Equations Hammett

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, 

The result is a substituent constant (er) which is a numerical description of die electronic effect of a substituent relative to a hydrogen atom on the model reaction. Stated a different way, a substituent constant a is a quantitative way to 

These substituent constants can be used with rate data to evaluate the type and extent of charge development in the activated complex of the rate-determining step for a wide variety of chemical reactions. The rates of reaction for a particular transformation are measured using a series of compounds which differ only by the phenyl substituents present for example, 

Then the differences in rate caused by the electronic effect of the substituent are correlated by the Hammett equation log(kz/kH) = poz, where kz is the rate constant obtained for a compound with a particular meta or para substituent, ku is the rate constant for the unsubstituted phenyl group, and crz is the substituent constant for each substituent used. The proportionality constant p relates the substituent constant (electron donating or wididrawing) and the substituent s effect on rate. It gives information about the type and extent of charge development in the activated complex. It is determined by plotting log(kz/kQ) versus ov for a series of substituents. The slope of the linear plot is p and is termed the reaction constant. For example, the reaction shown above is an elimination reaction in which a proton and the nosy late group are eliminated and a C-N n bond is formed in their place. The reaction is second order overall, first order in substrate, and first order in base. The rate constants were measured for several substituted compounds  

The reaction of A, A - d i m e t h v 1 b e n / v 1 a l ni ne s with methyl iodide is found to have p = —1.0. The negative sign indicates that partial positive charge is being 

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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. 

The application of the Taft equation, derived from the Hammett equation (262)... 

Many equilibrium and rate processes can be systematized when the influence of each substituent on the reactivity of substrates is assigned a characteristic constant cr and the reaction parameter p is known or can be calculated. The Hammett equation... 

Hamamelis [84696-19-5] Hamamelis virginiana Ham curing Hammerhead ribozyme Hammer mills Hammett equation Hamposyl 0 Hamposyl C Hamposyl C-30 Hamposyl L Hamposyl L-30 Hand factor Hand lay-up... 

If the perturbations thus caused are relatively slight, the accepted perturbation theory can be used to interpret observed spectral changes (3,10,39). The spectral effect is calculated as the difference of the long-wavelength band positions for the perturbed and the initial dyes. In a general form, the band maximum shift, AX, can be derived from equation 4 analogous to the weU-known Hammett equation. Here p is a characteristic of an unperturbed molecule, eg, the electron density or bond order change on excitation or the difference between the frontier level and the level of the substitution. The other parameter. O, is an estimate of the perturbation. 

Linear Free Energy—Linear Solvation Energy Relationships. Linear free energy (LFER) and linear solvation energy (LSER) relationships are used to develop correlations between selected properties of similar compounds. These are fundamentally a collection of techniques whereby properties can be predicted from other properties for which linear dependency has been observed. Linear relationships include not only simple y = rax + b relationships, but also more compHcated expressions such as the Hammett equation (254) which correlates equiUbrium constants for ben2enes,... 

The numerical values of the terms a and p are defined by specifying the ionization of benzoic acids as the standard reaction to which the reaction constant p = 1 is assigned. The substituent constant, a, can then be determined for a series of substituent groups by measurement of the acid dissociation constant of the substituted benzoic acids. The a values so defined are used in the correlation of other reaction series, and the p values of the reactions are thus determined. The relationship between Eqs. (4.12) and (4.14) is evident when the Hammett equation is expressed in terms of fiee energy. For the standard reaction, o%K/Kq = ap. Thus,... 

The Hammett equation in the form of Eq. (4.14) or Eq. (4.15) is free of complications due to steric effects, since it is applied only to meta and para substituents. The geometry of the benzene ring ensures that groups in these positions cannot interact stoically with the site of reaction. Tables of a values for many substituents have been collected some values are given in Table 4.5, but substituent constants are available for a much wider range of... 

Given in Table 4.5 in addition to the substituent constant sets which reflect a recognition that the extent of resonance participation can vary for different reactions. The values are used for reactions in which there is direct resonance interaction between an electron-donor substituent and a cationic reaction center, hereas the a set pertains to reactions in which there is a direct resonance interaction between the substitutent and an electron-rich reaction site. These are cases in which the resonance conqionent of the... 

One approach is to correct for the added resonance interaction. This is done in a modification of the Hammett equation known as the Yukawa-Tsuno equation. ... 

The additional parameter r is adjusted from reaction to reaction it reflects the extent of the additional resonance contribution. A large r corresponds to a reaction with a large resonance component, whereas when r goes to zero, the equation is identical to the original Hammett equation. When there is direct conjugation with an electron-rich reaction center, an equation analogous to Eq. (4.17) can be employed, but a is used instead of [Pg.210]

Not all reactions can be fitted by the Hammett equations or the multiparameter variants. There can be several reasons for this. The most common is that the mechanism of the reaction depends on the nature of the substituent. In a multistep reaction, for example, one step may be rate-determining in the case of electron-withdrawing substituents, but a different step may become rate-limiting when the substituent is electron-releasing. The rate of semicarbazone formation of benzaldehydes, for example, shows a nonlinear Hammett... 

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

The rates of substituted benzaldehydes are correlated by the Hammett equation with p = +3.76. 

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 chlorination of a series of compounds having electron-withdrawing substituents has been studied. The relative rates of chlorination and the isomer distributions are known. The data give a satisfactory correlation with the Hammett equation using (t, but no rate measurement for benzene under precisely comparable conditions is possible. How could you estimate f,f y and fp for chlorination from the available data ... 

Nevertheless, many free-radical processes respond to introduction of polar substituents, just as do heterolytic processes that involve polar or ionic intermediates. The substituent effects on toluene bromination, for example, are correlated by the Hammett equation, which gives a p value of — 1.4, indicating that the benzene ring acts as an electron donor in the transition state. Other radicals, for example the t-butyl radical, show a positive p for hydrogen abstraction reactions involving toluene. ... 

The classic example, and still the most useful one, of a LFER is the Hammett equation, which correlates rates and equilibria of many side-chain reactions of meta- and para-substituted aromatic compounds. The standard reaction is the aqueous ionization equilibrium at 25°C of meta- and para-substituted benzoic acids. 

The Hammett equation is said to be followed when a plot of log k against a is linear. Most workers take as the criterion of linearity the correlation coefficient r, which is required to be at least 0.95 and preferably above 0.98. A weakness of r as a statistical measure of goodness of fit is that r is a function of the slope p if the slope is zero, the correlation coefficient is zero. A slope of zero in an LEER is a chemically informative result, for it demonstrates an absence of a substituent... 

Table 7-2 lists 15 reactions whose rates are correlated by the Hammett equation. Besides the reaction constant p, the table gives a value for k° (from the fitted line), which provides all the information needed to estimate k for any member of the series, if the corresponding o is available, by means of Eq. (7-24). Note that kP in Table 7-2 is generally not identical to the experimental value of k for the ct = 0 member of the series, because this experimental point may deviate from the regression line. 

The discussion in Section 7.1 should prepare us to expect deviations from such a simple relationship as the Hammett equation if the reaction being correlated differs greatly from the standard reaction. When this happens we have two choices (within this extrathermodynamic approach) We can select a different standard reaction, or we can increase the number of parameters. 

Reactions that occur with the development of an electron deficiency, such as aromatic electrophilic substitutions, are best correlated by substituent constants based on a more appropriate defining reaction than the ionization of benzoic acids. Brown and Okamoto adopted the rates of solvolysis of substituted phenyldimeth-ylcarbinyl chlorides (r-cumyl chlorides) in 90% aqueous acetone at 25°C to define electrophilic substituent constants symbolized o-. Their procedure was to establish a conventional Hammett plot of log (.k/k°) against (t for 16 /wcra-substituted r-cumyl chlorides, because meta substituents cannot undergo significant direct resonance interaction with the reaction site. The resulting p value of —4.54 was then used in a modified Hammett equation. 

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. 

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