Stability comparison between tropylium, cyclopropylmethylium and dicyclopropylmethylium cations

Question

Write the correct stability order of the following compounds:

I don't have any concern with estimating stability of (1), only (2), (3) and (4). Our teacher said that unless the carbocation has three isopropyl groups, it won't be as stable as the quasi-aromatic compound — in this case, the tropylium cation.

My friends claim the isopropylmethylium cation should be more stable than the tropylium cation.

Is there any experimental data saying which one is more stable? How many cyclopropyl rings are needed to “dominate” over a tropylium cation?

Previously, I reviewed the following questions about triisopropylmethylium carbocation:

• Stability Comparison between the Tropylium and Tricyclopropylcarbinyl Carbocation
• Why does cyclopropane react with bromine?

Answer 1

There are quite a few quantitative ways to measure the stability of carbocations (you could have a brief image of them if you look at March's Advanced Organic Chemistry or F.A.Carey's organic chemistry).

In this case, I'll take HIA (Hydrogen Ion affinity) as the criterion. The lower the HIA, the more stable it is.

Data below are from [1] if not mentioned. All of the values are in kcal/mol.

(2)'s HIA is 201, 200, 238 (Last one could be taken as an outlier, as [2] gives a value of 199, consistent with the former two results.)

(3)'s HIA is 241.

I failed to find the exact HIA for (4) in essays, but the HIA for 1,1‐dicyclopropylethylium is 207. Taking the stabilization of an extra methyl into consideration, (4) is less stable than (2). As (4) is obviously more stable than (3), the stability is (2)>(4)>(3).

[1] D.H.Aue and M.T.Bowers, Gas Phase Ion Chemistry, M.T.Bowers, ed., Academic Press, New York, 1979.

[2] Würthwein, E.-U., Lang, G., Schappele, L. H., & Mayr, H. (2002). Rate-Equilibrium Relationships in Hydride Transfer Reactions:  The Role of Intrinsic Barriers. Journal of the American Chemical Society, 124(15), 4084–4092. doi:10.1021/ja0121540