DENSITY-FUNCTIONAL APPROXIMATIONS FOR CLASSICAL FLUIDS

The free energy density functional approximations formulated in terms of two weighted densities are considered and are applied to calculate the higher-order direct correlation functions of hard sphere fluids. Our results are compared with those obtained from various model approximations and computer simulation studies available in the literature. A good agreement with computer simulations is observed. To investigate the relationship between the homogeneous and inhomogeneous properties of the free energy density functional approximations, the free energy density functional approximation using a semi-empirical basis of weighted densities is applied here to predict the structural properties of hard sphere fluids confined within a spherical cage by a hard structureless wall. The resulting density profiles are compared with those obtained from the various model approximations and also from computer simulations. For the density profiles at the lower density rho3 = 0.62, the hard-sphere oscillatory structures are reproduced qualitatively and quantitatively. At the higher density rhosigma3 = 0.75, our results also show a reasonable agreement with computer simulations except for the region close to the cavity center where the range and magnitude of oscillations are overstimated. The results confirm that the thermodynamic and structural properties of our approximation are more sensitive on the density expansion than those of the Tarazona model based on the density expansion of the weighted density related to the excess free energy functional. Through these calculations, it is also deduced that there is no close relationship between the homogeneous and inhomogeneous properties of the free energy density functional approximations.