The Marcus-Hush Model

The first attempt to describe the dynamics of dissociative electron transfer started with the derivation from existing thermochemical data of the standard potential for the dissociative electron transfer reaction, rx r.+x-,12 14 with application of the Butler-Volmer law for electrochemical reactions12 and of the Marcus quadratic equation for a series of homogeneous reactions.1314 Application of the Marcus-Hush model to dissociative electron transfers had little basis in electron transfer theory (the same is true for applications to proton transfer or SN2 reactions). Thus, there was no real justification for the application of the Marcus equation and the contribution of bond breaking to the intrinsic barrier was not established. 

As with the Marcus-Hush model of outer-sphere electron transfers, the activation free energy, AG, is a quadratic function of the free energy of the reaction, AG°, as depicted by equation (7), where the intrinsic barrier free energy (equation 8) is the sum of two contributions. One involves the solvent reorganization free energy, 2q, as in the Marcus-Hush model of outer-sphere electron transfer. The other, which represents the contribution of bond breaking, is one-fourth of the bond dissociation energy (BDE). This approach is... 

FIGURE 1.13. Free-energy profiles in outer-sphere electron transfer according to the Butler-Volmer approximation (a) and to the Marcus-Hush model (b). 

When electron transfer is forced to take place at a large distance from the electrode by means of an appropriate spacer, the reaction quickly falls within the nonadiabatic limit. H is then a strongly decreasing function of distance. Several models predict an exponential decrease of H with distance with a coefficient on the order of 1 A-1.39 The version of the Marcus-Hush model presented so far is simplified in the sense that it assumed that only the electronic states of the electrode of energy close or equal to the Fermi level are involved in the reaction.31 What are the changes in the model predictions brought about by taking into account that all electrode electronic states are actually involved is the question that is examined now. The kinetics... 

Coming back to solvent reorganization, the reduction of aromatic hydrocarbons in an aprotic solvent such as DMF provides a series of data that may be used for testing the Marcus-Hush model of solvent reorganization13,61-63... 

When conformational change and electron transfer are concerted, the structural change may be treated as an internal reorganization factor in the electron transfer dynamics. This is the A, term of the Marcus-Hush model (Section 1.4.2 see also Section 1.4.4 for experimental examples). The model is applicable as long as the conformational changes are not so strong as to invalidate the harmonic approximation. 

It is thus, in principle, possible to derive from the potential location and from its shape all the parameters contained in the Marcus-Hush model, namely, the standard potential, , and the intrinsic barrier, AGq (Klinger... 

Let us again emphasize the connection between the Marcus-Hush model. 

In other words, under these restrictive conditions, outer sphere electron-transfer reactions obeying the Marcus-Hush model are typical examples where the Hammond-Leffler postulate and the reactivity-selectivity principle (see, for example, Pross, 1977, and references cited therein, for the definition of these notions) are expected to apply. 

In long distance ET, the presence of a wave function in the medium between donor and acceptor is the only means for donor and acceptor to communicate. The nature of this connection is expected to influence the reaction rates for ET or EET between the subsystems. Partitioning technique together with the Marcus-Hush model [6,7] may be viewed as an adaptation to practical chemistry of a full quantum mechanical treatment [21], where nuclei and electrons are treated as equal partners. In particular the influence on ET from the medium between the redox centres is formalized. 

Fig. 1.15 Schematic of the energy curves in the Marcus-Hush model with a single, global reaction coordinate q such that the potential energy hypersurface reduces to two parabolas and the activation energy can he calculated from the intersection point between them. The electronic coupling (Sect. 1.7.2.2) and the continuum of electronic levels in the metal electrode (Sect. 1.7.2.1) are not shown...

The differences between BV and MH also have implications in the concentration profiles of the electro-active species. Thus, whereas the BV model predicts a zero surface concentration of the oxidized species at the electrode surface, in the Marcus-Hush model the surface concentration of species O also depends on the electrode kinetics such that for small values of the heterogeneous... 

In relation to the application of the Marcus-Hush model to immobilized redox groups in LSV and CV, the behavior predicted by MH matches that of the BV... 

The Marcus Inverted Region (MIR) is that part of the function of rate constant versus free energy where a chemical reaction becomes slower as it becomes more exothermic. It has been observed in many thermal electron transfer processes such as neutralization of ion pairs, but not for photoinduced charge separation between neutral molecules. The reasons for this discrepancy have been the object of much controversy in recent years, and the present article gives a critical summary of the theoretical basis of the MIR as well as of the explanations proposed for its absence in photoinduced electron transfer. The role of the solvent receives special attention, notably in view of the possible effects of dielectric saturation in the field of ions. The relationship between the MIR and the theories of radiationless transitions is a topic of current development, although in the Marcus-Hush Model electron transfer is treated as a thermally activated process. 

Figure 2 Two parameters defining the Marcus-Hush model of two intersecting parabolas the equilibrium free energy gap AFo and the classical reorganization energy Xci- The parabolas curvature is l/(2Xd).

The understanding of optical experiments demonstrating different optical widths (second spectral moments) for absorption and emission spectral lines requires an extension of the Marcus-Hush model that would incorporate different reorganization energies for forward and backward charge transfers... 

It is actually much easier to measure X spectroscopically than kinetically. The Marcus-Hush model of charge-transfer transitions predicts two fundamental relations between the kinetic parameters and spectroscopic observables. The first relations is between the reorganization energy and the Stoke... 

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