Jaffe equation

The relative effectiveness of the two transmission routes in systems such as those discussed in structures 5 to 9 can be determined by use of the Jaffe Equation (6). 

The intramolecular acid-catalysed hydrolysis (Equation 7) provides a good example of the application of the Jaffe equation. 

Figure 2 Graphical analysis of Jaffe equation by use of Equation (8)...

Although the advent of high-speed computers has enabled data to be directly fitted to the Jaffe Equation, the results cannot be directly illustrated. Instead the results for p and pg are determined statistically and the goodness of fit is demonstrated graphically by plotting (observed) against its calculated value (PaCTa + Pb b) (Figure 3). 

Al.1.4.2 Bilinear Equation. This equation is used, for example, to fit the Jaffe equation - Chapter 4. 

Figure 5 Fz Z of data to Jaffe equation using the rearranged equation and linear fit...

The values obey the Jaffe equation employing Hammett a parameters for the 4-nitro substituents (Figure 7) ... 

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. ... 

The ultraviolet spectra of the pyridinecarboxylic acids (334) were initially interpreted assuming that the proportion of the zwitterion structure 335 was not appreciable,and the early pK work was inconclusive. However, Jaffe s calculations based on the Hammett equation indicated that about 95% of nicotinic and isonicotinic acids existed in the zwitterion form, and ultraviolet spectral data showed that the actual percentages of picolinic, nicotinic, and isonieotinie acids existing in the zwitterion form in aqueous solution are 94, 91, and 96%, respectively.This was later confirmed by Stephenson and Sponer, who further demonstrated that the proportion of the zwitterion form decreases in solvents of low dielectric constant, becoming very low in ethanol. Dipole moment data indicate that isonicotinic acid exists as such in dioxane, and 6-hydroxypyridine-3-carboxyiic acid has been shown to exist in form 336 u.sing pK data. ... 

The only reaction series involving a reaction at a heteroatom which has been extensively studied is the basicity of substituted pyridines. The Hammett equation was first applied to this reaction simultaneously by Brown and co-workers and by Jaffe and Doak. A sampling... 

The third volume of this series covers three specific groups of compounds the carbolines (reviewed by R. A. Abramovitch and I. D. Spenser), the thiatriazoles (K. A. Jensen and C. Pedersen), and the pentazoles (I. Ugi). The remaining four chapters deal with topics of general chemical interest from the heterocyclic viewpoint the quaternization of heterocyclics (G. F. Duffin), carbene reactions (C. W. Rees and C. E. Smithen), applications of the Hammett equation (H. H. Jaffe and H. Lloyd Jones), and some aspects of the nucleophilic substitution of heterocyclic azines (G. Rluminati). 

Jaffe (1953)52 showed that while many rate or equilibrium data conform well to the Hammett equation (as indicated by the correlation coefficient), many such data are outside the scope of the equation in its original form and mode of application. Deviations are commonly shown by para-substituents with considerable + Rot — R effect53. Hammett himself found that p-NOz (+ R) showed deviations in the correlation of reactions of anilines or phenols. The deviations were systematic in that a a value of ca. 1.27 seemed to apply, compared with 0.78 based on the ionization of p-nitrobenzoic acid. Other examples were soon discovered and it became conventional to treat them similarly in terms of a duality of substituent constants . 

Like all chemical equations, this one has an equilibrium constant. The discussion of basic chemistry is outside the purview of this book. Readers who may need a refresher are referred to Tse and Jaffe (1991). For every chemical, a pKa can be calculated, based on its equilibrium constant, which represents the proportion of ionized and unionized material in solution. The lower the pKa of a chemical, the more likely it is to be nonionized in the stomach. 

While it has been known for some time that pyridine-1-oxides are protonated on oxygen (Gardner and Katritzky, 1957), amino-pyridine-1-oxides have attracted more attention recently. Using the Hammett equation, it was concluded that the cation of 3-amino-pyridine-1-oxide was an equilibrium mixture of O- and N-protonated forms in the ratio 8 1 (Jaffe, 1965), A similar conclusion was reached for 3-dimethylaminopyridine-l-oxide (Forsythe et al.,... 

Now it should be recalled that the first ionization energy and the electron affinity are merely two of the multiple ionization potential-electron affimiy energies that fit a polynomial equation (see Chapter 2) that is quite close to being quadratic (the coefficients uf the higher order terms are small). Jaffe and coworkers have pointed out... 

It is now 13 years since the appearance of Volume 1 of Advances in Heterocyclic Chemistry, and significant progress in many of the subjects covered in the early volumes of the series has been made since publication. We have therefore embarked on the policy of updating appropriate chapters, and three of the articles in the present volume are of this type. Adrien Albert has written an account of the progress of covalent hydration since its first appearance in Volume 4. P. Tomasik and C. D. Johnson have reported on progress in the application of the Hammett equation to heterocycles since the Jaffe and Lloyd Jones article in Volume 3, and A. Holm has similarly taken on the account of 1,2,3,4-thiatriazoles given by Jensen and Pedersen in the same volume. 

H. H. Jaffe (1919-1989)297 was professor of chemistry at the University of Cincinnati. His research interests were quantum chemistry, the basicity of weak bases, spectroscopy, excited state chemistry, and the Hammett equation, of which he wrote a comprehensive review article in 1953.298 At one time, according to Science Citation Index, this was the most cited article in the chemical literature. 

The problem of the application of the Hammett equation to the electronic transmission of substituent effects through five-membered rings has recently been discussed by Jaffe and Jones.279... 

Applications of the Hammett Equation to Heterocyclic Compounds H. H. Jaffe and H. Lloyd Jones... 

In these equations the ionization potential corresponds to the valence state. For atoms contributing one electron to the jr-system, the values Ip are given6 by Hinze and Jaffe (1962). On the other hand, for atoms contributing two electrons, it has been shown by Hinze and Jaffe (1962) that the corresponding It may be calculated from the ionization potentials for the ground state and the promotion energies P for the cation and the neutral atom,... 

Evaluation of steric effects can also be made by separating electronic from steric effects with the help of linear free energy relationship and appropriate parameters. Applications of the Hammett equation to heterocycles have been reviewed (64AHC(3)209 76AHC(20)1) and the influence of substituent effects on the basicity and N-alkylation of pyridines, which have been by far the most widely studied, shows the difficulties in this approach. Jaffe and Jones (64AHC(3)209) reported a good correlation between pKA of 3- and 4-substituted pyridines and Hammett a parameters ([Pg.179]

This is known as the Jaffe series [117]. The important recurrence relations (6.468) can be represented by the matrix eigenvalue equation [118]... 

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