An extension of the Fries rule to non-benzenoid hydrocarbons having four-atomic rings

Abstract

The study contains a deductive search for the principal monocyclic substructures determining different importances (weights) of separate Kekule valence structures of phenylenes and their congeners. Individual Kekule structures are modelled as continuous conjugated systems consisting of uniform double (C=C) bonds connected by uniform single (C–C) bonds, the latter being substantially weaker as compared to the former. The relevant total $$\pi$$ -electron energies are shown to offer an adequate criterion for ordering of the structures concerned according to their weights. These energies, in turn, are derived in the form of power series with respect to the small resonance parameter of C–C bonds. Analysis of expressions for separate members of this series shows that the cyclobutadienoid rings (if any) are the most important destabilizing contributors to the energy of the given structure, whereas the benzenoid rings and cycles like 3,4-dimethylene cyclobutene take the second place (their increments are stabilizing and destabilizing, respectively). Additivity and transferability of the above-enumerated contributions to energies of Kekule valence structures also are among the conclusions. These results provide us with an extension of the classical Fries rule to non-benzenoid hydrocarbons having four-atomic rings. Specific examples of the given class of compounds are considered in a detail, viz. biphenylene, [3]phenylene, as well as benzo- and naphthocyclobutenes. The relation of the approach applied to the theory of conjugated circuits also is discussed.