Hammett-Brown equation

For the tautomeric equilibria of perhydro-l,3-oxazines and their benzo derivatives bearing an X-substituted phenyl group at position 2, the proportion of the ring-closed forms has been found to be strongly dependent on the electronic character of the substituent X on the phenyl ring. For these compounds, a linear correlation (Equation 1) has been found between the log values of the equilibria (Xx= [ring]/[chain]) and the Hammett-Brown parameters of the substituents X on the 2-aryl group ... 

When r) values are plotted against the g values, Hammett s equation is satisfied for all the substituents except for bromine and iodine, as shown in Figure 12.2. The p value is 4.8, which is within the range of p values reported for a variety of substituted reactions such as nitration, bromination, and hydrolysis (Stock and Brown, 1956). Therefore, Hammett s equation for substituted benzenes reaction with e can be expressed as ... 

B. Application of the Hammett-Brown- Taft Equation to Hydrogen... 

For the quantitative treatment of substituent effects in such reactions, Brown proposed (Brown and Okamoto, 1957) a new Hammett-type structure-reactivity relationship, the Brown equation (1), in terms of substituent constant instead of a in the original Hammett equation. 

Oxazolidines are subject to ring-chain tautomerism. A variety of substituted oxazolidines in the solid state exist in the chain form, based on C NMR experiments <85X5919,92X4979). In solution, the two forms are in equilibrium, the position of which depends on the solvent and the substituents. Oxazolidines prepared from meta- and para-substituted benzaldehydes and 2-amino-2-methyl-propanol, norephedrine, norpseudoephedrine, and serine esters all give good linear plots for the equation log -l-log Ax=h where a are the Hammett-Brown values <93X6701,93JOC1967). 

Attempts to relate the efficiency of inhibition with the Hammett— Taft equation were soon abandoned in favour of more accurate correlations with Brown s electrophilic substituent constants, o+, as given by [43]... 

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. 

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... 

Values of a l were calculated from thepKa of 4-substituted-[2.2.2]bicy-clooctane-1-carboxylic acids in 50% w/w ethanol-water at 25 by setting in Equation 41 equal to every odd value in the range 1.45 to 1.67. This range was chosen to include all of the choices of L, which had been made previously from the value of 1.464 used by Roberts and Moreland to the value of 1.65 used by Hansch et al. The corresponding o d values were obtained by means of Equation 42, using the Op values of McDaniel and Brown (28). The a and a o values are given in Table 1. The pKa values reported by Thuaire (30) for 4-substituted benzoic acids in ethanol-water mixtures and in ethanol (Table 2) were correlated with the 12 sets of and a n values obtained above by means of the extended Hammett equation. Also studied were pKa values for 4-substituted benzoic adds in ethanol-water mixtures determined by Wepster (31). The substituents studied are set 7 H, Me, Et, OH, OMe, Cl, Br, NO2, CF3, C02Me Set 8 = Set 7, less CF3 Set 6 = Set 8 less Br. 

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