The Marcus Theory of Electron Transfer

The basic assumption of the Marcus theory of electron transfer is that only a weak interaction between the reactants is needed in order for a simple electron-transfer process to occur. Marcus theory considers 

According to the collision theory, the rate constant (kET) of the electron-transfer process is given by  

Research on photochemical reaction centres has been important for our understanding of the relationship between the structures and the rates 

The maximum rate of electron transfer occurs when l = -AG° and  

AG° for the single electron-transfer reaction can be obtained from the redox potentials of the systems involved in the process and is given by  

The basic assumption of the Marcus theory of electron transfer process is that the reactants needed a weak interaction between them for this process to operate. The Marcus theory considers the reaction rate theory, potential energy surfaces and reorganization of the system to explain the electron transfer process [22]. The potential energy curves of an electron transfer reaction for the initial (i) and final (f) states of the system are represented by parabolic curves (Fig. 6.18). These curves quantitatively relate the rate of electron transfer to the reorganizational energy (A) and the See energy changes for the electron transfer process (AG ) and activation (AG ). 

In a polar solvent, the solvent dipoles are arranged around the molecules taking part in PET. The solvent reorganization is required to accommodate and stabilize the changed species (Fig. 6.19) and this reorganization process requires some energy from the system. 

The free energy change, AG , of an electron transfer process is the driving force of the process. The free energy of activation, AG, is needed to reach the transition state,. It is related to the reorganizational energy, k of the system. From the geometry of the parabolas  

According to the collision theory, the rate constant is given by 

This equation based on Marcus model gives the relation between the kinetics (ATet) and thermodynamic driving force (AG ) of PET process. Analysis of this equation gives three distinct kinetic regions, as shown in Fig. 6.20, depending on AG°. 

In the semi-classical approach [18], the golden-rule type expression is used (Eq. 2) in which the rate is a product of an electronic matrix element squared 

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Samec Z, Weber J (1973) The influence of chemisorbed sulfur on the kinetic parameters of the reduction of Fe " ions on a platinum electrode on the basis of the Marcus theory of electron transfer. J Electroanal Chem Interfacial Electrochem 44 229-238... 

In summary, to apply the Marcus theory of electron transfer, it is necessary to see if the temperature dependence of the electron transfer rate constant can be described by a function of the Arrhenius form. When this is valid, one can then determine the activation energy AEa only under this condition can we use AEa to determine if the parabolic dependence on AG/ is valid and if the reaction coordinate is defined. 

In our description of the Marcus theory of electron-transfer reactions we have found it helpful to plot the free energy change in the three dimensional picture shown in Fig. 10 (Albery, 1975c, 1980). This picture emphasizes that... 

Electron Transfer Far From Equilibrium. We have shown how the Marcus Theory of electron transfer provides a quantitative means of analysis of outer-sphere mechanisms in both homogeneous and heterogeneous systems. It is particularly useful for predicting electron transfer rates near the equilibrium potential,... 

A well defined theory of chemical reactions is required before analyzing solvent effects on this special type of solute. The transition state theory has had an enormous influence in the development of modern chemistry [32-37]. Quantum mechanical theories that go beyond the classical statistical mechanics theory of absolute rate have been developed by several authors [36,38,39], However, there are still compelling motivations to formulate an alternate approach to the quantum theory that goes beyond a theory of reaction rates. In this paper, a particular theory of chemical reactions is elaborated. In this theoretical scheme, solvent effects at the thermodynamic and quantum mechanical level can be treated with a fair degree of generality. The theory can be related to modern versions of the Marcus theory of electron transfer [19,40,41] but there is no... 

Fig. 9 Test of the Marcus theory of electron transfer where fcca,c for the cross-reaction O, + R - R, + On is calculated from the thermodynamic free energies and the free energies of activation of the symmetrical reactions. The symbols are as follows O, Ce(IV), x IrCl -, + Mo(CN)j-, Fe(CN) ", R O, Fe(CN)J , A Mo(CN)f, W(CN)<-...

The plateau in Fig. 13.9 corresponds to the diffusion-limited region where the rate of electron transfer is faster than the rate of diffusion. According to the Marcus theory of electron transfer, the observed rate constant of an intermolecular electron transfer is given by [23]... 

The dependence of intervalence transition energy on the activation barrier to thermal electron transfer in Eqs. (1) and (3) allows the solvent dependence of intervalence transitions to be understood in terms of relationships developed for the Marcus Theory of electron transfer (5, 6). 

Mason, R. P. Redox cycling of radical anion metabohtes of toxic chemicals and drugs and the Marcus theory of electron transfer. Environ. Health Perspect. 1990, 87, 237-243. 

Figure 10.5. The protein environment can influence hydrogenic wavefunction overlap via asymmetrically coupled modes which bring hydrogenic wavefunctions into energetic coincidence [vertical perturbation, shown on left-hand side of figure]. These modes give rise to terms analogous to the Marcus theory of electron transfer [122]. Additionally,...

Many electron transfer reactions of inorganic radicals conform to the outer-sphere model and hence can be modeled with the Marcus theory of electron transfer.71 This model relies, in part, on the concept of self-exchange reactions, and the inference that self-exchange reactions can be defined for radicals. For many years, it was simply... 

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