Topological dependency of the aromatic sextets in polycyclic benzenoid hydrocarbons. Recursive relations of the sextet polynomial

Abstract

Mathematical meaning of the Clar's “aromatic sextet” is clarified by analysing the topological dependency of the sextet polynomial. Generalised recursive method for obtaining the sextet polynomial of a polyhex graph is presented. It is shown that the concept of the “super sextet” is necessarily introduced, if one-to-one correspondence between the Kekule and sextet patterns is assumed. Topological dependency of the maximum number of resonant sextets is clarified and discussed in relation to the aromaticity and stability of polycyclic benzenoid hydrocarbons.