Why Does D2Bind Better Than H2? A Theoretical and Experimental Study of the Equilibrium Isotope Effect on H2Binding in a M(η2-H2) Complex. Normal Coordinate Analysis of W(CO)3(PCy3)2(η2-H2)

Vibrational data (IR, Raman and inelastic neutron scattering) and a supporting normal coordinate analysis for the complex trans -W(CO) 3 (PCy 3 ) 2 (η 2 -H 2 ) ( 1 ) and its HD and D 2 isotopomers are reported. The vibrational data and force constants support the well-established η 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/Å, 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 × EXC × 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 (PCy 3 ) 2 over the temperature range 12−36 °C in THF solution. For the binding of H 2 Δ H = −6.8 ± 0.5 kcal mol - 1 and Δ S = −24.7 ± 2.0 cal mol - 1 deg - 1; for D 2 Δ H = −8.6 ± 0.5 kcal/mol and Δ S = −30.0 ± 2.0 cal/(mol deg). The EIE at 22 °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 (PCy 3 ) 2 (N 2 ) in THF yielded a value of K H / K D = 0.70 ± 0.15 at 22 °C.