Density functional theory confirms the experimentally known triply bridged Rh-4(CO)(9)(mu-CO)(3) structure to be the lowest-energy structure. The lowest-energy structures of the unsaturated systems Rh-4(CO)n (n = 11, 10, 9, 8) are also triply bridged structures with central Rh-4 tetrahedra that can be derived from this Rh-4(CO)(9)(mu-CO)(3) structure by removal of terminal CO groups in various ways. The M-M distances in these central M-4 tetrahedra change very little as CO groups are lost, suggesting reluctance to form metalmetal multiple bonds in these unsaturated systems. The natural bond orbital (NBO) Wiberg bond indices provide depth to this analysis. All of these unsaturated systems are predicted to be highly fluxional, as two to three isomeric structures lie within similar to 4 kcal/mol of the global minima. The Rh-4(CO)(8)(mu-CO)(2)(mu(4)-CO) structure analogous to the lowest-energy Co-4(CO)(11) structure with all four atoms of a central Co4 butterfly bridged by a mu-CO group is predicted to lie similar to 6 kcal/mol in energy above the lowest-energy Rh-4(CO)(11) structure. Comparisons of the relative energies of analogous Rh-4(CO)(n) and Ir-4(CO())n structures indicate that more highly bridged M-4(CO)(n) structures are energetically much more favorable for rhodium than for iridium. Dissociation energies (for loss of CO) and disproportionation energies are reported.