Using density functional techniques the H-D spin-spin coupling constant J(HD) has been calculated for a range of osmium(II)-dihydrogen complexes [Os(NH3)(4)L’(eta(2)-H-2)]((z+2)+)) in which properties of the H-H bond are modulated by variation of the trans ligand L(z) (L(z) = (CH3)(2)CO, H2O, CH3COO-, Cl-, H- C5H5N, CH3CN, NH3, NH2OH, aad CN-). The results of the calculations are compared with the available experimental values. A high degree of correlation between the calculated J(HD), H-H bond length r(HH), and Os-Ha interaction energy is demonstrated. Consistent with the experimentally established trends in a wide variety of complexes, J(HD) varies inversely with r(HH). This behavior, opposite to that in free HD, is explained in terms of the metal-dihydrogen bonding mechanism.