Ab initio wave-function-based methods are employed for the study of quasiparticle energy bands of zinc-blende ZnS, with focus on the Zn 3d "semicore" states. The relative energies of these states with respect to the top of the S 3p valence bands appear to be poorly described as compared to experimental values not only within the local density approximation (LDA), but also when manybody corrections within the GW approximation are applied to the LDA or LDA+U mean-field solutions [T. Miyake, P. Zhang, M. L. Cohen, and S. G. Louie, Phys. Rev. B 74, 245213 (2006)].In the present study, we show that for the accurate description of the Zn 3d states a correlation treatment based on wave function methods is needed. Our study rests on a local Hamiltonian approach which rigorously describes the short-range polarization and charge redistribution effects around an extra hole or electron placed into the valence respective conduction bands of semicon- 2