Helmholtz free-energy high-temperature perturbation expansion for square-well and square-shoulder potentials

The Helmholtz free-energy high-temperature perturbation terms of the square-shoulder and the square-well potentials of variable range were calculated using the Microcanonical Ensemble simulation method up to the eight-order. The numerical evaluation of the coefficients can be useful to build improved equations of state for these systems. To our knowledge, this is the first work that reports values for the seventh and eighth expansion coefficients for these discrete potentials. The square-shoulder high temperature expansion coefficients are numerically compared with those of the square-well potential. We confirmed that there exists a simple relation among them: even terms are equal for both potentials and odd terms differ by a minus sign, for all the densities and ranges considered. This relation was first proposed in the work of Benavides and Gil-Villegas (Molecular Physics 97, 1225 (1999)) in the context of Discrete Perturbation theory but it was only analytically tested for the first and second-order perturbation terms, and, for the second-order term, it has only been analysed within the Barker and Henderson Local and Macroscopic Compressibility approximations.