KOHN-SHAM THEORY FOR ORBITAL DEPENDENT EXCHANGE-CORRELATION ENERGY FUNCTIONALS - APPLICATION TO THE CALCULATION OF IONIZATION-POTENTIALS AND ELECTRON-AFFINITIES

Available approximations to E(xc)[{n(sigma)}], the exchange-correlatio n energy functional of spin-density-functional theory, do not include self-interaction corrections (SIC). This leads to Kohn-Sham (KS) poten tials, V-xc sigma, that fail to satisfy some important analytic proper ties known to be exhibited by the exact potential. To resolve these di fficulties, we consider a KS theory for orbital-dependent exchange-cor relation energy functionals that explicitly includes SIC. Recent work by Krieger, Li, and Iafrate (KLI), which considers the analytic proper ties of the spin-polarized optimized effective potentials (OEP), V-xc sigma(0), i.e., the KS potentials corresponding to E(xc) = E(xc)[{phi( i sigma)}], is reviewed as well as the properties of V-xc sigma(KLI), an easily calculated approximation to the exact result which, unlike V -xc sigma(0), can be employed for systems of arbitrary symmetry. In ad dition, we compare the results of the exact and approximate OEP calcul ation of the properties of the ground state of atoms and singly charge d negative ions in the exchange-only case in which E(x) = E(x)(HF)[{ph i(i sigma)}] where HF = Hartree-Fock. We conclude that V-x sigma(KLI) maintains most of the important analytic properties of V-x sigma(0) an d provides an excellent numerical approximation to the exact result. W e also give detailed consideration to the calculation of the ionizatio n potential, I, and the electron affinity, A, in the exchange-only app roximation for atoms with Z less than or equal to 20. We find that the KLI results for both I and A are always within 0.1 milli-au of the ex act KS results, whereas both the local spin density (LSD) approximatio n and the Becke exchange only energy functional lead to deviations whi ch on average are two orders of magnitude larger and significantly exc eed the criterion for quantum chemistry accuracy. Finally, using the K LI method for orbital dependent E(xc), we compare the KS results for I and A for Z less than or equal to 20 with the experimental values by employing various approximations for E(xc)[{phi(i sigma)}] including. 1) HF exchange with LSD correlation with SIC, 2) LSD approximation for exchange and correlation with SIC, 3) the conventional spin density L SD approximation, and 4) the Becke exchange-energy functional with LSD correlation. In addition, we examine how closely the ionization theor em for epsilon(m), the energy eigenvalue for the highest occupied orbi tal, is satisfied in these approximations. (C) 1995 John Wiley & Sons, Inc.