Hammett and Taft relationships

In January 1937, Hammett published a paper on the Effects of structure upon the reactions of benzene derivatives . Let us consider the dissociation of benzoic acid 

Hammett realised that the addition of a substituent in the aromatic ring has a quantitative effect on the dissociation constant K. For para-nitrobenzoic acid the dissociation constant 

Hammett found, for example, that the nitro group has a stabilising effect on other dissociation reactions such as those of phenylacetic acid. He then proposed a quantitative relationship to account for such findings 

The same kind of expression is also valid for the rate constants, k 

K° and kP denotes the corresponding constants for the parent or unsubstituted compound. 

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The dehydration rate depends very strongly on substitution on Ca. Large differences in reactivity of primary, secondary and tertiary alcohols over solid catalysts were reported as early as in 1931 by Dohse [90]. Also, substituents on Cp affect the rate. Both influences can be quantitatively described by the Hammett and Taft relationships the published correlations are summarised in Table 4. Of special interest is the extensive set of alcohols of the type R R2R3COH [56], which includes primary, secondary and tertiary alcohols and gives a single Taft correlation with an excellent fit. The values of p and p which can give information about the mechanism and catalyst nature will be discussed in the following sections. 

Table 4 Hammett and Taft relationships for some equilibria...

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]. 

Monoparametric equation A relationship in which the effect of structure on a property is represented by a single generally composite parameter. Examples are the Hammett and Taft equations. 

The broad applicability of LFERs for heterogeneous catalytic reactions has been demonstrated independently by Kraus (23) and Yoneda (24-27). The first author concentrated mostly on the established relationships such as the Hammett and Taft equations, whereas Yoneda has concentrated particularly on correlations with reactivity indices and other quantities. Since then, LFERs have been widely applied to heterogeneous catalytic reactions, and experience has been gained as to the suitability of each different type. An important step has been made toward an interpretation of the slopes of linear correlations (parameter a in Eq. 3) as the quantities that are closely connected with reaction mechanisms. 

Among Type A relationships, the Hammett and Taft equations are most frequently employed for noncatalytic reactions. When utilizing them for catalytic reactions we must consider the reliability of the substituent parameters and their suitability for the given structural type of reactants. The Hammett equation... 

Linear-free-energy relationships such as the Hammett and Taft equations [Lowry and Richardson, 1987] have been used to correlate copolymerization behavior with structure, but the approach is limited to considering a series of monomers that are similar in structure. Walling [1957] applied the Hammett equation to copolymerization among various meta- and para-substituted styrenes. The Taft equation in the form... 

These and other investigators have shown, for many systems where a biological response can be measured quantitatively, that relative biological response can be expressed as functions of various molecular properties by using equations of the same forms as Hammett or Taft relationships ... 

The cyclic mechanism is probably seldom a fully concerted (E2) process, and the different timing of individual electron shifts results in a transition towards the El or ElcB mechanisms (cf. Sect. 2.1.1). The choice of the mechanism depends on the reactant structure as well as on the catalyst nature. As an indicator of the mechanism, either the degree of stereoselectivity (see refs. 68, 121, 132 and 141) or the value of the reaction parameter of a linear free energy relationship, e.g. p or p constants of the Hammett and Taft equations (cf. ref. 55), may be used. 

The Hammett and Taft equations are not the only linear free-energy relationships known. We shall encounter others—for example, the Bronsted relations, and the Grunwald-Winstein and Swain-Scott equations later in this book. 

The correlation of biological activity with physicochemical properties is often termed an extrathermodynamic relationship. Because it follows in the line of Hammett and Taft equations that correlate thermodynamic and related parameters, it is appropriately labeled. The Hammett equation represents relationships between the logarithms of rate or equilibrium constants and substituent constants. The linearity of many of these relationships led to their designation as linear free energy relationships. The Hansch approach represents an extension of the Hammett equation from physical organic systems to a biological milieu. It should be noted that the simplicity... 

Linear Free-Energy Relationships Hammett and Taft Correlations... 

The interactive properties of the derivatives of benzene vary widely, depending upon the nature of the substituent and its influence upon the aromatic ring. The effects of substituents have been categorized and quantified through the introduction of first the Hammett and then the Taft constants, which were obtained through the analysis of linear free-energy relationships (Exner 1988). The electrostatic potentials of benzene derivatives provide another means of ascertaining how the substituents affect the interactive behavior of the aromatic systems (Murray, Paulsen, and Politzer 1994). 

Hansch analysis Hansch analysis is a common quantitative structure-activity relationship approach in which a Hansch equation predicting biological activity is constructed. The equation arises from a multiple linear regression analysis of both observed biological activities and various molecular property parameters (Hammett, Hansch, and Taft parameters). 

Based on the o value for the HOCH2 group and the Hammett-Taft relationship governing the pKa values of tertiary amines (see Reference 46a, p. 163), one can estimate that carbinola-mines are ca 1.8-2.0 pK units weaker bases than the related tertiary amines. 

The simplest calculations utilise a free energy equation and the appropriate substituent constant both obtained from tables. Thus the Hammett, Taft and Charton relationships (see Appendix 4) may be combined with a, o and cr, values (see Appendix 1) to arrive at a calculated pA for a substrate. 

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