Hammett equation, formulation

Ever since its original formulation, the Hammett equation has been one of the most widely discussed and applied relations between structure and reactivity of organic compounds, and it has been... 

Br0nsted s correlation was developed some years before Hammett s. Here we present a formulation that shows how both LFERs are related for general acid catalysts. For the sake of simplicity, we ignore the statistical factors of p and q. The Hammett equation applied to the values of bh is... 

Pyridines are also well known as ligands in transition metal complexes, and if the equilibrium constants for the formation of such complexes can be related to base strength, it is expected that such constants would follow the Hammett equation. The problem has been reviewed,140 and a parameter S, formulated which is a measure of the contribution of the additional stabilization produced by bond formation to the stabilization constants of complexes expressed in terms of a.141 The Hammett equation has also been applied to pyridine 1 1 complexation with Zn(II), Cd(II), and Hg(II) a,/3,y,<5-tetraphenylporphins,142 143 the a values being taken as measures of cation polarizing ability. Variation of the enthalpy of complexation for adducts of bis(2,4-pentanediono)-Cu(II) with pyridines plotted against a, however, exhibited a curved relationship.144... 

In the early use of linear Gibbs energy relationships, simple single-term equations sueh as the Hammett equation were eonsidered suffieient to fit given sets of experimental data from reaetion series. Later on, more eomplieated multi-term equations with more than one produet term were formulated in order to model the simultaneous influence of several effects on chemical reactions or optical excitations one product term per effect [15], The connection between such multiparameter relationships and solvent effects will be described in Section 7.7. 

In the following decades, various a scales were derived for different systems and several attempts were made to derive such relationships also for biological activities of organic compounds. Bruice et al. [10] formulated group contributions to biological activity values in a series of thyroid hormone analogs, which may be considered as a first Free-Wilson-type analysis. Zahradnik and Chvapil [11] and Zahradnik [12,13] tried to apply the concept of the Hammett equation also to biological data (Eq. (5)) ... 

At the time that the basic formulation and testing of the mathematical models of quantitative structure-activity correlations were being made, another type of approach, the linear free-energy related model, was introduced (2). Using the basic Hammett equation (22, 36) for the chemical reactions of benzoic acid derivatives (Equation 12), several investigators attempted quantitative correlations between physicochemical properties... 

The concept of lateral validation was first formulated by Hansch for classical QSARs. In this approach, the choice of parameters, their sign, and the size of their coefficients are compared with those from other QSARs. A comparison is illustrated in Table 5 for the Hammett equation ... 

The work of Hammett and others in the early 1930s led to the formulation of the best known linear free energy relationship, the Hammett equation, which describes the influence of polar meta- or para-substituents on the side-chain reactions of benzene derivatives. This equation, its refinement in various ways, and its elaboration in the form of multiparameter extensions are the subjects of Section 2. 

The fundamental assumption of SAR and QSAR (Structure-Activity Relationships and Quantitative Structure-Activity Relationships) is that the activity of a compound is related to its structural and/or physicochemical properties. In a classic article Corwin Hansch formulated Eq. (15) as a linear frcc-cncrgy related model for the biological activity (e.g.. toxicity) of a group of congeneric chemicals [37, in which the inverse of C, the concentration effect of the toxicant, is related to a hy-drophobidty term, FI, an electronic term, a (the Hammett substituent constant). Stcric terms can be added to this equation (typically Taft s steric parameter, E,). 

In Hammett correlations, the descriptors, such as a.(or a.,J and o, can be used to derive equations for aromatic and aliphatic compounds, respectively. For aromatic compounds, the a., descriptor formulated better Hammett correlations than the om descriptor. Given the value of a molecular descriptor, a Hammett correlation for a particular chemical class may be used to predict kinetic rate constants for compounds with similar chemical structure. The QSAR models for each class of compounds studied by elementary hydroxyl radicals are summarized in Table 5.12. 

In the 1930s Hammett formulated the equation named in his honor. It is based on the observation of the constancy of the relative effects of substituents on aromatic rings, regardless of the reaction rate or equilibrium of interest. This relationship is expressed according to equation (3.3). 

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