RRKM theory loose transition state

Wardlaw D M and Marcus R A 1984 RRKM reaction rate theory for transition states of any looseness Chem. Rhys. Lett. 110 230-4... 

Perhaps the point to emphasise in discussing theories of translational energy release is that the quasiequilibrium theory (QET) neither predicts nor seeks to describe energy release [576, 720], Neither does the Rice— Ramspergei Kassel—Marcus (RRKM) theory, which for the purposes of this discussion is equivalent to QET. Additional assumptions are necessary before QET can provide a basis for prediction of energy release (see Sect. 8.1.1) and the nature of these assumptions is as fundamental as the assumption of energy randomisation (ergodic hypothesis) or that of separability of the transition state reaction coordinate (Sect. 2.1). The only exception arises, in a sense by definition, with the case of the loose transition state [Sect. 8.1.1(a)]. 

The modification to the RRKM theory that makes possible accurate modeling of loose transition states is variational transition state theory (Pechukas, 1981 Miller, 1983 Forst, 1991 Wardlaw and Marcus, 1984, 1985, 1988 Hase, 1983, 1987). In this approach the rate constant k E, J) is calculated as a function of the reaction coordinate, R. The location of the minimum flux is found by setting the derivative of the sum of states equal to zero and solving for / . Thus, we evaluate... 

RRKM theory is also at the basis of localization of loose transition states in the PES. Another assumption of the theory is that a critical configuration exists (commonly called transition state or activated complex) which separates internal states of the reactant from those of the products. In classical dynamics this is what is represented by a dividing surface separating reactant and product phase spaces. Furthermore, RRKM theory makes use of the transition state theory assumption once the system has passed this barrier it never comes back. Here we do not want to discuss the limits of this assumption (this was done extensively for the liquid phase [155] but less in the gas phase for large molecules we can have a situation similar to systems in a dynamical solvent, where the non-reacting sub-system plays the role... 

The procedure adopted here is to make use again of RRKM theory to calculate k2/k l as a function of the relative barrier height. In this case, the transition state for the, reaction is taken as the loose ion-molecule complex at the Langevin capture distance. The transition state for the reaction k2 is taken as the tetrahedral intermediate RCOYX ". By a suitable choice of the vibrational frequencies and moments of inertia, this type of calculation shows that E 0-E0 for Cl- + CH3COCl should be around — 7 kcal mol 1 in order to reproduce the experimental efficiency. This amounts to an E 0 of 4 kcal mol-1. 

The variational version of RRKM theory (VTST) can be used to locate the transition state on the basis of the minimum sum of states. However, if this level of effort does not appear appropriate for the particular reaction, it is perfectly possible to fit a given data set with the vibrator model of the RRKM theory simply by adjusting the transition-state vibrational frequencies until a fit is obtained (as was done in the calculations of figures 7.3 and 7.4). In fact, such a fitting procedure is one means for determining whether the reaction is characterized by a loose or a tight transition state. 

Vibrational and rotational constants for the energized molecule, [ML ], and for the transition state (TS) leading to products are needed to evaluate kinetic shifts using RRKM theory. For the simple bond cleavages appropriate for coordination complexes, it is a good approximation to treat the TS as loose and located at the centrifugal barrier for product formation. This makes the choice of the vibrational and rotational constants of the TS particularly simple as they equal those of the products. 

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