Understanding band gaps of solids in generalized Kohn-Sham theory

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

380 Scopus citations


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 densityfunctional 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.

Original languageEnglish
Pages (from-to)2801-2806
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number11
StatePublished - 14 Mar 2017
Externally publishedYes


  • Band gaps
  • Density-functional theory
  • Generalized Kohn-Sham theory
  • Kohn-Sham theory
  • Solids


Dive into the research topics of 'Understanding band gaps of solids in generalized Kohn-Sham theory'. Together they form a unique fingerprint.

Cite this