Vorticity: Simplifying the analysis of the current density

The induced current density ( J ( r )) provides useful information about the electronic structure of molecules under a magnetic field ( B ). However, the analysis of its topology is cumbersome because of its vectorial nature. We show that its tropicity (direction of rotation) and its strength can be compressed in the triple product B ? ? × J ( r ) (tp J ( r )) that is a scalar field. The topology of tp J ( r ) has clear similarities to the Laplacian of the electron density. Additionally, the topology of aromatic and antiaromatic compounds is notoriously different. The vorticity of J ( r ) is helpful to define the circulation of the current density, C, that contrary to other methods, can be easily defined for individual rings in polycyclic molecules. This allows tp J ( r ) to clearly reproduce the Clar's structure of polycyclic aromatic hydrocarbons. © 2019 Wiley Periodicals, Inc.