New integral equation for the calculation of the structure and properties of dense liquids

Conclusions

The modification of the relationship between the direct correlation function c(r) and the potential Φ(r) and the complete correlation function h(r), which has been carried out in the present work and in earlier work [1] and which has led to the approximation (1), is based on a simple idea. To the simplest approximations (the mean-statistical model for r^*>1 and the Percus-Yevick approximation for r^*<1) are added certain functions selected on the basis of model calculations in such a way that the relationship obtained effectively describes the behavior of the thermodynamic properties or makes it possible to reconstruct the potential from the given h(r). This essentially purely empirical approach could hardly be of importance for the problem of finding the integral equations for the paired correlation functions of a liquid if it had not been found that it is possible to select modifying functions which can be used to achieve a self-consistent description of three thermodynamic properties and the two correlation functions h(r) and c(r) and at the same time solve satisfactorily the problem of reconstructing the potential [1]. The demonstration of the possibility of a self-consistent description, which is not observed for any of the known integral equations of the first approximation of the method of functional differentiation, is the main result of the present work. This success leads to the hope that subsequent searches (by methods which are not so empirical as those used in the present work) for a satisfactory approximation for c(r) are not doomed to failure.