Hammett equation structural effects

The Hammett equation is not the only LFER." ° Some, like the Hammett equation, correlate structural changes in reactants, but the Grunwald-Winstein relationship (see p. 452) correlates changes in solvent and the Brpnsted relation (see p. 337) relates acidity to catalysis. The Taft equation is a structure-reactivity equation that correlates only field effects. ... 

The present findings suggest that mechanistic and reaction product variations are not necessarily accompanied by a clear difference in reactivity and the TS structure, and hence experimentally observable quantities, such as relative reactivities (Hammett equation) and kinetic isotope effects (KIEs), which are commonly considered to be useful means to detect a change in reaction mechanism (77,72), may not always be useful. 

The structure-reactivity relationship is a concept familiar to every organic chemist. As commonly used it refers to a linear free energy relationship, such as the Bronsted or Hammett equations, or some more general measure of the effect of changing substituent on the rate or equilibrium of a reaction. A substituent constant is conveniently defined as the effect of the substituent on the free-energy change for a control reaction. So the so-called structure-reactivity relationship is in fact usually a reactivity-reactivity relationship. 

A linear relationship between the standard enthalpies and entropies of a series of structurally related molecular entities undergoing the same reaction thus, AH° -I3AS° = constant or AAH° = (3AS°. When P > 0, this relationship is referred to as an isoequilibrium relationship. When the absolute temperature equals the factor P (often referred to as the isoequilibrium temperature), then all substituent effects on the reaction disappear (i e., AAG° = 0). In other words, a reaction studied at T = p will exhibit no substituent effects. This would suggest that, when one studies substituent effects on a reaction rate, the reaction should be studied at more than one temperature. Note also that the p factor in the Hammett equation changes sign at the isoequilibrium temperature. See Isokinetic Relationship... 

In a parallel development, structural effects on the chemical reactivity and physical properties of organic compounds were modelled quantitatively by the Hammett equation 8). The topic is well reviewed by Shorter 9>. Hansen 10) attempted to apply the Hammett equation to biological activities, while Zahradnik U) suggested an analogous equation applicable to biological activities. The major step forward is due to the work of Hansch and Fujita12), who showed that a correlation equation which accounted for both electrical and hydrophobic effects could successfully model bioactivities. In later work, steric parameters were included 13). 

As we have seen, the Hammett equation can, in principle, be applied to both equilibria and rate data. This implies that in certain cases, it is feasible to relate rate constants to equilibrium constants when both reflect the effects of a given structural moiety. In a general form a rate-equilibrium relationship can be written in terms of the corresponding changes in free energies of activation and of equilibration ... 

Because the effect of steric hindrance on different types of reactions is not expected to be the same, a given substituent is unlikely to exert the same relative steric effect in one reaction as in another. Consequently we cannot hope to find a very simple relationship such as the Hammett equation that will correlate structure and reactivity of ortho-substituted compounds. 

Hammett s equation was also established for substituted phenols from the elementary hydroxyl radical rate constants. The Hammett resonance constant was used to derive a QSAR model for substituted phenols. The simple Hammett equation has been shown to fail in the presence of electron-withdrawing or electron-donating substituents, such as an -OH group (Hansch and Leo, 1995). For this reason, the derived resonance constants such as o°, cr, and o+ were tested in different cases. In the case of multiple substituents, the resonance constants were summed. Figure 5.24 demonstrates a Hammett correlation for substituted phenols. The least-substituted compound, phenol, was used as a reference compound. Figure 5.24 shows the effects of different substituents on the degradation rates of phenols. Nitrophenol reacted the fastest, while methoxyphenol and hydroxyphenol reacted at a slower rate. This Hammett correlation can be used to predict degradation rate constants for compounds similar in structure. 

Systematic studies of the effects of structure on the biological activities of organic compounds and the analysis of the results are comprised in the term Quantitative Structure-Activity Relationships (QSAR). Many of the treatments employed in the correlation analysis of data in this field closely resemble those used for linear free-energy relationships, e.g. the Hammett equation and extensions thereof, and so the study of the biological properties of organic compounds is often regarded as a part of physical organic chemistry. In recent years, some historical study of work in... 

From the foregoing discussion it is evident that substituent groups in the organic inhibitor are likely to have a profound effect on the metal-inhibitor interactions and hence the inhibition efficiency. Thus structure-activity relationships in corrosion inhibition have evolved based on principles of physical organic chemistry. According to Hammett equation we have... 

The mechanism of reaction (19) was assumed to be dependent on the structure of the inhibitor (19) would involve the abstraction of the phenolic hydrogen atom. The whole idea was put forward, in part, to account for the failure of deuteriated inhibitors to show a kinetic isotope effect (Hammond et al., 1955). Another argument was that the Hammett equation, correlating the reactivities of the antioxidants, suggested the... 

For the quantitative treatment of substituent effects in such reactions, Brown proposed (Brown and Okamoto, 1957) a new Hammett-type structure-reactivity relationship, the Brown equation (1), in terms of substituent constant instead of a in the original Hammett equation. 

In principle, extrathermodynamic relationships that deviate from the simple Hammett equation (equation 8) can be treated by equation 14. The major problem is the determination of the different sets of o s, (e.g., set and 0 set) in a way that will indeed reflect their relation to independent properties. An example of such a procedure is the separation of polar and steric effects (10). The need for such a separation arose when a nearly complete lack of correlation was observed between substituent effects represented by the Hammet a constants and the rates for alkaline hydrolysis of aliphatic systems (12). Inspection of the structures indicated that the proximity of the substituents to the reaction site was a common feature. The steric interaction between R and X had to be considered separately from the electronic effects. Polar substituent constants were thus defined as the difference between the rate constants of base and acid catalyzed hydrolysis of esters. From the structural similarity of the transition states for these reactions (equation 15) it was assumed that the difference in their charge reflects only the polar effect of the substituent... 

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