Electron-transfer reaction continuum theory

Electron transfer reactions, treated by continuum theory, suggested that the Franck-Condon barrier (the barrier for the vertical transition of electrons), which is about four times the activation barrier for the isotopic electron transfer in solution, is due to Bom continuum solvation processes. Specific contributions for the activation of ions come from the solvent continuum far from the ion the important contribution from the solvent molecules oriented toward the central ion in the first and second solvation shells is neglected. ... 

The molecular models of electron transfer reactions are in general much more complicated and do not generate the simple relations of the free energy of activation as in the continuum theory. However, it is important to focus on alternative molecular models at this time because of the fundamental flaws of continuum theory and its inconsistencies with experiments, as pointed out earlier. 

The double adiabatic approach provides a convenient starting point for a detpt theory (2i). The principle modification is the treatment of the FC factors for the overlap of the proton initial and final eigenstates, when the final proton state is characterized by a repulsive surface. The sum over final proton states becomes an integration over a continuum of states, and bound-unbound FC factors need to be evaluated. An approach can be formulated with methods that have been used to discuss bond-breaking electron-transfer reactions (22). If the motion along the repulsive surface for the dissociation can treated classically. 

Unlike the original Marcus theory, which uses the continuum model for solvent, the method described above can provide a microscopic picture for the solvent fluctuation. It will be of great interest to explore the chemistry of the electron transfer reaction, including the specific dependence of the rate constant on the variety of solute and solvent. 

Dogonadze, Kuznetsov, and Levich " DKL) treat proton transfer in the same way (i.e., in terms of continuum solvent fluctuation) as that for simple electron transfer reactions, where no breakage or formation of bonds is involved. The reaction takes place only as a result of continuum solvent polarization fluctuation without taking into consideration the stretching of the H-OH2 bond and is not connected with the thermal heat sink, which is supposed to give the activated states in other theories. 

Another example of a process in which a charge is moved across an interface is interfacial electron transfer reactions. As in the case of ion transfer, experimental data on electron transfer across liquid-liquid interfaces are very limited. For this process, however, there exists a theoretical framework developed within a dielectric continuum model,which built on the fundamental theory of electron transfer in bulk media. Computer simulations, which complement experiments and theory, have not yet dealt with chemically realistic systems but, instead, considered idealized molecules to test the basic assumptions of the continuum model. 

In this article, a brief discussion will be given on the relevance of continuum theory in explaining the rate of electron transfer and the activation of species in solution we will concentrate in particular on molecular and quantum mechanical models of ET reactions at the electrode/electrolyte interface that are needed to replace those based on the continuum approach. ... 

Molecular modeling treatments of electron transfer kinetics for reactions involving bond breaking were developed much earlier than the continuum theories originated by Weiss in 1951. Gurney in 193l published a landmark paper (the foundation of quantum electrochemistry) on a molecular and quantum mechanical model of proton and electron transfer... 

It was recently shown (Ratner and Levine, 1980) that the Marcus cross-relation (62) can be derived rigorously for the case that / = 1 by a thermodynamic treatment without postulating any microscopic model of the activation process. The only assumptions made were (1) the activation process for each species is independent of its reaction partner, and (2) the activated states of the participating species (A, [A-], B and [B ]+) are the same for the self-exchange reactions and for the cross reaction. Note that the following assumptions need not be made (3) applicability of the Franck-Condon principle, (4) validity of the transition-state theory, (5) parabolic potential energy curves, (6) solvent as a dielectric continuum and (7) electron transfer is... 

This multistate continuum theory has been generalized for charge-transfer reactions involving Ng transferring electrons and Np transferring protons. For this general case, the solute is represented by a VB model containing VB states. The free... 

The multistate continuum theory for PCET provides a framework for the analysis of the effects of specific solute and solvent properties on the rates and mechanisms of PCET reactions. The properties of interest include the relative energies of the gas phase solute charge transfer states, the distance between the proton donor and acceptor, the distance between the electron donor and acceptor, and the solvent polarity. In Ref. [32], a comprehensive study of the effects of these physical properties on the rates, mechanisms, and kinetic isotope effects of PCET reactions is presented. Some of the predictions obtained from this study are discussed in this section. 

Quantum mechanical approaches for describing electron transfer processes were first applied by Levich [4] and Dogonadze, and later also in conjunction with Kuznetsov [5]. They assumed the overlap of the electronic orbitals of the two reactants to be so weak that perturbation theory, briefly introduced in the previous section, could be used to calculate the transfer rate for reactions in homogeneous solutions or at electrodes. The polar solvent was here described by using the continuum theory. The most important step is the calculation of the Hamiltonians of the system. In general terms the latter are given for an electron transfer between two ions in solution by... 

Classical and semi-classical theories of electron transfer provide quantitative models for determining the reaction pathway. Of particular importance is the theory of nonequilibrium solvent polarization based on the dielectric continuum model.5 From these theories Eqs. 

The transition state theory assumes that as the reacting species proceeds over the energy barrier, the medium adjusts rapidly enough to stay in equilibrium. Classical electron-transfer theory takes the first step away from this idea by distinguishing rapid and slow polarization due to electronic and atomic motion, respectively. More recently, as faster reactions have been studied, interest has turned to the effects of rates of motion of solvent molecules. It is still possible to retain the notion of the solvent as a continuum, by introducing polarizations that respond at... 

Photoinduced ET in binuclear complexes with localized electronic states provides at the moment the best test of theory predictions for the solvent dependent ET barrier. This type of reaction is also called metal-metal charge-transfer (MMCT) or intervalence transfer (IT). The application of the theory to IT energies for valence localized biruthenium complexes and the acetylene-bridged biferricenium monocation revealed its superiority to continuum theories. The plots of E vs. E p are less scattered, and the slopes of the best-fit lines are closer to unity. As a major merit, the anomalous behavior of some solvents in the continuum description - in particular HMPA and occasionally water - becomes resolved in terms of the extreme sizes, as they appear at the opposite ends of the solvent diameter scale. 

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