Hammett equation deviations from

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. 

The discussion in Section 7.1 should prepare us to expect deviations from such a simple relationship as the Hammett equation if the reaction being correlated differs greatly from the standard reaction. When this happens we have two choices (within this extrathermodynamic approach) We can select a different standard reaction, or we can increase the number of parameters. 

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-... 

Haloform reaction, 237, 296 Halogenation alkanes, 300, 323 alkenes, 179,186, 313 benzene, 138,316 ketones, 295 Hammett equation, 362 additional parameters, 374, 388, 395 derivation of, 362 deviations from, 375 empirical nature of, 395 implications of, 394 reaction pathway, and, 375 solvent effects and, 388 spectroscopic correlations, 392 standard reaction for, 362, 395 steric effects and, 361, 383 thermodynamic implications of, 394 Hammett plots, 359 change in rate-limiting step and, 383 change in reaction pathway and, 378... 

We have stated earlier that because of proximity effects, no generally applicable aj values may be derived for ortho substitution. Nevertheless, one can determine a set of apparent 0)ortho values for a specific type of reaction, as for example, for the dissociation of substituted phenols. Table 8.7 gives such apparent O)ortho constants for estimating pKa values of substituted phenols and anilines. Of course, in cases of multiple substitution, substituents may interact with one another, thereby resulting in larger deviations of experimental from predicted pKa values. Some example calculations using the Hammett equation are given in Illustrative Example 8.2. 

The Hammett equation (1) was applied for more than ten years without major difficulty. With the extension of experimental knowledge to new areas and new reactions certain deviations from the relationship were detected. The deficiencies in the scope of the simple two-parameter Hammett expression (1) were recently discussed by van Bekkum and his associates (1959) and Yukawa and Tsuno (1959). Reactions which proceed without the development of important resonance interactions between the substituent and the side-chain adhere to the relationship. On the other hand, deviations are found for reactions such as the solvolysis of substituted phenyldimethyl-carbinyl chlorides which are now recognized to be of a different character... 

The first adequate examination of the applicability of the Hammett equation to aromatic substitution was made by Roberts and his associates (1954). New data on the nitration of the halobenzenes together with the results for other substituted benzenes (Ingold, 1953) revealed that the rates for nitration in the meta position were, indeed, correlated satisfactorily by the Hammett rr-constants. Para substituents, in particular groups directing to the ortho and para positions, exhibit important deviations from the line defined by the meta reactivities (Fig. 3). It was suggested that these deviations were the consequence of significant resonance interactions in the transition state. At the same time, de la Mare (1954) examined the application of the Hammett parameters for the correlation of the relative rate data for non-catalytic chlorination. The poor agreement achieved (Fig. 4) prompted his conclusion that variable resonance interactions in the... 

In principle, extrathermodynamic relationships that deviate from the simple Hammett equation (equation 8) can be treated by equation 14. The major problem is the determination of the different sets of o s, (e.g., set and 0 set) in a way that will indeed reflect their relation to independent properties. An example of such a procedure is the separation of polar and steric effects (10). The need for such a separation arose when a nearly complete lack of correlation was observed between substituent effects represented by the Hammet a constants and the rates for alkaline hydrolysis of aliphatic systems (12). Inspection of the structures indicated that the proximity of the substituents to the reaction site was a common feature. The steric interaction between R and X had to be considered separately from the electronic effects. Polar substituent constants were thus defined as the difference between the rate constants of base and acid catalyzed hydrolysis of esters. From the structural similarity of the transition states for these reactions (equation 15) it was assumed that the difference in their charge reflects only the polar effect of the substituent... 

The fastest and easiest way to determine the pKa is to look it up in tables of pKa values stored within the CHESS system. If no value is found there, it can be calculated using LFER1s such as the Hammett equation. Hammett rho and sigma values are stored in tables inside the CHESS system. Situations that deviate from linear additivity are noted in an exceptions table to prevent erroneous calculations. If a calculation is not possible, the user would be asked to determine the value experimentally. 

George Hammond began his independent research career as a physical organic chemist studying the benzidine rearrangement. He studied the effects of remote substituents in solvolytic displacement reactions and was one of the first to point out the existence of systematic deviations from the Hammett equation. He also undertook studies of the reactions of free radicals and... 

Inspection of the Hammett equation with those calculated from Equations 86 and 86 shows that in the case of the Op constants, significant deviations ( 0.03) occur in 14 of the 37 groups examined. In the case of the protic solvents should not be used for the determination of ct avoided. 

Under ideal conditions, where the stereoinversion is infinitely faster than the reaction (k yi kj and kg) and the Curtin-Hammett principle safely applies, Sjj and Sg are present in equal amounts at any given conversion and the k /kg ratio is equivalent to the product ratio, realizing eeP(O) = eeP(lOO). In reality, however, the final Pn/Pg ratio at 100% conversion or eeP(lOO) deviates from the initial values as illustrated in Figure 5.3 [k- yjkg = 100 vs 0.1). The above equation correlates with the degree of this deviation. 

The application of an extended Hammett equation based on the separation of enthalpy and entropy effects appears to provide a very good empirical description of substituent effects for systems in which a large deviation from the simple... 

VII. Multi-parameter Correlation Equations All authors who have seriously considered the scope and limitations of the linear free-energy relationships have recognized the existence of real deviations. Frequently, the limitations of the Hammett eq. (1) for certain substituents in certain situations were considered to be indicative of a duality of u-constants. Hammett noticed that the reactions of anilines and phenols required a special value for aJt NOt, 1.27, in contrast to the value, 0.778, derived from benzoic acids. An example is the increased acidity of p-nitrophenol over that expected on the basis of the a constant based on benzoic acid. Resonance interaction between the substituent and the side-chain is presumed to be responsible ... 

Three main conclusions can be deduced from Fig. 15. One, the oxidation of all the monomers proceeds via the same mechanism as shown by their linear fit (with a slope of m = 0.80). The mechanism requires the removal of a tt electron from the aromatic thiophene unit. Two, the less electronegative the monomer, the more easily it will be oxidized as the substituent constant p has a positive sign. Three, substituents do not deviate significantly from a linear relationship, as can be directly observed from Fig. 15. Thus, the S term is not important. Therefore, the j8 substituents exert primarily an electronic effect, which is adequately described by the p a term in the Hammett-Taft equation. 

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