A simple model for counter-rotating ring currents in [n]circulenes

Abstract

Ab initio current density maps for [7]circulene computed using the ipsocentric CTOCD-DZ/6-31G**//RHF/6-31G** method show that in both planar [3a (D 7h Þ] and non-planar, saddle-shaped [3b (C 2 Þ] geometries this molecule sustains similar counter-rotating rim (diatropic) and hub (strongly paratropic) currents. A survey of the orbital contributions to the current density reveals that 3 like corannulene (1) is a 4d + 4p system with just eight magnetically active and 20 magnetically inactive p electrons. The graph-theoretical H€ u uckel-London model describes the ring-current patterns of [n]circulenes in terms of a coupling strength (the ratio of radial and tangential resonance integrals) that charts the variation from the decoupled con-rotating currents of the [n]annulene-within-an-[m]annulene model to the fully coupled counter-rotating currents of the real [n]circulene. Ó

Efficient mapping of ring currents in fullerenes and other curved carbon networks

“…Given their paratropic pentagonal ring currents, neither C 60 nor C 70 should be considered as especially aromatic on the magnetic criterion. The paratropicity of the pentagons in C 60 and C 70 is consistent with the diatropic-rim, paratropic-hub pattern of current found in bowl-shaped corannulene [55], which is itself part of a more general pattern in which the central ring of an [n]circulene is paratropic and the perimeter diatropic [56].…”

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

“…[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] The simplicity of this HLPM topological formalism is that, unlike with most other methods for calculating ring currents, there is no requirement to determine atomic coordinates in order to perform these calculations. All that is required is the connectivity matrix and the geometric areas of the constituent rings, and we choose to perform the calculation in two stages -a purely topological stage, followed by one that involves the actual geometry of the conjugated system.…”

“…The AWA model arises in the context of conjugated systems that consist of a central ring of carbon atoms joined by 'transverse' 25 ('spokes') 21 bonds to a larger, outer ring, as in 26,27 It has long been known [28][29][30][31] that annulenes -and we refer here strictly to the classic, monocyclic annulenes -are associated with paramagnetic π-electron 26,27 is said to obey the AWA model [14][15][16][17][18][19][20][21][22][23][24] if both its central ring and its outer perimeter bear calculated π-electron currents according to the pattern described above -implying that the inner and outer rings effectively behave as if they were independent annulenes. Most super-ring 26,27 structures seem, however, to violate the AWA model when tested against the results of ab-initio ipso-centric calculations [17][18][19][20][21]32,33 and of 'pseudo-π' calculations 34 of the type frequently presented by Fowler and co-workers, and also when confronted with topological [9][10][11] π-electron ring-currents and bond-currents that we ourselves have calculated 22,23 by means of the HLPM approach.…”

“…Most super-ring 26,27 structures seem, however, to violate the AWA model when tested against the results of ab-initio ipso-centric calculations [17][18][19][20][21]32,33 and of 'pseudo-π' calculations 34 of the type frequently presented by Fowler and co-workers, and also when confronted with topological [9][10][11] π-electron ring-currents and bond-currents that we ourselves have calculated 22,23 by means of the HLPM approach. [1][2][3][4] By contrast, the present authors have recently shown 12,13 that, in a homologous series called the p-coronenes, 12 in which the inner ring and outer perimeter are 'decoupled' in the sense defined by Fowler et al, [17][18][19][20][21] the AWA rule is respected -at least, when HLPM 'topological' bond-currents are used as the criterion. 12 (It should however be noted that this conclusion is not supported by some very recent calculations 24 based on the 'ipso-centric' ab-initio approach).…”

“…12 (It should however be noted that this conclusion is not supported by some very recent calculations 24 based on the 'ipso-centric' ab-initio approach). [17][18][19][20][21]32,33 The AWA model is likewise complied with 13 by the one member of the regular [r,s]-coronene series 25 in which the outer and inner rings are 'decoupled', but not by other regular [r,s]-coronenes, 25 in which these two sets of rings are 'coupled'. 13 The present account further evaluates the possible connection between the decoupled or coupled nature [17][18][19][20][21] of the outer perimeter and inner ring and compliance with, or violation of, the AWA rule.…”