Marcus theory details

Table 6.6 lists some reactions of the electron in water, ammonia, and alcohols. These are not exhaustive, but have been chosen for the sake of analyzing reaction mechanisms. Only three alcohols—methanol, ethanol, and 2-propanol—are included where intercomparison can be effected. On the theoretical side, Marcus (1965a, b) applied his electron transfer concept (Marcus, 1964) to reactions of es. The Russian school simultaneously pursued the topic vigorously (Levich, 1966 Dogonadze et al, 1969 Dogonadze, 1971 Vorotyntsev et al, 1970 see also Schmidt, 1973). Kestner and Logan (1972) pointed out the similarity between the Marcus theory and the theories of the Russian school. The experimental features of eh reactions have been detailed by Hart and Anbar (1970), and a review of various es reactions has been presented by Matheson (1975). Bolton and Freeman (1976) have discussed solvent effects on es reaction rates in water and in alcohols. 

The requisite value for k x was only approximately defined by the fitting procedures, and because of uncertainty in the standard potential for the Br2/Br redox couple it was likewise deemed unsuitable to use the value of kx and the principle of detailed balancing to derive the value of k x. Further reason to be doubtful of the derived value of k x was a major disagreement between it and the value predicted by the cross relationship of Marcus theory. 

Electron transfer may also dominate the excited state chemistry of open shell radical ions. The fluorescence of the radical anions of anthraquinone and 9,10-dicyanoanthracene and the radical cation of thianthrene are quenched by electron acceptors and donors, respectively, although detailed kinetic analysis of the electron exchange do not correspond exactly either with Weller or Marcus theory (258). The use of excited radical cations as effective electron acceptors represents a... 

Detailed analysis of the rate and equilibrium constants determined for both phases of intramolecular aldol condensation reactions (13 —>15, 16—>18, and 19—>21) in terns of Marcus theory, has established that the intrinsic barriers for die intramolecular reactions are the same as those determined previously for the intermolecular counterparts.31 Consequently, rate constants for intramolecular aldol reactions are predictable from the energetics of the reactions and the effective molarity can be calculated. An associated discussion of Baldwin s rales suggests that they are a consequence of the need to achieve a conformation from which reaction can take place... 

A large number of radical reactions proceed by redox mechanisms. These all require electron transfer (ET), often termed single electron transfer (SET), between two species and electrochemical methods are very useful to determine details of the reactions (see Chapter 6). We shall consider two examples here - reduction with samarium di-iodide (Sml2) and SRN1 (substitution, radical-nucleophilic, unimolecular) reactions. The SET steps can proceed by inner-sphere or outer-sphere mechanisms as defined in Marcus theory [19,20]. 

However, even for the simple methyl transfer reactions, there is considerable confusion and some disagreement about the details of the mechanism. Some authors (Sneen, 1973) have suggested that ionization of RX always precedes attack by the nucleophile, while others have maintained that the nucleophile attacks the covalent substrate. Extensive references to both points of view are given by McLennan (1976). In the present review the application of the Marcus theory of atom transfer (Marcus, 1968a) allows us to deduce values of the parameter a which describes the symmetry of the transition state. We shall compare this information about the transition state with that from changing the solvent, from isotope effects, and from Hammett relations. We shall then attempt to deduce a model for the transition state which is consistent for all the different types of data. 

Improta et studied large molecules with a well-separated electron donor and electron acceptor pair. In this case, the electron-transfer process may lead to a dissociation of the molecule. Improta et al. applied the Marcus theory to obtain an expression for the electron transfer rate constant. Subsequently, the values of the parameters entering this expression were calculated using a density-functional approach for the solute together with the polarizable continuum model for the solvent. They applied their approach for a specific system (for the present purpose, the details are less important) and found the results of Table 24. Here, three different... 

Andrzej Kapturkiewicz gives a thorough account on the theory of electron transfer reactions that lead to electrochemiluminescence (ECL). He discusses in detail the conditions under which the Marcus theory can give a more quantitative description of ECL processes. 

Many technologically important electrochemical processes are more complicated than the simple electron transfer in the Ee /Fe couple, in which neither of the reactants is supposed to adsorb onto the electrode surface. Typically, however, reactants or products are adsorbed onto the electrode surface, or the electron-transfer act induces the breaking of a bond in the reacting molecule. It is quite clear that in these more complex situations the Marcus theory is expected to break down and a more detailed description of the solvent-reactant-metal interaction is required. 

Electron and proton transfer (see Eqs. (13.1) and (13.2), involve obvious similarities. When the starting materials are neutral, both result in the formation of charge and in the necessity for separation of charge to stabilize the product states. In principle, both can occur in the ground state, but transfer that is exoergic only in the excited state allows the use of time-resolved spectroscopic techniques to determine the details of solvation and structural reorganization. For electron transfer, the development of such techniques and the accompanying theoretical rationale, most especially the Marcus theory, has been one of the triumphs of modern mechanistic chemistry. 

However it turned out that the structural, chemical and dynamical details are essential for complex descriptions of long-range proton transport. These parameters appear to be distinctly different for different families of compounds, preventing proton conduction processes from being described by a single model or concept as is the case for electron transfer reactions in solutions (described within Marcus theory [23]) or hydrogen diffusion in metals (incoherent phonon assisted tunneling [24]). 

As discussed in Section 4.1, these reactions are described by Marcus theory and their rates depend on the thermodynamic driving force of the reaction and on the selfexchange rate constants for the oxidant (02/02 ") and the reducing agent (the metal complex).29,30 Unfortunately, the self-exchange rates for dioxygen/superoxide couple are difficult to determine, and the reported values varied by several orders of magnitude. This controversy and the current state-of-the-art in the field are described in detail in Section 4.1, and will not be further discussed here. 

To conclude this section, it is important to note that, in its classical form, Marcus s theory only implies two parameters the activation energy to the free energy of the reaction and the reorganization energy. It does not explicitly depend on the importance of the energetic coupling between the initial (reactant) and final (product) state. This effect is explored in the semi-classical Marcus theory [88] and will not be detailed here. 

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