Participation of Vibration in Exchange Reactions

Abstract

Exothermic exchange reactions of the type A+BC→AB+C sometimes leave the product AB in a highly excited vibrational state. Simple theoretical considerations related to the description of the molecular collision show that the fraction of the reaction energy available for this vibrational mode is limited by the kinematic factor sin²β, where β is the angle of rotation required to take a coordinate system describing the reactants into one suited to the products, and ${\tan }^2{\mathrm{\beta =(m}}_{\mathrm{B}}{\mathrm{/m}}_{\mathrm{A}}{\mathrm{)+(m}}_{\mathrm{B}}{\mathrm{/m}}_{\mathrm{C}}{\mathrm{)+(m}}_{\mathrm{B}}^2{\mathrm{/m}}_{\mathrm{A}}{m}_{\mathrm{C}})$ . In the reaction A+BCD→AB+CD, similar results apply to the newly formed bond AB, and no excitation of vibration in CD is predicted. Although effects to be expected from details of the potential energy surface are ignored, comparison of the kinematic factor alone with experimental results shows excellent agreement. Applied to the reverse reaction, the theory gives a criterion for predicting the effect on the reaction rate of the distribution of energy between translational and vibrational modes in the collision. In the reaction O₃+O₂^*→O+2O₂, it is predicted that the oxygen atom comes preferentially from the vibrationally excited oxygen molecule. Incidentally, it is shown that the transformation from a properly normalized center‐of‐mass coordinate system describing the reactants to one describing the products can always be resolved into a sequence of simple rotations.