def _calculate_integrals(mol,
hf_method='rhf',
conv_tol=1e-9,
max_cycle=50,
init_guess='minao'):
"""Function to calculate the one and two electron terms. Perform a Hartree-Fock calculation in
the given basis.
Args:
mol (gto.Mole) : A PySCF gto.Mole object.
hf_method (str): rhf, uhf, rohf
conv_tol (float): Convergence tolerance
max_cycle (int): Max convergence cycles
init_guess (str): Initial guess for SCF
Returns:
QMolecule: QMolecule populated with driver integrals etc
Raises:
QiskitChemistryError: Invalid hf method type
"""
enuke = gto.mole.energy_nuc(mol)
if hf_method == 'rhf':
m_f = scf.RHF(mol)
elif hf_method == 'rohf':
m_f = scf.ROHF(mol)
elif hf_method == 'uhf':
m_f = scf.UHF(mol)
else:
raise QiskitChemistryError(
'Invalid hf_method type: {}'.format(hf_method))
m_f.conv_tol = conv_tol
m_f.max_cycle = max_cycle
m_f.init_guess = init_guess
ehf = m_f.kernel()
logger.info('PySCF kernel() converged: %s, e(hf): %s', m_f.converged,
m_f.e_tot)
if isinstance(m_f.mo_coeff, tuple):
mo_coeff = m_f.mo_coeff[0]
mo_coeff_b = m_f.mo_coeff[1]
# mo_occ = m_f.mo_occ[0]
# mo_occ_b = m_f.mo_occ[1]
else:
# With PySCF 1.6.2, instead of a tuple of 2 dimensional arrays, its a 3 dimensional
# array with the first dimension indexing to the coeff arrays for alpha and beta
if len(m_f.mo_coeff.shape) > 2:
mo_coeff = m_f.mo_coeff[0]
mo_coeff_b = m_f.mo_coeff[1]
# mo_occ = m_f.mo_occ[0]
# mo_occ_b = m_f.mo_occ[1]
else:
mo_coeff = m_f.mo_coeff
mo_coeff_b = None
# mo_occ = mf.mo_occ
# mo_occ_b = None
norbs = mo_coeff.shape[0]
if isinstance(m_f.mo_energy, tuple):
orbs_energy = m_f.mo_energy[0]
orbs_energy_b = m_f.mo_energy[1]
else:
# See PYSCF 1.6.2 comment above - this was similarly changed
if len(m_f.mo_energy.shape) > 1:
orbs_energy = m_f.mo_energy[0]
orbs_energy_b = m_f.mo_energy[1]
else:
orbs_energy = m_f.mo_energy
orbs_energy_b = None
if logger.isEnabledFor(logging.DEBUG):
# Add some more to PySCF output...
# First analyze() which prints extra information about MO energy and occupation
mol.stdout.write('\n')
m_f.analyze()
# Now labelled orbitals for contributions to the MOs for s,p,d etc of each atom
mol.stdout.write('\n\n--- Alpha Molecular Orbitals ---\n\n')
dump_mat.dump_mo(mol, mo_coeff, digits=7, start=1)
if mo_coeff_b is not None:
mol.stdout.write('\n--- Beta Molecular Orbitals ---\n\n')
dump_mat.dump_mo(mol, mo_coeff_b, digits=7, start=1)
mol.stdout.flush()
hij = m_f.get_hcore()
mohij = np.dot(np.dot(mo_coeff.T, hij), mo_coeff)
mohij_b = None
if mo_coeff_b is not None:
mohij_b = np.dot(np.dot(mo_coeff_b.T, hij), mo_coeff_b)
eri = mol.intor('int2e', aosym=1)
mo_eri = ao2mo.incore.full(m_f._eri, mo_coeff, compact=False)
mohijkl = mo_eri.reshape(norbs, norbs, norbs, norbs)
mohijkl_bb = None
mohijkl_ba = None
if mo_coeff_b is not None:
mo_eri_b = ao2mo.incore.full(m_f._eri, mo_coeff_b, compact=False)
mohijkl_bb = mo_eri_b.reshape(norbs, norbs, norbs, norbs)
mo_eri_ba = ao2mo.incore.general(
m_f._eri, (mo_coeff_b, mo_coeff_b, mo_coeff, mo_coeff),
compact=False)
mohijkl_ba = mo_eri_ba.reshape(norbs, norbs, norbs, norbs)
# dipole integrals
mol.set_common_orig((0, 0, 0))
ao_dip = mol.intor_symmetric('int1e_r', comp=3)
x_dip_ints = ao_dip[0]
y_dip_ints = ao_dip[1]
z_dip_ints = ao_dip[2]
d_m = m_f.make_rdm1(m_f.mo_coeff, m_f.mo_occ)
if hf_method in ('rohf', 'uhf'):
d_m = d_m[0]
elec_dip = np.negative(np.einsum('xij,ji->x', ao_dip, d_m).real)
elec_dip = np.round(elec_dip, decimals=8)
nucl_dip = np.einsum('i,ix->x', mol.atom_charges(), mol.atom_coords())
nucl_dip = np.round(nucl_dip, decimals=8)
logger.info("HF Electronic dipole moment: %s", elec_dip)
logger.info("Nuclear dipole moment: %s", nucl_dip)
logger.info("Total dipole moment: %s", nucl_dip + elec_dip)
# Create driver level molecule object and populate
_q_ = QMolecule()
_q_.origin_driver_version = pyscf_version
# Energies and orbits
_q_.hf_energy = ehf
_q_.nuclear_repulsion_energy = enuke
_q_.num_orbitals = norbs
_q_.num_alpha = mol.nelec[0]
_q_.num_beta = mol.nelec[1]
_q_.mo_coeff = mo_coeff
_q_.mo_coeff_b = mo_coeff_b
_q_.orbital_energies = orbs_energy
_q_.orbital_energies_b = orbs_energy_b
# Molecule geometry
_q_.molecular_charge = mol.charge
_q_.multiplicity = mol.spin + 1
_q_.num_atoms = mol.natm
_q_.atom_symbol = []
_q_.atom_xyz = np.empty([mol.natm, 3])
_ = mol.atom_coords()
for n_i in range(0, _q_.num_atoms):
xyz = mol.atom_coord(n_i)
_q_.atom_symbol.append(mol.atom_pure_symbol(n_i))
_q_.atom_xyz[n_i][0] = xyz[0]
_q_.atom_xyz[n_i][1] = xyz[1]
_q_.atom_xyz[n_i][2] = xyz[2]
# 1 and 2 electron integrals AO and MO
_q_.hcore = hij
_q_.hcore_b = None
_q_.kinetic = mol.intor_symmetric('int1e_kin')
_q_.overlap = m_f.get_ovlp()
_q_.eri = eri
_q_.mo_onee_ints = mohij
_q_.mo_onee_ints_b = mohij_b
_q_.mo_eri_ints = mohijkl
_q_.mo_eri_ints_bb = mohijkl_bb
_q_.mo_eri_ints_ba = mohijkl_ba
# dipole integrals AO and MO
_q_.x_dip_ints = x_dip_ints
_q_.y_dip_ints = y_dip_ints
_q_.z_dip_ints = z_dip_ints
_q_.x_dip_mo_ints = QMolecule.oneeints2mo(x_dip_ints, mo_coeff)
_q_.x_dip_mo_ints_b = None
_q_.y_dip_mo_ints = QMolecule.oneeints2mo(y_dip_ints, mo_coeff)
_q_.y_dip_mo_ints_b = None
_q_.z_dip_mo_ints = QMolecule.oneeints2mo(z_dip_ints, mo_coeff)
_q_.z_dip_mo_ints_b = None
if mo_coeff_b is not None:
_q_.x_dip_mo_ints_b = QMolecule.oneeints2mo(x_dip_ints, mo_coeff_b)
_q_.y_dip_mo_ints_b = QMolecule.oneeints2mo(y_dip_ints, mo_coeff_b)
_q_.z_dip_mo_ints_b = QMolecule.oneeints2mo(z_dip_ints, mo_coeff_b)
# dipole moment
_q_.nuclear_dipole_moment = nucl_dip
_q_.reverse_dipole_sign = True
return _q_
def run(
self, qmolecule: QMolecule
) -> Tuple[WeightedPauliOperator, List[WeightedPauliOperator]]:
""" run method"""
logger.debug('Processing started...')
# Save these values for later combination with the quantum computation result
self._hf_energy = qmolecule.hf_energy
self._nuclear_repulsion_energy = qmolecule.nuclear_repulsion_energy
self._nuclear_dipole_moment = qmolecule.nuclear_dipole_moment
self._reverse_dipole_sign = qmolecule.reverse_dipole_sign
core_list = qmolecule.core_orbitals if self._freeze_core else []
reduce_list = self._orbital_reduction
if self._freeze_core:
logger.info(
"Freeze_core specified. Core orbitals to be frozen: %s",
core_list)
if reduce_list:
logger.info("Configured orbital reduction list: %s", reduce_list)
reduce_list = [
x + qmolecule.num_orbitals if x < 0 else x for x in reduce_list
]
freeze_list = []
remove_list = []
# Orbitals are specified by their index from 0 to n-1, where n is the number of orbitals the
# molecule has. The combined list of the core orbitals, when freeze_core is true, with any
# user supplied orbitals is what will be used. Negative numbers may be used to indicate the
# upper virtual orbitals, so -1 is the highest, then -2 etc. and these will
# be converted to the
# positive 0-based index for computation.
# In the combined list any orbitals that are occupied are added to a freeze list and an
# energy is stored from these orbitals to be added later.
# Unoccupied orbitals are just discarded.
# Because freeze and eliminate is done in separate steps,
# with freeze first, we have to re-base
# the indexes for elimination according to how many orbitals were removed when freezing.
#
orbitals_list = list(set(core_list + reduce_list))
num_alpha = qmolecule.num_alpha
num_beta = qmolecule.num_beta
new_num_alpha = num_alpha
new_num_beta = num_beta
if orbitals_list:
orbitals_list = np.array(orbitals_list)
orbitals_list = \
orbitals_list[(cast(np.ndarray, orbitals_list) >= 0) &
(orbitals_list < qmolecule.num_orbitals)]
freeze_list_alpha = [i for i in orbitals_list if i < num_alpha]
freeze_list_beta = [i for i in orbitals_list if i < num_beta]
freeze_list = np.append(
freeze_list_alpha,
[i + qmolecule.num_orbitals for i in freeze_list_beta])
remove_list_alpha = [i for i in orbitals_list if i >= num_alpha]
remove_list_beta = [i for i in orbitals_list if i >= num_beta]
rla_adjust = -len(freeze_list_alpha)
rlb_adjust = -len(freeze_list_alpha) - len(
freeze_list_beta) + qmolecule.num_orbitals
remove_list = np.append(
[i + rla_adjust for i in remove_list_alpha],
[i + rlb_adjust for i in remove_list_beta])
logger.info("Combined orbital reduction list: %s", orbitals_list)
logger.info(
" converting to spin orbital reduction list: %s",
np.append(np.array(orbitals_list),
np.array(orbitals_list) + qmolecule.num_orbitals))
logger.info(" => freezing spin orbitals: %s", freeze_list)
logger.info(
" => removing spin orbitals: %s (indexes accounting for freeze %s)",
np.append(remove_list_alpha,
np.array(remove_list_beta) + qmolecule.num_orbitals),
remove_list)
new_num_alpha -= len(freeze_list_alpha)
new_num_beta -= len(freeze_list_beta)
new_nel = [new_num_alpha, new_num_beta]
fer_op = FermionicOperator(h1=qmolecule.one_body_integrals,
h2=qmolecule.two_body_integrals)
fer_op, self._energy_shift, did_shift = \
Hamiltonian._try_reduce_fermionic_operator(fer_op, freeze_list, remove_list)
if did_shift:
logger.info("Frozen orbital energy shift: %s", self._energy_shift)
if self._transformation == TransformationType.PARTICLE_HOLE.value:
fer_op, ph_shift = fer_op.particle_hole_transformation(new_nel)
self._ph_energy_shift = -ph_shift
logger.info("Particle hole energy shift: %s",
self._ph_energy_shift)
logger.debug('Converting to qubit using %s mapping',
self._qubit_mapping)
qubit_op = Hamiltonian._map_fermionic_operator_to_qubit(
fer_op, self._qubit_mapping, new_nel, self._two_qubit_reduction)
qubit_op.name = 'Electronic Hamiltonian'
logger.debug(' num paulis: %s, num qubits: %s', len(qubit_op.paulis),
qubit_op.num_qubits)
aux_ops = []
def _add_aux_op(aux_op, name):
aux_qop = Hamiltonian._map_fermionic_operator_to_qubit(
aux_op, self._qubit_mapping, new_nel,
self._two_qubit_reduction)
aux_qop.name = name
aux_ops.append(aux_qop)
logger.debug(' num paulis: %s', aux_qop.paulis)
logger.debug('Creating aux op for Number of Particles')
_add_aux_op(fer_op.total_particle_number(), 'Number of Particles')
logger.debug('Creating aux op for S^2')
_add_aux_op(fer_op.total_angular_momentum(), 'S^2')
logger.debug('Creating aux op for Magnetization')
_add_aux_op(fer_op.total_magnetization(), 'Magnetization')
if qmolecule.has_dipole_integrals():
def _dipole_op(dipole_integrals, axis):
logger.debug('Creating aux op for dipole %s', axis)
fer_op_ = FermionicOperator(h1=dipole_integrals)
fer_op_, shift, did_shift_ = self._try_reduce_fermionic_operator(
fer_op_, freeze_list, remove_list)
if did_shift_:
logger.info("Frozen orbital %s dipole shift: %s", axis,
shift)
ph_shift_ = 0.0
if self._transformation == TransformationType.PARTICLE_HOLE.value:
fer_op_, ph_shift_ = fer_op_.particle_hole_transformation(
new_nel)
ph_shift_ = -ph_shift_
logger.info("Particle hole %s dipole shift: %s", axis,
ph_shift_)
qubit_op_ = self._map_fermionic_operator_to_qubit(
fer_op_, self._qubit_mapping, new_nel,
self._two_qubit_reduction)
qubit_op_.name = 'Dipole ' + axis
logger.debug(' num paulis: %s', len(qubit_op_.paulis))
return qubit_op_, shift, ph_shift_
op_dipole_x, self._x_dipole_shift, self._ph_x_dipole_shift = \
_dipole_op(qmolecule.x_dipole_integrals, 'x')
op_dipole_y, self._y_dipole_shift, self._ph_y_dipole_shift = \
_dipole_op(qmolecule.y_dipole_integrals, 'y')
op_dipole_z, self._z_dipole_shift, self._ph_z_dipole_shift = \
_dipole_op(qmolecule.z_dipole_integrals, 'z')
aux_ops.append(op_dipole_x)
aux_ops.append(op_dipole_y)
aux_ops.append(op_dipole_z)
logger.info('Molecule num electrons: %s, remaining for processing: %s',
[num_alpha, num_beta], new_nel)
nspinorbs = qmolecule.num_orbitals * 2
new_nspinorbs = nspinorbs - len(freeze_list) - len(remove_list)
logger.info(
'Molecule num spin orbitals: %s, remaining for processing: %s',
nspinorbs, new_nspinorbs)
self._add_molecule_info(self.INFO_NUM_PARTICLES,
(new_num_alpha, new_num_beta))
self._add_molecule_info(self.INFO_NUM_ORBITALS, new_nspinorbs)
self._add_molecule_info(
self.INFO_TWO_QUBIT_REDUCTION, self._two_qubit_reduction
if self._qubit_mapping == 'parity' else False)
z2symmetries = Z2Symmetries([], [], [], None)
if self._z2symmetry_reduction is not None:
logger.debug('Processing z2 symmetries')
qubit_op, aux_ops, z2symmetries = self._process_z2symmetry_reduction(
qubit_op, aux_ops)
self._add_molecule_info(self.INFO_Z2SYMMETRIES, z2symmetries)
logger.debug('Processing complete ready to run algorithm')
return qubit_op, aux_ops
def run(self) -> QMolecule:
"""Constructs a QMolecule instance out of a FCIDump file.
Returns:
A QMolecule instance populated with a minimal set of required data.
"""
fcidump_data = parse(self._fcidump_input)
q_mol = QMolecule()
q_mol.nuclear_repulsion_energy = fcidump_data.get('ecore', None)
q_mol.num_orbitals = fcidump_data.get('NORB')
q_mol.multiplicity = fcidump_data.get('MS2', 0) + 1
q_mol.charge = 0 # ensures QMolecule.log() works
q_mol.num_beta = (fcidump_data.get('NELEC') -
(q_mol.multiplicity - 1)) // 2
q_mol.num_alpha = fcidump_data.get('NELEC') - q_mol.num_beta
if self.atoms is not None:
q_mol.num_atoms = len(self.atoms)
q_mol.atom_symbol = self.atoms
q_mol.atom_xyz = [[float('NaN')] * 3] * len(
self.atoms) # ensures QMolecule.log() works
q_mol.mo_onee_ints = fcidump_data.get('hij', None)
q_mol.mo_onee_ints_b = fcidump_data.get('hij_b', None)
q_mol.mo_eri_ints = fcidump_data.get('hijkl', None)
q_mol.mo_eri_ints_bb = fcidump_data.get('hijkl_bb', None)
q_mol.mo_eri_ints_ba = fcidump_data.get('hijkl_ba', None)
return q_mol
max_cycle=5000,
max_memory=1024 * 128,
basis='sto3g'
)
#driver = PySCFDriver(atom='H .0 .0 .0; H .0 .0 0.735',
# unit=UnitsType.ANGSTROM,
# basis='sto3g')
#FILENAME = "hdf5_files/femoco_sto3g_(-1,3).hdf5"
#FILENAME = "hdf5_files/femoco_nosulfer_sto3g_(-1,3).hdf5"
FILENAME = "hdf5_files/lih_sto3g_(0,0).hdf5"
#FILENAME = "hdf5_files/hydrogen.hdf5"
if os.path.exists(FILENAME):
print(f"Found {FILENAME}. Loading...")
molecule = QMolecule(FILENAME)
molecule.load()
else:
# Regenerate
print(f"Couldn't find {FILENAME}. Regenerating...")
molecule = driver.run()
molecule.save(FILENAME)
#print("Loading 1 body integrals...")
#one_body_integrals = molecule.one_body_integrals
##np.save("results/old/lih_1d.npy", one_body_integrals)
#np.save("results/new/lih_1d.npy", one_body_integrals)
#
#print("Loading 2 body integrals...")
#two_body_integrals = molecule.two_body_integrals
#np.save("results/new/lih_2d.npy", two_body_integrals)
def _parse_matrix_file(self, fname, useao2e=False):
# get_driver_class is used here because the discovery routine will load all the gaussian
# binary dependencies, if not loaded already. It won't work without it.
try:
# add gauopen to sys.path so that binaries can be loaded
gauopen_directory = os.path.join(
os.path.dirname(os.path.realpath(__file__)), 'gauopen')
if gauopen_directory not in sys.path:
sys.path.insert(0, gauopen_directory)
# pylint: disable=import-outside-toplevel
from .gauopen.QCMatEl import MatEl
except ImportError as mnfe:
msg = ('qcmatrixio extension not found. '
'See Gaussian driver readme to build qcmatrixio.F using f2py') \
if mnfe.name == 'qcmatrixio' else str(mnfe)
logger.info(msg)
raise QiskitChemistryError(msg)
mel = MatEl(file=fname)
logger.debug('MatrixElement file:\n%s', mel)
# Create driver level molecule object and populate
_q_ = QMolecule()
_q_.origin_driver_version = mel.gversion
# Energies and orbits
_q_.hf_energy = mel.scalar('ETOTAL')
_q_.nuclear_repulsion_energy = mel.scalar('ENUCREP')
_q_.num_orbitals = 0 # updated below from orbital coeffs size
_q_.num_alpha = (mel.ne + mel.multip - 1) // 2
_q_.num_beta = (mel.ne - mel.multip + 1) // 2
moc = self._get_matrix(mel, 'ALPHA MO COEFFICIENTS')
moc_b = self._get_matrix(mel, 'BETA MO COEFFICIENTS')
if np.array_equal(moc, moc_b):
logger.debug(
'ALPHA and BETA MO COEFFS identical, keeping only ALPHA')
moc_b = None
_q_.num_orbitals = moc.shape[0]
_q_.mo_coeff = moc
_q_.mo_coeff_b = moc_b
orbs_energy = self._get_matrix(mel, 'ALPHA ORBITAL ENERGIES')
_q_.orbital_energies = orbs_energy
orbs_energy_b = self._get_matrix(mel, 'BETA ORBITAL ENERGIES')
_q_.orbital_energies_b = orbs_energy_b if moc_b is not None else None
# Molecule geometry
_q_.molecular_charge = mel.icharg
_q_.multiplicity = mel.multip
_q_.num_atoms = mel.natoms
_q_.atom_symbol = []
_q_.atom_xyz = np.empty([mel.natoms, 3])
syms = mel.ian
xyz = np.reshape(mel.c, (_q_.num_atoms, 3))
for n_i in range(0, _q_.num_atoms):
_q_.atom_symbol.append(QMolecule.symbols[syms[n_i]])
for idx in range(xyz.shape[1]):
coord = xyz[n_i][idx]
if abs(coord) < 1e-10:
coord = 0
_q_.atom_xyz[n_i][idx] = coord
# 1 and 2 electron integrals
hcore = self._get_matrix(mel, 'CORE HAMILTONIAN ALPHA')
logger.debug('CORE HAMILTONIAN ALPHA %s', hcore.shape)
hcore_b = self._get_matrix(mel, 'CORE HAMILTONIAN BETA')
if np.array_equal(hcore, hcore_b):
# From Gaussian interfacing documentation: "The two
# core Hamiltonians are identical unless
# a Fermi contact perturbation has been applied."
logger.debug(
'CORE HAMILTONIAN ALPHA and BETA identical, keeping only ALPHA'
)
hcore_b = None
logger.debug('CORE HAMILTONIAN BETA %s',
'- Not present' if hcore_b is None else hcore_b.shape)
kinetic = self._get_matrix(mel, 'KINETIC ENERGY')
logger.debug('KINETIC ENERGY %s', kinetic.shape)
overlap = self._get_matrix(mel, 'OVERLAP')
logger.debug('OVERLAP %s', overlap.shape)
mohij = QMolecule.oneeints2mo(hcore, moc)
mohij_b = None
if moc_b is not None:
mohij_b = QMolecule.oneeints2mo(
hcore if hcore_b is None else hcore_b, moc_b)
eri = self._get_matrix(mel, 'REGULAR 2E INTEGRALS')
logger.debug('REGULAR 2E INTEGRALS %s', eri.shape)
if moc_b is None and mel.matlist.get('BB MO 2E INTEGRALS') is not None:
# It seems that when using ROHF, where alpha and beta coeffs are
# the same, that integrals
# for BB and BA are included in the output, as well as just AA
# that would have been expected
# Using these fails to give the right answer (is ok for UHF).
# So in this case we revert to
# using 2 electron ints in atomic basis from the output and
# converting them ourselves.
useao2e = True
logger.info(
'Identical A and B coeffs but BB ints are present - using regular 2E ints instead'
)
if useao2e:
# eri are 2-body in AO. We can convert to MO via the QMolecule
# method but using ints in MO already, as in the else here, is better
mohijkl = QMolecule.twoeints2mo(eri, moc)
mohijkl_bb = None
mohijkl_ba = None
if moc_b is not None:
mohijkl_bb = QMolecule.twoeints2mo(eri, moc_b)
mohijkl_ba = QMolecule.twoeints2mo_general(
eri, moc_b, moc_b, moc, moc)
else:
# These are in MO basis but by default will be reduced in size by
# frozen core default so to use them we need to add Window=Full
# above when we augment the config
mohijkl = self._get_matrix(mel, 'AA MO 2E INTEGRALS')
logger.debug('AA MO 2E INTEGRALS %s', mohijkl.shape)
mohijkl_bb = self._get_matrix(mel, 'BB MO 2E INTEGRALS')
logger.debug(
'BB MO 2E INTEGRALS %s',
'- Not present' if mohijkl_bb is None else mohijkl_bb.shape)
mohijkl_ba = self._get_matrix(mel, 'BA MO 2E INTEGRALS')
logger.debug(
'BA MO 2E INTEGRALS %s',
'- Not present' if mohijkl_ba is None else mohijkl_ba.shape)
_q_.hcore = hcore
_q_.hcore_b = hcore_b
_q_.kinetic = kinetic
_q_.overlap = overlap
_q_.eri = eri
_q_.mo_onee_ints = mohij
_q_.mo_onee_ints_b = mohij_b
_q_.mo_eri_ints = mohijkl
_q_.mo_eri_ints_bb = mohijkl_bb
_q_.mo_eri_ints_ba = mohijkl_ba
# dipole moment
dipints = self._get_matrix(mel, 'DIPOLE INTEGRALS')
dipints = np.einsum('ijk->kji', dipints)
_q_.x_dip_ints = dipints[0]
_q_.y_dip_ints = dipints[1]
_q_.z_dip_ints = dipints[2]
_q_.x_dip_mo_ints = QMolecule.oneeints2mo(dipints[0], moc)
_q_.x_dip_mo_ints_b = None
_q_.y_dip_mo_ints = QMolecule.oneeints2mo(dipints[1], moc)
_q_.y_dip_mo_ints_b = None
_q_.z_dip_mo_ints = QMolecule.oneeints2mo(dipints[2], moc)
_q_.z_dip_mo_ints_b = None
if moc_b is not None:
_q_.x_dip_mo_ints_b = QMolecule.oneeints2mo(dipints[0], moc_b)
_q_.y_dip_mo_ints_b = QMolecule.oneeints2mo(dipints[1], moc_b)
_q_.z_dip_mo_ints_b = QMolecule.oneeints2mo(dipints[2], moc_b)
nucl_dip = np.einsum('i,ix->x', syms, xyz)
nucl_dip = np.round(nucl_dip, decimals=8)
_q_.nuclear_dipole_moment = nucl_dip
_q_.reverse_dipole_sign = True
return _q_
def _calculate_integrals(mol, calc_type='rhf'):
"""Function to calculate the one and two electron terms. Perform a Hartree-Fock calculation in
the given basis.
Args:
mol : A PySCF gto.Mole object.
calc_type: rhf, uhf, rohf
Returns:
ehf : Hartree-Fock energy
enuke : Nuclear repulsion energy
norbs : Number of orbitals
mohij : One electron terms of the Hamiltonian.
mohijkl : Two electron terms of the Hamiltonian.
mo_coeff: Orbital coefficients
orbs_energy: Orbitals energies
x_dip_ints: x dipole moment integrals
y_dip_ints: y dipole moment integrals
z_dip_ints: z dipole moment integrals
nucl_dipl : Nuclear dipole moment
"""
enuke = gto.mole.energy_nuc(mol)
if calc_type == 'rhf':
mf = scf.RHF(mol)
elif calc_type == 'rohf':
mf = scf.ROHF(mol)
elif calc_type == 'uhf':
mf = scf.UHF(mol)
else:
raise QiskitChemistryError('Invalid calc_type: {}'.format(calc_type))
ehf = mf.kernel()
if type(mf.mo_coeff) is tuple:
mo_coeff = mf.mo_coeff[0]
mo_occ = mf.mo_occ[0]
else:
mo_coeff = mf.mo_coeff
mo_occ = mf.mo_occ
norbs = mo_coeff.shape[0]
orbs_energy = mf.mo_energy
hij = mf.get_hcore()
mohij = np.dot(np.dot(mo_coeff.T, hij), mo_coeff)
eri = ao2mo.incore.full(mf._eri, mo_coeff, compact=False)
mohijkl = eri.reshape(norbs, norbs, norbs, norbs)
# dipole integrals
mol.set_common_orig((0, 0, 0))
ao_dip = mol.intor_symmetric('int1e_r', comp=3)
x_dip_ints = QMolecule.oneeints2mo(ao_dip[0], mo_coeff)
y_dip_ints = QMolecule.oneeints2mo(ao_dip[1], mo_coeff)
z_dip_ints = QMolecule.oneeints2mo(ao_dip[2], mo_coeff)
dm = mf.make_rdm1(mf.mo_coeff, mf.mo_occ)
if calc_type == 'rohf' or calc_type == 'uhf':
dm = dm[0]
elec_dip = np.negative(np.einsum('xij,ji->x', ao_dip, dm).real)
elec_dip = np.round(elec_dip, decimals=8)
nucl_dip = np.einsum('i,ix->x', mol.atom_charges(), mol.atom_coords())
nucl_dip = np.round(nucl_dip, decimals=8)
logger.info("HF Electronic dipole moment: {}".format(elec_dip))
logger.info("Nuclear dipole moment: {}".format(nucl_dip))
logger.info("Total dipole moment: {}".format(nucl_dip+elec_dip))
return ehf, enuke, norbs, mohij, mohijkl, mo_coeff, orbs_energy, x_dip_ints, y_dip_ints, z_dip_ints, nucl_dip
def compute_integrals(atom,
unit,
charge,
spin,
basis,
max_memory,
calc_type='rhf'):
# Get config from input parameters
# molecule is in PySCF atom string format e.g. "H .0 .0 .0; H .0 .0 0.2"
# or in Z-Matrix format e.g. "H; O 1 1.08; H 2 1.08 1 107.5"
# other parameters are as per PySCF got.Mole format
atom = _check_molecule_format(atom)
if max_memory is None:
max_memory = param.MAX_MEMORY
calc_type = calc_type.lower()
try:
mol = gto.Mole(atom=atom, unit=unit, basis=basis, max_memory=max_memory, verbose=pylogger.QUIET)
mol.symmetry = False
mol.charge = charge
mol.spin = spin
mol.build(parse_arg=False)
ehf, enuke, norbs, mohij, mohijkl, mo_coeff, orbs_energy, x_dip, y_dip, z_dip, nucl_dip = _calculate_integrals(mol, calc_type)
except Exception as exc:
raise QiskitChemistryError('Failed electronic structure computation') from exc
# Create driver level molecule object and populate
_q_ = QMolecule()
# Energies and orbits
_q_.hf_energy = ehf
_q_.nuclear_repulsion_energy = enuke
_q_.num_orbitals = norbs
_q_.num_alpha = mol.nelec[0]
_q_.num_beta = mol.nelec[1]
_q_.mo_coeff = mo_coeff
_q_.orbital_energies = orbs_energy
# Molecule geometry
_q_.molecular_charge = mol.charge
_q_.multiplicity = mol.spin + 1
_q_.num_atoms = mol.natm
_q_.atom_symbol = []
_q_.atom_xyz = np.empty([mol.natm, 3])
atoms = mol.atom_coords()
for _n in range(0, _q_.num_atoms):
xyz = mol.atom_coord(_n)
_q_.atom_symbol.append(mol.atom_pure_symbol(_n))
_q_.atom_xyz[_n][0] = xyz[0]
_q_.atom_xyz[_n][1] = xyz[1]
_q_.atom_xyz[_n][2] = xyz[2]
# 1 and 2 electron integrals. h1 & h2 are ready to pass to FermionicOperator
_q_.mo_onee_ints = mohij
_q_.mo_eri_ints = mohijkl
# dipole integrals
_q_.x_dip_mo_ints = x_dip
_q_.y_dip_mo_ints = y_dip
_q_.z_dip_mo_ints = z_dip
# dipole moment
_q_.nuclear_dipole_moment = nucl_dip
_q_.reverse_dipole_sign = True
return _q_
def _calculate_integrals(molecule,
basis='sto3g',
hf_method='rhf',
tol=1e-8,
maxiters=100):
"""Function to calculate the one and two electron terms. Perform a Hartree-Fock calculation in
the given basis.
Args:
molecule (pyQuante2.molecule): A pyquante2 molecular object.
basis (str) : The basis set for the electronic structure computation
hf_method (str): rhf, uhf, rohf
tol (float): tolerance
maxiters (int): max. iterations
Returns:
QMolecule: QMolecule populated with driver integrals etc
Raises:
QiskitChemistryError: Invalid hf methods type
"""
bfs = basisset(molecule, basis)
integrals = onee_integrals(bfs, molecule)
hij = integrals.T + integrals.V
hijkl = twoe_integrals(bfs)
# convert overlap integrals to molecular basis
# calculate the Hartree-Fock solution of the molecule
if hf_method == 'rhf':
solver = rhf(molecule, bfs)
elif hf_method == 'rohf':
solver = rohf(molecule, bfs)
elif hf_method == 'uhf':
solver = uhf(molecule, bfs)
else:
raise QiskitChemistryError(
'Invalid hf_method type: {}'.format(hf_method))
ehf = solver.converge(tol=tol, maxiters=maxiters)
logger.debug('PyQuante2 processing information:\n%s', solver)
if hasattr(solver, 'orbs'):
orbs = solver.orbs
orbs_b = None
else:
orbs = solver.orbsa
orbs_b = solver.orbsb
norbs = len(orbs)
if hasattr(solver, 'orbe'):
orbs_energy = solver.orbe
orbs_energy_b = None
else:
orbs_energy = solver.orbea
orbs_energy_b = solver.orbeb
enuke = molecule.nuclear_repulsion()
# Get ints in molecular orbital basis
mohij = simx(hij, orbs)
mohij_b = None
if orbs_b is not None:
mohij_b = simx(hij, orbs_b)
eri = hijkl.transform(np.identity(norbs))
mohijkl = hijkl.transform(orbs)
mohijkl_bb = None
mohijkl_ba = None
if orbs_b is not None:
mohijkl_bb = hijkl.transform(orbs_b)
mohijkl_ba = np.einsum('aI,bJ,cK,dL,abcd->IJKL', orbs_b, orbs_b, orbs,
orbs, hijkl[...])
# Create driver level molecule object and populate
_q_ = QMolecule()
_q_.origin_driver_version = '?' # No version info seems available to access
# Energies and orbits
_q_.hf_energy = ehf[0]
_q_.nuclear_repulsion_energy = enuke
_q_.num_orbitals = norbs
_q_.num_alpha = molecule.nup()
_q_.num_beta = molecule.ndown()
_q_.mo_coeff = orbs
_q_.mo_coeff_b = orbs_b
_q_.orbital_energies = orbs_energy
_q_.orbital_energies_b = orbs_energy_b
# Molecule geometry
_q_.molecular_charge = molecule.charge
_q_.multiplicity = molecule.multiplicity
_q_.num_atoms = len(molecule)
_q_.atom_symbol = []
_q_.atom_xyz = np.empty([len(molecule), 3])
atoms = molecule.atoms
for n_i in range(0, _q_.num_atoms):
atuple = atoms[n_i].atuple()
_q_.atom_symbol.append(QMolecule.symbols[atuple[0]])
_q_.atom_xyz[n_i][0] = atuple[1]
_q_.atom_xyz[n_i][1] = atuple[2]
_q_.atom_xyz[n_i][2] = atuple[3]
# 1 and 2 electron integrals
_q_.hcore = hij
_q_.hcore_b = None
_q_.kinetic = integrals.T
_q_.overlap = integrals.S
_q_.eri = eri
_q_.mo_onee_ints = mohij
_q_.mo_onee_ints_b = mohij_b
_q_.mo_eri_ints = mohijkl
_q_.mo_eri_ints_bb = mohijkl_bb
_q_.mo_eri_ints_ba = mohijkl_ba
return _q_
def mol_r_matrices(MoleculeFlag,check_r_matrix_flag,is_atomic):
mol = gto.Mole()
#=================================
# Hydrogen molecule
#=================================
if MoleculeFlag == 'H2':
r_matrices=[]
num_particles = 2
if is_atomic:
try:
data = np.load(MoleculeFlag+'ao.npz')
data.files
one_b = data['one_b']
two_b = data['two_b']
except IOError:
mol.atom = [['H',(0, 0, -0.3707)], ['H',(0,0.0,0.3707)]]
mol.build()
_q_=int_func.qmol_func(mol, atomic=True)
one_b=_q_.one_body_integrals
two_b=_q_.two_body_integrals
# np.savez(MoleculeFlag+'_ao.npz',one_b=_q_.one_body_integrals,two_b=_q_.two_body_integrals)
two_body_temp = QMolecule.twoe_to_spin(_q_.mo_eri_ints)
temp_int = np.einsum('ijkl->ljik', _q_.mo_eri_ints)
two_body_temp = QMolecule.twoe_to_spin(temp_int)
mol = gto.M(atom=mol.atom, basis='sto-3g')
O = get_ovlp(mol)
X = np.kron(np.identity(2), np.linalg.inv(scipy.linalg.sqrtm(O)))
fer_op = FermionicOperator(h1=_q_.one_body_integrals, h2=two_body_temp)
fer_op.transform(X)
else:
mol.atom = [['H',(0, 0, -0.3707)], ['H',(0,0.0,0.3707)]]
mol.build()
_q_=int_func.qmol_func(mol, atomic=is_atomic)
one_b=_q_.one_body_integrals
two_b=_q_.two_body_integrals
fer_op = FermionicOperator(h1=_q_.one_body_integrals, h2=_q_.two_body_integrals)
one_b = fer_op.h1
two_b = fer_op.h2
# Defining R-matrix --> r
# Swapping the spatial orbitals. This involves swapping both the spin orbitals corresponding to a spatial orbital.
# This could be treated as a reflection symmetry or rotational symmetry.
r1 = np.zeros([4,4])
r1[0,1]=1
r1[1,0]=1
r1[2,3]=1
r1[3,2]=1
# Swapping the spin oritals. Spin symmetry.
r2=np.zeros([4,4])
for i in range(4):
if i<2:
r2[i+2,i]=1.
else:
r2[i-2,i]=1.
r_matrices.append(r1)
r_matrices.append(r2)
if check_r_matrix_flag:
if bool(check_r_mat(r_matrices,fer_op,one_b,two_b)):
print('All the above matrices work!')
#=================================
# Water molecule (with different basis sets)
#=================================
elif MoleculeFlag== 'H2O_L':
r_matrices = []
print(MoleculeFlag)
# Configuration from
# mol.atom = [['O',(0.8638, 0.4573,0.0)], ['H',(0, 0, 0)], ['H',(1.7785,0.0,0.0)]]
# mol.atom = [['O',(0.0, 0.0,0.0)],['H',(1, 0, 0)], ['H',(-1.0,0.0,0.0)]]
#mol.atom = [['O',(0, 0, 0)], ['H',(0, 1, 0)], ['H@2',(0, 0, 1)]]
#mol.basis = {'O': 'sto-3g', 'H': 'cc-pvdz', 'H@2': '6-31G'}
num_particles=10
if is_atomic:
try:
data = np.load(MoleculeFlag+'ao.npz')
data.files
one_b = data['one_b']
two_b = data['two_b']
except IOError:
mol.atom = [['O',(0.0, 0.0,0.0)],['H',(1, 0, 0)], ['H',(-1.0,0.0,0.0)]]
mol.build()
_q_=int_func.qmol_func(mol, atomic=True)
one_b=_q_.one_body_integrals
two_b=_q_.two_body_integrals
# np.savez(MoleculeFlag+'_ao.npz',one_b=_q_.one_body_integrals,two_b=_q_.two_body_integrals)
two_body_temp = QMolecule.twoe_to_spin(_q_.mo_eri_ints)
temp_int = np.einsum('ijkl->ljik', _q_.mo_eri_ints)
two_body_temp = QMolecule.twoe_to_spin(temp_int)
mol = gto.M(atom=mol.atom, basis='sto-3g')
O = get_ovlp(mol)
X = np.kron(np.identity(2), np.linalg.inv(scipy.linalg.sqrtm(O)))
fer_op = FermionicOperator(h1=_q_.one_body_integrals, h2=two_body_temp)
fer_op.transform(X)
else:
mol.atom = [['O',(0.0, 0.0,0.0)],['H',(1, 0, 0)], ['H',(-1.0,0.0,0.0)]]
mol.build()
_q_=int_func.qmol_func(mol, atomic=is_atomic)
one_b=_q_.one_body_integrals
two_b=_q_.two_body_integrals
fer_op = FermionicOperator(h1=_q_.one_body_integrals, h2=_q_.two_body_integrals)
one_b = fer_op.h1
two_b = fer_op.h2
# R-matrix for plane of symmetry \sigma_{xy}. Everything remains the same, only pz-orbitals pick up negative sign.
r1=np.zeros([14,14])
r1[0,0]=1
r1[1,1]=1
r1[2,2]=1
r1[3,3]=1
r1[4,4]=-1
r1[5,5]=1
r1[6,6]=1
r1[7,7]=1
r1[8,8]=1
r1[9,9]=1
r1[10,10]=1
r1[11,11]=-1
r1[12,12]=1
r1[13,13]=1
r_matrices.append(r1)
# R-matrix for plane of symmetry \sigma_{xz}. Everything remains the same, only py-orbitals pick up negative sign.
r2=np.eye(14)
r2[3,3]=-1
r2[10,10]=-1
r_matrices.append(r2)
# R-matrix for plane of symmetry \sigma_{yz}. Everything remains the same, only px-orbitals pick up negative sign and hydrogen atoms swap.
r3=np.zeros([14,14])
r3[0,0]=1
r3[1,1]=1
r3[2,2]=-1
r3[3,3]=1
r3[4,4]=1
r3[5,6]=1
r3[6,5]=1
r3[7,7]=1
r3[8,8]=1
r3[9,9]=-1
r3[10,10]=1
r3[11,11]=1
r3[12,13]=1
r3[13,12]=1
r_matrices.append(r3)
# R-matrix for symmetry-axis C_2. Linear water molecule has three axis of symmetry:
# About z-axis
r4=np.zeros([14,14])
r4[0,0]=1
r4[1,1]=1
r4[2,2]=-1
r4[3,3]=-1
r4[4,4]=1
r4[5,6]=1
r4[6,5]=1
r4[7,7]=1
r4[8,8]=1
r4[9,9]=-1
r4[10,10]=-1
r4[11,11]=1
r4[12,13]=1
r4[13,12]=1
r_matrices.append(r4)
#About y-axis
r5=np.zeros([14,14])
r5[0,0]=1
r5[1,1]=1
r5[2,2]=-1
r5[3,3]=1
r5[4,4]=-1
r5[5,6]=1
r5[6,5]=1
r5[7,7]=1
r5[8,8]=1
r5[9,9]=-1
r5[10,10]=1
r5[11,11]=-1
r5[12,13]=1
r5[13,12]=1
r_matrices.append(r5)
#Symmetry about x-axis:
r6=np.zeros([14,14])
r6[0,0]=1
r6[1,1]=1
r6[2,2]=1
r6[3,3]=-1
r6[4,4]=-1
r6[5,5]=1
r6[6,6]=1
r6[7,7]=1
r6[8,8]=1
r6[9,9]=1
r6[10,10]=-1
r6[11,11]=-1
r6[12,12]=1
r6[13,13]=1
r_matrices.append(r6)
#Spin symmetry:
r7=np.zeros([14,14])
for i in range(14):
if i<7:
r7[i+7,i]=1.
else:
r7[i-7,i]=1.
r_matrices.append(r7)
if check_r_matrix_flag:
if bool(check_r_mat(r_matrices,fer_op,one_b,two_b)):
print('All the above matrices work!')
#=================================
# Water molecule (with different basis sets)
#=================================
elif MoleculeFlag== 'H2O':
r_matrices=[]
print(MoleculeFlag)
num_particles = 10
if is_atomic:
try:
data = np.load(MoleculeFlag+'ao.npz')
data.files
one_b = data['one_b']
two_b = data['two_b']
except IOError:
mol.atom = [['O',(0.0000, 0.0000, 0.0000)],
['H',(0.757, 0.586, 0.0)],
['H',(-0.757, 0.586, 0.0)]]
# mol.atom = [['N', (0.0000, 0.0000, 0.0000)],
# ['H', (0.0000, -1.,-0.3816)],
# ['H', (0.8, 0.6 ,-0.3816)],
# ['H', (-0.8, 0.6 ,-0.3816)]]
mol.build()
_q_=int_func.qmol_func(mol, atomic=True)
one_b=_q_.one_body_integrals
two_b=_q_.two_body_integrals
# np.savez(MoleculeFlag+'_ao.npz',one_b=_q_.one_body_integrals,two_b=_q_.two_body_integrals)
two_body_temp = QMolecule.twoe_to_spin(_q_.mo_eri_ints)
temp_int = np.einsum('ijkl->ljik', _q_.mo_eri_ints)
two_body_temp = QMolecule.twoe_to_spin(temp_int)
mol = gto.M(atom=mol.atom, basis='sto-3g')
O = get_ovlp(mol)
X = np.kron(np.identity(2), np.linalg.inv(scipy.linalg.sqrtm(O)))
fer_op = FermionicOperator(h1=_q_.one_body_integrals, h2=two_body_temp)
fer_op.transform(X)
else:
mol.atom = [['O',(0.0000, 0.0000, 0.0000)],
['H',(0.757, 0.586, 0.0)],
['H',(-0.757, 0.586, 0.0)]]
mol.build()
_q_=int_func.qmol_func(mol, atomic=is_atomic)
one_b=_q_.one_body_integrals
two_b=_q_.two_body_integrals
fer_op = FermionicOperator(h1=_q_.one_body_integrals, h2=_q_.two_body_integrals)
one_b = fer_op.h1
two_b = fer_op.h2
#Spin symmetry:
r1=np.zeros([14,14])
for i in range(14):
if i<7:
r1[i+7,i]=1.
else:
r1[i-7,i]=1.
# r_matrices.append(r1)
# R-matrix for plane of symmetry \sigma_{xy}. Everything remains the same, only pz-orbitals pick up negative sign.
r2=np.eye(14)
r2[4,4]=-1
r2[11,11]=-1
r_matrices.append(r2)
# R-matrix for plane of symmetry \sigma_{yz}. Everything remains the same, only px-orbitals pick up negative sign and the hydrogen atoms swap.
r3=np.eye(14)
r3[2,2]=-1
r3[9,9]=-1
r3[12,12]=0
r3[13,13]=0
r3[12,13]=1
r3[13,12]=1
r3[5,6]=1
r3[6,5]=1
r3[5,5]=0
r3[6,6]=0
# print(r)
r_matrices.append(r3)
#Axial symmetry about y-axis
r4=np.zeros([14,14])
r4[0,0]=1
r4[1,1]=1
r4[2,2]=-1
r4[3,3]=1
r4[4,4]=-1
r4[5,6]=1
r4[6,5]=1
r4[7,7]=1
r4[8,8]=1
r4[9,9]=-1
r4[10,10]=1
r4[11,11]=-1
r4[12,13]=1
r4[13,12]=1
r_matrices.append(r4)
if check_r_matrix_flag:
if bool(check_r_mat(r_matrices,fer_op,one_b,two_b)):
print('All the above matrices work!')
#=================================
# Ammonia molecule
#=================================
elif MoleculeFlag=='NH3':
print(MoleculeFlag)
num_particles = 10
if is_atomic:
try:
data = np.load(MoleculeFlag+'ao.npz')
data.files
one_b = data['one_b']
two_b = data['two_b']
except IOError:
mol.atom = [['N' , ( 0.0000000, 0.0000000, 0.1493220)],
['H' , ( 0.0000000 , 0.9474830 , -0.3484190)],
['H' , ( 0.8205440 , -0.4737420 , -0.3484190)],
['H' , ( -0.8205440 , -0.4737420 , -0.3484190)]]
mol.build()
_q_=int_func.qmol_func(mol, atomic=True)
one_b=_q_.one_body_integrals
two_b=_q_.two_body_integrals
# np.savez(MoleculeFlag+'_ao.npz',one_b=_q_.one_body_integrals,two_b=_q_.two_body_integrals)
two_body_temp = QMolecule.twoe_to_spin(_q_.mo_eri_ints)
temp_int = np.einsum('ijkl->ljik', _q_.mo_eri_ints)
two_body_temp = QMolecule.twoe_to_spin(temp_int)
mol = gto.M(atom=mol.atom, basis='sto-3g')
O = get_ovlp(mol)
X = np.kron(np.identity(2), np.linalg.inv(scipy.linalg.sqrtm(O)))
fer_op = FermionicOperator(h1=_q_.one_body_integrals, h2=two_body_temp)
fer_op.transform(X)
else:
mol.atom = [['N' , ( 0.0000000, 0.0000000, 0.1493220)],
['H' , ( 0.0000000 , 0.9474830 , -0.3484190)],
['H' , ( 0.8205440 , -0.4737420 , -0.3484190)],
['H' , ( -0.8205440 , -0.4737420 , -0.3484190)]]
mol.build()
_q_=int_func.qmol_func(mol, atomic=is_atomic)
one_b=_q_.one_body_integrals
two_b=_q_.two_body_integrals
fer_op = FermionicOperator(h1=_q_.one_body_integrals, h2=_q_.two_body_integrals)
one_b = fer_op.h1
two_b = fer_op.h2
r_matrices=[]
#Spin symmetry:
r1=np.zeros([16,16])
for i in range(16):
if i<8:
r1[i+8,i]=1.
else:
r1[i-8,i]=1.
r_matrices.append(r1)
# R-matrix for plane of symmetry \sigma_{yz}. Two hydrogen atoms are swapped and the px orbital picks up
# a negative sign.
r3=np.zeros([16,16])
r3[0,0]=1
r3[1,1]=1
r3[2,2]=-1
r3[3,3]=1
r3[4,4]=1
r3[5,5]=1
r3[6,7]=1
r3[7,6]=1
r3[8,8]=1
r3[9,9]=1
r3[10,10]=-1
r3[11,11]=1
r3[12,12]=1
r3[13,13]=1
r3[14,15]=1
r3[15,14]=1
r_matrices.append(r3)
######################################
# The following mtrices commute with Hamiltonian
# and hence are symmetries, but these cannot be used
# to taper off qubits.
theta = -2*np.pi/3
r4 = np.eye(16)
r4[5,5]=r4[6,6]=r4[7,7]=0
r4[13,13]=r4[14,14]=r4[15,15]=0
r4[5,6]=r4[6,7]=r4[7,5]=1
# r4[6,5]=r4[7,6]=r4[5,7]=1
r4[13,14]=r4[14,15]=r4[15,13]=1
# r4[14,13]=r4[15,14]=r4[13,15]=1
r4[2,2]=r4[3,3]=r4[10,10]=r4[11,11]=np.cos(theta)
r4[2,3]= np.sin(theta)
r4[3,2]= -np.sin(theta)
r4[10,11]=np.sin(theta)
r4[11,10]=-np.sin(theta)
r5 = r4.copy()
theta = np.pi/3
r4 = np.eye(16,dtype=complex)
r4[5,5]=r4[6,6]=0
r4[13,13]=r4[14,14]=0
r4[5,6]=r4[6,5]=1
r4[13,14]=r4[14,13]=1
r4[2,2]=r4[10,10]=np.cos(theta)
r4[3,3]=r4[11,11]=-np.cos(theta)
r4[2,3]= np.sin(theta)
r4[3,2]= np.sin(theta)
r4[10,11]=np.sin(theta)
r4[11,10]=np.sin(theta)
if check_r_matrix_flag:
if bool(check_r_mat(r_matrices,fer_op,one_b,two_b)):
print('All the above matrices work!')
#=================================
# Methane molecule
#=================================
elif MoleculeFlag=='CH4':
# print(MoleculeFlag)
mol.atom=[['C', (0.0000 , 0.0000 , 0.0000 )],
['H', (0.6276 , 0.6276 , 0.6276 )],
['H', (0.6276 , -0.6276, -0.6276)],
['H', (-0.6276, 0.6276 , -0.6276)],
['H', (-0.6276, -0.6276, 0.6276 )]]
mol.basis='sto-3g'
mol.build()
_q_=int_func.qmol_func(mol, atomic=True)
fer_op = FermionicOperator(h1=_q_.one_body_integrals, h2=_q_.two_body_integrals)
# Spin symmetry:
r1=np.zeros([18,18])
for i in range(18):
if i<8:
r1[i+9,i]=1.
else:
r1[i-9,i]=1.
if check_r_matrix_flag:
if bool(check_r_mat(r_matrices,fer_op,one_b,two_b)):
print('All the above matrices work!')
#=================================
# Carbon dioxide molecule
#=================================
elif MoleculeFlag=='CO2':
r_matrices = []
# print(MoleculeFlag)
mol.atom = [['C',(0., 0., 0.)],
['O',(-1.1621, 0., 0.)],
['O',(1.1621, 0., 0.)]]
mol.basis='sto-3g'
mol.build()
_q_=int_func.qmol_func(mol, atomic=True)
fer_op = FermionicOperator(h1=_q_.one_body_integrals, h2=_q_.two_body_integrals)
# Spin symmetry:
r1=np.zeros([30,30])
for i in range(30):
if i<15:
r1[i+15,i]=1.
else:
r1[i-15,i]=1.
r_matrices.append(r1)
# Permutation matrix for inversion. \sigma{yz} All the oxygen orbitals are swapped.
# Oxygen px orbital picks up a negative sign and the px of carbon picks up a
# negative sign.
r2=np.zeros([30,30])
r2[0,0]=1
r2[1,1]=1
r2[3,3]=1
r2[2,2]=-1
r2[4,4]=r2[19,19]=1
r2[5,10]=r2[10,5]=1
r2[11,6]=r2[6,11]=1
r2[7,12]=r2[12,7]=-1
r2[8,13]=r2[13,8]=1
r2[14,9]=r2[9,14]=1
r2[15,15]=1
r2[16,16]=1
r2[17,17]=-1
r2[18,18]=1
r2[20,25]=r2[25,20]=1
r2[21,26]=r2[26,21]=1
r2[22,27]=r2[27,22]=-1
r2[23,28]=r2[28,23]=1
r2[24,29]=r2[29,24]=1
r_matrices.append(r2)
# Permutation matrix for inversion. \sigma{xy}
# pz orbitals of oxygen and carbon pick up negative sign
r3=np.eye(30)
r3[4,4]=-1
r3[19,19]=-1
r3[9,9]=-1
r3[14,14]=-1
r3[24,24]=-1
r3[29,29]=-1
r_matrices.append(r3)
# Permutation matrix for inversion. \sigma{xz}
# py orbitals of oxygen and carbon pick up negative sign
r4=np.eye(30)
r4[3,3]=-1
r4[18,18]=-1
r4[8,8]=-1
r4[13,13]=-1
r4[23,23]=-1
r4[28,28]=-1
r_matrices.append(r4)
# Permutation matrix for axial symmetry. C_2{x}
# pz and py orbitals of oxygen and carbon pick up negative sign
r5=np.eye(30)
r5[3,3]=-1
r5[18,18]=-1
r5[8,8]=-1
r5[13,13]=-1
r5[23,23]=-1
r5[28,28]=-1
r5[4,4]=-1
r5[19,19]=-1
r5[9,9]=-1
r5[14,14]=-1
r5[24,24]=-1
r5[29,29]=-1
r_matrices.append(r5)
# Permutation matrix for axial symmetry. C_2{y} All the oxygen orbitals are swapped.
# Oxygen px and pz orbital picks up a negative sign and the px and pz of carbon picks up a
# negative sign.
r6=np.zeros([30,30])
r6[0,0]=r6[1,1]=1
r6[3,3]=r6[18,18]=1
r6[17,17]=r6[2,2]=-1
r6[4,4]=r6[19,19]=-1
r6[5,10]=r6[10,5]=1
r6[11,6]=r6[6,11]=1
r6[7,12]=r6[12,7]=-1
r6[8,13]=r6[13,8]=1
r6[14,9]=r6[9,14]=-1
r6[15,15]=r6[16,16]=1
r6[20,25]=r6[25,20]=1
r6[21,26]=r6[26,21]=1
r6[22,27]=r6[27,22]=-1
r6[23,28]=r6[28,23]=1
r6[24,29]=r6[29,24]=-1
r_matrices.append(r6)
# Permutation matrix for axial symmetry. C_2{z} All the oxygen orbitals are swapped.
# Oxygen px and py orbital picks up a negative sign and the px and py of carbon picks up a
# negative sign.
r7=np.zeros([30,30])
r7[0,0]=r7[1,1]=1
r7[3,3]=r7[18,18]=-1
r7[17,17]=r7[2,2]=-1
r7[4,4]=r7[19,19]=1
r7[5,10]=r7[10,5]=1
r7[11,6]=r7[6,11]=1
r7[7,12]=r7[12,7]=-1
r7[8,13]=r7[13,8]=-1
r7[14,9]=r7[9,14]=1
r7[15,15]=r7[16,16]=1
r7[20,25]=r7[25,20]=1
r7[21,26]=r7[26,21]=1
r7[22,27]=r7[27,22]=-1
r7[23,28]=r7[28,23]=-1
r7[24,29]=r7[29,24]=1
r_matrices.append(r7)
if check_r_matrix_flag:
if bool(check_r_mat(r_matrices,fer_op,one_b,two_b)):
print('All the above matrices work!')
#=================================
# Ethyne molecule
#=================================
elif MoleculeFlag=='C2H2':
r_matrices =[]
print(MoleculeFlag)
num_particles = 14
if is_atomic:
try:
data = np.load(MoleculeFlag+'.npz')
data.files
one_b = data['one_b']
two_b = data['two_b']
except IOError:
mol.atom = [['C',(-0.6000, 0.0000, 0.0000 )],
['C',(0.6000, 0.0000, 0.0000 )],
['H',(-1.6650,0.0000, 0.000 )],
['H',(1.6650,0.0000, 0.000 )]]
mol.build()
_q_=int_func.qmol_func(mol, atomic=True)
one_b=_q_.one_body_integrals
two_b=_q_.two_body_integrals
# np.savez(MoleculeFlag+'_ao.npz',one_b=_q_.one_body_integrals,two_b=_q_.two_body_integrals)
two_body_temp = QMolecule.twoe_to_spin(_q_.mo_eri_ints)
temp_int = np.einsum('ijkl->ljik', _q_.mo_eri_ints)
two_body_temp = QMolecule.twoe_to_spin(temp_int)
mol = gto.M(atom=mol.atom, basis='sto-3g')
O = get_ovlp(mol)
X = np.kron(np.identity(2), np.linalg.inv(scipy.linalg.sqrtm(O)))
fer_op = FermionicOperator(h1=_q_.one_body_integrals, h2=two_body_temp)
fer_op.transform(X)
else:
mol.atom = [['C',(-0.6000, 0.0000, 0.0000 )],
['C',(0.6000, 0.0000, 0.0000 )],
['H',(-1.6650,0.0000, 0.000 )],
['H',(1.6650,0.0000, 0.000 )]]
mol.build()
_q_=int_func.qmol_func(mol, atomic=is_atomic)
one_b=_q_.one_body_integrals
two_b=_q_.two_body_integrals
fer_op = FermionicOperator(h1=_q_.one_body_integrals, h2=_q_.two_body_integrals)
one_b = fer_op.h1
two_b = fer_op.h2
# Spin symmetry:
r1=np.zeros([24,24])
for i in range(24):
if i<12:
r1[i+12,i]=1.
else:
r1[i-12,i]=1.
# r_matrices.append(r1)
# R-matrix for plane of symmetry \sigma_{xy}. Everything remains the same, only pz-orbitals pick up negative sign.
r2=np.eye(24)
r2[4,4]=-1
r2[9,9]=-1
r2[16,16]=-1
r2[21,21]=-1
# R-matrix for plane of symmetry \sigma_{xz}. Everything remains the same, only py-orbitals pick up negative sign.
r3=np.eye(24)
r3[3,3]=-1
r3[8,8]=-1
r3[15,15]=-1
r3[20,20]=-1
# R-matrix for plane of symmetry \sigma_{yz}.
r4=np.zeros([24,24])
#Swapping px picks up a negative sign
r4[2,7]=r4[7,2]=-1
r4[14,19]=r4[19,14]=-1
#Swapping 1s, 2s, 2py and 2pz of Carbon
r4[0,5]=r4[5,0]=1
r4[1,6]=r4[6,1]=1
r4[12,17]=r4[17,12]=1
r4[13,18]=r4[18,13]=1
r4[3,8]=r4[8,3]=1
r4[15,20]=r4[20,15]=1
r4[21,16]=r4[16,21]=1
r4[9,4]=r4[4,9]=1
#Swapping 1s of hydrogen
r4[10,11]=r4[11,10]=1
r4[22,23]=r4[23,22]=1
# R-matrix for axis of symmetry C_2 around y axis.
r5=np.zeros([24,24])
#Swapping px picks up a negative sign
r5[2,7]=r5[7,2]=-1
r5[14,19]=r5[19,14]=-1
r5[21,16]=r5[16,21]=-1
r5[9,4]=r5[4,9]=-1
#Swapping 1s, 2s, 2py and 2pz of Carbon
r5[0,5]=r5[5,0]=1
r5[1,6]=r5[6,1]=1
r5[12,17]=r5[17,12]=1
r5[13,18]=r5[18,13]=1
r5[3,8]=r5[8,3]=1
r5[15,20]=r5[20,15]=1
#Swapping 1s of hydrogen
r5[10,11]=r5[11,10]=1
r5[22,23]=r5[23,22]=1
# R-matrix for axis of symmetry C_2 around z axis.
r6=np.zeros([24,24])
#Swapping px picks up a negative sign
r6[2,7]=r6[7,2]=-1
r6[14,19]=r6[19,14]=-1
r6[15,20]=r6[20,15]=-1
r6[3,8]=r6[8,3]=-1
#Swapping 1s, 2s, 2py and 2pz of Carbon
r6[0,5]=r6[5,0]=1
r6[1,6]=r6[6,1]=1
r6[12,17]=r6[17,12]=1
r6[13,18]=r6[18,13]=1
r6[9,4]=r6[4,9]=1
r6[21,16]=r6[16,21]=1
#Swapping 1s of hydrogen
r6[10,11]=r6[11,10]=1
r6[22,23]=r6[23,22]=1
# R-matrix for x-axis symmetry. pz and py orbitals of both the carbon atoms pick up a negative sign.
r7=np.eye(24)
r7[3,3]=-1
r7[4,4]=-1
r7[8,8]=-1
r7[9,9]=-1
r7[16,16]=-1
r7[15,15]=-1
r7[20,20]=-1
r7[21,21]=-1
r_matrices.append(r7)
r_matrices.append(r6)
r_matrices.append(r5)
r_matrices.append(r2)
r_matrices.append(r3)
r_matrices.append(r4)
r_matrices.append(r1)
if check_r_matrix_flag:
if bool(check_r_mat(r_matrices,fer_op,one_b,two_b)):
print('All the above matrices work!')
#=================================
# Ethylene molecule
#=================================
elif MoleculeFlag=='C2H4':
r_matrices =[]
print(MoleculeFlag)
try:
data = np.load(MoleculeFlag+'.npz')
data.files
one_b = data['one_b']
two_b = data['two_b']
except IOError:
mol.atom = [['C',( 0.6695, 0.0000 , 0.0000)],
['C',(-0.6695, 0.0000 , 0.0000)],
['H',( 1.2321, 0.9289 , 0.0000)],
['H',( 1.2321, -0.9289, 0.0000)],
['H',(-1.2321, 0.9289 , 0.0000)],
['H',(-1.2321, -0.9289, 0.0000)]]
mol.build()
_q_=int_func.qmol_func(mol, atomic=True)
one_b=_q_.one_body_integrals
two_b=_q_.two_body_integrals
np.savez(MoleculeFlag+'.npz',one_b=_q_.one_body_integrals,two_b=_q_.two_body_integrals)
fer_op = FermionicOperator(h1=one_b, h2=two_b)
r_matrices = []
# Spin symmetry:
r1=np.zeros([28,28])
for i in range(28):
if i<14:
r1[i+14,i]=1.
else:
r1[i-14,i]=1.
# r_matrices.append(r1)
# R-matrix for plane of symmetry \sigma_{xy}. Everything remains the same, only pz-orbitals pick up negative sign.
r2=np.eye(28)
r2[4,4]=-1
r2[9,9]=-1
r2[18,18]=-1
r2[23,23]=-1
# R-matrix for plane of symmetry \sigma_{xz}.
r3=np.eye(28)
r3[3,3]=-1
r3[8,8]=-1
r3[17,17]=-1
r3[22,22]=-1
r3[10,10]=r3[11,11]=r3[12,12]=r3[13,13]=0
r3[24,24]=r3[25,25]=r3[26,26]=r3[27,27]=0
r3[10,11]=r3[11,10]=r3[12,13]=r3[13,12]=1
r3[24,25]=r3[25,24]=r3[26,27]=r3[27,26]=1
# R-matrix for plane of symmetry \sigma_{yz}.
r4=np.zeros([28,28])
# #Swapping px picks up a negative sign
r4[2,7]=r4[7,2]=-1
r4[16,21]=r4[21,16]=-1
# #Swapping 1s, 2s, 2py and 2pz of Carbon
r4[0,5]=r4[5,0]=1
r4[1,6]=r4[6,1]=1
r4[3,8]=r4[8,3]=1
r4[4,9]=r4[9,4]=1
r4[14,19]=r4[19,14]=1
r4[15,20]=r4[20,15]=1
r4[17,22]=r4[22,17]=1
r4[18,23]=r4[23,18]=1
# #Swapping 1s of hydrogen
r4[10,12]=r4[12,10]=1
r4[24,26]=r4[26,24]=1
r4[11,13]=r4[13,11]=1
r4[25,27]=r4[27,25]=1
# R-matrix for axis of symmetry C_2 around y axis.
r5=np.zeros([28,28])
#Swapping px picks up a negative sign
r5[2,7]=r5[7,2]=-1
r5[4,9]=r5[9,4]=-1
r5[16,21]=r5[21,16]=-1
r5[18,23]=r5[23,18]=-1
#Swapping 1s, 2s, 2py and 2pz of Carbon
r5[0,5]=r5[5,0]=1
r5[1,6]=r5[6,1]=1
r5[3,8]=r5[8,3]=1
r5[14,19]=r5[19,14]=1
r5[15,20]=r5[20,15]=1
r5[17,22]=r5[22,17]=1
#Swapping 1s of hydrogen
r5[10,12]=r5[12,10]=1
r5[24,26]=r5[26,24]=1
r5[11,13]=r5[13,11]=1
r5[25,27]=r5[27,25]=1
# R-matrix for axis of symmetry C_2 around z axis.
r6=np.zeros([28,28])
#Swapping px picks up a negative sign
r6[2,7]=r6[7,2]=-1
r6[3,8]=r6[8,3]=-1
r6[16,21]=r6[21,16]=-1
r6[17,22]=r6[22,17]=-1
#Swapping 1s, 2s, 2py and 2pz of Carbon
r6[0,5]=r6[5,0]=1
r6[1,6]=r6[6,1]=1
r6[4,9]=r6[9,4]=1
r6[14,19]=r6[19,14]=1
r6[15,20]=r6[20,15]=1
r6[18,23]=r6[23,18]=1
#Swapping 1s of hydrogen
r6[10,13]=r6[13,10]=1
r6[24,27]=r6[27,24]=1
r6[11,12]=r6[12,11]=1
r6[25,26]=r6[26,25]=1
# # R-matrix for x-axis symmetry. pz and py orbitals of both the carbon atoms pick up a negative sign.
r7=np.eye(28)
r7[3,3]=-1
r7[4,4]=-1
r7[8,8]=-1
r7[9,9]=-1
r7[17,17]=-1
r7[18,18]=-1
r7[22,22]=-1
r7[23,23]=-1
r7[10,10]=r7[11,11]=r7[12,12]=r7[13,13]=0
r7[24,24]=r7[25,25]=r7[26,26]=r7[27,27]=0
r7[10,11]=r7[11,10]=r7[12,13]=r7[13,12]=1
r7[24,25]=r7[25,24]=r7[26,27]=r7[27,26]=1
r_matrices.append(r1)
r_matrices.append(r2)
r_matrices.append(r3)
r_matrices.append(r4)
r_matrices.append(r5)
r_matrices.append(r6)
r_matrices.append(r7)
if check_r_matrix_flag:
if bool(check_r_mat(r_matrices,fer_op,one_b,two_b)):
print('All the above matrices work!')
#=================================
# Boron trifluoride molecule
#=================================
elif MoleculeFlag == 'BF3':
r_matrices = []
try:
data = np.load(MoleculeFlag+'.npz')
one_b = data['one_b']
two_b = data['two_b']
except IOError:
mol.atom = [['B',(0.0000 ,0.0000 ,0.000000 )],
['F',(0.0000 ,1.3070 ,0.00000 )],
['F',(1.1319 ,-0.6535, 0.000 )],
['F',(-1.1319 ,-0.6535, 0.00)]]
mol.basis = 'sto-3g'
mol.build()
_q_=int_func.qmol_func(mol, atomic=True)
one_b=_q_.one_body_integrals
two_b=_q_.two_body_integrals
np.savez(MoleculeFlag+'.npz',one_b=_q_.one_body_integrals,two_b=_q_.two_body_integrals)
fer_op = FermionicOperator(h1=one_b, h2=two_b)
# Spin symmetry:
r1=np.zeros([40,40])
for i in range(40):
if i<20:
r1[i+20,i]=1.
else:
r1[i-20,i]=1.
r_matrices.append(r1)
# R-matrix for plane of symmetry \sigma_{xy}.
r2=np.eye(40)
r2[4,4]=-1
r2[9,9]=-1
r2[14,14]=-1
r2[19,19]=-1
r2[24,24]=-1
r2[29,29]=-1
r2[34,34]=-1
r2[39,39]=-1
r_matrices.append(r2)
# R-matrix for plane of symmetry \sigma_{yz}.
r3=np.eye(40)
r3[2,2]=-1
r3[7,7]=-1
r3[22,22]=-1
r3[27,27]=-1
for i in range(5):
r3[10+i,10+i]=0
r3[15+i,15+i]=0
r3[30+i,30+i]=0
r3[35+i,35+i]=0
r3[10+i,15+i]=1
r3[15+i,10+i]=1
r3[30+i,35+i]=1
r3[35+i,30+i]=1
r3[12,17]=-1
r3[17,12]=-1
r3[32,37]=-1
r3[37,32]=-1
r_matrices.append(r3)
# R-matrix for axis of symmetry C_2 around y axis.
r4=np.eye(40)
r4[2,2]=-1
r4[4,4]=-1
r4[7,7]=-1
r4[9,9]=-1
r4[22,22]=-1
r4[24,24]=-1
r4[29,29]=-1
r4[27,27]=-1
for i in range(5):
r4[10+i,10+i]=0
r4[15+i,15+i]=0
r4[30+i,30+i]=0
r4[35+i,35+i]=0
r4[10+i,15+i]=1
r4[15+i,10+i]=1
r4[30+i,35+i]=1
r4[35+i,30+i]=1
r4[12,17]=-1
r4[17,12]=-1
r4[14,19]=-1
r4[19,14]=-1
r4[32,37]=-1
r4[37,32]=-1
r4[34,39]=-1
r4[39,34]=-1
r_matrices.append(r4)
# R-matrix for plane of symmetry \sigma_{yz}.
# r4=np.zeros([24,24])
# #Swapping px picks up a negative sign
# r4[2,7]=r4[7,2]=-1
# r4[14,19]=r4[19,14]=-1
# #Swapping 1s, 2s, 2py and 2pz of Carbon
# r4[0,5]=r4[5,0]=1
# r4[1,6]=r4[6,1]=1
# r4[12,17]=r4[17,12]=1
# r4[13,18]=r4[18,13]=1
# r4[3,8]=r4[8,3]=1
# r4[15,20]=r4[20,15]=1
# r4[21,16]=r4[16,21]=1
# r4[9,4]=r4[4,9]=1
# #Swapping 1s of hydrogen
# r4[10,11]=r4[11,10]=1
# r4[22,23]=r4[23,22]=1
# # R-matrix for axis of symmetry C_2 around z axis.
# r6=np.zeros([24,24])
# #Swapping px picks up a negative sign
# r6[2,7]=r6[7,2]=-1
# r6[14,19]=r6[19,14]=-1
# r6[15,20]=r6[20,15]=-1
# r6[3,8]=r6[8,3]=-1
# #Swapping 1s, 2s, 2py and 2pz of Carbon
# r6[0,5]=r6[5,0]=1
# r6[1,6]=r6[6,1]=1
# r6[12,17]=r6[17,12]=1
# r6[13,18]=r6[18,13]=1
# r6[9,4]=r6[4,9]=1
# r6[21,16]=r6[16,21]=1
# #Swapping 1s of hydrogen
# r6[10,11]=r6[11,10]=1
# r6[22,23]=r6[23,22]=1
# # R-matrix for x-axis symmetry. pz and py orbitals of both the carbon atoms pick up a negative sign.
# r7=np.eye(24)
# r7[3,3]=-1
# r7[4,4]=-1
# r7[8,8]=-1
# r7[9,9]=-1
# r7[16,16]=-1
# r7[15,15]=-1
# r7[20,20]=-1
# r7[21,21]=-1
# print(r4)
# print(np.real(fer_op.h1[0:int(np.size(fer_op.h1,0)/2),0:int(np.size(fer_op.h1,0)/2)]))
# fer_op.transform(r4)
# # print(np.real(fer_op.h1[0:int(np.size(fer_op.h1,0)/2),0:int(np.size(fer_op.h1,0)/2)]))
# # print(np.real(fer_op.h1[0:int(np.size(fer_op.h1,0)/2),0:int(np.size(fer_op.h1,0)/2)]-_q_.one_body_integrals[0:int(np.size(fer_op.h1,0)/2),0:int(np.size(fer_op.h1,0)/2)]))
# # print(np.real(fer_op.h1[int(np.size(fer_op.h1,0)/2):int(np.size(fer_op.h1,0)),int(np.size(fer_op.h1,0)/2):int(np.size(fer_op.h1,0))]-_q_.one_body_integrals[int(np.size(fer_op.h1,0)/2):int(np.size(fer_op.h1,0)),int(np.size(fer_op.h1,0)/2):int(np.size(fer_op.h1,0))]))
# print(MoleculeFlag)
# # print(np.real(fer_op.h1[0:int(np.size(fer_op.h1,0)/2),0:int(np.size(fer_op.h1,0)/2)]))
# # print(np.real(fer_op.h1[int(np.size(fer_op.h1,0)/2):int(np.size(fer_op.h1,0)),int(np.size(fer_op.h1,0)/2):int(np.size(fer_op.h1,0))]))
# # print(np.real(fer_op.h1[0:int(np.size(fer_op.h1,0)/2),0:int(np.size(fer_op.h1,0)/2)]))
# print(np.all(np.abs(fer_op.h1-_q_.one_body_integrals)<1.e-14))
# print(np.all(np.abs(fer_op.h2-_q_.two_body_integrals)<1.e-14))
# print(np.linalg.norm(fer_op.h2-_q_.two_body_integrals))
if check_r_matrix_flag:
if bool(check_r_mat(r_matrices,fer_op,one_b,two_b)):
print('All the above matrices work!')
#=================================
# Lithium hydride
#=================================
elif MoleculeFlag == "LiH":
r_matrices =[]
print(MoleculeFlag)
if is_atomic:
try:
data = np.load(MoleculeFlag+'.npz')
data.files
one_b = data['one_b']
two_b = data['two_b']
except IOError:
mol.atom = [['Li',(0.000, 0.0000, 0.0000 )],
['H',(1.5949,0.0000, 0.000 )]]
mol.build()
_q_=int_func.qmol_func(mol, atomic=is_atomic)
one_b=_q_.one_body_integrals
two_b=_q_.two_body_integrals
np.savez(MoleculeFlag+'_ao.npz',one_b=_q_.one_body_integrals,two_b=_q_.two_body_integrals)
two_body_temp = QMolecule.twoe_to_spin(_q_.mo_eri_ints)
temp_int = np.einsum('ijkl->ljik', _q_.mo_eri_ints)
two_body_temp = QMolecule.twoe_to_spin(temp_int)
mol = gto.M(atom=mol.atom, basis='sto-3g')
O = get_ovlp(mol)
X = np.kron(np.identity(2), np.linalg.inv(scipy.linalg.sqrtm(O)))
print(_q_.one_body_integrals)
fer_op = FermionicOperator(h1=_q_.one_body_integrals, h2=two_body_temp)
fer_op.transform(X)
else:
mol.atom = [['Li',(0.000, 0.0000, 0.0000 )],
['H',(1.5949,0.0000, 0.000 )]]
mol.build()
_q_=int_func.qmol_func(mol, atomic=is_atomic)
one_b=_q_.one_body_integrals
two_b=_q_.two_body_integrals
fer_op = FermionicOperator(h1=_q_.one_body_integrals, h2=_q_.two_body_integrals)
one_b = fer_op.h1
two_b = fer_op.h2
# Spin symmetry:
r1=np.zeros([12,12])
for i in range(12):
if i<6:
r1[i+6,i]=1.
else:
r1[i-6,i]=1.
r_matrices.append(r1)
# sigma{xy}
r2 = np.eye(12)
r2[4,4]=-1
r2[10,10]=-1
r_matrices.append(r2)
#sigma(yz)
r3 = np.eye(12)
r3[3,3]=-1
r3[9,9]=-1
r_matrices.append(r3)
if bool(check_r_mat(r_matrices,fer_op,one_b,two_b)):
print('All the above matrices work!')
#=================================
# Beryllium hydride
#=================================
elif MoleculeFlag == "BeH2":
num_particles = 6
r_matrices =[]
print(MoleculeFlag)
if is_atomic:
try:
data = np.load(MoleculeFlag+'.npz')
data.files
one_b = data['one_b']
two_b = data['two_b']
except IOError:
mol.atom = [['Be',(0.000, 0.0000, 0.0000 )],
['H',(1.291,0.0000, 0.000 )],
['H',(-1.291,0.0000, 0.000 )]]
mol.build()
_q_=int_func.qmol_func(mol, atomic=True)
one_b=_q_.one_body_integrals
two_b=_q_.two_body_integrals
# np.savez(MoleculeFlag+'_ao.npz',one_b=_q_.one_body_integrals,two_b=_q_.two_body_integrals)
two_body_temp = QMolecule.twoe_to_spin(_q_.mo_eri_ints)
temp_int = np.einsum('ijkl->ljik', _q_.mo_eri_ints)
two_body_temp = QMolecule.twoe_to_spin(temp_int)
mol = gto.M(atom=mol.atom, basis='sto-3g')
O = get_ovlp(mol)
X = np.kron(np.identity(2), np.linalg.inv(scipy.linalg.sqrtm(O)))
fer_op = FermionicOperator(h1=_q_.one_body_integrals, h2=two_body_temp)
fer_op.transform(X)
else:
mol.atom = [['Be',(0.000, 0.0000, 0.0000 )],
['H',(1.291,0.0000, 0.000 )],
['H',(-1.291,0.0000, 0.000 )]]
mol.build()
_q_=int_func.qmol_func(mol, atomic=is_atomic)
one_b=_q_.one_body_integrals
two_b=_q_.two_body_integrals
fer_op = FermionicOperator(h1=_q_.one_body_integrals, h2=_q_.two_body_integrals)
one_b = fer_op.h1
two_b = fer_op.h2
# fer_op = FermionicOperator(h1=one_b, h2=two_b)
# R-matrix for plane of symmetry \sigma_{xy}. Everything remains the same, only pz-orbitals pick up negative sign.
r1=np.zeros([14,14])
r1[0,0]=1
r1[1,1]=1
r1[2,2]=1
r1[3,3]=1
r1[4,4]=-1
r1[5,5]=1
r1[6,6]=1
r1[7,7]=1
r1[8,8]=1
r1[9,9]=1
r1[10,10]=1
r1[11,11]=-1
r1[12,12]=1
r1[13,13]=1
r_matrices.append(r1)
# R-matrix for plane of symmetry \sigma_{xz}. Everything remains the same, only py-orbitals pick up negative sign.
r2=np.eye(14)
r2[3,3]=-1
r2[10,10]=-1
r_matrices.append(r2)
# R-matrix for plane of symmetry \sigma_{yz}. Everything remains the same, only px-orbitals pick up negative sign and hydrogen atoms swap.
r3=np.zeros([14,14])
r3[0,0]=1
r3[1,1]=1
r3[2,2]=-1
r3[3,3]=1
r3[4,4]=1
r3[5,6]=1
r3[6,5]=1
r3[7,7]=1
r3[8,8]=1
r3[9,9]=-1
r3[10,10]=1
r3[11,11]=1
r3[12,13]=1
r3[13,12]=1
r_matrices.append(r3)
# R-matrix for symmetry-axis C_2. Linear water molecule has three axis of symmetry:
# About z-axis
r4=np.zeros([14,14])
r4[0,0]=1
r4[1,1]=1
r4[2,2]=-1
r4[3,3]=-1
r4[4,4]=1
r4[5,6]=1
r4[6,5]=1
r4[7,7]=1
r4[8,8]=1
r4[9,9]=-1
r4[10,10]=-1
r4[11,11]=1
r4[12,13]=1
r4[13,12]=1
# r_matrices.append(r4)
#About y-axis
r5=np.zeros([14,14])
r5[0,0]=1
r5[1,1]=1
r5[2,2]=-1
r5[3,3]=1
r5[4,4]=-1
r5[5,6]=1
r5[6,5]=1
r5[7,7]=1
r5[8,8]=1
r5[9,9]=-1
r5[10,10]=1
r5[11,11]=-1
r5[12,13]=1
r5[13,12]=1
# r_matrices.append(r5)
#Symmetry about x-axis:
r6=np.zeros([14,14])
r6[0,0]=1
r6[1,1]=1
r6[2,2]=1
r6[3,3]=-1
r6[4,4]=-1
r6[5,5]=1
r6[6,6]=1
r6[7,7]=1
r6[8,8]=1
r6[9,9]=1
r6[10,10]=-1
r6[11,11]=-1
r6[12,12]=1
r6[13,13]=1
# r_matrices.append(r6)
#Spin symmetry:
r7=np.zeros([14,14])
for i in range(14):
if i<7:
r7[i+7,i]=1.
else:
r7[i-7,i]=1.
r_matrices.append(r7)
if check_r_matrix_flag and is_atomic:
if bool(check_r_mat(r_matrices,fer_op,one_b,two_b)):
print('All the above matrices work!')
elif MoleculeFlag == "test":
r_matrices =[]
num_particles = 6
print(MoleculeFlag)
# try:
# data = np.load(MoleculeFlag+'.npz')
# data.files
# one_b = data['one_b']
# two_b = data['two_b']
# except IOError:
mol.atom = [['Be',(0.000, 0.0000, 0.0000 )],
['H',(1.3264,0.0000, 0.000 )],
['H',(-1.3264,0.0000, 0.000 )]]
mol.atom = [['Be',(0.000, 0.0000, 0.0000 )],
['H',(1.291,0.0000, 0.000 )],
['H',(-1.291,0.0000, 0.000 )]]
mol.atom = [['Be',(0.000, 0.0000, 0.0000 )],
['H',(1.3,0.0000, 0.000 )],
['H',(-1.3,0.0000, 0.000 )]]
mol.basis = 'sto-6g'
# mol.symmetry=True
# mol.atom = [['H',(0, 0, -0.3707)], ['H',(0,0.0,0.3707)]]
mol.build()
# is_atomic =
_q_ = qmol_func(mol, atomic=is_atomic)
if is_atomic:
two_body_temp = QMolecule.twoe_to_spin(_q_.mo_eri_ints)
temp_int = np.einsum('ijkl->ljik', _q_.mo_eri_ints)
two_body_temp = QMolecule.twoe_to_spin(temp_int)
mol = gto.M(atom=mol.atom, basis='sto-3g')
O = get_ovlp(mol)
X = np.kron(np.identity(2), np.linalg.inv(scipy.linalg.sqrtm(O)))
fer_op = FermionicOperator(h1=_q_.one_body_integrals, h2=two_body_temp)
fer_op.transform(X)
else:
fer_op = FermionicOperator(h1=_q_.one_body_integrals, h2=_q_.two_body_integrals)
one_b = fer_op.h1
two_b = fer_op.h2
# np.savez(MoleculeFlag+'.npz',one_b=_q_.one_body_integrals,two_b=_q_.two_body_integrals)
# fer_op = FermionicOperator(h1=one_b, h2=two_b)
# print(fer_op.h1)
# exit()
# r_matrices.append(np.eye(14))
# R-matrix for plane of symmetry \sigma_{xy}. Everything remains the same, only pz-orbitals pick up negative sign.
r1=np.zeros([14,14])
r1[0,0]=1
r1[1,1]=1
r1[2,2]=1
r1[3,3]=1
r1[4,4]=-1
r1[5,5]=1
r1[6,6]=1
r1[7,7]=1
r1[8,8]=1
r1[9,9]=1
r1[10,10]=1
r1[11,11]=-1
r1[12,12]=1
r1[13,13]=1
r_matrices.append(r1)
# R-matrix for plane of symmetry \sigma_{xz}. Everything remains the same, only py-orbitals pick up negative sign.
r2=np.eye(14)
r2[3,3]=-1
r2[10,10]=-1
r_matrices.append(r2)
# R-matrix for plane of symmetry \sigma_{yz}. Everything remains the same, only px-orbitals pick up negative sign and hydrogen atoms swap.
r3=np.zeros([14,14])
r3[0,0]=1
r3[1,1]=1
r3[2,2]=-1
r3[3,3]=1
r3[4,4]=1
r3[5,6]=1
r3[6,5]=1
r3[7,7]=1
r3[8,8]=1
r3[9,9]=-1
r3[10,10]=1
r3[11,11]=1
r3[12,13]=1
r3[13,12]=1
r_matrices.append(r3)
# R-matrix for symmetry-axis C_2. Linear water molecule has three axis of symmetry:
# About z-axis
r4=np.zeros([14,14])
r4[0,0]=1
r4[1,1]=1
r4[2,2]=-1
r4[3,3]=-1
r4[4,4]=1
r4[5,6]=1
r4[6,5]=1
r4[7,7]=1
r4[8,8]=1
r4[9,9]=-1
r4[10,10]=-1
r4[11,11]=1
r4[12,13]=1
r4[13,12]=1
# r_matrices.append(r4)
#About y-axis
r5=np.zeros([14,14])
r5[0,0]=1
r5[1,1]=1
r5[2,2]=-1
r5[3,3]=1
r5[4,4]=-1
r5[5,6]=1
r5[6,5]=1
r5[7,7]=1
r5[8,8]=1
r5[9,9]=-1
r5[10,10]=1
r5[11,11]=-1
r5[12,13]=1
r5[13,12]=1
# r_matrices.append(r5)
#Symmetry about x-axis:
r6=np.zeros([14,14])
r6[0,0]=1
r6[1,1]=1
r6[2,2]=1
r6[3,3]=-1
r6[4,4]=-1
r6[5,5]=1
r6[6,6]=1
r6[7,7]=1
r6[8,8]=1
r6[9,9]=1
r6[10,10]=-1
r6[11,11]=-1
r6[12,12]=1
r6[13,13]=1
# r_matrices.append(r6)
#Spin symmetry:
r7=np.zeros([14,14])
for i in range(14):
if i<7:
r7[i+7,i]=1.
else:
r7[i-7,i]=1.
# r_matrices.append(r7)
r8=np.zeros([14,14])
r8[0,0]=1
r8[1,1]=1
r8[2,2]=-1
r8[3,3]=-1
r8[4,4]=-1
r8[5,6]=1
r8[6,5]=1
r8[7,7]=1
r8[8,8]=1
r8[9,9]=-1
r8[10,10]=-1
r8[11,11]=-1
r8[12,13]=1
r8[13,12]=1
# r_matrices.append(r8)
# r_matrices=[]
# r_matrices.append(np.eye(fer_op.modes))
if check_r_matrix_flag:
if bool(check_r_mat(r_matrices,fer_op,one_b,two_b)):
print('All the above matrices work!')
if is_atomic:
return [r_matrices,fer_op,num_particles]
else:
r_matrices =[]
r_matrices.append(np.eye(fer_op.modes))
return [r_matrices,fer_op, num_particles]
def _do_transform(
self,
qmolecule: QMolecule,
aux_operators: Optional[List[FermionicOperator]] = None
) -> Tuple[WeightedPauliOperator, List[WeightedPauliOperator]]:
"""
Args:
qmolecule: qmolecule
aux_operators: Additional ``FermionicOperator``s to map to a qubit operator.
Returns:
(qubit operator, auxiliary operators)
"""
logger.debug('Processing started...')
# Save these values for later combination with the quantum computation result
self._hf_energy = qmolecule.hf_energy
self._nuclear_repulsion_energy = qmolecule.nuclear_repulsion_energy
self._nuclear_dipole_moment = qmolecule.nuclear_dipole_moment
self._reverse_dipole_sign = qmolecule.reverse_dipole_sign
core_list = qmolecule.core_orbitals if self._freeze_core else []
reduce_list = self._orbital_reduction
if self._freeze_core:
logger.info(
"Freeze_core specified. Core orbitals to be frozen: %s",
core_list)
if reduce_list:
logger.info("Configured orbital reduction list: %s", reduce_list)
reduce_list = [
x + qmolecule.num_orbitals if x < 0 else x for x in reduce_list
]
freeze_list = []
remove_list = []
# Orbitals are specified by their index from 0 to n-1, where n is the number of orbitals the
# molecule has. The combined list of the core orbitals, when freeze_core is true, with any
# user supplied orbitals is what will be used. Negative numbers may be used to indicate the
# upper virtual orbitals, so -1 is the highest, then -2 etc. and these will
# be converted to the
# positive 0-based index for computation.
# In the combined list any orbitals that are occupied are added to a freeze list and an
# energy is stored from these orbitals to be added later.
# Unoccupied orbitals are just discarded.
# Because freeze and eliminate is done in separate steps,
# with freeze first, we have to re-base
# the indexes for elimination according to how many orbitals were removed when freezing.
#
orbitals_list = list(set(core_list + reduce_list))
num_alpha = qmolecule.num_alpha
num_beta = qmolecule.num_beta
new_num_alpha = num_alpha
new_num_beta = num_beta
if orbitals_list:
orbitals_list = np.array(orbitals_list)
orbitals_list = orbitals_list[
(cast(np.ndarray, orbitals_list) >= 0)
& (orbitals_list < qmolecule.num_orbitals)]
freeze_list_alpha = [i for i in orbitals_list if i < num_alpha]
freeze_list_beta = [i for i in orbitals_list if i < num_beta]
freeze_list = np.append(
freeze_list_alpha,
[i + qmolecule.num_orbitals for i in freeze_list_beta])
remove_list_alpha = [i for i in orbitals_list if i >= num_alpha]
remove_list_beta = [i for i in orbitals_list if i >= num_beta]
rla_adjust = -len(freeze_list_alpha)
rlb_adjust = -len(freeze_list_alpha) - len(
freeze_list_beta) + qmolecule.num_orbitals
remove_list = np.append(
[i + rla_adjust for i in remove_list_alpha],
[i + rlb_adjust for i in remove_list_beta])
logger.info("Combined orbital reduction list: %s", orbitals_list)
logger.info(
" converting to spin orbital reduction list: %s",
np.append(np.array(orbitals_list),
np.array(orbitals_list) + qmolecule.num_orbitals))
logger.info(" => freezing spin orbitals: %s", freeze_list)
logger.info(
" => removing spin orbitals: %s (indexes accounting for freeze %s)",
np.append(remove_list_alpha,
np.array(remove_list_beta) + qmolecule.num_orbitals),
remove_list)
new_num_alpha -= len(freeze_list_alpha)
new_num_beta -= len(freeze_list_beta)
new_nel = [new_num_alpha, new_num_beta]
# construct the fermionic operator
fer_op = FermionicOperator(h1=qmolecule.one_body_integrals,
h2=qmolecule.two_body_integrals)
# try to reduce it according to the freeze and remove list
fer_op, self._energy_shift, did_shift = \
FermionicTransformation._try_reduce_fermionic_operator(fer_op, freeze_list, remove_list)
# apply same transformation for the aux operators
if aux_operators is not None:
aux_operators = [
FermionicTransformation._try_reduce_fermionic_operator(
op, freeze_list, remove_list)[0] for op in aux_operators
]
if did_shift:
logger.info("Frozen orbital energy shift: %s", self._energy_shift)
# apply particle hole transformation, if specified
if self._transformation == FermionicTransformationType.PARTICLE_HOLE.value:
fer_op, ph_shift = fer_op.particle_hole_transformation(new_nel)
self._ph_energy_shift = -ph_shift
logger.info("Particle hole energy shift: %s",
self._ph_energy_shift)
# apply the same transformation for the aux operators
if aux_operators is not None:
aux_operators = [
op.particle_hole_transformation(new_nel)[0]
for op in aux_operators
]
logger.debug('Converting to qubit using %s mapping',
self._qubit_mapping)
qubit_op = FermionicTransformation._map_fermionic_operator_to_qubit(
fer_op, self._qubit_mapping, new_nel, self._two_qubit_reduction)
qubit_op.name = 'Fermionic Operator'
logger.debug(' num paulis: %s, num qubits: %s', len(qubit_op.paulis),
qubit_op.num_qubits)
aux_ops = [] # list of the aux operators
def _add_aux_op(aux_op: FermionicOperator, name: str) -> None:
"""
Add auxiliary operators
Args:
aux_op: auxiliary operators
name: name
"""
aux_qop = FermionicTransformation._map_fermionic_operator_to_qubit(
aux_op, self._qubit_mapping, new_nel,
self._two_qubit_reduction)
aux_qop.name = name
aux_ops.append(aux_qop)
logger.debug(' num paulis: %s', aux_qop.paulis)
# the first three operators are hardcoded to number of particles, angular momentum
# and magnetization in this order
logger.debug('Creating aux op for Number of Particles')
_add_aux_op(fer_op.total_particle_number(), 'Number of Particles')
logger.debug('Creating aux op for S^2')
_add_aux_op(fer_op.total_angular_momentum(), 'S^2')
logger.debug('Creating aux op for Magnetization')
_add_aux_op(fer_op.total_magnetization(), 'Magnetization')
# the next three are dipole moments, if supported by the qmolecule
if qmolecule.has_dipole_integrals():
self._has_dipole_moments = True
def _dipole_op(dipole_integrals: np.ndarray, axis: str) \
-> Tuple[WeightedPauliOperator, float, float]:
"""
Dipole operators
Args:
dipole_integrals: dipole integrals
axis: axis for dipole moment calculation
Returns:
(qubit_op_, shift, ph_shift_)
"""
logger.debug('Creating aux op for dipole %s', axis)
fer_op_ = FermionicOperator(h1=dipole_integrals)
fer_op_, shift, did_shift_ = self._try_reduce_fermionic_operator(
fer_op_, freeze_list, remove_list)
if did_shift_:
logger.info("Frozen orbital %s dipole shift: %s", axis,
shift)
ph_shift_ = 0.0
if self._transformation == FermionicTransformationType.PARTICLE_HOLE.value:
fer_op_, ph_shift_ = fer_op_.particle_hole_transformation(
new_nel)
ph_shift_ = -ph_shift_
logger.info("Particle hole %s dipole shift: %s", axis,
ph_shift_)
qubit_op_ = self._map_fermionic_operator_to_qubit(
fer_op_, self._qubit_mapping, new_nel,
self._two_qubit_reduction)
qubit_op_.name = 'Dipole ' + axis
logger.debug(' num paulis: %s', len(qubit_op_.paulis))
return qubit_op_, shift, ph_shift_
op_dipole_x, self._x_dipole_shift, self._ph_x_dipole_shift = \
_dipole_op(qmolecule.x_dipole_integrals, 'x')
op_dipole_y, self._y_dipole_shift, self._ph_y_dipole_shift = \
_dipole_op(qmolecule.y_dipole_integrals, 'y')
op_dipole_z, self._z_dipole_shift, self._ph_z_dipole_shift = \
_dipole_op(qmolecule.z_dipole_integrals, 'z')
aux_ops += [op_dipole_x, op_dipole_y, op_dipole_z]
# add user specified auxiliary operators
if aux_operators is not None:
for aux_op in aux_operators:
if hasattr(aux_op, 'name'):
name = aux_op.name
else:
name = ''
_add_aux_op(aux_op, name)
logger.info('Molecule num electrons: %s, remaining for processing: %s',
[num_alpha, num_beta], new_nel)
nspinorbs = qmolecule.num_orbitals * 2
new_nspinorbs = nspinorbs - len(freeze_list) - len(remove_list)
logger.info(
'Molecule num spin orbitals: %s, remaining for processing: %s',
nspinorbs, new_nspinorbs)
self._molecule_info['num_particles'] = (new_num_alpha, new_num_beta)
self._molecule_info['num_orbitals'] = new_nspinorbs
reduction = self._two_qubit_reduction if self._qubit_mapping == 'parity' else False
self._molecule_info['two_qubit_reduction'] = reduction
self._untapered_qubit_op = qubit_op
z2symmetries = Z2Symmetries([], [], [], None)
if self._z2symmetry_reduction is not None:
logger.debug('Processing z2 symmetries')
qubit_op, aux_ops, z2symmetries = self._process_z2symmetry_reduction(
qubit_op, aux_ops)
self._molecule_info['z2_symmetries'] = z2symmetries
logger.debug('Processing complete ready to run algorithm')
return qubit_op, aux_ops
def compute_integrals(atoms,
units,
charge,
multiplicity,
basis,
calc_type='rhf'):
# Get config from input parameters
# Molecule is in this format xyz as below or in Z-matrix e.g "H; O 1 1.08; H 2 1.08 1 107.5":
# atoms=H .0 .0 .0; H .0 .0 0.2
# units=Angstrom
# charge=0
# multiplicity=1
# where we support symbol for atom as well as number
units = _check_units(units)
mol = _parse_molecule(atoms, units, charge, multiplicity)
calc_type = calc_type.lower()
try:
ehf, enuke, norbs, mohij, mohijkl, orbs, orbs_energy = _calculate_integrals(mol, basis, calc_type)
except Exception as exc:
raise QiskitChemistryError('Failed electronic structure computation') from exc
# Create driver level molecule object and populate
_q_ = QMolecule()
# Energies and orbits
_q_.hf_energy = ehf
_q_.nuclear_repulsion_energy = enuke
_q_.num_orbitals = norbs
_q_.num_alpha = mol.nup()
_q_.num_beta = mol.ndown()
_q_.mo_coeff = orbs
_q_.orbital_energies = orbs_energy
# Molecule geometry
_q_.molecular_charge = mol.charge
_q_.multiplicity = mol.multiplicity
_q_.num_atoms = len(mol)
_q_.atom_symbol = []
_q_.atom_xyz = np.empty([len(mol), 3])
atoms = mol.atoms
for _n in range(0, _q_.num_atoms):
atuple = atoms[_n].atuple()
_q_.atom_symbol.append(QMolecule.symbols[atuple[0]])
_q_.atom_xyz[_n][0] = atuple[1]
_q_.atom_xyz[_n][1] = atuple[2]
_q_.atom_xyz[_n][2] = atuple[3]
# 1 and 2 electron integrals
_q_.mo_onee_ints = mohij
_q_.mo_eri_ints = mohijkl
return _q_
def _calculate_integrals(mol, calc_type='rhf', atomic=False):
"""Function to calculate the one and two electron terms. Perform a Hartree-Fock calculation in
the given basis.
Args:
mol : A PySCF gto.Mole object.
calc_type: rhf, uhf, rohf
Returns:
ehf : Hartree-Fock energy
enuke : Nuclear repulsion energy
norbs : Number of orbitals
mohij : One electron terms of the Hamiltonian.
mohijkl : Two electron terms of the Hamiltonian.
mo_coeff: Orbital coefficients
orbs_energy: Orbitals energies
x_dip_ints: x dipole moment integrals
y_dip_ints: y dipole moment integrals
z_dip_ints: z dipole moment integrals
nucl_dipl : Nuclear dipole moment
"""
enuke = gto.mole.energy_nuc(mol)
if calc_type == 'rhf':
mf = scf.RHF(mol)
elif calc_type == 'rohf':
mf = scf.ROHF(mol)
elif calc_type == 'uhf':
mf = scf.UHF(mol)
else:
raise QiskitChemistryError('Invalid calc_type: {}'.format(calc_type))
ehf = mf.kernel()
if type(mf.mo_coeff) is tuple:
mo_coeff = mf.mo_coeff[0]
mo_occ = mf.mo_occ[0]
else:
mo_coeff = mf.mo_coeff
mo_occ = mf.mo_occ
norbs = mo_coeff.shape[0]
orbs_energy = mf.mo_energy
# print(np.dot(mo_coeff,mo_coeff.T))
O = get_ovlp(mol)
# print(np.dot(O,O.T))
mo_tr = np.dot(np.dot(O, mo_coeff), O.T)
# print(np.dot(mo_tr,mo_tr.T))
# two_body_temp = QMolecule.twoe_to_spin(_q_.mo_eri_ints)
# temp_int = np.einsum('ijkl->ljik', _q_.mo_eri_ints)
# two_body_temp = QMolecule.twoe_to_spin(temp_int)
# mol = gto.M(atom=mol.atom, basis='sto-3g')
# X = np.kron(np.identity(2), np.linalg.inv(scipy.linalg.sqrtm(O)))
### for atomic basis
if atomic:
mo_coeff = np.identity(len(mo_coeff))
###
# print(mo_coeff)
hij = mf.get_hcore()
mohij = np.dot(np.dot(mo_coeff.T, hij), mo_coeff)
# mohij = hij
eri = ao2mo.incore.full(mf._eri, mo_coeff, compact=False)
# eri_1 = mf._eri
# print(np.shape(eri))
# print(np.shape(eri_1))
mohijkl = eri.reshape(norbs, norbs, norbs, norbs)
# exit()
# dipole integrals
mol.set_common_orig((0, 0, 0))
ao_dip = mol.intor_symmetric('int1e_r', comp=3)
x_dip_ints = QMolecule.oneeints2mo(ao_dip[0], mo_coeff)
y_dip_ints = QMolecule.oneeints2mo(ao_dip[1], mo_coeff)
z_dip_ints = QMolecule.oneeints2mo(ao_dip[2], mo_coeff)
dm = mf.make_rdm1(mf.mo_coeff, mf.mo_occ)
if calc_type == 'rohf' or calc_type == 'uhf':
dm = dm[0]
elec_dip = np.negative(np.einsum('xij,ji->x', ao_dip, dm).real)
elec_dip = np.round(elec_dip, decimals=8)
nucl_dip = np.einsum('i,ix->x', mol.atom_charges(), mol.atom_coords())
nucl_dip = np.round(nucl_dip, decimals=8)
logger.info("HF Electronic dipole moment: {}".format(elec_dip))
logger.info("Nuclear dipole moment: {}".format(nucl_dip))
logger.info("Total dipole moment: {}".format(nucl_dip + elec_dip))
return ehf, enuke, norbs, mohij, mohijkl, mo_coeff, orbs_energy, x_dip_ints, y_dip_ints, z_dip_ints, nucl_dip
def qmol_func(mol, calc_type='rhf', atomic=False):
ehf, enuke, norbs, mohij, mohijkl, mo_coeff, orbs_energy, x_dip, y_dip, z_dip, nucl_dip = _calculate_integrals(
mol, calc_type, atomic)
# Create driver level molecule object and populate
_q_ = QMolecule()
# Energies and orbits
_q_.hf_energy = ehf
_q_.nuclear_repulsion_energy = enuke
_q_.num_orbitals = norbs
_q_.num_alpha = mol.nelec[0]
_q_.num_beta = mol.nelec[1]
_q_.mo_coeff = mo_coeff
_q_.orbital_energies = orbs_energy
# Molecule geometry
_q_.molecular_charge = mol.charge
_q_.multiplicity = mol.spin + 1
_q_.num_atoms = mol.natm
_q_.atom_symbol = []
_q_.atom_xyz = np.empty([mol.natm, 3])
atoms = mol.atom_coords()
for _n in range(0, _q_.num_atoms):
xyz = mol.atom_coord(_n)
_q_.atom_symbol.append(mol.atom_pure_symbol(_n))
_q_.atom_xyz[_n][0] = xyz[0]
_q_.atom_xyz[_n][1] = xyz[1]
_q_.atom_xyz[_n][2] = xyz[2]
# 1 and 2 electron integrals. h1 & h2 are ready to pass to FermionicOperator
_q_.mo_onee_ints = mohij
_q_.mo_eri_ints = mohijkl
# dipole integrals
_q_.x_dip_mo_ints = x_dip
_q_.y_dip_mo_ints = y_dip
_q_.z_dip_mo_ints = z_dip
# dipole moment
_q_.nuclear_dipole_moment = nucl_dip
_q_.reverse_dipole_sign = True
return _q_
def _calculate_integrals(mol, hf_method='rhf', conv_tol=1e-9, max_cycle=50, init_guess='minao',outfile=None):
"""Function to calculate the one and two electron terms. Perform a Hartree-Fock calculation in
the given basis.
Args:
mol (gto.Mole) : A PySCF gto.Mole object.
hf_method (str): rhf, uhf, rohf
conv_tol (float): Convergence tolerance
max_cycle (int): Max convergence cycles
init_guess (str): Initial guess for SCF
Returns:
QMolecule: QMolecule populated with driver integrals etc
Raises:
QiskitChemistryError: Invalid hf method type
"""
enuke = gto.mole.energy_nuc(mol)
if hf_method == 'rhf':
m_f = scf.RHF(mol)
elif hf_method == 'rohf':
m_f = scf.ROHF(mol)
elif hf_method == 'uhf':
m_f = scf.UHF(mol)
else:
raise QiskitChemistryError('Invalid hf_method type: {}'.format(hf_method))
m_f.conv_tol = conv_tol
m_f.max_cycle = max_cycle
m_f.init_guess = init_guess
ehf = m_f.kernel()
from pyscf import tools
from prettytable import PrettyTable
C = m_f.mo_coeff
irr = get_irreps(mol,C)
table_ancillary_info = [[str(round(m_f.mo_energy[i],4)),irr[i],str(int(m_f.mo_occ[i]))] for i in range(mol.nao_nr())]
outfile.write("SCF orbitals\n")
t = PrettyTable(['MO']+mol.ao_labels()+['E','irr','occ'])
for i in range(C.shape[1]):
if(C[np.argmax(np.abs(C[:,i])),i]<0): C[:,i] *= -1
t.add_row([str(i)]+[str(round(x,4)) for x in C[:,i]]+table_ancillary_info[i])
outfile.write(str(t))
filename = 'mos'
for i in range(m_f.mo_coeff.shape[1]):
moldenfile = filename+'-'+str(i)+'.molden'
tools.molden.from_mo(mol,moldenfile,m_f.mo_coeff)
jmol_script = filename+'-'+str(i)+'.spt'
fspt = open(jmol_script,'w')
fspt.write('''
initialize;
set background [xffffff];
set frank off
set autoBond true;
set bondRadiusMilliAngstroms 66;
set bondTolerance 0.5;
set forceAutoBond false;
load %s
''' % moldenfile)
fspt.write('''
zoom 130;
rotate -20 z
rotate -60 x
axes
MO COLOR [xff0020] [x0060ff];
MO COLOR translucent 0.25;
MO fill noDots noMesh;
MO titleformat "";
''')
fspt.write('MO %d cutoff 0.02;\n' % (i+1))
fspt.write('write IMAGE 400 400 PNG 180 "%s-%02d.png";\n' % (filename,i+1))
fspt.close()
logger.info('PySCF kernel() converged: %s, e(hf): %s', m_f.converged, m_f.e_tot)
if isinstance(m_f.mo_coeff, tuple):
mo_coeff = m_f.mo_coeff[0]
mo_coeff_b = m_f.mo_coeff[1]
# mo_occ = m_f.mo_occ[0]
# mo_occ_b = m_f.mo_occ[1]
else:
# With PySCF 1.6.2, instead of a tuple of 2 dimensional arrays, its a 3 dimensional
# array with the first dimension indexing to the coeff arrays for alpha and beta
if len(m_f.mo_coeff.shape) > 2:
mo_coeff = m_f.mo_coeff[0]
mo_coeff_b = m_f.mo_coeff[1]
# mo_occ = m_f.mo_occ[0]
# mo_occ_b = m_f.mo_occ[1]
else:
mo_coeff = m_f.mo_coeff
mo_coeff_b = None
# mo_occ = mf.mo_occ
# mo_occ_b = None
norbs = mo_coeff.shape[0]
if isinstance(m_f.mo_energy, tuple):
orbs_energy = m_f.mo_energy[0]
orbs_energy_b = m_f.mo_energy[1]
else:
# See PYSCF 1.6.2 comment above - this was similarly changed
if len(m_f.mo_energy.shape) > 1:
orbs_energy = m_f.mo_energy[0]
orbs_energy_b = m_f.mo_energy[1]
else:
orbs_energy = m_f.mo_energy
orbs_energy_b = None
if logger.isEnabledFor(logging.DEBUG):
# Add some more to PySCF output...
# First analyze() which prints extra information about MO energy and occupation
mol.stdout.write('\n')
m_f.analyze()
# Now labelled orbitals for contributions to the MOs for s,p,d etc of each atom
mol.stdout.write('\n\n--- Alpha Molecular Orbitals ---\n\n')
dump_mat.dump_mo(mol, mo_coeff, digits=7, start=1)
if mo_coeff_b is not None:
mol.stdout.write('\n--- Beta Molecular Orbitals ---\n\n')
dump_mat.dump_mo(mol, mo_coeff_b, digits=7, start=1)
mol.stdout.flush()
hij = m_f.get_hcore()
mohij = np.dot(np.dot(mo_coeff.T, hij), mo_coeff)
mohij_b = None
if mo_coeff_b is not None:
mohij_b = np.dot(np.dot(mo_coeff_b.T, hij), mo_coeff_b)
eri = mol.intor('int2e', aosym=1)
mo_eri = ao2mo.incore.full(m_f._eri, mo_coeff, compact=False)
mohijkl = mo_eri.reshape(norbs, norbs, norbs, norbs)
mohijkl_bb = None
mohijkl_ba = None
if mo_coeff_b is not None:
mo_eri_b = ao2mo.incore.full(m_f._eri, mo_coeff_b, compact=False)
mohijkl_bb = mo_eri_b.reshape(norbs, norbs, norbs, norbs)
mo_eri_ba = ao2mo.incore.general(m_f._eri,
(mo_coeff_b, mo_coeff_b, mo_coeff, mo_coeff),
compact=False)
mohijkl_ba = mo_eri_ba.reshape(norbs, norbs, norbs, norbs)
# dipole integrals
mol.set_common_orig((0, 0, 0))
ao_dip = mol.intor_symmetric('int1e_r', comp=3)
x_dip_ints = ao_dip[0]
y_dip_ints = ao_dip[1]
z_dip_ints = ao_dip[2]
d_m = m_f.make_rdm1(m_f.mo_coeff, m_f.mo_occ)
if hf_method in ('rohf', 'uhf'):
d_m = d_m[0]
elec_dip = np.negative(np.einsum('xij,ji->x', ao_dip, d_m).real)
elec_dip = np.round(elec_dip, decimals=8)
nucl_dip = np.einsum('i,ix->x', mol.atom_charges(), mol.atom_coords())
nucl_dip = np.round(nucl_dip, decimals=8)
logger.info("HF Electronic dipole moment: %s", elec_dip)
logger.info("Nuclear dipole moment: %s", nucl_dip)
logger.info("Total dipole moment: %s", nucl_dip+elec_dip)
# Create driver level molecule object and populate
_q_ = QMolecule()
_q_.origin_driver_version = pyscf_version
# Energies and orbits
_q_.hf_energy = ehf
_q_.nuclear_repulsion_energy = enuke
_q_.num_orbitals = norbs
_q_.num_alpha = mol.nelec[0]
_q_.num_beta = mol.nelec[1]
_q_.mo_coeff = mo_coeff
_q_.mo_coeff_b = mo_coeff_b
_q_.orbital_energies = orbs_energy
_q_.orbital_energies_b = orbs_energy_b
# Molecule geometry
_q_.molecular_charge = mol.charge
_q_.multiplicity = mol.spin + 1
_q_.num_atoms = mol.natm
_q_.atom_symbol = []
_q_.atom_xyz = np.empty([mol.natm, 3])
_ = mol.atom_coords()
for n_i in range(0, _q_.num_atoms):
xyz = mol.atom_coord(n_i)
_q_.atom_symbol.append(mol.atom_pure_symbol(n_i))
_q_.atom_xyz[n_i][0] = xyz[0]
_q_.atom_xyz[n_i][1] = xyz[1]
_q_.atom_xyz[n_i][2] = xyz[2]
# 1 and 2 electron integrals AO and MO
_q_.hcore = hij
_q_.hcore_b = None
_q_.kinetic = mol.intor_symmetric('int1e_kin')
_q_.overlap = m_f.get_ovlp()
_q_.eri = eri
_q_.mo_onee_ints = mohij
_q_.mo_onee_ints_b = mohij_b
_q_.mo_eri_ints = mohijkl
_q_.mo_eri_ints_bb = mohijkl_bb
_q_.mo_eri_ints_ba = mohijkl_ba
# dipole integrals AO and MO
_q_.x_dip_ints = x_dip_ints
_q_.y_dip_ints = y_dip_ints
_q_.z_dip_ints = z_dip_ints
_q_.x_dip_mo_ints = QMolecule.oneeints2mo(x_dip_ints, mo_coeff)
_q_.x_dip_mo_ints_b = None
_q_.y_dip_mo_ints = QMolecule.oneeints2mo(y_dip_ints, mo_coeff)
_q_.y_dip_mo_ints_b = None
_q_.z_dip_mo_ints = QMolecule.oneeints2mo(z_dip_ints, mo_coeff)
_q_.z_dip_mo_ints_b = None
if mo_coeff_b is not None:
_q_.x_dip_mo_ints_b = QMolecule.oneeints2mo(x_dip_ints, mo_coeff_b)
_q_.y_dip_mo_ints_b = QMolecule.oneeints2mo(y_dip_ints, mo_coeff_b)
_q_.z_dip_mo_ints_b = QMolecule.oneeints2mo(z_dip_ints, mo_coeff_b)
# dipole moment
_q_.nuclear_dipole_moment = nucl_dip
_q_.reverse_dipole_sign = True
return _q_
