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

Without incurring additional computational cost, the\nHubbard model\ncan prevalently address the electron self-interaction problems of\nthe local or semilocal exchange–correlation functions within\ndensity functional theory. However, determining the value of the Hubbard\nparameter, <i>U</i>, promptly, efficiently, and accurately\nhas been a long-standing challenge. Here, we develop a method for\npredicting the Hubbard <i>U</i> of iron oxides by establishing\na potential relationship through machine learning fitting of structural\nfingerprints and the <i>U</i> evaluated by the linear response-constrained\ndensity functional theory method. This method performs well in calculating\nthe properties of wüstite, hematite, and magnetite, aligning\nwith experimental measurements or more costly hybrid functional results.\nUsing this method, we redefine the convex hulls of the Fe–O\nsystem at 0, 50, and 100 GPa; the obtained results are in good agreement\nwith experimental observations. We also provide insights into the\ndebates surrounding the high-pressure phases of Fe<sub>2</sub>O<sub>3</sub> and Fe<sub>3</sub>O<sub>4</sub>.