Machine-Learning-Based Non-Local Kinetic Energy Density Functional for Simple Metals and Alloys*

The development of an accurate kinetic energy density functional (KEDF) remains a major hurdle in orbital-free density functional theory (OFDFT). By constructing a series of truncated non-local KEDFs, we find that considering the interactions between an atom and its next nearest neighbor atoms is crucial for a non-local KEDF to distinguish the energy orderings among bulk structures, as well as to accurately predict the surface energies and point vacancy energies of Al and Si systems. Furthermore, we propose a machine-learning-based non-local KEDF, which is subject to 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 machine-learning-based KEDF is systematically tested for simple metals, including Li, Mg, Al, and 59 alloys. We conclude that incorporating non-local 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 KEDFs.