Semiclassical Quantum Mechanics, Bond Delocalization and the Mills–Nixon Effect

Abstract

Conjugated π electrons in a ring system are described in terms of a transverse wave propagated along the carbon skeleton. Kekule benzene is forbidden because the π electron quantal wave self-interferes. The characteristics of an aromatic system are expressed in terms of the weighted combination of Kekule structures, and resonance energy occurs through combining canonical structures with conservation of momentum. The resonance energy of benzene is calculated as 1·045 times the energy difference between two carbon-carbon single bonds and one double bond, or 162 kJ/mol on one bond energy scheme. Bond localization is due to differences in wave impedance between zones represented by adjacent phase space cells; wave reinforcement occurs in one zone, cancellation in another as a consequence of the directional asymmetry of phase changes of the quantal wave. Quantal wave impedance can be altered by altering the localized potential, and it is proposed that the so-called Mills-Nixon effect arising from the annelation of bicyclic rings occurs because the bicyclic ring better focuses a polarization field. The polarization field arising as a consequence of strain is shown to semiquantitatively account for the bond alternation. The difference between exo and endo bond lengths in tris(bicyclo[2.1.1]hexeno)benzene is calculated to be 7·2 pm, compared with 9 pm as determined experimentally.