Continuum dielectric theory of electron transfer processes

Continuum dielectric theory of electron transfer processes 

An electron transfer process is essentially a change in the electronic charge distribution in the molecular system. For example, an electron transfer between species A and B is schematically described by the following transition from the electronic states 0 and 1 

As in our simple treatment of solvation dynamics in Chapter 15, the solvent in Marcus theory is taken as a dielectric continuum characterized by a local dielectric function ( )). Thus, the relation between the source, D (electrostatic displacement) and the response, (electric field) is (cf. Eqs (15.1) and (15.2)) 

Following Marcus, we simplify this picture by assuming that the solvent is characterized by only two timescales, fast and slow, associated, respectively with its electronic and the nuclear response. Correspondingly, the solvent dielectric response function is represented by the total, or static, dielectric coefficient Sg and by its fast electronic component Sg (sometimes called optical response and related to the refraction index n by Sg = n ). includes, in addition to the fast electronic component, also contributions from solvent motions on slower nuclear timescales Translational, rotational, and vibrational motions. The working assumption of the 

Marcus theory is that the actual change in the electronic charge distribution of the ET system is fast relative to the nuclear motions underlying the static response, but is slow relative to the electronic motions which determine s. In other words the electron transfer occurs at constant nuclear polarization, or at fixed nuclear positions. This is an expression of the Franck-Condon principle in this continuum dielectric theory of electronic transitions. 

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CONTINUUM DIELECTRIC THEORY OF ELECTRON TRANSFER PROCESSES... 

Continuum dielectric theory of electron transfer processes 16.3.3 Transition assisted by dielectric flnctnations... 

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. 

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... 

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