Equilibrium, chemical Hammett correlation

The DSP approach nicely answers the controversial question about which substituent parameters should be employed to correlate pKa data for 4-substituted pyridinium ions. Statistically, the best correlation is given by Eq. (9), which has values to measure the resonance contribution of a substituent, a result in keeping with chemical intuition. This correlation is statistically superior to a Hammett treatment, where both resonance and inductive effects of a group are combined into a single parameter, p or ap.53,54 Moreover, now it is possible to rationalize why a simple Hammett treatment using ap works so well. Equation (9) reveals that the protonation equilibrium is much more sensitive to an inductive effect (p, — 5.15) than to a resonance effect (p = 2.69). Hence, substituent parameters, such as erp, which are derived from a consideration of the dissociation constants for benzoic acids where resonance contributions are small serve as a useful approximation. The inductive effect is said to have a larger influence on pKa values for pyridinium ions than for benzoic acids because the distance between the substituent and the reactive site is shorter in the pyridine series.53... 

Physical phenomena other than rates and equilibrium constants can be correlated by Hammett-type relationships. For example, as Figure 2.4 shows, in 13C nuclear magnetic resonance spectroscopy (called Cmr) the chemical shift of the cationic carbon in 17 is correlated by Brown s cr + values.21 And the C=0... 

The impressive success of the Hammett equation in correlating literally hundreds of observed properties (17) (e.g., rate and equilibrium constants, spectroscopic properties, etc.) may be attributable to the multitude of interaction mechanisms that is implicitly embedded in the values of a. The validity of the separability and additivity axioms used in the derivation of extra-thermodynamic relationships is confirmed by the ability to separate experimentally multiple interaction mechanisms (e.g., inductive and resonance (19, 20, 21), polar and steric (10), enthalpic and entropic (22)). This separation fostered significant progress in the application of quantitative structure-activity relationships to the study of chemical mechanisms. For these relationships can now be expressed in terms of more basic properties of the molecules under study. 

The study of structure-reactivity relationships by the organic chemist Hammett showed that there is often a quantitative relationship between the two-dimensional structure of organic molecules and their chemical reactivity. Specifically, he correlated the changes in chemical properties of a molecule that result from a small change in its chemical structure that is, the quantitative linear relationship between electron density at a certain part of a molecule and its tendency to undergo reactions of various types at that site. For example, there is a linear relationship between the effea of remote substituents on the equilibrium constant for the ionization of an acid with the effect of these substituents on the rate or equilibrium constant for many other types of chemical reaction. The relative value of Hammett substituent constants describes the similarity of molecules in terms of electronic properties. Taft expanded the method to include the steric hindrance of access of reagents to the reaction site by nearby substituents, a quantitation of three-dimensional similarity. In addition, Charton, Verloop, Austel, and others extended and refined these ideas. Finally, Hansch and Fujita showed that biological activity frequently is also quantitatively correlated with the hydrophobic character of the substituents. They coined the term QSAR, Quantitative Structure-Activity Relationships, for this type of analysis. 

The history of quantitative structure-activity relationships dates back to the last century, when Crum-Brown and Fraser in 1865 postulated that there ought to be a relationship between physiological activities <1> and chemical structures C. Later, Richet correlated toxicities with aqueous solubility. Around 1900, Meyer and Overton found linear relationships between the narcotic potencies of organic compounds and their partitioning behavior. In the mid-1930s, Hammett defined a reaction constant p to describe the reactivity of aromatic systems R, expressed by rate constants k (or equilibrium constants K) and a parameter o to describe the electronic properties of aromatic substituents X (1 equation 1) (see Linear Free Energy Relationships (LFER)) ... 

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