Optical properties and electronic structures of semiconductors with screened-exchange LDA

Results of first-principles calculations of the optical properties and electronic structure, determined by employing the screened-exchange LDA method to obtain accurate electronic structures as well as self-consistent eigenfunctions, are presented for some cubic semiconductors (Si, Ge, InSb, and GaAs). As implemented in the full-potential linearized augmented-plane-wave method, this approach does not require any adjustable parameters to calculate optical properties. The inadequacy of using the transverse expression of the dielectric function (involving $\mathbf{ê}\cdot \mathbf{p}$ matrix elements) is shown numerically for the optical spectra and dielectric constants even when the renormalization factor associated with the LDA eigenvalues is included. This is because the nonlocality of the Hamiltonian and the difference of the self-consistent eigenfunctions from the LDA ones are not negligible. In contrast, the optical properties evaluated using the longitudinal expression (with $e^{i\mathbf{q}\cdot \mathbf{r}}$ matrix elements) yield excellent agreement with experiment considering the neglect of lifetime, local-field, and excitonic effects.