The vorticity of the current density tensor and 3D-aromaticity

The induced current density ( J ( r )) vector field has been extensively used as a criterion of aromaticity and electron delocalization. However, the selection of the direction of the perturbing magnetic field ( B ) is arbitrary and in the case of three-dimensional electron delocalization/aromaticity the selection could be ambiguous. The J ( r ) has also recently received some criticism as an aromaticity index. We propose the Trace of the Vorticity of the Current Density tensor (TVCD) scalar field as a more suitable quantity for the evaluation of electron delocalization of three-dimensional systems. It does not depend on the orientation of B and contrary to other related scalar fields like the anisotropy of the induced current density, it does not lose the information of the direction of the currents. We show that not only the currents parallel to the molecular plane are important in the evaluation of the aromaticity, as is largely believed, but also the perpendicular ones, which information is included in the TVCD. The TVCD is very useful to study planar and 3D delocalized molecules (eg, fullerenes). Moreover, the integration of the TVCD over an internal surface of the 3D-cages serves as index for 3D-aromaticity.