A theoretical study of the stretched molecular hydrogen complexes [Os(NH3)(4)L(z)(eta(2)-H-2)]((z+2)+)(L(z) = (CH3)(2)-CO, H2O, CH3COO-, Cl-, H-, C5H5N, and CH3CN) is reported. Using SCF and MP2 methods in conjunction with effective core potentials and basis sets of triple-zeta quality on Os and double-zeta on the ligand atoms the geometries, HD spin-spin coupling constants, and binding energies have been calculated and compared with the available experimental data. The calculated H-H distances are remarkably uniform : all fall in the range 1.30-1.40 Angstrom and correspond to stretched eta 2-H-2 complexes, i.e. no cis-dihydrides have been found. The predicted H-H distance in the acetate complex is consistent with the observed distance of 1.34 Angstrom in the ethylenediamine derivative. A unique feature of these complexes is the crucial role that electron correlation has on the H-H bond lengths; this is a consequence of the unusual potential energy surfaces that are extraordinarily flat with respect to the H-H stretch. The calculated Os-H bond lengths and stretching frequencies are also consistent with experiment. The calculated HD spin-spin coupling constants (J(HD)) are of the same order of magnitude as those observed, yet the trend in the latter with changing trans ligand L(z) is not adequately reproduced by the calculations, although a reasonable correlation between experimental J(HD) and calculated H-H distance is demonstrated. In order to elucidate the nature of the Os-H-2 bonding, population analyses as well as an analysis of the binding energy of the Cl- complex have been carried out and these further emphasize the importance of electron correlation. At the simplest level, the effect of the trans ligand L(z) on the properties of the complexes can be related to its spectrochemical constant, which correlates with H-H distance and binding energy as well as HD spin-spin coupling constant.