Carbocation Stability on Fused Rings

[pzona]

So I just had a question on a quiz (did not go well) about carbocation stability on the fused rings bicyclo[2.2.1]heptane, with the positive charge on a bridgehead carbon and 2-methylbicyclo[2.2.1]heptane with the positive charge on C2. The question was which is more stable and why?

The question stated that the second option is far more stable, but I have little to no idea why. Both are tertiary carbons, so that doesn't factor in. I answered that the first option was more symmetrical, so will be less likely to deprotonate at the bridgehead, but in retrospect this doesn't make sense as deprotonation wouldn't leave a positive charge in the first place.

A friend of mine said that the bridgehead carbon is under a ton of stress geometrically, and to think of it as an intermediate in a hydrohalogenation across what used to be a double bond. So with respect to this, why would the charge not be placed on the bridgehead? I'm thinking of this in terms of tertiary vs. secondary carbons (maybe this is where I'm going wrong?), and a tertiary carbon is more likely to hold a charge.

Can anyone help? I won't get a chance to ask about this in detail until next Tuesday and I'm really bothered by this question so I don't want to wait. Let me know if I need to clarify on anything.

 

[carguies]

I think it is because the tensile stress, a carbocation usually go to reorder in a more stable specimen, and c+ in specimen 1 is really unestable.
Specimen two is a quasi normal sp2, but specimen 1 its really stressed because of the bridge.

 

[chemisttree]

That's right. In the first case the carbocation is for, essentially, an sp3-hybridized bridgehead carbon and in the second case it is for your standard, run-of-the-mill sp2-hybridized carbon. Tying back those other carbons surrounding the bridgehead carbon prevents it from rehybridizing completely to sp2 in the first case.

 

[pzona]

Ah, back to hybridization; I should have known. Thanks for the help.

 

[LudusRex]

I can understand your confusion and frustration with this question. Carbocation stability on fused rings can be a complex topic, but I will do my best to provide an explanation that will hopefully clarify things for you.

Firstly, let's define what a carbocation is. A carbocation is a positively charged carbon atom that has six electrons in its valence shell instead of the usual eight. This makes it highly reactive and unstable, as it is constantly seeking to gain more electrons to achieve a stable octet.

Now, let's look at the two options given in the question. Bicyclo[2.2.1]heptane has a bridgehead carbon with a positive charge, while 2-methylbicyclo[2.2.1]heptane has a positive charge on C2. When determining the stability of a carbocation, we need to consider two factors: the inductive effect and the hyperconjugation effect.

The inductive effect refers to the electron-donating or electron-withdrawing ability of nearby atoms or groups. In this case, both options have a tertiary carbon, which means they have three carbon groups attached to them. However, the first option has two methyl groups attached to the bridgehead carbon, while the second option has only one methyl group attached to C2. This means that the first option has a stronger inductive effect, making the positive charge on the bridgehead carbon more stable.

The hyperconjugation effect refers to the delocalization of electrons from a neighboring bond into the empty p orbital of the carbocation. In simpler terms, it means that nearby bonds can stabilize the positive charge by sharing their electrons with the carbocation. In the first option, there are two methyl groups attached to the bridgehead carbon, which can contribute to the hyperconjugation effect. This makes the positive charge on the bridgehead carbon more stable.

Now, let's consider the geometric stress of the bridgehead carbon. It is true that the bridgehead carbon is under a lot of stress due to its position in the fused ring system. However, this stress does not necessarily affect the stability of the carbocation. In fact, the bridgehead carbon is often the most stable position for a carbocation in a fused ring system, as it is surrounded by multiple carbon groups that can contribute to its stability through the inductive and hyperconjugation effects.

In summary, the first option with the positive charge on