Integration of global ring currents using the Ampère–Maxwell law

Abstract

Magnetically induced ring currents are calculated from the magnetic shielding tensor by employing the Ampère-Maxwell law. The feasibility of the method is demonstrated by integrating the <i>zz</i> component of the shielding tensor along the symmetry axis of highly symmetric ring-shaped aromatic, antiaromatic and nonaromatic molecules. The calculated ring-current strengths agree perfectly with the ones obtained by integrating the current-density flux passing through a plane cutting half the molecular ring. The method can be used in combination with all electronic structure codes capable of calculating nuclear magnetic resonance (NMR) shielding tensors in general points in space. We also show that nucleus independent chemical shifts (NICS) along the symmetry axis are related to the spatial derivative of the strength of the global ring-current along the <i>z</i> axis.