Capturing electronic substituent effect with effective atomic orbitals

The occupations of the effective atomic orbitals (eff-AOs) of the carbon atoms in the aromatic ring serve as the basis for deriving accurate descriptors of the inductive (F) and resonance (R) effects exerted by substituents in substituted benzene derivatives. The eff-AOs enable a clear separation of the σ-type electron density into contributions originating from the C-H/X bonds (where X represents a substituent) and those from the C-C bonding framework. Our analysis reveals that the inductive effect of a substituent is effectively captured by the shift in the occupation of the eff-AOs associated with the C-C bonding framework at the meta position. In contrast, the resonance effect is well-described by the shifts in the occupations of the 2p_z-type eff-AOs at the ortho and para positions. The two introduced descriptors for inductive and resonant effects, namely I^X and R^X, are also applied to predict Hammett's σ_m and σ_p in meta- and para-substituted benzoic acid derivatives. In the case of the meta-substituted derivatives, the predictions of the σ_m values are excellent, with a mean average error of just 0.04. This approach provides a robust and systematic framework for quantifying substituent effects in aromatic systems.