Hammett methods

Despite seven decades of technical and scientific progress, the original Hammett method has not become obsolete. The colorimeter has been replaced by modern spectrophotometers that can be operated at selected wavelengths extending the spectra beyond visible into the ultraviolet region of the electromagnetic spectrum. The experimental variable, which is wavelength-dependent, is the optical density D. D is related to the concentration by the Beer-Lambert law [Eq. (1.23)]. 

The initial temperatures of resinificahon were compared with the Ho values of superacids as determined by the Hammett method, and a linear relationship was observed. The TPRa results gave the Ho value of S04/Sn02 as -18 the value was not determined by the Hammett method because -16.12 relates to 1,3,5-trichlorobenzene indicator which has the lowest pRgH+ value among the Hammett indicators used to date (Table 17.1). 

The basic assumption of the Hammett method is that the activity coefficient ratio /bh+//b is independent of the nature of B at any given solvent composition. This seems to be a reasonably good assumption for a closely related series of bases, such as the primary anilines, but may not be true for bases of different structural types. This has led to the proposal of many different types of acidity function, and to much controversy as to the meaning and usefulness of the Hammett and related acidity functions. This subject has been extensively reviewed elsewhere [16]. Although it now appears that the concept of the acidity function is perhaps not as generally useful as was originally believed, at the present time we do not have any more reliable method of assessing the acidities of superacid media. 

Let us illustrate this with the example of the bromination of monosubstituted benzene derivatives. Observations on the product distributions and relative reaction rates compared with unsubstituted benzene led chemists to conceive the notion of inductive and resonance effects that made it possible to explain" the experimental observations. On an even more quantitative basis, linear free energy relationships of the form of the Hammett equation allowed the estimation of relative rates. It has to be emphasized that inductive and resonance effects were conceived, not from theoretical calculations, but as constructs to order observations. The explanation" is built on analogy, not on any theoretical method. 

Fujita et al. were the first to develop a calculation method that was based, analogously to the Hammett approach, on substituent constants r[6] (see Eq. (7))... 

In subsequent studies attempting to find a correlation of physicochemical properties and antimicrobial activity, other parameters have been employed, such as Hammett O values, electronic distribution calculated by molecular orbital methods, spectral characteristics, and hydrophobicity constants. No new insight on the role of physiochemical properties of the sulfonamides has resulted. Acid dissociation appears to play a predominant role, since it affects aqueous solubiUty, partition coefficient and transport across membranes, protein binding, tubular secretion, and reabsorption in the kidneys. An exhaustive discussion of these studies has been provided (10). 

Ho, the acidity function introduced by Hammett, is a measure of the ability of the solvent to transfer a proton to a base of neutral charge. In dilute aqueous solution ho becomes equal to t d Hq is equal to pH, but in strongly acid solutions Hq will differ from both pH and — log ch+. The determination of Ho is accomplished with the aid of Eq. (8-89) and a series of neutral indicator bases (the nitroanilines in Table 8-18) whose pA bh+ values have been measured by the overlap method. Table 8-19 lists Ho values for some aqueous solutions of common mineral acids. Analogous acidity functions have been defined for bases of other structural and charge types, such as // for amides and Hf for bases that ionize with the production of a carbocation ... 

The most reliable method of preparing benzofuroxans is by decomposition of o-nitrophenyl azides. Decomposition can be achieved by irradiation, or more usually by pyrolysis temperatures between 100° and 1.50° are commonly used. Refluxing in glacial acetic acid is the recommended procedure for 4- or 5-sub-stituted 2-nitrophenyl azides, but with 3- or 6-substituted compounds higher boiling solvents are usually necessary. Quantitative studies on the reaction rate have been made, and a cyclic transition state invoked, an argument which has been used to account for the greater difficulty of decomposition of the 6-substituted 2-nitrophenyl azides. Substituent effects on the reaction rate have also been correlated with Hammett a constants, ... 

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. 

Finally, the Hammett equation has been applied in a few instances to heterocycles of the indole-benzofuran type. The double p method of Eq. (3) was first designed for this type of system and was here applied. When this approach was originally proposed, the only truly hetero-cychc system to which it was apphed was the substituted phthahds 14, and pertinent data on the hydrolysis of these compounds are included in Table IX. 

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 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... 

Taken from Reference 170. The values are averaged ones obtained by U V and N MR methods in H2S04 or HC104. Bunnett-Olsen s values, 0.4-0.6 in equation 29. This suggested that sulphoxides are not Hammett bases (J. F. Bunnett and F. P. Olsen, Can. J. Chem., 44, 1899 (1966))... 

Ritchie and Sager (124) distinguish three types of reaction series according to whether the Hammett equation or the isokinetic relationship is obeyed, or both. The result that the former can be commonly valid without the latter seems to be based on previous incorrect statistical methods and contradicts the theoretical conclusions. Probably both equations are much more frequently valid together than was anticipated. The last case, when the isokinetic relationship holds and the Hammett equation does not, may be quite common, of course, and has a clear meaning. Such a series meets the condition for an extrathermo-dynamic treatment when enough experimental material accumulates, it is only necessary to define a new kind of substituent constant. 

Deutsch and Hansch applied this principle to the sweet taste of the 2-substituted 5-nitroanilines. Using the data available (see Table VII), the calculated regression Eqs. 5-7 (using the method of least squares) optimally expressed the relationship between relative sweetness (RS), the Hammett constant, cr, and the hydrophobic-bonding constant, ir. 

The probe molecules of greatest historical interest in catalysis are the Hammett indicators [13]. The difficulty of making reliable visual or spectrophotometric observations of the state of protonation of these species on solids is well known. We have recently carried out the first NMR studies of Hanunett indicators on solid acids [ 14]. This was also the occasion of the first detailed collaboration between the authors of this article, and theoretical methods proved to strongly compliment the NMR experiments. The Hanunett story is told after first reviewing the application of theoretical chemistry to such problems. Central to the application of any physical method in chemistry is the process of modeling the relationship between the observables and molecular structure. However often one does this, it is rarely an exact process. One can rationalize almost any trend in isotropic chemical shift as a function of some variation in molecular structure - after the fact, but the quantitative prediction of such trends in advance defies intuition in most nontrivial cases. Even though the NMR spectrum is a function... 

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