Abstract
Aromatic compounds represent about two-thirds of known molecules. Despite that, aromaticity still lacks a precise definition, leading to the use of various descriptors to quantify it. In this work, we employ a new set of six descriptors (ACS Omega 2025, 10, 14157) built from components of the quadrupole moment Q2 tensor from the Stone's Distributed Multipole Analysis (DMA) to examine the aromaticity trends in monosubstituted benzene derivatives ( C6H5CH3 , C6H5CH2- , C6H5CH2+ , C6H5NH2 , C6H5NH- , C6H5NH+ , C6H5OH , C6H5O- , and C6H5O+ ) and para-homodisubstituted analogs ( C6H4(CH3)2 , C6H4(CH2)2 , C6H4(NH2)2 , C6H4(NH)2 , C6H4(OH)2 , and C6H4(O)2 ). The Q2 tensor is the first term in the DMA electric multipole expansion to include out-of-plane electron density contributions. Using a machine learning clustering technique, we identified four groups of molecules: neutral with minimal Q2 variation, neutral with strong Q2 perturbation ( C6H4(O)2 and C6H4(NH2)2 ), positively, and negatively charged species. Comparisons with the traditional aromaticity descriptors HOMA , AI(vib) , Iring , NICS , ELFπ , and MCI were carried out. Among the Q2 -based descriptors, Q2(1)zz , which is computed 1 Å above the ring plane, exhibited the highest correlation with those descriptors, though small ( R2 ≈ 0.6 ). All the Q2 -based descriptors reproduced the same trends of the traditional indices, except for the negative substituents, which were only correctly described by the former ones. We found that Q2 -based descriptors correlated with ionization potentials ( IPs ), electron affinities ( EAs ), electronegativities ( χ ), electrophilicity indexes ( ω ), and electron-donating/accepting power ( ω- , ω+ ), but not with the chemical hardness ( η ). In contrast, Iring , NICS , ELFπ , and MCI correlated only with η , while HOMA and AI(vib) showed no correlation. Therefore, our results show that the Q2 -based descriptors reflect the π-electron delocalization characteristic of aromaticity and also can describe frontier-orbital reactivity trends.