Carbocations rate-equilibrium correlations

Figure 1.3. Rate-equilibrium correlation for hydration of carbocations triarylmethyl and 9-aryl-9-fluorenyl ( and , respectively, slope =—0.60) diarylmethyl (A, —0.54) aryltropylium (O, —0.68) 9-xanthylium and cyclic phenyldialkoxycarbocations ( and A, respectively, slope = —0.63).

The rate constants for the solvent-recombination process of the carbocations [3C (X,Y,Z)] were determined by the use of the azide clock method (Richard etal., 1984 Richard and Jencks, 1984a,b,c McClelland et al., 1991) and the rate constant of the forward reaction was derived using (38b) as /Ch = /CwXr+ (McClelland et al., 1989,1991). While ordinary Hammett-type relationships were found to be inapplicable to the substituent effects on solvent recombination, there is a rate-equilibrium correlation for all available data on triarylmethyl cations, shown as the linear log/c , vs. p/Cr<- plot, in Fig. 34 with a slope of 0.64. Such a relationship was earlier suggested by Arnett and Hofelich (1983) and Ritchie (1986). The correlation of ky, with the cr scale was... 

Fig. 5 Logarithmic plots of rate-equilibrium data for the formation and reaction of ring-substituted 1-phenylethyl carbocations X-[6+] in 50/50 (v/v) trifluoroethanol/water at 25°C (data from Table 2). Correlation of first-order rate constants hoh for the addition of water to X-[6+] (Y) and second-order rate constants ( h)so1v for the microscopic reverse specific-acid-catalyzed cleavage of X-[6]-OH to form X-[6+] ( ) with the equilibrium constants KR for nucleophilic addition of water to X-[6+]. Correlation of first-order rate constants kp for deprotonation of X-[6+] ( ) and second-order rate constants ( hW for the microscopic reverse protonation of X-[7] by hydronium ion ( ) with the equilibrium constants Xaik for deprotonation of X-[6+]. The points at which equal rate constants are observed for reaction in the forward and reverse directions (log ATeq = 0) are indicated by arrows.

A similar picture holds for other nucleophiles. As a consequence, there might seem little hope for a nucleophile-based reactivity relationship. Indeed this has been implicitly recognized in the popularity of Pearson s concept of hard and soft acids and bases, which provides a qualitative rationalization of, for example, the similar orders of reactivities of halide ions as both nucleophiles and leaving groups in (Sn2) substitution reactions, without attempting a quantitative analysis. Surprisingly, however, despite the failure of rate-equilibrium relationships, correlations between reactivities of nucleophiles, that is, comparisons of rates of reactions for one carbocation with those of another, are strikingly successful. In other words, correlations exist between rate constants and rate constants where correlations between rate and equilibrium constants fail. 

Although the value of the coefficient 1.16 in (20) does not have as direct a physical significance as the a-exponent in the extended Brpnsted equation (19) because the reaction, solvents and temperature are different, there is still a good linear rate-equilibrium relationship for benzhydryl carbocation formation the overall correlation embraces clearly concave partial correlations with varying slopes for the respective Y series. The whole pattern of substituent effects, pXr vs should be essentially identical (with only the ordinate scale being slightly different) to that of log (/ xy/Z hh) vs 2 a for the solvolyses shown in Fig. 8. 

Ritchie, 1986 McClelland et al., 1989, 1991) for a wide set of triarylmethyl cations, and that there is a reasonably linear correlation encompassing the entire set of triarylmethyl carbocations over 16 p/Cr+ units with a small amount of scatter (Fig. 34). The implication of this behaviour is that despite a change in the cation stability, there is a little change in the apparent position of the transition state, at least as revealed in this rate-equilibrium relationship. 

The starting point for most discussions of reactivity is a correlation of rate and equilibrium constants. One such correlation is shown in Fig. 1 of this chapter. It applies not to reactions of the carbocation with water as a nucleophile but to water acting as base, that is, the removal of a [3-proton from the carbocation to form an alkene or aromatic product. We will consider this reaction below, but here note that for most of the carbocations in Fig. 1 values of kH2o> the rate constants for reaction of the carbocation with water as a nucleophile are also available.25... 

In estimating these barriers Richard addresses a problem that so far has been avoided. When discussing the correlation of log h2o with pATR in Fig. 3, it was implied that the rate and equilibrium constants refer to the same reaction step. That is not strictly true, because attack of water on a carbocation yields initially a protonated alcohol which subsequently loses a proton in a rapid equilibrium step. As we are reminded in Equation (26) the equilibrium constant AR refers to the combination of these two steps. To calculate an intrinsic barrier for reaction of the carbocation with water therefore the equilibrium constant KR should be corrected for the lack of stoichiometric protonation of the alcohol. Fortunately, there have been enough measurements of pA,s of protonated alcohols240 (e.g. pAa = -2.05 for CthOHi1") for the required corrections to be made readily. 

Reactions of carbocations with water as a base removing a [3-proton to form an alkene or aromatic product have been less studied than nucleophilic reactions with water. Nevertheless, the correlations included in Fig. 1 (p. 43) represent a considerable range of measurements and these can be further extended to include loss of a proton a to a carbonyl group.116 Indeed, if one places these reactions in the wider context of proton transfers, it can be claimed that they constitute the largest of all groups of reactions for which correlations of rate and equilibrium constants have been studied.116,244,245... 

It is not intended to pursue this discussion to a firmer conclusion. However, it is reasonable to infer that our understanding of reactivity and selectivity in carbocations has been brought to a point where the origins of differences in reactivities of hard and soft nucleophiles and of lack of correlation of rate and equilibrium constants have been greatly clarified. Particularly, in the hands of... 

On the basis of these considerations it has been concluded that under given reaction conditions (Lewis acid/solvent) the reactivity maximum is found for an alkylating system (RA7R+) that is approximately half-ionized [60,61]. Scheme 11 suggests that the electrophilic reactivity of RA" increases with increasing stabilization of R+ if only small equilibrium concentrations of carbocations are involved. In accord with this analysis, the relative alkylating abilities of alkyl chlorides have been found to be proportional to their ethanolysis rates (Fig. 2) [62]. The only compound that deviates from this correlation is trityl chloride which alkylates considerably more slowly than expected from its solvolysis rate. 

The correlation with suggests that the equilibrium population of the benzylic carbocation (23) is enhanced by a substituent X that can stabilize the carbocation through a resonance interaction. The correlation with o-y suggests that substituent Y has a much weaker effect. This result is not compatible with an alternative mechanism involving rate-limiting formation of a bridged cationic intermediate such as 24, since in that case the X and Y substituents would be expected to have a similar effect on cation stability. ... 

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