Electrochemical potential gap in radicals: Why organic radicals do not disproportionate in solution?

Abstract

The physical origin of the electrochemical potential gap (ΔE0 = E0Ox − E0Red) in radicals is discussed. It was shown that the EC gap in radicals is well approximated by two-electron Coulomb repulsion between the unpaired electron of the parent radical and an additional electron appeared in the SOMO after reduction. This repulsion prevents the disproportionation of radicals and makes possible their existence in solution. Assuming the density distribution of both electrons to be similar to that in the parent radical, the self-Coulomb integral of the spin density (K) provides a quantitative measure for the spin delocalization and for the estimation of a vertical electron transfer energy gap. Linear correlation between the experimentally measured electrochemical gaps and the integral K was found. Validity of the theoretical model was supported by experimental and computational data for a representative set of persistent radicals (46 examples).