Reformulation of density functional theory for generation of the nonuniform density distribution

The concept of universality of the free energy density functional and the weighted density approximation are combined to provide the density distribution profile of nonuniform fluids from the predictions of integral equation theory for the corresponding uniform fluids. To obtain the expression for the free energy as a function of the density distribution, the present formalism expresses the difference of the first order direct correlation function of a nonuniform fluid with respect to its uniform fluid counterpart as a function of the weighted density, which is also a function of the space position. The input parameters used in the present approach are the radial distribution function and the second order direct correlation function of the corresponding uniform fluid. All of these parameters can be easily obtained from numerical solution of Ornstein-Zernike integral equation theory. The present approach is based on the formalism of classical density functional theory (DFT) and its application to two kinds of fluid under different external potentials is presented. The agreement of the theoretical predictions with the corresponding computer simulation data is good. The present formulation of DFT can treat fluids of different interaction potential under nonzero external fields in a unified way.