Theoretical studies predict the lowest energy structures of the binuclear cyclopentadienylrhenium hydrides CpReH (Cp = η-CH; n = 4, 6, 8) to have a central doubly bridged Re(μ-H) unit with terminal η-Cp rings and the remaining hydrides as terminal ligands. However, the lowest energy CpReH structure by more than 12 kcal mol has one terminal η-Cp ring, a bridging η,η-Cp ring, and two terminal hydride ligands bonded to the same Re atom. The lowest energy hydride-free CpRe structure is a perpendicular structure with two bridging η,η-Cp rings. The previously predicted bent singlet CpRe structure with terminal η-Cp rings and a formal Re-Re sextuple bond lies ∼37 kcal mol above this lowest energy (η,η-Cp)Re structure. The thermochemistry of the CpReH and CpReH systems is consistent with the reported synthesis of the permethylated derivatives Cp*ReH and Cp*ReH (Cp* = η-MeC) as very stable compounds. Additionally, natural bond orbital analysis, atoms-in-molecules and overlap population density-of-state in AOMIX were applied to present the existence of rhenium-rhenium multiple bonds. [Figure not available: see fulltext.] [ABSTRACT FROM AUTHOR]