Freezing of the Hard Spheres: Re-Examination of the Weighted-Density-Functional Theories

Abstract

Freezing of the hard spheres is re-examined using the modifiedweighted-density approximation (MWDA) of Denton and Ashcroft and thegeneralized effective-liquid approximation (GELA) of Lutsko andBaus. It is found that one owes part of success of these theories tothe use of the Percus-Yevick (PY) direct correlation function and thecorresponding equation of state of uniform fluids as the input data inthese theories. In fact, if one uses virtually “ exact'' inputdata in place of the PY ones, the free energies of the solid phase aresomewhat lowered and predicted freezing properties worsen. It isargued that this unfavorable feature of the MWDA and the GELA becomesmuch more serious when these theories are applied to the referencehard spheres in the thermodynamic perturbation approach to freezing ofsystems with long-ranged potentials.