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$\mathrm{S}_{\mathrm{N}}1$ reaction involves only one molecule in the rate determining step. So, the molecule which undergoes $\mathrm{S}_{\mathrm{N}}1$ reaction should be stable when it forms a positive ion. $\ce{(CH3)3C^+}$ is considered stable due to inductive effect from the three carbon atoms and also hyper-conjugation. But, what about bridged compounds like 1-bromobicyclo[2.2.1]heptane:
1-bromobicyclo[2.2.1]heptane

When $\ce{Br^-}$ is abstracted the positive ion formed will be stable and therefore this will undergo $\mathrm{S}_{\mathrm{N}}1$ reaction. Am I thinking right? Please help me correct myself.

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  • $\begingroup$ angle strain prevents this molecule from undergoing $\mathrm{S_N1}$ reaction $\endgroup$ – ShankRam Dec 25 '15 at 14:22
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Very interesting question… I would give two answers, at different levels:

  • At undergrad level, I think the carbenium ion formed at the bridge head is less stabilized that “regular” ternary carbenium ions, because it cannot adopt the planar trigonal geometry which would be ideal for it.
  • At higher level, this is much more complicated: the norboryl cation is an example of non-classical ion
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    $\begingroup$ Bridgeheads carbocations are a violation of Bredt's Rule, which, for the reasons mentioned, are not common. $\endgroup$ – Ben Norris Oct 4 '13 at 13:42
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As already pointed out by previous contributors, 1-bromobicyclo[2.2.1]heptane will not undergo substitution via $S_{N}1$. A fully solvated and relaxed bridgehead cation is unlike to be formed. Whether a short-lived ion pair in a common solvent cage is possible... who knows.

But fortunately, the title compound isn't as dead as it seems: I'm sure I've seen it converted to the corresponding Grignard reagent and then quenched with $\ce{CO2}$.

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If this compound can undergo nucleophilic substitution, it can only be via SN1 fashion, as the reverse side attack in the anti-bonding $\ce{C-Br}$ orbital is blocked by the other bridgehead.

The reason that is often given why bridgehead carbon cations are not stable is strain. Strain itself is a concept that is difficult to grasp and it more often depends on what you choose as a reference system. For the sole qualitative purpose the cation is more strained than a non-constricted tertiary cation.
Another reason that is often given is that the carbocation cannot adopt a trigonal planar structure. While this is technically true, the deviation from an ideal trigonal surrounding is quite small; it's just about 25°. (DF-BP86/def2-SVP)
molecular structure of norbonene cation

I believe the reason for this instability is a bit different. In $\ce{C+(CH3)3}$ the hydrogen carbon bonds can neatly align with the empty p orbital of the central carbon. Hence electron density can be transferred into this orbital or from another point of view, the positive charge can be delocalised into the neighbouring bonds.
empty-occupied overlap in CMe3

The above is just one example configuration calculated at DF-BP86/def2-SVP. It is not the lowest structure, but one chosen for the purpose of showing the overlap in the hyperconjugation. Since the molecule is not rigid at all and the methyl groups rotate, the stabilising effect will be there most of the time, in this conformation it is easiest to see.

That stabilising effect is not present for the carbon hydrogen bonds in proximity to the bridgehead. Those hydrogens actually point away from the cationic centre, hence overlap is not at all possible. Therefore the charge cannot be stabilised by those bonds.
empty-occupied (non)-overlap in norbornane cation C-H to p

However, there is a small stabilising configuration between the carbon-carbon bonds and the unoccupied orbital and this is the reason, why bridgehead carbocations become more stabilized with larger ring structure.
empty-occupied overlap in norbornane cation C-C to p

Like always there are a couple of different points at play, that help stabilise certain positions, or cease to do so.
So with the right motivation, a SN1 reaction might be possible.


Colourcode
Occupied orbitals are displayed in orange and blue, while virtual orbitals are displayed in red and yellow. Phases are chosen randomly.

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Well, t-butyl cation isn't really stabilized by inductive effects only. Interaction of empty $p$ orbital of the central carbon with the $\ce{C-H}$ sigma bonds are really important in that manner. And they are not present in norbornyl cation due to strain.

So: no, it is very unlikely for that compound to undergo an $S_N1$ reaction.

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The bridgehead carbon in the pictured compound is $sp^3$ hybridized. Upon solvolysis of the bromide ion, it should rehybridize to $sp^2$. However, this does not occur because the bridgehead carbon is too strained. Therefore, a bridged compound will not undergo an $S_N1$ mechanism st the bridgehead carbon.

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Few bridge head carbons (1-bromobicyclo[2.2.1]heptane) are observed to give the corresponding alcohols with aqueous $\ce{AgNO3}$ at $150~\mathrm{^\circ C}$, i.e. With $\mathrm{S_N1}$ slowly. It has been suggested that the extra bonds in the larger ring help to relieve the strain in the formation of carbocation which tries to assume a planar configuration. (source: Cengage organic chemistry, by K.S. Verma)

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