Hammett plots

Figure 2.3. Hammett plots for the Diels-Alder reaction of2.4a-e with 2.5 in water ( J 1,1,1-trifluoroethanol (A) ethanol(9) and acetonitrile iW).

For unknown reasons the point for 2.4a in the Hammett plot for ethanol strongly deviates from the otherwise good correlation. The data for 2.4a in ethanol have therefore not been used in the calculation of p. Instead the data for another compound 2.4 with X = CO2CH3 (k2 = 0.655 M" s" ) were used in the correlation. 

Good to excellent Hammett plots were obtained using substituent constants (see Figure 2.6). Surprisingly, literature examples of good Hammett correlations of stability constants are rare The p-values are shown in Table 2.7. 

The effect of substituents on the rate of the reaction catalysed by different metal ions has also been studied Correlation with resulted in perfectly linear Hammett plots. Now the p-values for the four Lewis-acids are of comparable magnitude and do not follow the Irving-Williams order. Note tlrat the substituents have opposing effects on complexation, which is favoured by electron donating substituents, and reactivity, which is increased by electron withdrawirg substituents. The effect on the reactivity is clearly more pronounced than the effect on the complexation equilibrium. 

Figure 2.6. Hammett plots for the equilibrium constant of binding of 2.4 to Co, NL, Cu and (open symbols), and for the rate constants of reaction of the metal-ion - 2.4 complex with 2.5 (solid symbols).

Any reaction w4iich shows a major shift in transition-state structure over the substituent series would be expected to give a nonlinear Hammett plot, since a variation in the extent of resonance participation would then be expected. 

In the bromination of styrene, a po-+ plot is noticeably curved. If the extremes of the curves are taken to represent straight lines, the curve can be resolved into two Hammett relationships with p = —2.8 for electron-attracting substituents and p = —4.4 for electron-releasing substituents. When the corresponding -methylstyrenes are examined, a similarly curved ap plot is obtained. Furthermore, the stereospecificity of the reaction in the case of the -methylstyrenes varies with the aryl substituents. The reaction is a stereoespecific anti addition for strongly electron-attracting substituents but becomes only weakly stereoselective for electron-releasing substituents, e.g., 63% anti, 37% syn, forp-methoxy. Discuss the possible mechanistic basis for the Hammett plot curvature and its relationship to the stereochemical results. 

There are two opposing substituent effects on this reaction. Electron-attracting aiyl substituents favor the deprotonation but disfavor the elimination step. The observed substituent effects are small, and under some conditions the Hammett plot is nonlinear. 

A Hammett plot of the pK values of p-substituted phenols against the Op values shows serious deviations for the members of the series at the extremes of the o scale, that is, for substituents that are strongly electron donating or electron withdrawing. It was recognized very early that such deviations could be rectified by choosing an appropriate o value for such substituents in effect, this means a different model reaction was adopted. The chemical basis of the procedure can be illustrated with the p-nitro substituent. The p-nitrophenolate ion is stabilized by through resonance as shown in 2. 

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. 

Not all free energy relationships (Hammett plots) are linear. Aside from occasional scatter or unexplained deviations from an otherwise linear plot, it sometimes happens that the plot is smooth but nonlinear. Two causes have been identified, and many examples are known. One cause is a change in a rate-determining... 

Figure 7-2. Hammett plot for solvolysis of substituted norbomyl esters (7) and norbomenyl esters (8) in 70 30 dioxaneiwater at 25°C. ...

It will be obvious that the treatment thus far includes only substituents that are meta or para to the reaction site. When Hammett plots are made with data for ortho-substituted reactants, scatter diagrams usually result. This failure might be attributed to steric effects, but this is not very helpful, and many attempts have been made... 

Instead of the definition in Eq. (7-82), the selectivity is often written as log k,). Another way to consider a selectivity-reactivity relationship is to compare the relative effects of a series of substituents on a pair of reactions. This is what is done when Hammett plots are made for a pair of reactions and their p values are compared. The slope of an LEER is a function of the sensitivity of the process being correlated to structural or solvent changes. Thus, in a family of closely related LFERs, the one with the steepest slope is the most selective, and the one with the smallest slope is the least selective.Moreover, the intercept (or some arbitrarily selected abscissa value, usually log fco for fhe reference substituent) should be a measure of reactivity in each reaction series. Thus, a correlation should exist between the slopes (selectivity) and intercepts (reactivity) of a family of related LFERs. It has been suggested that the slopes and intercepts should be linearly related, but the conditions required for linearity are seldom met, and it is instead common to find only a rough correlation, indicative of normal selectivity-reactivity behavior. The Br nsted slopes, p, for the halogenation of a series of carbonyl compounds catalyzed by carboxylate ions show a smooth but nonlinear correlation with log... 

Make the Hammett plot, neglecting the 2,6-dimethyl substituents, and calculate p. 

Fig. 2. A Hammett plot of the rates of alkylation of substituted pyridines with allyl bromide in nitromethane. Circles represent 4-substituted compounds and crosses 3-substituted compounds. Cf. ref. 54.

Fig. 6. The Hammett plot for the methoxy-dechlorination of meto-substituted 2-chloroquinolines.

A typical Hammett plot is shown in Figure 8-1. The very large scatter indicates clearly that the Hammett equation cannot be applied. Dickson and Eaborn (1959) were the first to point out that the rates of these dediazoniations could be described... 

Analysis of substituent effects in the reaction revealed random correlations of rate with a values of substituents for the uncatalysed reaction, but for the acid-catalysed reaction, reasonable Hammett plots with p factors of —1.27 (HC104) and -1.12 (H3P04) were obtained (Table 253). 

A gas chromatographic analysis of the reaction products showed that although some of the predicted side reactions do occur, their magnitude would not be sufficient to account for the large deviations of the Hammett plots. 

Figure 10-2 presents the Hammett plots for these two reactions. Each correlation is successful, in that a straight line results. The scatter in these plots is reasonably typical of these correlations, where 10-15 percent deviations are not uncommon. The slope for log k versus cr is +0.91. As one can see, this step accelerates with electron-withdrawing substituents, which are the X s with the positive values of a. A positive reaction constant means that the reaction center (here the carbonyl carbon) is more negative in the transition state. This finding supports the suggestion that the RCS is the addition of the semicarbazide to the carbonyl carbon. 

A second example is given in Eq. (10-12), which represents the denitrosation of A-methyl-Af-nitrosoanilines by acid.10 The Hammett plot shows upward curvature because the mechanism changes along the series. 

A Hammett plot (a) of the apparent first-order rate constants for semicarbazone formation at pH 3.9, where a change in the RCS occurs, and (b) of the denitrosation of A-methyl-A-nitrosoanilines, where the mechanism changes. Data are from Refs. 9 and 10. 

Hammett equation. Consider the reaction39 of a series of benzenediazonium ions with OH" and CIST. Construct Hammett plots, calculate the p s, and discuss their signs and magnitudes. 

LFER. Consider the rate of base hydrolysis of a series of ethyl benzoates given by d[C2HsOH]/dt = LfdALQ COOQHsHOH"]. Show that a plot of log Jfcx versus log Ka, where Ka is the ionization constant of the parent benzoic acid, should be linear, and relate its slope to that given by a conventional Hammett plot of log k versus a. 

Very recently equilibrium ion-pair acidities of substituted diphenylmethanes have been measured in cyclohexylamine188. The meta series gives a normal Hammett plot (p = 9.69)... 

Miller226 applied the Hammett equation to the rate constants for the reaction of 4-substituted l-chloro-2-nitrobenzenes with OMe in methanol at 50°C. a values (denoted ct in accordance with the practice briefly in vogue at that time, 1956) were used for + R substituents, and S02Me conformed well at a a value of 1.04952. Act value of 1.117 for S02Ph was derived from the Hammett plot, intermediate between the values based on phenol and anilinium ionizations by Szmant and Suld88 at about the same time. 

FIGURE 3. Hammett plots for bases and substituted phenols refers to ethyl acetate, O lV,JV-dimethylacetamide, DMSO, A pyridine and x triethylamine. 

Waters61 have measured relative rates of p-toluenesulfonyl radical addition to substituted styrenes, deducing from the value of p + = — 0.50 in the Hammett plot that the sulfonyl radical has an electrophilic character (equation 21). Further indications that sulfonyl radicals are strongly electrophilic have been obtained by Takahara and coworkers62, who measured relative reactivities for the addition reactions of benzenesulfonyl radicals to various vinyl monomers and plotted rate constants versus Hammett s Alfrey-Price s e values these relative rates are spread over a wide range, for example, acrylonitrile (0.006), methyl methacrylate (0.08), styrene (1.00) and a-methylstyrene (3.21). The relative rates for the addition reaction of p-methylstyrene to styrene towards methane- and p-substituted benzenesulfonyl radicals are almost the same in accord with their type structure discussed earlier in this chapter. 

This contradictory behaviour is reflected in the Hammett plots by a high slope value e = 0.80 for the thiophenes and a tower q = 0.56 for the indoles. Waltmann, Diaz and Bargon explain this in terms of differences in the expansion of the... 

This is adhered to experimentally and for Ar-CgHs, IC2 = 0.0893 l.mole sec under the conditions specified. Results for a set of ring-substituted analogues give a good Hammett plot with p = -1-0.565. Certain aspects of this system remain unclear, e.g. the non-appearance of polymer at very low Cu(II) concentrations and the exact nature of the Cu(I) species. 

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