Kohn-Sham theory for orbital dependent exchange-correlation energy functionals: Application to the calculation of ionization potentials and electron affinities

Abstract

Available approximations to Exc[{nσ}], the exchange-correlation energy functional of spin-density-functional theory, do not include self-interaction corrections (SIC). This leads to Kohn–Sham (KS) potentials, Vxcσ, that fail to satisfy some important analytic properties known to be exhibited by the exact potential. To resolve these difficulties, we consider a KS theory for orbital-dependent exchange-correlation energy functionals that explicitly includes SIC. Recent work by Krieger, Li, and lafrate (KLI), which considers the analytic properties of the spin-polarized optimized effective potentials (OEP), V, i.e., the KS potentials corresponding to Exc = Exc[{ϕiσ,}], is reviewed as well as the properties of VxcσKLI, an easily calculated approximation to the exact result which, unlike Vxcσ0, can be employed for systems of arbitrary symmetry. In addition, we compare the results of the exact and approximate OEP calculation of the properties of the ground state of atoms and singly charged negative ions in the exchange-only case in which Ex = ExHF [{ϕiσ}] where HF = Hartree–Fock. We conclude that V maintains most of the important analytic properties of V, and provides an excellent numerical approximation to the exact result. We also give detailed consideration to the calculation of the ionization potential, I, and the electron affinity, A, in the exchange-only approximation for atoms with Z ≤ 20. We find that the KLI results for both I and A are always within 0.1 milli-au of the exact KS results, whereas both the local spin density (LSD) approximation and the Becke exchange only energy functional lead to deviations which on average are two orders of magnitude larger and significantly exceed the criterion for quantum chemistry accuracy. Finally, using the KLI method for orbital dependent Exc, we compare the KS results for I and A for Z ≤ 20 with the experimental values by employing various approximations for Exc[{ϕiσ] including: (1) HF exchange with LSD correlation with SIC, (2) LSD approximation for exchange and correlation with SIC, (3) the conventional spin density LSD approximation, and (4) the Becke exchange-energy functional with LSD correlation. In addition, we examine how closely the ionization theorem for ∈m, the energy eigenvalue for the highest occupied orbital, is satisfied in these approximations. © 1995 John Wiley & Sons, Inc.