An Analysis of Topological Ring-Currents and their Use in Assessing the Annulene-Within-an-Annulene Model for Super-Ring Conjugated Systems

The Huckel-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) Keywords: topological ring-currents and bond-currents, graph theory, conjugated hydrocarbons, coupled and decoupled super-ring systems, annulene-within-an-annulene rule