Physical Content of the Exact Kohn-Sham Orbital Energies: Band Gaps and Derivative Discontinuities

John P. Perdew; Mel Levy

doi:10.1103/PhysRevLett.51.1884

Physical Content of the Exact Kohn-Sham Orbital Energies: Band Gaps and Derivative Discontinuities

John P. Perdew and Mel Levy

Phys. Rev. Lett. 51, 1884 – Published 14 November 1983

Abstract

The local-density approximation for the exchange-correlation potential understimates the fundamental band gaps of semiconductors and insulators by about 40%. It is argued here that underestimation of the gap width is also to be expected from the unknown exact potential of Kohn-Sham density-functional theory, because of derivative discontinuities of the exchange-correlation energy. The need for an energy-dependent potential in band theory is emphasized. The center of the gap, however, is predicted exactly by the Kohn-Sham band structure.

Received 17 June 1983

DOI:https://doi.org/10.1103/PhysRevLett.51.1884

Authors & Affiliations

John P. Perdew

Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, and Department of Physics and Quantum Theory Group, Tulane University, New Orleans, Louisiana 70118

Mel Levy