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

T K Dickens,R B Mallion

doi:10.5562/cca2291

Abstract

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

Highlights

INTRODUCTIONA detailed re-consideration is presented of the Hückel1-London2-Pople3-McWeeny[4] (HLPM) approach to calculating ring-currents and bond currents in conjugated systems (see Refs. 5–8 for reviews), in which a step-by-step account is given of how these calculations are in practice carried out, with special reference to the ‘topological’ variant of this formalism, recently emphasised.[9,10,11] Application of this approach will be illustrated by using it to compute numerical values of ring currents and bond currents in order to re-enforce a recent re-evaluation[12,13] of the ‘AnnuleneWithin-an-Annulene’ (AWA) model,[14,15,16,17,18,19,20,21,22,23,24] a model which has been of interest to several groups of workers,[14,15,16,17,18,19,20,21,22,23,24] especially over the last decade or so.[16,17,18,19,20,21,22,23,24]
A detailed re-consideration is presented of the Hückel1-London2-Pople3-McWeeny[4] (HLPM) approach to calculating ring-currents and bond currents in conjugated systems, in which a step-by-step account is given of how these calculations are in practice carried out, with special reference to the ‘topological’ variant of this formalism, recently emphasised.[9,10,11]
When the data are examined in more detail it is seen that the intensity of the diamagnetic ring-current in the central ring is, in every case, smaller than the diamagnetic ring-current intensity in any of the outer, peripheral rings

Summary

INTRODUCTION

A detailed re-consideration is presented of the Hückel1-London2-Pople3-McWeeny[4] (HLPM) approach to calculating ring-currents and bond currents in conjugated systems (see Refs. 5–8 for reviews), in which a step-by-step account is given of how these calculations are in practice carried out, with special reference to the ‘topological’ variant of this formalism, recently emphasised.[9,10,11] Application of this approach will be illustrated by using it to compute numerical values of ring currents and bond currents in order to re-enforce a recent re-evaluation[12,13] of the ‘AnnuleneWithin-an-Annulene’ (AWA) model,[14,15,16,17,18,19,20,21,22,23,24] a model which has been of interest to several groups of workers,[14,15,16,17,18,19,20,21,22,23,24] especially over the last decade or so.[16,17,18,19,20,21,22,23,24]. J. Klein, the honorand of this issue of Croatica Chemica Acta, and others (including one of us [RBM]).[65] In the Appendix this value of 176400 for the number of spanning trees in the coronene molecular-graph is confirmed by an application of the traditional Matrix Tree Theorem.[63] the motto here is: ‘one is enough’ — only a single one of these 176400 spanningtrees is required in practice in order to able to effect the ring-current calculation that is being carried out here. In order explicitly to circumvent this problem, Gayoso and Boucekkine,[74] in a seldom-cited and undeservedly neglected paper, proposed a generalisation of McWeeny’s unitary transformation on the basis orbitals[4] in the presence of the external magnetic-field in such a way that the new transformation enables a ring-current calculation to be based on a branched spanning-tree, such as that illustrated on the right-hand side of Figure 6. The resulting ‘London’ susceptibility-ratios for 1–7 are presented in the right-hand column of Table 6

DISCUSSION

Findings

CONCLUSIONS