Koopmans' theorem in the restricted open-shell Hartree-Fock method. 1. A variational approach

Area of Science:

• Quantum Chemistry
• Computational Chemistry

Background:

• Restricted open-shell Hartree-Fock (ROHF) method is crucial for describing systems with unpaired electrons.
• Koopmans' theorem provides a link between orbital energies and ionization potentials/electron affinities.
• Challenges exist in applying Koopmans' theorem to open-shell systems.

Purpose of the Study:

• To derive a general formulation of Koopmans' theorem for high-spin, half-filled open shells within the ROHF framework.
• To investigate the relationship between canonical ROHF orbitals and natural CI orbitals.
• To compare computational approaches for systems where canonical orbital energies violate the Aufbau principle.

Main Methods:

• Variational treatment of the initial open-shell system and its corresponding ions.
• Full CI in the restricted active space (FCI-RAS) method applied to ions.
• Utilizing arbitrary ROHF orbitals optimal for the initial system.

Main Results:

• Canonical ROHF orbitals and orbital energies satisfying Koopmans' theorem are shown to generally appear as natural CI orbitals and eigenvalues for the respective ions.
• Demonstrated equivalence between the CI approach and canonical ROHF treatment under specific conditions.
• Provided a comparison of results from the CI approach and canonical ROHF method.

Conclusions:

• The derived formulation offers a robust application of Koopmans' theorem to high-spin, half-filled open shells.
• The study clarifies the connection between ROHF and CI methods in describing electronic properties.
• The findings are particularly relevant for systems where standard approximations may fail.