Ab initiosecond-harmonic susceptibilities of semiconductors: Generalized tetrahedron method and quasiparticle effects

We report numerical calculations of the frequency-dependent second-order optical susceptibility. The results are based on an ab initio treatment of the geometry and the electronic structure within the density-functional theory in local-density approximation. The plane-wave-pseudopotential method is combined with a generalized tetrahedron method to perform the $\mathbf{k}$-space integration. The analytic linear tetrahedron method has to be improved because of the energy-dependent prefactors of the $\delta$ functions describing the energy conservation. We also present results for spectra of the second-harmonic generation where many-body quasiparticle effects are included beyond the scissors-operator approximation. Zinc-blende semiconductors are considered as model substances.