Maximal entropy approach to reactivity and selectivity in elementary chemical reactions

A unified approach to statistical theories of reaction probabilities and to the specificity and selectivity of molecular collisions is presented with applications to collinear reactive collisions in classical mechanics. Statistical theories have previously been derived by using the distribution of trajectories in terms of their number of crossings of a critical surface. Selectivity and specificity refer to the distribution of trajectories in terms of the action variables of phase space (which have quantal analogues). Here we consider the joint distribution, in both number of crossings and the action variables. The result is an expression for the reaction probability which does take the role of selectivity and specificity into account. It reduces to known previous results (e.g., the unified statistical theory, transition state theory, phase space theory, the branching ratio in terms of the entropy deficiency) in suitable limits. Computational examples are provided. An appendix provides an explicit proof of the reactivity-selectivity theorem in the framework of statistical theories: For a given flux of all trajectories through a critical surface, the flux of reactive trajectories increases as the selectivity/specificity of the reactive trajectories diminishes.