High-order direct correlation functions of uniform classical liquids

Analytic approximations for the third- and higher-order direct correlation functions of uniform classical liquids are presented. These are derived from a weighted-density approximation for the one-particle direct correlation function of a nonuniform liquid which requires as input only the two-particle function of the corresponding uniform liquid. The three-particle result is shown to have the same accuracy as two recently proposed approximations, but has a much simpler form. The four- and five-particle results are new, and in principle can be tested by simulation methods.