The geometry of transition states: How invariant manifolds determine reaction rates

Over the last years, a new geometrical perspective on transition state theory has been developed that provides a deeper insight on the reaction mechanisms of chemical systems. This new methodology is based on the identification of the invariant structures that organize the dynamics at the top of the energetic barrier that separates reactants and products. Moreover, it has allowed to solve, or at least circumvent, the recrossing-free problem in rate calculations. In this paper, we will discuss which kind of objects determine the reaction dynamics in the presence of dilute, dense and condensed phase baths.