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The kinetic energy (KE) kernel, which is defined as the second order functional derivative of the KE functional with respect to density, is the key ingredient to the construction of KE models for orbital free density functional theory applications. For solids, KE kernels are usually approximated using the uniform electron gas (UEG) model or the UEG-with-gap model. These kernels do not have knowledge about the core electrons since there are no orbitals directly available to couple with nonlocal pseudopotentials (NLPs). To illuminate this aspect, we provide a methodology for computing KE kernels from pseudopotential Kohn–Sham DFT and apply them to the valence electrons in bulk aluminum (Al) with a face-centered cubic lattice and in bulk silicon (Si) in a semiconducting crystal diamond state. We find that bulk-derived local pseudopotentials provide accurate KE kernels in the interstitial region. However, the effect of using NLPs manifests at short wavelengths, roughly defined by the cutoff radius of the nonlocal part of the Kohn–Sham DFT pseudopotential. In this region, we record significant deviations between KE kernels and the von Weizsäcker result. 

Orbital-free density functional theory constitutes a computationally highly effective tool for modeling electronic structures of systems ranging from room-temperature materials to warm dense matter. Its accuracy critically depends on the employed kinetic energy (KE) density functional, which has to be supplied as an external input. In this work we consider several nonlocal and Laplacian-level KE functionals and use an external harmonic perturbation to compute the static density response at T=0 K in the linear and beyond-linear response regimes. We test for the satisfaction of exact conditions in the limit of uniform densities and for how approximate KE functionals reproduce the density response of realistic materials (e.g., Al and Si) against the Kohn-Sham DFT reference, which employs the exact KE. The results illustrate that several functionals violate exact conditions in the uniform electron gas (UEG) limit. We find a strong correlation between the accuracy of the KE functionals in the UEG limit and in the strongly inhomogeneous case. This empirically demonstrates the importance of imposing the limit of UEG response for uniform densities and validates the use of the Lindhard function in the formulation of kernels for nonlocal functionals. This conclusion is substantiated by additional calculations for bulk aluminum (Al) with a face-centered cubic (fcc) lattice and silicon (Si) with an fcc lattice, body-centered cubic (bcc) lattice, and semiconducting crystal diamond state. The analysis of fcc Al, and fcc as well as bcc Si data follows closely the conclusions drawn for the UEG, allowing us to extend our conclusions to realistic systems that are subject to density inhomogeneities induced by ions.