Local field effects and the dielectric response matrix of insulators: A model

A simple model relating the low-optical-frequency dielectric response matrix of Adler and Wiser, ${\epsilon }_{\overrightarrow{\mathrm{K}},\overrightarrow{\mathrm{G}}}$, to the random-phase-approximation dielectric constant and to the Fourier coefficients of the valence-charge density, is presented. The model is derived by use of Kramers-Kronig relations and $f$ sum rules. The results of a recent band-structure calculation and other model calculations are compared with this model.