Double-Hard-Sphere perturbation theory: a perturbation theory that is less dependent on the value of the hard-sphere diameter

Perturbation theories for fluids of molecules with soft-repulsive cores, such as the Lennard-Jones fluid, are usually based on the description of a fluid of hard spheres of temperature-dependent, and sometimes also density-dependent, diameter. The results obtained from such theories are typically rather sensitive towards the value of this diameter. We here derive an alternative implementation of perturbation theory that significantly reduces this sensitivity. The method allows the development of perturbation theories for high-density fluids without necessitating a density-dependent hard-sphere diameter. We refer to the approach as double-hard-sphere (DHS) perturbation theory. When applied using a Weeks-Chandler-Andersen (WCA) division of the intermolecular potential, and considering the expansion up to first order in the Helmholtz energy, we recover the HS-WCA theory of Ben-Amotz and Stell [J. Phys. Chem. B 108, 6877 (2004)] if certain correlation integrals are neglected. The DHS expansion thereby provides a formal basis of the HS-WCA theory, clearly showing the underlying assumptions and how to improve on them. Applying the DHS expansion to a Barker-Henderson division of the Lennard-Jones (or Mie) potential is shown to extend the accuracy of the Barker-Henderson theory to densities up to the freezing density, leading to a substantial improvement in predicted fluid-solid equilibria.