Going beyond the mean field approximation in classical density functional theory andapplication to one attractive core-softened model fluid

Abstract

A novel scheme is advanced for an excess Helmholtz free energy density functional. Thepresent scheme is isomorphic to one frequently used mean field approximation (MFA)methodology, but goes beyond the latter in that the present scheme contains a bulksecond-order direct correlation function (DCF) which can be obtained by numericallysolving a bulk Ornstein–Zernike (OZ) integral equation theory (IET), and is therefore ingeneral more accurate than the bulk second-order DCF expected from MFA methodology.The scheme is applied in the framework of classical density functional theory (DFT) toone so-called attractive core-softened model potential with a double square wellattraction in homogeneous conditions. Quantitatively it is found that the presentscheme is in general more accurate than two previously confirmed third-order + second-order perturbation DFT and non-uniform fifth-order thermodynamic perturbation theory,even if the present scheme is implemented in a purely predictive manner and the third-order + second-order perturbation DFT is implemented in a partially predictive manner. Qualitatively thepresent scheme is characterized by several desirable features not possessed by previousmethodologies: (i) It is not concerned with any adjustable parameters, and this allows forhandy applications. (ii) It does not deal with problems of determining self-consistently bothan effective hard sphere diameter and a tail contribution to the full pair potentialunder consideration. (iii) Although the present scheme uses OZ IET to supplyinput information, it is safely applicable to subcritical regions of the bulk phasediagram.