Induced Orbital Paramagnetism and Paratropism in Closed-Shell Molecules

Abstract

Three-dimensional models of the quantum-mechanical current density induced by a uniform magnetic field in the electron cloud have been obtained for closed-shell systems BeH(-), BH, and CH(+), characterized by induced orbital paramagnetism, and in planar unsaturated hydrocarbons C(4)H(4) and clamped C(8)H(8), exhibiting pi paramagnetism. It is shown that, even for these paramagnetic systems, the paramagnetic contributions to magnetic susceptibilities and nuclear magnetic shielding, customarily taken into account in perturbation theory approaches, can formally be eliminated via the procedure of continuous transformation of the origin of the current density-paramagnetic zero. The definition of magnetic response properties can therefore be recast as a sum of two formally "diamagnetic" terms for any molecule, including systems showing strong induced orbital paramagnetism. It is shown that the paramagnetism in the compounds studied arises from the nodal topology of the electronic wave function. In particular, paratropic vortices circulate about stagnation lines at the intersection of nodal surfaces of the highest-occupied zero-order molecular orbital and corresponding first-order orbital.