Carbocations stability trend

Use the carbocation stability trend to decide which of the following two alternatives is the lower-energy process. 

One of the most important and general trends in organic chemistry is the increase in carbocation stability with additional alkyl substitution. This stability relationship is fundamental to imderstanding many aspects of reactivity, especially of nucleophilic... 

This behavior is exceptional. Nevertheless, the assumption that pAR and p AR measure equivalent trends in carbocation stability needs to be treated with caution. Richard and coworkers measured values of pAR to assess the influence of (3-fluoro substituents on the stability of the a-methyl /)-mcUioxybcn/yi cation 58 (R = Me). As indicated in Scheme 29, replacement of an a-methyl by an a-trifluoromethyl group decreases the stability of the carbocation by 7 powers of 10 in AR. 221... 

Since fluorine is the most electronegative element, it should inductively destabilize carbocations. The stability of fluoromethyl cations in the gas phase decreases in the order CFH2+ > CF2H+ > CF3+ > CH3+. The trend in solution, however, could be different, due to solvent effects, ion pairing, and so on. Indeed, fluorine has been shown to provide stabilization for carbocations. The existence of CH3CF2+, in contrast to the elusive ethyl cation CH3CH2+, is a clear evidence that replacement of H atoms by F atoms provides stabilization for carbocations.524 Furthermore, it was found that in perfluorobenzyl cation C6F5CF2+ fluorine atoms in resonance positions (ortho and para) are more deshielded than those in meta positions.536 This indicates carbocation stabilization by back-donation. 

In addition to the linear free energy studies discussed, there have been many attempts to estimate the thermodynamic stabilities of electrophilic species, such as carbocations.7 The pKr+ values for carbocations reveal trends in relative stability and is defined as, according to the equilibrium established between the carbinol... 

This trend is exactly opposite to that observed for the Spj2 mechanism. To explain this result, we must examine the rate-determining step, the formation of the carbocation, and learn about the effect of alkyl groups on carbocation stability. 

A second explanation for the observed trend in carbocation stability is based on orbital overlap. A 3° carbocation is more stable than a 2°, 1°, or methyl carbocation because the positive charge is delocalized over more than one atom. 

We make comparisons based on these data in very broad terms. Looking first at protonation, represented in Figure 5.7 by circles, we see that reactivity rises sharply with substitution from ethene to propene to 2-methylpropene, but 2-methyl-2-butene and 2,3-dimethyl-2-butene have rates roughly similar to 2-methylpropene. The degree of substitution at the more-substituted carbon is the major factor in reactivity. We can surmise from this trend that carbocation stability is the major factor in determining the protonation rates. Note also that styrene is more reactive than propene, again consistent with carbocation stability as the major influence on reactivity. In terms of the Hammond postulate, the carbocation is a good model of the TS because the protonation step is substantially endothermic and the TS is late. 

One of the most important and general trends in organic chemistry is the increase in carbocation stability with additional alkyl substitution. This stability relationship is fundamental to understanding many aspects of reactivity, especially of nucleophilic substitution. In recent years, it has become possible to put the stabilization effect on a quantitative basis. One approach has been gas phase measurements which determine the proton affinity of alkenes leading to carbocation formation. From these data, the hydride affinity of the carbocation can be obtained. 

HIA values reflect differences in the energies of the initial and final systems under analysis, not just carbocation stabilities (see Section 2.2.2 for similar reasoning related to radicals), However, in the case of HIAs, factors other than cation stability are not as influential as with radicals and carbanions (see below), and therefore the HIA values track very nicely carbocation stability. This is in part because the differences between the HIA values for various cations are much larger than the differences between BDEs for various bonds, and thus the HIA trends are less sensitive to other factors. 

Perhaps the most classic example of hyperconjugation, certainly invoked in all introductory organic textbooks, is the trend in stabilities observed for substituted carbocations (see Carbocation Stabilities Comparison of Theory and Experiment). Thus, as illustrated in Figure 1, the ethyl cation (a primary carbocation) is more stable than the methyl cation because a electrons associated with C-H bonds in the attached methyl group may delocalize into the empty p orbital on the cationic center. In the limit of complete delocalization, the C-H bond is broken and the pair of electrons that formerly gave rise to it is instead employed in the formation of a rr bond between the formerly cationic carbon and the former methyl carbon. Such a resonance structure (mesomer) is called a bond/no-bond structure in recognition of the detached status of the proton whose bonding electrons have been redistributed within the carbon framework. 

In SnI reactions, the stability of the carbocation is the paramount issue. Recall that alkyl groups are electron donating. Therefore, 3° is best because the three alkyl groups stabilize the carbocation. 1° is the worst because there is only one alkyl group to stabilize the carbocation. This has nothing to do with sterics this is an argument of electronics (stability of charge). So we have two opposite trends, for completely different reasons ... 

For now, let s consider the effect of the substrate on the rate of an El process. The rate is fonnd to be very sensitive to the nature of the starting aUcyl halide, with tertiary halides reacting more readily than secondary halides and primary halides generally do not nndergo El reactions. This trend is identical to the trend we saw for SnI reactions, and the reason for the trend is the same as well. Specihcally, the rate-determining step of the mechanism involves formation of a carbocation intermediate, so the rate of the reaction will be dependent on the stability of the carbocation (recall that tertiary carbocations are more stable than secondary carbocations). 

The activation energies for the fragmentation of the carbene in CH2C12 were calculated by the B3LYP/6-31G method to be 14.6, 2.2, and —0.95 for the bicyclo[2.2.1]heptyl, bicyclo[2.2.2]octyl, and adamantyl systems, respectively. Are the product trends consistent with these computational results, which presumably reflect the relative stability of the carbocation formed by the fragmentation ... 

Figure 6.10 Electrostatic potential maps for (a) tert-butyl (3°), (b) isopropyl (2°), (c) ethyl (1°), and (d) methyl carbocations show the trend from greater to lesser delocalization (stabilization) of the positive charge. (The structures are mapped on the same scale of electrostatic potential to allow direct comparison.)...

The relative stabilities of radicals follow the same trend as for carhoca-tions. Like carbocations, radicals are electron deficient, and are stabilized by hyperconjugation. Therefore, the most substituted radical is most stable. For example, a 3° alkyl radical is more stable than a 2° alkyl radical, which in turn is more stable than a 1° alkyl radical. Allyl and benzyl radicals are more stable than alkyl radicals, because their unpaired electrons are delocalized. Electron delocalization increases the stability of a molecule. The more stable a radical, the faster it can be formed. Therefore, a hydrogen atom, bonded to either an allylic carbon or a benzylic carbon, is substituted more selectively in the halogenation reaction. The percentage substitution at allylic and benzyhc carbons is greater in the case of bromination than in the case of chlorination, because a bromine radical is more selective. 

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