Understanding band gaps of solids in generalized Kohn-Sham theory

Journal article
(Original article)

Publication Details

Author(s): 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
Journal: Proceedings of the National Academy of Sciences
Publisher: National Academy of Sciences
Publication year: 2017
Volume: 114
Journal issue: 11
Pages range: 2801-2806
ISSN: 0027-8424
eISSN: 1091-6490


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.

FAU Authors / FAU Editors

Görling, Andreas Prof. Dr.
Lehrstuhl für Theoretische Chemie
Trushin, Egor
Sonderforschungsbereich 953/2 Synthetische Kohlenstoffallotrope

External institutions
Duke University
Fritz-Haber-Institut der Max-Planck-Gesellschaft (FHI)
Max-Planck-Institut für Mikrostrukturphysik (MSP) / Max Planck Institute for Microstructure Physics
Rice University
Temple University
The University of Texas at El Paso
University of California Irvine

How to cite

Perdew, J.P., Yang, W., Burke, K., Yang, Z., Gross, E.K.U., Scheffler, M.,... Görling, A. (2017). Understanding band gaps of solids in generalized Kohn-Sham theory. Proceedings of the National Academy of Sciences, 114(11), 2801-2806. https://dx.doi.org/10.1073/pnas.1621352114

Perdew, John P., et al. "Understanding band gaps of solids in generalized Kohn-Sham theory." Proceedings of the National Academy of Sciences 114.11 (2017): 2801-2806.


Last updated on 2018-09-11 at 20:50