Density functional theory of freezing of the hard sphere liquid into FCC against HCP structures

The density functional theory is applied to study the freezing of the hard sphere liquid into the close packed structures. To describe the short-range correlations in the solid phases a reference liquid is introduced, whose density is fixed by a stationary condition. The thermodynamic properties of the two solid structures are calculated for increasing numbers of order parameters until convergence is achieved. According to the calculation the FCC structure is slightly more stable than the HCP one, but the difference in the grand potentials is comparable with the error of the calculation.