Why can so few benzenoids be completely drawn with Clar's resonant sextets? An analysis using ‘Branching graphs’ and a ‘coiled-hexagon code’

Abstract

Kekulé structures are made use of in a manner unrelated to their traditional role in conjugation theory. ‘Branching graphs’(recently introduced polyhex subgraphs containing the branching vertices, and edges that connect pairs of such vertices) that have Kekulé structures, but no terminal vertices, can be used to generate the sextet 2-factorable benzenoids, predicted to have high stability by Clar's aromatic sextet rule, in such a way as to illuminate their comparative rarity. Other 2-factorable benzenoids can be found too, though more laboriously. A simple ‘coiled-hexagon’ code is introduced for referring both to benzenoids and to many of the constrained branching graphs used here. A polyhex structure is described by reference to a hexagon lattice numbered sequentially in the tightest possible outward spiral.