Long-range behavior and frequency dependence of exchange-correlation kernels in solids

We define an effective exchange-correlation kernel (formula presented) which allows us to obtain correct absorption and energy loss spectra starting from an electronic structure obtained within some given approximation. We consider, in particular, the Kohn Sham electronic structure calculated in the local-density approximation and that obtained from a quasiparticle calculation. We show that in both cases the main feature able to account for the experimental spectra is a sizable, complex, and frequency- and material-dependent long-range contribution to (formula presented) We write, in terms of this contribution, an expression for the macroscopic dielectric function which is a generalization of the well-known contact-exciton approximation. Accurate absorption (for silicon and diamond) and electron energy loss (for silicon) spectra are obtained.