Towards a state-to-state transition state theory

We assume that, having arrived at the transition state, the branching into the different product states is independent of the initial quantum states of the reactants. This assumption plus the familiar transition state approximation (that the reaction rate is the rate of the passage across the barrier) yields an expression for the state-to-state cross section in terms of the state-to-all one, as well as microcanonical rate constants. Models, adiabatic correlations, purely statistical considerations, or collinear computations can provide the required input for the theory. Exact quantal computations on the 3D H+H ₂ reaction are found to satisfy the assumed factorization quite well. Furthemore, reaction probabilities derived from a line-of-centers model, with a barrier height dependent on the approach angle, account for the probabilities derived from the exact quantal computation.