Transition path theory

E. Vanden-Eijnden Transition Path Theory, Lect. Notes Phys. 703, 453-493 (2006)... 

In this chapter, we have shown why the recent transition path theory (TPT) offers the correct probabilistic framework to understand the mechanism by which rare events occur by analyzing the statistical properties of the reactive trajectories involved in these events. The main results of TPT are the probability density of reactive trajectories and the probability current (and associated streamlines) of reactive trajectories, which also allows one to compute the probability flux of these trajectories and the rate of the reaction. It was also shown that TPT is a constructive theory under the assumption that the reaction channels are local, TPT naturally leads to algorithms that allow to identify these channels in practice and compute the various quantities that TPT offers. 

In the string method [37-Al] and the associated transition path theory (TPT)... 

Metzner, P, Schutte, C., Vanden-Eijnden, E. Illustration of transition path theory on a collection of simple examples, J. Chem. Phys. 2006,125,084110. 

E W, Vanden-Eijnden E (2010) Transition-path theory and path-finding algorithms for the study of rare events. Aram Rev Phys Chem 61 391-420... 

In the string method, ° " which is based on the transition path theory... 

Illustration of Transition Path Theory on a Collection of Simple Examples. 

As discussed in previous sections, the committor is the ideal reaction coordinate in the sense that it exactly quantifies how far a reaction has proceeded. This concept also provides the basis for transition path theory (TPT) [33,278], a probabilistic framework developed by Vanden-Eijnden and collaborators to study the statistical properties of rare event trajectories. In TPT, isocommittor surfaces, i.e., surfaces on which all points have the same conunittor value, play a prominent role. Trajectories initiated from any point of an isocommittor surface have the same probability to reach the final rather than the initial state first. It can be shown [31] that the distribution of points where reactive trajectories pierce a given isocommittor surface is identical to the equiUbrium distribution confined to that surface. From the committor and the equilibrium distribution one can determine the distribution of reactive trajectories, so-called reaction tubes, which contain entire reaction pathways with high probabUity, as well as the reaction rates, providing useful statistical information about the reaction mechanism. 

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