The Mixture-Model MM Approach General Considerations

The general idea of the mixture-model (MM) approach is very simple and quite old. In particular, it has been applied extensively in the theory of water and aqueous solutions. In this section, we outline the basic procedure employed in the MM approach. We choose two examples in which the idea of a classification procedure, a fundamental step in the theory, is very simple and vivid. Then, with a little imagination, we can generalize the classification procedure so that contact with the notion of GMDF s is achieved. This is deferred to the next section. 

Consider a system of N molecules in a volume V and temperature T, Furthermore, we assume that the density is very low, so that the partition 

q is the full partition function of a single molecule, which can be written as 

Suppose we now wish to split the sum in (5.71) into two (or more) sums. This can be achieved in many ways, for instance. 

The splittings in (5.72) can be arbitrary or motivated by theoretical or experimental reasoning. The important thing is that once we have been given a rule by which we can classify all the states into two groups, we can split the partition function into a sum of two partition functions 

---