Obtaining integrals#

Forte2 uses the Libint2 integral engine. It provides a straightforward way of accessing atomic integrals through its API. You can obtain the integrals for a given molecular system by first specifying a molecular system and using the forte2.ints module. Almost all operators supported by Libint2 (see Libint2 documentation) are available. Here are some examples of how to obtain the most common integrals. First one needs to set up the molecular system:

import forte2

# Set up your molecular system
system = forte2.system(
    xyz="""C 0 0 0
    N 0 0 1.4""",
    basis_set={"C": "cc-pvdz", "N": "cc-pvtz"},
    auxiliary_basis_set="cc-pvdz-jkfit",
    minao_basis_set="ano-r0",
)

The system object will now contain parsed geometry under atoms, the basis set under basis, the auxiliary basis set under auxiliary_basis, and the minimal atomic basis set under minao_basis. Getting integrals is now straightforward:

# overlap integrals
overlap = forte2.ints.overlap(system.basis)

# "mixed basis" overlap integrals are available simply as:
mixed_overlap = forte2.ints.overlap(system.minao_basis, system.basis)

# kinetic energy integrals
kinetic = forte2.ints.kinetic(system.basis)

# potential energy integrals
potential = forte2.ints.potential(system.basis, system.atoms)

# dipole integrals (ordered x,y,z)
# the zeroth element is the overlap
dipole = forte2.ints.emultipole1(system.basis, system.atoms)[1:]

# 4-center-2-electron integrals
eri = forte2.ints.coulomb_4c(system.basis)

# 3-center-2-electron integrals (for density-fitting)
B = forte2.ints.coulomb_3c(system.auxiliary_basis, system.basis, system.basis)

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