Transition State Characterization for the Reversible Binding of Dihydrogen to Bis(2,2'-bipyridine)rhodium(I) from Temperature- and Pressure-Dependent Experimental and Theoretical Studies

Thermodynamic and kinetic parameters for the oxidative addition of H_2 to [Rh^I(bpy)_2]^+ (bpy = 2,2‘-bipyridine) to form [Rh^(III)(H)_2(bpy)_2]^+ were determined from either the UV−vis spectrum of equilibrium mixtures of [Rh^I(bpy)_2]^+ and [Rh^(III)(H)_2(bpy)_2]^+ or from the observed rates of dihydride formation following visible-light irradiation of solutions containing [Rh^(III)(H)_2(bpy)_2]^+ as a function of H_2 concentration, temperature, and pressure in acetone and methanol. The activation enthalpy and entropy in methanol are 10.0 kcal mol^(-1) and −18 cal mol^(-1) K^(-1), respectively. The reaction enthalpy and entropy are −10.3 kcal mol^(-1) and −19 cal mol^(-1) K^(-1), respectively. Similar values were obtained in acetone. Surprisingly, the volumes of activation for dihydride formation (−15 and −16 cm^3 mol^(-1) in methanol and acetone, respectively) are very close to the overall reaction volumes (−15 cm^3 mol^(-1) in both solvents). Thus, the volumes of activation for the reverse reaction, elimination of dihydrogen from the dihydrido complex, are approximately zero. B3LYP hybrid DFT calculations of the transition-state complex in methanol and similar MP2 calculations in the gas phase suggest that the dihydrogen has a short H−H bond (0.823 and 0.810 Å, respectively) and forms only a weak Rh−H bond (1.866 and 1.915 Å, respectively). Equal partial molar volumes of the dihydrogenrhodium(I) transition state and dihydridorhodium(III) can account for the experimental volume profile found for the overall process