A density functional-variational treatment of the hard sphere transition

Abstract

A density functional-variational version of the Ramakrishnan-Yussouff theory of freezing is used to reconsider the problem of the hard sphere transition. This calculation differs from previous ones in that the solid density and the lattice constant are included as independent variational parameters. Besides giving an unambiguous method for determining the lattice constant of the solid this method allows the computation of the average density of defects in the solid. In addition, we use real, rather than Fourier, space techniques in solving the resulting equations. We argue that real space techniques are numerically more accurate for the narrow distributions found by these methods. Our results for the densities of the coexisting solid and liquid phases are very close to those given by molecular dynamics studies. The width of the solid density peaks is too small as is the case with previous calculations. The average density of defects has the correct sign but is much too large (ρ_D ⋍ -0·1) for a realistic solid.