Hammett plot, nonlinear

Changes in mechanism or transition state cause discontinuities in Hammett plots. Nonlinear plots are often found in reactions that proceed by two concurrent pathways (83, 84). 

Any reaction w4iich shows a major shift in transition-state structure over the substituent series would be expected to give a nonlinear Hammett plot, since a variation in the extent of resonance participation would then be expected. 

There are two opposing substituent effects on this reaction. Electron-attracting aiyl substituents favor the deprotonation but disfavor the elimination step. The observed substituent effects are small, and under some conditions the Hammett plot is nonlinear. 

Not all free energy relationships (Hammett plots) are linear. Aside from occasional scatter or unexplained deviations from an otherwise linear plot, it sometimes happens that the plot is smooth but nonlinear. Two causes have been identified, and many examples are known. One cause is a change in a rate-determining... 

Instead of the definition in Eq. (7-82), the selectivity is often written as log k,). Another way to consider a selectivity-reactivity relationship is to compare the relative effects of a series of substituents on a pair of reactions. This is what is done when Hammett plots are made for a pair of reactions and their p values are compared. The slope of an LEER is a function of the sensitivity of the process being correlated to structural or solvent changes. Thus, in a family of closely related LFERs, the one with the steepest slope is the most selective, and the one with the smallest slope is the least selective.Moreover, the intercept (or some arbitrarily selected abscissa value, usually log fco for fhe reference substituent) should be a measure of reactivity in each reaction series. Thus, a correlation should exist between the slopes (selectivity) and intercepts (reactivity) of a family of related LFERs. It has been suggested that the slopes and intercepts should be linearly related, but the conditions required for linearity are seldom met, and it is instead common to find only a rough correlation, indicative of normal selectivity-reactivity behavior. The Br nsted slopes, p, for the halogenation of a series of carbonyl compounds catalyzed by carboxylate ions show a smooth but nonlinear correlation with log... 

Evidence for a possibility that both the [2+2] and the [3+2] mechanism might well be involvec in the AD process was detailed by Sharpless [38]. Nonlinear Hammett plots for the AD in the presence of DHQD-CLB revealed that under the usual AD conditions a metallaoxetane pathway is favored, whereas for certain substrate ligand combinations a [3+2] mechanism is evidenced. 

A detailed kinetic study using UV-vis, FTIR (Fourier-transform infrared), and NMR spectroscopy a Hammett plot with /0 = -h1.98 using para-substituted styrene oxides an inverse solvent kinetic isotope effect (KIE) (fcnHp/ HHP-d2) = 0.86 and nonlinear effects studies" have all shown that the (salen)Co- (J) and amidine-co-catalysed enantioselective ring opening of terminal- and mew-epoxides by fluoride ion (forming trans- -ttuoTO alcohols in a 42-89% yield with 84-99% ee) occurs by the mechanism shown in Scheme 5. /-BuOOH oxidizes the Co(H) to Co(III) in the (salen)Co(III) catalyst. PhCOF provides the fluorine for the reaction. 

A detailed kinetic study, a Hammett plot with /0 = h-1.98 using para-substituted styrene oxides, an inverse solvent KIE (fcjjpjp/A jjp[p.(i2) = 0.86, and studies on nonlinear effects" indicating the mechanism of the (salen)Co- and amine-co-catalysed... 

The FCaq reduction of [Fe(phen)3] would generally be predicted as outer sphere in nature, but an inner-sphere mechanism has been proposed to explain a nonlinear Hammett plot obtained for substituted phenanthroline derivatives. Covalent hydration, that is, addition of H2O to the 2-position of the phenanthroline, is suggested to provide a hydroxo bridge for an inner-sphere mechanism but the evidence is not convincing. Kinetic evidence has been presented for an intermediate in the reduction of a variety of iron(III) complexes with donor ligands by [Fe(3,4,7,8-Me4phen)3] in acetonitrile. Both inner-sphere and outer-sphere pathways are found and the intermediate is thought to result from the former pathway. 

Hansch analysis tries to correlate biological activity with physico-chemical properties by linear and nonlinear regression analysis, finding property-activity relationship models. A Craig plot is a plot of two substituent parameters (e.g., Hansch-Fujita n and Hammett a values). The simplest Hansch analysis is based on the Hansch linear model [Kubinyi, 1988b], defined... 

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