The geometries of [Os(NH3)(4)L(z)(eta(2)-H-2)]((z+2)+) complexes, where molecular hydrogen is trans to the L(z) ligand, have been calculated using density functional theory (DFT) and compared with the results of MP2 calculations. The quality of agreement between the DFT and MP2 geometries is found to be dependent on the trans ligand L(z). When L(z) = acetone, water, acetate, and chloride, the agreement between the DFT and MP2 calculations is generally reasonable, and for the L(z) = acetate complex, the DFT and the MP2 predictions are in acceptable agreement with the experimental geometry. When L(z) = hydride, pyridine, acetonitrile, cyanide, hydroxylamine, and ammonia, the DFT calculations predict a much shorter H-H bond length and slightly longer Os-H distances when compared with the MP2 values. As the potential energy surfaces are very flat with respect to the H-H stretch, the differences between the DFT and MP2 geometries correspond to energy differences of approximately 3 kcal mol(-1) when calculated at the same level of theory. The differences between the DFT and MP2 predictions appear to correlate with the properties of the trans ligand L(z), in particular its sigma-donor and pi-acceptor/donor properties. The DFT predictions of the Os-H-2 interaction energy are consistently smaller by similar to 25% than the corresponding MP2 values, but the agreement is much better in the case of the Os-L(z) bond. Solvation by water, estimated by a self-consistent reaction field technique, is found to have little effect on the binding of H-2, while significantly reducing the binding energies of the trans ligands, especially those that are charged. The integrated atomic charges for the dihydrogen ligand, obtained by the atoms in molecules method, are slightly negative, while Os varies between 1.01 and 1.81. The DFT calculations generally predict both species to be somewhat closer to neutral than those obtained at the MP2 level; this is consistent with the notion that DFT predicts stronger H-H but weaker Os-H bonding than MP2, i.e., less donation by Os into the antibonding sigma* MO of H-2.