The solvation effect solute-solvent interaction

Our approach is to treat solvation as a stoichiometric equilibrium process. Let W symbohze water, M an organic cosolvent, and R the solute. Then we postulate the 2-step (3-state) system shown below. 

In this scheme K, and K2 are dimensionless solvation equilibrium constants, the concentrations of water and cosolvent being expressed in mole fractions. The symbols RW2, RWM, RM2 are not meant to imply that exactly two solvent molecules are associated with each solute molecule rather RW2 represents the fully hydrated species, RM2 the fully cosolvated species, and RWM represents species including both water and cosolvent in the solvation shell. This description obviously could be extended, but experience has shown that a 3-state model is usually adequate, probably because the mixed solvate RWM cannot be algebraically (that is, functionally) differentiated into sub-states with data of ordinary precision. 

Now we further postulate that the solvation free energy is a weighted average of contributions by the various states, or 

Obviously when X2 = 0, AGs iv=AG w Eq. [5.5.13] is the desired expression relating the solvation energy to the solvent composition. 

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Because biomolecules normally exist in liquid water, this article will be largely concerned with their ordered structures in aqueous media and therefore with hydration effects. In order to understand better the influence of solute-solvent interactions on molecular order, also solvation in organic liquids will be considered to some extent. 

The partition and displacement model considers retention to result from a two step process. The first involves formation of a mixed stationary phase by intercalation of solvent molecules from the mobile phase. The composition of the solvents in the stationary phase is established according to thermodynamic equilibrium and is usually different to the bulk mobile phase composition. Competitive sorption of solvents is modeled as a displacement process and is complete before the solute is introduced into the two-phase system. Solute retention is then modeled as a partition process between the solvent modified stationary phase and the mobile phase by taking into account all solute-solvent interactions in both phases. The phenomenological model of solvent effects attempts to model retention as a combination of solute-solvent interactions (the solvation effect) and solvent-solvent interactions (the general medium... 

From the several continuum solvation methods available in the literature, the PCM model and its derivatives seem to be most used for pK calculations. In fact, the best pK results reported so far have been obtained with one of the PCM-based methods. Nevertheless, the fact that these calculations differ in many respects precludes any comparative evaluation of the different solvation models employed. More systematic studies are needed, taking into consideration the level of theory (method and basis sets) employed, the various continuum solvation models, and different classes of compounds. The introduction of solvent molecules into the solute cavity, in order to better represent the short-range solute-solvent interactions, must also be carefully examined. There is no apparent relationship between the structure of the solute and the number of intracavity solvent molecules that best reproduces the solvation energy. Hence, this best number is generally established on a trial-and-error basis. Also, the use of a such hybrid (discrete -I- continuum) description of the solvent molecules seems to be inconsistent with the fact that for some of the solvation models employed, the effects of the first solvation shell have been already incorporated when parameterizing the cavity. 

Solvent effects on chemical equilibria and reactions have been an important issue in physical organic chemistry. Several empirical relationships have been proposed to characterize systematically the various types of properties in protic and aprotic solvents. One of the simplest models is the continuum reaction field characterized by the dielectric constant, e, of the solvent, which is still widely used. Taft and coworkers [30] presented more sophisticated solvent parameters that can take solute-solvent hydrogen bonding and polarity into account. Although this parameter has been successfully applied to rationalize experimentally observed solvent effects, it seems still far from satisfactory to interpret solvent effects on the basis of microscopic infomation of the solute-solvent interaction and solvation free energy. 

Because the key operation in studying solvent effects on rates is to vary the solvent, evidently the nature of the solvation shell will vary as the solvent is changed. A distinction is often made between general and specific solvent effects, general effects being associated (by hypothesis) with some appropriate physical property such as dielectric constant, and specific effects with particular solute-solvent interactions in the solvation shell. In this context the idea of preferential solvation (or selective solvation) is often invoked. If a reaction is studied in a mixed solvent. 

Now knowing how to evaluate solvation-free energies, we are ready to explore the effect of the solvent on the potential surface of the reacting solute atoms. Adapting the EVB approach we can describe the reaction by including the solute-solvent interaction in the diagonal elements of the solute Hamiltonian, using... 

Since around 1950, in studies of solvent effects for organic reactions, empirical solvent parameters have been used these parameters represent the capabilities of solvents for the solute-solvent interactions (especially Lewis acid-base interactions). Though the solute-solvent interactions should depend on the solute as well as on the solvent, the empirical solvent parameters are considered to be irrelevant to solutes in other words, the use of only these parameters enables us to evaluate the solvation energies. Strictly... 

As has been suggested in the previous section, explanations of solvent effects on the basis of the macroscopic physical properties of the solvent are not very successful. The alternative approach is to make use of the microscopic or chemical properties of the solvent and to consider the detailed interaction of solvent molecules with their own kind and with solute molecules. If a configuration in which one or more solvent molecules interacts with a solute molecule has a particularly low free energy, it is feasible to describe at least that part of the solute-solvent interaction as the formation of a molecular complex and to speak of an equilibrium between solvated and non-solvated molecules. Such a stabilization of a particular solute by solvation will shift any equilibrium involving that solute. For example, in the case of formation of carbonium ions from triphenylcarbinol, the equilibrium is shifted in favor of the carbonium ion by an acidic solvent that reacts with hydroxide ion and with water. The carbonium ion concentration in sulfuric acid is greater than it is in methanol-... 

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