CCL: translational entropy in solvent

 Sent to CCL by: "Michael K. Gilson" [gilson[*]umbi.umd.edu]
There can be some real semantic issues here, but I think it's safe to say that a correctly done solvation free energy calculation -- whether implicit or explicit-- will not include a translational contribution associated with the solute. There is no need at all for such a term in a solvation free energy, whether approximate or exact. Here are some more extended (i.e., rambling) comments.
The concept of an implicit solvent model can be cleanly derived from statistical thermodynamics. See, e.g., Biophys. J. 72:1047-1069, 1994. (I'm referring to my own work, not because it is necessarily best, but because I'm most familiar with it.)
There, Eq. 5 gives the standard chemical potential of a molecule in solution in terms of an integral that explicitly includes solvent degrees of freedom. It is a "standard" chemical potential in the sense that, instead of allowing an arbitrary system volume of V, it effectively integrates the motions of the solute molecule over a "standard volume" equal to the reciprocal of the standard concentration, Co.
Eqs. 34-37 of the same paper then show how this chemical potential can be rewritten in an implicit solvent form, where the solvent integrals have not been discarded or approximated, but only mathemetically tucked inside the solvation free energy as a function of solute conformation. The form of this expression exactly matches what one would obtain for an ideal gas IF the solvent term were magically turned into part of the potential energy and thereby lost its temperature dependence. In this specific sense, then, the contribution of translation to the chemical potential of a molecule in solution is, indeed, the same as what one would obtain from an ideal gas model.
It's maybe more immediately relevant to point out that the solvation free energy of the solute is equal to the difference between its standard chemical potential in solution vs gas phase, where we have to use the same standard concentration (e.g., 1 mol/liter) in both phases. When this difference is taken, the contribution of translation (i.e., the contribution of Co) cancels entirely, so that there is no translational contribution to the solvation free energy to worry about in the first place. Hence my opening comment. (Actually, this cancellation occurs for any concentration, so long as it is the same in both phases and ideality is assumed.)
Note too, that, for a molecule at a given concentration in both solution and in gas phase, the spatial probability distribution function p(x) is the same in both phases. Therefore, if one (somewhat simplistically) writes the translational entropy as -R\int p(x)\ln p(x), one finds the translational entropies are equal in both phases. Indeed, although "solvent caging" certainly occurs in solution, it operates only a short time-scale; over the experimental time-frame, the solutes wander freely. So, although "caging" presumably is a factor in the solvation free energy, I would not say it contributes to a translational term. It should already be included in the model itself, perhaps via some kind of surface energy, scaled particle theory, etc. 
 Regards,
 Mike