We describe our progress in developing an ab initio computational scheme for the calculation of the dielectric response function of solids, with special emphasis here on Si and C clusters. All calculations are carried out employing a basis of localized atomic-like orbitals and include the evaluation of quasiparticle corrections. The self-energy operator is evaluated in the GW approximation, with a full frequency dependence for the dielectric matrix. The approach is convenient and computationally optimal for the calculation of optical properties of complex systems lacking full periodicity, such as surfaces and clusters. We present here the dielectric response functions of clusters with structures found after full equilibration via molecular dynamical simulations, and discuss the sensitivity of the optical properties to quasiparticle corrections.