Solvation thermodynamics: An approach from analytic temperature derivatives

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Abstract
A method is presented that uses integral equation theory to determine analytic temperature derivatives of the radial distribution functions. It is illustrated by studying the solvation thermodynamics of monatomic solutes in aqueous solution. The results agree well with the density derivative method developed previously [Yu and Karplus, J. Chem. Phys. 8 9, 2366 (1988)]. An expression for the solvation enthalpy is derived which allows direct comparison with experimental and isobaric–isothermal (NPT) ensemble simulation data. Satisfactory agreement with experiment is found for pure water and for the aqueous solvation of monovalent ions. Simple equations that exploit the site–site HNC closures are given for the decomposition of the potential of mean force into its enthalpic (or energetic) and entropic components. Since the extended RISM (HNC‐RISM) theory yields an incorrect (trivial) value of the dielectric constant, two different ways to correct for the asymptotic behavior of the solute–solute potential of mean force are compared. They lead to similar results but the method in which the solvent dielectric constant is modified from the outset can be applied more generally. The interactions between nonpolar and between polar solutes in water are decomposed into enthalpic and entropic contributions. This is difficult to do by computer simulations because of the lack of precision in such calculations. The association of nonpolar solutes in water is found to have comparable enthalpic and entropic contributions; this result disagrees with the usual description of an entropy‐dominated hydrophobic interaction. For ions, the somewhat surprising result is that the association of like‐charged species is enthalpy driven while for oppositely charged ions entropic effects are dominant. The process of bringing two like‐charged ions together leads to higher local charge density; the more favorable solvation enthalpy arising from this increase in charge density (q2 dependence) more than compensates for the Coulombic repulsion. For oppositely charged ions, association leads to a partial charge neutralization in which the favorable Coulombic attraction is overwhelmed by the loss of stabilizing solvation enthalpy. The entropic increase is due to the greater freedom of the surrounding water molecules resulting from the partial charge neutralization.