Marcus simplified model

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... 

The fast component is clearly related to electronic polarization, Pfast = Pd, while the slow component, connected to nuclear motions of the solvent molecules, is often called the orientational polarization (Pslow = Pot), or inertial component (PsioW = Pin)- This simplified model has been developed and applied by many authors we shall recall here Marcus (see the papers already quoted), who first had the idea of using Psiow as a dynamical coordinate. For description of solvent dynamical coordinates in discrete solvent models see Warshel (1982) and other papers quoted in Section 9. 

Subsequently, Marcus extended his theory to electrochemical electron transfer reactions/ " However, the role played by the electron energy spectrum in the electrode in these works was not elaborated. All the calculations were performed for a simplified model, where the potential energy surfaces for different electronic states were replaced by two potential energy surfaces (one for the initial state and one for the final state). Further calculations have shown that such considerations do not enable us to explain the fact that the transfer coefficient, a, for electrochemical reactions takes values in the interval from 0 to 1. In particular, it does not enable us to explain the existence of barrierless and activationless process (see Chapter 3 by Krishtalik in this volume). 

We now turn to the electronically adiabatic ET reaction problem (cf. Sec. 2.2). There has been a spate oftheoretical papers [8,11 28,33,35,36,50] dealing with the possible role of solvent dynamics in causing departures from the standard Marcus TST rate theory [27,28] (although many of these deal with nonadiabatic reactions). The ET reaction considered is a simplified symmetric model, A1 2 A1/2 A1/2 A1/2, in a model solvent similar to CH3C1. The technical and computational... 

In order to further explore the validity of the stepwise modified Marcus model, we developed recently [85] a simplified EVB model which represents the given conduction chain by an explicit EVB, while representing the rest of the environment (protein and solvent) implicitly. This is done by using the same type of solute surface as in Eq. (8.8), while omitting the explicit solute-solvent and solvent-solvent terms (the t/ss and Uss terms) and replacing them by implicit terms using ... 

Outer-sphere electron-transfer from BPH2 to 1 involves ion pairing, local ordering of solvent molecules (coordination of water to M ), steric (/-butyl groups in BPH2) and orientational (specific orientations of both Donor and Acceptor) constraints. These phenomena are not consistent with the simplifying assumptions used to calculate essential parameters in theoretical models, such as that of Marcus, that relate standard free-energies... 

The semi-classical Marcus equation derives from quantum-mechanical treatments of the Marcus model, which consider in wave-mechanical terms the overlap of electronic wave-functions in the donor-acceptor system, and the effects of this overlap on electronic and nuclear motions (see Section 9.1.2.8 above). Such treatments are essential for a satisfactory theory of D-A systems in which the interaction between the reactant and product free-energy profiles is relatively weak, such as non-adiabatic reactions. A full quantum-mechanical treatment, unfortunately, is cumbrous and (since the wave-functions are not accurately known) difficult to relate to experimental measurements but one can usefully test equations based on simplified versions. In a well-known treatment of this type, leading to the semi-classical Marcus equation introduced in Section 9.1.2.8, the vibrational motions of the atomic nuclei in the reactant molecule (as well as the motions of the transferring electron) are treated wave-mechanically, while the solvent vibrations (usually of low frequency) are treated classically. The resulting equation, already quoted (Equation (9.25)), is identical in form with the classical equation (9.16) (Section 9.1.2.5), except that the factor... 

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