Solvent effect dielectric continuum mode

The concentration dependence of ionic mobility at high ion concentrations and also in the melt is still an unsolved problem. A mode coupling theory of ionic mobility has recently been derived which is applicable only to low concentrations [18]. In this latter theory, the solvent was replaced by a dielectric continuum and only the ions were explicitly considered. It was shown that one can describe ion atmosphere relaxation in terms of charge density relaxation and the elctrophoretic effect in terms of charge current density relaxation. This theory could explain not only the concentration dependence of ionic conductivity but also the frequency dependence of conductivity, such as the well-known Debye-Falkenhagen effect [18]. However, because the theory does not treat the solvent molecules explicitly, the detailed coupling between the ion and solvent molecules have not been taken into account. The limitation of this approach is most evident in the calculation of the viscosity. The MCT theory is found to be valid only to very low values of the concentration. 

Onsager s SCRF is the simplest method for taking dielectric medium effects into account and more accurate approaches have been developed such as polarizable continuum modes, " continuum dielectric solvation models, - explicit-solvent dynamic-dielectric screening model, - and conductor-like screening model (COSMO). Extensive refinements of the SCRF method (spherical, elliptical, multicavity models) in conjunction with INDO/CIS were introduced by Zerner and co-workers ° as well. 

We present a derivation of the broadening due to the solvent according to a system/ bath quantum approach, originally worked out in the field of solid-state physics to treat the effect of electron/phonon couplings in the electronic transitions of electron traps in crystals [67, 68]. This approach has the advantage to treat all the nuclear degrees of freedom of the system solute/medium on the same foot, namely as coupled oscillators. The same type of approach has been adopted by Jortner and co-workers [69] to derive a quantum theory of thermal electron transfer in polar solvents. In that case, the solvent outside the first solvation shell was treated as a dielectric continuum and, in the frame of the polaron theory, the vibrational modes of the outer medium, that is, the polar modes, play the same role as the lattice optical modes of the crystal investigated elsewhere [67,68]. The total Hamiltonian of the solute (5) and the medium (m) can be formally written as... 

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. 

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