Analytical formulation of the optimized-random-phase-approximation for a hard-core Yukawa fluid

Abstract

A method for analytical calculation of thermodynamic functions (the internal energy, free energy, chemical potential, energy and virial pressure, compressibility) for a hard-core Yukawa fluid (HCYF) in the optimized random phase approximation (ORPA) is presented. The method makes use of the analytical solution of the Ornstein-Zernike equation with a hard-core condition and the direct correlation function of two-Yukawa-function form. One Yukawa function is related to the interaction potential whereas the second one serves to obtain the generalized mean spherical approximation form of the hard-sphere direct correlation function. All thermodynamic quantities are analytical functions of the six parameters γ1, γ2, d 1, a and b whose values may be easily found with the use of an existing efficient algorithm. When the hard-sphere system is described in the Percus-Yevick approximation then the derived formulae reduce to the analytical mean-spherical-approximation (MSA) expressions derived by Høye and Stell. If the properties of the HCYF are evaluated in the ORPA then the first order quantum correction to the classical value of the free energy is also an analytical function of these parameters. The ORPA results for the internal energy and pressure are close to the Monte Carlo data and they are slightly better than the MSA and Barker and Henderson (BH) perturbation theory results. The ORPA free energies are always lower than the MSA or BH results although the differences between them are small.