The Electron Transfer Process

Consider now the electron transfer process. In contrast to the problem discussed in Sections 16.3 and 16.4, of electron transfer between molecular donor and acceptor states, where the role of nuclear motion was critical for converting a two-state dynamics into a rate process, in the present situation a rate exists even in the absence of nuclear relaxation because of the presence of a continuum of metal levels. We will start by considering this problem, disregarding nuclear motion. 

1 Electron transfer to/from a metal electrode without nuclear relaxation 

The theoretical treatment in this case is similar to that of a level interacting with a continuum (Section 9.1) but with some new twists. The result will have a golden-rule form, that is, contains a product V p, but we need to identify the coupling and the density of states involved. 

We use a simple picture in which the molecular species S is a two-state system, where the oxidized state ) has one electron more than the reduced state b. The corresponding energies are a and /, and their difference is denoted Eab = Ea—Ey. For the metal electrode we use a free electron model, so that a state of the metal is specified by a set of occupation numbers m = (/ i, m, . ..) ofthe single electron levels. For the single electron level j of energy Ej, mj = 1 with probability f Ej) and mj = 0 with probability 1 —/ Ej), where/( ) is given by (17.4). A basis of states forthe overall SM system is written s, m) = Iv) m) where s = a,b and m) is an antisymmetrized product of single electron metal states. 

Next consider the rate of such electron transfer process. The golden-rule expression for this rate is 

We use a simple picture in which the molecular species S is a two-state system, where the oxidized state la) has one electron more than the reduced state b). The corresponding energies axsEa 33x6. Et, and their difference is denoted = Ea —Eb. 

Firstly, it is the electrode potential which determines whether sufficient energy is being supplied for the electron transfer to occur. If we consider the simple electrode reaction (omitting charge designation for the oxidized and reduced species O and R) 

In these reactions, (2) is the process taking place at the reference electrode which therefore determines the potential scale. In practice other reference electrodes, such as the saturated calomel electrode are frequently used but the data are normally expressed on the hydrogen scale. 

The equilibrium (1) at the electrode surface will lie to the right, i.e. the reduction of O will occur if the electrode potential is set at a value more cathodic than B . Conversely, the oxidation of R would require the potential to be more anodic than B . Since the potential range in certain solvents can extend from — 3 0 V to + 3-5 V, the driving force for an oxidation or a reduction is of the order of 3 eV or 260 kJ mol and experience shows that this is sufficient for the oxidation and reduction of most organic compounds, including many which are resistant to chemical redox reagents. For example, the electrochemical oxidation of alkanes and alkenes to carbonium ions is possible in several systems 

It is instructive to draw up a free-energy cycle for the cell reaction (3) so as to illustrate the dominant energy terms in the single electrode reaction (1)  

As in chemical systems, however, the requirement that the reaction is thermodynamically favourable is not sufficient to ensure that it occurs at an appreciable rate. In consequence, since the electrode reactions of most organic compounds are irreversible, i.e. slow at the reversible potential, it is necessary to supply an overpotential, tj — S—E, in order to make the reaction proceed at a conveniently high rate. Thus, secondly, the potential of the working electrode determines the kinetics of the electron transfer process. 

By changing the electrode potential across the El we can raise the energy of the Fermi level to accomplish the required exact matching of the two levels (Fig. 9b). This situation allows for the quantum mechanical tunnelling of the electron in the Fermi level through the energy barrier separating it from the LUMO of the molecule. 

Let us continue to change the electrode potential towards more negative potentials and accordingly the Fermi level to a value higher 

1 This is the same situation as in electron transfer mechanisms in homogeneous medium, where we have to take into account two transition states, identical in energy but differing with respect to the position of the electron (Reynolds and Lumry, 1966). 

to go to the experimental situation, what happens as we insert a metal electrode into an electrolyte solution without connecting it to an external electron source As we have discussed before (p. 22), an El is built up and hence a certain potential is established across the interface region. At this potential, charge transfer between electrode and electroactive species takes place, but, since no net current flows, the rates of electronation and de-electronation are identical. The system has reached the equilibrium potential at which the current density z for electronation is equal to the current density of de-electronation i. This current density is designated i0, the equilibrium exchange current density (cf. Table 6), given by the expression  

Here F is the Faraday, kc and kc the heterogeneous rate constants for electron transfer in either direction, cM and cM- are the concentrations of the electroactive species M and its electronated form M, (x is the transfer coefficient, and eq is the potential difference across the interface at equilibrium. This equilibrium potential is given by the Nernst equation, 

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Electrochemistry is concerned with the study of the interface between an electronic and an ionic conductor and, traditionally, has concentrated on (i) the nature of the ionic conductor, which is usually an aqueous or (more rarely) a non-aqueous solution, polymer or superionic solid containing mobile ions (ii) the structure of the electrified interface that fonns on inunersion of an electronic conductor into an ionic conductor and (iii) the electron-transfer processes that can take place at this interface and the limitations on the rates of such processes. 

The rate of the electron-transfer process, at least in solution, is defined in the usual way ... 

Knowledge of photoiaduced electroa-transfer dyaamics is important to technological appUcations. The quantum efficiency, ( ), ie, the number of chemical events per number of photons absorbed of the desired electron-transfer photoreaction, reflects the competition between rate of the electron-transfer process, eg, from Z7, and the radiative and radiationless decay of the excited state, reflected ia the lifetime, T, of ZA ia abseace ofM. Thus,... 

One apparent discrepancy between the spectroscopic data and the crystal structure is that no spectroscopic signal has been measured for participation of the accessory chlorophyll molecule Ba in the electron transfer process. However, as seen in Figure 12.15, this chlorophyll molecule is between the special pair and the pheophytin molecule and provides an obvious link for electron transfer in two steps from the special pair through Ba to the pheophytin. This discrepancy has prompted recent, very rapid measurements of the electron transfer steps, still without any signal from Ba- This means either... 

The redox properties of quinones are crucial to the functioning of living cells, where compounds called ubiquinones act as biochemical oxidizing agents to mediate the electron-transfer processes involved in energy production. Ubiquinones, also called coenzymes Q, are components of the cells of all aerobic organisms, from the simplest bacterium to humans. They are so named because of their ubiquitous occurrence in nature. 

Let us discuss now the conditions required for the electron transfer process. This reaction requires, of course, a suitable electron donor (a species characterized by a low ionization potential) and a proper electron acceptor, e.g., a monomer characterized by a high electron affinity. Furthermore, the nature of the solvent is often critical for such a reaction. The solvation energy of ions contributes substantially to the heat of reaction, hence the reaction might occur in a strong solvating solvent, but its course may be reversed in a poorly solvating medium. A good example of this behavior is provided by the reaction Na -f- naphthalene -> Na+ + naphthalene". This reaction proceeds rapidly in tetrahydrofuran or in dimethoxy... 

The ESR spectrum of the furan radical anion indicates that the Cem-0 bond is ruptured in the electron transfer process whereby the oxygen atom acquires the negative charge and the C-2 end of the open ring possesses a free radical character ... 

Many anodic oxidations involve an ECE pathway. For example, the neurotransmitter epinephrine can be oxidized to its quinone, which proceeds via cyclization to leukoadrenochrome. The latter can rapidly undergo electron transfer to form adrenochrome (5). The electrochemical oxidation of aniline is another classical example of an ECE pathway (6). The cation radical thus formed rapidly undergoes a dimerization reaction to yield an easily oxidized p-aminodiphenylamine product. Another example (of industrial relevance) is the reductive coupling of activated olefins to yield a radical anion, which reacts with the parent olefin to give a reducible dimer (7). If the chemical step is very fast (in comparison to the electron-transfer process), the system will behave as an EE mechanism (of two successive charge-transfer steps). Table 2-1 summarizes common electrochemical mechanisms involving coupled chemical reactions. Powerful cyclic voltammetric computational simulators, exploring the behavior of virtually any user-specific mechanism, have... 

This review is concerned with the formation of cation radicals and anion radicals from sulfoxides and sulfones. First the clear-cut evidence for this formation is summarized (ESR spectroscopy, pulse radiolysis in particular) followed by a discussion of the mechanisms of reactions with chemical oxidants and reductants in which such intermediates are proposed. In this section, the reactions of a-sulfonyl and oc-sulfinyl carbanions in which the electron transfer process has been proposed are also dealt with. The last section describes photochemical reactions involving anion and cation radicals of sulfoxides and sulfones. The electrochemistry of this class of compounds is covered in the chapter written by Simonet1 and is not discussed here some electrochemical data will however be used during the discussion of mechanisms (some reduction potential values are given in Table 1). 

The second mechanism involves the formation of a covalent bridge through which the electron is passed in the electron transfer process. This is known as the inner-sphere mechanism (Fig. 9-5). 

However, metal ions in higher oxidation states are generally smaller than the same metal ion in lower oxidation states. In the above example, the Co(ii)-N bonds are longer than Co(iii)-N bonds. Consider what happens as the two reactants come together in their ground states and an outer-sphere electron transfer occurs. We expect the rate of electron transfer from one center to another to be very much faster than the rate of any nuclear motion. In other words, electron transfer is very much faster than any molecular vibrations, and the nuclei are essentially static during the electron transfer process (Fig. 9-6). 

Although the kinetic studies summarised here are useful guides to the gross features of mechanism it is evident from apparently closely related autoxidations, e.g. those of V(III) and U(IV), that subtle factors operate. Fallab has pointed out that these reductants give similar kinetics and possess similar reduction potentials, yet differ in autoxidation rate by a factor of 3 x 10 , and has discussed differences of this type in terms of the stereochemistry of the electron-transfer process in the coordination sphere. 

Carloni et al.91 applied the DFT(PZ) calculations to investigate the electronic structure of various models of oxydized and reduced Cu, Zn superoxide dismutase. The first stage of the enzymatic reaction involves the electron transfer from Cu" ion to superoxide. The theoretical investigations provided a detailed description of the electronic structure of the molecules involved in the electron transfer process. The effect of charged groups, present in the active center, on the electron transfer process were analyzed and the Argl41 residue was shown to play a crucial role. 

A solid-liquid interface will have three aspects to its structure the atomic 1.1 structure of the solid electrode, the structure of any adsorbed layer and the Structure structure of the liquid layer above the electrode. All three of these are of fundamental importance in the understanding of the electron transfer processes at the core of electrochemistry and we must consider all three if we are to arrive at a fundamental understanding of the subject. 

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