Singlet distribution function specific

The interpretation of (RfidR follows from the same argument as in the case of Pi(S) in (2.8). This is the probability of finding a specific particle, say 1, in dR at R. Hence, P(1)(R ) is often referred to as the specific singlet distribution function. 

Let us now make a specific choice of two components for water, which seems to be the most useful one for interpreting the thermodynamic behavior of aqueous solutions. We use the singlet distribution function xcn(K) based on coordination number (CN), and define the two mole fractions by... 

Thus in order to obtain Pr(5i = Of), we take the probability distribution of the entire system, fix the state of a specific unit, say z = 1, at of, and sum over all possible states of all other units. The resulting probability distribution is called the singlet distribution function. 

The calculation of the correlation functions is essentially the same as in Section 7.2, except for the additional complexity due to the existence of more states. Thus, the singlet distribution, i.e., the probability of finding any specific single site occupied, is... 

As in the case of the singlet MDF, here we also start with the specific pair distribution function defined in (2.28). To get the generic pair distribution function, consider the list of events and their corresponding probabilities in table 2.2. Note that the probabilities of all the events on the left-hand column of table 2.2 are equal. 

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