Dielectric Continuum Solvation

As seen in Fig. 1.1, and as I will explain in detail in this book, the dielectric continuum solvation model COSMO and the subsequent COSMO-based thermodynamics COSMO-RS are two clearly separable and very different steps. However, I have found that many researchers in this field refer to both methods as COSMO, which is both inaccurate and confusing. To avoid this confusion, I find it necessary to emphasize the importance of using the correct notations—COSMO and COSMO-RS-for these methods in all discussions and written literature on these subjects. 

Born s idea of the dielectric continuum solvation approximation became very popular, and many researchers worked on its further development. Hence a brief overview of the most important development steps will be given, but it is impossible to mention all the different modifications and all workers who have been contributing to this field. Readers who seek a broader overview are referred to some reviews on continuum solvation methods, e.g., by Cramer and Truhlar [22] or by Tomasi and Persico [23]. The goal of the history given here is to enable... 

Born s idea was taken up by Kirkwood and Onsager [24,25], who extended the dielectric continuum solvation approach by taking into account electrostatic multipole moments, Mf, i.e., dipole, quadrupole, octupole, and higher moments. Kirkwood derived the general formula ... 

Here, r denotes the position vector of the charges qt with respect to the center of the sphere, and r, the distance from the center. By applying the dielectric scaling function for dipoles (Eq. (2.3)), which—as we have seen in Fig. 2.1—is also a good approximation for most other multipole orders, it was immediately clear that the idea of using a scaled conductor instead of the EDBC leads to a considerable simplification of the mathematics of dielectric continuum solvation models, with very small loss of accuracy. It may also help the finding of closed analytic solutions where at present only multipole expansions are available, as in the case of the spherical cavity. Thus the Conductor-like Screening Model (COSMO) was bom. 

We have now achieved a situation in which dielectric continuum solvation models in general, and especially COSMO, are quite well established for SCF ground-state calculations of organic molecules. Many of the methods, tools, and properties available for gas-phase calculation can also be performed in a dielectric continuum solvation model. The PCM model including C-PCM provides the greatest breadth of implemented functionality. 

Thus, without any doubt, the situation of a polar solute in a polar solvent is very different from the situation of a solute in a dielectric continuum. The solvent is neither homogeneous, nor does it give a linear polarization response. Hence, the considerable success of dielectric continuum solvation models for the... 

Having recognized the theoretical inadequacy of the dielectric theory for polar solvents, I started to reconsider the entire problem of solvation models. Because the good performance of dielectric continuum solvation models for water cannot be a result of pure chance, in some way there must be an internal relationship between these models and the physical reality. Therefore I decided to reconsider the problem from the north pole of the globe, i.e., from the state of molecules swimming in a virtual perfect conductor. I was probably the first to enjoy this really novel perspective, and this led me to a perfectly novel, efficient, and accurate solvation model based upon, but going far beyond, the dielectric continuum solvation models such as COSMO. This COSMO for realistic solvation (COSMO-RS) model will be described in the remainder of this book. 

A nowadays more easily applicable framework to treat local field effects in optical processes involving pure liquids or solutions has been discussed at length elsewhere in this book, and it consists in resorting to dielectric continuum solvation models. In the last pages of this section some application of such models the study of birefringences in condensed phases will be briefly discussed. 

E. V. Stefanovich and T. N. Truong, Optimized atomic radii for quantum dielectric continuum solvation models, Chem. Phys. Lett., 244 (1995) 65-74. 

Explicit vs. Implicit (Dielectric Continuum) Solvation Models... 

For reactions in solution, one may implement explicit or implicit hydration schemes. In explicit hydration, water molecules are included in the system. These additional water molecules have a significant effect on the reaction coordinates of a reaction (e g., Felipe et al. 2001). Implicit hydration schemes, or dielectric continuum solvation models (see Cramer and Truhlar 1994), refer to one of several available methods. One may choose between an Onsager-type model (Wong et al. 1991), a Tomasi-type model (Miertus et al. 1981 Cances et al. 1997), a static isodensity surface polarized continuum model or a self consistent isodensity polarized continuum model (see Frisch et al. 1998). 

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