Hammett’s equation

The best-known equation of the type mentioned is, of course, Hammett s equation. It correlates, with considerable precision, rate and equilibrium constants for a large number of reactions occurring in the side chains of m- and p-substituted aromatic compounds, but fails badly for electrophilic substitution into the aromatic ring (except at wi-positions) and for certain reactions in side chains in which there is considerable mesomeric interaction between the side chain and the ring during the course of reaction. This failure arises because Hammett s original model reaction (the ionization of substituted benzoic acids) does not take account of the direct resonance interactions between a substituent and the site of reaction. This sort of interaction in the electrophilic substitutions of anisole is depicted in the following resonance structures, which show the transition state to be stabilized by direct resonance with the substituent ... 

There were two schools of thought concerning attempts to extend Hammett s treatment of substituent effects to electrophilic substitutions. It was felt by some that the effects of substituents in electrophilic aromatic substitutions were particularly susceptible to the specific demands of the reagent, and that the variability of the polarizibility effects, or direct resonance interactions, would render impossible any attempted correlation using a two-parameter equation. - o This view was not universally accepted, for Pearson, Baxter and Martin suggested that, by choosing a different model reaction, in which the direct resonance effects of substituents participated, an equation, formally similar to Hammett s equation, might be devised to correlate the rates of electrophilic aromatic and electrophilic side chain reactions. We shall now consider attempts which have been made to do this. 

Hammett s equation, and substituent effects, 137-43 heteromolecules, 130 Holleman s product rule, 3 hyperconjugation, in nitration of alkyl-benzenes, 165-7 in nitration of positive poles, 169... 

Price i was the first to suggest that the factor of specificity in monomer addition is owing to electrostatic interaction of net charges on the monomer double bond and on the radical arising from polarization by the substituent. Alfrey and Price proposed that the rate constant be written, in analogy with Hammett s equation for the effects of nuclear substituents on the reactivity of aromatic compounds, as follows ... 

The basicity of compounds containing the amidino group N=C—N depends on the substituents at the three sites (both nitrogens and the amidino carbon atom) and the protonation site is the imino nitrogen atom75. It has been shown76 that, at any of the three sites, in the series of monosubstituted amidines, their pKa values obey Hammett s equation. 

In series Nos. 10 and 11, where Hammett s equation is not followed, it is possible that the extent of bond-making and bond-breaking in the transition state no longer remains constant along the series. The p-nitro substituent might well induce a much greater degree of extension in the C-Hg bond in the transition state and so provide some SE1-character to the substitution. 

Most commonly, correlations are made to chemical constants that are defined by the effect of substituents on a reference reaction. They are usually designated o and are applied to QSARs in the form of Hammett s equation or its various extensions. Alternatively, a descriptor can be a property of a substrate molecule that is available, is readily measurable, and/or can be calculated by independent means, such as octanol/water partition coefficients. Despite their numerous successful applications in QSAR studies, experimentally determined o constants also have some disadvantages. They are available only for a limited set of substituents and are not of very good quality for uncommon functional groups. As an alternative, the use of quantum-chemical parameters may be a solution. 

Sigma Minus (o ) and Sigma Plus (important organic reactions that do not correlate well by Hammett s equation includes compounds connected with electrophilic... 

Hammett s equation of rate constants of substituted alcohols reacting with hydroxyl radical. Experimental conditions k values obtained at pH 9, k values defined as (l/m sec 108). 

Hammett s equation was also established for substituted phenols from the elementary hydroxyl radical rate constants. The Hammett resonance constant was used to derive a QSAR model for substituted phenols. The simple Hammett equation has been shown to fail in the presence of electron-withdrawing or electron-donating substituents, such as an -OH group (Hansch and Leo, 1995). For this reason, the derived resonance constants such as o°, cr, and o+ were tested in different cases. In the case of multiple substituents, the resonance constants were summed. Figure 5.24 demonstrates a Hammett correlation for substituted phenols. The least-substituted compound, phenol, was used as a reference compound. Figure 5.24 shows the effects of different substituents on the degradation rates of phenols. Nitrophenol reacted the fastest, while methoxyphenol and hydroxyphenol reacted at a slower rate. This Hammett correlation can be used to predict degradation rate constants for compounds similar in structure. 

For Hammett s equation for rate constants of substituted alkenes reacting with hydroxyl radicals under experimental conditions of pH 9, the elementary hydroxyl radical rate constants (l/m sec 108) containing butene, propylene, butadiene, and cyclohepatriene correlate with o as follows ... 

Quantitative structure-activity relationships (QSARs) are important for predicting the oxidation potential of chemicals in Fenton s reaction system. To describe reactivity and physicochemical properties of the chemicals, five different molecular descriptors were applied. The dipole moment represents the polarity of a molecule and its effect on the reaction rates HOMo and LUMO approximate the ionization potential and electron affinities, respectively and the log P coefficient correlates the hydrophobicity, which can be an important factor relative to reactivity of substrates in aqueous media. Finally, the effect of the substituents on the reaction rates could be correlated with Hammett constants by Hammett s equation. 

The effect of the substituents can also be expressed by Hammett s equation, which shows the value of log k/kg, as a function of the o values of the... 

Usually the most convenient way to use Hammett s equation is to plot log k/k0 or just log k of the reaction of interest on the vertical axis and o values for the substituents on the horizontal axis. The slope of the plot of log k vs. o may change as a result of changes in the mechanism and in response to the variable electron demand of each substituent. It is anticipated that the various substituents will exert the same kinds of effects on the rate constants as they do on the benzoic acid rate constants, but the greater separation between substitution site and reaction site in the same chemical family makes the reaction less sensitive to the substituent effects. Many different oxidation reactions have been treated using Hammett s equation. The consistent trend of linear relationship with all of the Hammett s constants holds for all chemical classes except halogenated phenols. 

Figure 9.14 is a plot of experimental vs. predicted values for log k/k0. Hammett s equation for the photocatalytic degradation of substituted phenols was able to predict kinetic rate constants with 92.9% accuracy. The above... 

Hammett s equation for rate constants of substituted phenol degradation by UV/Ti02. Experimental conditions 2.5 g/L TiO, pH = 4.4-5. 

Hammett s equation for CL formation during degradation of chlorinated phenols. Experimental conditions 20-mL reactor volume initial concentration, 20 mg/L 2.5 g/L Ti02 initial pH = 4.4-5. 

Figure 9.19 shows the Hammett s equation for degradation rates of substituted nitrobenzenes from experimental data. Photocatalytic degradation of the nitro aromatic compounds by UV/Ti02 from the experimental data reported by Dillert et al. (1995) are used to construct the model. The degradation of nitrobenzenes can be described according to the number of nitro substituents nitrobenzene > dinitrobenzene > 1,3,5-trinitrobenzene (Dillert et al., 1995). 

Hammett s equation for rate constants of substituted benzene degradation by TiOj/UV. Experimental conditions 5-mL reactor volume 100-pmol/L initial concentration 1 g/L Ti02 30°C pH = 9. 

Hammett s equation for substituted alcohols. Experimental conditions batch reactor with 0.1 wt% TiO, 10-100 ppm initial concentration pH = 9. 

For each class of compounds studied by UV/Ti02, reaction mechanisms agree with the slope of the Hammett s equations developed. A comparison... 

Substituents have a profound effect on the electrophilic substitution rate constants of organic compounds reacting with e (Anbar and Hart, 1964). Table 12.5 lists the rate constants for substituted benzenes, toluene, and phenols. Four orders of magnitude of rate constants may vary from 4 x 106 Mr1 s 1 for phenol to 3 x 1010 M 1 s 1 for nitrobenzene. To gain insight into the reaction mechanisms involving e, Anbar and Hart (1964) applied Hammett s equation to the rate constants and the substituent constants. T is defined as the ratio of rate constants of substituted compounds vs. nonsub-stituted reference compounds such as benzene, toluene, and phenol as follows ... 

When r) values are plotted against the g values, Hammett s equation is satisfied for all the substituents except for bromine and iodine, as shown in Figure 12.2. The p value is 4.8, which is within the range of p values reported for a variety of substituted reactions such as nitration, bromination, and hydrolysis (Stock and Brown, 1956). Therefore, Hammett s equation for substituted benzenes reaction with e can be expressed as ... 

Therefore, the p value of the benzoic acid series is equal to 4.8/6.5 = 0.74. Hammett s equation for benzoic acid is ... 

Hammett s equation (Hammett, 1940) correlates the rate of reactions with the electronic nature of the substituent in aromatic compounds. The Hammett a constants characterize the conjugation eifect and the inductive effect of the substituent for side-chain reactions. 

The iV-acyl group is easily removed in weakly acidic or basic media, especially from those 1 -acylpyrazoles with electron-withdrawing substituents. The kinetics of hydrolysis and aminolysis of variously substituted acylpyrazoles was studied in great detail by Hiittel,102 using ultraviolet spectroscopy. Rate constants were found for both reactions, and an attempt was made to apply Hammett s equation to substituted pyrazoles. 

Finally (13), the relative rate constants for the reaction of ozone with selected ring-substituted styrenes in CC14 solution indicate that the second-order rate constants obey Hammett s equation log k = log k0 + per. The negative value of p (—0.91 0.03) confirms that for these olefins the ozone attack is electrophilic in nature. 

The apparent dissociation constant of different substituted osazones has been measured in acetic acid, and shown to follow Hammett s equation. The reduction potential has been followed polarographically and used, as noted previously (see p. 159), to demonstrate the chelated nature of osazones. 

---