Variations in Rotational Barriers of Allyl and Benzyl Cations, Anions, and Radicals

High accuracy quantum chemical calculations show that the barriers to rotation of a CH₂ group in the allyl cation, radical, and anion are 33, 14, and 21 kcal/mol, respectively. The benzyl cation, radical, and anion have barriers of 45, 11, and 24 kcal/mol, respectively. These barrier heights are related to the magnitude of the delocalization stabilization of each fully conjugated system. This paper addresses the question of why these rotational barriers, which at the Hückel level of theory are independent of the number of nonbonding electrons in allyl and benzyl, are in fact calculated to be factors that are of 2.4 and 4.1 higher in the cations and 1.5 and 1.9 higher in the anions than in the radicals. We also investigate why the barrier to rotation is higher for benzyl than for allyl in the cations and in the anions. Only in the radicals is the barrier for benzyl lower than that for allyl, as Hückel theory predicts should be the case. These fundamental questions in electronic structure theory, which have not been addressed previously, are related to differences in electron-electron repulsions in the conjugated and nonconjugated systems, which depend on the number of nonbonding electrons.