Resonance effect in the allyl cation and anion: a revisit

The interest over the magnitude of the conjugation effect in the allyl cation (1) and anion (2) has been revived recently by Barbour and Karty (J. Org. Chem. 2004, 69, 648-654), who derived the resonance energies of 20-22 and 17-18 kcal/mol for 1 and 2, respectively, using an empirical extrapolation approximation. This paper revisits the case by explicitly calculating the Pauling-Wheland resonance energy, which measures the stabilization from the most stable resonance structure to the delocalized energy-minimum state of a conjugated system, using our newly developed block-localized wave function (BLW) method. This BLW method has the geometrical optimization capability. The computations result in adiabatic resonance energies of 37 kcal/mol for 1 and 38 kcal/mol for 2. The significant disagreement between these values and Barbour and Karty's results originates from the neglect of structural and electronic variations in their derivation which are energy costing.