A new density functional for fractionally occupied orbital systems with application to ionization and transition energies

The use of fractional occupation of energy levels in the self-interaction-corrected local spin density (SIC-LSD) theory of electronic energy structure is studied with reference to calculation of ionization and excitation energies. With the original form of the SIC-LSD energy functional for fractional occupation, the one-electron eigenvalues exhibit nonlinear dependence on the occupation number. A new SIC-LSD density functional for fractional occupation based on the general behavior of the universal functional is proposed. The one-electron eigenvalues derived from this new functional vary quite linearly with the occupation number. This makes it possible to obtain ionization and excitation energies by a simple numerical integration over the occupation number. A one-point integration gives ionization energies that agree on the average with the results on taking the difference in self-consistent-field total energy between the atom and the ion to within 0.4% for the atoms He, Li, Be,...,Ar. Improvement can be made by using a three-point integration over the occupation number. This method is also applied to calculate excitation energies of selected transitions for He through Ar and the results are in good agreement with the corresponding total-energy differences.