Ab Initio molecular orbital calculations have been made for Rh(x) (x = 1-4), Rh(CO)2, RhCO, Rh2CO, RhH, RhH3, RhC, HRhC, RhCH, RhO, RhO2, Rh..O2, H2RhOH, and Rh2O3. All-electron calculations used the best basis set of Huzinaga, the Shim extension, and a further extension. Effective core potential calculations were performed by using the Los Alamos single- and double-zeta basis sets. In addition relativistic effective core potential calculations were employed. The Rh(x) calculations find a node in the HOMO that may offer an explanation for variation in catalytic efficiency with cluster size. Rhodium carbonyls were found to be weakly bound at the SCF level and will require correlation for meaningful investigation. RhH3 was confirmed to have C3-nu symmetry. The energy and structures shown by the RhCH calculations suggest a mechanism for methanation. Unoptimized structures for Rh2O3 suggest that the oxygen triple-bridged structure is more stable than the bent O=RhORh=O structure.