Density functional theory and the band gap problem

How can the fundamental band gap of an insulator be predicted? As a difference of ground-state energies, the fundamental gap seems to fall within the reach of density functional theory, yet the predicted gaps from band structure calculations within the local density approximation (LDA) are about 40% too small. It is argued here that even the exact Kohn-Sham potential veff(r), which generates the exact density in a self-consistent-field calculation, generates a band structure which underestimates the gap. Within the context of the band gap problem, several recent developments in the density-functional theory of many-electron systems are reviewed: (1) The Langreth-Mehl approximation to the Kohn-Sham…