Analytic dynamical corrections to transition state theory

We present a theory of reaction kinetics that accurately accounts for recrossing effect at the transition state. Using perturbation theory we solve the equations of motion in the neighborhood of the transition state and derive a simple condition that determines whether a trajectory is truly reactive or not. We apply our theory to adatom diffusion on an aluminum surface and show that our analytical results compare well with those of a direct dynamical simulation. Our theory gives us a better understanding of the limitations of transition state theory and a simple analytic formula for quantifying the recrossing effects.