Analytical properties of a direct interaction model for gas-phase chemical reactions A+BC = AB+C

Abstract

Analytical expressions for the translational energy and angular distributions of the products of the chemical reaction A+BC = AB+C are derived for a direct interaction model (DIPR model) as a function of a single model parameter. An approximate analytical expression for the dependence of this parameter on the masses and relative kinetic energy of the reactants is found by treating the system A+BC as a pair of mass-coupled harmonic oscillators. This expression quantitatively reproduces values of the model parameter estimated from previous trajectory studies for a wide range of reactant masses. The derived dependence of the model parameter on the reactants' relative energy is used to determine conditions of validity of the model. By requiring that the translational energy of the products not exceed the total energy available, a lower bound on the model parameter is obtained, and by requiring that the product molecule AB be stable with respect to dissociation, an upper bound on the relative energy of the reactants results. At higher energies fragmentation occurs and the cross section for reaction falls gradually to zero.