Observations on the PDT

The PDT partition function formula (9.5) does not require that AUa adopt a specifically simplified form such as additive contributions over pairs of molecules involved. AUa is simply 

To evaluate physical averages involving the two subsystems considered jointly, supply the Boltzmann factor of the coupling energy in a numerator and denominator according to 

Taking the case Fa = f)AU - leads to a nontrivial formula for the inverse of (9.5) 

The brackets on the left of (9.15) indicate the fully coupled thermal averages, involving the actual interactions between the solution and the distinguished molecule of the joint system, specifically with the distinguished solute present. Equation (9.12) made a preliminary presentation of this result. 

This casts the PDT partition function as a normalizing denominator, as is customary for a partition function. 

---