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Journal Article

Understanding band gaps of solids in generalized Kohn-Sham theory


Scheffler,  Matthias
Theory, Fritz Haber Institute, Max Planck Society;
Department of Chemistry and Biochemistry, University of California;
Materials Department, University of California;


Zhang,  Igor Ying
Theory, Fritz Haber Institute, Max Planck Society;

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

Cite as: https://hdl.handle.net/11858/00-001M-0000-002C-2E4B-C
The fundamental energy gap of a periodic solid distinguishes insulators from metals and characterizes low-energy single-electron excitations. But the gap in the and-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 new theorem: In generalized KS theory (GKS), the band gap 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 meta-generalized gradient approximations (meta-GGAs) and hybrid functionals can be more realistic than those from GGAs or even from the exact KS potential, It 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 provides a numerical illustration.