Machine learning approaches to predict the apparent rate constants for aqueous organic compounds by ferrate

The apparent second-order rate constant with hexavalent ferrate (Fe(VI)) (k_Fe(VI)) is a key indicator to evaluate the removal efficiency of a molecule by Fe(VI) oxidation. k_Fe(VI) is often determined by experiment, but such measurements can hardly catch up with the rapid growth of organic compounds (OCs). To address this issue, in this study, a total of 437 experimental second-order k_Fe(VI) rate constants at a range of conditions (pH and temperature) were used to train four machine learning (ML) algorithms (lasso regression (LR), ridge regression (RR), extreme gradient boosting (XGBoost), and the light gradient boosting machine (LightGBM)). Using the Morgan fingerprint (MF)) of a range of organic compounds (OCs) as the input, the performance of the four algorithms was comprehensively compared with respect to the coefficient of determination (R²) and root-mean-square error (RMSE). It is shown that the RR, XGBoost, and LightGBM models displayed generally acceptable performance k_Fe(VI) (R²_test > 0.7). In addition, the shapely additive explanation (SHAP) and feature importance methods were employed to interpret the XGBoost/LightGBM and RR models, respectively. The results showed that the XGBoost/LightGBM and RR models suggestd pH as the most important predictor and the tree-based models elucidate how electron-donating and electron-withdrawing groups influence the reactivity of the Fe(VI) species. In addition, the RR model share eight common features, including pH, with the two tree-based models. This work provides a fast and acceptable method for predicting k_Fe(VI) values and can help researchers better understand the degradation behavior of OCs by Fe(VI) oxidation from the perspective of molecular structure.