Asymptotic Behavior of Exact Exchange for Slabs: Beyond the Leading Order.

Far outside the surface of slabs, the exact exchange (EXX) potential v x falls off as − 1 / z , if z denotes the direction perpendicular to the surface and the slab is localized around z = 0 . Similarly, the EXX energy density e x behaves as − n / ( 2 z ) , where n is the electron density. Here, an alternative proof of these relations is given, in which the Coulomb singularity in the EXX energy is treated in a particularly careful fashion. This new approach allows the derivation of the next-to-leading order contributions to the asymptotic v x and e x . It turns out that in both cases, the corrections are proportional to 1 / z 2 in general. [ABSTRACT FROM AUTHOR]