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 ω=0, →q=0, and →q→0 ε matrices of diamond, Si, Ge, α-Sn, MgO, and NaCl. Comparison with a nearly-free-electron model is also discussed.