Nonlocal Kohn-Sham exchange corrections to Si band gaps and binding energy

We compare the binding energy and energy band gaps of Si calculated with the local-density approximation to the Kohn-Sham exchange potential and with the correction to that potential which is exact to first order in {ρ}(K)/ρ₀. Although the correction is not small, running between 1 eV and -3.5 eV in the unit cell, its effect on both the band gaps and binding energy is very small. Thus we conclude that the discrepancy between calculated energy band gaps and experiment must be almost entirely due to the discontinuity in the zeroth Fourier component of the exchange-correlation potential.