Perturbative Analogue for the Concept of Conjugated Circuits in Benzenoid Hydrocarbons

The study contains an application to individual Kekule valence structures of benzenoid hydrocarbons of the general form of power series for total energies of molecules obtained previously by means of the so-called non-commutative Rayleigh-Schrodinger perturbation theory, as well as an additional derivation of expressions for energy corrections of the fifth order. The structures concerned are modeled as sets of weakly-interacting initially-double (C=C) bonds, bonding and anti-bonding orbitals of which play the role of basis functions. Accordingly, the averaged resonance parameter of initially-single (C-C) bonds is chosen to underly the energy expansion. The main aim of the study consists in revealing an anticipated interrelation between the above-specified perturbative approach to relative stabilities of separate Kekule valence structures and the well-known models based on the concept of conjugated circuits (CC). It is shown that the principal properties of the power series for total energies resemble those of the CC models. This especially refers to additivity of contributions of individual circuits to the relevant total energy and to their extinction when the size of the circuit grows. On this basis, the approach suggested is concluded to offer a perturbative analogue for the concept of conjugated circuits in benzenoid hydrocarbons and thereby a new justification of the CC model(s). An additional discriminative potential of the approach applied vs. the CC model(s) also is concluded by demonstrating distinct total energies for Kekule valence structures of the same composition in terms of conjugated circuits. The simplest hydrocarbons are considered in a detail as examples, viz. naphthalene, anthracene and phenanthrene.