Marcus Theory - The One-Electron Redox Reaction

The One-Electron Redox Reaction

Chemical reactions may lead to a substitution of a group in a molecule or a ligand in a complex, to the elimination of a group of the molecule or a ligand, or to a rearrangement of a molecule or complex. A chemical reaction may, however, also cause simply an exchange of charges between the reactants, and these redox reactions without making or breaking a bond seem to be quite simple in Inorganic Chemistry for ions and complexes. These reactions often become manifest by a change of colour, e.g. for ions or complexes of transition metal ions, but organic molecules, too, may change their colour by accepting or giving away an electron (like the herbicide Paraquat (4,4'-bipyridyl) which becomes blue when accepting an electron, thence the alternative name of methyl viologen). For this type of redox reactions R.A. Marcus has developed his theory. Here the trace of argument and the results are presented. For the mathematical development and details the original papers should be consulted.

In a redox reaction one partner acts as an electron donor D the other as an acceptor A. For a reaction to take place D and A must diffuse together. They form the precursor complex, usually a kinetic, unstable, solvated encounter complex, which by electron transfer is transformed to the successor complex, and finally this separates by diffusion. For a one electron transfer the reaction is

(D and A may already carry charges). Here k₁₂, k₂₁ and k₃₀ are diffusion constants, k₂₃ and k₃₂ rate constants of activated reactions. The total reaction may be diffusion controlled (the electron transfer step is faster than diffusion, every encounter leads to reaction) or activation controlled (the "equilibrium of association" is reached, the electron transfer step is slow, the separation of the successor complex is fast).