Pk. Chattaraj et al., Woodward-Hoffmann rule in the light of the principles of maximum hardness and minimum polarizability: DFT and ab initio SCF studies, J AM CHEM S, 122(2), 2000, pp. 348-351
Electrocyclic transformation between cis-butadiene and cyclobutene has been
studied at the HF and DFT levels with 6-311G** basis sets. The disrotatory
stationary point with two imaginary vibrational frequencies is associated
with higher energy and polarizability values and a smaller hardness value i
n comparison to those of the symmetry-allowed conrotatory transition state
for the thermolysis of cyclobutene. For cis-butadiene, the actual minimum e
nergy structure is of C-2 symmetry. cis-Butadiene and cyclobutene have ener
gy and polarizability values lower than those of both stationary points, an
d the respective hardness values are higher than the stationary point hardn
ess values.