Equivalence of Two Models for Partitioning of π-Electrons in Rings of Benzenoid Hydrocarbons

Kekulé structures belong to the classical concepts of theoretical chemistry of polycyclic conjugated molecules and, in particular, of benzenoid hydrocarbons [1 – 3]. Nevertheless, it was only quite recently recognized [4] that in addition to the standard representation of a Kekulé structure (in which the locations of the double bonds are indicated), also an “algebraic” representation is possible. For a given Kekulé structure k of a polycyclic conjugated molecule consisting of rings R1 , R2 , . . . , Rh , its algebraic representation is constructed by inscribing a number EC(k|R j) into the ring R j for j = 1,2, . . . ,h . These numbers count the π-electrons which (in the Kekulé structure k) belong to the respective rings. Let b be a carbon-carbon bond belonging to the ring R. Then its contribution to the π-electron content of R (in the Kekulé structure k) is determined by the following rules: