Performance of the π-electron density anisotropy for planner-ring metal clusters

Recent studies have shown that the shape and the anisotropy of the π-electron density (ρπ) onplanes parallel to the molecular ring can be used to assess the aromaticity of a large numberof annulenes (CnHn), azines (nitrogen-containing six-membred rings), substituted penta- andhepta-fulvenes, and hetero-monocyclic compounds with different charges, multiplicities andring sizes [1, 2]. This topological property of ρπ can be simply measured through the ratio oftwo in-plane positive eigenvalues of the π-electron density Hessian matrix at the ring criticalpoint (RCP) and all scanned points along the axis perpendicular to the molecular ring plane.For the aromatic compounds, the two positive local curvatures are degenerate and the mannerof the π-electron density distribution on the parallel planes is isotropical and undirected,whereas the degeneracy of the eigenvalues for antiaromatic rings completely disappear andthe shape of the electron density distribution on the planes is anisotropical and directed. Inthis report, we extend our recent methodology to investigate the aromatic character of a set offour planner monocyclic molecules, composed of Al, Ga, Si and Ge atoms.