In this perspective, different expert opinions are gathered on the definition and concept of aromaticity.

Concise information on the general features of the quantum-mechanical current density induced in the electrons of a molecule by a spatially uniform, time-independent magnetic field is obtained via a stagnation graph that shows the isolated singularities and the lines at which the current-density vector field vanishes. Stagnation graphs provide compact description of current-density vector fields and help the interpretation of molecular magnetic response, e.g., magnetic susceptibility and nuclear magnetic shielding. The stagnation graph of six cyclic, planar aromatic molecules has been obtained at the Hartree-Fock level via a procedure based on continuous transformation of the origin of the current density formally annihilating the diamagnetic contribution. Some common distinctive elements observed for cyclic aromatic rings ${\mathrm{C}}_n{\mathrm{H}}_n$, with $n=3,4,\dots ,8$, in the presence of a magnetic field normal to the molecular plane, are discussed. The results can be used for a general discussion of diatropism in aromatic systems.

A gauge-invariant formalism is developed to describe the effect of parity-violating weak-nuclear interactions on nuclear magnetic chemical shift in molecules. Such effect is computed for two molecules with ab initio techniques and it is found to be orders of magnitude smaller than experimental resolution for the molecules considered.

It is shown that nonsymmetric second-rank current density tensors, related to the current densities induced by magnetic fields and nuclear magnetic dipole moments, are fundamental properties of a molecule. Together with magnetizability, nuclear magnetic shielding, and nuclear spin-spin coupling, they completely characterize its response to magnetic perturbations. Gauge invariance, resolution into isotropic, deviatoric, and antisymmetric parts, and contributions of current density tensors to magnetic properties are discussed. The components of the second-rank tensor properties are rationalized via relationships explicitly connecting them to the direction of the induced current density vectors and to the components of the current density tensors. The contribution of the deviatoric part to the average value of magnetizability, nuclear shielding, and nuclear spin-spin coupling, uniquely determined by the antisymmetric part of current density tensors, vanishes identically. The physical meaning of isotropic and anisotropic invariants of current density tensors has been investigated, and the connection between anisotropy magnitude and electron delocalization has been discussed.