Radiationless electron transfer, quantum mechanical treatment

The first quantum mechanical treatment for the radiationless electron transfer was developed by Gurney [68] for hydrogen evolution on mercury. In his model, Gurney assumed that the intermediate H " is not... 

The quantum mechanical treatment of non-adiabatic electron transfers are normally considered in terms of the formalism developed for multiphonon radiationless transitions. This formalism starts from Fermi s golden rule for the probability of a transition from a vibronic state Ay of the reactant (electronic state A with vibrational level v) to a set of vibronic levels B of the product... 

The basic idea of the theory of electron-transfer concerning the dynamic role of the solvent, first suggested by LIBBI /150/, has been developed by MARCUS /40a/ for outer-sphere redox processes on the basis of a classical continuum model for solvent polarization. A quantum-mechanical treatment of the same model was done by LEVICH and DO-GONADZE /40b,143/, making use of the theory of non-adiabatic radiationless electron transfer in polar crystals. 

In the quantum mechanical formulation of electron transfer (Atkins, 1984 Closs et al, 1986) as a radiationless transition, the rate of ET is described as the product of the electronic coupling term J2 and the Frank-Condon factor FC, which is weighted with the Boltzmann population of the vibrational energy levels. But Marcus and Sutin (1985) have pointed out that, in the high-temperature limit, this treatment yields the semiclassical expression (9). 

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