Empirical Solvent Parameters

On the basis of such a classification an empirical approach based on the so-called solvent empirical parameters was formulated to evaluate solvent effects on nuclear shieldings. In brief, this approach, originally proposed by Kamlet, Taft and co-workers [20] for electronic excitations, does not involve QM or other types of calculations but introduces a numerical treatment of experimental data obtained for a given reference system to obtain an estimate of solvent effects on various properties. 

Solvents exert their influence on organic reactions through a complicated mixture of all possible types of noncovalent interactions. Chemists have tried to unravel this entanglement and, ideally, want to assess the relative importance of all interactions separately. In a typical approach, a property of a reaction (e.g. its rate or selectivity) is measured in a laige number of different solvents. All these solvents have unique characteristics, quantified by their physical properties (i.e. refractive index, dielectric constant) or empirical parameters (e.g. ET(30)-value, AN). Linear correlations between a reaction property and one or more of these solvent properties (Linear Free Energy Relationships - LFER) reveal which noncovalent interactions are of major importance. The major drawback of this approach lies in the fact that the solvent parameters are often not independent. Alternatively, theoretical models and computer simulations can provide valuable information. Both methods have been applied successfully in studies of the solvent effects on Diels-Alder reactions. 

Many approaches have been used to correlate solvent effects. The approach used most often is based on the electrostatic theory, the theoretical development of which has been described in detail by Amis [114]. The reaction rate is correlated with some bulk parameter of the solvent, such as the dielectric constant or its various algebraic functions. The search for empirical parameters of solvent polarity and their applications in multiparameter equations has recently been intensified, and this approach is described in the book by Reich-ardt [115] and more recently in the chapter on medium effects in Connor s text on chemical kinetics [110]. 

Nonetheless, in practice, it may prove more effective just to measure the interaction parameter directly and treat it as an empirical parameter independent of a specific theory. This can be done by measuring the solvent activity of the... 

Modeling relaxation-influenced processes has been the subject of much theoretical work, which provides valuable insight into the physical process of solvent sorption [119], But these models are too complex to be useful in correlating data. However, in cases where the transport exponent is 0.5, it is simple to apply a diffusion analysis to the data. Such an analysis can usually fit such data well with a single parameter and provides dimensional scaling directly, plus the rate constant—the diffusion coefficient—has more intuitive significance than an empirical parameter like k. 

The solvatochromic phenolbetaine Reichardt s Dye (RD) allows to calculate a single parameter that indicates the overall polarity of the polymer. It is obtained by dissolving the dye in the polymer and measuring the absorbance maximum. The molar transition energy (Ex(30)) of RD is an empirical parameter to scale solvent polarity and is obtained by calculating18 Et(30) - hcvmaxNA OT 2.859vmaX R >. 

Perhaps the most widely discussed source of uncertainty in electrostatic calculations is the location of the solute/solvent boundary. The most common treatment is to place the boundary at the surface of a set of overlapping spheres centered at the nuclei. But what radius should one use for those spheres One common answer is van der Waals radii times I.2.46 In our own quantum mechanical solvation models,12 27 and those of several others59, 69, these radii are empirical parameters. Recently Barone et al.70 have modified the PCM to use charge-dependent united-atom spheres instead of all-atom spheres, and they optimized the electrostatic radii for a... 

Notes [1] Empirical solvent polarity parameter (see Reference 32)... 

Therefore, one must accept that the description of the solvent effect is rather complex and cannot be simplistically made on the basis of single physical parameters. A large number of parameters (including empirical parameters) must be considered which derive from thermodynamic calculations (equilibrium constant) and kinetic calculations (rate constants) performed on a large number of chemical reactions. 

The empirical parameters most frequently encountered in the description of the solvent effect (still in non-SI units) are 7... 

The measurement units of each parameter give a preliminary indication of the nature of these parameters, but for a more precise idea of their chemical and physical significance the reader is referred to the literature7-9. In the present context it is sufficient to bear in mind that most of these empirical parameters can be subdivided into parameters which measure the Lewis acidity (hence, the electrophilic power) and Lewis basicity (hence, the nucleophilic power) of a solvent. 

Table 7 reports a few of these empirical parameters for those solvents used most frequently in electrochemistry, together with dielectric constants (e) and dipole moments (ju, in Debye). 

Table 7 Empirical parameters for solvents commonly used in electrochemical studies...

Table 9 shows that the electrode potential of the reversible, one-electron oxidation exhibited by such a derivative [which corresponds to the redox change Rh(II)Rh(II)/Rh(II)Rh(III)], is very dependent on the solvent. In the same table the values of the empirical parameters for the basicity (DN), acidity (isT(30)) and polarizability (n ) of the solvents used are also reported.10... 

Table 9 Formal electrode potentials (V vs. Fc/Fc+) for the one-electron oxidation of [ Rh2(form )4] in different solvents and pertinent empirical parameters...

One does not gain a clear indication of the dominance of any of the empirical parameters of the solvent from an examination of the dependence of the redox potential on those parameters, as the coefficients of the linear correlation are 0.72 (DN), 0.57 (ZiT(30)) and 0.69 (7i ), respectively. However, using equations which take simultaneously into account the acidity, basicity and polarizability of the solvent,11 one can obtain, for example, a linear variation of the redox potential according to the following equation ... 

For a complete quantitative description of the solvent effects on the properties of the distinct diastereoisomers of dendrimers 5 (G = 1) and 6 (G = 1), a multiparameter treatment was used. The reason for using such a treatment is the observation that solute/solvent interactions, responsible for the solvent influence on a given process—such as equilibria, interconversion rates, spectroscopic absorptions, etc.—are caused by a multitude of nonspecific (ion/dipole, dipole/dipole, dipole/induced dipole, instantaneous dipole/induced dipole) and specific (hydrogen bonding, electron pair donor/acceptor, and chaige transfer interactions) intermolecular forces between the solute and solvent molecules. It is then possible to develop individual empirical parameters for each of these distinct and independent interaction mechanisms and combine them into a multiparameter equation such as Eq. 2, "... 

Prior to the introduction of the solubility parameter (solpar) concept, paint chemists used Kauri butanol values, mixed aniline points, and heptane numbers to predict the solubility of resins in aliphatic solvents. These parameters have been replaced, to a large extent, by solpars, but heptane numbers are still used, and these empirical parameters can be converted to solpar values. 

As outlined in Section 1.3, the solvent acidity and basicity have a significant influence on the reactions and equilibria in solutions. In particular, differences in reactions or equilibria among the solvents of higher permittivities are often caused by differences in solvent acidity and/or basicity. Because of the importance of solvent acidity and basicity, various empirical parameters have been proposed in order to express them quantitatively [1, 2]. Examples of the solvent acidity scales are Kosower s Z-values [8], Dimroth and Reichard s Er scale [1, 9], Mayer, Gutmann and Gergefs acceptor number (AN) [10, 11], and Taft and Kalmefs a parameter [12]. On the other hand, examples of the solvent basicity scales are Gut-... 

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