Marcus Levich framework

Placing these two cases in context, simple electron transfer (ET) is generally defined within the Marcus-Levich framework,... 

Despite the fact that electron transfer reactions at the electrode/electrolyte interface are of fundamental importance to many chemical processes, a quantitative understanding of the factors that influence the rate of these reactions is still lacking. Although the general theoretical framework was established many years ago by Marcus, Levich, Dogonadze, and oth-... 

Theoretical treatments of charge transfer at electrodes were developed by Gurney, Horiuti, and Eyring and the more recent work of Gerischer, Marcus, Hush, and Levich, among others, permitted the study of simple redox electrode reactions under the same theoretical framework developed for homogeneous redox reactions in solution. 

The basic theoretical framework for describing electron transfer in bulk solid/Uquid interfaces was developed in the 1960s (Marcus, 1965 Gerischer, 1970 Levich, 1970). Fundamentally, photoinduced electron injection from the molecular excited state to a semiconductor nanoparticle can be described as electron transfer from a discrete and localised molecular state to a continuum of delocalised k states in the semiconductor. As shown in Fig. 11.5, the reactant state corresponds to the electron in the molecular excited state and the product states correspond to the oxidised molecule and the transferred electron in the semiconductor conduction band. There is a continuous manifold of product states, corresponding to the injected electron at different electronic levels in the semiconductor. 

The adiabatic redox reactions at electrodes were first considered by MARCUS /40a,145/ in a classical (semiclassical) framework. lEVICH, DOGONADZE and KUSNETSOV /146,147/, SGHMICKLER and VIELSTICH /169/ a.o. have developed a quantum theory for non-adiabatic electron transfer electrode reactions based on the oscillator-model. The complete quantum-mechanical treatment of the same model by CHRISTOV /37d,e/ comprises adiabatic and non-adiabatic redox reactions at electrodes. 

Marcus[195] gave a quantitative interpretation of this idea and above all, the role of solvent rearrangement within the framework of the absolute rate theory. Later, he also extended these concepts to electrochemical processes[196]. Similar concepts were also developed by Hush[197,198]. An important result of this work was the establishment of the relation between the transfer coefficient for adiabatic reactions and the charge distribution in the transient state. Gerischer[93,199] proposed a very useful and lucid treatment of the process of electron transfer in reactions with metallic as well as semiconductor electrodes. While the works mentioned above were mainly based on transition state theory, a systematic quantum-mechanical analysis of the problem was started by Levich, Dogonadze, and Chizmadzhev[200-202] and continued in a series of investigations by the same group. They extensively used the results and methods of solid state physics, and above all the Landau-Pekar polaron theory[203]. 

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