Multi-parameter Solvent Equations

Another problem that has been tackled by multivariate statistical methods is the characterization of the solvation capability of organic solvents based on empirical parameters of solvent polarity (see Chapter 7). Since such empirical parameters of solvent polarity are derived from carefully selected, strongly solvent-dependent reference processes, they are molecular-microscopic parameters. The polarity of solvents thus defined cannot be described by macroscopic, bulk solvent characteristics such as relative permittivities, refractive indices, etc., or functions thereof. For the quantitative correlation of solvent-dependent processes with solvent polarities, a large variety of empirical parameters of solvent polarity have been introduced (see Chapter 7). While some solvent polarity parameters are defined to describe an individual, more specific solute/solvent interaetion, others do not separate specific solute/solvent interactions and are referred to as general solvent polarity scales. Consequently, single- and multi-parameter correlation equations have been developed for the description of all kinds of solvent effects, and the question arises as to how many empirical parameters are really necessary for the correlation analysis of solvent-dependent processes such as chemical equilibria, reaction rates, or absorption spectra. 

A multi-parameter approach is preferable and the re scale of Kamlet and Taft (Kamlet et al., 1977) deserves special recognition because it has been successfully applied to the positions or intensities of maximal absorption in IR, NMR, ESR and UV-visible absorption and fluorescence spectra, and many other physical or chemical parameters (reaction rate, equilibrium constant, etc.). Such observables are denoted XYZ and their variations as a function of solvent polarity can be expressed by the generalized equation... 

Many different approaches have been reported in the last decade toward a better understanding of the medium factors that influence reaction rates. Fundamental studies have been devoted to probe the reaction at a microscopic level in order to obtain information on the nature of several specific solvent-solute interactions on S Ar and to attempt a description of these effects quantitatively. Recent works have shown the wide applicability of a single parameter scale such as the Ex(30) Dimroth and Reichardt37, as well as other multi-parameter equations. 

Consequently, it is also apparent that the solvent effect can be described on the basis of mathematical relationships between parameters which fall within the relationships defined as free energy correlations. In fact, the more parameters that are included in the mathematical treatment (multi-parameter equations), the better the description of the solvent effect that results. However, we will consider here only those parameters which take into account the solvent effect on redox potentials. 

Rates of the alkaline hydrolysis of 12 ortho-, meta- and ) ara-X-substituted phenyl tosylates, 4-MeC6H4S02C6H4X, in aqueous 0.5 m Bu4NBr over a wide temperature range have been analysed using the modified Fujita-Nishioka multi-parameter equation. It was concluded from both these and previously reported data by the same group that solvent electrophilicity was the main factor responsible for changes in the ortho, meta and para polar substituent effects with medium.60... 

Further single- and multi-parameter equations for eorrelations between iiT(30) values and other empirieal solvent polarity parameters, between various other empirical solvent parameters e.g. tt-jZ, a./AN, P/DN, etc.), and between empirical solvent parameters and macroscopic physical solvent properties have been collected in the reviews of Marcus [294b], Abboud and Notario [295], and Catalan [296]. 

The SPP general solvent seale, and the SA and SB speeifie solvent scales, are orthogonal to one another, as can be inferred from the small correlation eoefficients obtained in mutual fittings involving the 200 solvents listed in Table 10.3.1 [r (SPPvs. SA) = 0.13, r (SPP vs. SB) = 0.10 and r (SA vs. SB) = 0.01]. These results support the use of these seales for the multi-parameter analysis of other solvent scales or data sets sensitive to the solvent effeet on the basis of the following equation ... 

Among the approaches proposed so far, we recall here single-parameter models [102-111, 115, 118-120, 122, 123, 125, 126, 129], and multi-parametric correlation equations (either based on the combination of two or more existing scales or on the use of specific parameters to account for distinct types of effects) [112, 113, 116, 117, 121, 124]. Additional popular models are the Abraham s scales of solute hydrogen-bond acidity and solute hydrogen-bond basicity [127, 128], and the Catalan et al. solvatochromic scales [130,132, 133]. Methods based on quantitative stmcture-property relationships (QSPR) with solvent descriptors derived from the molecular structure [131, 134], and on principal component analysis (PCA) [135, 136] have been also proposed. An exhaustive review concerning the quantification of the solvent polarity has been recently published [138-140], including a detailed list of solvent scales, interrelations between parameters and statistical approaches. 

In this respect, the solvatochromic approach developed by Kamlet, Taft and coworkers38 which defines four parameters n. a, ji and <5 (with the addition of others when the need arose), to evaluate the different solvent effects, was highly successful in describing the solvent effects on the rates of reactions, as well as in NMR chemical shifts, IR, UV and fluorescence spectra, sol vent-water partition coefficients etc.38. In addition to the polarity/polarizability of the solvent, measured by the solvatochromic parameter ir, the aptitude to donate a hydrogen atom to form a hydrogen bond, measured by a, or its tendency to provide a pair of electrons to such a bond, /, and the cavity effect (or Hildebrand solubility parameter), S, are integrated in a multi-parametric equation to rationalize the solvent effects. 

Another statistical treatment of a set of 32 solvent parameter scales for 45 solvents using the program SMIRC ( election of a set of minimally mterrelated columns) has been carried out by Palm et al. [246], who, incidentally, introduced the first multi(four)-parameter equation for the correlation analysis of solvent effects in 1971 [cf. Eq. (7-50) in Chapter 7]. The minimum sufficient set of residual descriptors for the multilinear description of solvent effects consists of nine solvent parameter scales. This set of nine (purified) descriptors has been successfully applied to an extended set of 359 different solvent-dependent processes for more details, see reference [246]. 

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