Models of solvation

T. A. Keith and M. J. Frisch, A Fully Self-Consistent Polarizable Continuum Model of Solvation with Analytic Energy Gradients, in preparation (1996). 

Continuum models of solvation treat the solute microscopically, and the surrounding solvent macroscopically, according to the above principles. The simplest treatment is the Onsager (1936) model, where aspirin in solution would be modelled according to Figure 15.4. The solute is embedded in a spherical cavity, whose radius can be estimated by calculating the molecular volume. A dipole in the solute molecule induces polarization in the solvent continuum, which in turn interacts with the solute dipole, leading to stabilization. 

Molecules do not consist of rigid arrays of point charges, and on application of an external electrostatic field the electrons and protons will rearrange themselves until the interaction energy is a minimum. In classical electrostatics, where we deal with macroscopic samples, the phenomenon is referred to as the induced polarization. I dealt with this in Chapter 15, when we discussed the Onsager model of solvation. The nuclei and the electrons will tend to move in opposite directions when a field is applied, and so the electric dipole moment will change. Again, in classical electrostatics we study the induced dipole moment per unit volume. 

Prediction of tautomeric equilibria by a quantum mechanical continuum model of solvation Tautomerism of thiophenes... 

Hall, R. J., M. M. Davidson, N. A. Burton, and I. H. Hiller. 1995. Combined Density Functional Self-Consistent Reaction Field Model of Solvation. J. Phys. Chem. 99, 921. 

Abstract This chapter reviews the theoretical background for continuum models of solvation, recent advances in their implementation, and illustrative examples of their use. Continuum models are the most efficient way to include condensed-phase effects into quantum mechanical calculations, and this is typically accomplished by the using self-consistent reaction field (SCRF) approach for the electrostatic component. This approach does not automatically include the non-electrostatic component of solvation, and we review various approaches for including that aspect. The performance of various models is compared for a number of applications, with emphasis on heterocyclic tautomeric equilibria because they have been the subject of the widest variety of studies. For nonequilibrium applications, e.g., dynamics and spectroscopy, one must consider the various time scales of the solvation process and the dynamical process under consideration, and the final section of the review discusses these issues. 

The present chapter thus provides an overview of the current status of continuum models of solvation. We review available continuum models and computational techniques implementing such models for both electrostatic and non-electrostatic components of the free energy of solvation. We then consider a number of case studies, with particular focus on the prediction of heterocyclic tautomeric equilibria. In the discussion of the latter we center attention on the subtleties of actual chemical systems and some of the dangers of applying continuum models uncritically. We hope the reader will emerge with a balanced appreciation of the power and limitations of these methods. 

At this point we note the existence of several classic and recent reviews devoted to, or with considerable attention paid to, continuum models of solvation effects, and we direct the reader to these works [71-83] for other perspectives that we consider complementary to what is presented here. 

In addition to heterocycles, other molecular systems have attracted theoretical attention with respect to prediction of tautomeric equilibria and solvation effects thereon. The most commonly studied example in this class is the equilibrium between formamide and formamidic acid, discussed in the next section. In addition, some continuum modeling of solvation effects on keto/enol equilibria have appeared these are presented in section 4.2.2.2. We note that the equilibrium... 

The continuum model of solvation has evolved from these beginnings. The solvent is treated as a continuous polarizable medium, usually assumed to be homogeneous and isotropic, with a uniform dielectric constant e.11-16 The solute molecule creates and occupies a cavity within this medium. The free energy of solvation is usually considered to be composed of three primary components ... 

Equation (32) can be viewed as a forerunner of the cavity/continuum models of solvation that were discussed earlier... 

The Born model of solvation overestimates solvation free energies but indicates the general trends correctly. Potential inversion, as observed in many other systems containing two identical oxidizable or reducible groups separated by an unsaturated bridge (Scheme 1.4), can be rationalized in the same manner. 

Recapitulating the foregoing discussion, it is clearly not our opinion that solution experiments appear to be inadequate for the purpose of comparison with molecular theories. However, we want to point out that due to the evident shortcomings of present theoretical and computational facilities a distinct scepticism is necessary in order to avoid the production of meaningless data. Of course, the solution experiments remain the main source of information, the data of which must be explained by theory. At the present stage of knowledge it is only possible to pick out selected properties of solutions which can be described satisfactorily on a molecular basis. For instance, referring to Frank and Wen s model of solvation shells W, the structure of the inner shell should not be modified too much by... 

The dielectric constants play a particular role in the characterization of solvents. Their importance over other criteria is due to the simplicity of electrostatic models of solvation and they have become a useful measure of solvent polarity. Since both the dielectric constant r and the dipole moment p are important complementary solvent properties, it has been recommended that organic solvents should be classified according to their electrostatic factor EF (defined as the product of 8 and p). 

Fig. 2.6 Typical model of solvated ions in structured solvents such as water and alcohols.

G. Scalmani, V. Barone, K. N. Kudin, C. S. Pomelli, G. E. Scuseria and M. J. Frisch, Achieving linear-scaling computation cost for the polarizable continuum model of solvation, Theoret. Chem. Acc., Ill (2004) 90. 

V. Dillet, D. Rinaldi, J. Bertran, and J. L. Rivail, Analytical energy derivatives for a realistic continuum model of solvation application to the analysis of solvent effects on reaction paths, J. Chem. Phys., 104 (1996) 9437. 

Recent perspective concerning DC models of solvation has been provided by molecular-level theories and simulations [18,19,27], Such studies, for example, draw attention to the importance of departures from the homogeneous, spatially local models discussed above, and help to elucidate the nature of effective molecular cavities. Examples of these effects will be included in the specific results illustrated in Section 3.5.5, Comparison of s Based on Molecular-level and Continuum Models. 

To end this part of the contribution, we should note efforts made to combine explicit and GB models of solvation. Thus, Lee et al. [56] have developed a hybrid approach where a macromolecule is solvated by a first shell of explicit water molecules, while long-range solvation effects are captured by GB models. The method takes advantage of... 

Chipot C, Rinaldi D, Rivail JL (1992) Intramolecular electron correlation in die self-consistent reaction field model of solvation. A MP2/6-31G ab initio study of the NH3—HC1 complex. Chem Phys Lett 191 287- 292... 

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