The nuclear reorganization

In the high-temperature/strong electron-phonon coupling limit the functions F(E) take the form (16.58). 

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So far, only the nuclear reorganization energy attending electron transfer has been discussed, yielding the expressions above of the free energy of activation in the framework of classical transition state theory. A second series of important factors are those that govern the preexponential factor, k, raising in particular the question of the adiabaticity or nonadiabaticity of electron transfer between a molecule and the electronic states in the electrode. 

So far the attention has been on the nuclear reorganization barrier. Nevertheless, other important factors previously hidden in the pre-exponential factor (and ultimately in the standard rate constant) have to be considered, namely, the fundamental question of the magnitude of the electronic interaction between electroactive molecules and energy levels in the electrode (i.e., the degree of adiabaticity) and its variation with the tunneling medium (electrode-solution interface), the tunneling distance, and the electrode material. Thus, within the transition-state formalism, the rate constant for electron transfer can be expressed as the product of three factors [39—42] ... 

The other model parameters entering Eq. [66] are the nuclear reorganization energies defined through the second cumulants of the reaction coordinate... 

The interfacial kinetics processes at semiconductor/liquid contacts for reactions with one-electron, outer-sphere, redox species can be understood in a conventional theoretical framework. The rate constant can be broken down into a term representing the attempt frequency, Vn, a term representing the electronic coupling between the electrons in the conduction band of the semiconductor and the redox acceptor state, k x, and a term representing the nuclear reorganization energy in the transition state from reactants to products, For outer-sphere electron transfer processes, the nuclear term is well-known to be ... 

Problems associated with precursor formation and successor dissociation are circumvented when the nonspecific interaction between donor and acceptor in Eq. 1, represented by, is replaced by a covalent linker. As the many chapters of this Series attest, the restriction of electron transfer to an intramolecular process, where the distance between donor and acceptor is fixed, has led, in the past two decades, to an explosion in our knowledge of electron transfer processes and the factors that control them. These include the donor-acceptor separation distance the nature of the intervening medium and the relative orientation between the donor and acceptor sites (all of which influence electronic coupling) the driving force of the reaction (AG°) and the nuclear reorganization of reactants and solvent (2). 

The rates of photoinduced electron transfer (ET) reactions in a series of iridium (spacer)pyridinium complexes, [Ir(/r-dmpz)(CO)(Ph2PO-CH2-CH2-py+)]2 and [Ir( -dmpz)(CO)(Ph2PO-C6H4(CH2) -py+)]2 ( = 0 - 3), have been studied in acetonitrile solution at room temperature (99). The nuclear reorganization energies and electronic couplings in these systems have been evaluated. 

In addition to the driving force or overpotential, the activation free energy contains the nuclear reorganization free energy, r, addressed further in Section 2.2.2. 

We address briefly the two central quantities, the nuclear reorganization free energy and the electronic turmeling factor. 

All these areas are covered in a broad literature, overviewed, for example in refs. 24 and 25. We do not here address all these elements of molecular charge transfer theory. Instead we discuss the two central factors in the interfacial (bio)electrochemical electron transfer process, first the nuclear reorganization (free) energy and then the electronic tunneling factor. 

The electronic system part follows smoothly ( adiabatically ) the nuclear reorganization in the proton resonance state. The proton motion may, however, be obstructed by a prohibitive tunneling barrier. This limit is denoted as the partially adiabatic limit. Or, the proton may follow adiabatically the environmental nuclear... 

It has been argued that polarization acts as a potential well. Unfortunately, such a treatment tends to obscure the difference between a potential well for the electron and the total energy potential that is part of the Marcus model The nuclear reorganization of the nuclei appears to be omitted or built into the quasiparticle concept. Nuclear tunneling, leading to a larger rate at low temperatures, is easily confused with electron tunneling. 

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