A two-dimensional model for collisional energy transfer in bimolecular ion-molecule dynamics: M++(H2; D2; or HD)?(MH++H; MD++D; MH++D; or MD++H)

Abstract

Guided ion beam kinetic energy thresholds in the ion-molecule reactions M++H2→MH++H, where M+ is a closed-shell atomic ion B+, Al+, or Ga+, were found to exceed by 0.4 to ca. 5 eV the thermodynamic energy requirements (or the theoretically computed barrier heights) for 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 the production of MH+ or MD+ product ions are very small (10−17 to 10−20 cm2), being largest for B+ and smallest for Ga+. A previous paper from this group proposed that collisional-to-internal energy transfer is the rate-limiting step for this class of reactions. It also suggested, based on a dynamical resonance picture, that collisions occurring at or near C2v symmetry are more effective than other collisions even though C2v geometries provide no lower potential energy barriers than others. By examining the collision paths characteristic of flux early in the bimolecular collision and searching for geometries along such paths where collisional-to-internal energy transfer is optimal, our earlier efforts predicted reaction thresholds in reasonable agreement with the (previously perplexing) experimental data. In the present work, we introduce a model Hamiltonian whose classical and quantum dynamics we apply to the M++H2, D2, HD reactive collisions. We calculate the classical collisional-to-internal energy transfer cross-sections and find energy transfer thresholds that resemble the experimental reaction thresholds but whose isotopic mass trends are not entirely consistent with experiment. We then use a Green function method and a local quadratic approximation to the potential surface to obtain analytical expressions for the isotopic mass dependences of the collisional-to-vibrational energy transfer and for the subsequent fragmentation of the three-atom system. Finally, we analyze the origin of the threshold energy asymmetry in the M++HD reactions.