Nonpolar Solvation Model

As discussed above, solvation free energy is t3q)ically divided into two contributions polar and nonpolar components. In one popular description, polar portion refers to electrostatic contributions while the nonpolar component includes all other effects. Scaled particle theory (SPT) is often used to describe the hard-sphere interactions between the solute and the solvent by including the surface free energy and mechanical work of creating a cavity of the solute size in the solvent [148,149]. 

The SPT model can be used in combination with other solute-solvent nonpolar interactions e.g. [71,74,131,150], 

In our earlier work, we have shown that the surface area in Eq. 12.1 can be evaluated via a two-dimensional (2D) integral for arbitrarily shaped molecules [123,124]. For variation purposes, the total free functional must be set up as a 3D integral in M. To this end, we take advantage of geometric measure theory by considering the mean surface area [74] and the coarea formula [151]  

Therefore, we have the following nonpolar solvation free energy functional [1,71,74]  

It is important to understand the nature of the solvent-solute non-electrostatic interaction, U. Assume that the aqueous environment has multiple species labeled by a, and their interactions with each solute atom near the interface can be given by 

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The accuracy of the nonpolar solvation model performance is crucial to the success of other expanded versions of the differential geometry formalism. In particular, as the electrostatic effect and its associated approximation error are excluded, the major factor impacting the nonpolar solvation model is the solvent-solute boundary, which is governed by the DG-based formalism. Therefore, the nonpolar model provides the most direct and essential validation of the DG-based models. In our recent work [1], the DG-based nonpolar solvation (DG-NP) model was tested using a... 

Table 12.1 Solvation energies calculated with the differential geometry nonpolar solvation model for a set of 11 alkanes in comparison with an explicit solvent model [154]...

Giesen, D. J., Storer, J., Cramer, C. J. and Truhlar, D. J. General semiempirical quantum mechanical solvation model for nonpolar solvation free energies, n-hexadacane., J.Am. Chem.Soc., 117 (1995), 1057-1068... 

One of the crucial parameters describing the solvation phenomena is the free energy change. The main idea in most implicit solvation models is the decomposition of the solvation free energy, AGsolv into the electrostatic and nonpolar part,... 

A General Semiempirical Quantum Mechanical Solvation Model for Nonpolar Solvation Free Energies. n-Hexadecane. 

These experiments have shown that the slower component of solvation is linked to the overall structural dynamics of the liquid, and that mode coupling theory predicts many of the overall features of these dynamics. Dielectric solvation, which is the most widely studied solvation mechanism, does not play a major role for this nonpolar solute. Two theories of nonpolar solvation give better agreement with the data. Bagchi s theory is more rigorously derived, but our model permits a more detailed and rigorous comparison with experiment. 

A number of approximate solvation models are available by now. However, most of these methods focus on the description of the electrostatic effects of charged species in a solvent such as water, with a high dielectric constant. In the case of olefin polymerization nonpolar solvents are used. In addition, delicate interactions can be expected between individual solvent molecules like toluene with the cationic catalyst [37]. 

Chen, J., Brooks III, C.L. Implicit modeling of nonpolar solvation for simulating protein folding and conformational transitions. Phys. Chem. Chem. Phys. 2008,10,471-81. 

As mentioned above, a parallel line of research has been carried out by Dzubiella, Hansen, McCammon, and Li. Early work by Dzubiella and Hansen demonstrated the importance of the self-consistent treatment of polar and nonpolar interactions in solvation models [137, 138]. These observations were then incorporated into a self-consistent variational framework for polar and nonpolar solvation behavior by Dzubiella, Swanson, and McCammon [131, 139] which shared many common elements with our earlier geometric flow approach but included an additional term to represent nonpolar energetic contributions from surface curvature. Li and co-workers then developed several mathematical methods for this variational framework based on level-set methods and related approaches [140-142] which they demonstrated and tested on a... 

In this chapter, we review a number of DG-based models. Initially, we discuss solvation models, i.e., nonpolar and polar solvation models at equilibrium. To improve the accuracy and make our models robust, quantum mechanics is applied to the solute s electron structure. As an important extension, we also consider... 

The simplicity of idealized electrostatic solvation models has led to the use of dielectric constant (e) and of the permanent dipole moment (p) as parameters of the so-called solvent polarity. However, the dielectric constant describes only the change in the electric field intensity that occurs between the plates of a condenser, when the latter is removed from vacuum and placed into a solvent. This induces a dipole moment in nonpolar solvent molecules and dipolar molecules are aligned. Hence, the dielectric constant describes only the ability of a solvent to separate electrical charges and orient its dipolar molecules. The intermolecular forces between solute and solvent molecules are, however, much more complicated in addition to the non-specific coulombic, directional, inductive and dispersion interactions, can also be present specific hydrogen bond, electron-pair donor (EPD)/electron-pair acceptor (EPA), and solvophobic interactions in solutions. 

The two basic choices concern (i) the solvation model and (ii) the method to use. As discussed above, a continuum model such as PCM offers several advantages over purely supramolecular methods. On the other hand, PCM is expected to provide a good estimate of the electrostatic contribution to the solute-solvent interaction, whereas less accurate results can be obtained when dealing with nonpolar or... 

For this study, we use our extended database [11] of 47 radical systems, so 12 more than our previously published gas-phase radical electrophilicity scale [1], including C-, N-, O- and S-centered radicals, as well as some halogens, thus comprising a representative set of radicals for applications in organic chemistry. The structures can be retrieved from the Supporting Information. In order to compute the electrophilicity index, Parr s definition was apphed to the solution phase as shown in Eq. 1, using lEF-PCM and—in the case of water—COSMO as the implicit solvation models. Five solvents were chosen, for which the static dielectric constant covers the entire range of nonpolar to polar solvents n-hexane = 1.8819), dichloromethane (Sr — 8.9300), 2-propanol = 19.2640), acetonitrile (Sr = 35.6880) and water = 78.3553). 

The solvation thermodynamics have been interpreted in a classical study by Frank and Evans in terms of the iceberg model . This model states that the water molecules around an nonpolar solute show an increased quasi-solid structuring. This pattern would account for the strongly negative... 

The continuum model, in which solvent is regarded as a continuum dielectric, has been used to study solvent effects for a long time [2,3]. Because the electrostatic interaction in a polar system dominates over other forces such as van der Waals interactions, solvation energies can be approximated by a reaction field due to polarization of the dielectric continuum as solvent. Other contributions such as dispersion interactions, which must be explicitly considered for nonpolar solvent systems, have usually been treated with empirical quantity such as macroscopic surface tension of solvent. 

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