Dielectric continuum model, electron-transfer

Since Eq. (28) was obtained under assumptions similar to those used by Born, the calculation of AGq suffers from the same limitations as the Born solvation model. The dielectric continuum model is valid for electron transfer in a structureless dielectric medium with a reactant approximated by a hard conducting sphere. It is obeyed when the specific solute-solvent interactions are negligible. 

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. 

In this section we refer, selectively, to studies of medium effects on the rates of electron transfer reactions, which can be classed as equilibrium effects in the sense that they affect the stability, but not the lifetime of the transition state. The principle of calculating solvent reorganization energies, Aout equation (7), in terms of a dielectric continuum model has been critically examined and placed on a sounder thermodynamic basis than before. The two equations frequently cited are (9a) and (9b), where D, and Dy are the displacement, or induction,... 

Unlike most of the articles in Comprehensive Coordination Chemistry II this chapter is not a review. Exploration of charge transfer on the nanoscale is just beginning. We anticipate that, over the first few years of the twenty-first century and beyond, coordination complexes and coordination chemistry approaches will be exploited extensively to create new materials of both fundamental and applied importance. Here we try to provide tools to assist coordination chemists who engage in this exciting new research area. We provide a broad overview of types of systems that may be important in the future, with lead-in references, and analyses of the energetics and electron transfer barriers from a dielectric continuum model for a range of conditions. 

The classical theory of electron transfer developed by Marcus starts with the same kind of hard spheres in a dielectric continuum model that is used to derive the free energy of solvation of an ion. A central role in the theory is played by the reorganisation energy X, which in its simplest definition is given by... 

The complexity of an exact treatment of the solvent effects on intramolecular electron transfer has precluded such an analysis until now. Thus one has to use, for some time still further, macroscopic models such as the dielectric continuum model. Such models have indeed good predictive properties but they fail to describe specific solvent effects such as the donor ability or the H bonding ability. Even the more sophisticated quantum model, in its present form, is an oversimplification since the solvent motion is described by a single vibrational mode. The quantum model has some success because the vibronic levels corresponding to solvent modes are so closely spaced that in fact they can be approximated by a continuum. There is no doubt however that the progress in computing ability will allow in the future the simulation of the exact behaviour of the solvent in these reactions. 

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 a recent upsurge of studies on electron transfer kinetics, importance was placed on the outer shell solvent continuum, and the solvent was replaced by an effective model potential or a continuum medium with an effective dielectric constant. Studies in which the electronic and molecular structure of the solvent molecules are explicitly considered are still very rare. No further modem quantum mechanical studies were made to advance the original molecular and quantum mechanical approach of Gurney on electron and proton (ion) transfer reactions at an electrode. 

The theoretical modeling of electron transfer reactions at the solution/metal interface is challenging because, in addition to the difficulties associated with the quantitative treatment of the water/metal surface and of the electric double layer discussed earlier, one now needs to consider the interactions of the electron with the metal surface and the solvated ions. Most theoretical treatments have focused on electron-metal coupling, while representing the solvent using the continuum dielectric media. In keeping with the scope of this review, we limit our discussion to subjects that have been adi essed in recent years using molecular dynamics computer simulations. 

The Marcus treatment uses a classical statistical mechanical approach to calculate the activation energy required to surmount the barrier. It assumes a weakly adiabatic electron transfer process and non-equilibrium dielectric polarization of the solvent (continuum) as the source of activation. This model also considers the vibrational contributions of the inner solvation sphere. The Hush treatment considers ion-dipole and ligand field concepts in the treatment of inner coordination sphere contributions to the energy of activation [55, 56]. 

The energy spacings between levels associated with solvent dipole reorientations are small, 1-10 cm-1. Since the spacings are well below kBT at room temperature ( 200 cm-1), the contribution of the solvent to the energy 6f activation for electron transfer can be treated classically. The results of classical treatments, where the solvent is modelled as a structureless dielectric continuum, will be discussed in later sections. 

With respect to the solvation energy, this is usually approximated by modeling the reactants and products as spheres and the solvent as a dielectric continuum (Bom theory), which in the case of an interface electron transfer gives rise to the following expression [30, 36] ... 

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... 

A simple way to model this effect is to treat the solvent as a dielectric continuum. This treatment often fails quantitatively, but is a useful qualitative framework in which to consider solvent effects. For example, the effect of solvent on the driving force for electron transfer, AG°, is given by Eq. 3, which is taken from the work of Weller [7]. This treatment assumes electron transfer from the first excited singlet state of a donor D to an acceptor A and... 

---