  We show that, at high densities, fully variational solutions of solid-like
type can be obtained from a density functional formalism originally designed
for liquid 4He. Motivated by this finding, we propose an extension of the
method that accurately describes the solid phase and the freezing transition of
liquid 4He at zero temperature. The density profile of the interface between
liquid and the (0001) surface of the 4He crystal is also investigated, and its
surface energy evaluated. The interfacial tension is found to be in
semiquantitative agreement with experiments and with other microscopic
calculations. This opens the possibility to use unbiased DF methods to study
highly non-homogeneous systems, like 4He interacting with strongly attractive
impurities/substrates, or the nucleation of the solid phase in the metastable
liquid.
