Polarizable solvents

To this point, the theory has been developed assuming that the medium is a conductor (e = oo), rather than a polarizable solvent of finite dielectric e. Fortunately, (2.88) can be extended to solvents by the introduction of a correction factor, f(e) ... 

To answer this question, let us first consider a neutral molecule that is usually said to be polar if it possesses a dipole moment (the term dipolar would be more appropriate)1 . In solution, the solute-solvent interactions result not only from the permanent dipole moments of solute or solvent molecules, but also from their polarizabilities. Let us recall that the polarizability a of a spherical molecule is defined by means of the dipole m = E induced by an external electric field E in its own direction. Figure 7.1 shows the four major dielectric interactions (dipole-dipole, solute dipole-solvent polarizability, solute polarizability-solvent dipole, polarizability-polarizability). Analytical expressions of the corresponding energy terms can be derived within the simple model of spherical-centered dipoles in isotropically polarizable spheres (Suppan, 1990). These four non-specific dielectric in-... 

A most comprehensive discussion of the effect of solvent on spectra has been given by Bayliss and McRae.21 They point out that polarization or dispersion forces are the most general interactions involved in solution and that all solution spectra are subject to a generalized polarization red shift, relative to vapor spectra, due to solvent polarization by the transition dipole. However, these dispersion forces are relatively weak and are easily obscured by the effect of dipole-dipole and dipole-static charge forces in polar, but not highly polarizable, solvents. By applying the Franck-Condon principle, they showed... 

A mean field theory for the stndy of solvent effects considers polarizable solvent molecules. The model, which combines qnantnm chemistry and simnlation calculations, splits the system into three parts ... 

Owing to its particular importance, polarizable solvent models have largely been restricted to water, for which a sizable number have been developed (see, for example, Dang 1992 Rick, Stuart, and Berne 1994 Bernardo et al. 1994 Zhu and Wong 1994 Lefohn, Ovchinnikov, and Voth 2001). Because evaluating the terms deriving from solvent polarizability... 

QM/MM approaches where the solute is QM and the solvent MM are in principle useful for computing the effect of the slow reaction field (represented by the solute point charges) but require a polarizable solvent model if electronic equilibration to the excited state is to be included (Gao 1994). With an MM solvent shell, it is no more possible to compute differential dispersion effects directly than for a continuum model. An option is to make the first solvent shell QM too, but computational costs for MC or MD simulations quickly expand with such a model. Large QM simulations with explicit solvent have appeared using the fast semiempirical INDO/S model to evaluate solvatochromic effects, and the results have been promising (Coutinho, Canute, and Zemer 1997 Coutinho and Canute 2003). Such simulations offer the potential to model solvent broadening accurately, since they can compute absorptions for an ensemble of solvent configurations. 

Molar Kerr constants mK and dipole moments squared of polytoxyethylene giycoils (POEG) and polyjoxyethylene dimethyl ether)s (POEDE) are reported in the isotropically polarizable solvents carbon tetrachloride, cyclohexane, and dioxane. Data for mK/x for POEG appear to reach an asymptotical value, Calculations of mK/x and /x based on the RIS model show good agreement with the experimental results. 

This is of course the major solvation energy of polar molecules in non-polar solvents, but it can be an important term in polar solvents as well, especially in highly polarizable solvents such as aromatic derivatives. 

Solvent polarity also affects the rate of peroxide decomposition. Most peroxides decompose faster in more polar or polarizable solvents. This is true even if the peroxide is not generally susceptible to higher order decomposition reactions. This phenomenon is illustrated by various half-life data for tert-butyl peroxypivalate [927-07-1]. The 10-h half-life temperature for tert-butyl peroxypivalate varies from 62°C in decane (nonpolar) to 55°C in benzene (polarizable) and 53°C in methanol (polar). 

Even for a simple reaction, involving just one reactant species and one product species, such as a keto-enol tautomerism or a cis-trans isomerization, Eq. (2.21) for a given solvent is complicated enough, not to speak of a comparison between several solvents. Still, in specific cases it is possible to unravel the solvent effects of cavity formation, if the solute species have different volumes, polarity/polarizability if the solute species differ in their dipole moments or polarizabilities, and solvent Lewis acidity and basicity if the solutes differ in their electron pair and hydrogen bond acceptance abilities. Thus, the enol form has a greater ability than the keto form to accept an electron pair from the solvent to form a hydrogen bond with it, but the keto form may have a larger dipole moment to interact with a polarizable solvent. 

The Kamlet-Taft u polarity/polarizability scale is based on a linear solvation energy relationship between the n it transition energy of the solute and the solvent polarity ( 1). The Onsager reaction field theory (11) is applicable to this type of relationship for nonpolar solvents, and successful correlations have previously been demonstrated using conventional liquid solvents ( 7 ). The Onsager theory attempts to describe the interactions between a polar solute molecule and the polarizable solvent in the cybotatic region. The theory predicts that the stabilization of the solute should be proportional to the polarizability of the solvent, which can be estimated from the index of refraction. Since carbon dioxide is a nonpolar fluid it would be expected that a linear relationship... 

Gao, J., Energy components of aqueous solution Insight from hybrid QM/MM simulations using a polarizable solvent model. J. Comput. Chem. (1997) 18 1061—1071. 

In order to clarify the role played by the solvent in the stabilization of the different structures it is useful to split the AGint term into two terms A int and AGsoiv. The last term, AGsoiv, provides the solvent distortion energy, i.e., the energy spent in changing the solvent structure from the initial to the final state. The term A nt accounts for the difference in the solute-solvent interaction energy between the final and initial states. For a non-polarizable solvent this term reads... 

If one wants to consider explicitly the electron polarization of the solvent it is necessary to add to Eq. (6-22) the energy spent in polarizing the solvent dipoles. In a previous work [36], we have shown that for a polarizable solvent, the final expression that the solute-solvent interaction energy takes is... 

Polarizable solvents induce a red shift which balances the effects of ion pairing and of permanent-dipole solvation (132). ... 

To derive the instantaneous free energies E, one needs an explicit model for a dipolar polarizable solute in a dipolar polarizable solvent. This need is addressed by the Drude model for induced solute and solvent dipole... 

Thus, the net influence of increased polarity on the rate (instants is, in this case as well as in polymerization of THF, eventually not attributable to the solvation phenomenon itself but to the stronger electrical microfields formed by more easily induced dipoles in more polar (and more polarizable) solvent molecules (e.g. CH3NO2 vs. 004). In this way, the energy of the ground state decreases and AGp becomes larger in more polar solvents, decreasing eventually the corre nding rate constants. 

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