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.