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