Proton-transfer reactions tunneling mechanisms

Quantum-mechanical tunnelling has been recognized as a possible contributor to the rate of a chemical reaction for many years. For instance, the theory of tunnelling for proton transfer reactions was developed by Bell (1959) in his famous book The Proton in Chemistry. Later, Bell (1980a) published a more thorough treatment of tunnelling in his book The Tunnel Effect in Chemistry. 

Very recently, some attempts were undertaken to uncover the intimate mechanism of the cation radical deprotonation. Thus, the reaction of 9-methyl-10-phenylanthracene cation radical with 2,6-lutidine was studied (Lu et al. 2001). The reaction takes place by a two-step mechanism that involves the intermediate formation of a cation radical/base complex prior to unimolecular proton transfer and separation of products. Based on the value of the kinetic isotope effect observed, it was concluded that extensive proton tunneling is involved in the proton-transfer reaction. The assumed structure of the intermediate complex involves 77-bonding between the unshared electron pair on nitrogen of the lutidine with the electron-deficient 77-system of the cation radical. 

In electrochemical proton transfer, such as may occur as a primary step in the hydrogen evolution reaction (h.e.r.) or as a secondary, followup step in organic electrode reactions or O2 reduction, the possibility exists that nonclassical transfer of the H particle may occur by quantum-mechanical tunneling. In homogeneous proton transfer reactions, the consequences of this possibility were investigated quantitatively by Bernal and Fowler and Bell, while Bawn and Ogden examined the H/D kinetic isotope effect that would arise, albeit on the basis of a primitive model, in electrochemical proton discharge and transfer in the h.e.r. 

The quantum mechanical nature of the proton transfer reaction has been dealt with in analytic theory and simulations by Warshel and Chu and by Borgis and Hynes.i s-i o xhe methods they describe explicitly take into account the solvent effect on the proton tunneling process. In that sense, they are perhaps more closely related to simulations of electron transfer reactions than to the simulations we have described so far. For that reason, we shall refer the reader to the original papers for further description of these techniques. 

It should be kept in mind that conventional AIMD simulation techniques, both BOMD and CPMD, are not able to describe all types of dynamics encountered in chemistry. One thing they lack is an ability to handle dynamics that can only be explained with frill quantum mechanics. Proton tunneling and ion dispersion, for example, are purely quantum effects that can play a fundamentally important role in biological systems, in polymer electrolyte fuel cells, and in many other water-containing systems. In fact, the commonly accepted mobility mechanism is the so-called stmctural diffusion or Grotthuss mechanism, in which solvation stmctures diffuse through the hydrogen bond network via sequential proton transfer reactions. 

We have seen that 10" M s is about the fastest second-order rate constant that we might expect to measure this corresponds to a lifetime of about 10 " s at unit reactant concentration. Yet there is evidence, discussed by Grunwald, that certain proton transfers have lifetimes of the order 10 s. These ultrafast reactions are believed to take place via quantum mechanical tunneling through the energy barrier. This phenomenon will only be significant for very small particles, such as protons and electrons. 

First, we shall discuss reaction (5.7.1), which is more involved than simple electron transfer. While the frequency of polarization vibration of the media where electron transfer occurs lies in the range 3 x 1010 to 3 x 1011 Hz, the frequency of the vibrations of proton-containing groups in proton donors (e.g. in the oxonium ion or in the molecules of weak acids) is of the order of 3 x 1012 to 3 x 1013 Hz. Then for the transfer proper of the proton from the proton donor to the electrode the classical approximation cannot be employed without modification. This step has indeed a quantum mechanical character, but, in simple cases, proton transfer can be described in terms of concepts of reorganization of the medium and thus of the exponential relationship in Eq. (5.3.14). The quantum character of proton transfer occurring through the tunnel mechanism is expressed in terms of the... 

Since the probability of tunnelling depends inversely on the square root of the mass, tunnelling effects are common for electrons and less so for protons, although many reaction mechanisms depend on proton transfer against potential barriers. 

At 100 the rate of the OH -catalyzed conversion of parahydrogen is, at most, twice that of the D2-H2O exchange. The small magnitude of this isotope effect suggests that proton transfer in the rate-determining step occurs by a classical mechanism rather than by tunneling. This is also indicated by the normal value (8 X 10 l.m. sec. 0 of the frequency factor of the reaction. 

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