Vibrational potential energy electron transfer

Figure 8 Vibrational potential energy vs. configurational coordinate for electron transfer via vibronic coupling betweeg two symmetric states of a single oscillator A, initial state B, vibration-ally excited state B, thermally excited state X9 vibronic coupling parameter E f optical transition energy E t thermal transition energy (Reproduced with permission from Ref 33 Copyright 1987 The Clay Minerals Society) ...

In fact, electron transfer occurs at the microscopic level where quantum mechanics provides the necessary description of the phenomenon (5-13). In the quantum mechanical solution, associated with the potential curves in Figure 1 are quantized energy levels, Ej = (vj + 1/2) 100., where Vj and 2ttvj are the vibrational... 

A typical example of a special state is as follows. Electron transfer reactions at an atom are aided by vibrations that equilibrate the interatomic distances that differ for the two oxidation states. Thus a low-energy, high-amplitude vibration is desirable. The vibration could have the further function that it provided a time-dependent fluctuation of the redox potential. As I and Goldanskii in this volume have pointed out, this allows a precise matching of the redox potential of one redox couple with another leading to tunneling of electrons. 

An objection to consideration of vibrational states above the ground state (Levich, 1970) was that if such states were indeed involved in electron transfer, then there would be no smooth Tafel lines because as a change in overpotential altered the energy of the Fermi level (from which, e.g., cathodic electrons come), matching levels in the solution species would not be available until the next vibrational state, perhaps 1/2 eV away, was reached by the change in the electrode potential. Hence, in this picture, the... 

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