Definability of no-return transition states in the high-energy regime above the reaction threshold

No-return transition states (TSs) defined in multidimensional phase space, where recrossing trajectories through the commonly used "configuration" TS pass only once, robustly exist up to a moderately high-energy regime above the reaction threshold, even when nonlinear resonances among the bath degrees of freedom perpendicular to the reaction coordinate result in local chaos. However, at much higher energy when global chaos appears in the bath space, the separability of the reaction coordinate from the bath degrees of freedom starts to lose locally. In the phase space near the saddles, it is found that the slower the system passes the TS, the more recrossing trajectories reappear. Their implications and mechanisms are discussed concerning to what extent one can define no-return TSs in the high-energy regime above the reaction threshold.