Fast and stable tight-binding framework for nonlocal kinetic energy density functional reconstruction in orbital-free density functional calculations

Nonlocal kinetic energy density functionals (KEDFs) with density-dependent kernels are currently the most accurate functionals available for orbital-free density functional theory (OF-DFT) calculations. However, despite advances in numerical techniques and using only (semi)local density-dependent kernels, nonlocal KEDFs still present substantial computational costs in OF-DFT, limiting their application in large-scale material simulations. To address this challenge, we propose an efficient framework for reconstructing nonlocal KEDFs by incorporating the density functional tight-binding approach, in which the energy functionals are simplified through a first-order functional expansion based on the superposition of free-atom electron densities. This strategy allows the computationally expensive nonlocal kinetic energy and potential calculations to be performed only once during the electron density optimization process, significantly reducing computational overhead while maintaining high accuracy. Benchmark tests using advanced nonlocal KEDFs, such as revHC and LDAK-MGPA, on standard structures including Li, Mg, Al, Ga, Si, III-V semiconductors, as well as Mg$_{50}$ and Si$_{50}$ clusters, demonstrate that our method achieves orders-of-magnitude improvements in efficiency, providing a cost-effective balance between accuracy and computational speed. Additionally, the reconstructed functionals exhibit improved numerical stability for both bulk and finite systems, paving the way for developing more sophisticated KEDFs for realistic material simulations using OF-DFT.