Photoelectron spectra of sodium clusters: The problem of interpreting Kohn-Sham eigenvalues

We calculated the Kohn-Sham eigenvalues for small sodium cluster anions using the exact Kohn-Sham exchange functional with the optimized effective potential, the exchange functional in the Krieger-Li-Iafrate approximation, a nonempirical generalized gradient approximation, and the local density approximation. The eigenvalue spectra obtained from the different functionals are compared to measured photoelectron spectra. The strengths and limitations of this pragmatic interpretation of Kohn-Sham eigenvalues are discussed. We further investigate how much the eigenvalues from (semi-)local functionals are affected by a nonlinear core correction to the pseudopotential and by an earlier proposed scheme that is supposed to convert Kohn-Sham eigenvalues into electron binding energies.