Calculation of the dielectric matrix of Si

The inverse microscopic dielectric matrix of crystalline silicon is evaluated within the time-dependent density-functional theory using one-electron energies and wave functions obtained by all-electron modified augmented-plane-wave band-structure calculations. Local fields are taken into account by inverting the dielectric matrix. The dependency of the exchange and correlation on the frequency and momentum is described using different approximations. We find that the polarization of the 2s and 2p core electrons changes the inverse dielectric function by up to 8%. In the long-wavelength limit our results for the region below 5 eV deviate from optical experiments by an almost constant energy shift, which is the same size as the band-gap error in local density approximation. Our results correspond with inelastic x-ray scattering spectroscopy measurements.