The Hammett relationship

The validity of the Hammett relationship log K/Ko = pa- has been extensively investigated for five-membered heteroaromatic compounds and their benzo analogues. The ratio Pheterocycie/Pbenzene is closest to Unity for thiophene. Judged from work on the polarographic reduction of nitro compounds, the ability to transmit electronic effects is HC=CH = S < O < NH. 

For a general discussion of the Hammett relationship see Section 7.2. Unfortunately the present author never received details of that work. 

Just as electrophilic aromatic substitutions were found more or less to follow the Hammett relationship (with a" " instead of o see p. 692), so do nucleophilic substitutions, with cr instead of a for electron-withdrawing groups. ... 

The effect of a substituent on the aromatic substitution reaction is similar to its effect on electrophilic side chain reactions, but not precisely parallel. Thus the Hammett relationship using the usual sigma or substituent constants gives considerable scatter when applied to aromatic substitution. The scatter is probably due to an increased importance of resonance effects in the nuclear substitution reaction as compared with the side chain reactions. 

Mercury(II) reacts with organochromium complexes by electrophilic substitution. Rate constants have been reported for Hg2+ attack at a series of alkylchromium complexes with the macrocyclic ligand 1,4,8,11-tetrazacyclotetradecane, CrR(H20)([14]aneN4). The Hammett relationship established for a series of meta and para substituted benzyl analogues is consistent with attack of the Hg2+ at a-carbon (89). 

However, the effects on the rates in nonpolar solvent systems is dramatically larger and often of apparent contradiction. For example, the Hammett rho value for the oxidation of substituted methyl cinnamates and cinnamic acids by tetrabutylammonium permanganate in methylene chloride solutions is positive (33,49). See Figure lb. However, a rho value of converse sign (-0.6) is obtained from a Taft plot (Figure Ic) for the oxidation of vinyl ethers in aqueous tetrahydrofuran (33,50). For many other compounds the Hammett relationships are no longer linear, but concave upward ... 

Recently, a direct kinetic study on the amination of substituted phenyhnagnesium bromides using Af,Af-dimethyl O-mesitylenesulfonyl hydroxylamine 3b as amination reagent has been reported by Erdik and Ate Ulkii . Rate data, the Hammett relationship and activation entropy support an Sn2 displacement of the carbon nucleophile on the electrophilic nitrogen. These results are consistent with the competition kinetics for electrophilic amination of substituted phenyl Grignard reagents with O-methylhydroxylamine In. ... 

Illustrative Example 13.6 Estimating Hydrolysis Rate Constants Using the Hammett Relationship Bronsted Relationship... 

The Hammett relationship formalizes and puts into quantitative terms much of the qualitative reasoning we have used for reactions involving aliphatic, alicyclic, and aromatic compounds. Considerable effort has been made to extend the Hammett idea to cover reactions other than of meta- and para-substituted benzene derivatives, but these will not be discussed here.1... 

H and, 3C NMR spectra of monoimines have been reported and are shown in Table 3. These data fit the Hammett relationship and good correlations are found between various o constants and, 3C chemical shifts at positions remote from the substituent.1413C chemical shifts of imines derived from BA and variously substituted benzylamines are affected by substituents through up to 11 bonds.15 The influence of ZjE isomerism (Figure 3) and the effect of substituents on NMR spectra of some unsaturated imines have been studied.16 The photochemically induced isomerization of several substituted Schiff bases derived from BA and arylamines and their chemical shifts, as well... 

The oxidation of glutamic acid to cyanopropionic acid with CAB in acid solution showed an inverse fractional dependence on acidity. Similarly in alkaline medium, the order in alkali is fractional inverse.143 Kinetics of ruthenium(III)-catalysed oxidation of diols with CAB have been obtained. The products arise due to a fission of the glycol bond.144 The oxidation of isatins with CAB, in alkaline solutions, showed a first-order dependence on CAB and isatin and fractional order in alkali. The rates correlate with the Hammett relationship, the reaction constant p being —0.31. The observed results have been explained by a plausible mechanism and the related rate law has been deduced.145 The oxidation of cysteine with CAB in sulfuric acid medium is first order in CAB and cysteine and the rate is decreased with an increase in the hydrogen ion concentration.146... 

In the Bronsted relationship, the reference equilibria are dissociations of protic acids, used directly as ApK i, and the constant of proportionality r = fi (or a, see Chapter 11). In the Hammett relationship, acid dissociation constants are also used for the reference equilibria, but indirectly. The dissociation constants of substituted benzoic acids in water at 25°C are used to define a set of substituent parameters, cr, which are then used in the equation of correlation, and r = p in Equation 9.18. 

In 1959, four independent and simultaneous reports defined the problem, van Bekkum et al. (1959), not distinguishing among the ordinary and electrophilic side-chain reactions, showed the o--constants to be broadly variable. They tabulated the a-parameters for twelve groups as derived from each reaction of an extended series. Just as illustrated in Fig. 50 for the p-methoxy, p-methyl, and p-chloro substituents, they detected extensive variations in the apparent values of the constants. The authors concluded that the postulation of two or three sets of -constants could not be regarded as sound. By eliminating all those reactions involving important resonance contributions Wepster and his associates (van Bekkum et al., 1959) obtained a series of reactions similar to those presented in Table 23, and hence derived a series of normal, an, parameters for meta and para substituents. These normal values, presumably representing the reactions for which the Hammett relationship is most precise, exhibit standard deviations of 10-30%. 

To evaluate the effect of the substituent more accurately, a competition study with equimolar mixtures of C6H6-C6H5X(X = OH, F, Cl) was carried out by Norseyev and colleagues50. Quantitative evaluation of intermolecular competition for hydrogen replacement was performed on the basis of the Hammett relationship applying the yields of replacement products instead of reaction rate constants, according to equation 10 ... 

The values of k2 for ring-substituted phenylacetylenes are well correlated by the Hammett relationship, using a+ constants, and p is very large, — 5-2. The p value compares well with those obtained in the acid-catalysed hydration of arylacetylene derivatives (see Table 1) and is entirely consistent with the formation of a vinyl cation 45 in which the positive charge is at the carbon next to the phenyl ring and is largely shared by it. Interestingly, the p value (by use of a+) based on k2 rate coefficients for the bromination of styrene in acetic acid is — 4-5. 

The woik of Tuleen and Stevens on the regioselectivity of chlorination of a series of unsymmetrically substituted dialkyl sulfides with NCS provides clues to Ae directive effects implicit in the mechanisms encompassed by Scheme 3. These observations are collected in Scheme 6 where the preferred site of chlorination in each case is indicated with an arrow, the number over the arrow indicating the majortminor product ratio (minor = 1). In the first example, chlorination of benzyl methyl sulfide (2) produces chlorobenzyl methyl sulfide exclusively. Secondly, chlorination of benzyl ethyl sulfide (3) and benzyl isopropyl sulfide (4) also shows a marked, though not exclusive, preference for the benzylic position. In the latter case the extent of benzylic chlorination can be modulated by ring substitution. The directive effects in these internal competitions for p-methyl and p-chloro substituents are correlated by the Hammett relationship with a value of p = 1.0, which is consistent with a mechanism involving abstraction of the more acidic proton in the chlorosulfonium ion intermediate. Further indications of the im-... 

Azo coupling reaction rates of substituted benzenediazonium ions with a given nucleophile under standard conditions (solvent, temperature, pH, etc.) are an ideal case for the application of the Hammett relationship in its classical form (71) kj, and k refer to the rate constants of the benzenediazonium ion and its m- or p-substi-tuted derivatives, respectively, with the given coupling component, p and a are Hammett s reaction and substituent constants, respectively. 

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