Ionic solvation models

Many attempts have been made to calculate important macroscopic properties of ionic solutions without a detailed knowledge of their molecular structure. All models developed for this purpose can be classified into three categories according to the way the surrounding of the central ion is accounted for. Usually, continuous and discontinuous theories of ionic solvation are distinguished. Furthermore, it seems appropriate also to mention various attempts to apply statistical mechanics directly to ionic solutions. 

Theoretical considerations based upon a molecular approach to solvation are not yet very sophisticated. As in the case of ionic solvation, but even more markedly, the connection between properties of liquid mixtures and models on the level of molecular colculations is, despite all the progress made, an essentially unsolved problem. Even very crude approximative approaches utilizing for example the concept of pairwise additivity of intermolecular forces are not yet tractable, simply because extended potential hypersurfaces of dimeric molecular associations are lacking. A complete hypersurface describing the potential of two diatomics has already a dimensionality of six In this light, it is clear that advanced calculations are limited to very basic aspects of intermolecular interactions,... 

The main goal of the molecular dynamics computer simulation of ionic solvation and adsorption on a metal surface has been to test the above model and to provide more quantitative information about the different factors that influence the structure of hydrated ions at the interface. Unfortunately, most of the experimental information about these issues has been obtained from indirect measurements such as capacity and current-potential plots, although in recent years in situ experimental techniques have begun to provide an accurate test of the above model. For a recent review of experimental techniques and the theory of ionic adsorption at the water/metal interface, see the excellent paper by Philpott. ... 

The information discussed above can, however, yield only the overall trend in transfer quantities, and it would be unrealistic to expect, for example, that in aqueous mixtures, 6m (ion) is a linear function of mole fraction. Nevertheless it is noteworthy that the transfer quantities between pure solvents are not in agreement with trends expected from a simple Born model for ionic solvation. 

In 1954 Weiss32 used Bernal and Fowler s simplified solvation model,16 with an Inner Sphere of ionic coordination, i.e., a small spherical double layer around the ion of charge ze, followed by a sharp discontinuity at radius q, the edge of the Outer Sphere or Dielectric Continuum. He used a simple electrostatic argument to determine the energy to remove an electron at optical frequency from the Inner Sphere ... 

Holz et al. (47) have recently presented a relaxation model for mixed ionic solvation in binary solvent mixtures. The model, which is an extension of the Hertz electrostatic relaxation theory for ionic quadrupole relaxation at infinite dilution, is based on partial field gradients produced by a single solvent dipole. In a single solvent the quadrupole relaxation rate may be formulated as ... 

With the NDDO methods, tautomeric equilibria,22o especially in heterocycles,216-219,223,224,227,232,233 have been a favorite topic for study using the BKO approach. The tautomeric equilibria of many heterocyclic systems are exquisitely sensitive to solvation,i i3>2i4 making them interesting test cases for the validation of any solvation model. A detailed comparison is presented later in the section on relative free energies in heterocyclic equilibria. A comprehensive study of the stabilization of a wide variety of carbon radical and ionic centers has also been reported.21 ... 

The GB/SA model also correlates quite well with experiment for the neutral solutes. As expected, the regression slope and intercept are also nearly ideal. Conversely, based on the four ions for which results have been reported, there seems to be a tendency to overestimate ionic solvation free energies, but definite conclusions cannot be drawn from so small a sampling. Whereas the available data span a larger range of functionality than do those from the SASA model, there is still a paucity of results for complex and polyfunctional solutes. It would be very interesting to see how robust the model is in such instances. 

Dynamics In light of the encouraging results for absolute solvation energies and equilibria, applications of continuum solvation models to the dynamics of organic reactions also are expected to be very fruitful. Ionic reactions (e.g., the classical S[s 2 mechanism) may proceed in qualitatively different ways in solution and in the gas phase, and continuum solvation models provide a convenient and economical way to map out solvation energy changes as a function of the reaction coordinate. 

The change in free energy of solvation calculation for the reaction is the largest source of error in pKa calculations. To determine the most accurate method we must look both at the type of solvation model used, implicit, explicit, or cluster continuum method (likewise described as implicit-explicit), and the specific level of theory. As previously mentioned, ionic species, in particular, are extremely difficult to calculate because of their strong electrostatic effects and large free energy of solvation values [8,14,23,25]. 

Radii have also been tabulated for polyatomic ions [7]. Since these species are not truly spherical, such radii must be regarded as effective. However, it is useful to have estimates of effective radii when comparing ionic solvation parameters. In the following section, methods of determining the solvation parameters of single ions in infinitely dilute electrolyte solutions are considered. This is followed by a discussion of simple models of ionic solvation in which ionic size is an important factor. 

In summary, the empirical approach to ionic solvation based on the MSA is quite successful for monoatomic ions of the main group elements. It helps one to understand the important differences between the way cations and anions are solvated in water. It can also be applied to other ions, including polyatomic ions, provided the solvation is essentially electrostatic in character. Thus, one may estimate effective radii for anions such as nitrate and perchlorate from the Gibbs solvation energy using the value of 8s calculated for the halide ions. Considering the simplicity of the model, it provides an useful means of understanding the thermodynamics of solvation. 

The preferential solvation model allowed us to explain the positive and negative deviations from ideal behaviour and the synergetic effect exhibited for the solvato-chromic properties with the predominance of a species in the solvation sphere of the indicators. In the solvent systems comprised of [BF ]/[PF ] anions, the probes are preferentially solvated by the mixed solvent, while in the systems with [Cl]/ [Br] anions, the IL controls the solvation behaviour. These results are indicative of the involvement of ion-pair character of the IL. Additionally, it was possible to select binary mixtures with particular solvating properties varying not only in the solvent compositions but also the nature of the ionic or the molecular component of the mixture. 

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