General Formulation of the Partition Function

We start by writing the GPF of a single system in various forms  

In the first equality the GPF is written in the most general form (for the case m = 3). Here, 2(0 is the (canonical) PF for a system with / ligands. The second form is used whenever the sites are all different, here denoted by a, b, and c. Clearly, in this case 

Note that we always assume that the ligand is very small relative to the adsorbent molecule. Otherwise, even when the binding energy the same for each site, the PFs for singly occupied molecules could differ, e.g., the rotational PF of a molecule having a ligand bound to the center or to the edge will be different. See also Section 5.10 and Appendix B. 

The last form on the rhs of Eq. (5.2.1) is used whenever the three sites are identical in a strict sense. This is defined whenever the PF for any specific arrangement of I ligands has the same value, denoted by QJJ). Hence, we simply write 3 2s(l) and 2 Qf2) without specifying the specific arrangement of the ligands. 

An example that conforms to this definition would be benzene-l,3,5-tricar-boxylic acid (Section 5.9). Clearly, owing to the symmetry of the molecule there is only one intrinsic binding constant k, and only one intrinsic binding constant for pairs fcj, or, equivalently, only one pair correlation function 

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