Band structure calculation for GaAs and Si beyond the local density approximation

We have performed pseudopotential self-consistent band-structure calculations for bulk solids in the framework of the Kohn-Sham density-functional theory, applying the nonlocal exchange-correlation functional of Gunnarsson and Jones to valence electrons with no further approximation. We present our method together with representative results for GaAs and Si, the main interest being focused on single-particle energy eigenvalues and gaps. An accurate comparison of the results obtained with this approach and the local-density-approximation results is given. The dependence of such a comparison on the choice of the basis set (localized Gaussian orbitals or plane waves) is also examined, and found to be unimportant. The reliability of the method, the changes in band structure, their k→ dependence, and the behavior of the exchange-correlation potential throughout the unit cell are discussed. We find that the inclusion of nonlocality in the description of exchange and correlation does not change valence-band states significantly and increases by a very small amount the energy difference between some conduction-band states and the top of the valence band. The increase (≲0.2 eV) is, however, insufficient to solve the problem of the local-density-approximation minimum band gaps, which remain much smaller than the measured energy gaps.