Machine Learning Model for the Prediction of Hubbard <i>U</i> Parameters and Its Application to Fe–O Systems

Without incurring additional computational cost, the Hubbard model can prevalently address the electron self-interaction problems of the local or semilocal exchange-correlation functions within density functional theory. However, determining the value of the Hubbard parameter, <i>U</i>, promptly, efficiently, and accurately has been a long-standing challenge. Here, we develop a method for predicting the Hubbard <i>U</i> of iron oxides by establishing a potential relationship through machine learning fitting of structural fingerprints and the <i>U</i> evaluated by the linear response-constrained density functional theory method. This method performs well in calculating the properties of wüstite, hematite, and magnetite, aligning with experimental measurements or more costly hybrid functional results. Using this method, we redefine the convex hulls of the Fe-O system at 0, 50, and 100 GPa; the obtained results are in good agreement with experimental observations. We also provide insights into the debates surrounding the high-pressure phases of Fe₂O₃ and Fe₃O₄.