Electron transfer: Marcus theory

BAND STRUCTURE CALCULATIONS AND ELECTRON TRANSFER MARCUS THEORY... 

We now turn to the hierarchy of electron-transfer rate theories that have developed since the 1950s, starting with classical Marcus theory of homogeneous reactions and the development of eq. 4.4. In later sections we shall consider theories of nonadiabatic ET, which allow the identification and evaluation of the prefactor A in eq. 4.4, and also electrochemical ET, which differs from homogeneous reactions in that an electronic conductor is one of the reactants . 

An alternative approach to describe charge transport in polarizable media uses Marcus s electron transfer (ET) theory. Originally, the theory aimed at describing electron transfer from an electron donor to an electron acceptor in solution, according to... 

On the other hand, it is striking to note that transition state theory has been applied extensively in quantum chemistry ever since the computational facilities needed for this were made available, while Marcus Electron Transfer (ET) theory has only been used systematically since the last decade. 

Starting with transition state theory and assuming simple quadratic potential surfaces with equal force constants (curvature) for the initial and final states, Marcus derived an expression for the rate of thermal electron transfer (Marcus, 1956) ... 

Turning to the Marcus theory of electron transfer (Marcus and Sutin (1985)) for guidance in efforts to improve the 4% overall yield of charge separated species, we note that in other studies of dyad systems in solvents such as methylene chloride the total reoiganization energy, X, is around... 

Eig. 2. Electron-transfer reaction rate, vs exoergicity of reaction the dashed line is according to simple Marcus theory the soUd line and data poiats are... 

This section contains a brief review of the molecular version of Marcus theory, as developed by Warshel [81]. The free energy surface for an electron transfer reaction is shown schematically in Eigure 1, where R represents the reactants and A, P represents the products D and A , and the reaction coordinate X is the degree of polarization of the solvent. The subscript o for R and P denotes the equilibrium values of R and P, while P is the Eranck-Condon state on the P-surface. The activation free energy, AG, can be calculated from Marcus theory by Eq. (4). This relation is based on the assumption that the free energy is a parabolic function of the polarization coordinate. Eor self-exchange transfer reactions, we need only X to calculate AG, because AG° = 0. Moreover, we can write... 

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. ... 

R. A. Marcus (California Institute of Technology) contributions to the theory of electron transfer reactions in chemical systems. 

Applications of the Marcus theory are by no means limited to electron transfer. The generality of this approach has been cited.38... 

Figure 42. Scheme comparing expected potential-independent charge-transfer rates from Marcus-Gerischer theory of interfacia) electron transfer (left) with possible mechanisms for explaining the experimental observation of potential-dependent electron-transfer rates (right) a potential-dependent concentration of surface states, or a charge-transfer rate that depends on the thermodynamic force (electric potential difference) in the interface. 

Marcus theory can be applied to any single-step process where something is transferred from one particle to another. It was originally derived for electron... 

The ZN formulas can also be utihzed to formulate a theory for the direct evaluation of thermal rate constant of electronically nonadiabatic chemical reactions based on the idea of transition state theory [27]. This formulation can be further utilized to formulate a theory of electron transfer and an improvement of the celebrated Marcus formula can be done [28]. 

Figure 23. Arrhenius plot of the electron transfer rate. The electronic coupling strength is TIad = 0.0001 a.u. Solid line-Bixon-Jortner perturbation theory Ref. [109]. FuU-circle present results of Eq. (26 ). Dashed line-results of Marcus s high temperature theory [Eq.(129)]. Taken from Ref. [28].

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