Predicting rare earth extraction efficiency with organophosphorus ligands: A data-driven machine learning approach

Abstract

Organophosphorus ligands are widely employed as extractants in industrial rare-earth (RE) separation; however, their design and optimization have largely been guided by empirical methodologies rather than systematic, rational approaches. In this work, we present a data-driven machine learning framework for predicting the distribution ratios (D) of RE elements in extraction processes using various organophosphorus ligands. To support this effort, a curated database comprising over 3500 experimental D measurements was established, encompassing 43 distinct ligands and 16 RE elements (excluding radioactive promethium) under varied extraction conditions. By integrating ligand descriptors, metal ion properties, and extraction parameters, we developed a convolutional neural network (CNN) model that achieves robust performance, with R² values of approximately 0.98 for training and 0.83 for testing. Our analysis further identified key factors – such as aqueous pH, ligand structural fragments, partial charges, metal ionic radii and topological features – that govern extraction behavior and correlate with specific mechanisms. Finally, the predictive capability of model was validated by accurately forecasting the D value of a newly synthesized ligand HA.