Dear Hadi

I am afraid that a simple answer cannot be given as the separation of the potential of mean force in parts as you describe is not unique. However, usually there is an idea around this separation, for instance where g and U are those for a hard sphere system and w is the contribution of soft interactions such as electrostatic. I would be happy to be more of assistance, but then you should provide information on the literature that you are currently studying. Best would be a text book as one might expect some homogeneity in the treatment. My favorite is Hill's "An introduction to statistical thermodynamics"; it is by Dover and very cheap and moreover, there are sources on the internet.

Ger

Dear Dr. Koper,

I am following a book by A. Ben-Naim, "Molecular Theory of Water and Aqueous Solutions". I will also look Book T Hill that you referring here.

Dear Hari,

In addition to was suggested by Ger, you cal read the following publications by Horák et al.:

1- Spectrochimica Acta

Volume 21, Issue 5, May 1965, Pages 911-917

 Studies of solute-solvent interactions—I. General considerations ☆

Author links open the overlay panel. Numbers correspond to the affiliation list which can be exposed by using the show more link.M. Horák, J. Plíva

Abstract

Conditions for the applicability of the theories of solvent shifts of characteristic vibrational frequencies based on the reaction field model are considered and the mechanisms of the various types of salvation processes are discussed in detail. On the basis of these considerations it proves possible to devise systems and experimental conditions suitable for testing the existing theories of solvent shifts and proposed mechanisms of solvation processes in a wide range of solvent properties.

http://www.sciencedirect.com/science/article/pii/037119516580159X

2-Spectrochimica Acta

Volume 21, Issue 5, May 1965, Pages 919-930

 Studies of solute-solvent interactions—II. Formation of collision complexes in solutions of some phenols

Author links open the overlay panel. Numbers correspond to the affiliation list which can be exposed by using the show more link.M. Horák, J. Moravec 1, J. Plíva

Abstract

Experimental study of the (OH)-stretching bands observed in solutions of phenol in mixtures of nonpolar solvents provides evidence for the existence of weak complexes of phenol with nonpolar solvents referred to as collision complexes. For 2,6-di-tert·butyl-4-methyl phenol in which the OH group is effectively screened from the surrounding medium such collision complexes are formed even with strongly polar solvents. It is found that provided orientation effects are unimportant the (OH)-stretching frequencies of the collision complexes follow the Buckingham relation in a wide range of solvent properties.

http://www.sciencedirect.com/science/article/pii/0371195165801606

Other interesting publications can be found in the following links:

http://www.sciencedirect.com/science/article/pii/S0167732207001158

Journal of Molecular Liquids

Volume 137, Issues 1–3, 10 January 2008, Pages 131–137

Study of solute–solvent and solvent–solvent interactions in pure and mixed binary solvents

Angshuman Maitra, Sanjib Bagchi,

Abstract

Solute–solvent and solvent–solvent interactions have been studied in fifteen pure solvents and seven binary aqueous mixtures by monitoring the solubility of a dye in the solvents. The standard Gibbs energy of solvation, as given by log s, where s is the solubility has been found to depend on various modes of solute–solvent interaction and also on the Hildebrand solubility parameter representing the cohesive energy density (solvent–solvent interaction) of solvent. In all the binary mixtures the value of log s has been found to deviate from the average of log s values in component pure solvents weighted with respect to their mole fractions. A dimensionless quantity has been defined to represent the deviation of the observed log s values from the mole fraction average. Results have been explained in terms of various modes of solvation interaction.

http://www.ncbi.nlm.nih.gov/pubmed/7699200

J Biochem Biophys Methods. 1994 Dec;29(3-4):217-35.

Correction for solute/solvent interaction extends accurate freezing point depression theory to high concentration range.

Fullerton GD1, Keener CR, Cameron IL.

Author information

Abstract

The authors describe empirical corrections to ideally dilute expressions for freezing point depression of aqueous solutions to arrive at new expressions accurate up to three molal concentration. The method assumes non-ideality is due primarily to solute/solvent interactions such that the correct free water mass Mwc is the mass of water in solution Mw minus I.M(s) where M(s) is the mass of solute and I an empirical solute/solvent interaction coefficient. The interaction coefficient is easily derived from the constant in the linear regression fit to the experimental plot of Mw/M(s) as a function of 1/delta T (inverse freezing point depression). The I-value, when substituted into the new thermodynamic expressions derived from the assumption of equivalent activity of water in solution and ice, provides accurate predictions of freezing point depression (+/- 0.05 degrees C) up to 2.5 molal concentration for all the test molecules evaluated; glucose, sucrose, glycerol and ethylene glycol. The concentration limit is the approximate monolayer water coverage limit for the solutes which suggests that direct solute/solute interactions are negligible below this limit. This is contrary to the view of many authors due to the common practice of including hydration forces (a soft potential added to the hard core atomic potential) in the interaction potential between solute particles. When this is recognized the two viewpoints are in fundamental agreement.

Hoping this will be helpful,

Rafik

Thanks Rafik,

Helpful articles. 

Dear Hari,

   Stat. Mech. provides a rigorous way to separate "direct" from "indirect" contributions to the pair correlation function h(r)=g(r)-1 (or its PMF counterpart) through the Ornstein-Zernike (OZ) equation,whose main outcome is the direct correlation function c(r) characterize by its short range  dependence.  While c(r) does not have a simple "geometric" interpretation as per the case of h(r), it provides unique ways to separate direct from indirect contribution to properties involved in different solvation processes, specially when these phenomena are analyzed in terms of Kirkwood-Buff's fluctuation formalism.  For specifics on the split and examples of the above ideas please check our work, available for download at ResearchGate, including:

Article: Solute-Induced Effects on the Structure and the Thermodynamics of Infinitely Dilute Mixture, Ariel A. Chialvo · Peter T. Cummings

Full-text · Article · Sep 1994 · AIChE Journal

 Article: Solvation in high-temperature electrolyte solutions. II. Some formal results, A. A. Chialvo · P. T. Cummings · J. M. Simonson · R. E. Mesmer

Full-text · Article · Jan 1999 · The Journal of Chemical Physics

Chapter: Solvation Phenomena in Dilute Solutions, Ariel Chialvo

Full-text · Chapter · Feb 2013

Best wishes,

Ariel.-

As said, this is one closure one may use. There are more ...

But Ariel is right that once you have made that choice, the path is clear ...

Good luck!

Thanks Dr.  Chialvo and Dr. Koper for suggestions.