TY - JOUR

T1 - Understanding band gaps of solids in generalized Kohn-Sham theory

AU - Perdew, John P.

AU - Yang, Weitao

AU - Burke, Kieron

AU - Yang, Zenghui

AU - Gross, Eberhard K.U.

AU - Scheffler, Matthias

AU - Scuseria, Gustavo E.

AU - Henderson, Thomas M.

AU - Zhang, Igor Ying

AU - Ruzsinszky, Adrienn

AU - Peng, Haowei

AU - Sun, Jianwei

AU - Trushin, Egor

AU - Görling, Andreas

PY - 2017/3/14

Y1 - 2017/3/14

N2 - 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.

AB - 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.

KW - Band gaps

KW - Density-functional theory

KW - Generalized Kohn-Sham theory

KW - Kohn-Sham theory

KW - Solids

UR - http://www.scopus.com/inward/record.url?scp=85015363624&partnerID=8YFLogxK

U2 - 10.1073/pnas.1621352114

DO - 10.1073/pnas.1621352114

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C2 - 28265085

AN - SCOPUS:85015363624

SN - 0027-8424

VL - 114

SP - 2801

EP - 2806

JO - Proceedings of the National Academy of Sciences of the United States of America

JF - Proceedings of the National Academy of Sciences of the United States of America

IS - 11

ER -