Transition state theory reactive flux method

In the very short time limit, q (t) will be in the reactants region if its velocity at time t = 0 is negative. Therefore the zero time limit of the reactive flux expression is just the one dimensional transition state theory estimate for the rate. This means that if one wants to study corrections to TST, all one needs to do munerically is compute the transmission coefficient k defined as the ratio of the numerator of Eq. 14 and its zero time limit. The reactive flux transmission coefficient is then just the plateau value of the average of a unidirectional thermal flux. Numerically it may be actually easier to compute the transmission coefficient than the magnitude of the one dimensional TST rate. Further refinements of the reactive flux method have been devised recently in Refs. 31,32 these allow for even more efficient determination of the reaction rate. 

R. A. Marcus It certainly is a good point that transition state theory, and hence RRKM, provides an upper bound to the reactive flux (apart from nuclear tunneling) as Wigner has noted. Steve Klippenstein [1] in recent papers has explored the question of the best reaction coordinate, e.g., in the case of a unimolecular reaction ABC — AB + C, where A, B, C can be any combination of atoms and groups, whether the BC distance is the best choice for defining the transition state, or the distance between C and the center of mass of AB, or some other combination. The best combination is the one which yields the minimum flux. In recent articles Steve Klippenstein has provided a method of determining the best (in coordinate space) transition state [1]. 

In Chapter 5, attention is directed toward the direct calculation of k(T), i.e., a method that bypasses the detailed state-to-state reaction cross-sections. In this approach the rate constant is calculated from the reactive flux of population across a dividing surface on the potential energy surface, an approach that also prepares for subsequent applications to condensed-phase reaction dynamics. In Chapter 6, we continue with the direct calculation of k(T) and the whole chapter is devoted to the approximate but very important approach of transition-state theory. The underlying assumptions of this theory imply that rate constants can be obtained from a stationary equilibrium flux without any explicit consideration of the reaction dynamics. 

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