Aqueous solvation energy

I cite three papers to show that standard continuum calculations can give satisfactory first-principles pKa values Shields and coworkers used a thermodynamic cycle with gas phase and continuum calculations to obtain satisfactory results for six simple carboxylic acids [46]. These were absolute calculations in the sense that no acid was used as a reference point, although the experimental gas phase free energy and aqueous solvation energy of the proton were resorted to. Not quite as esthetically satisfying perhaps, were relative calculations in which acetic acid was used as a reference compound [47]. Similar to the absolute acid calculations was work with phenols that was said to be among the most accurate of any such calculations for any group of compounds [48]. 

Through this approximation they were able to arrive at an absolute value for the free energy of solvation of the proton by analysing a large number of experimental results. Subsequently, they could determine the free energy of solvation for any other ion, without or with a cluster of water molecules. Some representative results are listed in Table 16, where it is seen that the aqueous solvation energy for clustered ions show a clear convergence trend when the number of water molecules in the cluster exceeds 2. Ultimately, the authors also compared calculated values with experimental values and found that the calculated values in most cases were within 3-5 kcal/mol of the experimental values. 

This preference is not overridden by slight differences in the aqueous solvation energy. The bispidine moiety was combined with crown-ether functionality to form a molecular cavity (19 ring members, including the cleft of bispidine, two N and four Sparteine (37) is less... 

Comparison of Experimental Aqueous Solvation Energies with Those Calculated by the Generalized Born Model ... 

In many processes involving solutes, solution-solid interfaces, and adsorption, solvation energetics are an important consideration. Since, the magnitude of aqueous solvation energies is of the order of hydrogen bond energy, or nominally lOkcal/mol, it is a subject worthy of examination. 

Stabilization of the syn conformer in the gas phase is explained rather intuitively in terms of the extra stabilization due to increased interactions between the H atom in the OH group and the O atom in C=0 group. As one can see in Figure 5, the extra stabilization in the anti confonner in aqueous solution arises from the solvation energy, especially at the carbonyl oxygen site. 

However, solubility, depending as it does on the rather small difference between solvation energy and lattice energy (both large quantities which themselves increase as cation size decreases) and on entropy effects, cannot be simply related to cation radius. No consistent trends are apparent in aqueous, or for that matter nonaqueous, solutions but an empirical distinction can often be made between the lighter cerium lanthanides and the heavier yttrium lanthanides. Thus oxalates, double sulfates and double nitrates of the former are rather less soluble and basic nitrates more soluble than those of the latter. The differences are by no means sharp, but classical separation procedures depended on them. 

Yang G, Ran Y and Yalkowsky SH. Prediction of the aqueous solubility comparison of the general solubility equation and the method using an amended solvation energy relationship. J Pharm Sci 2002 91 517-33. 

Dissolution of an ionic salt is essentially a separation process carried out by the interaction of the salt with water molecules. The separation is relatively easy in water because of its high dielectric constant. Comparison of the energies needed to separate ions of NaCl from 0-2 nm to infinity shows that it takes 692-89 kJ mol" in vacuum, but only 8-82 kJ moF in aqueous solution (Moore, 1972). Similar arguments have been used to try to estimate solvation energies of ions in aqueous solution, but there are difficulties caused by the variations in dielectric constant in the immediate vicinity of individual ions. 

Calculation of the Solvation Energy from Experimental Data The solvation energies of individual ions can be calculated from experimental data for the solvation energies of electrolytes when certain assumptions are made. If it is assumed that an ion s solvation energy depends only on its crystal radius (as assumed in Bom s model), these energies should be the same for ions K+ and F , which have similar values of these radii (0.133 0.002nm). It follows that in aqueous solutions, K+ = F- = = 414.0 kJ/mol. With the aid of these values we can now determine... 

Figure 4.11 Optimized structures of CH cO species, as indicated, over aqueous-solvated Pt(lll) as determined by DFT in Cao et al. [2005]. Horizontal and vertical arrows indicate C—H and O—H cleavage steps, respectively. Reaction energies are included for the aqueous phase [Cao et al., 2005] and the vapor phase (in parentheses) [Desai et al., 2002]. The thermodynamically preferred aqueous phase pathway is indicated by bold arrows (in blue). (See color insert.)...

The solvation energies, AG, which in the present example are for solvation in aqueous solution, correspond to the transfer process for species X from the gas phase to solution ... 

So far we have not touched on the fact that the important topic of solvation energy is not yet taken into account. The extent to which solvation influences gas-phase energy values can be considerable. As an example, gas-phase data for fundamental enolisation reactions are included in Table 1. Related aqueous solution phase data can be derived from equilibrium constants 31). The gas-phase heats of enolisation for acetone and propionaldehyde are 19.5 and 13 keal/mol, respectively. The corresponding free energies of enolisation in solution are 9.9 and 5.4 kcal/mol. (Whether the difference between gas and solution derives from enthalpy or entropy effects is irrelevant at this stage.) Despite this, our experience with gas-phase enthalpies calculated by the methods described in this chapter leads us to believe that even the current approach is most valuable for evaluation of reactivity. 

Kamlet, M. J., Doherty, R. M., Abraham, M. H., Carr, P. W., Doherty, R. F., Raft, R. W. (1987) Linear solvation energy relationships. Important differences between aqueous solubility relationships for aliphatic and aromatic solutes. J. Phys. Chem. 91, 1996-2004. 

Leahy, D. E. (1986) Intrinsic molecular volume as a measure of the cavity term in linear solvation energy relationships octanol-water partition coefficients and aqueous solubilities. J. Pharm. Sci. 75, 629-636. 

The source of some of the difficulties encountered in trying to explain the effects of structural changes on ionization rates may be due to the different parts played by the solvent, as for example, the sulfur dioxide of the trityl chloride equilibrium experiments and the aqueous acetone of the benzhydryl chloride rate data. The solvent is bound to modify the effect of a substituent, and although the solvent is usually ignored in discussing substituent effects this is because of a scarcity of usable data and not because the importance of the solvent is not realized "... solvation energy and entropy are the most characteristic determinants of reactions in solution, and... for this class of reactions no norm exists which does not take primary account of solvation. 220 Precisely how best to take account of solvation is an unanswered problem that is the subject of much current research. 

G. D. Hawkins, C. J. Cramer, and D. G. Truhlar, Parameterized models of aqueous free energies of solvation based on pairwise descreening of solute atomic charges from a dielectric medium, J. Phys. Chem. 100 19824 (1996) erratum to be published. 

---