Sigma Bond Activation by Cooperative Interaction with ns² Atoms:  B⁺ + nH₂

The reactions of B⁺ + nH₂ to produce BH₂⁺(H₂)_n-1 have been studied by high-level ab initio techniques. The reaction mechanism and associated activation energy is found to depend dramatically on the number of H₂ molecules present. For n = 1, the reaction proceeds stepwise:  first breaking the H₂ bond and forming one BH bond followed by forming the second BH bond. This process has an activation energy of about 57 kcal/mol. For n = 2, the reaction proceeds via a pericyclic mechanism though a planar cyclic transition state where two H₂ bonds are broken while simultaneously two BH bonds and one new H₂ bond are formed. The activation energy for this process decreases dramatically from the n =1 value to only about 11 kcal/mol. For n = 3, the reaction proceeds through a true insertion mechanism; however, the actual insertion occurs late in the reaction after over 75% of the exothermicity has been realized. The addition of the third H₂ molecule decreases the activation energy to only about 3.4 kcal/mol. For n = 4, the reaction mechanism is essentially identical to that of the n = 3 case. However, the fourth H₂ causes the activation energy to increase by about 2 kcal/mol relative to the n = 3 case because the additional H₂ molecule causes one of the other three H₂ molecules to be slightly further away from the boron ion in the transition state geometry. The computational results are compared with the experimental results of Kemper, Bushnell, Weis, and Bowers (J. Am Chem. Soc. 1998, 120, xxxx) and are in full agreement with the experimental conclusion that the n = 3 electrostatic cluster ion is the most reactive. On the basis of a comparison of experimentally determined magnitude and isotopic dependence of the activation energies with the computed adiabatic reaction barriers, it is suggested that the observed reaction rate may be dominated by a nonclassical tunneling contribution.