Why does D-2 bind better than H-2? A theoretical and experimental study of the equilibrium isotope effect on H-2 binding in a M(eta(2)-H-2) complex. Normal coordinate analysis of W(CO)(3)(PCy3)(2)(eta(2)-H-2)

Vibrational data (IR, Raman and inelastic neutron scattering) and a supporting normal coordinate analysis for the complex trans-W(CO)(3)(PCy3)(2)(eta(2)-H-2) (1) and its HD and D-2 isotopomers are reported. The vibrational data and force constants support the well-established eta(2)-bonding mode for the H-2 ligand and provide unambiguous assignments for all metal-hydrogen stretching and bending frequencies. The force constant for the HH stretch, 1.3 mdyn/Angstrom, is less than one-fourth the value in free H-2 and is similar to that for the WH stretch, indicating that weakening of the H-H bond and formation of W-H bonds are well along the reaction coordinate to oxidative addition. The equilibrium isotope effect (EIE) for the reversible binding of dihydrogen (H-2) and dideuterium (D-2) to 1 and 1-d(2) has been calculated from measured vibrational frequencies for 1 and 1-d(2). The-calculated EIE is ''inverse'' (1-d(2) binds D-2 better than 1 binds H-2), With K-H/K-D = 0.78 at 300 K. The EIE calculated from vibrational frequencies may be resolved into a large normal mass and moment of inertia factor (MMI = 5.77), an inverse vibrational excitation factor (EXC=0.67), and an inverse zero-point energy factor (ZPE=0.20), where EIE = MMI x EXC x ZPE. An analysis of the zero-point energy components of the EIE shows that the large decrease in the HH stretching frequency (force constant) predicts a large normal EIE but that zero-point energies from five new vibrational modes (which originate from translational and rotational degrees of freedom from hydrogen) offset the change in zero-point energy from the H-2(D-2) stretch. The calculated EIE is compared to experimental data obtained for the binding of H-2 or D-2 to Cr(CO)(3)(PCy3)(2) over the temperature range 12-36 degrees C in THF solution. For the binding of H-2 Delta H=-6.8+/-0.5 kcal mol(-1) and Delta S=-24.7+/-2.0 cal mol(-1) deg(-1); for D-2 Delta H=-8.6+/-0.5 kcal/mol and Delta S=-30.0+/-2.0 cal/(mol deg). The EIE at 22 degrees C has a value of K-H/K-D=0.65+/-0.15. Comparison of the equilibrium constants for displacement of N-2 by H-2 or D-2 in the complex W(CO)(3)(PCy3)(2)(N-2) in THF yielded a value of K-H/K-D=0.70+/-0.15 at 22 degrees C.