Fifth-order thermodynamic perturbation theory of uniform and nonuniform fluids

A recently proposed numerical third-order thermodynamic perturbation theory (TPT) is extended to its fifth-order counterpart. Extensive performance evaluation based on several model potentials indicates that the fifth-order version is generally superior to both the third-order version and a well-known second-order macroscopic compressibility approximation TPT, and is at least comparable to an accurate self-consistent Ornstein-Zernike integral equation approximation (SCOZA) with regard to predictions of varying bulk thermodynamic properties. A bulk second-order direct correlation function (DCF) free of numerical solution of a bulk OZ integral equation, is proposed, which, in combination with the framework of classical density functional theory (DFT) and a thermodynamic consistency condition, extends the uniform fifth-order TPT to nonuniform case. Grand canonical ensemble Monte Carlo simulation is carried out to produce density profile of a core-softened fluid confined in a hard spherical cavity, the resultant density profile is employed to evaluate the performance of the present nonuniform fifth-order TPT and a recently proposed third +second-order perturbation DFT. It is found that the present nonuniform fifth-order TPT is generally more accurate than the third+second-order perturbation DFT. Additional advantages of the present nonuniform fifth-order TPT over the third +second-order perturbation DFT is discussed.