Transition state theory and dynamical corrections in ergodic systems

The results of transition state theory are derived rigorously in the general context of ergodic dynamical systems defined by a vector field on a Riemannian manifold. A new perspective on how to compute the dynamical corrections to the transition state theory transition frequency is given. Hamiltonian dynamical systems are considered a special case and the so-called Marcus formula for the rate constant is re-derived.