Hammett equation, quantitative

Let us illustrate this with the example of the bromination of monosubstituted benzene derivatives. Observations on the product distributions and relative reaction rates compared with unsubstituted benzene led chemists to conceive the notion of inductive and resonance effects that made it possible to explain" the experimental observations. On an even more quantitative basis, linear free energy relationships of the form of the Hammett equation allowed the estimation of relative rates. It has to be emphasized that inductive and resonance effects were conceived, not from theoretical calculations, but as constructs to order observations. The explanation" is built on analogy, not on any theoretical method. 

Because the substituent groups have a direct resonance interaction with the charge that develops in the a-complex, quantitative substituent effects exhibit a high resonance component. Hammett equations usually correlate best with the substituent constants (see Section 4.3). ... 

The Hammett equation and LFER in general added no new concepts to the qualitative picture that had been built up of electronic effects in organic reactions, but they did provide a quantitative measure that had been lacking and that has been found very useful. Here we will describe the further development of ideas concerning the substituent constant. 

Pyridine bases are well known as ligands in complexes of transition metals, and it might well be anticipated that the equilibrium constants for the formation of such complexes, which are likely to be closely related to the base strength, would follow the Hammett equation. Surprisingly, only very few quantitative studies of such equilibria seem to have been reported, and these only for very short series of compounds. Thus, Murmann and Basolo have reported the formation constants, in aqueous solution at 25°, of the silver(I) complexes... 

The fundamental understanding of the diazonio group in arenediazonium salts, and of its reactivity, electronic structure, and influence on the reactivity of other substituents attached to the arenediazonium system depends mainly on the application of quantitative structure-reactivity relationships to kinetic and equilibrium measurements. These were made with a series of 3- and 4-substituted benzenediazonium salts on the basis of the Hammett equation (Scheme 7-1). We need to discuss the mechanism of addition of a nucleophile to the P-nitrogen atom of an arenediazonium ion, and to answer the question, raised several times in Chapters 5 and 6, why the ratio of (Z)- to ( -additions is so different — from almost 100 1 to 1 100 — depending on the type of nucleophile involved and on the reaction conditions. However, before we do that in Section 7.4, it is necessary to give a short general review of the Hammett equation and to discuss the substituent constants of the diazonio group. 

Hammett equation(s) 78, 93, 148ff., 151 f., 153ff., 167f., 190, 193, 196, 297, 299, 308, 312, 375, 381, 392, see also Dual substituent parameter, and Quantitative structure-reactivity relationships Hammond postulate, in additions of nucleophiles to diazonium ions 157 Hard and soft acids/bases principle (Pearson) 49, 54, 109... 

Linear free energy relationships, see Bronsted equation, Dual substituent parameter (equations), Hammett equation(s), Quantitative structure-activity relationships, Ritchie nucleophilicity equation... 

One of the oldest and most familiar quantitative relationships for relating the structure of substituted benzene derivatives to both equilibrium constants and rate constants is the "Hammett Equation." See Louis Hammett, Physical Organic Chemistry, 184199. 

In order to put the discussion on a more quantitative basis we consider one of the more traditional and conceptually simpler methods. Obviously, when speaking about ligands one must take into account that a ligand can bear different substituents. To correlate the variation of the redox potential of a metal complex with the electronic effects played by the substituents of an aromatic ring ligand one uses the Hammett equation in its electrochemical form ... 

Extensive collections of pK values are available in the literature, e.g., [98-101]. It is also possible to predict pK values for a broad range of organic acids and bases using linear free energy relationships based on a systematic treatment of electronic (inductive, electrostatic, etc.) effects of substituents which modify the charge on the acidic and basic center. Quantitative treatment of these effects involves the use of the Hammett Equation which has been a real landmark in mechanistic organic chemistry. A Hammett parameter (a), defined as follows ... 

Positive values of a indicate electron withdrawing by the substituent, while negative values indicate electron release to the benzene ring of the acid. A listing of some avalues is provided in the literature [98-101]. Quantitative predictions of pK values use the Hammett equation as follows ... 

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). 

Organic functional groups exert characteristic electronic effects upon other groups to which they are attached. The quantitative expression of such effects can sometimes be correlated by linear Gibbs energy relationships. The best known of these is the Hammett equation, which deals with the transmission of electronic effects across a benzene or other aromatic ring. Consider the acid dissociation constants of three classes of compounds ... 

By the use of a model reaction (ionization of benzoic acids), die ability of a substituent to modify die electron-donating or electron-withdrawing ability of die phenyl group and tiius influence tiiat reaction can be defined quantitatively by the Hammett equation,... 

Hammett, after illustrating the existence of linear relationships among the data for a variety of side-chain reactions, defined the (7-constants to characterize the behavior of substituent groups. In the application of the Hammett equation the cr-parameters are assumed to be constant. The assessment of the validity of this same assumption for substituents in aromatic substitution reactions is the major problem which must be considered prior to the adoption of a simple two-parameter linear free-energy relationship for these reactions. Preliminary evaluations of linear relationships were undertaken through somewhat modified procedures as discussed in Section IV. Now, however, with many quantitative data available it is no longer necessary to rely on the less direct Selectivity Relationship. Rather, the more straightforward conventional Hammett approach is applicable. This procedure requires the adoption of the a1 -constants derived from the study of substituted phenyldimethylcarbinyl chlorides and the assumption of constancy of the values. This assumption is shown to be fully justified in subsequent tests of the relationship. 

The success of the modified patterns treatment shows that radical reactivities in the gas phase are governed to a major extent by polar forces as given quantitative expression in the Hammett equation. These correlations support the conclusions reached in earlier sections that both the polarity of the alkene and the polar character of the radical are important. They also help to establish a common pattern of behaviour for radicals in gas-phase addition reactions and in liquid-phase polymerization processes. 

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... 

A second quantitative comparison of the reactivity of selenophene with that of thiophene is by the kinetics of mercuration (at the 5-position) of 2-substituted derivatives of the two series. It was found that 2-bromo-, 2-acetyl-, 2-carbethoxy-, and 2-nitroselenophenes59 are mercurated 1.5 to 3 times faster than the corresponding derivatives of thiophene.89 The substituent effects for selenophenes follow the Hammett equation using a+ values. 

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. 

Although a detailed discussion of the influence of aromatic substituents on the rates of aromatic substitution is outside the scope of this book, it is nevertheless helpful to note that quantitative correlations of directing effects have been made using various forms of the Hammett equation ... 

Derived from physical organic chemistry and the - Hammett equation, this can be considered to be the first approach to modern QSAR studies. Proposed by Hansch and co-workers in the early 1960s [Hansch et al, 1962 Hansch et al, 1963 Hansch and Fujita, 1964 Hansch et al, 1965 Hansch and Anderson, 1967 Hansch, 1969 Hansch, 1971 Hansch, 1978], it is the investigation of the quantitative relationships between... 

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. 

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... 

An electronically induced change in the adsorption energy of I by some group j can be expressed quantitatively in terms of the Hammett equation (Section 3-4B) ... 

Molecular Similarity and QSAR. - In a first contribution on the design of a practical, fast and reliable molecular similarity index Popelier107 proposed a measure operating in an abstract space spanned by properties evaluated at BCPs, called BCP space. Molecules are believed to be represented compactly and reliably in BCP space, as this space extracts the relevant information from the molecular ab initio wave functions. Typical problems of continuous quantum similarity measures are hereby avoided. The practical use of this novel method is adequately illustrated via the Hammett equation for para- and me/a-substituted benzoic acids. On the basis of the author s definition of distances between molecules in BCP space, the experimental sequence of acidities determined by the well-known a constant of a set of substituted congeners is reproduced. Moreover, the approach points out where the common reactive centre of the molecules is. The generality and feasibility of this method will enable predictions in medically related Quantitative Structure Activity Relationships (QSAR). This contribution combines the historically disparate fields of molecular similarity and QSAR. 

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