Degenerate electron-transfer reactions

Having discussed the electron-transfer reactions of cyclopropane derivatives in some detail, we only touch briefly on the related reactions of the larger ring systems. Cyclobutane, cyclohexane, and cyclooctane have degenerate HOMOs (Section 2.3.1) thus, their radical cations are Jahn-Teller active. It is reasonable to expect that suitable substitution will lift the degeneracy and favor one radical cation structure over the other. Qualitative predictions of the preferred structure are readily derived. 

Figure 3. Correlation between logA obs for the reaction of Cf,o with alkyl halides and logfcet for the electron-transfer reaction of Me4Q with the same alkyl halides in degenerated PhCN at 298 K [161],...

The first quantum mechanical calculations for nonadiabatic electrochemical electron transfer reactions at metals and semiconductors were performed by Dogonadze, Chizmadzhev, and Kuznetsov(1962-1964). In Ref. 27 the totally degenerated Fermi gas model was used to describe the state of the electrons in the electrode, and in Ref. 28 an integration over the energy spectrum was performed, taking account of the Fermi distribution of the electrons over a range of energy. Later that theory was extended to other processes at semiconductors and thin semiconductor films. 

Hale in 1968 calculated the limiting electric current for an electron transfer reaction associated with the activationless process. The degenerate Fermi gas model was used to describe the electrons in the metal. 

For heavily doped materials, either notp type, the surface is degenerated and the material behaves like a metal electrode, meaning that the charge transfer reaction in the Helmholtz double layer is the rate-determining step. This is supported by the lack of an impedance loop associated with the space charge for the heavily doped materials. Also, for heavily doped n-Si large current in the dark is due to electron injection, which is not characterized by a slope of 60 mV/decade. For p-Si, electron injection into the conduction band may also occur during the anodic dissolution. 

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