title: Understanding band gaps of solids in generalized Kohn-Sham theory.
abstract: The fundamental energy gap of a periodic solid distinguishes insulators from metals and characterizes low-energy single-electron excitations. However, the gap in the band structure of the exact multiplicative Kohn-Sham (KS) potential substantially underestimates the fundamental gap, a major limitation of KS density-functional theory. Here, we give a simple proof of a theorem: In generalized KS theory (GKS), the band gap of an extended system equals the fundamental gap for the approximate functional if the GKS potential operator is continuous and the density change is delocalized when an electron or hole is added. Our theorem explains how GKS band gaps from metageneralized gradient approximations (meta-GGAs) and hybrid functionals can be more realistic than those from GGAs or even from the exact KS potential. The theorem also follows from earlier work. The band edges in the GKS one-electron spectrum are also related to measurable energies. A linear chain of hydrogen molecules, solid aluminum arsenide, and solid argon provide numerical illustrations.
authors.affiliation: Department of Physics, Temple University, Philadelphia, PA 19122; perdew@temple.edu.|Department of Chemistry, Temple University, Philadelphia, PA 19122.
authors.forename: John P
authors.initials: JP
authors.lastname: Perdew
authors.affiliation: Department of Chemistry, Duke University, Durham, NC 27708.
authors.forename: Weitao
authors.initials: W
authors.lastname: Yang
authors.affiliation: Department of Chemistry, University of California, Irvine, CA 92697.|Department of Physics, University of California, Irvine, CA 92697.
authors.forename: Kieron
authors.initials: K
authors.lastname: Burke
authors.affiliation: Department of Physics, Temple University, Philadelphia, PA 19122.
authors.forename: Zenghui
authors.initials: Z
authors.lastname: Yang
authors.affiliation: Max-Planck Institut für Mikrostrukturphysik, D-06120 Halle, Germany.
authors.forename: Eberhard K U
authors.initials: EK
authors.lastname: Gross
authors.affiliation: Fritz-Haber-Institut der Max-Planck-Gesellschaft, D-14195 Berlin, Germany.|Department of Chemistry and Biochemistry, University of California, Santa Barbara, CA 93106.|Materials Department, University of California, Santa Barbara, CA 93106.
authors.forename: Matthias
authors.initials: M
authors.lastname: Scheffler
authors.affiliation: Department of Chemistry, Rice University, Houston, TX 77005.|Department of Physics and Astronomy, Rice University, Houston, TX 77005.
authors.forename: Gustavo E
authors.initials: GE
authors.lastname: Scuseria
authors.affiliation: Department of Chemistry, Rice University, Houston, TX 77005.|Department of Physics and Astronomy, Rice University, Houston, TX 77005.
authors.forename: Thomas M
authors.initials: TM
authors.lastname: Henderson
authors.affiliation: Fritz-Haber-Institut der Max-Planck-Gesellschaft, D-14195 Berlin, Germany.
authors.forename: Igor Ying
authors.initials: IY
authors.lastname: Zhang
authors.affiliation: Department of Physics, Temple University, Philadelphia, PA 19122.
authors.forename: Adrienn
authors.initials: A
authors.lastname: Ruzsinszky
authors.affiliation: Department of Physics, Temple University, Philadelphia, PA 19122.
authors.forename: Haowei
authors.initials: H
authors.lastname: Peng
authors.affiliation: Department of Physics, The University of Texas at El Paso, El Paso, TX 79968.
authors.forename: Jianwei
authors.initials: J
authors.lastname: Sun
authors.affiliation: Department of Chemistry and Pharmacy, Friedrich-Alexander Universität Erlangen-Nürnberg, 91058 Erlangen, Germany.
authors.forename: Egor
authors.initials: E
authors.lastname: Trushin
authors.affiliation: Department of Chemistry and Pharmacy, Friedrich-Alexander Universität Erlangen-Nürnberg, 91058 Erlangen, Germany.
authors.forename: Andreas
authors.initials: A
authors.lastname: Görling
keywords: Kohn–Sham theory; band gaps; density-functional theory; generalized Kohn–Sham theory; solids