Nonlocal vs local pseudopotentials affect kinetic energy kernels in orbital-free DFT

Abstract 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.