Calculation of density fluctuation contributions to thermodynamic properties of simple fluids

An equation of state, expressed in the form of a recursion relation for the Helmholtz free energy density, is presented. This equation of state represents the free energy density as an initial mean field free energy density, plus a sum of density fluctuation correction terms which serve both to dress the initial mean field equation of state into a more accurate analytic equation of state away from the critical region, and to provide the characteristic asymptotic singular behavior in the critical region. Numerical solutions of the recursion relations are described and presented as pressure isotherms and the calculated density coexistence curve. A comparison is made with simple fluid data for temperatures in the range 0.7≤T/Tc≤1.5 and densities in the range 0≤ρ/ρc≤2.5. In particular, good agreement is found near the critical point. Three critical exponents, δ, γ, and β, are calculated and found to be in good agreement with simple fluid data as well as with renormalization group results for the 3D Ising model.