Hammett, constant, 580, equation

The fundamental assumption of SAR and QSAR (Structure-Activity Relationships and Quantitative Structure-Activity Relationships) is that the activity of a compound is related to its structural and/or physicochemical properties. In a classic article Corwin Hansch formulated Eq. (15) as a linear frcc-cncrgy related model for the biological activity (e.g.. toxicity) of a group of congeneric chemicals [37, in which the inverse of C, the concentration effect of the toxicant, is related to a hy-drophobidty term, FI, an electronic term, a (the Hammett substituent constant). Stcric terms can be added to this equation (typically Taft s steric parameter, E,). 

Many equilibrium and rate processes can be systematized when the influence of each substituent on the reactivity of substrates is assigned a characteristic constant cr and the reaction parameter p is known or can be calculated. The Hammett equation... 

Linear Free Energy—Linear Solvation Energy Relationships. Linear free energy (LFER) and linear solvation energy (LSER) relationships are used to develop correlations between selected properties of similar compounds. These are fundamentally a collection of techniques whereby properties can be predicted from other properties for which linear dependency has been observed. Linear relationships include not only simple y = rax + b relationships, but also more compHcated expressions such as the Hammett equation (254) which correlates equiUbrium constants for ben2enes,... 

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,... 

The Hammett equation in the form of Eq. (4.14) or Eq. (4.15) is free of complications due to steric effects, since it is applied only to meta and para substituents. The geometry of the benzene ring ensures that groups in these positions cannot interact stoically with the site of reaction. Tables of a values for many substituents have been collected some values are given in Table 4.5, but substituent constants are available for a much wider range of... 

Given in Table 4.5 in addition to the Hammett equation are ct and substituent constant sets which reflect a recognition that the extent of resonance participation can vary for different reactions. The values are used for reactions in which there is direct resonance interaction between an electron-donor substituent and a cationic reaction center, hereas the a set pertains to reactions in which there is a direct resonance interaction between the substitutent and an electron-rich reaction site. These are cases in which the resonance conqionent of the... 

Because the substituent groups have a direct resonance interaction with the charge that develops in the a-complex, quantitative substituent effects exhibit a high resonance component. Hammett equations usually correlate best with the substituent constants (see Section 4.3). ... 

Table 7-2 lists 15 reactions whose rates are correlated by the Hammett equation. Besides the reaction constant p, the table gives a value for k° (from the fitted line), which provides all the information needed to estimate k for any member of the series, if the corresponding o is available, by means of Eq. (7-24). Note that kP in Table 7-2 is generally not identical to the experimental value of k for the ct = 0 member of the series, because this experimental point may deviate from the regression line. 

Reactions that occur with the development of an electron deficiency, such as aromatic electrophilic substitutions, are best correlated by substituent constants based on a more appropriate defining reaction than the ionization of benzoic acids. Brown and Okamoto adopted the rates of solvolysis of substituted phenyldimeth-ylcarbinyl chlorides (r-cumyl chlorides) in 90% aqueous acetone at 25°C to define electrophilic substituent constants symbolized o-. Their procedure was to establish a conventional Hammett plot of log (.k/k°) against (t for 16 /wcra-substituted r-cumyl chlorides, because meta substituents cannot undergo significant direct resonance interaction with the reaction site. The resulting p value of —4.54 was then used in a modified Hammett equation. 

The Hammett equation and LFER in general added no new concepts to the qualitative picture that had been built up of electronic effects in organic reactions, but they did provide a quantitative measure that had been lacking and that has been found very useful. Here we will describe the further development of ideas concerning the substituent constant. 

Table 7-8 lists these ortho E% constants. An LFER can now be written by analogy with the Hammett equation. 

The ultraviolet spectra of the pyridinecarboxylic acids (334) were initially interpreted assuming that the proportion of the zwitterion structure 335 was not appreciable,and the early pK work was inconclusive. However, Jaffe s calculations based on the Hammett equation indicated that about 95% of nicotinic and isonicotinic acids existed in the zwitterion form, and ultraviolet spectral data showed that the actual percentages of picolinic, nicotinic, and isonieotinie acids existing in the zwitterion form in aqueous solution are 94, 91, and 96%, respectively.This was later confirmed by Stephenson and Sponer, who further demonstrated that the proportion of the zwitterion form decreases in solvents of low dielectric constant, becoming very low in ethanol. Dipole moment data indicate that isonicotinic acid exists as such in dioxane, and 6-hydroxypyridine-3-carboxyiic acid has been shown to exist in form 336 u.sing pK data. ... 

Following the early work by one of the authors and by Sixma on the evaluation of substituent and reaction constants by molecular orbital theory, little more has been done along these hnes. Reaction constants have further been treated theoretically with at least moderate success, and a complete theoretical treatment of the Hammett equation awaits detailed testing. 

Similar, although less well documented, is Bryson s observation that a constant term must occasionally be included in the Hammett equation, i.e. A K = ap +a, which means that the intercept is significantly different from the equilibrium constant for the parent compound. 

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. 

Pyridine bases are well known as ligands in complexes of transition metals, and it might well be anticipated that the equilibrium constants for the formation of such complexes, which are likely to be closely related to the base strength, would follow the Hammett equation. Surprisingly, only very few quantitative studies of such equilibria seem to have been reported, and these only for very short series of compounds. Thus, Murmann and Basolo have reported the formation constants, in aqueous solution at 25°, of the silver(I) complexes... 

Finally, two sets of physical properties have been correlated by the Hammett equation. Sharpe and Walker have shown that changes in dipole moment are approximately linearly correlated with ct-values, and Snyder has recently correlated the free energies of adsorption of a series of substituted pyridines with u-values. All the reaction constants for the series discussed are summarized in Table V. 

In the manner outlined, a few attempts have been made to apply the Hammett equation to the transmission of substituent effects in the pyridine series. In the alkaline hydrolysis of 5-substituted ethyl picolinates (5-R-2-COOEt) in 85% ethanol at 25, 35, and 45°, the reaction constants are about 60% as large as those in the corresponding benzene series the overall fit to the Hammett equation, however, is at best fair, since out of four points (R = Et, H, I, Ac) one (Ac) deviates widely. 

One interesting problem frequently recurring in heterocyclic chemistry, particularly with respect to nitrogen heterocycles, is tautomeric equilibria. Too many methods are available for the elucidation of equilibrium positions and tautomeric equilibrium constants (Kj) to adequately review the whole question here. However, the Hammett equation provides one independent method this method has the advantage that it can be used to predict the equilibrium position and to estimate the equilibrium constant, even in cases where the equilibrium position is so far to one side or the other that experimental determination of the concentration of the minor component is impossible. The entire method will be illustrated using nicotinic acid as an example but is, of course, completely general. 

These constants, K toK/, may be estimated by use of the Hammett equation. Estimation of 1 and K 4 involves application of the methods outlined in Section II, A, i.e., application of substituent constants for and N+H to the Hammett equation for the acid-base equilibria of benzoic acids. Estimation of A2 and involves application of the method used in Section III,A, i.e., the p-value for the basicity of substituted pyridines, with cr-values for COOH and COO . Provided the necessary a- and p-values are known, this procedure permits the calculation of four independent, or virtually independent, estimates of Krp. A check on the method is available from the relationships shown in Eq. (16) which is readily obtained by multiplication of Eq. (12) and (14) and of Eq. (13) and (15). 

The fundamental understanding of the diazonio group in arenediazonium salts, and of its reactivity, electronic structure, and influence on the reactivity of other substituents attached to the arenediazonium system depends mainly on the application of quantitative structure-reactivity relationships to kinetic and equilibrium measurements. These were made with a series of 3- and 4-substituted benzenediazonium salts on the basis of the Hammett equation (Scheme 7-1). We need to discuss the mechanism of addition of a nucleophile to the P-nitrogen atom of an arenediazonium ion, and to answer the question, raised several times in Chapters 5 and 6, why the ratio of (Z)- to ( -additions is so different — from almost 100 1 to 1 100 — depending on the type of nucleophile involved and on the reaction conditions. However, before we do that in Section 7.4, it is necessary to give a short general review of the Hammett equation and to discuss the substituent constants of the diazonio group. 

In our opinion the reliability of the basis of the Hammett equation and of the parameters F, R, R+, and R is now clearly sufficient for practically all physical organic purposes. A compilation of all substituent constants and the four parameters F, R, R +, and R was published by Hansch et al. (1991). In the main table of that paper the constants om and ap as well as the parameters F and R are listed for no less than 530 substituents ... 

Substituent effects as evaluated on the basis of the Hammett equation and its extended forms, are - this has to be emphasized again — empirical results. Nevertheless, it is very soothing to know that theoretical approaches, i. e., calculations of substituent effects using ab initio molecular orbital theory (Topsom, 1976, 1981, 1983 Taft and Topsom, 1987, STO-3G and 4-31G level), give results that are consistent with the experimental data. However, it is not recommended to use only theoretically calculated substituent constants and values for F, R, and other parameters for the interpretation of experimental data. 

Before we close this section we make reference to an extended form of the Hammett equation in which the substituent constant and the reaction constant are separated into contributions from the field effect (F) and the mesomeric effect (R). This procedure was suggested by Taft in 1957 for 4-substituted benzene derivatives. It is called a dual substituent parameter (DSP) equation (Scheme 7-2). 

Over the years, the Hammett equation has been modified many times, usually by defining an alternative scale of a constants, the better to allow for special features found in some mechanisms, such as resonance stabilization and mesomeric effects. Thus, there are substituent scales known at cr+, er , crj, etc. The reader is referred to specialized treatises for further details.5-811... 

The Hammett equation is not successful for reactions of aliphatic compounds if the normal cr constants are used. A new scale of substituent constants, labeled cr, was invented to allow the extension of the method to such systems. The difference in the rates of hydrolysis of esters in basic versus acidic solutions is used to define the scale. The transition states are... 

Hammett equation. What form does TST give for the temperature dependence of Hammett s p for a series in which AS is essentially constant, as is often the case ... 

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