Robust existence of a reaction boundary to separate the fate of a chemical reaction.

Nonlinear dynamics around a rank-one saddle is investigated in a high energy regime above the reaction threshold. The transition state (TS) is considered as a surface of a "point of no return" through which all reactive trajectories pass only once in the process of climbing over the saddle before being captured in the product state. A no-return TS ceases to exist above a certain high energy regime. However, even at high energies where the no-return TS can no longer exist, it is shown that "an impenetrable barrier" in the phase space robustly persists, which acts as a boundary between reactive and nonreactive trajectories. This implies that we can yet predict the fate of reactions even when the no-return TS may not exist. As an example, we show the analysis of dynamical systems theory for a hydrogen atom in crossed electric and magnetic fields.