Franck-Condon redox

The elementary act of an electrochemical redox reaction is the transition of an electron from the electrode to the electrolyte or conversely. Snch transitions obey the Franck-Condon principle, which says that the electron transition probability is highest when the energies of the electron in the initial and final states are identical. 

It follows from the Franck-Condon principle that in electrochemical redox reactions at metal electrodes, practically only the electrons residing at the highest occupied level of the metal s valence band are involved (i.e., the electrons at the Fermi level). At semiconductor electrodes, the electrons from the bottom of the condnc-tion band or holes from the top of the valence band are involved in the reactions. Under equilibrium conditions, the electrochemical potential of these carriers is eqnal to the electrochemical potential of the electrons in the solution. Hence, mntnal exchange of electrons (an exchange cnrrent) is realized between levels having the same energies. 

The Franck-Condon principle states that there must be no movement of nuclei during an electronic transition therefore, the geometry of the species before and after electron transfer must be unchanged. Consequently, the active site geometry of a redox metalloenzyme must approach that of the appropriate transition state for the electronic transfer. Every known copper enzyme has multiple possible copper oxidation states at its active site, and these are necessary for the enzyme s function. 

These levels of interfacial redox electrons are connected with the hydrogen and oxygen electrode reactions. As noted in Sec. 5.1.2, the electron level of adsorbate particles is broadened by contact adsorption and undergoes the Franck-Condon level splitting due to a difference in adsorption energy between the oxidized particle and the reduced particle on the interface of semiconductor electrodes as shown in Fig. 5-59. 

Figure 8-1 shows the potential energy barrier for the transfer reaction of redox electrons across the interface of metal electrode. On the side of metal electrode, an allowed electron energy band is occupied by electrons up to the Fermi level and vacant for electrons above the Fermi level. On the side of hydrated redox particles, the reductant particle RED is occupied by electrons in its highest occupied molecular orbital (HOMO) and the oxidant particle OX, is vacant for electrons in its lowest imoccupied molecular orbital (LUMO). As is described in Sec. 2.10, the highest occupied electron level (HOMO) of reductants and the lowest unoccupied electron level (LUMO) of oxidants are formed by the Franck-Condon level sphtting of the same frontier oihital of the redox particles... 

The basic theory of the kinetics of charge-transfer reactions is that the electron transfer is most probable when the energy levels of the initial and final states of the system coincide [5] following the Franck-Condon principle. Thus, the efficiency of the redox reaction processes is primarily controlled by the energy overlap between the quantum states in the energy bands of the semiconductor and the donor and acceptor levels of the reactants in the electrolyte (Fig. 1). In the ideal case, the anodic current density is given by the... 

Fig. 2. Energy cycle for electron transfer under Franck-Condon conditions (<> ) in relation to electron transfer at thermal equilibrium (°E) for redox species in solution...

Electron transfer is a fast reaction ( 10-12s) and obeys the Franck-Condon Principle of energy conservation. To describe the transfer of electron between an electrolyte in solution and a semiconductor electrode, the energy levels of both the systems at electrode-electrolyte interface must be described in terms of a common energy scale. The absolute scale of redox potential is defined with reference to free electron in vacuum where E=0. The energy levels of an electron donor and an electron acceptor are directly related to the gas phase electronic work function of the donor and to the electron affinity of the acceptor respectively. In solution, the energetics of donor-acceptor property can be described as in Figure 9.6. 

In the second chapter, Appleby presents a detailed discussion and review in modem terms of a central aspect of electrochemistry Electron Transfer Reactions With and Without Ion Transfer. Electron transfer is the most fundamental aspect of most processes at electrode interfaces and is also involved intimately with the homogeneous chemistry of redox reactions in solutions. The subject has experienced controversial discussions of the role of solvational interactions in the processes of electron transfer at electrodes and in solution, especially in relation to the role of Inner-sphere versus Outer-sphere activation effects in the act of electron transfer. The author distils out the essential features of electron transfer processes in a tour de force treatment of all aspects of this important field in terms of models of the solvent (continuum and molecular), and of the activation process in the kinetics of electron transfer reactions, especially with respect to the applicability of the Franck-Condon principle to the time-scales of electron transfer and solvational excitation. Sections specially devoted to hydration of the proton and its heterogeneous transfer, coupled with... 

Figure 2. Generalized excited state diagram. M represents a ground-state molecule, M and M are the Franck-Condon and thermally equilibrated excited states, respectively, hv is the excitation energy, Eqq the excited state energy, and tq is the inherent excited state lifetime. Relevant ground-and excited state redox couples are shown.

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