The results of Fenske-Hall band structure calculations for bulk Rh2S3 and RuS2 and for the (210) and (111) surfaces of RuS2 are described. Although the crystal structures of the two sulfides are quite different, the electronic structure of bulk Rh2S3 and RuS2 share several similarities. Unlike MoS2, which is also used as a hydrodesulfurization (HDS) catalyst, there is no metal-metal bonding and only negligible metal-sulfur rr bonding in both Rh2S3 and RuS2. As a result, both sulfides are characterized by a narrow high energy occupied metal t(2g) band localized on the metal. Results of calculations for two-dimensional RuS2 slabs exposing (210) and (111) surface planes provide a description of the electronic structure of 5-, 4-, and 3-coordinate Ru atoms on these surfaces. Stabilization of part or all of the unoccupied Ru e(g) band is observed for these surface atoms, and comparisons between the partial densities of states (DOS) of the surface Ru atoms and the orbital structures of isolated coordinatively unsaturated metal centers aid in the interpretation of the surface results. The electronic environments of the surface Ru atoms are also compared to the electronic environments and reactivities of metal centers found in d(6) transition metal complexes that incorporate thiophenic ligands. These comparisons suggest that if the heterogeneous and homogeneous HDS mechanisms are related, then 3-coordinate surface Ru atoms such as those found on the (111) surface could provide active sites.