Density functional theory and the asymptotic high density expansion of the free energy of classical solids and fluids

On the basis of the fundamental-measure free energy functional for hard spheres and thermodynamic perturbation theory, a unified analytical description of classical bulk solids and fluids is obtained, predicting correctly the major features of their equations of state and freezing parameters as obtained by simulations. The fundamentally different fluid and solid asymptotic high density expansions for the potential energy, featuring a static-lattice Madelung term and the harmonic 3/2k B T correction, on one hand, and a fluid Madelung energy with a ˜T 3/5 thermal energy correction, on the other, both originate from the same singularity in the hard sphere free energy functional.