Graph Theory of Ring-Current Diamagnetism

Abstract

Abstract Various magnetic criteria of aromaticity have been proposed so far, because they are easily calculated and applicable to a variety of cyclic π-systems. Many researchers, however, are reluctant to accept all or some of them. Our graph theory of ring-current diamagnetism revealed serious flaws in familiar magnetic criteria of aromaticity. Physically meaningful information on aromaticity can nevertheless be extracted from the ring-current diamagnetism. In particular, magnetic resonance energy (MRE), derived from the ring-current diamagnetic susceptibility, is interpretable as a kind of aromatic stabilization energy (ASE) and helps in consistently interpreting energetic and magnetic criteria of aromaticity. MRE and related quantities can be determined without reference to any hypothetical polyene-like structure but with a reasonable assumption that, when a magnetic field is applied to a cyclic π-system, a current is induced in each circuit in proportion to the ASE arising from the circuit. Unlike other conventional magnetic indexes, they are independent of the size and shape of the π-system.