Hydride Ion Affinities as a Measure of Stability

A common and very valuable measure of gas phase carbocation stability is the hydride ion affinity (HI A), defined as AH° for the reaction in Eq. 2.15. This is simply the heterolytic analogue of the homolytic cleavage associated with the bond dissociation energy (BDE) just discussed. Just as a larger BDE implies a less stable radical, a larger HIA implies a less stable carbocation. And, just as with the BDE, the usefulness of the HIA is that it provides a number that can be compared directly for cations of dissimilar structure. This is less true of other measures of cation stability. 

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. 

We did not have to worry greatly about this issue in our discussion of free radical stabilities in the gas phase. A neutral free radical in the gas phase is not desperate for solvation like an ion is. As such, adding spectator carbons to a free radical does not alter its stability significantly. 

Gas Phase Hydride Ion Affinities (HIA, in kcal/mol) for Selected Carbocations (in kcal/mol)  

Taking the carbon number into effect, we find that 2° ions are indeed more stable than 1° ions by 18-20 kcal / mol, and 3° ions are more stable than 2° ions by about 17 kcal/ mol. These are very large numbers—significantly larger than analogous comparisons for radicals. We will see in Chapter 11 that experimental differences for reactions in solution that are considered to involve carbocations are nowhere near this large. For reasons discussed in Chapter 3, solvation always attenuates ionic effects, so the gas phase data always represent the absolute maximum any ionic effect can show. 

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