Approximations to the rate constant for dissociation of diatomic molecules

Abstract

A number of results which pertain to the rate of collisionally induced gas phase dissociation of diatomic molecules were derived. In the standard model for this process collisions bring about random transitions between internal states of the diatom and ultimately lead to dissociation. The rate constant kd for such a model is simply related to λ1, the smallest eigenvalue of a matrix κ which is expressed in terms of rate constants for detailed transitions between states of the diatom. A standard approximation for λ1 is the solution of the linearized characteristic equation for κ. It was shown that the kd so obtained is very nearly the same as the kd obtained from the steady state approximation. If the states of the diatom are assumed to form a continuum, then κ becomes the kernel of an integral operator. Relations between discrete and continuum models were established. It was shown that equivalent diffusion equations which have been derived for the continuum case have analogs in the discrete case. These discrete analogs pertain to stepladder models, models for which transitions are allowed only between adjacent states. It was further shown how discrete (quantum) models and continuum (classical) models are linked by quasicontinuum models which, while still discrete, are formulated in terms of elements of the continuum rather than in terms of individual quantum states. Some of the foregoing results were illustrated by a treatment of the separable exponential model. Parameters α and β for this model have a straightforward physical interpretation. The rate constant and the state distribution for the model are obtainable in closed form via the steady state approximation. Their dependence on α and β is readily interpretable physically. The state distribution for the model was shown to be potentially useful in variational calculations of kd for other models. In such calculations, α and β would be chosen so as to maximize the variational lower bound to λ1 for the model in question.