Activation/driving force relationships for cyclopropylcarbinyl --> homoallyl-type rearrangements of radical anions

By using direct and indirect electrochemical methods, rate constants (ko) for cyclopropane ring opening of radical anions derived from the one-electron reduction of trans-1-benzoyl-2-phenylcyclopropane, trans-1-benzoyl-2-vinylcyclopropane, 2-methylenecyclopropyl phenyl ketone, spiro[anthracene-9,1'-cyclopropan-10-one], 3-cyclopropylcyclohex-2-en-1-one, and 3-(1-methylcyclopropyl)cyclohex-2-en-1-one were determined. Qualitatively, rate constants for ring opening of these (and other cyclopropyl- and cyclobutyl-containing radical anions) can be rationalized on the basis of the thermodynamic stability of the radical anion, the ability of substituents on the cyclopropyl group to stabilize the radical portion of the distonic radical anion, and the stability of the enolate portion of the distonic radical anion. On the basis of this notion, a thermochemical cycle for estimating deltaG(o) for ring opening was presented. For simple cyclopropyl-containing ketyl anions, a reasonable correlation between log(ko) and deltaG(o) was found, and stepwise dissociative electron transfer theory was applied to rationalize the results. Activation energies calculated with density functional theory (UB3LYP/6-31+G*) correlate reasonably well with measured log(ko). The derived log(ko) and deltaG(o) and log(ko) vs E(a) plots provide the basis for a "calibration curve" to predict rate constants for ring opening of radical anions derived from carbonyl compounds, in general.