An exact MM approach to the theory of liquids

A comment on terminology is in order. We use the term mixture model though no model is involved. The reason is that originally the MM approach was based on various choices of models for each of the components comprising the mixture. We shall use the term MM, though a more appropriate term would be the mixture view or the mixture approach to a one-component system. As we shall see below one can use a discrete MM or a continuous MM. This is quite different from the characterization of models as being an MM or a continuous model.  

It is not uncommon yet somewhat puzzling to see that some authors categorize their theory as belonging to an MM or a continuous model. I believe this distinction is now obsolete. 

Consider the ordinary singlet molecular distribution function MDF) in a one-component liquid  

We now systematize the generalization procedure of (2.3.16) as follows. Let us rewrite (2.3.16) in a somewhat different way. For each configuration of the entire system, we define the property of the particle i as 

The property of particle i defined in (2.3.17) is simply its location R/. This is the reason for using the letter L in the definition of the function Li R ). 

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