Woodward-Hoffmann rule in the light of the principles of maximum hardness and minimum polarizability: DFT and Ab initio SCF studies

Electrocyclic transformation between cis-butadiene and cyclobutene has been studied at the HF and DFT levels with 6-311Gαα basis sets. The disrotatory stationary point with two imaginary vibrational frequencies is associated with higher energy and polarizability values and a smaller hardness value in comparison to those of the symmetry-allowed conrotatory transition state for the thermolysis of cyclobutene. For cis-butadiene, the actual minimum energy structure is of C₂ symmetry, cis-Butadiene and cyclobutene have energy and polarizability values lower than those of both stationary points, and the respective hardness values are higher than the stationary point hardness values.