Koopmans' Theorem in the Restricted Open-Shell Hartree-Fock Method. 1. A Variational Approach

A general formulation of Koopmans' theorem is derived for high-spin half-filled open shells in the restricted open-shell Hartree-Fock (ROHF) method based on a variational treatment of both the initial (nonionized) open-shell system under study, e.g., X, kind the corresponding high-spin ions X-k(+), X-m(+), and X-v(-) having a hole or an extra electron in the closed, open, and virtual shell, respectively. The ions are treated within a FCI-RAS (full CI in the restricted active space) method with a use of arbitrary ROHF orbitals optimal for the initial system. We show that the desired canonical ROHF orbitals and orbital energies satisfying Koopmans' theorem, first defined within the canonical ROHF treatment [Plakhutin; et al. J. Chem. Phys. 2006, 125, 204110], generally appear as the natural CI orbitals and the eigenvalues of CI matrices for the respective ions X-+/-. A comparison is performed between the results derived with the present CI approach and the canonical ROHF method for the specific case where the canonical orbital energies satisfying Koopmans' theorem do not satisfy the Aufbau principle.