To what extent can aromaticity be defined uniquely

TLDR: The various manifestations of aromaticity are related and aromaticity can be regarded statistically as a one-dimensional phenomenon, but when comparisons are restricted to some regions or groups of compounds, the quality of the correlations can deteriorate or even vanish.

Abstract: Statistical analyses of quantitative definitions of aromaticity, ASE (aromatic stabilization energies), RE (resonance energies), Λ (magnetic susceptibility exaltation), NICS, HOMA, I5, and AJ, evaluated for a set of 75 five-membered π-electron systems:  aza and phospha derivatives of furan, thiophene, pyrrole, and phosphole (aromatic systems), and a set of 30 ring-monosubstituted compounds (aromatic, nonaromatic, and antiaromatic systems) revealed statistically significant correlations among the various aromaticity criteria, provided the whole set of compounds is involved. Hence, broadly considered, the various manifestations of aromaticity are related and aromaticity can be regarded statistically as a one-dimensional phenomenon. In contrast, when comparisons are restricted to some regions or groups of compounds, e.g., aromatic compounds with ASE > 5 kcal/mol or polyhetero-five-membered rings, the quality of the correlations can deteriorate or even vanish. In practical applications, energetic, geometric, ...