The Wang-Teter (WT)-like nonlocal kinetic energy density functional (KEDF) in the framework of orbital-free density functional theory, while successful in some bulk systems, exhibits a critical Blanc-Cancès instability [J. Chem. Phys. 122, 214106 (2005)] when applied to isolated systems, where the total energy becomes unbounded from below. We trace this instability to the use of an ill-defined average charge density, which causes the functional to simultaneously violate the scaling law and the positivity of the Pauli energy. By rigorously constructing a density-functional-dependent kernel, we resolve these pathologies while preserving the formal exactness of the original framework. By systematically benchmarking single-atom systems of 56 elements, we find the resulting KEDF retains computational efficiency while achieving an order-of-magnitude accuracy enhancement over the WT KEDF. In addition, this proposed KEDF preserves WT's superior accuracy in bulk metals, outperforming the semilocal functionals in both regimes.

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• Density functional theory
• Electronic structure
• Atoms
• Density functional approximations