Chemisorption on small, closed-ring CdS clusters and the electronic structure of the surface were studied using Hartree-Fock valence calculations based upon stepwise density matrix approximations. Detailed valence calculations gave stabilization energies similar to the all-electron results for the small CdS clusters, verifying our valence method in which the approximations of the density matrices were fitted against the atomic calculations. Chemisorption studies have shown that the 4d shell relaxation on the Cd atom plays a crucial role even though the 4d does not participate directly in the substrate-adsorbate bonds. Thus, the CdClr was found unbound to the surface in the case of implicit description of the 4d orbital of the Cd whereas treating the Cd 4d orbital explicitly in the variational calculation the CdCI2 bonds to the surface with the calculated adsorption energy of 107.4 kJ/mol.