Perimeter ring currents in benzenoids from Pauling bond orders

Abstract

It is shown that the ring currents in perimeter hexagonal rings of Kekulean benzenoids, as estimated within the Randić conjugated-circuit model, can be calculated directly without tedious pairwise comparison of Kekulé structures or Kekulé counting for cycle-deleted subgraphs. Required are only the Pauling bond orders of perimeter bonds and the number of Kekulé structures of the benzenoid, both readily available from the adjacency matrix of the carbon skeleton. This approach provides easy calculation of complete current maps for benzenoids in which every face has at least one bond on the perimeter (as in the example of cata-condensed benzenoids), and allows qualitative evaluation of the main ring-current contributions to ¹H chemical shifts in general benzenoids. A combined Randić–Pauling model for correlation of ring current and bond length through bond order is derived and shown to be consistent with resilience of current under bond alternation.