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How will the cyclobutane ring behave in the case of cyclobutylmethylium (cyclobutylmethyl cation)?

enter image description here

I initially thought there would be ring expansion to a five membered ring so that there may be less angle strain and a secondary carbocation instead of a primary one. But I have also been told that there will be ring contraction for stability purposes. I would be highly obliged if someone could explain the mechanism involved here.

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I think your friend is thinking of the cyclobutyl carbocation which does ring contract to the cycylopropyl carbinyl carbocation (and also equilibrates with the methallyl carbocation).

However, just as you thought, the cyclobutyl carbinyl carbocation does ring open to the cyclopentyl carbocation (ref_1, ref_2, ref_3). This rearrangement is driven by carbocation stability (primary to secondary) and relief of the steric strain present in the 4-membered ring, again, just as you suggested.

enter image description here

Note: this question has been asked previously on SE Chem, however I believe the accepted answer is incorrect, as it seems to primarily address the cyclopropyl carbinyl case, and what is said about the cyclobutyl carbinyl carbocation (little to no ring expansion) is incorrect.

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  • $\begingroup$ What would you think is more stable from the species $\ce{C4H7+}$, the cyclopropylmethylium (that you drew) or the methylcyclopropan-1-ylium? I tend to think the latter, but I am absolutely not certain. $\endgroup$ – Martin - マーチン Apr 30 '15 at 6:51
  • $\begingroup$ @Martin Good question, the cyclopropylmethylium is primary and resonance stabilized, while the 1-ylium is tertiary with a bit more ring strain. I'd vote for the former, but I dunno. Somebody must have done a good calculation. $\endgroup$ – ron Apr 30 '15 at 12:59
  • $\begingroup$ @ron in general, there's probably some level of delocalized charge between both carbons. $\endgroup$ – Geoff Hutchison Apr 30 '15 at 16:00
  • $\begingroup$ @GeoffHutchison How would you describe the delocalization in the methylcyclopropan-1-ylium case? $\endgroup$ – ron Apr 30 '15 at 17:47
  • $\begingroup$ The point would be that under QM, in either case, the charge will not wholly be on one carbon. That said, I ran a high-level CCSD calculation and it's pretty localized on the primary (as you drew): i.imgur.com/MhTrSzu.png $\endgroup$ – Geoff Hutchison Apr 30 '15 at 18:05
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In concluding Remarks of their work on the structural study of the 2-norbornyl cation, Olah and coworkers (Ref.1) stated that:

More importantly, rather than being rare, two-electron, three (or multi)-center bonding is characteristic of electron-deficient molecules, including nonclassical carbocations.

Later, they found computational evidence for the existence of nonclassical cyclobutylmethyl cation (Ref.2). According to the part of abstract in the Ref.2:

Ab initio calculations at the MP2/cc-pVTZ level show that the cyclobutylmethyl cation is a nonclassical σ-delocalized species, which is distinct from the global minimum $C_2$-symmetric cyclopentyl cation...

Nonclassical cyclobutylmethyl cation

However, in reality, they failed to achieve persistent ((long-lived) classical or nonclassical cyclobutylmethyl carbocation, even at lower than $\pu{-80 ^\circ C}$ (Ref.3). Nonetheless, just as you thought, the cyclobutyl carbinyl carbocation readily undergoes ring expansion-rearrangement to give the corresponding cyclopentyl cations (See B (i) in the scheme; NMR evidence are provided in the reference). During the extended study, the authors studied (2-methylcyclobutyl)methanol derivative in superacidic medium and, suggested a mechanism depicted in the following scheme (part A), which clearly shows the reaction goes through nonclassical carbocation:

Mechanism - cyclobutylmethyl cations

Moreover, cyclobutylmethanol took a different path under superacidic conditions, undergoing dimerization followed by rearrangement when warm a little bit. Mechanism C has been suggested to explan the outcome. All these evidence suggest that the chemical behavior of cycloalkanes depends on the ring size and the nature of the reagents used.

References:

  1. G. A. Olah, G. K. Surya Prakash, Martin Saunders, “Conclusion of the Classical-Nonclassical Ion Controversy Based on the Structural Study of the 2-Norbornyl Cation,” Acc. Chem. Res. 1983, 16(12), 440–448 (https://doi.org/10.1021/ar00096a003).
  2. V. Prakash Reddy, G. Rasul, G. K. Surya Prakash, G. A. Olah, “Structural Studies of Nonclassical Cyclobutylmethyl Cations by the ab initio Method,” J. Org. Chem. 2007, 72(8), 3076–3080 (https://doi.org/10.1021/jo0701334).
  3. G. K. Surya Prakash, V. Prakash Reddy, G. Rasul, J. Casanova, G. A. Olah, “The Search for Persistent Cyclobutylmethyl Cations in Superacidic Media and Observation of the Cyclobutyldicyclopropylmethyl Cation,” J. Am. Chem. Soc. 1998, 120(51), 13362–13365 (https://doi.org/10.1021/ja9828962).
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