Marcus nonadiabatic electron transfer

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)... 

The redox potentials of organic cofactors are directly responsible for controlling the equilibrium behavior of the corresponding cofactor-mediated electron transfer processes. The relative redox potentials of the cofactor and its redox partner are also intimately related to the rate of adiabatic electron transfer Ret through the classical Marcus equation [13, 14], and nonadiabatic electron transfer through the semi-classical Marcus equation [15, 16]. The direct dependence of both the kinetics and thermodynamics of electron transfer processes on the cofactor redox potential makes the control of these potentials a key determinant of the activity of redox proteins. 

Gosavi S. and Marcus R. A. (2000), Nonadiabatic electron transfer at metal surfaces , J. Phys. Chem. B 104, 2067-2072. 

The Marcus theory, as described above, is a transition state theory (TST, see Section 14.3) by which the rate of an electron transfer process (in both the adiabatic and nonadiabatic limits) is assumed to be determined by the probability to reach a subset of solvent configurations defined by a certain value of the reaction coordinate. The rate expressions (16.50) for adiabatic, and (16.59) or (16.51) for nonadiabatic electron transfer were obtained by making the TST assumptions that (1) the probability to reach transition state configuration(s) is thermal, and (2) once the reaction coordinate reaches its transition state value, the electron transfer reaction proceeds to completion. Both assumptions rely on the supposition that the overall reaction is slow relative to the thermal relaxation of the nuclear environment. We have seen in Sections 14.4.2 and 14.4.4 that the breakdown of this picture leads to dynamic solvent effects, that in the Markovian limit can be characterized by a friction coefficient y The rate is proportional to y in the low friction, y 0, limit where assumption (1) breaks down, and varies like y when y oo and assumption (2) does. What stands in common to these situations is that in these opposing limits the solvent affects dynamically the reaction rate. Solvent effects in TST appear only through its effect on the free energy surface of the reactant subspace. 

R.A. Marcus, Nonadiabatic processes involving quantum-like and classical-like coordinates with applications to nonadiabatic electron transfers, J. Chem. Phys., 81, 4494—4500 (1984). 

III. RELEVANT ELECTRON TRANSFER THEORY MARCUS S DESCRIPTION OF HETEROGENEOUS NONADIABATIC ELECTRON TRANSFER REACTIONS... 

The research groups of Lewis and Wasielewski estimated the rate constants of the charge separation (kcs) and recombination (kcR) between the nucleobase, which acts as the electron donor, and the electron acceptor at the loop position of the DNA hairpins, and also investigated the free energy dependence of the electron transfer rate. " It was found that the single-step electron transfer in DNA mediated by nucleobases can be described by the Marcus theory (4) developed for nonadiabatic electron transfer system. 

The Marcus equation for nonadiabatic electron-transfer reactions (Eq. B5.3.4), and the Forster theory that we discussed in Chap. 7 apply only to systems with weak intermolecular interactions, which we now can define more precisely as meaning that H21 lh steady-state approximation to the stochastic Liouville equation for a two-state reaction in this limit From Eqs. (BIO.1.15), (10.29a), (10.29b), and (10.30), we have... 

Gosavi S, Qin Gao Y, Marcus RA (2001) Temperature dependtmee of the electronic factor in the nonadiabatic electron transfer at metal and semiconductra- electrodes. J Electroanal Chem 500 71-77... 

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]. 

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... 

In general, for the types of linked donor-acceptor systems to be discussed in this review, electron transfer is assumed to occur in the nonadiabatic regime. That is, the mixing between the electronic state of the donor and acceptor before electron transfer occurs and the corresponding state after electron transfer is weak (< kBT) [9], The actual electron transfer event is assumed to be fast compared to the time scale of nuclear motions. Marcus has proposed [11, 15] that the electron transfer rate constant ke, is given by Eq. 1. 

The nontraditional example of applying the AMSA theory is connected with the treatment of electrolyte effects in intramolecular electron transfer (ET) reactions [21, 22], Usually the process of the transfer of the electron from donor (D) to acceptor (A) in solutions is strongly nonadiabatic. The standard description of this process in connected with semiclassical Marcus theory [35], which reduces a complex dynamical problem of ET to a simple expression of electron... 

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 . 

In the case where the electron transfer is faster than molecular reorganization (nonadiabatic transfer), the path for electron transfer in the dimer coordinate representation illustrated in Figure 2.2.7 can be decomposed in a vertical activation from the minimum of Vp to the Vp curve, followed by a relaxation to the equilibrium configuration of the product. Accordingly, the Marcus theory of electron transfer [23] introduces the reorganization energy X... 

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