Band gap calculations with Becke–Johnson exchange potential

Recently, a simple analytical form for the exchange potential was proposed by Becke and Johnson. This potential, which depends on the kinetic-energy density, was shown to reproduce very well the shape of the exact exchange potential (obtained with the optimized effective potential method) for atoms. Calculations on solids show that the Becke–Johnson potential leads to a better description of band gaps of semiconductors and insulators with respect to the standard local density and Perdew–Burke–Ernzerhof approximations for the exchange–correlation potential. Comparison is also made with the values obtained with the Engel–Vosko exchange potential which was also developed using the exact exchange potential.