[NewSoul]

So my textbook gives this handy dandy picture of relative stabilities of carbocations vs (primary) allylic and benzylic cations.



However, what it unfortunately doesn't tell me is how the stabilities of secondary and tertiary allylic and benzylic cations fit into the model.  I know that they are more stable than the primary allylic and benzylic compounds shown in the chart, but how do they compare with a tertiary carbocation?  Are they more or less stable?  Is it not important to know?

My professor said that she thinks secondary allylic and benzylic cations are approximately as stable as a tertiary carbocation, while tertiary allylic and benzylic cations are more stable than a tertiary carbocation.  But when she said this, it sounded as if she was guessing.

[MrTeo]

Actually I am guessing too. These rules of thumb aren't made to build universal energy ladders as they would almost certainly fail (it is kind of obvious that adding functional groups with various (mesomeric or inductive) electron-withdrawing or electron-donating effects can heavily affect the stability of carbocations), but they are meant to give you a rough idea (not so rough, after all) of the stability trends, which is what you need in OChem.

[...] while tertiary allylic and benzylic cations are more stable than a tertiary carbocation.

Makes perfects sense, you can imagine that the two stabilizing effects sum up.

My professor said that she thinks secondary allylic and benzylic cations are approximately as stable as a tertiary carbocation, [...]

I would say they're more stable, but it's only a guess as I said. (Usually mesomeric effects are much greater than hyperconjugation or inductive effects, just like those involved in tertary carbocations stability.)

[spirochete]

I once learned this some time in first year grad school. Personally I wouldn't worry too much about having all that memorized, as Mr Teo has said there are so many competing factors that in many cases you can't make any predictions from first principles. If you are ever in a situation where you really need to know the relative stability of two or three unusual cations you can always do your own research into the literature, but having all that information in your head 24/7 seems pointless to me. If anyone disagrees feel free to offer suggestions for how to best memorize all that info.

The fact that you are even asking these questions shows that you are probably an advanced student who is able to grasp all of the different trends and is now trying to put them together to see an even bigger picture. Unfortunately at some point there starts to be so many details and competing trends that it's impossible to know off the top of your head what's going to happen in every single situation.

Instead of trying to memorize what happens in every case, at a certain point it's better to start familiarizing yourself with the tools you'll need to study and prove what actually did happen, either experimentally in a lab or computationally.

There is one set of carbocations that I think it would be useful to have additional knowledge about. These are the especially unstable ones, the ones that are even less stable than your average primary carbocation. Specifically I'm talking about SP hybridized cations. I think they're interesting because their extreme instability explains why vinylic halides never do carbocation chemistry.

[AdiDex]

As we can see benzylic carbonation has more resonatic structures than allylic carbocation so it should be more stable than allylic carbocation.
But stability of any specie does not only depends upon the no. Of resonatic structures .
Actually,
They have approximately same energy instead of allylic should have approximately 1.5 times more energy than benzylic carbocation as benzylic carbocation have 4 resonatic structures and allylic carbocation have only 2.
But both of the resonatic structure of allylic carbocation are identical(looks similar as you rotate one you will get another one).
As the fact the resonane stabilization is greater in such species which have identical resonatic structure.
That why both of them have comparable energies.