Microscopic Screening and Phonon Dispersion of Silicon: Moment Expansion for the Polarizability

A phonon dispersion curve of Si is calculated using the microscopic theory of dielectric screening. The electron energies and wave functions are calculated from a crystal pseudopotential which is self-consistent with the electron-ion pseudopotential. For the polarizability matrix a continued fraction expansion including the zeroth and first moment is used. The first moment is treated as a constant. The results are sensitive to both the self-consistency condition and the closure approximation.