Truncated nonlocal kinetic energy density functionals for simple metals and silicon

The adoption of an accurate kinetic energy density functional (KEDF) to characterize the noninteracting kinetic energy within the framework of orbital-free density functional theory (OFDFT) is challenging. We propose a form of the nonlocal KEDF with a real-space truncation cutoff that satisfies the uniform electron gas limit and design KEDFs for simple metals and silicon. These KEDFs are obtained by minimizing a residual function, which contains the differences in the total energy and charge density of several representative systems with respect to the Kohn-Sham DFT results. By systematically testing different cutoffs of these KEDFs, we find that the cutoff plays a crucial role in determining the properties of metallic Al and semiconductor Si systems. We conclude that the KEDF with a sufficiently long cutoff performs even better than some representative non-local KEDFs in some aspects, which sheds light on optimizing the KEDFs in OFDFT to achieve better accuracy.