def uhf_simple(geo,basisname='sto3g',maxiter=25,verbose=False):
if geo.nopen() == 0: return scf_simple(geo,basisname,maxiter,verbose)
bfs = basisset(geo,basisname)
i1 = onee_integrals(bfs,geo)
i2 = twoe_integrals(bfs)
h = i1.T + i1.V
E,U = geigh(h,i1.S)
Enuke = geo.nuclear_repulsion()
Eold = Energy = 0
ca = cb = U
na,nb = geo.nup(),geo.ndown()
for i in xrange(maxiter):
Energy = Enuke
Da = dmat(ca,na)
Db = dmat(cb,nb)
h = i1.T + i1.V
Energy += trace2(Da+Db,h)/2
Ja,Ka = i2.get_j(Da),i2.get_k(Da)
Jb,Kb = i2.get_j(Db),i2.get_k(Db)
Fa = h + Ja + Jb - Ka
Fb = h + Ja + Jb - Kb
orbea,ca = geigh(Fa,i1.S)
orbeb,cb = geigh(Fb,i1.S)
Energy += trace2(Fa,Da)/2 + trace2(Fb,Db)/2
print ("UHF: %d %10.4f : %10.4f" % ((i+1),Energy,Enuke))
if np.isclose(Energy,Eold):
break
Eold = Energy
else:
print ("Warning: Maxiter %d hit in scf_simple" % maxiter)
return Energy,E,U
def uhf_simple(geo,basisname='sto3g',maxiter=25,verbose=False):
if geo.nopen() == 0: return scf_simple(geo,basisname,maxiter,verbose)
bfs = basisset(geo,basisname)
i1 = onee_integrals(bfs,geo)
i2 = twoe_integrals(bfs)
h = i1.T + i1.V
E,U = geigh(h,i1.S)
Enuke = geo.nuclear_repulsion()
Eold = Energy = 0
ca = cb = U
na,nb = geo.nup(),geo.ndown()
for i in xrange(maxiter):
Energy = Enuke
Da = dmat(ca,na)
Db = dmat(cb,nb)
h = i1.T + i1.V
Energy += trace2(Da+Db,h)/2
Ja,Ka = i2.get_j(Da),i2.get_k(Da)
Jb,Kb = i2.get_j(Db),i2.get_k(Db)
Fa = h + Ja + Jb - Ka
Fb = h + Ja + Jb - Kb
orbea,ca = geigh(Fa,i1.S)
orbeb,cb = geigh(Fb,i1.S)
Energy += trace2(Fa,Da)/2 + trace2(Fb,Db)/2
print ("UHF: %d %10.4f : %10.4f" % ((i+1),Energy,Enuke))
if np.isclose(Energy,Eold):
break
Eold = Energy
else:
print ("Warning: Maxiter %d hit in scf_simple" % maxiter)
return Energy,E,U
def scf_simple(geo,basisname='sto-3g',maxiter=25,verbose=False):
bfs = basisset(geo,basisname)
i1 = onee_integrals(bfs,geo)
i2 = twoe_integrals(bfs)
if verbose: print ("S=\n%s" % i1.S)
h = i1.T + i1.V
if verbose: print ("h=\n%s" % h)
if verbose: print ("T=\n%s" % i1.T)
if verbose: print ("V=\n%s" % i1.V)
E,U = geigh(h,i1.S)
if verbose: print ("E=\n%s" % E)
if verbose: print ("U=\n%s" % U)
Enuke = geo.nuclear_repulsion()
nocc = geo.nocc()
Eold = Energy = 0
if verbose: print ("2e ints\n%s" % i2)
for i in xrange(maxiter):
D = dmat(U,nocc)
if verbose: print ("D=\n%s" % D)
Eone = trace2(h,D)
G = i2.get_2jk(D)
H = h+G
Etwo = trace2(H,D)
E,U = geigh(H,i1.S)
Energy = Enuke+Eone+Etwo
print ("HF: %d %10.4f : %10.4f %10.4f %10.4f" % ((i+1),Energy,Enuke,Eone,Etwo))
if np.isclose(Energy,Eold):
break
Eold = Energy
else:
print ("Warning: Maxiter %d hit in scf_simple" % maxiter)
return Energy,E,U
def rhf_simple(geo,basisname='sto3g',maxiter=25,verbose=False):
bfs = basisset(geo,basisname)
i1 = onee_integrals(bfs,geo)
i2 = twoe_integrals(bfs)
if verbose: print ("S=\n%s" % i1.S)
h = i1.T + i1.V
if verbose: print ("h=\n%s" % h)
if verbose: print ("T=\n%s" % i1.T)
if verbose: print ("V=\n%s" % i1.V)
E,U = geigh(h,i1.S)
if verbose: print ("E=\n%s" % E)
if verbose: print ("U=\n%s" % U)
Enuke = geo.nuclear_repulsion()
nocc = geo.nocc()
Eold = Energy = 0
if verbose: print ("2e ints\n%s" % i2)
for i in xrange(maxiter):
D = dmat(U,nocc)
if verbose: print ("D=\n%s" % D)
Eone = trace2(h,D)
G = i2.get_2jk(D)
H = h+G
Etwo = trace2(H,D)
E,U = geigh(H,i1.S)
Energy = Enuke+Eone+Etwo
print ("HF: %d %10.4f : %10.4f %10.4f %10.4f" % ((i+1),Energy,Enuke,Eone,Etwo))
if np.isclose(Energy,Eold):
break
Eold = Energy
else:
print ("Warning: Maxiter %d hit in scf_simple" % maxiter)
return Energy,E,U
def __init__(self,geo,bfs):
self.geo = geo
self.bfs = bfs
self.i1 = onee_integrals(bfs,geo)
self.i2 = twoe_integrals(bfs)
self.energies = []
self.energy = 0
self.converged = False
def __init__(self,geo,bfs):
self.geo = geo
self.bfs = bfs
self.i1 = onee_integrals(bfs,geo)
self.i2 = twoe_integrals(bfs)
self.energies = []
self.energy = 0
self.converged = False
def _calculate_integrals(molecule, basis='sto3g', calc_type='rhf'):
"""Function to calculate the one and two electron terms. Perform a Hartree-Fock calculation in
the given basis.
Args:
molecule : A pyquante2 molecular object.
basis : The basis set for the electronic structure computation
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.
orbs: Molecular orbital coefficients
orbs_energy: Orbital energies
"""
bfs = basisset(molecule, basis)
integrals = onee_integrals(bfs, molecule)
hij = integrals.T + integrals.V
hijkl_compressed = twoe_integrals(bfs)
# convert overlap integrals to molecular basis
# calculate the Hartree-Fock solution of the molecule
if calc_type == 'rhf':
solver = rhf(molecule, bfs)
elif calc_type == 'rohf':
solver = rohf(molecule, bfs)
elif calc_type == 'uhf':
solver = uhf(molecule, bfs)
else:
raise QiskitChemistryError('Invalid calc_type: {}'.format(calc_type))
logger.debug('Solver name {}'.format(solver.name))
ehf = solver.converge()
if hasattr(solver, 'orbs'):
orbs = solver.orbs
else:
orbs = solver.orbsa
norbs = len(orbs)
if hasattr(solver, 'orbe'):
orbs_energy = solver.orbe
else:
orbs_energy = solver.orbea
enuke = molecule.nuclear_repulsion()
# Get ints in molecular orbital basis
mohij = simx(hij, orbs)
mohijkl_compressed = transformintegrals(hijkl_compressed, orbs)
mohijkl = np.zeros((norbs, norbs, norbs, norbs))
for i in range(norbs):
for j in range(norbs):
for k in range(norbs):
for l in range(norbs):
mohijkl[i, j, k,
l] = mohijkl_compressed[ijkl2intindex(i, j, k, l)]
return ehf[0], enuke, norbs, mohij, mohijkl, orbs, orbs_energy
def _populate_driver_result_electronic_energy(
self, driver_result: ElectronicStructureDriverResult) -> None:
# pylint: disable=import-error
from pyquante2 import onee_integrals
from pyquante2.ints.integrals import twoe_integrals
basis_transform = driver_result.get_property(ElectronicBasisTransform)
integrals = onee_integrals(self._bfs, self._mol)
hij = integrals.T + integrals.V
hijkl = twoe_integrals(self._bfs)
one_body_ao = OneBodyElectronicIntegrals(ElectronicBasis.AO,
(hij, None))
two_body_ao = TwoBodyElectronicIntegrals(
ElectronicBasis.AO,
(hijkl.transform(np.identity(self._nmo)), None, None, None),
)
one_body_mo = one_body_ao.transform_basis(basis_transform)
two_body_mo = two_body_ao.transform_basis(basis_transform)
electronic_energy = ElectronicEnergy(
[one_body_ao, two_body_ao, one_body_mo, two_body_mo],
nuclear_repulsion_energy=self._mol.nuclear_repulsion(),
reference_energy=self._calc.energy,
)
if hasattr(self._calc, "orbe"):
orbs_energy = self._calc.orbe
orbs_energy_b = None
else:
orbs_energy = self._calc.orbea
orbs_energy_b = self._calc.orbeb
orbital_energies = ((orbs_energy, orbs_energy_b)
if orbs_energy_b is not None else orbs_energy)
electronic_energy.orbital_energies = np.asarray(orbital_energies)
electronic_energy.kinetic = OneBodyElectronicIntegrals(
ElectronicBasis.AO, (integrals.T, None))
electronic_energy.overlap = OneBodyElectronicIntegrals(
ElectronicBasis.AO, (integrals.S, None))
driver_result.add_property(electronic_energy)
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:
QiskitNatureError: 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 QiskitNatureError("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_molecular_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 _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 : A pyquante2 molecular object.
basis : The basis set for the electronic structure computation
hf_method: rhf, uhf, rohf
Returns:
QMolecule: QMolecule populated with driver integrals etc
"""
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{}'.format(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 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_.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 gvb(geo,npair=0,basisname='sto3g',maxiter=25,verbose=False,
return_orbs=False, input_orbs=None):
"""\
This is a trivial test for the gvb module, because other
pyquante modules are simpler if you're doing closed shell rhf,
and should give the same results.
# -0.46658184546856041 from uhf/sto3g
>>> gvb(h) # doctest: +ELLIPSIS
-0.4665818...
# -1.117099582955609 from rhf/sto3g
>>> gvb(h2) # doctest: +ELLIPSIS
-1.117099...
>>> gvb(lih,maxiter=5) # doctest: +ELLIPSIS
-7.86073...
>>> gvb(li,maxiter=5) # doctest: +ELLIPSIS
-7.31552...
>>> gvb(h2,npair=1) # doctest: +ELLIPSIS
-1.13730...
"""
# Get the basis set and the integrals
bfs = basisset(geo,basisname)
i1 = onee_integrals(bfs,geo)
i2 = twoe_integrals(bfs)
h = i1.T + i1.V
# Get a guess for the orbitals
if input_orbs is not None:
U = input_orbs
else:
E,U = geigh(h,i1.S)
# Set the parameters based on the molecule
nopen = geo.nopen()
ncore = geo.nclosed() - npair
nocc = ncore + nopen + 2*npair
norb = len(bfs)
virt = range(nocc,norb)
orbs_per_shell = get_orbs_per_shell(ncore,nopen,npair)
nsh = len(orbs_per_shell)
shell = orbital_to_shell_mapping(ncore,nopen,npair)
Enuke = geo.nuclear_repulsion()
f,a,b = fab(ncore,nopen,npair)
if verbose:
np.set_printoptions(precision=4)
print("**** PyQuante GVB ****")
print(geo)
print("Nuclear repulsion energy: %.3f" % Enuke)
print("Basis set: %s" % basisname)
print(" ncore/open/pair: %d,%d,%d" % (ncore,nopen,npair))
print(" occ/bf/orb: %d,%d,%d" % (nocc,len(bfs),norb))
for i in range(nsh):
print("Shell %d" % i)
print(" occupation = %.2f" % f[i])
print(" orbitals in shell %s" % orbs_per_shell[i])
print(" couplings to other shells %s" % zip(a[i,:],b[i,:]))
print("Starting guess at orbitals:\n%s"%U)
print("Shell array: %s" % shell)
print("****")
Eold = 0
for it in range(maxiter):
# Make all of the density matrices:
Ds = [dmat_gen(U,orbs) for orbs in orbs_per_shell]
# Compute the required Hamiltonian matrices:
Js = [i2.get_j(D) for D in Ds]
Ks = [i2.get_k(D) for D in Ds]
# Perform the ROTION step and compute the energy
Eel,Eone,Uocc = ROTION(U[:,:nocc],h,Js,Ks,f,a,b,nocc,shell,
verbose=verbose)
if nsh > 1:
U[:,:nocc] = Uocc
# Perform the OCBSE step
U = OCBSE(U,h,Js,Ks,f,a,b,orbs_per_shell,virt)
#E = Enuke+Eone+Etwo
E = Enuke+Eel
Etwo = Eel-2*Eone
# Update CI coefs
coeffs = update_gvb_ci_coeffs(Uocc,h,Js,Ks,f,a,b,ncore,nopen,npair,
orbs_per_shell,verbose)
f,a,b = fab(ncore,nopen,npair,coeffs)
if verbose:
print ("---- %d : %10.4f %10.4f %10.4f %10.4f" % ((it+1),E,Enuke,Eone,Etwo))
if np.isclose(E,Eold):
if verbose:
print("Energy converged")
break
Eold = E
else:
print("Maximum iterations (%d) reached without convergence" % (maxiter))
if return_orbs:
return E,U
return E
def gvb(geo,
npair=0,
basisname='sto3g',
maxiter=25,
verbose=False,
return_orbs=False,
input_orbs=None):
"""\
This is a trivial test for the gvb module, because other
pyquante modules are simpler if you're doing closed shell rhf,
and should give the same results.
# -0.46658184546856041 from uhf/sto3g
>>> gvb(h) # doctest: +ELLIPSIS
-0.4665818...
# -1.117099582955609 from rhf/sto3g
>>> gvb(h2) # doctest: +ELLIPSIS
-1.117099...
>>> gvb(lih,maxiter=5) # doctest: +ELLIPSIS
-7.86073...
>>> gvb(li,maxiter=5) # doctest: +ELLIPSIS
-7.31552...
>>> gvb(h2,npair=1) # doctest: +ELLIPSIS
-1.13730...
"""
# Get the basis set and the integrals
bfs = basisset(geo, basisname)
i1 = onee_integrals(bfs, geo)
i2 = twoe_integrals(bfs)
h = i1.T + i1.V
# Get a guess for the orbitals
if input_orbs is not None:
U = input_orbs
else:
E, U = geigh(h, i1.S)
# Set the parameters based on the molecule
nopen = geo.nopen()
ncore = geo.nclosed() - npair
nocc = ncore + nopen + 2 * npair
norb = len(bfs)
virt = range(nocc, norb)
orbs_per_shell = get_orbs_per_shell(ncore, nopen, npair)
nsh = len(orbs_per_shell)
shell = orbital_to_shell_mapping(ncore, nopen, npair)
Enuke = geo.nuclear_repulsion()
f, a, b = fab(ncore, nopen, npair)
if verbose:
np.set_printoptions(precision=4)
print("**** PyQuante GVB ****")
print(geo)
print("Nuclear repulsion energy: %.3f" % Enuke)
print("Basis set: %s" % basisname)
print(" ncore/open/pair: %d,%d,%d" % (ncore, nopen, npair))
print(" occ/bf/orb: %d,%d,%d" % (nocc, len(bfs), norb))
for i in range(nsh):
print("Shell %d" % i)
print(" occupation = %.2f" % f[i])
print(" orbitals in shell %s" % orbs_per_shell[i])
print(" couplings to other shells %s" % zip(a[i, :], b[i, :]))
print("Starting guess at orbitals:\n%s" % U)
print("Shell array: %s" % shell)
print("****")
Eold = 0
for it in range(maxiter):
# Make all of the density matrices:
Ds = [dmat_gen(U, orbs) for orbs in orbs_per_shell]
# Compute the required Hamiltonian matrices:
Js = [i2.get_j(D) for D in Ds]
Ks = [i2.get_k(D) for D in Ds]
# Perform the ROTION step and compute the energy
Eel, Eone, Uocc = ROTION(U[:, :nocc],
h,
Js,
Ks,
f,
a,
b,
nocc,
shell,
verbose=verbose)
if nsh > 1:
U[:, :nocc] = Uocc
# Perform the OCBSE step
U = OCBSE(U, h, Js, Ks, f, a, b, orbs_per_shell, virt)
#E = Enuke+Eone+Etwo
E = Enuke + Eel
Etwo = Eel - 2 * Eone
# Update CI coefs
coeffs = update_gvb_ci_coeffs(Uocc, h, Js, Ks, f, a, b, ncore, nopen,
npair, orbs_per_shell, verbose)
f, a, b = fab(ncore, nopen, npair, coeffs)
if verbose:
print("---- %d : %10.4f %10.4f %10.4f %10.4f" %
((it + 1), E, Enuke, Eone, Etwo))
if np.isclose(E, Eold):
if verbose:
print("Energy converged")
break
Eold = E
else:
print("Maximum iterations (%d) reached without convergence" %
(maxiter))
if return_orbs:
return E, U
return E