Marcus theory high-temperature limit

The theory of the multi-vibrational electron transitions based on the adiabatic representation for the wave functions of the initial and final states is the subject of this chapter. Then, the matrix element for radiationless multi-vibrational electron transition is the product of the electron matrix element and the nuclear element. The presented theory is devoted to the calculation of the nuclear component of the transition probability. The different calculation methods developed in the pioneer works of S.I. Pekar, Huang Kun and A. Rhys, M. Lax, R. Kubo and Y. Toyozawa will be described including the operator method, the method of the moments, and density matrix method. In the description of the high-temperature limit of the general formula for the rate constant, specifically Marcus s formula, the concept of reorganization energy is introduced. The application of the theory to electron transfer reactions in polar media is described. Finally, the adiabatic transitions are discussed. 

We have thus found that in this high temperature, strong electron-phonon coupling limit the electronic transition is dominated by the lowest crossing point of the two potential surfaces, that is, the system chooses this pathway for the electronic transition. It is remarkable that this result, with a strong characteristic of classical rate theory, was obtained as a limiting fonn of the quantum golden-rule expression for the transition rate. Equation (12.69) was first derived by Marcus in the context of electron transfer theory (Chapter 16). 

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