A non-perturbative density functional theory (DFT) for inhomogeneous f
luids is developed by partitioning the functional into short range ('e
ntropic') and long range ('energetic') contributions. The short range
part is treated using standard weighted density functional techniques
and the long range contribution is evaluated exactly. This method, whi
ch is a generalization of a method due to Likes, C., and Senatore, G.,
1995, J. Phys.: Condens. Matter, 7, 6797, does not require the use of
a reference system. Results are presented for the calculation of the
crystal/fluid phase coexistence for systems interacting with inverse-p
ower potentials of the form r(-n), where n = 4, 6 and 12. These result
s show that this non-perturbative DFT is capable of predicting the fre
ezing of long range inverse power systems (n = 4, 6) into a body-centr
ed-cubic lattice. Improvements over earlier methods also are noted in
the current results for the solid structure as measured by the Lindema
nn ratio.