Cluster expansions for hydrogen bonded fluids. II. Dense liquids

The cluster expansion theory of Mayer is formulated in a way that makes it useful for application to dense hydrogen bonded fluids, or, in general, to fluids with very strong attractive intermolecular potentials that are very dependent upon the relative orientations of the molecules. In the resulting diagrammatic series, the hydrogen bond appears only in a renormalized form that is much weaker than the Mayer f function for the original unrenormalized hydrogen bond potential. The diagram series for the pair correlation function is divided into various parts according to the topological structure and physical interpretation of the diagrams, and exact relationships among these parts are derived. These exact relationships can become the starting point for approximate calculations of the pair correlation function for hydrogen bonded liquids such as water.