Hammett equation table

As we mentioned earlier, not all reaction series can be correlated by a Hammett equation. An underlying reason for the inability of Hammett and values to correlate all reaction series is that the substituent effects used to assign ct are a mixture of resonance and polar components. When direct resonance interaction with a reaction site is possible, the extent of the resonance increases and the substituent constants appropriate to the normal mix of resonance and polar effects fail. There have been various attempts to develop sets of a values that take extra resonance interactions into account. In addition to the and values used with the classical Hammett equation Table 3.27 lists substituent constants and ct . These are substituent constant sets that reflect enhanced resonance participation. The values are used for reactions in which there is direct resonance interaction between an electron donor substituent and a cationic reaction center, whereas the set pertains to reactions in which there is a direct resonance interaction between an electron acceptor and an anionic reaction site. In these cases, the resonance component of the substituent effect is particularly important. 

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... 

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. 

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

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. 

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. 

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... 

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 ... 

The Hammett equation has correlated more than 400 reaction series, and can accommodate many others if the equation is modified.5-8 A very early list9 of the successful application of the Hammett equation in its original form is given in Table 10-2. 

The special substituent constants for + R para-substituents are denoted by a, and those for — R para-substituents are denoted by a+ 54. They are based respectively on the reaction series discussed above. Selected values are given in Table 1. Characteristic a or a+ values are sometimes distinguished for meta-substituents also, but only for a minority of substituents which show very marked + R or — R effects do these differ significantly from ordinary a values. The range of applicability of the Hammett equation is greatly extended by means of a and cr+, notably to nucleophilic (by a ) and to electrophilic (by cr+) aromatic substitution. 

Table IV lists comparative SD and / values for fittings of all of the reactions of Table II and III with each of the gr scales derived in this paper. The comparison includes figures for fittings with F and R values of Swain and Lupton (S L) and fitting with the Hammett equation. We believe the results given in Table IV provide a clear confirmation of the uniqueness and limited generality of the o/2(ba) scale. Very consistently, the fit achieved by the or (BA) scale is shown in Table IV to be superior by significant factors to that achieved by any of the other scales or by the simple op treatment. This fact is clearly reflected in the overall / values and the similarly weighted root-mean-square / values, F = y/lfnif lN, sum taken over all reactions. The value of F is. 067 for the basis sets of Table II (compare with overall / of. 058). The comparable F values are. 140 for Or, . 088 for S L, and. 155 for 0(p) with the data differences as explained in Table IV. For all sets of Table IV, the corresponding figures are. 073 for o (ba). -143 for a%, . 097 for S L, and. 209 for 0(py...

A number of correlations of ionization potentials for substituted benzenes (40-42), benzyl (43), phenoxy (44), and alkyl (45) radicals and substituted pyridines (46) with the simple Hammett equation have been reported. Charton (47) has studied the application of the extended Hammett equation to substituted ethylenes and carbonyl compounds. The sets studied here are reported in Table II (sets 2-10 and 2-11). Results of the correlations are set forth in Table 111. The results obtained are much improved by the exclusion of the values for X = C2 H3, Ac, F, H and OAc from set 2-10 (set 2-lOA) and the value for X = H from set 2-11 (set 2-11 A). The composition of the electrical effect corresponds to that found for the Op constants as is shown by the pR values reported in Table IV. 

As was noted previously, Hine and Bailey (16, 17) have obtained correlation of rate data for the reaction of tra s-3-substituted acrylic acids and diphenyl-diazomethane with the Hammett equation. Bowden has reported correlation of rate data for the reaction of tra s-3-substituted acrylic acids with diphenyl-diazomethane (59) and the alkaline hydrolysis of trans-3-substituted methyl acrylates (69) with the Hammett equation. Sufficient data are available for nine sets of rate studies. The sets studied are reported in Table VIII. The results of the correlations are given in Table IX. Of the nine sets studied, seven gave... 

Ionization constants of czs-3-substituted acrylic acids have been correlated with the Hammett equation by Hogeveen (58) and by Charton (60). Charton has correlated ionization constants for a number of other c/s-vinylene sets with the Hammett equation (60). Charton and Charton have correlated some cw-vinylene sets with the extended Hammett equation [eq. (2)] (73). Sufficient data are available for twelve sets of cis-vinylene equilibria, of which four sets represent ionization constants of hydroxy compounds (sets 12-1 to 12-4) and eight sets represent ionization constants of carboxylic acids (sets 12-5 to 12-12). All sets have been correlated with eq. (24) and eq. (2). Sets studied are reported in Table XII. Results of the correlations are reported in Table XIII. Sets designated A were correlated with eq. (24), sets designated B were correlated with eq. (2). In the case of the second ionization constant of 2,3,5,6-tetrahydroxy-l,4-benzoquinone (set 12-3), it is uncertain which hydroxyl group ionizes therefore, the value for X = OH was excluded from the correlation. All of the sets 12-1 to 12-4 gave significant correlations with both eq. (24) and eq. (2),... 

Data for fra s-heterovinylene sets were first correlated with the extended Hammett equation by Charton and Charton (73). It must be noted that in frans-heterovinylene sets, the reaction sites and substituent are tram to each other. There are available in the literature data for three fraws-heterovinylene sets, all oximes. The sets studied are presented in Table XXVII (sets 27-1 through 27-3). Results of the codelations and values of are given in... 

Values of pKa for substituted amidines were correlated with the Hammett equation by Charton (190). Data are available for one set of substituted amidinium ions and one set of C-substituted-N-phenylamidinium ions. The sets studied are shown in Table XXX. Results of the correlations are set forth in Table XXXI and values of pj in Table XXXII. Significant correlations were obtained for both sets. In the case of the ionization of N-phenyl amidinium ions, the possibility of tautomerism exists, Charton (170) has presented arguments which suggest that the predominant tautomer is 30. The localized effect is predominant in both of the sets of amidinium ions studied. 

Data are extant in the literature for five sets of substituted acetylene dipole moments. The correlation of dipole moments with the Hammett equation was discussed in section II.A.l. of this work. The application of the Hammett equation to dipole moments of acetylenes was first reported by Charton (18). The sets studied here are reported in Table XXXIII. Results of the correlations are presented in Table XXXIV, and values of Pr are set forth in Table XXXV. 

There are almost no studies of substituent effects on additions to carbon-carbon triple bonds extant in the literature. Bowden and Price (208) have reported a correlation of rates of addition of hydrogen bromide to 3-substituted propiolic acids with the Hammett equation using the Op constants. Unfortunately, there are only three substituents in the set. Sufficient data are available for a single set of 1,3-dipolar cycloaddition. The set studied is shown in Table XXXIII, and the results of the correlation are in Table XXXIV. The correlation was significant the delocalized effect is predominant in this set. 

The simplest possible use that can be made of the Hammett equation is to calculate k or K for a specific reaction of a specific compound, where this information is not available in the literature, or indeed where the actual compound has not even been prepared yet. Thus it is known that the base-catalysed hydrolysis of ethyl m -nitrobenzoate is 63-5 times as fast as the hydrolysis of the corresponding unsubstituted ester under parallel conditions what then will be the comparable rate for base-catalysed hydrolysis of ethyl p-methoxybenzoate under the same conditions Looking at the table of [Pg.374]

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