A third and fourth order perturbation theory for dipolar hard spheres

Abstract

In this work, we develop and analyze a third order and a fourth order perturbation theory for non-polarizable dipolar hard spheres. The electrostatic potential is split into a short-ranged and a long-ranged part. A perturbation expansion is applied for the short-ranged potential where the contribution of higher order terms is approximated through a [2,1]-Padé approximation for the third order theory and by a [2,2]-Padé approximation for the fourth order theory. Rodgers and Weeks [J. Chem. Phys. 131, 244108 (2010)] developed the Local Molecular Field (LMF) theory for the long-ranged contribution of the electrostatic energy. The LMF theory requires the relative permittivity of the considered fluid. We apply a perturbation theory for the relative permittivity and show that the LMF is then in very good agreement with the results for the long-ranged energy from molecular simulations. The short-ranged contribution to the Helmholtz energy from the third order and from the fourth order perturbation theory is, for densities ρ* ≤ 1 and for dipole moments of μ*2 ≤ 1, in very good agreement with the data from molecular simulations. For larger dipole densities (up to μ*2 ≤ 4 for ρ* ≲ 1), we observe significantly improved results for the fourth order perturbation theory compared to the third order perturbation theory.