Obtaining integrals
===================

Forte2 uses the `Libint2 <https://github.com/evaleev/libint>`_ 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 <https://github.com/evaleev/libint/wiki/using-modern-CPlusPlus-API#create-an-integral-engine>`_) 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)