Correlation between the out-of-plane components of magnetizability and central magnetic shielding in unsaturated cyclic molecules

A simple classical model of magnetic-field induced π-electron flow is discussed, showing that the contribution to the σ(∥) out-of-plane component of the virtual magnetic shielding provided by π-ring currents, at points P along the C(n) axis of cyclic planar unsaturated hydrocarbons C(n)H(n) with D(nh) symmetry, in the presence of a magnetic field B(ext) at right angles to the σ(h) plane, is, with good approximation, connected with the π-electron contribution to the out-of-plane component of the magnetizability, ξ(∥). The relationship is σ(∥)(h) = -(μ(0)/2π)(s(2) + h(2))(-3/2)ξ(∥), where s is the distance of a C nucleus from the center of the carbon ring, and h is the distance of P from σ(h). The ring current susceptibility, that is, the strength of the π currents, expressed in nA/T (nano ampe?re per tesla) within the SI system of units, is given by ?I/?B(ext) = -ξ(∥)/(πs(2)), which can be used as a reliable virtual measure of magnetotropicity and relative π-electron mobility in isoelectronic systems. Criteria for the practicality of the proposed ring current model are discussed.