Hammett correlation curved

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... 

In some cases curved or bent Hammett correlation plots are found. These situations can arise when a reaction mechanism involves more than one step, either of which can be rate-limiting under certain conditions, or when different mechanisms may occur, depending on substituents. In such cases, changing a substituent can change the step that is rate-limiting or can change... 

Sometimes correlations of kinetic results with Hammett a constants present difficulties. Reactions (a), (d) and (i) of Table 8 give curved plots, all with the concavity upwards, independently of the signs of the average slopes. For reaction (d), however, it has been shown that a linear plot can be obtained using a (T scale, based on ionisation of phenols in various solvents adopting the new abscissa, the p value is lowered to something between 0.2 and 0.3. 

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