Current density, current-density pathways and molecular aromaticity

Current densities are induced in the electronic structure of molecules when they are exposed to external magnetic fields. Aromatic molecular rings sustain net diatropic ring currents, whereas the net ring current in antiaromatic molecular rings is paratropic and flows in the opposite, non-classical direction. We present computational methods and protocols to calculate, analyse and visualise magnetically induced current densities in molecules. Calculated ring-current strengths are used for quantifying the degree of aromaticity. The methods have been demonstrated by investigating ring-current strengths and the degree of aromaticity of aromatic, antiaromatic and non-aromatic six-membered hydrocarbon rings. Current-density pathways and ring-current strengths of aromatic and antiaromatic porphyrinoids and other polycyclic molecules have been studied. The aromaticity and current density of M\"obius-twisted molecules has been investigated to find the dependence on the twist and the spatial deformation of the molecular ring. Current densities of fullerene, gaudiene and toroidal carbon nanotubes have also been studied.