Equilibrium isotope effects (EIE) on the binding of H-2 and D-2 to transition metal complexes are calculated for a modeled version of W(CO)(3)(PCy3)(2)(eta(2)-H-2), [Ru(H ... H)(C5Me5)(dppm)](+) and trans-[Os(H ... H)Cl-(dppe)(2)](+). Being probably unsatisfactorily described by the harmonic approach (specially in the elongated dihydrogen complexes), the thermodynamic contribution of the H-H stretching related modes is evaluated by means of nuclear motion quantum calculations. The Discrete Variable Representation (DVR) methodology is applied to obtain the anharmonic vibrational spectrum on the bidimensional B3LYP potential surface. From these results, the associated partition function is calculated and used to correct the harmonic EIE and other thermodynamic magnitudes. In agreement with experimental results, the anharmonically corrected EIE for the W. complex turns out to be inverse (0.534 at 300 K). On the contrary, the corrected EIE for the Ru and Os complexes is clearly normal(1.217 and 1.685 at 300 K, respectively), predicting an unusual behavior for MLnH2 compounds. Comparison with the pure harmonic EIE's leads to the conclusion that the harmonic approach is inadequate to describe the properties of the elongated dihydrogen complexes.