Application to electron transfer

An electron-transfer reaction is the transition between two electronic states, an initial state labeled i, which in our example corresponds to 

In the general case R denotes a set of coordinates, and Ui(R) and Uf (R) are potential energy surfaces with a high dimension. However, the essential features can be understood from the simplest case, which is that of a diatomic molecule that loses one electron. Then Ui(R) is the potential energy curve for the ground state of the molecule, and Uf(R) that of the ion (see Fig. 19.2). If the ion is stable, which will be true for outer-sphere electron-transfer reactions, Uf(R) has a stable minimum, and its general shape will be similar to that of Ui(R). We can then apply the harmonic approximation to both states, so that the nuclear Hamiltonians Hi and Hf that correspond to Ui and Uf are sums of harmonic oscillator terms. To simplify the mathematics further, we make two additional assumptions  

The normal coordinates in the initial and the final state are the same except for a possible shift in the equilibrium position. 

The frequencies of the normal modes are the same in both states. The first assumption holds for systems such as the [Fe (H2 O) g ]2+ 3+ 

Let us summarize The wavefunctions for the initial (reduced) and final (oxidized) states are  

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A simpler procedure has been implemented in applications to electron transfer in collisions of ions with metal surfaces.[35] Returning to Eq.(31), the second line can be interpreted as describing the rate of change of coherence of p- and s-regions over time. This is not likely to change much from its initial value for short collision times, so that the equation can be replaced on the average by a phenomenological rate equation,... 

Only at the fastest diffusion, when Rq < a, the contact theory is applicable to electron transfer. Under this condition the Collins-Kimball expression (3.21) integrated in Eq. (3.4) constitutes a reasonable approximation to R(t) and for both long and short times. However, it was recognized long ago that for slower diffusion the Collins-Kimball model works better if a is considered as a fitting... 

Fig. 13. A hypothetical representation of solvent molecule orientation in the transition state involving electron transfer between two charged reactants. Each solvent molecule possesses a permanent dipole, which in this idealized diagram is depicted by an ellipsoidal shape. Solvent molecules reorganize to the geometry of the transition state. The electronic polarization of the solvent molecules, represented here by the bold arrows, then responds practically instantaneously with electron transfer. Finally, the permanent dipoles of the solvent molecules readjust to the successor state. This model may not be applicable to electron transfer between neutral reetants (see text)...

The concept of free energy surfaces has proven its vitality over many years of fruitful applications to electron transfer kinetics. The direct connection... 

Karatani H, Wada N, Sugimoto T. Voltammetric and spectroelectrochemical characterization of a water-soluble viologen polymer and its application to electron-transfer mediator for enzyme-free regeneration of NADH. Bioelectrochem, 2003 60 57-64. 

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