Energy requirements and energy disposal: reaction probability matrices and a computational study of a model system

The joint distribution of reactant and product energy states (a reaction probability matrix) is considered for the quantal case and the corresponding classical limit, and the implications of microscopic reversibility are noted. Measures of the selectivity of energy consumption, the specificity of energy release, and their interdependence (the relevance) are defined in terms of the joint distribution. To illustrate these principles, a computational study has been carried out for a model problem, namely rearrangement collisions (A + BC-AB + C) for simple square-well potential energy surfaces. Classical trajectory calculations and coarse-grained joint probability matrices are presented for systems moving in one and three dimensions. The model, while simplistic, illustrates the method for constructing P matrices and shows several interesting systematic features. The probability matrices are strongly dependent on the Eyring-Polanyi skewing angle β[where cos²β = m _Am_c/(m _A±m_B) (m_B + m_C)], and for a given β, are much less sensitive to variations in the individual atomic masses. The entropy defects and relevance are calculated for three different three-dimensional systems and the relevance is shown to be a compact measure of the dependence of the product energy partitioning on the energy distribution of the reactants.