Partitioning Hückel–London Currents into Cycle Contributions

Abstract

Ring-current maps give a direct pictorial representation of molecular aromaticity. They can be computed at levels ranging from empirical to full ab initio and DFT. For benzenoid hydrocarbons, Hückel–London (HL) theory gives a remarkably good qualitative picture of overall current patterns, and a useful basis for their interpretation. This paper describes an implemention of Aihara’s algorithm for computing HL currents for a benzenoid (for example) by partitioning total current into its constituent cycle currents. The Aihara approach can be used as an alternative way of calculating Hückel–London current maps, but more significantly as a tool for analysing other empirical models of induced current based on conjugated circuits. We outline an application where examination of cycle contributions to HL total current led to a simple graph-theoretical approach for cycle currents, which gives a better approximation to the HL currents for Kekulean benzenoids than any of the existing conjugated-circuit models, and unlike these models it also gives predictions of the HL currents in non-Kekulean benzenoids that are of similar quality.