Solvation and the Pair Correlation Function

Consider again a solvent / at any given temperature, volume, and composition. Let 5 be a simple spherical molecule. The solvation Helmholtz energy of s is given by 

Note that we have explicitly introduced the location Ri at which we have placed the solvaton s. This is in general not necessary since all points in the solvent are equivalent. In this section, however, we shall produce inhomogeneity by introducing two particles at Ri and R2 therefore, the recording of their locations is important. Also, in this section we treat the very dilute solution of. y in a solvent. Theoretically, we can think of having just one 5 in a pure solvent. The symbol 0 stands for an average over all the configurations of the solvent molecules in the 7, F, N ensemble, i.e.. 

suppose we have one solute j at Ri and we introduce a second 5 at a different location R2. The corresponding work is obtained by taking the ratio of the two partition functions 

Note that P(X7Ri) may be viewed as the probability density in a presence of an external field produced by j at R. If the external field is zero, we recover (6.14.3). Equation (6.14.4) can be rewritten in another equivalent form as 

Thus the correlation function connects between the solvation Helmholtz energy on the first site and on the second site. This is formally the same relation as we encountered several times in Chapter 3. Equation (6.14.7) can also be read as 

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