Atomic Charges from Machine-Learned Charge Densities: Consistency and Substituent Effects

Atomic charges are widely used to analyze molecular electronic structure and substituent effects, yet their numerical values and interpretations are inherently dependent on the adopted density partitioning scheme. Here, we adapt the Equivariant Atomic Contribution framework to molecular systems (EAC-qm), enabling prediction of atom-resolved continuous charge densities from which atomic charges are obtained as spatial moments. The predicted densities reproduce reference density functional theory results with high accuracy and preserve global charge conservation. To assess chemical interpretability, we examine charge responses in monosubstituted aromatic systems using Hammett substituent constants as external empirical references. Atomic charges derived from EAC-qm exhibit a strong linear association with Hammett parameters, compared with values obtained from traditional density partitioning approaches applied to the same electronic structures. These correlations indicate that density-derived charges respond systematically to established substituent electronic trends. Beyond scalar charges, atom-resolved dipole moments can be evaluated as first-order moments of the same continuous density representation. Illustrative examples for formaldehyde (H₂CO) and formamide (HCONH₂) show that local dipole vectors provide directional information about intra-atomic polarization that is not captured by point-charge models. Overall, the results suggest that machine-learned continuous electron densities provide a representation-consistent basis for constructing atom-centered electronic descriptors with chemical interpretability.