Associating fluids pair correlation function

The approximation Eq. (66) accounts for interactions within the associated cluster and between the clusters and the reference fluid, but not the interactions between associated clusters. This approximation is accurate for cases in which the pair correlation function between associating molecules is similar to that of the reference fluid. 

In Section V it was shown how Wertheim s multi-density approach could be used to develop an equation for associating fluids with an arbitrary number of association sites provided a number of assumptions were satisfied. The simplicity of the TPTl solution results from the fact that the solution is that of an effective two-body problem. Only one bond at a time is considered. This allows the theory to be written in terms of pair correlation functions only, as well as obtain analytical solutions for the bond volume. Moving beyond TPTl is defined as considering irreducible graphs that contain more than one association bond. 

This strategy is common in atomic fluid theory at low to moderate densities, and for Coulombic systems, and corresponds to the reference idea ubiquitous in liquid state theory [5], The purely hard core problem is treated using the accurate [27] PY closure. (2) The construction of a closure approximation for the tail part of the potential is subject to the constraint of exactly describing the weak coupling limit. In physical terms, for fractal-like interpenetrating molecules these indirect processes may strongly couple the direct correlation functions associated with those pairs of sites which are in simultaneous contact The number of such two-molecule pair contacts. Me. scales with N as [23] ... 

The fluctuations in the number of particles of a quantum fluid in the absence of an external field can be determined with any of the three types of k-space response functions (or their associated pair radial correlations). This result is fully consistent with the fact that the response from the fluid to a zero-momentum transfer must be the same independently of the type of structure factor considered. Therefore, although there are three general different ways for the density to fluctuate in a quantum fluid (ET2, TLR2, and CM2), one finds the... 

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