Hammett correlation with maximum

Dorn and Knackmuss et al. (1978) correlated the maximum reaction rate for ring scission of a series of substituted catechols with Hammett s a value... 

From the nature of the salt effects, it has been argued that the rates for acidities less than that for the maximum rate correlate with the Hammett acidity function Aq. The decrease in rate above this acidity is quite gradual, but the rate law is then approximately represented by... 

Park and Cho108 have found that the first hyperpolarizabilities of 1,3,5-tricyano-2,4,6-tris(styryl)benzene derivatives attain a maximum value of 262 x 10-30 esu when an oxyanion is used as donor. A correlation with the Hammett constants is explored. 

The calculated energy differences give a good correlation with Hammett ct+ values. The p parameter (p = -17) is considerably larger than that observed experimentally for proton exchange (p -8). A physical interpretation of this difference is that the computational results pertain to the gas phase, where substituents are at a maximum because of the absence of any leveling effect owing to solvation. Note that the numerical results parallel the conclusions from qualitative application of resonance... 

Pd°(dba)2 + nP(p-Z-CgH4)3 mixtures behave as for PPh3 (Scheme The values of the equilibrium constants (Eq. 4 of Scheme 3) have been determined as a function of the Z substituent. For a given value of n(n> 2), the equilibrium between Pd°(dba)L2 and Pd°L3 lies more in favor of Pd°(dba)L2 when the phosphine is more basic (Hammett correlation for with p = + 4). Similarly, when n = 2, Pd°L2 is less easily released from Pd°(dba)L2 (Eq. 2 of Scheme 3) when the phosphine is more basic. The oxidative addition involves Pd°L2 as the reactive species (Schemae 4), which is more reactive when the phosphine is more basic. Thus, two opposite effects are at hand when the basicity of the phosphine is varied, so that the resulting overall rate constants do not follow linear Hanunett correlations. Instead, bell-shaped curves are obtained whose maximum value and position depend on n, that is, on the phosphine concentration (Figure... 

For the compounds obeying the Hammett equation, the distribution pattern for the OH attack can be estimated by assuming that the position on the ring with the maximum C7 value has the least probability, while the one with the minimum has the greatest probability. In our recent work > on cinnamate derivatives where the addition of the OH radical to the olefmic double bond is an additional pathway, a value of-0.3 was estimated from the Hammett plot (Fig. 5). This value is in agreement with those reported earlier for several substituted benzenes (p" = -0.52 to -0.4). However, the Hammett treatment for reactions with rate constants close to diffusion-controlled ones may not be satisfactory due to limited variation in kinetic data and large experimental uncertainty. In contrast, better correlation is expected in the corresponding gas phase reactions. 

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