Activationless electron transfer processes

Photoinitiated and optical electron-transfer processes and their relationship to corresponding ground-state thermal processes provide important new tests of theory, especially when comparisons are made for a given DBA system, of charge separation (CS) and charge recombination (CR), or of thermal and optical electron transfer (e.g., [27]). Photoinitiated processes have also been valuable in providing access to the dynamics of electron transfer in the activationless and inverted kinetic regimes (e.g., [43, 44]). 

Figure 2. Theoretical prediction for the temperature dependence of the electron transfer rate for activated and for activationless processes. Solid lines are calculated for a continuum of vibrational modes dotted lines represent the single-mode approximation (6, 8). Upper curve AE, —2000 cm 1 P, 20 and S, 20. Lower curves AE, —800 cm"1 P, 8 and S, 20.

A third and provisionally accepted explanation is that electron transfer can take place to vibrationally excited states of the products, i.e. nuclear tunnelling of the reactants to vibrationally excited states of the products takes place (Efrima and Bixon, 1974, 1976). The potential surfaces depicted in Fig. 10 show the rationale behind this mechanism. For AG° > — X (Fig. 10a) we have the normal situation with an activation barrier for electron transfer. At AG0 = —X (Fig. 106) the maximum rate for an activationless process has been reached, whereas for AG° < —X an activation barrier appears again (Fig. 10c, representing the inverted region). With electron transfer allowed to an excited vibrational level (dotted line in Fig. 10d) we have once again an activationless reaction proceeding at the maximum rate. For large molecules there is a... 

As the driving force for the reaction increases the rate constant increases, reaches a maximum, and then decreases again. When the rate of reaction is a maximum, there is no barrier to electron transfer and the process is activationless. This condition is reached for a rate constant of 1 x 10 s. For higher driving forces, the electron transfer reaction occurs in the Marcus inverted region. Other examples of this behavior have been described in the literature. They give strong confirmation of the model for electron transfer presented here. 

Subsequently, Marcus extended his theory to electrochemical electron transfer reactions/ " However, the role played by the electron energy spectrum in the electrode in these works was not elaborated. All the calculations were performed for a simplified model, where the potential energy surfaces for different electronic states were replaced by two potential energy surfaces (one for the initial state and one for the final state). Further calculations have shown that such considerations do not enable us to explain the fact that the transfer coefficient, a, for electrochemical reactions takes values in the interval from 0 to 1. In particular, it does not enable us to explain the existence of barrierless and activationless process (see Chapter 3 by Krishtalik in this volume). 

Hale in 1968 calculated the limiting electric current for an electron transfer reaction associated with the activationless process. The degenerate Fermi gas model was used to describe the electrons in the metal. 

X = 8000 cm" ). It is seen that the charge recombination process leading to the Cr(ni) doublet state is expected to be in the nearly activationless regime, whereas that leading to the ground state is likely to lie deep into the "inverted region" of electron transfer (section 1.3.2). In terms of radiationless transition theory, the excited-state charge recombination is favored by its... 

The current view is that the electron-transfer event itself is a fast activationless process the barrier for the reaction stems from the necessity to adjust the orientation of the solvent dipoles around ions and the lengths of some bond in the inner-coordination shells prior to the transfer step. According to this view, which was due largely to Rudolph Marcus [3], for the solvent, and to Noel Hush [4], for the metal-Ugand bond lengths, there are no proper transition states in electron-transfer reactions, because the solvent molecules are not in equilibrium distribution with the charges of the oxidised and reduced species. 

In other barrierless reactions, particularly chlorine evolution on graphite, no limiting current in the backward process was observed, the reason being that, in these cases, the slow step of the forward reaction was the transfer of the first electron, followed by that of the second, e.g., in an electrochemical desorption step. In the backward process, the slow activationless step is, in this case, preceded by the transfer of a single electron. The relationship between the rate of this process and the potential masks the limiting current phenomenon. 

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