Partition function liberation

Ben-Naim s definition has many merits it is not limited to dilute solutions, it avoids some assumptions about the structure of the liquid, it allows to use microscopical molecular partition functions moreover, keeping M fixed in both phases is quite useful in order to implement this approach in a computationally transparent QM procedure. The liberation free energy may be discarded when examining infinite isotropic solutions, but it must be reconsidered when M is placed near a solution boundary. 

It is instructive to recognize the three different sources that contribute to the liberation free energy. First, the particle at a fixed position is devoid of momentum partition function (though it still has all other internal partition functions such as rotational and vibrational). Upon liberation, the particle... 

Next, we identify the liberation Helmholtz energy of the pair A and B. For any specific configuration, this may be obtained from the ratio of the partition functions (7.188) and (7.189), i.e.,... 

Here is the internal partition function of S (=1 for a strnctureless particle, such as a noble gas atom), is its number density, and Ag is its momentum partition function. The qnantity p in either phase pertains to the particle at a fixed position where it is devoid of the translational degrees of freedom, and kj In pJl expresses its liberation from this constraint. The Gibbs energy of solvation, is expressed as the change in the chemical potential of S at equilibrium, where is then ... 

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