Electron transfer potential energy description

Figure 6.23 Potential energy description of an electron-transfer reaction. The parabolic curves intersect at the transition state (if)...

In fact, electron transfer occurs at the microscopic level where quantum mechanics provides the necessary description of the phenomenon (5-13). In the quantum mechanical solution, associated with the potential curves in Figure 1 are quantized energy levels, Ej = (vj + 1/2) 100., where Vj and 2ttvj are the vibrational... 

Finally, we consider the performance of the MFT method for nonadiabatic dynamics induced by avoided crossings of the respective potential energy surfaces. We start with the discussion of the one-mode model. Model IVa, describing ultrafast intramolecular electron transfer. The comparison of the MFT method (dashed line) with the quantum-mechanical results (full line) shown in Fig. 5 demonstrates that the MFT method gives a rather good description of the short-time dynamics (up to 50 fs) for this model. For longer times, however, the dynamics is reproduced only qualitatively. Also shown is the time evolution of the diabatic electronic coherence which, too, is... 

It is important to note that the description of electron transfer kinetics is different in the case of semiconductor electrodes. For an n-type semiconductor electrode in the dark, the rate of electron transfer depends not only on the concentration of redox species in the solution but also on the potential dependent density of electrons in the semiconductor. Under depletion conditions, most of the potential drop is located in the solid, so that to a good approximation the activation energy for electron transfer is independent of potential. Electron transfer at semiconductor electrodes is therefore characterised in terms of a second order heterogeneous rate constant with units cm4 s-1. 

It is a point peculiar to electrochemical reaction kinetics (77), however, that the rates of charge-transfer processes at electrodes measured, as they have to be, at some well-defined potential relative to that of a reference electrode, are independent of the work function of the electrocatalyst metal surface. This is due to cancellation of electron-transfer energies, O, at interfaces around the measuring circuit. In electrochemistry, this is a well-understood matter, and its detailed origin and a description of the effect may be found, among other places, in the monograph by Conway (77). 

---