Activation energy tunneling reactions

Many computational studies in heterocyclic chemistry deal with proton transfer reactions between different tautomeric structures. Activation energies of these reactions obtained from quantum chemical calculations need further corrections, since tunneling effects may lower the effective barriers considerably. These effects can either be estimated by simple models or computed more precisely via the determination of the transmission coefficients within the framework of variational transition state calculations [92CPC235, 93JA2408]. 

Methyl- and 2,6-dimethylpyridine as catalysts with sterically hindered a-com-plexes give greater isotope effects (k2n/k2D up to 10.8). Such values are understandable qualitatively, since the basic center of these pyridine derivatives cannot easily approach the C-H group. The possibility of tunneling can be excluded for these reactions, as the ratio of the frequency factors 4h 4d and the difference in activation energies ED—EU (Arrhenius equation) do not have abnormal values. 

Relationships between reaction rate and temperature can thus be used to detect non-classical behaviour in enzymes. Non-classical values of the preexponential factor ratio (H D i 1) and difference in apparent activation energy (>5.4kJmoRi) have been the criteria used to demonstrate hydrogen tunnelling in the enzymes mentioned above. A major prediction from this static barrier (transition state theory-like) plot is that tunnelling becomes more prominent as the apparent activation energy decreases. This holds for the enzymes listed above, but the correlation breaks down for enzymes... 

We should remember (1) that the activation energy of eh reactions is nearly constant at 3.5 0.5 Kcal/mole, although the rate of reaction varies by more than ten orders of magnitude and (2) that all eh reactions are exothermic. To some extent, other solvated electron reactions behave similarly. The theory of solvated electron reaction usually follows that of ETR in solution with some modifications. We will first describe these theories briefly. This will be followed by a critique by Hart and Anbar (1970), who favor a tunneling mechanism. Here we are only concerned with fe, the effect of diffusion having been eliminated by applying Eq. (6.18). Second, we only consider simple ETRs where no bonds are created or destroyed. However, the comparison of theory and experiment in this respect is appropriate, as one usually measures the rate of disappearance of es rather than the rate of formation of a product. 

The activation energy of most of the eh reactions, 3.5+0.5 Kcal/mole, is much less than the hydration energy of the electron, -40 Kcal/mole. There are other barriers against reaction, such as repulsion by electrons in molecules. This can only be an accident in the classical mechanism, but not in electron tunneling theory as long as the reaction is exothermic overall. 

In Chapter 7 general kinetics of electrode reactions is presented with kinetic parameters such as stoichiometric number, reaction order, and activation energy. In most cases the affinity of reactions is distributed in multiple steps rather than in a single particular rate step. Chapter 8 discusses the kinetics of electron transfer reactions across the electrode interfaces. Electron transfer proceeds through a quantum mechanical tunneling from an occupied electron level to a vacant electron level. Complexation and adsorption of redox particles influence the rate of electron transfer by shifting the electron level of redox particles. Chapter 9 discusses the kinetics of ion transfer reactions which are based upon activation processes of Boltzmann particles. 

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