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

By using direct and indirect electrochemical methods, rate constants (k,,) for cyclopropane ring opening of radical anions derived from the one-electron reduction of trans-1-benzoyl-2-phenylcyclopropane, trans-1-benzoyl-2-vinyleyclopropane, 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 substiments 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 thermochernical cycle for estimating Delta G degrees for ring opening was presented. For simple cyclopropyl-containg ketyl anions, a reasonable correlation between log(k(o)) and Delta G degrees 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(k(o)). The derived log(k(o)) and Delta G degrees and log(k(o)) vs Ea plots provide the basis for a "calibration curve" to predict rate constants for ring opening of radical anions derived from carbonyl compounds, in general.