Tunneling RRKM theory

The RRKM theory is a ubiquitous tool for studying dissociation or isomerization rates of molecules as a function of their vibrational energy. Still highly active in the theoretical field, Marcus has tackled such issues as the semiclassical theory for inelastic and reactive collisions, devising reaction coordinates, new tunneling paths, and exploring solvent dynamics effects on unim-olecular reactions in clusters. 

The RRKM theory is a transition state theory with the reaction coordinate treated classically. It inherits any defects of the parent, separability of coordinates, non-equilibrium effects, and the assumption of unit transmission coefficient (trajectories do not turn back to regenerate X ). It is expected to give an upper bound to the reaction rate in cases where tunnelling through the potential energy barrier is... 

Although the use of the correct energy levels for calculating the density of states is strictly a quantum correction of the classical RRKM theory, there are two other effects that are much more fundamental to the theory quantum mechanical tunnelling and fluctuations. The first of these is dealt with in Chapter 2, and the second is the main subject of Chapter 3. 

Conventional RRKM theory with Eckart tunneling... 

For wideranging studies of multiple reaction channels conventional RRKM theory with Eckart tunneling provides a readily implemented methodology that generally provides meaningful predictions. Consider for example the self-... 

ChemRate program of Tsang and coworkers [102], and the VariFlex program [103] provide more general kinetics programs which include conventional RRKM theory with Eckart or other simple one-dimensional tunneling corrections. 

Figure 35 Measured dissociation rate constant k E) for CD2CO. The solid line is a fit based on RRKM theory including tunneling corrections. Redrawn from Ref. 33.

The parameter v in equation (A3.12.59) has also been related to RRKM theory. Polik et al [80] have shown that for decomposition by quantum mechanical tunnelling... 

Results of a PEPICO study of the dissociation dynamics of 2-bromobutane ions have been analysed with tunnelling-corrected RRKM statistical theory using vibrational frequencies obtained from ab initio MO calculations. It has been concluded that the slow rate of loss of HBr, to form the but-2-ene ion, occurs via a concerted mechanism in which tunnelling is a feature of the proton transfer. 

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]. 

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