Hammett derivation

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. 

Table 12.2 A list of some of the more common descriptors. Details of some of these descriptors can be found elsewhere as indicated. This table is restricted to those descriptors which can be computed it therefore excludes certain classes (such as the Hammett substituent constants) which are derived from experimental studies (sec Section 12.12).

Chemistry as it was realized substantially derives from the interae-tion of electrons. The electronic theory of chemistry, particularly of organic chemistry, emerged, explaining the great richness of chemical observations and transformation, as expressed by Ingold, Robinson, Hammett, and many others following in their footsteps. 

The application of the Taft equation, derived from the Hammett equation (262)... 

H-nmr chemical shifts of N-1—H and N-3—H signals have been used as a criterion for distinguishing between N-l-substituted and N-3-substituted hydantoin derivatives (22). They can often be related to electronic properties, and thus good linear correlations have been found between the shifts of N—H and Hammett parameters of the substituents attached to the aryl group of 5-arylmethylenehydantoins (23). 

C-nmr data have been recorded and assigned for a great number of hydantoin derivatives (24). As in the case of H-nmr, useful correlations between chemical shifts and electronic parameters have been found. For example, Hammett constants of substituents in the aromatic portion of the molecule correlate weU to chemical shifts of C-5 and C-a in 5-arylmethylenehydantoins (23). Comparison between C-nmr spectra of hydantoins and those of their conjugate bases has been used for the calculation of their piC values (12,25). N-nmr spectra of hydantoins and their thio analogues have been studied (26). The N -nmr chemical shifts show a linear correlation with the frequencies of the N—H stretching vibrations in the infrared spectra. 

If the perturbations thus caused are relatively slight, the accepted perturbation theory can be used to interpret observed spectral changes (3,10,39). The spectral effect is calculated as the difference of the long-wavelength band positions for the perturbed and the initial dyes. In a general form, the band maximum shift, AX, can be derived from equation 4 analogous to the weU-known Hammett equation. Here p is a characteristic of an unperturbed molecule, eg, the electron density or bond order change on excitation or the difference between the frontier level and the level of the substitution. The other parameter. O, is an estimate of the perturbation. 

A Hammett relationship of the form ApK = 5.8am has been proposed for 4-substituted pyrazoles (74TL1609) in order to explain the effect of 4-nitro ApK = 4.5, am = 0.71) and 4-diazo groups (Apiifa = 10.0, am = 1.76). The acidity constants of a series of pyrazolidine-3,5-diones have been determined (75AJC1583) and the 4- -butyl-1,2-diphenyl derivative phenylbutazone has a pK of 4.33. 

According to a kinetic study which included (56), (56a) and some oxaziridines derived from aliphatic aldehydes, hydrolysis follows exactly first order kinetics in 4M HCIO4. Proton catalysis was observed, and there is a linear correlation with Hammett s Ho function. Since only protonated molecules are hydrolyzed, basicities of oxaziridines ranging from pii A = +0.13 to -1.81 were found from the acidity rate profile. Hydrolysis rates were 1.49X 10 min for (56) and 43.4x 10 min for (56a) (7UCS(B)778). O-Protonation is assumed to occur, followed by polar C—O bond cleavage. The question of the place of protonation is independent of the predominant IV-protonation observed spectroscopically under equilibrium conditions all protonated species are thermodynamically equivalent. 

C Hansch, RM Muir, T Fujita, PP Maloney, E Geiger, M Streich. The correlation of biological activity of plant growth regulators and chloromycetm derivatives with Hammett constants and partition coefficients. J Am Chem Soc 85 2817-2824, 1963. 

While generation of a Mn(V)oxo salen intermediate 8 as the active chiral oxidant is widely accepted, how the subsequent C-C bond forming events occur is the subject of some debate. The observation of frans-epoxide products from cw-olefins, as well as the observation that conjugated olefins work best support a stepwise intermediate in which a conjugated radical or cation intermediate is generated. The radical intermediate 9 is most favored based on better Hammett correlations obtained with o vs. o . " In addition, it was recently demonstrated that ring opening of vinyl cyclopropane substrates produced products that can only be derived from radical intermediates and not cationic intermediates. ... 

Hydroxypyridine 1-oxide is insoluble in chloroform and other suitable solvents, and, although the solid-state infrared spectrum indicates that strong intermolecular hydrogen bonding occurs, no additional structural conclusions could be reached. Jaffe has attempted to deduce the structure of 4-hydroxypyridine 1-oxide using the Hammett equation and molecular orbital calculations. This tautomeric compound reacts with diazomethane to give both the 1- and 4-methoxy derivatives, " and the relation of its structure to other chemical reactions has been discussed by Hayashi. ... 

Although the application of the Hammett equation to side-chain reactions of disubstituted benzene derivatives (1) is relatively straightforward, the introduction of a heteroatom somewhere in the aromatic... 

Few other reactions of series of substituted pyridines have been investigated extensively. Dondoni, Modena, and Todesco have measured the rate of N-oxidation of a limited series of pyridines and found a good correlation with normal u-values with a p-value of — 2.23. The A-alkylation of pyridines with alkyl iodides in nitrobenzene has been studied by Brown and Cahn and by Clarke and Rothwell. Unfortunately, the only data available are for the parent compound and for alkyl derivatives, and, since the a-values for the various alkyl groups in a given position are substantially constant, this leaves a correlation of only three independent points. However, the rates of A-alkylation of the j8- and y-alkyl derivatives are so nearly equal that it appears as if no correlation existed. Clarke and Rothwell have also studied the alkylation with allyl bromide in nitromethane at various temperatures, and in this case a more extensive series is available. The authors state that no overall Hammett correlation is obtained however, the j8-substituted derivatives fall on one straight line and the y-derivatives on another one with a different slope. The data are shown in Fig. 2. The line for the j8-compounds, p = — 2.53 0.31, r = 0.95, is seen not to be very good the line for the y-derivatives, p = — 1.42 0.06, r = 0.99, is much more satisfactory. It does not seem likely that the discrepancy is due to the intervention of resonance effects, since in this case one would expect the correlation for the y-derivatives to be poorer than that for the j8-analogs. More extensive studies with a wider variety of substituents would seem very desirable. 

The problems encountered in any attempt to treat the transmission of the effects of one substituent in a disubstituted heterocycle through the heterocyclic nucleus to a reaction site in the other substituent (i.e. the side-chain) are enormous, and it is consequently not surprising that relatively little work has been done in this area. First, while in benzene derivatives there are three positions, i.e. three relations between substituent and reacting side-chain to be considered, the number of complexities is much greater in heterocycles. Thus, e.g., in pyridine alone, after elimination of the orientations involving a vicinal relationship between substituent R and the side-chain Y to which no Hammett-type relation is likely to be applicable, the following cases should be considered ... 

Once the concept that the Hammett equation may be applied to heterocyclic systems as well as to simple benzene derivatives is accepted the possibilities of its use are virtually unlimited. Curiously enough, not too many such applications seem to have been reported. 

It seems reasonable to assume that in regard to their formation and decomposition the derivatives of phenylpentazole correspond roughly to the unsubstituted compound (see Table V). The rate data for m-and p-substituted phenylpentazoles conform to the Hammett equation with p= -f-1.01. Finally, the high rate of decomposition and... 

The traditional means of assessment of the sensitivity of radical reactions to polar factors and establishing the electrophilicity or nucleophilieity of radicals is by way of a Hammett op correlation. Thus, the reactions of radicals with substituted styrene derivatives have been examined to demonstrate that simple alkyl radicals have nucleophilic character38,39 while haloalkyl radicals40 and oxygcn-ccntcrcd radicals " have electrophilic character (Tabic 1.4). It is anticipated that electron-withdrawing substituents (e.g. Cl, F, C02R, CN) will enhance overall reactivity towards nucleophilic radicals and reduce reactivity towards electrophilic radicals. Electron-donating substituents (alkyl) will have the opposite effect. 

From the results of Malek et al.49,561 m 205,206,211) it may be concluded that the various metal derivatives used in esterifications exhibit many common catalytic characteristics. Thus, these authors190 established relationships concerning the free energies of esterification of thirteen ortho-, meta- and para-substituted benzoic adds by 1,2-ethanediol. They obtained Hammett parameters which do not differ greatly from those found for the add-catalyzed esterifications of the same adds with various alcohols. They concluded... 

Much earlier information on the structure of diazonium ions than that derived from X-ray analyses (but still useful today) was obtained by infrared spectroscopy. The pioneers in the application of this technique to diazonium and diazo compounds were Le Fevre and his school, who provided the first IR evidence for the triple bonds by identifying the characteristic stretching vibration band at 2260 cm-1 (Aroney et al., 1955 see also Whetsel et al., 1956). Its frequency lies between the Raman frequency of dinitrogen (2330 cm-1, Schrotter, 1970) and the stretching vibration frequency of the C = N group in benzonitrile (2255 cm-1, Aroney et al., 1955). In substituted benzenediazonium salts the frequency of the NN stretching vibration follows Hammett op relationships. Electron donor substituents reduce the frequency, whereas acceptor substituents increase it. The 4-dimethylamino group, for example, shifts it by 103 cm-1 to 2177 cm-1 (Nuttall et al., 1961). This result supports the hypothesis that... 

Hammett discovered linear relationships between two sets of equilibrium or rate constants of substituted benzene derivatives (reviews Hammett 1937, 1940, 1970, Johnson 1973, Exner 1988, and others see Scheme 7-1). 

In Scheme 7-1 kx and kn refer to the rate constants for a benzene derivative, in our case the benzenediazonium ion, bearing a substituent X in the 3- or 4-position, and the corresponding unsubstituted benzene derivative respectively. The term p is Hammett s reaction constant for the reaction, and o is Hammett s substituent constant which is, at least in principle, independent of the nature of the reaction but different for the 3- and 4-positions. A plot of log kx (or log kx - log kH) versus o should give a straight line. Its slope (positive or negative) corresponds to the reaction constant p. Equilibrium relationships are treated analogously. 

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). 

Recently, a kinetic study has been made of the substitution of diazotised sulphanilic acid in the 2 position of 4-substituted phenols under first-order conditions (phenol in excess) in aqueous buffer solutions at 0 °C131a. A rough Hammett correlation existed between reaction rates and am values, with p about -3.8 however, the point for the methoxy substituent deviated by two orders of magnitude and no explanation was available for this. The unexpectedly low p-factor was attributed to the high reactivities of the aromatic substrates, so that the transition state would be nearer to the ground state than for reaction of monosubstituted benzene derivatives. 

The Hammett equation is the best-known example of a linear free-energy relationship (LFER), that is, an equation which implies a linear relationship between free energies of reaction or activation for two related processes48. It describes the influence of polar meta-or para-substituents on reactivity for side-chain reactions of benzene derivatives. 

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. 

---