Density functional theory confirms the experimentally known triply bridged Rh4(CO)9(μ-CO)3 structure to be the lowest-energy structure. The lowest-energy structures of the unsaturated systems Rh4(CO)n (n = 11, 10, 9, 8) are also triply bridged structures with central Rh4 tetrahedra that can be derived from this Rh4(CO)9(μ-CO)3 structure by removal of terminal CO groups in various ways. The M-M distances in these central M4 tetrahedra change very little as CO groups are lost, suggesting reluctance to form metal-metal 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 ∼4 kcal/mol of the global minima. The Rh4(CO)8(μ-CO)2(μ4-CO) structure analogous to the lowest-energy Co4(CO)11 structure with all four atoms of a central Co4 butterfly bridged by a μ-CO group is predicted to lie ∼6 kcal/mol in energy above the lowest-energy Rh4(CO)11 structure. Comparisons of the relative energies of analogous Rh4(CO)n and Ir4(CO)n structures indicate that more highly bridged M4(CO)n structures are energetically much more favorable for rhodium than for iridium. Dissociation energies (for loss of CO) and disproportionation energies are reported.