Exact Kohn-Sham Exchange Potential in Semiconductors

A new Kohn-Sham method that treats exchange interactions within density functional theory exactly is applied to Si, diamond, GaN, and InN. The exact local exchange potential leads to significantly increased band gaps that are in good agreement with experimental data. Generalized gradient approximations yield exchange energies that are much closer to the exact values than those predicted by the local density approximation. The exchange contribution to the derivative discontinuity of the exchange-correlation potential is found to be very large (of the order of 5--10 eV).