Paramagnetic Vortices and Proton Magnetic Shielding in Aromatic Molecules.

By means of symmetry considerations it is shown that aromatic hydrocarbons, perturbed by a magnetic field perpendicular to the molecular plane, are characterized by an interatomic paramagnetic circulation of electrons, flowing around the highest symmetry axis, which is related to the nodal topology of the wave function. An actual calculation confirms that the field of quantum-mechanical current density presents an axial vortex due to σ electrons in benzene, which overcomes the diamagnetic π streamlines. The analysis of the orbital contributions to proton nuclear shielding reveals that σ electrons cause low field shifts, in the NMR spectrum, comparable in magnitude with those arising from π circulation. These results would imply the need for modifying some features of London's ring current model.