Local Quadrupole Ellipticity as Predictor of Anion-Affinity in Nanographenes

Anion binding to nanographenes is governed by noncovalent interactions, particularly anion-π interactions in electron-deficient aromatic regions and CH---anion hydrogen bonding in electron-rich domains. These interactions are primarily driven by electrostatic effects, with the quadrupole moment of the aromatic system playing a central role in determining the strength and directionality of anion-π binding. The perpendicular component of the quadrupole moment (Q_zz) correlates with binding energies for both anion-π and CH---anion interactions, though polycyclic systems present challenges due to competing interaction modes. In this study, we investigate the role of the local quadrupole moment in anion binding across 171 Cl^--aromatic complexes, comparing various descriptors including aromaticity indices, Fukui functions, and electron density at ring critical points. We find that electrostatic descriptors, particularly the local quadrupole moment, provide a more consistent and robust explanation for binding energies than conventional descriptors. Specifically, two geometric descriptors derived from the local quadrupole moment-the scale factor ( $S_R^{\max }$ ) and the ellipticity ( $e_c^{\text{'}}$ )-show good correlation with binding strength, with $S_R^{\max }$ reflecting π-acidity and ellipticity quantifying charge distribution anisotropy. These descriptors are validated across fluorinated naphthalenes and nanographenes, demonstrating their general applicability. Regression models based on $S_R^{\max }$ and $e_c^{\text{'}}$ effectively predict binding energies, with enhanced accuracy when combined with polarization-dependent penalty functions, especially for larger nanographene systems. While the predictive model is still somewhat constrained by polarization effects, its simplicity, robustness, and transferability across a wide range of systems offer distinct advantages over more complex, multilayered machine learning models. These results underscore the critical role of quadrupole moment anisotropy in anion-π interactions and offer a practical framework for predicting anion binding affinities and designing π-acidic receptors.