Ring currents and proton magnetic resonance in aromatic molecules

A Unified Orbital Model of Delocalised and Localised Currents in Monocycles, from Annulenes to Azabora‐heterocycles

“…[6] In this model, as formulated by McWeeny, [23] the ring current per unit area of a cycle is proportional to the reduced bond current, J rs , where p rs is the p bond-order between adjacent atoms r and s and p rs,rs is the imaginary bond-bond polarisability. [1] J rs ¼ ðp rs þbp rs,rs Þb…”

“…In the McWeeny form of the Hückel-London theory, [23] the ring current of the eight-membered cycle when h is small is dominated by the HOMO-LUMO contribution to the imaginary bond-bond polarisability, which is À 1 = 16 bh, and hence falls sharply as h increases from the planar-constrained form of COT (where h = 0) to the heterocycle. When h = 1, the eight-membered cycle has p = 1 = 2 ( 1 ffiffi…”

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

“…The computations were carried out by the HLPM method [2][3][4][5] as described in step-by-step detail in Ref. 6, the main crux of which is equation (14) of that reference.…”

“…N THIS PAPER, we take the opportunity afforded by the availability of certain ab initio calculations [1] to assess how well predictions of π-electron ring-current and bondcurrent intensities calculated for conjugated systems by the rudimentary Hückel [2] -London [3] -Pople [4] -McWeeny [5] ('HLPM') formalism [6] mimic those of more-sophisticated approaches, notably the ab initio 'ipso-centric' [7] and 'pseudo-π' [8] methods. Ab initio procedures frequently depend first on the application of elaborate software, such as the Gaussian program, [9] in order to optimise starting geometries, and then on the choice of wave-function basis-set employed (see, for example, ' [2][3][4][5][6] on the other hand, depends only on knowledge of how the carbon atoms forming the conjugated system in question are joined to each other in the σ-bonded network, and on the areas of its constituent rings.…”

“…Ab initio procedures frequently depend first on the application of elaborate software, such as the Gaussian program, [9] in order to optimise starting geometries, and then on the choice of wave-function basis-set employed (see, for example, ' [2][3][4][5][6] on the other hand, depends only on knowledge of how the carbon atoms forming the conjugated system in question are joined to each other in the σ-bonded network, and on the areas of its constituent rings. [6] Once the matter of ring areas has been decided, topological π-electron bond-currents and ring-currents in such systems are thus effectively latent in the molecular graph of the hydrocarbon under study and, accordinglyeven though their actual computation may still have to be effected -these currents are at least implicitly and immediately predetermined as soon as the structure's molecular graph [12] has been written down.…”