Flexible RRKM theory

Phase space theory, flexible RRKM theory, and the statistical adiabatic channel model... 

The expression for the transitional mode contribution to the canonical transition state partition function in flexible RRKM theory is particularly simple [200] ... 

The proper evaluation of the quantized energy levels within the SACM requires a separable reaction coordinate and thus numerical implementations have implicitly assumed a center-of-mass separation distance for the reaction coordinate, as in flexible RRKM theory. Under certain reasonable limits the underlying adiabatic channel approximation can be shown to be equivalent to the variational RRKM approximations. Thus, the key difference between flexible RRKM theory and the SACM is in the focus on the underlying potential energy surface in flexible RRKM theory as opposed to empirical interpolation schemes in the SACM. Forst s recent implementation of micro-variational RRKM theory [210], which is based on interpolations of product and reactant canonical partition functions, provides what might be considered as an intermediate between these two theories. 

Flexible RRKM theory and the reaction path Hamiltonian approach take two quite different perspectives in their evaluation of the transition state partition functions. In flexible RRKM theory the reaction coordinate is implicitly assumed to be that which is appropriate at infinite separation and one effectively considers perturbations from the energies of the separated fragments. In contrast, the reaction path Hamiltonian approach considers a perspective that is appropriate for the molecular complex. Furthermore, the reaction path Hamiltonian approach with normal mode vibrations emphasizes the local area of the potential along the minimum energy path, whereas flexible RRKM theory requires a global potential for the transitional modes. One might well imagine that each of these perspectives is more or less appropriate under various conditions. 

Fig. 2.8. Schematic plot of the dividing surfaces for reaction path (vertical solid line), flexible RRKM theory (solid circle centered about the C atom), and VRC-RRKM theory (dashed circles centered about solid dot pivot points).

The determination of the microcanonical rate coefficient k E) is the subject of active research. A number of techniques have been proposed, and include RRKM theory (discussed in more detail in Section 2.4.4) and the derivatives of this such as Flexible Transition State theory. Phase Space Theory and the Statistical Adiabatic Channel Model. All of these techniques require a detailed knowledge of the potential energy surface (PES) on which the reaction takes place, which for most reactions is not known. As a consequence much effort has been devoted to more approximate techniques which depend only on specific PES features such as reaction threshold energies. These techniques often have a number of parameters whose values are determined by calibration with experimental data. Thus the analysis of the experimental data then becomes an exercise in the optimization of these parameters so as to reproduce the experimental data as closely as possible. One such technique is based on Inverse Laplace Transforms (ILT). 

RRKM theory to dissociation reactions having no barrier to the reverse process of association. Accordingly one must, in the general case, allow for the influence of exit channel couplings in order to predict the properties of separated products based on the transition state distributions embodied in N E, J). Two ways to accomplish this in approximate fashion are outlined below. One models the effect of exit channel dynamics within the framework of the flexible transition states discussed in chapter 7 and the other handles the exit channel dynamics explicitly using classical dynamics. The former model is referred to as variational RRKM theory with exact channel couplings (VRRKM/ECC). 

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