Dynamical Emergence Principle of Reaction Selectivity and Molecular Memory in Chemical Reactions' and Biomolecular Systems

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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 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 ceases to hold 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 high energy regime above the reaction threshold.We also developed a new empirical self-consistent scheme to elucidate the local ergodic state distribution function and construct effective multidimensional free energy landscape from an ensemble of short single molecule time series. It is possible to capture not the entire topography of the multidimensional free energy landscape but the regions where the system wanders frequently. Using local ergodicity ansatz as a 0^<th> order description, we constructed the multidimensional "free energy" landscape where several local ergodic states are linked with introducing a "distance" among them. Evaluating on the probability of transition sequences sampled in an ensemble of single molecule time series, one can analyze non-Markovianity along several transition paths. e.g., relationship between memory and length of transition paths. As a function of n_s time window to estimate the short time distribution, we can also assign the number of accessible superbasins (a set of states) within time n_s.