Solvent effects multi-parameter correlation

A detailed reassessment of several multi-parameter correlations describing the solvent effects on the rates of four solvolytic SN reactions has shown that great caution should be exercised when using these relationships.85 The conclusions based on the multi-parameter correlations are not reliable because (i) both random and systematic errors have been underestimated, (ii) mechanisms may change when different substrates are involved, (iii) data extrapolated from different temperatures, and (iv) only small numbers of samples have been used in establishing these relationships. 

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. 

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. 

Because of the different effects of electrophilic solvation of the various negative charges (i.e. Cl- for Y, "OTs for Tots I" for Z, 0 for Ej), direct comparisons between the various scales should be done cautiously. A wide variety of correlations giving clear indications of trends, has been reported by Reichardt and Dimroth (1968), but the significance of a recent general survey of scales of solvent polarity is doubtful, because of the many parameters used in the correlations (Fowler et al., 1971). The multi-parameter approach has also been adopted and reviewed by Koppel and Palm (1972). 

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]. 

The SPP general solvent scale, and the SA and SB specific solvent scales, are orthogonal to one another, as can be inferred fi om the small correlation coefficients 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 scales for the multi-parameter analysis of other solvent scales or data sets sensitive to the solvent effect 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. 

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