A modified soft-core fluid model for the direct correlation function of the square-shoulder and square-well fluids

We propose a simple analytical expression of the direct correlation function for the square-shoulder and square-well fluids. Our approximation is based on an ansatz for the direct correlation function of a modified soft-core fluid, whose parameters are adjusted by fitting the data obtained from Monte Carlo computer simulations. Moreover, it is complemented with a Wertheim-like parametrization to reproduce correctly the direct correlation inside the hard-core. We demonstrate that this approach is in quantitative agreement with the numerical solution of the Ornstein–Zernike equation within the Percus–Yevick approximation. We also show that our results are accurate in a large regime of densities for different interaction ranges and potential strengths. Therefore, this opens up the possibility of introducing the square-shoulder or the square-well potentials as new reference systems in advanced theoretical approximations.