Linear solvent effect relationships

Univariate LSERs may possess the conventional LEER form, as exemplified by Eq. (8-67), the Grunwald-Winstein equation, or they may simply be plots of log k against a solvent parameter such as Z, (30), or ir. Brownstein developed an LEER form for the latter type of correlation, writing 

Langhals has described a remarkable relationship of most of the empirieal solvent parameters [Z. t (30), Y, ete.] to composition in binary solvent mixtures  

Numerous authors have devised multiple linear regression approaches to the eorrelation of solvent effects, the intent being to widen the applieability of the eorrelation and to develop insight into the moleeular factors controlling the eorrelated proeess. For example, Zilian treated polarity as a eombination of effeets measured by molar refraction, AN, and DN. Koppel and Palm write 

The most familiar multivariate LSER is that of the Kamlet—Taft group, whieh in its fully rigged form is now written 

8 is an empirical polarizability correction term 8 = 0.0 (nonchlorinated aliphatic solvents). 

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Spectroscopic Measures 435 Linear Solvent Effect Relationships 442 Statistical Approaches 444... 

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. 

Another method for studying solvent effects is the extrathermodynamic approach that we described in Chapter 7 for the study of structure-reactivity relationships. For example, we might seek a correlation between og(,kA/l ) for a reaction A carried out in a series of solvents and log(/ R/A R) for a reference or model reaction carried out in the same series of solvents. A linear plot of og(k/iJk ) against log(/ R/ linear free energy relationship (LFER). Such plots have in fact been made. As with structure-reactivity relationships, these solvent-reactivity relationships can be useful to us, but they have limitations. 

The second aspect is more fundamental. It is related to the very nature of chemistry (quantum chemistry is physics). Chemistry deals with fuzzy objects, like solvent or substituent effects, that are of paramount importance in tautomerism. These effects can be modeled using LFER (Linear Free Energy Relationships), like the famous Hammett and Taft equations, with considerable success. Quantum calculations apply to individual molecules and perturbations remain relatively difficult to consider (an exception is general solvation using an Onsager-type approach). However, preliminary attempts have been made to treat families of compounds in a variational way [81AQ(C)105]. 

The effect of solvent has been treated quantitatively (for SnI mechanisms, in which the solvent pulls off the leaving group) by a linear free energy relationship "... 

The rate constants in organic reaction in a solvent generally reflect the solvent effect. Various empirical measures of the solvent effect have been proposed and correlated with the reaction rate constant [5]. Of these, some measures have a linear relation to the solubility parameter of the solvent. The logarithms of kj and k2/ki were plotted against the solubility parameter of toluene, NMP and DMSO[6] in Fig. 2. As shown in Fig.2, the plots satisfied the linear relationship. The solvent polarity is increased by the increase of solubility parameter of the solvent. It may be assumed that increase of unstability and solvation of Ci due to the increase of solvent polarity make the dissociation reaction of Ci and the reaction between Ci and COisuch as SNi by solvation[7] easier, respectively, and then, k2/ki and ks increases as increasing the solubility parameter as shown in Fig. 2. 

Dimers (73) and (74) were formed in approximately equal amounts in all cases, although, as in the cases of 2-cyclopentenone and 2-cyclohexenone, the relative amount of (72) (either cis-syn-cis or cis-anti-cis) was found to vary substantially with solvent polarity. As in 2-cyclopentenone, this increase in the rate of head-to-head dimerization was attributed to stabilization of the increase in dipole moment in going to the transition state leading to (72) in polar solvents. It is thought that the solvent effect in this case is not associated with the state of aggregation since a plot of Stem-Volmer plot and complete quenching with 0.2 M piperylene indicate that the reaction proceeds mainly from the triplet manifold. However, the rates of formation of head-to-head and head-to-tail dimers do not show the same relationship when sensitized by benzophenone as in the direct photolysis. This effect, when combined with different intercepts for head-to-head and head-to-tail dimerizations quenched by piperylene in the Stem-Volmer plot, indicates that two distinct excited triplet states are involved with differing efficiencies of population. The nature of these two triplets has not been disclosed. 

Kamlet MJ, Dickinson C, Taft RW (1981) Linear solvation energy relationship. Solvent effects on some fluorescent probes. Chem Phys Lett 77 69-72... 

While p for the polar effects of alkyl groups does not vary with the solvent, pn for the polar effects of aromatic substituents is solvent-dependent. For example, there is a fairly linear log/log relationship between the bromination rates of styrenes in acetic acid and methanol (36) with a slope higher than unity, to be compared with 0.99 in (24). The p+-value for styrenes... 

The relationship between the structure of 1,2,4-thiadiazolidines and their H NMR spectral solvent effects has been studied by measurement of the NMR chemical shift differences (Av) of 39 derivatives in various solvents (CgDg, CCU) for methyl or methylene groups attached to an sp2-hybridized nitrogen, Av correlates linearly with Hammett a constants and for those attached to an sp3 4-hybridized nitrogen, with Taft a° constants <1982AHC285>. 

Kamlet M. J., Dickinson C. and Taft R. W. (1981) Linear Solvation Energy Relationships. Solvent Effects on Some Fluorescent Probes, Chem. Phys. Lett. 77, 69-72. 

B. Solvent Effects and Linear Solvation Free Energy Relationships.43... 

Now we consider the solvent effects on the mutual relationship between the p/C, values of different adds. Figure 3.2 shows the relations between pfC, of non-ortho-substituted phenols and the Hammett er-values of the substituents [8]. Good linear relations are observed in four solvents.3 It is of special interest that the slopes in AN, DMF and DMSO are almost the same and are nearly 2.0 times the slope in water. Similar linear relations have also been obtained for non-ortho-sub-... 

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