A machine learning-driven prediction of Hammett constants using quantum chemical and structural descriptors

Abstract

Understanding and predicting chemical reaction behavior is a fundamental challenge in chemistry. The Hammett equation, introduced in 1935, has been a cornerstone in modelling structure–activity relationships, particularly in physical organic chemistry. In this study, machine learning (ML) is employed to predict Hammett constants (σ_m and σ_p) for a diverse collection of benzoic acid derivatives, based on a dataset previously developed by our group that includes over 900 molecules spanning meta-, para-, and symmetrically substituted variants. Quantum chemical descriptors, combined with Mordred-based electronic, steric, and topological descriptors, were used to train models such as Extra Trees (ET) and Artificial Neural Networks (ANNs). The ANN model achieved the highest accuracy, with a test R² of 0.935 and an RMSE of 0.084, outperforming other models and a previously developed graph neural network. Feature importance analysis revealed key descriptors, including NBO charges and HOMO energies, driving the predictions. Applicability domain (AD) analysis identified outliers and compounds outside the AD, ensuring model reliability. This work highlights the potential of ML in predicting Hammett constants, offering a robust tool for chemical reactivity analysis and molecular design.