Mean Spherical Approximation-Based Partitioned Density Functional Theory

Previous literature claims that the density functional theory for non-uniform non-hard sphere interaction potential fluid can be improved on by treating the tail part by the third order functional perturbation expansion approximation (FPEA) with the symmetrical and intuitive consideration-based simple function C₀⁽³⁾(r₁,r₂,r₃)=ς∫dr₄a(r₄-r₁)a(r₄-r₂)a(r₄-r₃) as the uniform third order direct correlation function (DCF) for the tail part, here kernel function a(r)=(6/πσ³)Heaviside(σ/2-r). The present contribution concludes that for the mean spherical approximation-based second order DCF, the terms higher than second order in the FPEA of the tail part of the non-uniform first order DCF are exactly zero. The reason for the partial success of the previous a kernel function-based third order FPEA for the tail part is due to the adjustable parameter ς and the short range of the a kernel function. Improvement over the previous theories is proposed and tested.