The structures of (PbS), (n = 1-9) clusters are investigated with density functional theory at the B3LYP level. Various pseudopotential basis sets on lead and the 6-31+G* basis set on sulfur were employed. Full geometry optimization and extensive searches of the potential energy surface were carried out for clusters with n = 1-6. We find that even small PbS clusters (n > 2) start to take on the characteristic features of the rock salt structure of solid-state PbS (galena). The origin of some of the structural aspects of these crystals is shown to be associated with the partial covalent nature of the Pb-S bond. The magnitude of the HOMO-LUMO gap oscillates with increasing size of the clusters, in agreement with the observed behavior of the corresponding UV absorption bands of ultrasmall PbS quantum dots. Direct conformation of this oscillation was found by CIS(D) calculations, for which the absorption with the largest oscillator strength oscillates as the clusters grow from PbS to (PbS)g.