The Hammett constant a

The distribution of electrons within a molecule depends on the nature of the electron withdrawing and donating groups found in that structure. Hammett used this concept to calculate what are now known as Hammett constants (try) for a variety of monosubstituted benzoic acids (Equation (4.5)). He used these constants to calculate equilibrium and rate constants for chemical reactions. However, they are now used as electronic parameters in QSAR relationships. Hammett constants (crx) are defined as  

Substituent Hammett constants Inductive constants Tl Taft constants a Swain-Lupton constants  

Hammett postulated that the cr values calculated for the ring substituents of a series of benzoic acids could also be valid for those ring substituents in a different series of similar aromatic compounds. This relationship has been found to be in good agreement for the meta and para substituents of a wide variety of aromatic compounds but not for their ortho substituents. The latter is believed to be due to steric hindrance and other effects, such as intramolecular hydrogen bonding. 

Hammett substitution constants suffer from the disadvantage that they only apply to substituents directly attached to a benzene ring. Consequently, a number of other electronic constants (Table 4.5) have been introduced and used in QSAR studies in a similar manner to the Hammett constants. However, attempts to relate biological activity exclusively to the values of Hammett substitution and similar constants have been largely unsuccessful, since electron distribution is not the only factor involved (see section 4.4). 

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The values of the Hammett constant , a, normally refer to the inductive electronic effects of the substituents in meta (crm) or para (crp) positions of aromatic rings. 

Another QSAR study utilizing 14 flavonoid derivatives in the training set and 5 flavonoid derivatives in the test set was performed by Moon et al. (211) using both multiple linear regression analysis and neural networks. Both statistical methods identified that the Hammett constant a, the HOMO energy, the non-overlap steric volume, the partial charge of C3 carbon atom, and the HOMO -coefficient of C3, C3, and C4 carbon atoms of flavonoids play an important role in inhibitory activity (Eqs. 3-5, Table 5). 

Fig. 4. Plot of loglflrf) versus the Hammett constant a of various para substituents in [W(CO)5 E=C(C6H4R-p)H ] (E = S, Se) in n-hcxane at 25°C.

Most aquatic oxidation reactions are attributable to well-defined chemical oxidants. As a result, model systems can be designed where second-order rate constants can be determined precisely for families of organic congeners. The comparatively high quality of these data allows mechanistic models of electron transfer to describe aquatic oxidations of environmental interest. Kinetic studies of these processes have produced many QSARs, mostly simple empirical correlations with common convenient descriptors such as the Hammett constant (a), half-wave oxidation potential ( j/2)> energies of the highest occupied molecular orbital ( HOMO), or rate constants for other oxidation reactions as descriptors (Canonica and Tratnyek, 2003). Their predictive power has lead to engineering applications in water treatment and remediation. 

Use has recently been made of dual- and multiple-substituent parameter equations, which requires a precise knowledge of the values of inductive and resonance constants. The Hammett constants a and Op can be readily calculated from the values of inductive and resonance constants, but they find a limited application. Such constants as a, 3F, and Si are used even less often. 

In the luminol-H202-HRP chemiluminescence system, some of the aniline derivatives were functionalized as enhancers, while some were inhibitors of the fluorescence [26,27]. A variety of meta-, para-, and ortlzo-substituted aniline were studied. The structures of some of these aniline derivatives are listed in Scheme 5. The reaction constants with HRP-I and HRP-II were measured, and the Hammett constants (a) of their substituents were determined. The results indicated that the aniline substituents with a less than - 0.27 exhibited inhibition behavior. The aniline derivatives acted as enhancers when a was between - 0.27 and + 0.18. A slight enhancement or inhibition was observed if a is greater than -l- 0.18. The factors of enhancement were determined by the potential of reduction of its aniline radicals, the reaction rates of the aniline with HRP-I and HRP-II, and the maximum concentration of the aniline radicals allowed during the oxidation [28]. 

Intensities of the deformation vibration band near 1600 cm plotted for 2-aminothiazole and other 2-substituted thiazoles versus the Hammett constant give a linear relationship (123). 

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,... 

AS can be obtained. In most practical applications, the parameter is the solvent composition (41-44, 192-194) however, the functional relationships are of complicated form and have not been expressed algebraically. A slightly different approach makes use of the relationship between log k and the parameter usually the substituent constant a—at different temperatures. From the temperature dependence of the slope—the reaction constant p—the value of /3 is then obtained indirectly (3, 155). Consider the generalized Hammett equation (9, 17) in the form... 

Having considered the main individual investigations of S02Me and SOMe in respect of their ordinary Hammett a constants and of the exalted constant a", we must examine... 

Modifications of the arylamino moiety profoundly influence the rate of hydrolysis. Thus, the hydrolysis of N- ace ty 1 -4-am i no be n zo i c acid was ca. 1000-fold slower than that of acetanilide [66]. Sorci and Macalady [67] investigated the influence of ring substitution on the hydrolysis of para-substituted acetanilides (4.104) in alkaline solution and in soil bacteria. No correlation was found between alkaline and biotic hydrolysis, which appeared to be controlled by different physicochemical properties. Bacterial hydrolysis was best correlated with the Van der Waals radius of the substituent, whereas chemical hydrolysis was correlated with the Hammett constant characterizing the electron-withdrawing capacity of the substituent. Other studies confirmed that a correspondence between bacterial and mammalian esterases... 

If a series of bases obeys a Hammett type of treatment toward a constant acid, the above discussion is applicable to this problem also. Now the transformed base parameter Eb is related to the substituent constant a and Ea is related to g. The appropriate transformation equations result by simply interchanging the subscripts B and A in all of the above equations. It should also be mentioned that the constancy of — R, the requirement for a Hammett-t5q)e equation, is a different requirement than the constancy of the C/E ratio for a one term equation. A limited set of data can obey a one term equation and not be amenable to a Hammett-type of approach. For example, the parameters of all of the alcohols (aliphatic and aromatic) undergoing a hydrogen bonding interaction have a fairly constant C/E ratio and give fair agreement with a one term treatment. 

Effects on the redox potential of substituents at the reducible ligand have also been investigated and linear correlations recognized with the Hammett s a constant [66, 67]. 

When the periphery of the tetrapyrrolic cycle bears electron withdrawing groups, as in mac.2, instead of alkyl substituents, as in mac.l, the cross section in the B band region increases further (5 = 1.6 x 10 at 770 nm for mac.2), because of a decrease in AE and an increase in Me/, and the cross section was found to be proportional to the Hammett constant of the substituents [152]. 

The decomposition of arenediazonium tetrafluoroborates RC6H4N2 + BF4 (R = Me, OMe, Cl, Br, N02, C02R, OPh) in aqueous solutions (pH 1-7) which gives phenols and phenyl-diazenylphenols is first order with respect to the concentration of the diazonium salt.246 At lower pH, the rates (k) are constant but above a certain pH value, k increases with pH linearly. Correlations with the Hammett constants er have been proposed. 

Structural Effects and Solvent. The effect of solvent on the equilibrium of Reaction 4 can be first discussed in terms of effects on the susceptibility to substituent effects. The values of pK2, characterizing this equilibrium, are a satisfactorily linear function of the Hammett constants correlation coefficient r (Table VI). The values of reaction constant p are practically independent of the ethanol concentration (Table VI), as was already indicated by the almost constant value of the difference (A) between pK2(H20) and p 2 (mixed solvent) for a given composition of the mixed solvent (Table I). The same situation is indicated for DMSO mixtures (Table II) by the small variations in A for any given solvent composition. In this case, the number of accessible p 2 values was too small to allow a meaningful determination of reaction constants p. The structural dependence for various water-ethanol mixtures is thus represented by a set of parallel lines. The shifts between these lines are given by the differences between the pK2H values (p 2 of Reaction 4 for the unsubstituted benzaldehyde) in the different solvent mixtures. 

A good linear correlation between the equilibrium constant log(/f) and the Hammett constant back-bonding fragment W(CO)5 was substituted for Cr(CO)5 in [M(CO)5 Se = C(Ph)H ] the equilibrium... 

The Hammett equation (26-6) states that the relative reactivity (expressed in logarithmic form) of a substituted benzene derivative is proportional to the substituent constant a. For a given reaction, a plot of log (/c//c0) or of log (K/Ka) versus cr should be linear with slope p. Some idea of the validity of the Hammett equation can be gained from Figure 26-4, which shows plots of log kjko) or of log (KjKa) against a for several different reactions. For the examples given, the fit to the Hammett equation is fair. A number of p values (slopes) are listed separately in Table 26-7. It can be seen that p values vary... 

More complex catalysts have not been studied in detail. An exception is the work of Imoto and Takemoto (75) who investigated polymerization rates in benzene using a series of substituted benzoyl peroxides along and with dimethylaniline. They found a rough linear relationship between log () and er, where R and Rjj are rates with the substituted and unsubstituted peroxide and a is the Hammett constant. The overall rate depended on the monomer to the first power and peroxide and amine each to the one-half power. They concluded tentatively that the benzoyl-oxy radical is the initiating species. 

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