A Self-Consistent Approach to a Density-Functional for Homogeneous Fluids

A density functional, originally proposed by Rickayzen and Augousti for 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 self-consistently the two-particle direct correlation function, the equation of state and the strength of the excess free energy. In practice, it was found that, with the original form of excess free energy, convergence could not be achieved. With the generalized functional, however, it is possible to derive self-consistently the direct correlation function and, at the same time, obtain agreement between the virial pressure, the functional pressure, and the compressibility Moreover, good agreement is obtained between the resulting pair distribution function and direct correlation function and the corresponding quantities obtained from computer simulation At the largest reduced density studied, 0.90, there are small discrepancies which are most marked in the values of the direct correlation function near the origin.