Rate constant tunnelling influences

On the basis of a Landau-Zener curve crossing formalism, Borgis and Hynes derived the nonadiabatic rate constant k, which is similar to that expressed by the DKL model but where the tunneling term Cnm found in Eq. (4) is significantly modified due to the influence of the low-frequency promoting mode Q, with a frequency 0)q, on the tunneling rate. The dependence of Cnm on Q is given by [13]... 

Using eqns. (42)-(44) and assuming T > co /2n, i.e. that the temperature is not too low, we have that tunneling does not practicably influence the macroscopic reaction rate constant at high pressures when the molecules have an equilibrium energy distribution. In this case... 

In the early 1980s, the classical Marcus theory was reanalyzed to consider the influence of quantum effects, notably electron tunneling [23]. Qualitatively, this gives the right direction, since it increases the observed rate constants when the thermally activated process becomes slow but it was concluded that it could not account for the quantitative discrepancies of observed Rehm-Weller type plots from Marcus behaviour. For this reason the hypothesis was retained that the... 

Relatively little attention has been given in the literature to the electronic transmission coefficient for electrochemical reactions. On the basis of the conventional collisional treatment of the pre-exponential factor for outer-sphere reactions, Kel has commonly been assumed to equal unity, i.e. adiabatic reaction pathways are followed. Nevertheless, as noted above, the dependence of xei upon the spatial position of the transition state is of key significance in the "encounter pre-equilibrium treatment embodied in eqns. (13) and (14). Thus, the manner in which Kel varies with the reactant-electrode separation for outer-sphere reactions will influence the integral of reaction sites that effectively contribute to the overall measured rate constant and hence the effective electron-tunneling distance, Srx, in eqn. (14). 

An overall scheme for quantitative assessment of the influence of tunnelling effects upon the reaction rate has been developed by Miller [113, 114]. The simplest method for calculating the tunnelling rate constant is based on the theory of transition state with correction for tunnelling. This correction consists in formal replacement of the classical motion along the reaction coordinate with the quantum motion. This approach was first formulated in the works by Bell [115]. 

As mentioned above, a noticeable influence of tunneling is affecting the barrier height in the formamide-water complexes even at 300 K, so we cannot use the values of the barrier heights from Tables 11 - 15 to estimate the rate constants using simple transition state theory. Nevertheless, some comparisons using such information were obtained for the prototypic molecules. 

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