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A free energy functional for a crystal that contains both the symmetryconserved and symmetry broken parts of the direct pair correlation function hasbeen used to investigate the crystallization of fluids in three-dimensions. Thesymmetry broken part of the direct pair correlation function has beencalculated using a series in ascending powers of the order parameters and whichcontains three- and higher-bodies direct correlation functions of the isotropicphase. It is shown that a very accurate description of freezing transitions fora wide class of potentials is found by considering the first two terms of thisseries. The results found for freezing parameters including structure of thefrozen phase for fluids interacting via the inverse power potential u(r) =\epsilon (\sigma/r)^{n} for n ranging from 4 to \infty are in very goodagreement with simulation results. It is found that for n > 6.5 the fluidfreezes into a face centred cubic (fcc) structure while for n \leq 6 the bodycentred cubic (bcc) structure is preferred. The fluid-bcc-fcc triple point isfound to be at 1/n = 0.158 which is in good agreement with simulation result.

Correlation functions in liquids and crystals : Free energy functional and liquid - crystal transition