Abstract

(in collaboration with Dr Tim Dickens, University Chemical Laboratory)

In 1958, when working at the University Chemical Laboratory, Nobel Laureate the late Sir John Pople performed the first quantum-mechanical calculation of a π-electron ring-current intensity — a feat independently and almost simultaneously achieved by McWeeny, who published only136 pages later in Volume 1 of Molecular Physics, a newly founded journal edited by the Cambridge Professor of Theoretical Chemistry at the time, H. C. Longuet-Higgins, who himself later contributed to this field. The superficially different, but entirely equivalent, methods that Pople and McWeeny used were extensions of the approach introduced twenty years earlier by London, whose formalism was itself based on Hückel molecular-orbitals. During the 1960s and 1970s, the Hückel method was gradually superseded by more-sophisticated semi-empirical approaches and, ultimately, by ab-initio ones. Over the course of the last forty years, however, the Hückel model has, to some extent, been rehabilitated because it is now more generally appreciated that, when certain assumptions about ring areas are made, ring-current intensities calculated by the Hückel–London–Pople–McWeeny (HLPM) approach are effectively graph-theoretical in nature, their signs and relative sizes being dependent on (and, de facto, latent in) the carbon-carbon connectivity of the polycyclic, conjugated hydrocarbon under study, and the ring currents are thus completely pre-determined once the structural formula of the system in question has been written down.

The authors have recently revived this so-called ‘topological’ (HLPM) formalism and have applied it, with some success, to several problems such as the ‘emptiness’ (or otherwise) of the central ring in the family of structures related to perylene, and the so-called ‘annulene-within-an-annulene’ model of certain ‘super-ring’ conjugated systems. Attention has also been directed to the conceptual advantages and disadvantages of considering bond currents in conjugated structures, instead of the more-traditional ring currents — the two sets of quantities being connected by the analogue, in the context of microscopic molecular systems, of Kirchhoff’s First Law (as conventionally applied to macroscopic electrical networks). The ring currents for a given structure constitute a collection of independent quantities, whereas the family of bond currents in all the bonds of a given molecule are not themselves independent, by virtue of Kirchhoff’s First Law. The talk will also review four alternative topological methods that rely on the concept of ‘circuits of conjugation’ and which have recently been proposed by independent teams led by Mandadao, Fowler, Randić, and Ciesielski, in order to explore bond currents and ring currents.