Pekar model

The Holstein model was preceded by the Pekar model [34] and in chemistry by the Marcus model [6]. In chemistry donor-acceptor systems are more frequent objects of study than conducting wires but the coupling between electronic and nuclear motion of similar nature. For example if the coupling is large a small nuclear displacement is sufficient to change the wave function much and in a way which corresponds to ET or EET. We use the effective, many-electron Hamiltonian H of eq.(4) and assume that it is solved for donor and acceptor, giving the energies Haa and Hdd, respectively. We use the new nuclear coordinates ... 

Pekar, M, Pavlova, N. Erdman, L., Ilyin, I., Strukov, B., Gusev, A., Dutchak, S. (1998). Long-Range Transport of Persistant Organic Pollutants. Development of Transport Models for Undone, Polychlorinated Biphenyls, Benzo(a)pyrene. EMEP/MSCE-E Report 2/98. 

Thus, the medium dielectric constant e is varied by 40%, while Pekar s factor y is changed by 14% in the whole range of available viscosities. The change in e affects the Coulomb interactions in the [Ru3+ MV+] pair, while the change in y affects the outer-sphere reorganization energy. The viscosity dependence of both e and y is accurately interpolated by the two-exponential model function... 

Here, what said in Section 4.2 about time-dependent perturbations is worth recalling, trying to give a more detailed analysis. The best approach to treat problems characterized by the presence of a P(t) function is provided by the quantum electrodynamics theories, where P is described in terms of an expansion over normal modes of the dielectric polarization. This model can be simplified by considering only two terms, often called the fast and the slow contribution to P (the Pekar separation introduced in eq.(18) of Section 4.2) ... 

In recent years, the pre-transition-state idea of Gurney has been taken up again by Dogonadze, Levich, and co-workers, H who have used a model for the classical subsystem that is based on Landau s work, " and which was applied by Mott and Gurney and Pekar to crystals, and in modified form by Libby and Weiss to electrolytes. This idea makes use of continuum physics to obtain a description of the potential energy of an ion in solution, in a highly simplified model which is purely electrostatic. 

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