The role of σ and π stabilization in benzene, allyl cation and allyl anion. A canonical orbital energy derivative study

The orbital energy second derivatives with respect to the CC asymmetric stretchibng mode of benzene, allyl cation and allyl anion show unambigiously that the π orbitals are unstable with respect to a distorted geometry with alternating CC bonds. It is the σ frame which enforces the D6h form of benzene and the C2v form of the allyl anion.