Machine Learning Determination of New Hammett’s Constants for meta- and para-Substituted Benzoic Acid Derivatives Employing Quantum Chemical Atomic Charge Methods

Hammett's constants σ quantify the electron donor or electron acceptor power of a chemical group bonded to an aromatic ring. Their experimental values have been successfully used in many applications, but some are inconsistent or not measured. Therefore, developing an accurate and consistent set of Hammett's values is paramount. In this work,we employed different types of machine learning (ML) algorithms combined with quantum chemical calculations of atomic charges to predict theoretically new Hammett's constants σm, σp, σm0, σp0, σp+, σp-, σR, and σI for 90 chemical donor or acceptor groups. New σ values (219), including previously unknown 92, are proposed. The substituent groups were bonded to benzene and meta- and para-substituted benzoic acid derivatives. Among the charge methods (Mulliken, Löwdin, Hirshfeld, and ChelpG), Hirshfeld showed the best agreement for most kinds of σ values. For each type of Hammett constant, linear expressions depending on carbon charges were obtained. The ML approach overall showed very close predictions to the original experimental values, with meta- and para-substituted benzoic acid derivative values showing the most accurate values. A new consistent set of Hammett's constants is presented, as well as simple equations for predicting new values for groups not included in the original set of 90.