Collisional energy transfer in bimolecular ion-molecule dynamics M ⁺+(H₂; D₂; or HD) → (MH⁺+H; MD⁺+D; MH⁺+D; or MD⁺+H)

Guided ion beam kinetic energy thresholds in the ion-molecule reactions M⁺ + H₂ → MH⁺ + H, where M⁺ = B⁺, Al⁺, and Ga⁺ exceed by 0.4-∼5 eV the thermodynamic energy requirements or theoretically computed barrier heights of these reactions. In addition, the formation of MD⁺ occurs at a significantly lower threshold than MH⁺ when M⁺ reacts with HD. Moreover, the measured reaction cross sections for production of MH ⁺ product ions are very small (10^-17-10^-20 cm²). These facts suggest that a "dynamical bottleneck" may be operative in these reactions. In this work, the eigenvalues of the mass-weighted Hessian matrix, which provide local normal-mode frequencies, are used to identify locations on the ground-state MH₂⁺ potential energy surfaces where collisional-to-internal energy transfer can readily take place. In particular, the potential energies at geometries where eigenvalues corresponding to interfragment and to internal motions undergo avoided crossings are related to the kinetic energies of apparent reaction thresholds. This near-resonance energy transfer model, applied to M⁺ + HD reactions, displays the experimentally observed preference to form MD ⁺ at lower collision energies than MH⁺ as well as the fact that reaction thresholds may greatly exceed thermodynamic energy requirements. This model explains the small reaction cross sections in terms of high energy content and subsequent dissociation of nascent MH⁺ (or MD ⁺) ions. Although the mass-weighted Hessian matrix is used as a tool in this analysis, the model put forth here is not equivalent to a reaction-path Hamiltonian dynamics approach.