Dogonadze-Kuznetsov-Levich model

On the other hand, in the Dogonadze-Kuznetsov-Levich model the tunneling from the zero level of the initial state to the zero level of the final state is the main process. This result of the theory can be explained if we take into account the dynamic role of the solvent. The processes that could occur in the Horiuti-Polanyi model as a result of improbable casual coincidences become not only possible now, but are even obligatory for any value of the electrode potential. Indeed, for almost any arrangement of the zero levels of the initial and final equilibrium states, there is always a possibility of their equalization owing to fluctuations in the polarization of the solvent interacting with a proton. 

In 1967, Dogonadze, Kuznetsov, and Levich began the development of a theoretical model that would account for the full quantum nature of the transferring proton [10, 18, 52, 53]. In contrast to the model based on transition state theory where the quantum properties of the proton are an ad hoc addition to the model,... 

The Levich—Dogonadze—Kuznetsov (LDK) treatment [65] considers that the only source of activation is the polarization electrostatic fluctuations (harmonic oscillations) of the solvent around the reacting ion and uses essentially the same model as the Marcus—Hush approach. However, unlike the latter, it provides a quantum mechanical calculation of both the pre-exponential factor and the activation energy but neglects intramolecular (inner sphere) vibrations (1013—1014 s 1). 

Dogonadze and Kuznetsov showed for the first time the way to take into account the processes of transfer of heavy particles for reactions in liquids. This work was the basis for the first simplest quantum mechanical model of the electrochemical proton transfer process which was proposed by Dogonadze, Kuznetsov, and Levich in 1967 (see also Ref. 33). The expressions and conclusions of Dogonadze and Kuznetsov s work were used in a number of subsequent papers (also in some recent works, see, e.g.. Ref. 34). Therefore, it is necessary to consider this approach in more detail. 

The next step was taken by Dogonadze, Kuznetsov, and Levich[91], who extended these ideas to the more complex reaction of the cathodic evolution of hydrogen. An important stage in subsequent development of the theory was the establishment of the concept of quantum-mechanical and classical degrees of freedom[204], which led to a substantiation of the analysis of a number of specific reactions, and the development of a more detailed model of the polar medium (taking into account the spatial and frequency dispersion of permittivity)[205]. 

An important achievement of the early theories was the derivation of the exact quantum mechanical expression for the ET rate in the Fermi Golden Rule limit in the linear response regime by Kubo and Toyozawa [4b], Levich and co-workers [20a] and by Ovchinnikov and Ovchinnikova [21], in terms of the dielectric spectral density of the solvent and intramolecular vibrational modes of donor and acceptor complexes. The solvent model was improved to take into account time and space correlation of the polarization fluctuations [20,21]. The importance of high-frequency intramolecular vibrations was fully recognized by Dogonadze and Kuznetsov [22], Efrima and Bixon [23], and by Jortner and co-workers [24,25] and Ulstrup [26]. It was shown that the main role of quantum modes is to effectively reduce the activation energy and thus to increase the reaction rate in the inverted... 

How does the electron transfer occur in a redox process One description of this process was developed by Gerischer, based on the former work of Gurney and Essin. Another description goes back to the work of Marcus.Other contributions during the development of the basic theory came from Dogonadze, Levich, Chizmadzhev, Kuznetsov, and others. The model will be described for a simple redox reaction, the oxidation of a two-valent iron ion into a three-valent iron ion and vice versa. 

---