Understanding band gaps of solids in generalized Kohn–Sham theory

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 density-functional 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)…

• UD
  U.S. Department of Energy

  Awards: DE-SC0012575, DE-FG02-08ER46496, DE-FG02-, FG02-08ER46496, DE-FG02
• AV
  Alexander von Humboldt-Stiftung

  Award: 000000
• DF
  Deutsche Forschungsgemeinschaft

  Award: 000000
• OO
  Office of Science

  Award: DE-SC0012575
• BE
  Basic Energy Sciences

  Awards: DE-FG02, DE-FG02-08ER46496, SC0012575, DE-SC0012575