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

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’.