Understanding band gaps of solids in generalized Kohn–Sham theory

• DOI: 10.1073/pnas.1621352114
• Publication Date: 2017-03-07T02:00:34Z
• Authors: John P. Perdew; Weitao Yang; Kieron Burke; Zenghui Yang; Eberhard K. U. Gross; Matthias Scheffler; Gustavo E. Scuseria; Thomas M. Henderson; Igor Ying Zhang; Adrienn Ruzsinszky; Haowei Peng; Jianwei Sun; Egor Trushin; Andreas Görling
• Keywords: Kohn–Sham equations; Operator (biology); Functional theory

The fundamental energy gap of a periodic solid distinguishes insulators from metals and characterizes low-energy single-electron excitations. But the in band-structure exact multiplicative Kohn-Sham (KS) potential substantially underestimates gap, major limitation KS density functional theory. Here we give simple proof new theorem: In generalized theory (GKS), band an extended system equals for approximate if GKS operator is continuous change delocalized when electron or hole added. Our theorem explains how gaps meta-generalized gradient approximations (meta-GGAs) hybrid functionals can be more realistic than those GGAs even potential. also follows earlier work. edges one-electron spectrum are related to measurable energies. A linear chain hydrogen molecules, aluminum arsenide, argon provide numerical illustrations.