The Cp 2 M 2 H 2 (CO) n (M = Ir, Os, Re; n = 3, 2, 1) systems, related to the experimentally known and structurally characterized permethylated derivatives Cp ∗ 2 M 2 H 2 (CO) 2 (Cp ∗ = η 5 -Me 5 C 5 ; M = Ir, Os), provide examples of binuclear structures having metal–metal bonds of formal orders ranging from zero to four as determined by the 18-electron rule. The low-energy Cp 2 Ir 2 H 2 (CO) 3 structures lacking a direct iridium–iridium bond necessarily have a bridging CO group holding together the two iridium atoms. For Cp 2 Ir 2 H 2 (CO) 2 , low-energy unbridged structures are found corresponding to the experimental unbridged Cp ∗ 2 Ir 2 H 2 (CO) 2 structure. However, for Cp 2 Os 2 H 2 (CO) 2 the lowest energy structure has two hydrogen atoms bridging the formal Os Os double bond similar to the experimental doubly bridged Cp ∗ 2 Os 2 H 2 (CO) 2 structure. The lowest energy structures of the monocarbonyls Cp 2 M 2 H 2 (CO) have all three ligands (2H + CO) bridging a central metal–metal bond. The Cp 2 Re 2 H 2 (CO) structures provide examples of both bridged and unbridged structures containing formal Re Re quadruple bonds with highly bridged structures being preferred energetically. [ABSTRACT FROM AUTHOR]