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 quantify the electron or electron acceptor power of a chemical group bonded to an aromatic ring. Their experimental values have been successfully used in a large variety of applications, but some of them may have inconsistent values or were not measured. For this reason, developing an accurate and consistent set of Hammett's values is paramount. In this work, we employed the machine learning (ML) regression algorithms Decision Tree Regressor, the neural network Multilayer Perceptron Regressor, and Lasso Lars IC in a cross-validation (CV) approach combined with quantum chemical calculations of atomic charges to estimate theoretically the new Hammett's constants for 90 chemical donor or acceptor groups by employing different types of quantum chemical atomic charges of the groups as input properties. New 219 sigma values, including previously unknown ones, are proposed for 90 chemical donor or acceptor groups by employing different types of quantum chemical atomic charges of the groups as input properties. The different substituent groups were bonded to benzene and meta- and para-substituted benzoic acid derivatives. Among the investigated atomic charge methods (Mulliken, Lwdin, Hirshfeld, and ChelpG), Hirshfeld's method showed the best regressions for most of the different kinds of sigma values. For each type of Hammett constant, linear expressions depending only on the atomic charges of the group were obtained. Correlation coefficients as high as 0.945, mean squared errors (MSE) as low as 0.004, and root mean square errors (RMSE) as low 0.062, were found. The ML approach, in most cases, showed very close predictions to the original experimental values, with the values from meta- and para-substituted benzoic acid derivatives showing the most accurate values. A new consistent set of Hammetts constants is presented, as well as simple equations for predicting new values for groups not included in the original set of 90.