G. Rickayzen et al., A SELF-CONSISTENT APPROACH TO A DENSITY-FUNCTIONAL FOR HOMOGENEOUS FLUIDS, The Journal of chemical physics, 101(9), 1994, pp. 7963-7970
A density functional, originally proposed by Rickayzen and Augousti fo
r the study of the inhomogeneous hard sphere fluid, is generalized and
applied to investigate the properties of the homogeneous hard sphere
fluid. In principle, it is possible to determine simultaneously and se
lf-consistently the two-particle direct correlation function, the equa
tion of state and the strength of the excess free energy. In practice,
it was found that, with the original form of excess free energy, conv
ergence could not be achieved. With the generalized functional, howeve
r, it is possible to derive self-consistently the direct correlation f
unction and, at the same time, obtain agreement between the virial pre
ssure, the functional pressure, and the compressibility Moreover, good
agreement is obtained between the resulting pair distribution functio
n and direct correlation function and the corresponding quantities obt
ained from computer simulation At the largest reduced density studied,
0.90, there are small discrepancies which are most marked in the valu
es of the direct correlation function near the origin.