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The semiempirical tight-binding method was used to study the electronic structure of spherical PbS nanocrystals. The effects of spin−orbit coupling were included, and the calculated band gaps were found to agree well with previously published experimental values for PbS clusters. The size dependence of the band gaps was studied for clusters containing as many as 912 atoms (35-Å diameter). Direct diagonalization was used for small clusters, and Lanczos recursion was used to determine the band gaps and the eigenfunctions for the larger clusters. Analysis of the eigenfunctions revealed that the HOMO and LUMO states were spread throughout the cluster. Densities of states for the PbS nanoclusters converged to the bulk density of states, and the joint densities of states were computed as an approximation to the absorption spectra of the nanoclusters.