A Projector Augmented Wave Treatment of Fock Exchange in Hartree-Fock and Optimized Effective Potential Calculations

The use of orbital-dependent exchange-correlation functionals within electronic structure calculations has recently received renewed attention as a means of improving accuracy. In particular, the Fock exchange functional exactly cancels the electron self-interaction error which can be particularly significant in transition metals and other materials with localized orbitals. Since the Projector Augmented Wave (PAW) formalism\footnote{P. E. Bl\"{o}chl, {\em{Phys. Rev. B}} {\bf{50}}, 17953 (1994).} accurately evaluates the interaction integrals including all multiple moments, it is a natural choice for representing the Fock exchange functional within an efficient pseudopotential-like scheme. We have adapted the PAW formalism for use both in Hartree-Fock (HF) theory and in the KLI approximation to Optimized Effective Potential theory.\footnote{J. B. Krieger, Y. Li and G. J. Iafrate {\em{Phys. Rev. A}} {\bf{45}} 101 (1992).} We show that the effects of core electrons are significant and can be accurately treated within a frozen core orbital approximation.\footnote{Xiao Xu and N. A. W. Holzwarth, {\em{Phys. Rev. B}} {\bf{81}} 245105 (2010).} PAW-HF and PAW-KLI basis, projector, and pseudopotential functions are presented for several elements throughout the periodic table.