Determining liquid structure from the tail of the direct correlation function

In important early work. Stell showed that one can determine the pair corre lation function h(r) of the hard-sphere fluid for all distances r by specif ying only the "tail" of the direct Correlation function c(r) at separations greater than the hard-core diameter. We extend this idea in a very natural way to potentials with a soft repulsive core of finite extent and a weaker and longer ranged tail. We introduce a new continuous function T(r) which reduces exactly to the tail of c(r) outside the (soft) core region anti sho w that both h(r) and c(r) depend only on the "out projection" of T(r): i.e. , the product of the Boltzmann factor of the repulsive core potential times T(r). Standard integral equation closures can thus be reinterpreted and as sessed in terms of their predictions for the tail of c(r) and simple approx imations for its form suggest new closures. A new and very efficient variat ional method is proposed for solving the Ornstein-Zernike equation given an approximation for the tail of c. Initial applications of these ideas to th e Lennard-Jones and the hard-core Yukawa fluid are discussed.