The Leap-frog Effect of Ring Currents in Benzene

Symmetry arguments show that the ring-current model proposed by Pauling, Lonsdale, andLondon to explain the enhanced diamagnetism of benzene is flawed by an intrinsic drawback. The minimalbasis set of six atomic 2p orbitals taken into account to develop such a model is inherently insufficient topredict a paramagnetic contribution to the perpendicular component of magnetic susceptibility in planarring systems such as benzene. Analogous considerations can be made for the hypothetical H6 cyclicmolecule. A model allowing for extended basis sets is necessary to rationalize the magnetism of aromatics.According to high-quality coupled Hartree-Fock calculations, the trajectories of the current density vectorfield induced by a magnetic field perpendicular to the skeletal plane of benzene in the ð electrons arenoticeably different from those typical of a Larmor diamagnetic circulation, in that (i) significant deformationof the orbits from circular to hexagonal symmetry occurs, which is responsible for a paramagnetic contributionof ð electrons to the out-of-plane component of susceptibility, and (ii) a sizable component of the ð currentdensity vector parallel to the inducing field is predicted. This causes a waving motion of ð electrons;streamlines are characterized by a “leap-frog effect”.