Transition tube

Reaction Rate, Streamlines of the Current and Transition Tubes... 

The results presented so far indicates that the isocommittor functions q x) and q+ x) are essential to understand the mechanism of a reaction. However these results do not say how to compute q x) and q+ x), except via the solution of (24) and (23) which is a formidable task, even numerically, when the dimensionality of the system is large (that is, in any situation of interest). In this section, we show that the transition tube carrying most of the probability flux of reactive trajectories can be identified under the assumption that this tube is localized, in a sense made precise below. As show in Sect. 7, this is a way to make practical the probabilistic framework presented so far while standard numerical methods based on finite difference or finite element are inappropriate to determine q-(x) and q x), under the assumptions of this section one can develop algorithms to estimate these functions locally inside the tubes carrying most of the probability flux of reactive trajectories, i.e. where they matter most. 

In Sect. 6.1 we assumed that the local transition tube assumption was valid in the original variables x. This is a strong assumption which may fail in many situations of interest. On the other hand, it is reasonable to assume that the range of validity of the local transition tube assumption may be extended in some suitable set of collective variables which are sufficient to describe the reaction. This is the situation that we describe in this section. 

W. E, W. Ren and E. Vanden-Eijnden (2005) Transition pathways in complex systems Reaction coordinates, isocommittor surfaces, and transition tubes. Chem. Phys. Lett. 413, p. 242... 

TPT), a transition tube in configuration space is constructed by sampling the equilibrium distribution of the system in a collection of hyperplanes. 

Figure 10 Transition tube between two states A and B is shown with the dashed lines. Several isocommitor surfaces T are also shown and a string (solid line perpendicular to the isocommitor surfaces. (Adapted from Ren et al. )...

Pathways in Complex Systems Reaction Coordinates, Isocommittor Surfaces, and Transition Tubes. 

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