The “Anthracene Problem”: Closed-Form Conjugated-Circuit Models of Ring Currents in Linear Polyacenes

Abstract

Conjugated-circuit models for induced π ring currents differ in the types of circuit that they include and the weights attached to them. Choice of circuits for general π systems can be expressed compactly in terms of matchings of the circuit-deleted molecular graph. Variants of the conjugated-circuit model for induced π currents are shown to have simple closed-form solutions for linear polyacenes. Despite differing assumptions about the effect of cycle area, all the models predict the most intense perimeter current in the central rings, in general agreement with ab initio current-density maps. All tend to overestimate the rate of increase with N of the central ring current for the [N]polyacene, in comparison with molecular-orbital treatments using ipsocentric ab initio, pseudo-π, and Hückel-London approaches.

From C58to C62and back: Stability, structural similarity, and ring current

“…In fact, as noted earlier, some isomers with one or two squares are favoured over classical cages for C 24 and C 26 [18,19]; by extension it might be expected that a favoured square-containing isomer would be more likely for C 58 than the larger C 62 .…”

“…Frequency calculations at the B3LYP/6-31G* level were carried out to check that optimized geometrical structures of the favoured isomers correspond to local minima on the potential hypersurface; asphericity values and pyramidalization angles were calculated based on the optimized structures. Ring-current calculations were also performed at the pseudo-level [22][23][24] with the SYSMO program [25] for these 3D structures, as discussed below. …”

The Calculations of Ring Current of Some Benzenoids using Randić Model

“…5 The matchings are defined as a single conjugated circuits or a set of disjoint conjugated circuits. 8 Randić model weighs all conjugated circuits (single and set of disjoint) that contributes to each bond as ±2 [ − ] 2 , where the sign is determined by the orientation of conjugated circuit, (+) for anticlockwise direction of 4n+2 cycles, (-) for clockwise direction of 4n cycles and mis the perfect matching of conjugated circuit C in the molecular graph G. 8 Thismodel obeys Kirchhoff's first law thus the currents of two bonds with the same values and different directions are cancelled. 9 Randić model gives a qualitative insight of ring current.…”

“…Nevertheless it has a drawback that it has a lake of distinguish between the systems with similar geometry but different magnetic response such as benzene and borazine. 8 In the present work, the ring currents of a set of benzenoids were calculated using CC model of Randić. The unnormalised values were plotted as maps and the normalised currents were listed.…”

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.…”