Application of the Hammett Equation

The large success of the Hammett equation in relating and systematizing the side-chain reactivities of meta- and poro-substituted benzenes has stimulated similar studies in the thiophene series. 

The rate of saponification of ethyl 2-thenoate, in contrast to ethyl 3-thenoate, was found to be considerably slower than predicted from the pKa of the acid, showing that the reactivities of thiophenes do not parallel those of benzene. The first explanation, that this was produced by a steric effect of the ring sulfur similar to the case in or /lo-substituted benzenes and in ethyl 1-naphthoate, could not be upheld when the same effect was found in ethyl 2-furoate. It was later ascribed to a stereospecific acid strengthening factor, involving the proper relation of the carboxylic hydrogen and the heteroatom, as the rate of saponification of 2-thienylacrylic acid was in agreement with that predicted from the acid constants.  

So-called aryl values have been introduced by Imoto et ai. - for the piu pose of systematizing the reactivities of different aromatic systems by means of the linear free-energy relationship, which however, could not be applied to the decomposition rates of heterocyclic acyl azides in toluene.  

From measurements of acid constants, and rates of esteri- 

The aforementioned exception and the rather limited experimental material available do not allow any conclusions about the general applicability of the Hammett equation, using the same a- and p-values as for benzenes, to be drawn with certainty. The present author has pointed out that large deviations should be expected with strong - -M-substituents, as is also indicated from the rates of alkaline hydrolysis of methyl 5-amino- and 5-acylamino-2-thenoates. From the chemical shifts in the NMR spectra of thiophenes and benzenes it appears that another set of cr-values should be used in the thiophenes series which seems plausible since the transmission of the sub- 

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A completely different approach has been taken by Hine, who has considered that the substituent and reaction center are not really distinct, both being substituents in a benzene nucleus, and has then related substituent and reaction constants. Although of considerable theoretical interest, Hine s work has little bearing on practical applications of the Hammett equation since he starts from the premise of unique, single-valued substituent constants. This premise is invalid whether we are utilizing the naive approach with three separate, well-defined sets or the more refined methods with a continuous range of para values. 

The first application of the Hammett equation to a heterocyclic system is contained in Hammett s original work, where his reaction series 9 is the ionization of 5-substituted 2-furoic acids. In addition, one of Hammett s original substituents is the CH202-group, i.e., the cr-value which compares the reactivity of... 

Although the application of the Hammett equation to side-chain reactions of disubstituted benzene derivatives (1) is relatively straightforward, the introduction of a heteroatom somewhere in the aromatic... 

The application of the Hammett equation to bicyclic aromatic compounds of the quinoline and isoquinoline type may be envisaged in several ways. In quinoline, e.g., the homocyclic ring A in 9) may be... 

This shows that the assumption made in Eqs. (18) and (19), i.e., that the Hammett equation is separately applicable to the component reactions, does not imply linearity of a plot of vs. a. The assumption of the applicability of the Hammett equation to the component series seems undeniable since these reactions are extremely closely related to series which follow the Hammett equation very well. This assumption also implies... 

The third volume of this series covers three specific groups of compounds the carbolines (reviewed by R. A. Abramovitch and I. D. Spenser), the thiatriazoles (K. A. Jensen and C. Pedersen), and the pentazoles (I. Ugi). The remaining four chapters deal with topics of general chemical interest from the heterocyclic viewpoint the quaternization of heterocyclics (G. F. Duffin), carbene reactions (C. W. Rees and C. E. Smithen), applications of the Hammett equation (H. H. Jaffe and H. Lloyd Jones), and some aspects of the nucleophilic substitution of heterocyclic azines (G. Rluminati). 

The Hammett equation has correlated more than 400 reaction series, and can accommodate many others if the equation is modified.5-8 A very early list9 of the successful application of the Hammett equation in its original form is given in Table 10-2. 

The special substituent constants for + R para-substituents are denoted by a, and those for — R para-substituents are denoted by a+ 54. They are based respectively on the reaction series discussed above. Selected values are given in Table 1. Characteristic a or a+ values are sometimes distinguished for meta-substituents also, but only for a minority of substituents which show very marked + R or — R effects do these differ significantly from ordinary a values. The range of applicability of the Hammett equation is greatly extended by means of a and cr+, notably to nucleophilic (by a ) and to electrophilic (by cr+) aromatic substitution. 

Bowden has studied the application of the Hammett equation to the kinetics of the reaction of c/s-3-substituted acrylic acids with diphenyldiazom ethane (59) and with methanol (69) and the rates of alkaline hydrolysis of c -3-substituted methyl acrylates (69). The sets studied are reported in Table XII. Results of the... 

Data are extant in the literature for five sets of substituted acetylene dipole moments. The correlation of dipole moments with the Hammett equation was discussed in section II.A.l. of this work. The application of the Hammett equation to dipole moments of acetylenes was first reported by Charton (18). The sets studied here are reported in Table XXXIII. Results of the correlations are presented in Table XXXIV, and values of Pr are set forth in Table XXXV. 

Only electrical effects should be of major importance. The equilibrium constants were correlated with the Hammett equation (equation 5). This was necessary, due to the small size of the data set which included both meta and para substituents. The application of the Hammett equation to data sets including both meta and para substituents is most successful when the geometry of the system resembles that of the benzoic acids from which the Hammett constants were obtained. That is not the case in this reaction. The regression equation is equation 33 ... 

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