It is shown that a purely local-pseudopotential calculation is able to accurately reproduce the major optical gaps and cyclotron masses. However, deviations from the experimental results become manifest in photoemission and x-ray charge-density results as we extend our calculations to the lower valence bands. These deviations indicate the necessity of an energy-dependent nonlocal $s$-well potential, a conclusion which is also supported by an analysis of the Heine-Abarenkov pseudopotential scheme. A detailed comparison is made between experimental results obtained from optical, photoemission, x-ray, and cyclotron-resonance measurements, and the results of both the local calculation and an energy-dependent nonlocal calculation. Yang and Coppens's recent determination of the valence charge density in silicon makes it possible to assess the accuracy of the pseudocharge densities for the first time.

• Received 1 July 1974

DOI:https://doi.org/10.1103/PhysRevB.10.5095