Machine learning based nonlocal kinetic energy density functional for simple metals and alloys

Developing an accurate kinetic energy density functional (KEDF) remains a major hurdle in orbital-free density functional theory. We propose a machine-learning-based physical-constrained nonlocal (MPN) KEDF and implement it with the usage of the bulk-derived local pseudopotentials and plane wave basis sets in the abacus package. The MPN KEDF is designed to satisfy three exact physical constraints: the scaling law of electron kinetic energy, the free electron gas limit, and the non-negativity of Pauli energy density. The MPN KEDF is systematically tested for simple metals, including Li, Mg, Al, and 59 alloys. We conclude that incorporating nonlocal information for designing new KEDFs and obeying exact physical constraints are essential to improve the accuracy, transferability, and stability of ML-based KEDF. These results shed new light on the construction of ML-based functionals.