_coeff[0]))
h1b = reduce(numpy.dot, (mf.mo_coeff[1].T, mf.get_hcore(), mf.mo_coeff[1]))
efci, fcivec = fci.direct_uhf.kernel((h1a,h1b), (eri_aa,eri_ab,eri_bb),
h1a.shape[0], mol.nelec)
self.assertAlmostEqual(myci.e_tot-mol.energy_nuc(), efci, 9)
dm1ref, dm2ref = fci.direct_uhf.make_rdm12s(fcivec, h1a.shape[0], mol.nelec)
nmo = myci.nmo
rdm1 = myci.make_rdm1(myci.ci, nmo, mol.nelectron)
rdm2 = myci.make_rdm2(myci.ci, nmo, mol.nelectron)
idxa = eris.orbspin == 0
idxb = eris.orbspin == 1
self.assertAlmostEqual(abs(dm1ref[0] - rdm1[idxa][:,idxa]).max(), 0, 6)
self.assertAlmostEqual(abs(dm1ref[1] - rdm1[idxb][:,idxb]).max(), 0, 6)
self.assertAlmostEqual(abs(dm2ref[0] - rdm2[idxa][:,idxa][:,:,idxa][:,:,:,idxa]).max(), 0, 6)
self.assertAlmostEqual(abs(dm2ref[1] - rdm2[idxa][:,idxa][:,:,idxb][:,:,:,idxb]).max(), 0, 6)
self.assertAlmostEqual(abs(dm2ref[2] - rdm2[idxb][:,idxb][:,:,idxb][:,:,:,idxb]).max(), 0, 6)