Perturbational perspective on Kekul\`e valence structures of biphenylene and related hydrocarbons

TL;DR

This paper uses a perturbative approach to analyze Kekulé valence structures of biphenylene and related hydrocarbons, expressing their energies as power series to understand stability and substructure influences.

Contribution

It introduces a perturbation-based method to evaluate Kekulé structures' energies and extends the Fries rule to biphenylene-like hydrocarbons.

Findings

Energy corrections involve specific monocycles with exocyclic methylene groups.

Order of Kekulé structures by stability based on power series analysis.

Extended Fries rule accounts for unique substructures in biphenylene.

Abstract

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.