Unified formulation of fundamental and optical gap problems in density-functional theory for ensembles

Abstract

Solving the fundamental and optical gap problems, which yield information about charged and neutral excitations in electronic systems, is one of the biggest challenge in density-functional theory (DFT). Despite their intrinsic difference, we show that the two problems can be made formally identical by introducing a universal and canonical ensemble weight dependent exchange-correlation (xc) density functional. The weight dependence of the xc energy turns out to be the key ingredient for describing the infamous derivative discontinuity and represents a new path for its approximation.