Electron tunneling reactions

Zamaraev, K.I., Kairutdinov, R.F. Photoinduced Electron Tunneling Reactions in Chemistry and Biology. 163, 1-94 (1992). 

A great role in substantiating the importance of electron tunneling reactions was played by the work of De Vault and Chance in 1966 where the characteristic time, t1/z, of electron transfer from the heme site of the cytochrome molecule to the chlorophyll molecule in a bacterium was shown to be constant within the temperature range of 130 to 4.2 K [4]. The temperature independence of t1/2 permitted one to reject a diffusion mechanism for the process. However, it was still impossible to exclude the possibility of the reaction to proceeding via direct contact between the active sites of the reacting molecules. 

An essential step forward was also the development of kinetic models for electron tunneling reactions in solids [20-25]. Kinetic equations corresponding to these models were found to describe experimental data rather accurately. The agreement of experimental data with theory together with the absence of the temperature dependence for the reaction rate (which rules out its control by thermal diffusion) and with the evidence of considerable... 

The results of experimental research have also stimulated the appearance of theoretical papers devoted to the analysis of an elementary act of electron tunneling reactions in terms of the theory of non-radiative electron transitions in condensed media. It has been shown that this theory allows one to explain virtually all the known experimental data on electron tunneling reactions. 

The Theory of the Elementary Act of Electron Tunneling Reactions in Condensed Media... 

The probability of an electron tunneling reaction is directly proportional to the square of the exchange matrix element (see the following section). Therefore, the dependence of the rate constant of an electron tunneling reaction on the distance between the donor and the acceptor and on their mutual orientation is also determined, to a considerable degree, by the dependence of the exchange matrix element on these parameters. 

The possibility of the anomalous isotope effect for electron tunneling reactions was first noted by Ulstrup and Jortner [7]. This effect becomes possible when the reorganization energy is approximately equal to the reaction exothermicity. If, in this case, for example, the relationship Er - J + a) — 0 is satisfied, where co is the vibrational frequency for a heavy isotope, then from the viewpoint of the activation energy [see eqn. (42)1, the transition (0 - 1) is optimal for the heavy isotope. Compared with this transition for the heavy isotope, both the transitions (0 - 0)and(0 - 1) for the light isotope contain the additional activation multiplier. In this situation the anomalous isotope effect will be observed, provided that the Franck Condon factor for the transition (0 -> 1) of the heavy isotope is not too small compared with that of the light isotope. An example of the electron tunneling reaction for which the anomalous isotope effect is observed experimentally will be considered in Chap. 7, Sect. 4. 

If the donor has the vibrational quantum numbers ndl and ndf prior to and after the electron tunneling reaction then from eqn. (62) it follows that the transition matrix element is proportional to the multiplier a expC-y B). Employing this fact and using eqns. (63) and (64), Ivanov and Kozhushner [27] represent the probability of tunneling in the form... 

One of the interesting results of the work presented in ref. 27 is the conclusion that the parameter y depends not only on the properties of the donor, but also on those of the acceptor. Analysis of the experimental data shows that, for many electron tunneling reactions, the parameter y depends rather strongly upon the nature of the acceptor (see Chaps. 6 and 7). However, strictly speaking, it is not possible to conclude that this is the consequence only of non-adiabatic effects since the parameter y can also depend on the properties of the acceptor within the scope of the traditional description of the electron tunnel transfer (see Sect. 4). 

Peculiar features of the kinetics of electron tunneling reactions in condensed media... 

To summarise, the form of kinetic equations for electron tunneling reactions must strongly depend on two factors the type of dependence of the tunneling probability on the distance between the reagents and the form of the spatial distribution of the reagents. 

In the present chapter, (1) the macroscopic kinetics of the electron tunneling reaction is considered for various types of spatial distribution of the reagents and for situations when the reagents can be both immobile and mobile (2) the applicability of various kinetic models is analyzed under typical conditions of experimental studies on electron tunneling reactions and (3) methods are described of the determination, from the kinetic data, of various parameters which characterize the rates and distances of electron tunneling. 

It is expedient to begin the analysis of the kinetics of electron tunneling reactions for immobile reagents with the simplest case, i.e. when the probability of tunneling depends only upon the distance between the reagents and this dependence is purely exponential... 

It will be shown further that the employment of this simple formula allows a good enough description to be given of the kinetics observed for the majority of electron tunneling reactions which have been experimentally studied so far. 

When the reagents are located in the form of isolated pairs, so that it is possible to neglect the reactions between the particles from different pairs, the total kinetics of an electron tunneling reaction can be obtained by averaging the kinetics for the separate pairs. Let the distribution of pairs of donors and acceptors over the distance between them, R, at the initial instant of time (t = 0) be described by the function f(jR) normalized accord-... 

Very often in experimental studies of electron tunneling reactions it is not the absolute value of the concentration of the particles that is measured, but the ratio of the instantaneous concentration n(t) to the concentration n(tQ) at a certain fixed time t0. It follows from eqn. (5) that this ratio is... 

Let us now consider the kinetics of electron tunneling reactions for the exponential distribution of the pairs over the distances between the reacting particles... 

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