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

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 $$ {\boldsymbol{Q}}_2 $$ 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 $$ {\mathrm{C}}_6{\mathrm{H}}_5\mathrm{C}{\mathrm{H}}_3 $$ , C 6 H 5 C H 2 - $$ {\mathrm{C}}_6{\mathrm{H}}_5\mathrm{C}{\mathrm{H}}_2^{-} $$ , C 6 H 5 C H 2 + $$ {\mathrm{C}}_6{\mathrm{H}}_5\mathrm{C}{\mathrm{H}}_2^{+} $$ , C 6 H 5 N H 2 $$ {\mathrm{C}}_6{\mathrm{H}}_5\mathrm{N}{\mathrm{H}}_2 $$ , C 6 H 5 N H - $$ {\mathrm{C}}_6{\mathrm{H}}_5\mathrm{N}{\mathrm{H}}^{-} $$ , C 6 H 5 N H + $$ {\mathrm{C}}_6{\mathrm{H}}_5\mathrm{N}{\mathrm{H}}^{+} $$ , C 6 H 5 OH $$ {\mathrm{C}}_6{\mathrm{H}}_5\mathrm{OH} $$ , C 6 H 5 O - $$ {\mathrm{C}}_6{\mathrm{H}}_5{\mathrm{O}}^{-} $$ , and C 6 H 5 O + $$ {\mathrm{C}}_6{\mathrm{H}}_5{\mathrm{O}}^{+} $$ ) and para-homodisubstituted analogs ( C 6 H 4 C H 3 2 $$ {\mathrm{C}}_6{\mathrm{H}}_4{\left(\mathrm{C}{\mathrm{H}}_3\right)}_2 $$ , C 6 H 4 C H 2 2 $$ {\mathrm{C}}_6{\mathrm{H}}_4{\left(\mathrm{C}{\mathrm{H}}_2\right)}_2 $$ , C 6 H 4 N H 2 2 $$ {\mathrm{C}}_6{\mathrm{H}}_4{\left(\mathrm{N}{\mathrm{H}}_2\right)}_2 $$ , C 6 H 4 NH 2 $$ {\mathrm{C}}_6{\mathrm{H}}_4{\left(\mathrm{NH}\right)}_2 $$ , C 6 H 4 OH 2 $$ {\mathrm{C}}_6{\mathrm{H}}_4{\left(\mathrm{OH}\right)}_2 $$ , and C 6 H 4 O 2 $$ {\mathrm{C}}_6{\mathrm{H}}_4{\left(\mathrm{O}\right)}_2 $$ ). The Q 2 $$ {\boldsymbol{Q}}_2 $$ 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 $$ {\boldsymbol{Q}}_2 $$ variation, neutral with strong Q 2 $$ {\boldsymbol{Q}}_{\mathbf{2}} $$ perturbation ( C 6 H 4 O 2 $$ {\mathrm{C}}_6{\mathrm{H}}_4{\left(\mathrm{O}\right)}_2 $$ and C 6 H 4 N H 2 2 $$ {\mathrm{C}}_6{\mathrm{H}}_4{\left(\mathrm{N}{\mathrm{H}}_2\right)}_2 $$ ), positively, and negatively charged species. Comparisons with the traditional aromaticity descriptors HOMA $$ HOMA $$ , AI vib $$ AI(vib) $$ , I ring $$ {I}_{ring} $$ , NICS $$ NICS $$ , EL F π $$ EL{F}_{\pi } $$ , and MCI $$ MCI $$ were carried out. Among the Q 2 $$ {\boldsymbol{Q}}_2 $$ -based descriptors, Q 2 1 zz $$ {Q}_2{(1)}_{zz} $$ , which is computed 1 Å above the ring plane, exhibited the highest correlation with those descriptors, though small ( R 2 ≈ 0.6 $$ {R}^2\approx 0.6 $$ ). All the Q 2 $$ {\boldsymbol{Q}}_2 $$ -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 $$ {\boldsymbol{Q}}_2 $$ -based descriptors correlated with ionization potentials ( IPs $$ IPs $$ ), electron affinities ( EAs $$ EAs $$ ), electronegativities ( χ $$ \chi $$ ), electrophilicity indexes ( ω $$ \omega $$ ), and electron-donating/accepting power ( ω - $$ {\omega}^{-} $$ , ω + $$ {\omega}^{+} $$ ), but not with the chemical hardness ( η $$ \eta $$ ). In contrast, I ring $$ {I}_{ring} $$ , NICS $$ NICS $$ , EL F π $$ EL{F}_{\pi } $$ , and MCI $$ MCI $$ correlated only with η $$ \eta $$ , while HOMA $$ HOMA $$ and AI vib $$ AI(vib) $$ showed no correlation. Therefore, our results show that the Q 2 $$ {\boldsymbol{Q}}_2 $$ -based descriptors reflect the π-electron delocalization characteristic of aromaticity and also can describe frontier-orbital reactivity trends.