Theory of Resonance Topology of Fully Aromatic Hydrocarbons. I

Abstract

The computation of resonance forms of any specified number of unpaired electrons (``radicality'') of aromatic hydrocarbons is reduced to combinatorial problems, many of which can be solved on the basis of five simple lemmas. In this first of two papers, only unexcited (Kekulé) forms are computed. Algorithms are deduced for deriving the number N of such forms for classes covering practically all nonreticulate aromatic hydrocarbons and a number of singly, doubly, or triply infinite series of reticulate ones. One lemma leads to a simplification of the combinatorial problems from the hexagonal to the square lattice (``dot diagrams''). Points of purely mathematical interest arise and may merit further study.