Unified theory of resonance energies, ring currents, and aromatic character in the (4n + 2).pi.-electron annulenes

Abstract

It is demonstrated for the first time that, to high accuracy, there is an analytic relationship between the resonance energies (REs) and reduced ring currents (RCs) of the (4« + 2)rr-electron annulenes-the original subjects of the Hückel rule-which leads naturally to a unified theory of aromatic character. The resonance energy is obtained as RE = 2 ß/3 = 2 /6 2 where prs is the bond order, N is the number of carbon atoms, E is the total ir-electron energy, and ß is the resonance integral. The relationship between resonance energies and ring currents takes the form RE = rr2RC/35 or RC = 35 RE/ 2 where 5 is the area of the ring. The available experimental evidence is shown to be in excellent agreement with this relationship. Attention is drawn to the present lack of integrity of our knowledge of nondissipative currents in organic molecules and bulk superconductors, and common facets of present theories are discussed.

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…”

“…Hückel s long-standing 4n+2 rule distinguishes aromatic from antiaromatic monocycles, and correlates the energetics of these systems with their characteristic magnetic properties. [1] However, the periodic table offers wide possibilities for the construction of isoelectronic heterocycles, and for many of them, direct transferability of the implied relationship between aromaticity and electron count is questionable or even counterfactual. The replacement of CC by BN, for example, is known to lead to marked differences in magnetic properties: [2] the strong ring currents of the carbocycle vanish in the isoelectronic azabora-heterocycles, B N/2 N N/2 H N (1-3).…”

Graph Theory of Ring-Current Diamagnetism

“…Neither Haddon nor we could derive any analytical relationship between the intensity of the ring current and the ASE for antiaromatic annulenes. 83,86 In marked contrast to MRE, TRE and DRE 30,35 always take finite values even for antiaromatic annulenes. Bond-equalized antiaromatic annulenes, however, are not likely to have real existence since they are very unstable with respect to distortion.…”

“…82 Haddon found in 1979 that the intensity of a ring current induced in an aromatic annulene is proportional not only to the ring area but also to the ASE. 83 He employed as an ASE one formerly used by us called A-I resonance energy, 26,84 which we later ceased to use because it can be applied only to monocyclic π-systems. This kind of ASE (ASE A-I ) was evaluated by reference to the unit bond energy of infinite annulene.…”

“…Equations 80 and 81 tell us that the circuit-current susceptibility is proportional not only to the area enclosed by the circuit squared but also to CRE, whereas the intensity of the circuit current is proportional not only to the circuit area but also to CRE. We can now safely say that, as in the case of monocyclic aromatic annulenes, 83,86 the intensity of every circuit current and the circuit-current susceptibility for polycyclic π-systems run parallel with the ASE arising from the circuit. This fact supports the commonly accepted view that, for some reason or other, ring-current diamagnetism reflects the aromaticity of the π-system.…”