The orientation-dependent pair distribution function for molecular fluids on site-site potentials is expanded in a topological analog of the diagrammaticaUy proper site-site theory of liquids [D. Chandler et al., Mol. Phys. 46, 1335 (1982)]. The resulting functions are then used to diagrammatically renormalize the molecular fluid theory. A result is that the diagrammaticaUy proper interaction site model theory is shown to be a linearized, minimal angular basis set approximation to this site-renormalized molecular theory. This framework is used to propose a new, exact, and proper closure to the diagrammaticaUy proper interaction site model theory. The resulting equation system contains a bridge function expansion in the proper site-site theory. In addition, the construction of the theory is such that the molecular pair distribution function, in full dimensionality, is intrinsic to the theory. Furthermore, the theory is equivalent to the molecular Ornstein-Zernike treatment of site-site molecules in the basis set expansion of Blum and Torruella [J. Chem. Phys. 56, 303 (1971)]. A significant formal result of the theory is the demonstration that certain classes of diagrams which would otherwise be considered improper in the interaction site model formalism are included in the angular expansion of molecular interactions. Numerical results for several apolar homonuclear models and an apolar heteronuclear model are shown to quantitatively improve upon those of reference interaction site model and our recent proper variant with respect to simulation. Significant numerical results are that the various thermodynamic quantities obey the exact symmetries and sum rules within numerical error for the different sites in the heteronuclear case, even for the low order approximation used in this work, and the theory is independent of the so-called auxiliary site problem common to previous site-site theories.
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