  We apply density functional theory to study the freezing of superfluid
{$^{4}\rm{He}$}, charged bosons and charged fermions at zero temperature. We
employ accurate Quantum Monte Carlo data for the linear response function in
the uniform phase of these systems, a quantity that has different behavior for
large values of the wavevector than previously assumed. We find that, as a
result of this {\it{exact}} behavior, different approximations in the density
functional theory of freezing that involve linear response, all fail to
correctly describe the crystallization in {\it{three dimensions}}, while
yielding satisfactory predictions in {\it{two dimensions}}. This demonstrates
the shortcomings of the currently popular density functional approximate
theories to describe $3d$-freezing in the quantum regime. We also investigate
the consequences of the exact asymptotic behavior of response functions on the
form of effective interactions and polarization potentials in the electron gas,
at small distances.
