Correlations between various ways of accounting for the distribution of π-electrons in benzenoids

Abstract

The π-electrons in polycyclic benzenoid hydrocarbons can be counted in two different ways: (i) as partitions of π-electrons in each ring of the benzenoid (according to the conventions that all resonance structures contribute equally, that shared double bonds resonance structures contribute with one π-electron to each of the condensed rings, and that both π-electrons of an unshared double bond belong to the corresponding ring) and (ii) as benzenoid signature, i.e. a sequence of six real numbers counting for all resonance structures the numbers of times a ring is assigned according to the above conventions s_i π-electrons, where i takes integer values between 6 and 1. For bridging the gap between these two ways of accounting for the same number of π-electrons, various types of resonance structures (also called Kekule valence structures) are examined and mixed: Fries, Clar, anti-Fries, and quasi-Clar structures.