π-Electron ring-currents and bond-currents in [10,5]-Coronene and related structures conforming to the ‘Annulene-Within-an-Annulene’ model

T K Dickens,R B Mallion

doi:10.1039/c3cp00053b

Abstract

A series of hypothetical conjugated structures is defined; the series is called the p-Coronenes and the first four members of it are shown to respect the 'Annulene-Within-an-Annulene' (AWA) model when tested by means of Hückel-London-Pople-McWeeny (HLPM) π-electron ring-current and bond-current calculations. The first member of this series, 5-Coronene, is also a member of the regular [r,s]-Coronene series, where it is known as [10,5]-Coronene. It is shown that, as p is varied (with p always odd, and with p > 3) through the values 5, 7, 9, 11, etc., the resulting structures alternate between a '[4n + 2]-Annulene-Within-a-[4m]-Annulene' (if (p- 1) is divisible by 4) and a '[4n]-Annulene-Within-a-[4m + 2]-Annulene' (if (p- 1) is not divisible by 4). It is therefore claimed that the p-Coronenes constitute an ideal series for testing the AWA model. It is also remarked that each member of the p-Coronene series has only four Kekulé structures, and that the 'spokes' or 'transverse' bonds connecting the central [p(p- 3)]-membered ring to the outer [p(p- 1)]-membered periphery always have a Pauling bond-order of zero, ensuring that the outer and inner rings are 'decoupled'; such bonds also bear zero bond-current, by symmetry. It is argued that the former property of these transverse bonds, rather than the latter, determines that the p-Coronenes obey the AWA rule-which is in fact an exception, rather than a 'rule'per se. The paper concludes by explicitly stating our philosophy that a conceptually simple model depending on no subjective (or any other) parameters whatsoever can give intuitive chemical insight for certain systems equal to that available from far-more complex methods such as ab initio calculations-what Coulson once famously called 'primitive patterns of understanding'.

Highlights

A series of hypothetical conjugated structures is defined; the series is called the p-Coronenes and the first four members of it are shown to respect the ‘Annulene-Within-an-Annulene’ (AWA) model when tested by means of Huckel–London–Pople–McWeeny (HLPM) p-electron ring-current and bond-current calculations
These more-simplistic calculations agree with the conclusions of Monaco et al.2—based, in the main, on moresophisticated methods of calculation—that the bond currents in [10,5]-Coronene (I) are in accord with the qualitative predictions of the AWA model4–9 and we extend this conclusion to the other structures, ((II)–(IV)), of the p-Coronene series that are here investigated
It should be emphasised that the set of ring currents and the set of bond currents for each structure are consistent with each other and are connected by a common compliance with the microscopic analogy of Kirchhoff’s first law (‘Conservation of Currents at a Junction’) for macroscopic electrical-networks

Summary

Introduction

A series of hypothetical conjugated structures is defined; the series is called the p-Coronenes and the first four members of it are shown to respect the ‘Annulene-Within-an-Annulene’ (AWA) model when tested by means of Huckel–London–Pople–McWeeny (HLPM) p-electron ring-current and bond-current calculations.

Results

Conclusion