Correlations between Topological Ring-Currents, π-Electron Partitions, and Six-Centre Delocalisation Indices in Benzenoid Hydrocarbons

Abstract

Abstract. Comparison is made between three different indices that characterise the individual rings of a wide range of condensed benzenoid hydrocarbons. Two of these ("π-electron partitions" and the six-centre delocalisation-indices that have been called "Δ 6 -values") have been introduced only recently as potential indicators of what might be called "local aromaticity", whilst the third ("topological π-electron ringcurrents") was suggested as a possible discriminator in this regard nearly fifty years ago. Whilst linear correlations between ring currents and π-electron partitions within certain restricted classes of ring types are good (with correlation coefficients of up to 0.998), agreement between the two indices over all classes of ring types is poor. Predictions arising from a consideration of π-electron partitions and Δ 6 -values seem, on the other hand, to be in somewhat better accord. It is therefore concluded that, despite its superficially intuitive appeal, the ring-current index is out of step both with π-electron partitions and Δ 6 -values as a general indicator of so-called "local aromaticity". (doi: 10.5562/cca1846)

Comparisons of π-Electron Ring-Current and Bond-Current Patterns Calculated by Topological (‘HLPM’) and Ab Initio (‘Ipso-Centric’) Formalisms for Two Isomeric Conjugated Hydrocarbons, Corazulene and Cornaphthalene

“…It is perhaps material to point out at this stage that what we have for some time been calling [6,13,14,17,21,22,26,[28][29][30][31] 'topological HLPM calculations' are precisely what Fowler et al have very recently [34][35][36][37] given the appellation 'graphtheoretical Current-Density Hückel-London (CD-HL) calculations'. Given the same geometrical assumptions, the two 1 2 Figure 1.…”

“…In the present calculations we adopt C4h symmetry for corazulene (1) and D4h symmetry for cornaphthalene (2). The topological [6,28,29] HLPM ring-current and bond-current maps of 1 and 2, calculated as just described, are illustrated in Figures 2 and 3. As is conventional, [6] the ring currents and bond currents are presented as dimensionless numbers, expressed as a ratio to the corresponding quantities calculated, by the same method, for benzene.…”

“…[2,[38][39][40][41][42][43][44] We have, however, resisted applying this refinement here because, as we are testing a method that claims to depend on no empirical or subjective parameters whatsoever, we wish to maintain the description of the resulting π-electron currents as 'topological'. [6,28,29] Lillington et al [1] further observe that the 'chord bonds' completing the four pentagonal rings (C) in 1 also support current that closes a ring-current loop in which the circulation is in the diamagnetic direction, '...but this is much smaller than the main perimeter current.' [1] This finding is also supported by the topological HLPM calculations presented in Figure 2: the 'chord bonds' carry a current of about 0.15, whereas the main perimeter current varies between approximately 0.65 and ca.…”

“…6, the main crux of which is equation (14) of that reference. As is a requirement of the 'topological' version [6,28,29] of the HLPM approach, [2][3][4][5] adopted here, both 1 and 2 are assumed to be planar structures whose ring areas are those of regular polygons [4,29] of the appropriate number of sides, each of which is of uniform length (and equal to the carbon-carbon bond-length in benzene) -please see equation (16) of Ref. 6.…”

“…Maps for the topological [6,28,29] ring-currents (in black) and the associated topological [6,28,29] bond-currents (in red) for (non-alternant [2] ) corazulene (1 methods (HLPM [6,28,29] and CD-HL [34][35][36][37] ) should yield identical numerical ring-currents and bond-currents (within machine error of the computation), which, as already claimed, are themselves instantly latent in the molecular graph, once the latter has been specified. …”