  We investigate the source of error in the Thomas-Fermi-von Weizs\"acker (TFW)
density functional relative to Kohn-Sham density functional theory (DFT). In
particular, through numerical studies on a range of materials, for a variety of
crystal structures subject to strain and atomic displacements, we find that
while the ground state electron density in TFW orbital-free DFT is close to the
Kohn-Sham density, the corresponding energy deviates significantly from the
Kohn-Sham value. We show that these differences are a consequence of the poor
representation of the linear response within the TFW approximation for the
electronic kinetic energy, confirming conjectures in the literature. In so
doing, we find that the energy computed from a non-self-consistent Kohn-Sham
calculation using the TFW electronic ground state density is in very good
agreement with that obtained from the fully self-consistent Kohn-Sham solution.
