Structure-reactivity correlations in state-to-state chemistry

The idea that a transiton state is a "mixture" of reagents and products, previously used in the discussion of thermal structure-reactivity correlations ("Brønsted plots"), is now utilized to yield a simple, one-parameter analytical expression for the relative rate constants of state-to-state reaction series (i.e., where the initial or final internal state varies). The "weights" of reactants and products are determined by a maximal entropy or "thermodynamic-like" procedure. However, instead of using these weights to determine the free energy of activation, they are used directly in a novel statistical model for the reaction probability. The resulting equation is a generalization of the "exponential gap" law, which obtains when the parameter is very small. We demonstrate the utility of our correlation for both inelastic (energy-transfer) and reactive to processes.