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) (tpJ(r)) that is a scalar field. The topology of tpJ(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 tpJ(r) to clearly reproduce the Clar's structure of polycyclic aromatic hydrocarbons. © 2019 Wiley Periodicals, Inc.