CHEMICAL-POTENTIALS BASED ON THE MOLECULAR-DISTRIBUTION FUNCTIONS - AN EXACT DIAGRAMMATICAL REPRESENTATION AND THE STAR FUNCTION

A closed form for the chemical potentials of a fluid is presented that involves only integrals of the molecular distribution functions at the given state, (e.g., temperature and density). Thus no Kirkwood charging or thermodynamic integration is needed. An exact formula from a previous study is reanalyzed and a diagrammatical representation of the correlation functions involved is given. This representation involves in addition to the usual total correlations, direct correlations, and the bridge function, B(r), a new star function, S(r). Analysis shows that the integral of the star function is the primitive of the bridge function, i.e., its functional derivative yields B(r). It is also related to the free-energy functional F[rho] in density-functional theories for nonuniform systems. Methods for estimating the star function are given. Tests on uniform hard-sphere fluid are carried out to demonstrate the new formulas. We have examined several current closures: the Percus-Yevick, Martynov-Sarkisov, Ballone-Pastore-Galli-Gazzillo, and a Verlet-modified (VM) closure. The VM approach gives the best reproduction of the bridge function. Much improved results are obtained for the chemical potentials of hard spheres at densities rhod3 ranging from 0.3 to 0.85.