Electron transfer quantum-mechanical model

The theoretical aspects of electron transfer mechanisms in aqueous solution have received considerable attention in the last two decades. The early successes of Marcus Q, 2), Hush (3, 4), and Levich (5) have stimulated the development of a wide variety of more detailed models, including those based on simple transition state theory, as well as more elaborate semi-clas-sical and quantum mechanical models (6-12). 

In this article, a brief discussion will be given on the relevance of continuum theory in explaining the rate of electron transfer and the activation of species in solution we will concentrate in particular on molecular and quantum mechanical models of ET reactions at the electrode/electrolyte interface that are needed to replace those based on the continuum approach. ... 

Molecular modeling treatments of electron transfer kinetics for reactions involving bond breaking were developed much earlier than the continuum theories originated by Weiss in 1951. Gurney in 193l published a landmark paper (the foundation of quantum electrochemistry) on a molecular and quantum mechanical model of proton and electron transfer... 

A second concern for quantum mechanical models of electron-transfer is the level at which the model is constructed. There is a wide-range of possibilities, ranging from Hiickel and tight binding models which can be used for qualitative reasoning, to sophisticated ab initio methods. Likewise, time-dependent studies can be made with classical molecular dynamics (MD) simulations, or time-dependent quantum mechanical calculations. 

This states that the quantum mechanical model for diabatic electron transfer is given by the following expression ... 

Grigorov, L.N. and Chemavsky, D. S. (1972) Quantum-mechanical model of electron transfer from cytochrome to chlorophyll in photosynthesis, Biofizika, 17, 195-102. 

A remarkably modem quantum-mechanical model of electronic energy transfer was introduced in 1928 by Kallmann and London [7]. In their approach, two atoms with energy levels and are described by stationary Schrodinger equations... 

In these sections the classical, semiclassical, and quantum-mechanical models of electron transfer are outlined. In all three treatments the nuclear factors determining the rate are calculated using the zero-order or diabatic-energy surfaces. Interaction of these surfaces is necessary for the electronic factor to be nonzero. This interaction is introduced as a correction to the zero-order surfaces and determines the degree of adiabaticity of the reaction. 

The key step of the process is, of course, the electron- or energy-transfer step within the encounter complex (figure 5). Such a unimolecular step can be dealt with using classical or quantum mechanical models originally developed for electron-transfer processes [13,14] and later extended to... 

The question arises above which interaction energy must a reaction be considered to be adiabatic This is difficult to answer, especially for electrode reactions, because it depends on the distance of the reacting species during the electron transfer. In the case of reactions in homogeneous solutions, Newton and Sutin [10] have estimated for typical transition-metal redox reactions that V p 0.025 eV is a reasonable limit above which a reaction must be considered to be adiabatic. This problem will be discussed again later in connection with some quantum mechanical models for electron transfer. 

In all the previous models, the Boltzmann distribution is assumed to hold for the populations of the vibronic levels in the initial state. Thus it is assumed that the rate of electron transfer is slow with respect to the rate of equilibration between the different vibrational levels. This assumption is no longer true for ultrafast reactions which are currently studied by picosecond spectroscopy. In this case, the concept of a thermally averaged rate becomes meaningless. This situation has been recently discussed by Bixon and Jortner in the frame of a quantum mechanical model and it is clearly an open field of research. 

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