Extended Hammett equation

Certain physical properties of substituted ethylenes may be correlated with the extended Hammett equation. Included in this category are dipole moments and ionization potentials. 

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. 

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),... 

In eq. (32), pi and p2 denote the percent of the product containing boron at C and, respectively. Applying the extended Hammett equation to the partial rate constants ki and k2 for the compound bearing the X substituent gives... 

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... 

Three sets of nmr chemical shifts for the ethynyl proton have been correlated with eq. (2). Of these sets, two gave significant correlations with eq. (2). Nevertheless, as the most extensive collection of substituents is included in the set which did not give significant correlation, it seems likely that chemical shifts of ethynyl protons are not correlated by the extended Hammett equation. This behavior contrasts with that of chemical shifts for trans- and c/s-vinyl protons and is in agreement with the behavior of geminal vinyl protons. 

Data for substituted cyclopropane rings can be conveniently arranged in five categories substituted cyclopropane sets, cyclopropylidene sets, trans-cyc o-propylene sets, cis-cyclopropylene sets, and reactions of cyclopropane rings. The correlation of data for cyclopropanes with the Hammett equation (19) and the extended Hammett equation (215) has been reported by Charton. 

In the application of the extended Hammett equation to the system XGY, where X is a substituent and Y is a reaction site, both of which are attached to the skeletal group G, the question of the degree of transmission of substituent effects through G arises. The transmitivity of G is measured by the magnitude of a and (3. Now,... 

A slightly different procedure for carrying out multiple regression on cr/ and og-type parameters employs the extended Hammett equation of Charton95, which may be written as in equation 9. For the substituent X, Q is the absolute value of the property to be correlated (logfc or logX in the case of reactivity), i.e. not expressed relative to X = H, h is introduced as the appropriate intercept term, and the regression coefficients are a and fi. (Charton has used various symbols at various times.)... 

The most fruitful treatment of the electronic effects of ozt/zo-substituents involves the use of the same cr/ and correlation analysis for meta- and para-substituents by means of the dual substituent-parameter equation 91 or the extended Hammett equation 95 (Section II.B). Obviously it is a considerable assumption that these are valid for ort/zo-substituents and the implication is that in the correlation analysis any peculiarities may be adequately expressed through the coefficients of the inductive and resonance terms. Really satisfactory correlation analysis for any given reaction system requires a large amount of data and can only rarely be accomplished. 

Some further light on the behaviour of the nitro group as an orf/ o-subsliUicnl in affecting the strength of benzoic acid can be obtained by correlation analysis employing the extended Hammett equation (Section n.B) in the form of equation 14 ... 

The correlation analysis employed the extended Hammett equation in the form of equation 17 ... 

The symbols were defined in Section IV.B.) A full discussion of the ortfio-effect as revealed in this work would be inappropriate here. We must restrict ourselves to the more limited task of indicating the role of o-N02. We discuss first the work involving alcohols as solvents. To apply the extended Hammett equation, i.e. to determine the regression coefficients a, fi and

intercept term h, it is first necessary to select a set of substituents which can be expected to be well-behaved . Particular problems for or and v may be caused by conformational effects, and internal hydrogen-bonding may occur... 

Kinetic data for the reactions of diazodiphenylmethane in 10 different alcohols with 2-(4-phenyl substituted)cyclohex-l-enylcarboxylic acids (75) were correlated using the extended Hammett equation.68 Reaction of the species (76)-(78) with the light radioactive H isotope, the muonium atom, has been studied.69 The largest primary kinetic isotope effects ever reported (ca 850) are seen in this work for the addition of muonium to one of the C=0 groups. 

A slightly different procedure for carrying out multiple regression on 07 and op-type parameters employs the extended Hammett equation of Charton34, which may be written as in equation 9. 

In a review article on substituent effects in non-aromatic unsaturated systems. Charton101 treats many systems by means of his extended Hammett equation (Section B.B). There is much information on the transmission of the inductive and resonance components of substituent effects through C=C. 

Finally, we should mention a review article,425 some of whose content is already of historical interest and which will be increasingly of such interest as the years go by, since it will effectively summarize the state of the art of an important topic at the time it was written. This is an account by Tsuno and Fujio of the applications of the Yukawa-Tsuno equation (an extended Hammett equation originating in 1959) to car-bocationic systems. The article has about 120 pages and more than 200 references. 

Charton 152) has successfully applied the extended Hammett equation to these data and discussed the macroconstant, pA , in terms of the tautomerism... 

Charton (J52) has also applied the extended Hammett equation to the oxidation-reduction potentials of 5-substituted phenanthroline complexes of iron in various acidic media (95, 97, 651) and of bis-5- and 4,7-substituted phenanthroline complexes of copper in 50% dioxane (404). Thus, one should expect an overall similarity between the variations in pAa, stability constant, and oxidation-reduction potential data for the various ligands. The variations in a and )3 values found for various substitution positions and the tautomerism in the LH+ ions show that the correlation need not be good. A similar point may also be made about the comparison of data for the transoid bipyridylium ions and their cis complexes. Plots of A versus pA for various systems (95, 404) show a linear dependence to differing extents. As would be expected, the data for analogous complexes of iron (28), ruthenium (214, 217, 531), and osmium (111, 218, 220) show very good correlation. The assumption (152) that the effects of substituents are additive is borne out by these potential data, where the changes in potential on methyl substitution are additive (97). 

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