Linear free energy relationship Hammett equation

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. 

C. D. Johnson, The Hammett Equation, Camhndge University Press, Cambridge, 1973. P. R. Wells, Linear Free Energy Relationships, Academic Press, New bik, 1968. 

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]. 

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

The Hammett equation is the best-known example of a linear free-energy relationship (LFER), that is, an equation which implies a linear relationship between free energies of reaction or activation for two related processes48. It describes the influence of polar meta-or para-substituents on reactivity for side-chain reactions of benzene derivatives. 

In contrast to the steric effoits, the purely electronic influences of substituents are less clear. They are test documented by linear free-energy relationships, which, for the cases in question, are for the most part only plots of voltammetrically obtained peak oxidation potentials of corresponding monomers against their respective Hammett substituent constant As a rule, the linear correlations are very good for all systems, and prove, in aax>rdance with the Hammett-Taft equation, the dominance of electronic effects in the primary oxidation step. But the effects of identical substituents on the respective system s tendency to polymerize differ from parent monomer to parent monomer. Whereas thiophenes which receive electron-withdrawing substituents in the, as such, favourable P-position do not polymerize at all indoles with the same substituents polymerize particularly well... 

The Hammett equation is a linear free energy relationship (LFER). This can be demonstrated as follows for the case of equilibrium constants (for rate constants a similar demonstration can be made with AG instead of AG). For each reaction, where X is any group,... 

Before terminating our discussion of the Hammett equation, we should note that the existence of linear correlations of the type indicated by equation 7.4.20 implies a linear free energy relationship. The rate or equilibrium constants can be eliminated from this equation using equation 7.4.1 that is,... 

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. 

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 ... 

Hammett equation use, 17 92-96 of published data, 17 83-99 soUd catalysts limitations, 17 78-83 Taft equation use, 17 85-92 linear free energy relationships, 29 158-159 multiplet theory of, 19 1-195 of nature of catalyst, 19 159-176 metals, 19 159-161... 

Certain expressions describing a solvent acidity function, where S is a base that is protonated by an aqueous mineral acid solution. The equations describe a linear free-energy relationship between log([SH+]/[S]) + Ho and Ho + log[H ], where Ho is Hammett s acidity function and where Ho + log[H+] represents the activity function log(7s7H+/ysH ) for the nitroaniline reference bases to build Ho. Thus, log([SH+]/[S]) log[H+] = ( 1)... 

A plot of the logarithm of a rate constant (or an equilibrium constant) for one series of reactions versus the logarithm of the rate constant (or the equilibrium constant) for a related series of reactions. (Recall that at constant temperature and pressure the logarithm of an equilibrium constant is proportional to AG°, and the logarithm of a rate constant is proportional to AG ). An example of a linear free energy relationship is provided by the Hammett crp-equation. With equilibrium constants, this relationship is given by the expression ... 

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... 

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. 

Applications of Linear Free Energy Relationships to Polycyclic Arenes and to Heterocyclic Compounds , M. Charton, in Recent Advances in Correlation Analysis in Chemistry , ed. N. B. Chapman and J. Shorter, Plenum, New York, 1978, pp. 175-268. Applications of the Hammett Equation to Heterocyclic Compounds P. Tomasik and C. D. 

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. 

Organic chemists have studied the influence of substituents on various reactions for the better part of a century. Linear free energy relationships have played an important role in this pursuit by correlating equilibrium and rate processes. One of the earliest examples is now known as the Hammett equation. It emerged from the observation that the acidities of benzoic acids correlated with the rates at which ethyl esters of benzoic acids hydrolyzed. The relationship was expressed as follows in which K represents an equilibrium constant and k is a rate constant. The proportionality constant, m, is the slope of the log-log data plot for the two processes. 

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 reaction constants obtained in the previous section for numerous substitution reactions permit the examination of the applicability of a linear free-energy relationship by the Extended Selectivity Procedure. The utility of this approach is demonstrated by application to a series of data for side-chain reactions which are correlated with good precision by the Hammett equation. The variations as detected by the procedure serve as a convenient frame of reference for the behavior to be anticipated in other treatments. 

The problem was first approached in 1954, when de la Mare pointed out a major discrepancy in the observations for the para chlorination of biphenyl in an attempted correlation based on the Hammett equation. Subsequently, Eabom and his students examined the behavior of biphenyl in several additional reactions (Deans et al., 1959 Eaborn and Taylor, 1961b) concluding that reactivity in the para position of hiphenyl did not conform to a linear free-energy relationship. Moreover, the p-phenyl group did not accelerate the substitution to the anticipated extent. The peculiar behavior of the phenyl group prompted several investigations of the substitution reactions. These data are summarized in Table 7. 

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