Rhenium carbonyl hydride chemistry dates back to the 1959 synthesis of HRe(CO)(5) by Hieber and Braun. The binuclear H2Re2(CO)(8) was subsequently synthesized as a stable compound with a central Re-2(mu-H)(2) unit analogous to the B-2(mu-H)(2) unit in diborane. The complete series of HRe(CO)(n) (n = 5, 4, 3) and H2Re2(CO)(n) (n = 9, 8, 7, 6) derivatives have now been investigated by density functional theory. In contrast to the corresponding manganese derivatives, all of the triplet rhenium structures are found to lie at relatively high energies compared with the corresponding singlet structures consistent with the higher ligand field splitting of rhenium relative to manganese. The lowest energy HRe(CO)(5) structure is the expected octahedral structure. Low-energy structures for HRe(CO)(n) (n = 4, 3) are singlet structures derived from the octahedral HRe(CO)(5) structure by removal of one or two carbonyl groups. For H2Re2(CO)(9) a structure HRe2(CO)(9)(mu-H), with one terminal and one bridging hydrogen atom, lies within 3 kcal/mol of the structure Re-2(CO)(9)(eta(2)-H-2), similar to that of Re-2(CO)(10). For H2Re2(CO)(n) (n = 8, 7, 6) the only low-energy structures are doubly bridged singlet Re-2(mu-H)(2)(CO)(n) structures. Higher energy dihydrogen complex structures are also found.