  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 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 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 (cd) 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.
