Kinetic energy constructed from exact gradient expansion of second order in uniform gas limit

Abstract

Orbital-Free Density Functional Theory (OFDFT) has re-emerged as a viable alternative to Kohn-Sham DFT, driven by recent advances in kinetic energy density functionals (KEDFs). Nonlocal (NL) KEDFs have significantly extended OFDFT's applicability, particularly for bulk solids, but their high computational cost and dependence of system-specific parameters limit their universality. In this work, we propose a semilocal KEDF at the Generalized Gradient Approximation (GGA) level that achieves accuracy comparable to state-of-the-art NL and meta-GGA functionals, while remaining entirely parameter-free. Our construction revives the Thomas-Fermi-von Weizsacker (TFvW) framework by modulating the relative contributions of TF and vW terms through physically motivated constraints and preserving the exact second-order gradient expansion. Despite its simple form, the proposed functional (KGE2) performs remarkably well across both extended systems (metals and semiconductors) and finite systems (clusters), without any need for parameter tuning. These results mark a step toward a transferable, computationally efficient, and general-purpose KEDF suitable for large-scale OFDFT simulations.