Generalized-exchange local-spin-density-functional theory: Self-interaction correction

Abstract

The local-spin-density (LSD) generalized-exchange (GX) theory is corrected for self-interaction by splitting the single-particle Fermi hole into pure-exchange and self-interaction holes. An analysis of these components shows that the non-self-interaction-corrected GX scheme overestimates the pure exchange while underestimating the self-interaction. This self-interaction-corrected scheme is called the GX-SI scheme. Using this method of correcting for self-interaction, two other approximate self-interaction-corrected (SIC) GX schemes can be derived in which (1) the GX-LSD-SI total exchange does not include the nonlocal, self-interaction potential and (2) the GX-SIX exchange is very similar to the exchange derived by Gopinathan [Phys. Rev. A 15, 2135 (1977)]. Neither of these exchanges obeys the sum rule. The GX-SI scheme contains correction terms to the LSD GX which are smaller than the corresponding ones derived in the SIC of Perdew and Zunger [Phys. Rev. B 23, 5048 (1981)]. This shows that the LSD-GX exchange is a better approximation to the true exchange of an inhomogeneous electron gas around an atom than the LSD free-electron gas exchange.