Define an Active Space (Complete Active Space)

Goal

Create a ground-state problem that uses a CAS(n, m) active space, where \(n\) active electrons are distributed among \(m\) active spatial orbitals, with all other electrons frozen.

Steps

  1. Add the active space modifier to the ground-state problem builder

    import qrunch as qc

problem_builder = (
    qc.problem_builder_creator()
    .ground_state()
    .standard()
    .add_problem_modifier()
    .active_space(
        number_of_active_spatial_orbitals=8,
        number_of_active_alpha_electrons=6
    )
    .create()
)

    This defines an active space where:

    • number_of_active_spatial_orbitals = 8

    • number_of_active_alpha_electrons = 6

    • The number of active beta electrons is inferred from the spin difference in the molecular configuration, and the number of active_alpha_electrons.

    Example:

    • If spin difference = 2, the number of active beta electrons will be: active_beta = active_alpha - spin_difference = 6 - 2 = 4

    • Total active electrons = \(6_{\alpha} + 4_{\beta} = 10\) electrons in 8 spatial orbitals (16 active spin orbitals).

    The active space is a modifier, in the sense that it modifies the Hamiltonian of the ground-state problem to only include the active space.

  2. Build the ground-state problem

    The building of the ground state problem continues as in Construct a Ground State Energy Problem however, the problem will now include the “Inactive electrons energy” and after the calculation of the ground state energy, the result will include the energy of non-active electrons (non_active_electrons_energy) in the total energy.

Verify the Result

  • When you calculate the ground-state energy, the result object will include:

    • non_active_electrons_energy — the electronic energy contribution from electrons not included in the active space.

    • active_electrons_energy — the electronic energy contribution of the active electrons.

    • total_energy — The total energy of the system.

See Also