On the Ordering of Orbital Energies in the ROHF Method: Koopmans’ Theorem versus Aufbau Principle

The restricted open-shell Hartree-Fock (ROHF) method in its different formulations is a standard tool used by quantum chemists for studying open-shell systems. This work presents a discussion of specific difficulties which arise in the ROHF method in those cases where the orbital energies violate the Aufbau principle (AP). The AP violations are often treated in the literature as a deficiency of both a ROHF method leading to these violations and of the respective computational results. We summarize examples of different AP violations and analyze them from the viewpoint of both Koopmans’ theorem (KT) and experimental ionization potentials. We show that the main source of AP violations is a specific ordering of the ROHF orbital energies based on the orbital occupancies. In those cases, where the orbital energies obey KT, the violations of the AP reflect the physical reality. To overcome computational difficulties which arise in the iterative SCF procedure, we describe a simple and effective orbital-energy scaling technique which enables one to perform ROHF computations of systems violating the Aufbau principle.