Comparative study of a universal theoretical way and 3rd + 2nd-order perturbation density functional theory

Abstract

A universal theoretical way, proposed recently by Zhou, provides a general scheme which transforms any one of hard sphere density functional approximations (DFAs) into a DFA workable for non-hard sphere fluids. In this article, the universal theoretical way is combined with a hard sphere DFA as a Lagrangian theorem-based DFA to perform calculations for density profiles of a hard core attractive Yukawa model fluid influenced by diverse external fields, and the calculation results are compared with corresponding results due to a 3rd + 2nd-order perturbation density functional theory (DFT) and computer simulation previously reported. Several conclusions are drawn from a detailed analysis on the degree of accuracy of the two approximations relative to the computer simulation and described below. (i) Correspondence between the change of relative performance of the two DFAs and the change of the performance of the bulk 2nd-order direct correlation function (DCF) used as an input as a function of bulk state indicates that the bulk 2nd-order DCF is a key input information determining the accuracy of the approximations using them. (ii) For large inhomogeneity, non-perturbation approximation is evidently more successful than a 3rd-order truncation on the functional perturbation expansion series. (iii) The universal theoretical way is very promising given that a successful hard sphere DFA and accurate bulk 2nd-order DCF are incorporated. Under the present conditions, the universal theoretical way gives an excellent account of the density profiles even if the ‘dangerous’ coexistence bulk states are being under consideration. (iv) The present study helps in formulating new approximations for the inhomogeneous excess Helmholtz free energy functional.