Employing functional counterpart of Lagrangian theorem to improve on density functional theory for density profile of non-uniform fluids

A recently proposed density functional theory [New J. Phys. 4 (2002) 36], which is based on functional counterpart of Lagrangian theorem of differential calculus, is extended to calculate density distribution of an adhesive hard sphere fluid confined between two hard walls. The needed input parameters, i.e., bulk second order direct correlation function and equation of state, are employed from the analytical Percus–Yevick approximation and the compressibility equation. The present predictions are in very good agreement with available computer simulation data. Then the present formalism is applied to investigate the affecting factor for the adhesive hard sphere fluid adsorption behaviors. The continuity and differentiability of the density functional C (1) ( r ;[ρ]) , which underlies the application of the functional counterpart of Lagrangian theorem of differential calculus, is proven.