Using a time-dependent extension of a density-functional tight-binding method, we have calculated the excitation spectra of stoichiometric cadmium sulfide clusters up to 144 atoms. The spectra show a strong dependency of the lowest unoccupied molecular orbitals on the structural properties of the clusters, especially on the number of single-bonded surface atoms. Furthermore, we calculated the single-particle energy eigenvalues for a number of clusters up to 440 atoms without structural relaxation. Here, with increasing cluster size the gap between highest occupied and lowest unoccupied molecular orbitals (HOMO/LUMO gap) is decreasing asymptotically toward the bulk band gap of cadmium sulfide for clusters with no single-bonded surface atoms and tending to a zero gap for clusters with a large number of single-bonded surface cadmium atoms. The latter is caused by low-lying cadmium 5s states.