Some Comments on Topological Approaches to the π-Electron Currents in Conjugated Systems

Within the past two years, three sets of independent authors (Mandado, Ciesielski et al., and Randić) have proposed methods in which π-electron currents in conjugated systems are estimated by invoking the concept of circuits of conjugation. These methods are here compared with ostensibly similar approaches published more than 30 years ago by two of the present authors (Gomes and Mallion) and (likewise independently) by Gayoso. Patterns of bond currents and ring currents computed by these methods for the nonalternant isomer of coronene that was studied by Randić are also systematically compared with those calculated by the Hückel-London-Pople-McWeeny (HLPM) "topological" approach and with the ab initio, "ipso-centric" current-density maps of Balaban et al. These all agree that a substantial diamagnetic π-electron current flows around the periphery of the selected structure (which could be thought of as a "perturbed" [18]-annulene), and consideration is given to the differing trends predicted by these several methods for the π-electron currents around its central six-membered ring and in its internal bonds. It is observed that, for any method in which calculated π-electron currents respect Kirchhoff's Laws of current conservation at a junction, consideration of bond currents-as an alternative to the more-traditional ring currents-can give a different insight into the magnetic properties of conjugated systems. However, provided that charge/current conservation is guaranteed-or Kirchhoff's First Law holds for bond currents instead of the more-general current-densities-then ring currents represent a more efficient way of describing the molecular reaction to the external magnetic field: ring currents are independent quantities, while bond currents are not.