Induced orbital paramagnetism and paratropism inclosed-shell molecules

Three-dimensional models of the quantum-mechanical current density induced by auniform magnetic field in the electron cloud have been obtained for closed-shell systemsBeH−, BH, and CH+, characterized by induced orbital paramagnetism, and in planarunsaturated hydrocarbons C4H4 and clamped C8H8, exhibiting π paramagnetism. It isshown that, even for these paramagnetic systems, the paramagnetic contributions to mag-netic susceptibilities and nuclear magnetic shielding, customarily taken into account inperturbation theory approaches, can formally be eliminated via the procedure of continu-ous transformation of the origin of the current density-paramagnetic zero. The definitionof magnetic response properties can therefore be recast as a sum of two formally “diamag-netic” terms for any molecule, including systems showing strong induced orbital param-agnetism. It is shown that the paramagnetism in the compounds studied arises from thenodal topology of the electronic wavefunction. In particular, paratropic vortices circu-late about stagnation lines at the intersection of nodal surfaces of the highest-occupiedzero-order molecular orbital and corresponding first-order orbital.