Hammett equation, definition

In order to gain an insight into the mechanism on the basis of the slope of a Type A correlation requires a more complicated procedure. Consider the Hammett equation. The usual statement that electrophilic reactions exhibit negative slopes and nucleophilic ones positive slopes may not be true, especially when the values of the slopes are low. The correct interpretation has to take the reference process into account, for example, the dissociation equilibrium of substituted benzoic acids at 25°C in water for which the slope was taken, by definition, as unity (p = 1). The precise characterization of the process under study is therefore that it is more or less nucleophilic than the reference process. However, one also must consider the possible influence of temperature on the value of the slope when the catalytic reaction has been studied under elevated temperatures there is disagreement in the literature over the extent of this influence (cf. 20,39). The sign and value of the slope also depend on the solvent. The situation is similar or a little more complex with the Taft equation, in which the separation of the molecule into the substituent, link, and reaction center may be arbitrary and may strongly influence the values of the slopes obtained. This problem has been discussed by Criado (33) with respect to catalytic reactions. 

A similar system, (CH3)2C=CH X, was studied by Endrysova and Kraus (55) in the gas phase in order to eliminate the possible leveling influence of a solvent. The rate data were separated in the contribution of the rate constant and of the adsorption coefficient, but both parameters showed no influence of the X substituents (series 61). A definitive answer to the problem has been published by Kieboom and van Bekum (59), who measured the hydrogenation rate of substituted 2-phenyl-3-methyl-2-butenes and substituted 3,4-dihydro-1,2-dimethylnaphtalenes on palladium in basic, neutral, and acidic media (series 62 and 63). These compounds enabled them to correlate the rate data by means of the Hammett equation and thus eliminate the troublesome steric effects. Using a series of substituents with large differences in polarity, they found relatively small electronic effects on both the rate constant and adsorption coefficient. 

A common probe of reaction mechanisms used to infer charge distribution in the transition state involves variation of substituent groups near the reaction center. From the variation in reaction rate produced by electron-donating and electron-withdrawing groups or by the steric hindrance of various sized groups, transition state characteristics can be inferred. Two empirical correlations have been proposed and refined which provide a common framework for this process. The Hammett equation is applied to aromatic systems [45]. The Taft correlation is applied to aliphatic systems [45], Definitions of terms, collections of substituent constants (steric and electronic effects for various substituents), and listings of observed reaction response parameters (for typical reaction types) have been collected [45]. 

Equation (31) expresses the dependence of the relative rate (equilibrium) constant on the properties of the solvent characterized by the parameters Ap and Sp. The parameter Rp is proportional to the differences between the relative Gibbs free energies for the nth and sth solvent of the given and standard substrates. The parameter Sp characterizes the effect of a change of the substrate on the rate constant of the substrate with a standard substituent. In the Hammett equation this substituent is represented by hydrogen for which a was definitionally put equal to zero, while in the Taft and Taft-Pavelich equations methyl is used as the standard substituent [a = = 0). 

Molecular Similarity and QSAR. - In a first contribution on the design of a practical, fast and reliable molecular similarity index Popelier107 proposed a measure operating in an abstract space spanned by properties evaluated at BCPs, called BCP space. Molecules are believed to be represented compactly and reliably in BCP space, as this space extracts the relevant information from the molecular ab initio wave functions. Typical problems of continuous quantum similarity measures are hereby avoided. The practical use of this novel method is adequately illustrated via the Hammett equation for para- and me/a-substituted benzoic acids. On the basis of the author s definition of distances between molecules in BCP space, the experimental sequence of acidities determined by the well-known a constant of a set of substituted congeners is reproduced. Moreover, the approach points out where the common reactive centre of the molecules is. The generality and feasibility of this method will enable predictions in medically related Quantitative Structure Activity Relationships (QSAR). This contribution combines the historically disparate fields of molecular similarity and QSAR. 

The p a of benzoic acid is 4.2. Use the Hammett equation and Table 11.3 to calculate the pX of m-nitrobenzoic acid. Hint A calculator isn t required if you think carefully about the Hammett equation and the definition of pX. )... 

It should be recognized that all of the approaches to linear free-energy relationships have been developed on an empirical basis. The reaction constants, substituent constants, and other parameters involved are specified by the definitions of the correlation equation. The data are then treated by the equation, and the variable parameters arise from the best fit to the correlation equation. In the case of the Hammett equation, each reaction series gives rise to its characteristic p value. For the Swain-Lupton equation, the meta series and the para series would each give rise to / and r. 

Finally, in this account of multiparameter extensions of the Hammett equation, we comment briefiy on the origins of the aj scale. This had its beginnings around 1956 in the a scale of Roberts and Moreland for substituents X in the reactions of 4-X-bicyclo[2.2.2]octane-l derivatives. However, at that time few values of a were available. A more practical basis for a scale of inductive substituent constants lay in the cr values for XCH2 derived from Taft s analysis of the reactivities of aliphatic esters into polar, steric, and resonance effects (see Section 3.1). For the few a values available it was shown that a for X was related to a for XCH2 by the equation o = 0.45(t. Thereafter the factor 0.45 was used to calculate O / values of X from cr values of XCH2. Taft s analysis of ester reactivities was also important because it led to the definition of the scale of substituent steric parameters, thereby permitting the development of multiparameter extensions of the Hammett equation involving steric as well as electronic terms. 

This approach to separating the different types of interaetions eontributing to a net solvent effeet has elieited much interest. Tests of the tt, a, and p seales on other solvatochromie or related proeesses have been made, an alternative tt seale based on ehemieally different solvatochromie dyes has been proposed, and the contribution of solvent polarizability to ir has been studied. Opinion is not unanimous, however, that the Kamlet-Taft system eonstitutes the best or ultimate extrathermodynamie approaeh to the study of solvent effeets. There are two objections One of these is to the averaging process by which many model phenomena are eombined to yield a single best-fit value. We eneountered this problem in Section 7.2 when we eonsidered alternative definitions of the Hammett substituent eonstant, and similar eomments apply here Reiehardt has diseussed this in the eontext of the Kamlet-Taft parameters. - The seeond objeetion is to the elaim of generality for the parameters and the eorrelation equation we will return to this eontroversy later. 

Values of e are correlated by the Op constants in accord with eq. (61) (119, 120). Kawabata, Tsuruta, and Furukawa (121) have proposed a revised form of the Price-Alfrey equation based on the definition e = 0 for styrene. On the basis of this redefinition, they have calculated a new set of Q values. These Q values are linear in the Hammett 0 constants. It is not clear from their paper whether this linear relationship is for substituents directly bonded to the carbon-carbon double bond or whether it is applicable only to Q values for substituted styrenes. Charton and Capato (119) were unable to obtain significant correlations between any a constants and the q values of Schwan and Price (117). Zutty and Burkhart (122) have proposed a redefinition of the Price-Alfrey equation based on ethylene as the reference system with Qo and e defined as 1 and 0, respectively. 

The extent to which a given reaction responds to electronic perturbation constitutes a measure of the electronic demands of that reaction, which is determined by its mecha-, nism. The introduction of substituent groups into the framework and the subsequent alteration of reaction rates helps delineate the overall mechanism of reaction. Early work examining the electronic role of substituents on rate constants was first tackled by Burckhardt and firmly established by Hammett (13, 14, 77, 78). Hammett employed, as a model reaction, the ionization in water of substituted benzoic acids and determined their equilibrium constants K. See Equation 1.28. This led to an operational definition of o-, the substituent constant. It is a measure of the size of the electronic effect for a given substituent and represents a measure of electronic charge distribution in the benzene nucleus. 

In these equations, k or k2 refer to the rate or equilibrium constant for the unsubstituted molecule, p characterizes the sensitivity of the reaction to electronic substituent effects, and a is the relative electronic effect of the substituent. A substituent at the meta position has a different a value than that of the same substituent at the para position. By definition, p = 1.0 for the pi a of substituted benzoic acids and a is the substituent effect on this reaction. As an example, Figure 3.1 shows the relationship between Hammett a and the log of the acid dissociation constant (log Kf of metu-substituted phenols. The correlation coefficient of this relationship is 0.97. The data is presented in Table 3.1. 

Seeman JI (1986) The Curtin-Hammett principle and the Winstein-Holness equation. New definition and recent extensions to classical concepts. J Chem Educ 63 42-48... 

Charton [17] criticised Equation (16) on the inconvenience of having to make two measurements to obtain a new value of Oj. He proposed a definition based on the ionisation of -substituted acetic acids, suggesting that measurements are more reliable than rate constants, that only one determination was required and that values would be directly comparable with Hammett constants, since these too are based on the ionisation of a carboxy acid. He correlated pK values with selected Oj values [16] for 20 reactions, according to equation (17), evaluated b and d for various conditions and derived an extensive list of Oj values. 

Seeman, J. I. The Curtin-Hammett Principle and the Winstein-Holness Equation. New Definition and Recent Extensions to Classical Concepts /. Chem. Educ. 1986, 63, 42-48. Winstein, S. Holness, N. J. Neighboring Carbon and Hydrogen. XIX. rerf-Butylcyclohexyl Derivatives. Quantitative Conformational Analysis /. Awj. Chem. Soc. 1955, 77, 5562-5578. Curtin, D. Y. Stereochemical Control of Organic Reactions. Differences in Behavior of Diastereoisomers. I. Ethane Derivatives. The Cis Effect Rec. Chem. Pro ir. 1954, 15, 111-128. An alternative to the Curtin-Hammett argument presented on page 295 is that the epoxide reacts with thiophenoxide from conformation 64b such that the product is bom in the B ring boat (or twist-boat) conformation of 65b. 

C in equation (2) is a molar concentration which produces a certain biological effect, P is the -octanol/water partition coefficient (see Octanol/Water Partition Coefficients), and a is the electronic Hammett constant (equation 1). The definition of a parabolic model and the combination of different physicochemical properties in one model allowed for the first time the description of structure-activity relationships which could not be correlated with a single linear term. As an alternative to log P values, a lipophilicity parameter n can be used which is defined in an analogous manner as the electronic a parameter (1 equation 3). " ... 

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