Correlations Hammett, nonlinear

Nonlinear Hammett correlation observed for formation of benzal-dehyde semicarbazone at pH 3.9. (Reproduced from reference 204. Note that the vertical axis is a log scale.)... 

There has been a mechanistic investigation of the possible intermediates in the thermal C -C cyclization of enyne-carbodiimides [424]. Kinetic studies of enyne-carbodiimides with electron-withdrawing substituents gave a nonlinear Hammett correlation. This supported a concerted/nonpolar mechanism to produce a carbene intermediate. However, when electron-donating substituents were present, the results indicated a polar cyclization mechanism giving a carbene with zwitte-rionic character. Earlier, theoretical investigations by density functional theory (DFT) and NBO analysis had supported a diradical intermediate. 

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... 

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... 

In 1962, Hansen [14] derived a first Hammett-type relationship between the toxicities of substituted benzoic acids and the electronic a constants of their substituents. However, later, it turned out that this was a chance correlation that only resulted from a close interrelationship between the Hammett a parameter and the lipophilicity constant % (Sec. 4 Eqs. (42) and (43)). In the same year, for the very first time, a nonlinear multiparameter equation (Eq. 6) [15] was used to describe biological activity values ... 

The nonlinearity of the correlation between log k/ko) and Hammett (Tp constant at the cyclization of compounds 3.971 suggests that there is a change in reaction mechanism of C -C cyclization of the enyne carbodiimide, possibly from carbene to polar intermediates. Electron donor substituents X and Y increase probability of formation of the high polar zwitterionic carbene intermediate (Scheme 3.147, structures B and C), whereas electron-withdrawing substituents lead to a less polar carbenes (Scheme 3.147, structure A). The mechanism of polar intermediate is supported by a noticeable increase of the reaction rate with increasing the donor properties of the solvent that was observed for carbodiimide 3.971a. However, more detailed study of conditions of the... 

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