Mean-value point and dielectric properties of semiconductors and insulators

The mean-value-point technique for Brillouin-zone averages is shown to be applicable to the calculation of electronic dielectric screening matrices. The dielectric-matrix elements for which the technique is not accurate are only a few and for them a separate simple prescription is given. Detailed results are presented for the $\omega =0\mathrm{}$, $\overrightarrow{\mathrm{q}}=0\mathrm{}$, and $\overrightarrow{\mathrm{q}}\to 0$ $\epsilon$ matrices of diamond, Si, Ge, $\alpha -\mathrm{Sn}$, MgO, and NaCl. Comparison with a nearly-free-electron model is also discussed.