An essentially identical linear relationship between the spin-spin coupling constant J(HD) and internuclear separation r(HH) in closed-shell "eighteen electron" eta(2)-H-2 molecular hydrogen complexes is both predicted by quantum chemical calculations for complexes of the type [Os(II)(NH3)(4)L(eta(2)-H-2)] for a wide range of trans ligands L and found experimentally for a series of complexes of Fe, Cr, Ru, and Os, also containing a variety of ligands. Simple electronic structural considerations are proposed in order to provide a preliminary interpretation of these remarkable results.