A thermodynamic analysis of solvation

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Abstract
The free energy, energy, and entropy of solvation, relative to the pure liquid, are analyzed. By a coupling parameter integration it is shown that only averages over the solute–solvent interaction energy contribute to the free energy and that the solvent–solvent interaction term, which contributes the so-called cavity (solvent reorganization) term to the energy, is cancelled exactly by a corresponding term in the entropy. These terms exist even in the infinite dilution limit since they arise from the derivative of the free energy with respect to the solute density. Following the approach of Garisto et al. [J. Chem. Phys. 79, 6294 (1983)], the site–site Ornstein–Zernike integral equations and HNC closures are used to determine the derivatives of the distribution functions with respect to the density. This makes it possible to calculate the energetic and entropic contributions to the solvation free energy in the infinite dilution limit. The method is applied to pure solvent and to infinitely dilute aqueous solutions of cations, anions and neutral Lennard-Jones particles. The results are in agreement with numerical calculations of the thermodynamic quantities by use of finite difference values for the temperature derivatives. A simple empirical relation for the charge dependence of the solvation free energy is observed; it is shown for the case of an ion in a dipolar solvent, as typified by aqueous electrolyte solutions, that the free energy of solvation varies quadratically with the charge and is very nearly equal to one-half the solute–solvent portion of the solvation energy. Some discussion of the relation of the present results to entropy–enthalpy compensation and to computer simulations is given.