A quantitative theory of the structure of molecular fluids described by atoms or sites has remained elusive in soft condensed matter theory. Many-body and field theoretic approaches to the correlations liquids have advanced slowly since the 1930s. The qualitative and quantitative inconsistencies of the many-body integral equation theory for predicting the structure and thermodynamic properties of model molecular fluids have been understood for some time.

Several means have been proposed to correct these inconsistencies, many concentrating on the Goldstone theorem. A formally distinct method for constructing a diagrammatically proper theory eliminates terms in the expansion which correspond to unphysical intramolecular interactions, or so-called bad graphs. Unfortunately, while certain qualitative advances using the proper theory have been successful the quantitative results appear to be uniformly disappointing in comparison to simulation.

We present a new derivation from a topological expansion of a model for the single atom activity followed by a topological reduction and low order truncation. This leads to an approximate numerical value for the new density coefficient. The resulting equations give a substantial improvement over the standard construction as shown with a series of simple diatomic model simulations.