Analytical representation of the radial distribution function for classical fluids

The previously established general solution of the Ornstein-Zernike (OZ) equation is elaborated upon further. A systematic and consistent summary of the first-order OZ solutions for various types of potentials is made, which enables one to obtain the first-order radial distribution function (RDF) rapidly. Typical potentials, including the hard sphere, sticky hard sphere, Yukawa, square-well, Lennard-Jones and Kihara, are treated with emphasis in this work. A new approach for obtaining explicit RDF expressions is proposed. Established on a basic function B(n 1,n 2,n 3,i,a), it is capable of representing the explicit expressions in a compact and consistent manner for all the potentials mentioned above. Moreover, the proposed approach can yield RDF values directly in any number of shells corresponding to any r values. The resulting expressions can be programmed readily in a computer thus facilitating the RDF computation.