Topological Ring-Currents in Condensed Benzenoid Hydrocarbons

Topological ring-currents are defined as being pi-electron ring-current intensities in condensed, benzenoid hydrocarbons that (i) are calculated by the simplest Hückel-London-Pople- McWeeny method, (ii) are based on a molecular geometry of regular hexagons of carbon atoms, and (iii) are expressed as a ratio to the corresponding ring-current intensity calculated, by the same method, for benzene. Once a particular benzenoid hydrocarbon has been specified, such topological ring-currents are predetermined and do not further depend on any subjective (or other) parameters; they are, therefore, purely graph-theoretical indices, reliant solely on knowledge of a vertex-adjacency matrix for the graph representing the connectivity of the carbon atoms in the benzenoid molecule under study. For convenient reference, tables of all known topological ring-current intensities – some published, and others so-far unpublished – are presented for future evaluation and possible comparison with other graph-theoretical indices that characterise the individual rings of a condensed, benzenoid hydrocarbon.