Understanding band gaps of solids in generalized Kohn-Sham theory.


Journal Article

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.

Full Text

Duke Authors

Cited Authors

  • Perdew, JP; Yang, W; Burke, K; Yang, Z; Gross, EKU; Scheffler, M; Scuseria, GE; Henderson, TM; Zhang, IY; Ruzsinszky, A; Peng, H; Sun, J; Trushin, E; Görling, A

Published Date

  • March 6, 2017

Published In

Volume / Issue

  • 114 / 11

Start / End Page

  • 2801 - 2806

PubMed ID

  • 28265085

Pubmed Central ID

  • 28265085

Electronic International Standard Serial Number (EISSN)

  • 1091-6490

International Standard Serial Number (ISSN)

  • 0027-8424

Digital Object Identifier (DOI)

  • 10.1073/pnas.1621352114


  • eng