Simple Rules for Determining Valencies of f-electron Systems

The electronic structure of f-electron systems is calculated with the self-interaction-corrected local-spin-density (LSD) approximation. This scheme allows for a splitting of the f-electron manifold into an integral number of localized electrons and self-consistently determined fractional number of band electrons. Therefore, in comparison with the LSD approximation, where all f states are pinned at the Fermi energy, only a maximum of one f band is left at the Fermi energy. We show that this band is partially occupied with occupancy n(f), and the f-electron fluctuations are reduced compared with the LSD approximation. When n(f) exceeds a critical value of approximately 0.6, it becomes energetically more favourable to localize this state, and the number of valence bands is reduced by one.