Marcus equation electron transfer

Manganese(IV) complexes magnetic behavior, 272 Manganese(V) complexes magnetic behavior, 272 Mannich reaction metal complexes, 422 Marcus cross-reaction equation electron transfer, 355 Marcus Hush theory electron transfer, 340 Masking... 

So far our discussion of slow proton-transfers and Bronsted exponents has been a qualitative one, apart from the crude electrostatic model represented by Figures 15 and 16. Recently considerable use has been made of a general equation relating the rate of a reaction to its standard free energy change, which was first derived by Marcus for electron-transfer reactions, and later applied by him and by others to reactions involving the transfer of atoms or protons. For present purposes the Marcus equation can be written as ... 

Equation (5-69) is an important result. It was first obtained by Marcus " in the context of electron-transfer reactions. Marcus derivation is completely different from the one given here. In electron transfer from one molecule (or ion) to another, no bonds are broken or formed, so the transition state theory does not seem to be applicable. Marcus assumed negligible orbital overlap in the electron-transfer transition state, but he later obtained the same equation for group transfer reactions requiring significant overlap. Many applications have been made to proton transfers and nucleophilic displacements. ... 

Both Marcus27 and Hush28 have addressed electron transfer rates, and have given detailed mathematical developments. Marcus s approach has resulted in an important equation that bears his name. It is an expression for the rate constant of a net electron transfer (ET) expressed in terms of the electron exchange (EE) rate constants of the two partners. The k for ET is designated kAS, and the two k s for EE are kAA and bb- We write the three reactions as follows ... 

In many cases, the values of A n and k2i may be directly or indirectly determined. We shall say no more about this relationship here, other than to indicate that it proves to be generally applicable, and is sufficiently accepted that the Marcus-Hush equation is now used to establish when an outer-sphere pathway is operative. In the context of this chapter, the involvement of the Kn term is interesting for it relates to the relative stabilization of various oxidation states by particular ligand sets. The factors which stabilize or destabilize particular oxidation states continue to play their roles in determining the value of Kn, and hence the rate of the electron transfer reaction. 

Excited state electron transfer also needs electronic interaction between the two partners and obeys the same rules as electron transfer between ground state molecules (Marcus equation and related quantum mechanical elaborations [ 14]), taking into account that the excited state energy can be used, to a first approximation, as an extra free energy contribution for the occurrence of both oxidation and reduction processes [8]. 

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 5, Relationship of the activation free energy for electron transfer with the electrode potentials of various FeL33 according to Equation 6 (left), and the driving force according to the Marcus Equation 4 (right).

Figure 16. Relationship between the activation jree energy and the driving force for electron transfer for alkylmetals to TCNE (left) and IrCl6z (right) according to Marcus Equation 4.

Marcus, R. A. Schrodinger equation for strongly interacting electron-transfer systems, J.Phys.Chem., 96 (1992), 1753-1757... 

The coordinate pertaining to solvent reorganization, z, is the same fictitious charge number as already considered in the Hush-Marcus model of outer-sphere electron transfer (Section 1.4.2), and so is the definition of 2q [equation (1.27)] and the difference between the Hush and Marcus estimation of this parameter. The coordinated describing the cleavage of the bond is the bond length, y, referred to its equilibrium value in the reactant, yRX. Db is the bond dissociation energy and the shape factor ft is defined as... 

This equation, based on the Marcus model, therefore gives us a relationship between the kinetics (kEr) and the thermodynamic driving force (AG°) of the electron-transfer process. Analysis of the equation predicts that one of three distinct kinetic regions will exist, as shown in Figure 6.24, depending on the driving force of the process. 

As can be seen, the increase in separation between the electrode surface and the redox-active site operated by the variable-in-length carbon chain from (CH2)3 to (CH2)n makes the process change from electrochemically reversible to irreversible. In fact, in agreement with the (simplified) Marcus equation, ket = 1013/e, the rate of the electron transfer is considerably reduced with the distance d. 

In the previous section, we alluded to the Franck Condon factors (FCF) in controlling electron transfer rates. For this topic, detailed reviews of theory and experiment are provided elsewhere. In sum, it is now well known that the reaction free energy required to transfer charge can be reduced by the reaction free energy, AG°, as summarized in the famous Marcus equation AG = (AG° — where X, the reorganization energy, is related to the degree of... 

On the basis of the very negative activation entropies, the transition states for the addition are highly ionic, i.e. there is a large degree of electron transfer in the transition state as with the hydroxyalkyl radicals (Sect. 2.1.1). In support of this is the fact that the rate constants for addition depend on the reduction potentials of the nitrobenzenes, varied by the substituent R3 in a way describ-able by the Marcus equation for outer-sphere electron transfer [19]. 

Symbolized by A, the reorganization energy of a one-electron transfer reaction is that energy needed for all structural adjustments, not only in the two reactants but in the neighboring solvent molecules as well, required for the two reactants to assume the correct configuration needed to transfer the sole electron. See Intrinsic Barrier Marcus Equation... 

Electron-pair donor (or Lewis base), NUCLEOPHILE ELECTRON SINK ELECTRON SPIN RESONANCE ELECTRON TRANSEER MARCUS EQUATION ELECTRODE KINETICS Electron transfer mechanism,... 

By measuring the temperature dependence of kex, activation parameters (Aff and AS ) could be calculated and were reported. However, I am not sure how to physically interpret these numbers. The temperature dependence of rate can be fit to other expressions, and here it is fit to the Marcus equation for nonadiabatic electron transfer in the case of degenerate electron transfer (e.g., AG° = 0)... 

In the case of electron transfer reaction, a modification of Equation 17.1 due to R. Marcus has been proposed.14-16... 

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