Aromaticity of Substituted Benzene Derivatives Employing a New Set of Aromaticity Descriptors Based on the Partition...

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 $Q_2$ tensor from the Stone's Distributed Multipole Analysis (DMA) to examine the aromaticity trends in monosubstituted benzene derivatives ( $C_6{H}_{5}C{H}_3$ , $C_6{H}_{5}C{H}_2^{-}$ , $C_6{H}_{5}C{H}_2^{+}$ , $C_6{H}_{5}N{H}_2$ , $C_6{H}_{5}N{H}^{-}$ , $C_6{H}_{5}N{H}^{+}$ , $C_6{H}_5\mathrm{OH}$ , $C_6{H}_5{O}^{-}$ , and $C_6{H}_5{O}^{+}$ ) and para-homodisubstituted analogs ( $C_6{H}_4{\left(C{H}_3\right)}_2$ , $C_6{H}_4{\left(C{H}_2\right)}_2$ , $C_6{H}_4{\left(N{H}_2\right)}_2$ , $C_6{H}_4{\left(\mathrm{NH}\right)}_2$ , $C_6{H}_4{\left(\mathrm{OH}\right)}_2$ , and $C_6{H}_4{\left(O\right)}_2$ ). The $Q_2$ 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 $Q_2$ variation, neutral with strong $Q_2$ perturbation ( $C_6{H}_4{\left(O\right)}_2$ and $C_6{H}_4{\left(N{H}_2\right)}_2$ ), positively, and negatively charged species. Comparisons with the traditional aromaticity descriptors $\text{HOMA}$ , $\mathrm{AI}\left(\mathrm{vib}\right)$ , $I_{\text{ring}}$ , $\text{NICS}$ , $\mathrm{EL}{F}_{\pi }$ , and $\mathrm{MCI}$ were carried out. Among the $Q_2$ -based descriptors, $Q_2{\left(1\right)}_{\mathrm{zz}}$ , which is computed 1 Å above the ring plane, exhibited the highest correlation with those descriptors, though small ( $R^2\approx 0.6$ ). All the $Q_2$ -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 $Q_2$ -based descriptors correlated with ionization potentials ( $\mathrm{IPs}$ ), electron affinities ( $\mathrm{EAs}$ ), electronegativities ( $\chi$ ), electrophilicity indexes ( $\omega$ ), and electron-donating/accepting power ( ${\omega }^{-}$ , ${\omega }^{+}$ ), but not with the chemical hardness ( $\eta$ ). In contrast, $I_{\text{ring}}$ , $\text{NICS}$ , $\mathrm{EL}{F}_{\pi }$ , and $\mathrm{MCI}$ correlated only with $\eta$ , while $\text{HOMA}$ and $\mathrm{AI}\left(\mathrm{vib}\right)$ showed no correlation. Therefore, our results show that the $Q_2$ -based descriptors reflect the π-electron delocalization characteristic of aromaticity and also can describe frontier-orbital reactivity trends.