Chain approximations in the perturbation theory of liquids

Two recent versions of the perturbation theory of liquids, the optimized chain approximation of Andersen, Chandler and Weeks (ACW) and the renormalized one-chain approximation (ROC) by one of us (AF), are discussed. The ACW optimized version leads to better results than the ROC one. The main difference between these versions lies in the definition of the renormalized perturbation bond. The ACW form enables the optimization of the chain sum by the adjustment of the perturbation potential inside the hard core. This is impossible in the ROC approximation, which, however, may be ‘optimized’ by the replacement of the complete hard-sphere radial distribution function by its zeroth-order approximation. Both of these optimalization procedures are equivalent to the effective weakening of the repulsive interactions of the reference system. We infer that the hard-sphere fluid is too strongly repulsive to be the best reference system for perturbation theories of liquids.