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@article{faucris.122487024,
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.},
author = {Perdew, John P. and Yang, Weitao and Burke, Kieron and Yang, Zenghui and Gross, Eberhard K. U. and Scheffler, Matthias and Scuseria, Gustavo E. and Henderson, Thomas M. and Zhang, Igor Ying and Ruzsinszky, Adrienn and Peng, Haowei and Sun, Jianwei and Trushin, Egor and GĂ¶rling, Andreas},
doi = {10.1073/pnas.1621352114},
faupublication = {yes},
journal = {Proceedings of the National Academy of Sciences},
keywords = {Band gaps; Density-functional theory; Generalized Kohn-Sham theory; Kohn-Sham theory; Solids},
pages = {2801-2806},
peerreviewed = {Yes},
title = {{Understanding} band gaps of solids in generalized {Kohn}-{Sham} theory},
volume = {114},
year = {2017}
}