Imposing Correct Jellium Response Is Key to Predict Linear and Non-linear Density Response by Orbital-Free DFT

Orbital-free density functional theory (OF-DFT) 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 use an external harmonic perturbation in OF-DFT to compute the density response function. This allows us to test whether exact conditions in the limit of uniform densities (i.e. for the uniform electron gas, or UEG) are satisfied. We demonstrate the utility of this direct perturbation approach by considering different non-local and Laplacian-level KE functionals. The results illustrate that several functionals violate exact conditions in the UEG limit. Additionally, we also test KE functional approximations beyond the linear density response regime by gradually increasing the density perturbation amplitude and comparing against Kohn-Sham DFT results which employ the exact non-interacting KE functional. The results show 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 the UEG limit based constraint for the construction of accurate KE functionals. This conclusion is substantiated by additional calculations for bulk Aluminum (Al) with a face-centered cubic lattice with and without an external harmonic perturbation. The analysis of the Al data follows closely the conclusions drawn for the UEG, allowing us to extend our conclusions to realistic systems that experience density inhomogeneities induced by ions. Analyzing other classes of KE functionals (e.g., based on the quadratic UEG density response function and the jellium-with-gap model) and other types of systems, such as semiconductors, is left for future studies.