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What is the maximum extent of a hydride shift to form the most stable carbocation?

If we consider the reaction between 2-methylpropan-1-ol and $\ce{HBr}$, then of course, the carbocation formed after a hydride shift will be more stable (and lead to the major product). 3-methylbutan-1-ol will also undergo hydride shift to some extent to form the more stable carbocation, but is there a limit to it?

Like can the number of carbons be so much that there is almost no chance to make the product with hydride shift possible? Like consider the scenario below:

What can be the maximum $n$ possible here to make the product with hydride shift possible?

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Advances in Physical Organic Chemistry, volume 19, discusses the relative transition state barriers for 1,2-, 1,3-,1-4-, and 1,5-hydride shifts.

The specific cations considered are 2,3 dimethyl-2-butyl, 2,4 dimethyl-2-pentyl, 2,5 dimethyl-2-hexyl and 2,5 dimethyl-2-heptyl.

Interestingly, they report that whereas the barrier for 1,4 shift in 2,5 dimethyl-2-hexyl is 12 kcal/mole, this decreases dramatically to less than 6 kcal/mole for 1,5 shift in 2,6 dimethyl-2-heptyl

The reference draws the transition states as rings, with the H being transferred as a bridging member of the ring, a five membered ring for the 1,4 shift and a six member ring for the 1,5 shift.

The reference also makes a comparison to intermolecular hydride shift between isobutane and t-butyl cation, which has a barrier of 3.6 kcal/mole.

While the reference does not discuss the possibility of longer distance than 1,5 shifts, it seems that because the ends of a long ion can meet each other, long distance (in terms of number of bonds) shifts are possible because through space the distance is short.

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  • $\begingroup$ There could be multiple 1,2 shifts as well, as long as it is downhill or close to thermoneutral, right? $\endgroup$
    – ron
    Feb 5, 2015 at 1:53
  • $\begingroup$ Yes, like this butane.chem.uiuc.edu/jsmoore/chem232/notes_current/… $\endgroup$
    – DavePhD
    Feb 5, 2015 at 2:14
  • $\begingroup$ I don't know whether I should accept this answer. I think it is a partial answer, but I also think that it is the best answer one could come up with. What should I do? $\endgroup$
    – Rohinb97
    Feb 6, 2015 at 18:02
  • $\begingroup$ And by the way, the link you have just given says that the shifted hydride doesn't directly travel to the carbon, it goes step by step. So the main reason that there must be a limit is that if the carbon chain is too long or the barrier energy is very less. But can it be too drastic that the probability of its formation is nearly zero? $\endgroup$
    – Rohinb97
    Feb 6, 2015 at 18:04
  • $\begingroup$ Yes, the link in the comment says it "usually" doesn't occur in the way the Advances in Physical Organic Chemistry review article is describing. Advances in Physical Organic Chemistry draws the transition state as the ends of the molecule approaching each other to form a ring. Somebody could definitely write a better answer, going through the literature trying to determine to what extent the one transition state mechanism occurs vs. the step by step mechanism. I personally think as distance increases the one-step mechanism would be increasingly favored. $\endgroup$
    – DavePhD
    Feb 6, 2015 at 18:25

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