Mean Spherical Approximation-Based Partitioned Density Functional Theory**The project supported by National Natural Science Foundation of China (Grant No. 20206033) and the Scientific Research Fund of Hunan Provincial Education Department (Grant No. 02B033)

Abstract

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 as the uniform third order direct correlation function (DCF) for the tail part, here kernel function . 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.