15.8. Example Python scripts

The example files for obtaining excitation energies using the Jacobian matrix are collected in the directory data/examples/jacobian.

15.8.1. Jacobian pCCD calculations on the water molecule

This is a basic example of how to obtain excitation energies by diagonalizing the Jacobian matrix in PyBEST. This script performs an RHF calculation followed by a pCCD calculation. We target pair excitations in the water molecule using the cc-pVDZ basis set.

Listing 15.1 data/examples/jacobian/jacobian_water_pccd.py

from pybest import context
from pybest.ee_jacobian.jacobian_pccd import JacobianpCCD
from pybest.gbasis import (
    compute_eri,
    compute_kinetic,
    compute_nuclear,
    compute_nuclear_repulsion,
    compute_overlap,
    get_gobasis,
)
from pybest.geminals import RpCCD
from pybest.linalg import DenseLinalgFactory
from pybest.occ_model import AufbauOccModel
from pybest.wrappers import RHF

#
# Set up molecule, define basis set
#
# get the XYZ file from PyBEST's test data directory
fn_xyz = context.get_fn("test/water.xyz")
basis = get_gobasis("cc-pvdz", fn_xyz)

#
# Define occupation model, orbitals, and overlap
#
lf = DenseLinalgFactory(basis.nbasis)
occ_model = AufbauOccModel(basis)
orb_a = lf.create_orbital(basis.nbasis)
olp = compute_overlap(basis)

#
# Construct Hamiltonian
#
kin = compute_kinetic(basis)
ne = compute_nuclear(basis)
eri = compute_eri(basis)
external = compute_nuclear_repulsion(basis)

#
# Do a Hartree-Fock calculation
#
hf = RHF(lf, occ_model)
hf_output = hf(kin, ne, eri, external, olp, orb_a)

#
# Do pCCD optimization
#
oopccd = RpCCD(lf, occ_model)
oopccd_output = oopccd(kin, ne, eri, hf_output)

#
# Digonalizing the Jacobian-pCCD with Davidson
#
jac = JacobianpCCD(lf, occ_model)
jac_output = jac(kin, ne, eri, oopccd_output, nroot=3)

#
#  Exact diagonalization of the Jacobian-pCCD
#
ex_jac = JacobianpCCD(lf, occ_model)
ex_jac_output = ex_jac(kin, ne, eri, oopccd_output, nroot=3, davidson=False)

15.8.2. Jacobian pCCD+S calculations on the water molecule

This is a basic example of how to obtain excitation energies by diagonalizing the Jacobian matrix in PyBEST. This script performs an RHF calculation followed by a pCCD calculation and two different flavors based on a pCCD reference function. We consider pair and single excitations in the water molecule using the cc-pVDZ basis set.

Listing 15.2 data/examples/jacobian/jacobian_water_pccd_s.py

from pybest import context
from pybest.ee_jacobian.jacobian_pccd_s import JacobianpCCDS
from pybest.gbasis import (
    compute_eri,
    compute_kinetic,
    compute_nuclear,
    compute_nuclear_repulsion,
    compute_overlap,
    get_gobasis,
)
from pybest.geminals import RpCCD
from pybest.linalg import DenseLinalgFactory
from pybest.occ_model import AufbauOccModel
from pybest.wrappers import RHF

#
# Set up molecule, define basis set
#
# get the XYZ file from PyBEST's test data directory
fn_xyz = context.get_fn("test/water.xyz")
basis = get_gobasis("cc-pvdz", fn_xyz)

#
# Define occupation model, orbitals, and overlap
#
lf = DenseLinalgFactory(basis.nbasis)
occ_model = AufbauOccModel(basis, ncore=0)
orb_a = lf.create_orbital(basis.nbasis)
olp = compute_overlap(basis)

#
# Construct Hamiltonian
#
kin = compute_kinetic(basis)
ne = compute_nuclear(basis)
eri = compute_eri(basis)
external = compute_nuclear_repulsion(basis)

#
# Do a Hartree-Fock calculation
#
hf = RHF(lf, occ_model)
hf_output = hf(kin, ne, eri, external, olp, orb_a)

#
# Do pCCD optimization
#
oopccd = RpCCD(lf, occ_model)
oopccd_output = oopccd(kin, ne, eri, hf_output)

#
# Digonalizing the Jacobian-pCCD with Davidson
#
jac = JacobianpCCDS(lf, occ_model)
jac_output = jac(kin, ne, eri, oopccd_output, nroot=16)

#
#  Exact diagonalization of the Jacobian-pCCD
#
ex_jac = JacobianpCCDS(lf, occ_model)
ex_jac_output = ex_jac(kin, ne, eri, oopccd_output, nroot=3, davidson=False)