Understanding band gaps of solids in generalized Kohn-Sham theory

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 (2017)


Publication Status: Published

Publication Type: Journal article, Original article

Publication year: 2017

Journal

Publisher: National Academy of Sciences

Book Volume: 114

Pages Range: 2801-2806

Journal Issue: 11

DOI: 10.1073/pnas.1621352114

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 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.

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APA:

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 of the United States of America, 114(11), 2801-2806. https://dx.doi.org/10.1073/pnas.1621352114

MLA:

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

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