Lagrangian theorem-based density functional approach free of adjustable parameter

Abstract

An adjustable parameter associated with an recently proposed Lagrangian theorem-based density functional theory (DFT) approach is found to be a constant 0.5 by applying the non-uniform first-order direct correlation function (DCF) from the Lagrangian theorem-based DFT approach to an exact relation between the zero wave vector Fourier transform of the bulk DCFs and their density derivatives. The new parameter-free DFT approach is comparable or even more accurate in predicting density distribution than the original DFT approach. Based on functional integral procedure, a numerical procedure from approximation for non-uniform first-order DCF to non-uniform excess Helmholtz free energy is proposed, the predicted surface tension of a hard wall-hard sphere interface as a function of the bulk hard sphere fluid density from the original DFT approach and its parameter-free version is in very good agreement with the available simulation data.