Size-Consistency, Self-Interaction Correction, and Derivative Discontinuity in Density Functional Theory

Abstract

Three size-consistency principles of electronic structure theory are set forth. “Separability” and “extensivity” are respected even by local or semilocal density functional approximations, which succeed for that and other reasons. The strong tendency of a separated subsystem to reject fractional electron number is a consequence of the derivative discontinuity of the energy; this “integer preference” is probably not respected by any practical density functional approximation. However, all three size-consistency principles are obeyed by theories which construct the energy from localized orbitals. The self-interaction correction (SIC) to the local spin density approximation favors localized orbitals for most systems. If this fails for metals, then SIC gives rise to a “false surface energy”. The self-interaction correction is reviewed, along with its exact-theory “doppelganger”, the derivative discontinuity. The latter reveals the physical content of the exact Kohn-Sham orbital energies and resolves the “band-gap problem”.