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

Characterization of Local Aromaticity in Polycyclic Conjugated Hydrocarbons Based on Anisotropy of π‐Electron Density

“…For the aromatic compounds, the two positive eigenvalues are degenerate and the pattern of the π‐electron density distribution on the parallel planes is isotropical and undirected, whereas the degeneracy of the eigenvalues for antiaromatic rings completely disappears and the shape of the electron density distribution on the planes is anisotropical and directed. We also found that the degeneracy of the eigenvalues is insensitive to the geometrical distortions . The non‐equilibrium bond‐alternate benzene with D 3h symmetry (driven from the B 2u vibrational mode) has isotropical distribution of ρ π on the planes parallel to the molecular ring, which is similar to the observations for the undistorted D 6h benzene.…”

“…As mentioned in the Introduction and also discussed more fully in our recent paper, for the singlet ground state of benzene, with hexagonal equilibrium D 6h symmetry, the shape of the π‐electron density distribution on the planes parallel to the molecular ring is isotropical and undirected since the two in‐plane Hessian eigenvalues at the RCP and all scanned points along the normal axis to the ring surface have the same values and are degenerate. In the polyacenes, the structure and electron density distribution of benzene have been perturbed by the fusion with one or more benzenoid rings.…”

“…Several attempts have been made in recent years to use the topological properties of the electron density distribution to describe the aromatic character, but there is some doubt about the existence of a general straightforward link between the local properties of the electron density and the aromatic character, and also about the general applicability of them beyond simple compounds . These arguments stem from the fact that the electron density distribution and its topological properties at a point in molecular space highly depends on the distance from nuclei as well as the type of nuclei and, therefore, it seems reasonable to doubt that the local properties of the electron density are not suitable descriptors to measure the aromaticity in complex molecules such as heterocyclic compounds.…”

“…Recently, we have demonstrated that the anisotropy of the π‐electron density ( ρ π ) on planes parallel to the molecular ring can be used to assess the aromaticity of a large number of annulenes (C n H n ), azines (nitrogen‐containing six‐membred rings), substituted penta‐ and hepta‐fulvenes, and hetero‐monocyclic compounds with different charges, multiplicities and ring sizes ,. This topological property of ρ π can be simply determined through the ratio of two in‐plane positive eigenvalues of the π‐electron density Hessian matrix at the ring critical point (RCP) and all scanned points along the axis perpendicular to the molecular ring plane.…”

Electron Density Analysis of Hyperconjugation

“…However, in a recent work by the present author, electron density analysis is generalized to π‐type electron density topology, which enables the detection of a hyperconjugative interaction. This approach is also used for the characterization of several concepts and interactions including aromaticity, antiaromaticity, heteroaromaticity, metal–π interaction, and van der Waals complexes …”