EXACT KOHN-SHAM EXCHANGE POTENTIAL IN SEMICONDUCTORS

A new Kohn-Sham method that treats exchange interactions within densit y functional theory exactly is applied to Si, diamond. GaN, and InN. T he exact local exchange potential leads to significantly increased ban d gaps that are in good agreement viith experimental data. Generalized gradient approximations yield exchange energies that are much closer to the exact values than those predicted by the local density approxim ation. The exchange contribution to the derivative discontinuity of th e exchange-correlation potential is found to be very large (of the ord er of 5-10 eV).