Cluster diagrammatic analysis of the RISM equation

The interaction site cluster theory and the method of topological reduction are applied to determine the infinite class of cluster diagrams summed by the reference interaction site model (RISM) integral equation. It is shown that, along with summing a subset of allowed cluster graphs for the site-site correlation functions of molecular fluids, the equation also sums classes of graphs which are unallowed in a rigorous theory. The relationship between the RISM equation for molecular fluids and the Percus-Yevick equation for simple atomic fluids is analysed diagrammatically.