SEMICLASSICAL QUANTUM-MECHANICS, BOND DELOCALIZATION AND THE MILLS-NIXON EFFECT

Conjugated pi electrons in a ring system are described in terms of a t ransverse wave propagated along the carbon skeleton. Kekule benzene is forbidden because the ir electron quantal wave self-interferes. The c haracteristics of an aromatic system are expressed in terms of the wei ghted combination of Kekule structures, and resonance energy occurs th rough combining canonical structures with conservation of momentum. Th e 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 ph ase space cells; wave reinforcement occurs in one zone, cancellation i n another as a consequence of the directional asymmetry of phase chang es of the quantal wave. Quantal wave impedance can be altered by alter ing the localized potential, and it is proposed that the so-called Mil ls-Nixon effect arising from the annelation of bicyclic rings occurs b ecause the bicyclic ring better focuses a polarization field. The pola rization field arising as a consequence of strain is shown to semiquan titatively account for the bond alternation. The difference between ex o and endo bond lengths in tris(bicyclo[2.1.1]hexeno)benzene is calcul ated to be 7.2 pm, compared with 9 pm as determined experimentally.