  Individual Kekule valence structures of biphenylene and related hydrocarbons
are treated perturbatively by modelling them as sets of weakly-interacting
uniform double bonds. Total pi-electron energies of these structures are then
expressed in the form of power series with respect to the resonance parameter
of uniform single bonds. On this basis, the Kekule structures concerned are
ordered according to their relative stabilities and thereby importances when
building up the actual electronic structures. To rationalize the results,
interrelations are sought between separate members of the power series, on the
one hand, and presence of definite substructures in the given Kekule structure,
on the other hand. It is shown that monocycles containing two and four
exocyclic methylene groups participate in the formation of energy corrections
of the relevant Kekule valence structures along with the usual rings consisting
of uniform double and single bonds alternately and known as conjugated
circuits. An extension of the empirical Fries rule to the case of
biphenylene-like hydrocarbons is consequently formulated that embraces
monocycles of the above-specified types. The reasons are also discussed why the
results of the usual theory of conjugated circuits are less satisfactory for
phenylenes as compared to benzenoids.
