The degeneracy of the Hessian eigenvalues of the π-electron density: A new manifestation of aromaticity

This letter aims to demonstrate how the anisotropy of π-electron density can be used for distinguishing between aromatic and antiaromatic systems. For this purpose the total electron density and its σ- and π-components have been analyzed for a series of well-known aromatic and antiaromatic organic compounds with different sizes, charges, and multiplicities. In aromatic compounds, the anisotropy of π-electron density has a perfectly circular shape whereas in antiaromatic rings, it has an elliptical shape. It was found that this descriptor is in line with Hückel’s and Baird’s rules and also is insensitive to the size and geometrical deformation of rings.