Monatshefte für Chemie - Chemical Monthly

, Volume 149, Issue 6, pp 1031–1044 | Cite as

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

Original Paper


The study contains a deductive search for the principal monocyclic substructures determining different importances (weights) of separate Kekulè valence structures of phenylenes and their congeners. Individual Kekulè 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 Kekulè 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.

Graphical abstract


Arenes Electronic structure Fries rule Hydrocarbons Kekulè valence structure 



The author is grateful to his colleague Dr. Vaidas Juknevičius for his help with preparation of the figures of this paper.


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Theoretical Physics and AstronomyVilnius UniversityVilniusLithuania

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