def test_mat_on_vec_cisd(self):
nmo = 9
na = 2
nb = 2
thresh = 1e-14
ha = numpy.random.random((nmo, nmo))
ha = ha + ha.transpose((1, 0))
hb = ha
Ia = numpy.random.random((nmo, nmo, nmo, nmo))
Ia = Ia + Ia.transpose((1, 0, 3, 2))
Ib = Ia
Iabab = Ia
sa = ci_utils.s_strings(nmo, na)
sb = ci_utils.s_strings(nmo, nb)
da = ci_utils.d_strings(nmo, na)
db = ci_utils.d_strings(nmo, nb)
occ = [1 if i < na else 0 for i in range(nmo)]
ref = ci_utils.Dstring(nmo, occ)
basis = []
# scf ground state
basis.append((ref, ref))
# singly excited states
for a in sa:
basis.append((a, ref))
for b in sb:
basis.append((ref, b))
# doubly excited states
for a in da:
basis.append((a, ref))
for b in db:
basis.append((ref, b))
for a in sa:
for b in sb:
basis.append((a, b))
nd = len(basis)
vec = numpy.random.random(nd)
H = numpy.zeros((nd, nd))
for i, b in enumerate(basis):
for j, k in enumerate(basis):
H[i, j] = ci_utils.ci_matrixel(
b[0], b[1], k[0], k[1], ha, hb, Ia, Ib, Iabab, 0.0)
ref = numpy.einsum('ij,j->i', H, vec)
out = ci_utils.H_on_vec(basis, vec, ha, hb, Ia, Ib, Iabab)
diff = numpy.linalg.norm(out - ref)/numpy.linalg.norm(ref)
self.assertTrue(diff < thresh, "Difference: {}".format(diff))
def test_cis(self):
from pyscf import gto
from pyscf.tdscf.rhf import scf
# reference
mol = gto.Mole()
mol.build(
atom='H 0 0 0; H 0 0 0.77', # in Angstrom
basis='631g', verbose=0)
mf = scf.RHF(mol)
mf.conv_tol_grad = 1e-9
Escf = mf.kernel()
mf.verbose = 0
tda = mf.TDA()
tda.nstates = 6
erefs = tda.kernel()[0]
tda.singlet = False
ereft = tda.kernel()[0]
# run CIS calculation
mos = mf.mo_coeff
nmo = mos.shape[1]
hcore = mf.get_hcore()
ha = numpy.einsum('mp,mn,nq->pq', mos, hcore, mos)
hb = ha.copy()
I = integrals.get_phys(mol, mos, mos, mos, mos)
N = mol.nelectron
na = N//2
nb = na
basis = ci_utils.ucis_basis(nmo, na, nb, gs=False)
nd = len(basis)
H = numpy.zeros((nd, nd))
const = -Escf + mol.energy_nuc()
F = mf.get_fock()
F = numpy.einsum('mp,mn,nq->pq', mos, F, mos)
for i, b in enumerate(basis):
for j, k in enumerate(basis):
H[i, j] = ci_utils.ci_matrixel(
b[0], b[1], k[0], k[1], ha, hb, I, I, I, const)
eout, v = numpy.linalg.eigh(H)
eref = numpy.sort(numpy.concatenate((erefs, ereft)))
diff = numpy.linalg.norm(eref - eout)
self.assertTrue(diff < 1e-10)
def test_cisd(self):
from pyscf import gto, scf, ci
mol = gto.M(
atom='Be 0 0 0',
basis='631g', verbose=0)
mf = scf.RHF(mol)
mf.conv_tol = 1e-12
Escf = mf.kernel()
myci = ci.CISD(mf).run()
#print('RCISD correlation energy', myci.e_corr)
ref = myci.e_corr
# run naive CISD calculation
mos = mf.mo_coeff
nmo = mos.shape[1]
hcore = mf.get_hcore()
ha = numpy.einsum('mp,mn,nq->pq', mos, hcore, mos)
hb = ha.copy()
I = integrals.get_phys(mol, mos, mos, mos, mos)
N = mol.nelectron
na = N//2
nb = na
basis = ci_utils.ucisd_basis(nmo, na, nb)
nd = len(basis)
H = numpy.zeros((nd, nd))
const = -Escf + mol.energy_nuc()
for i, b in enumerate(basis):
for j, k in enumerate(basis):
H[i, j] = ci_utils.ci_matrixel(
b[0], b[1], k[0], k[1], ha, hb, I, I, I, const)
eout, v = numpy.linalg.eigh(H)
#print('RCISD correlation energy', eout[0])
diff = abs(ref - eout[0])
self.assertTrue(diff < 1e-12)
mf.conv_tol_grad = 1e-9
Escf = mf.kernel()
print(Escf)
myci = ci.CISD(mf).run()
print('RCISD correlation energy', myci.e_corr)
# run naive CISD calculation
mos = mf.mo_coeff
nmo = mos.shape[1]
hcore = mf.get_hcore()
ha = numpy.einsum('mp,mn,nq->pq', mos, hcore, mos)
hb = ha.copy()
I = integrals.get_phys(mol, mos, mos, mos, mos)
N = mol.nelectron
N = mol.nelectron
na = N // 2
nb = na
basis = ci_utils.ucisd_basis(nmo, na, nb)
nd = len(basis)
H = numpy.zeros((nd, nd))
const = -Escf + mol.energy_nuc()
for i, b in enumerate(basis):
for j, k in enumerate(basis):
H[i, j] = ci_utils.ci_matrixel(b[0], b[1], k[0], k[1], ha, hb, I, I, I,
const)
eout, v = numpy.linalg.eigh(H)
print('RCISD correlation energy', eout[0])