def setup_basis_set(
n,
l,
s,
h,
u,
dim=3,
particle_charge=-1,
np=None,
includes_spin=False,
anti_symmetrized_u=False,
**kwargs,
):
if np is None:
import numpy as np
bs = BasisSet(
l,
dim=dim,
np=np,
includes_spin=includes_spin,
anti_symmetrized_u=anti_symmetrized_u,
)
bs.h = h
bs.u = u
bs.s = s
bs.particle_charge = particle_charge
if "position" in kwargs.keys():
bs.position = kwargs["position"]
if "momentum" in kwargs.keys():
bs.momentum = kwargs["momentum"]
if "nuclear_repulsion_energy" in kwargs.keys():
bs.nuclear_repulsion_energy = kwargs["nuclear_repulsion_energy"]
return bs
def construct_pyscf_system_rhf(
molecule,
basis="cc-pvdz",
add_spin=True,
anti_symmetrize=True,
np=None,
verbose=False,
charge=0,
cart=False,
dip=None,
**kwargs,
):
"""Convenience function setting up a closed-shell atom or a molecule from
PySCF as a ``QuantumSystem`` in RHF-basis using PySCF's RHF-solver.
Parameters
----------
molecule : str
String describing the atom or molecule. This gets passed to PySCF which
means that we support all the same string options as PySCF.
basis : str
String describing the basis set. PySCF determines which options are
available.
add_spin : bool
Whether or not to return a ``SpatialOrbitalSystem`` (``False``) or a
``GeneralOrbitalSystem`` (``True``). Default is ``True``.
anti_symmetrize : bool
Whether or not to anti-symmetrize the two-body elements in a
``GeneralOrbitalSystem``. This only applies if ``add_spin = True``.
Default is ``True``.
np : module
Array- and linear algebra module.
dip : list
[position, momentum] f.ex. from Dalton
Returns
-------
SpatialOrbitalSystem, GeneralOrbitalSystem
Depending on the choice of ``add_spin`` we return a
``SpatialOrbitalSystem`` (``add_spin = False``), or a
``GeneralOrbitalSystem`` (``add_spin = True``).
See Also
-------
PySCF
Example
-------
>>> # Set up the Beryllium atom centered at (0, 0, 0)
>>> system = construct_pyscf_system_rhf(
... "be 0 0 0", basis="cc-pVDZ", add_spin=False
... ) # doctest.ELLIPSIS
converged SCF energy = -14.5723...
>>> # Compare the number of occupied basis functions
>>> system.n == 4 // 2
True
>>> gos = system.construct_general_orbital_system()
>>> gos.n == 4
True
>>> system = construct_pyscf_system_rhf(
... "be 0 0 0", basis="cc-pVDZ"
... ) # doctest.ELLIPSIS
converged SCF energy = -14.5723...
>>> system.n == gos.n
True
"""
import pyscf
if np is None:
import numpy as np
# Build molecule in AO-basis
mol = pyscf.gto.Mole()
mol.unit = "bohr"
mol.charge = charge
mol.cart = cart
mol.build(atom=molecule, basis=basis, **kwargs)
nuclear_repulsion_energy = mol.energy_nuc()
n = mol.nelectron
assert (
n %
2 == 0), "We require closed shell, with an even number of particles"
l = mol.nao
hf = pyscf.scf.RHF(mol)
hf_energy = hf.kernel()
if not hf.converged:
warnings.warn("RHF calculation did not converge")
if verbose:
print(f"RHF energy: {hf.e_tot}")
charges = mol.atom_charges()
coords = mol.atom_coords()
nuc_charge_center = np.einsum("z,zx->x", charges, coords) / charges.sum()
mol.set_common_orig_(nuc_charge_center)
C = np.asarray(hf.mo_coeff)
h = pyscf.scf.hf.get_hcore(mol)
s = mol.intor_symmetric("int1e_ovlp")
u = mol.intor("int2e").reshape(l, l, l, l).transpose(0, 2, 1, 3)
position = mol.intor("int1e_r").reshape(3, l, l)
momentum = -1j * mol.intor("int1e_ipovlp").reshape(3, l, l)
if dip is not None:
diplen = dip[0]
arr_eq0 = np.allclose(diplen[0], position[0])
arr_eq1 = np.allclose(diplen[1], position[1])
arr_eq2 = np.allclose(diplen[2], position[2])
if not (arr_eq0 and arr_eq1 and arr_eq2):
print('WARNING:')
print('dipole_array_pyscf != dipole_array_dalton')
bs = BasisSet(l, dim=3, np=np)
bs.h = h
bs.s = s
bs.u = u
bs.nuclear_repulsion_energy = nuclear_repulsion_energy
bs.particle_charge = -1
bs.position = position
bs.momentum = momentum
if dip is not None:
bs.momentum = dip[1]
bs.change_module(np=np)
system = SpatialOrbitalSystem(n, bs)
system.change_basis(C)
return (system.construct_general_orbital_system(
anti_symmetrize=anti_symmetrize) if add_spin else system)
def construct_pyscf_system_ao(
molecule,
basis="cc-pvdz",
add_spin=True,
anti_symmetrize=True,
np=None,
**kwargs,
):
"""Convenience function setting up an atom or a molecule from PySCF as a
``QuantumSystem``.
Parameters
----------
molecule : str
String describing the atom or molecule. This gets passed to PySCF which
means that we support all the same string options as PySCF.
basis : str
String describing the basis set. PySCF determines which options are
available.
add_spin : bool
Whether or not to return a ``SpatialOrbitalSystem`` (``False``) or a
``GeneralOrbitalSystem`` (``True``). Default is ``True``.
anti_symmetrize : bool
Whether or not to anti-symmetrize the two-body elements in a
``GeneralOrbitalSystem``. This only applies if ``add_spin = True``.
Default is ``True``.
np : module
Array- and linear algebra module.
Returns
-------
SpatialOrbitalSystem, GeneralOrbitalSystem
Depending on the choice of ``add_spin`` we return a
``SpatialOrbitalSystem`` (``add_spin = False``), or a
``GeneralOrbitalSystem`` (``add_spin = True``).
See Also
-------
PySCF
Example
-------
>>> # Set up the Beryllium atom centered at (0, 0, 0)
>>> system = construct_pyscf_system_ao(
... "be 0 0 0", basis="cc-pVDZ", add_spin=False
... )
>>> # Compare the number of occupied basis functions
>>> system.n == 4 // 2
True
>>> gos = system.construct_general_orbital_system()
>>> gos.n == 4
True
"""
import pyscf
if np is None:
import numpy as np
mol = pyscf.gto.Mole()
mol.unit = "bohr"
mol.build(atom=molecule, basis=basis, **kwargs)
nuclear_repulsion_energy = mol.energy_nuc()
n = mol.nelectron
l = mol.nao
# n_a = (mol.nelectron + mol.spin) // 2
# n_b = n_a - mol.spin
# assert n_b == n - n_a
h = pyscf.scf.hf.get_hcore(mol)
s = mol.intor_symmetric("int1e_ovlp")
u = mol.intor("int2e").reshape(l, l, l, l).transpose(0, 2, 1, 3)
position = mol.intor("int1e_r").reshape(3, l, l)
bs = BasisSet(l, dim=3, np=np)
bs.h = h
bs.s = s
bs.u = u
bs.nuclear_repulsion_energy = nuclear_repulsion_energy
bs.particle_charge = -1
bs.position = position
bs.change_module(np=np)
system = SpatialOrbitalSystem(n, bs)
return (system.construct_general_orbital_system(
anti_symmetrize=anti_symmetrize) if add_spin else system)