Abstract. The Hückel-London-Pople-McWeeny approach to calculating ring currents in conjugated systems is considered in detail, especially the 'topological' variant of this formalism, particularly emphasised during the last five years. A step-by-step account is given of how these calculations are effected in practice, in such a way as to enable any interested reader to carry out these computations himself. The method is illustrated by using it to assess the applicability of the so-called 'Annulene-Within-an-Annulene (AWA) Rule' to 'super-ring' conjugated hydrocarbons -some in which the inner ring and outer perimeter are 'coupled', and others in which they are 'decoupled'. Compliance with the AWA model appears more probable in decoupled super-ring structures than in coupled ones. The Appendix touches on previous work involving Professor D. J. Klein, the honorand of this issue. (doi: 10.5562/cca2291)

The novel series of conjugated systems called altans, defined nearly a decade ago, was subsequently extended to multiple ("iterated") altans, and their magnetic properties were calculated by Monaco and Zanasi using the ab initio ipso-centric formalism. Such properties of the single ("mono") altans of corannulene and coronene, calculated by this sophisticated ab initio approach, had earlier been compared with those calculated via the rudimentary Hückel-London-Pople-McWeeny (HLPM) method-a parameter-free topological, quasi graph-theoretical approach requiring knowledge only of the conjugated system's molecular graph and the areas of its constituent rings. These investigations are here extended to double and triple altans. HLPM bond currents in several neutral mono altans are found to differ from those in the corresponding dianion only in those bonds that lie on the structures' perimeters, while the HLPM bond currents in all bonds in the neutral double and triple altans of corannulene and coronene are precisely the same as in the respective dianions. Some rationalization of these unexpected phenomena is offered in terms of the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) nature of the role played by the lone nonbonding orbital in each of the neutral species and its respective dianion.

The Hückel-London-Pople-McWeeny (topological) approach for calculating π-electron ring currents and bond currents in conjugated systems is applied to the structures altan-corannulene and altan-coronene, recently designed by Monaco and Zanasi. These authors applied the ab initio ipso-centric formalism to calculate π-electron current-density maps and individual bond current intensities in these structures. In a parallel investigation the key findings of Monaco and Zanasi's ab initio study are here qualitatively confirmed by this much more rudimentary topological assessment: namely, that, in their three layers, the two structures altan-corannulene and altan-coronene reveal patterns of contra-rotating paramagnetic/diamagnetic/paramagnetic π-electron circulations in their innermost, middle, and outer cycles, respectively.

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.

π-Electron ring-currents for the altans of the four regular [r,s]-coronenes are calculated by the topological HLPM approach. The bond-current pattern of the parent structure is generally preserved in the core of the corresponding altan. Altan-[10,5]-coronene appears to support an anomalous diamagnetic current in its [4n]-periphery. This invites further investigation.