[rohitarura]

What is the order of stability of the following carbocations:
Cyclopropylmethyl carbocation,propylium carbocation,tropylium carbocation,tri-phenyl carbocation and
the one with a carbon atom with positive charge having 3 propyl rings attached to it(like Cyclopropylmethyl carbocation with 2 more rings)(I don't know its exact name)

Thanks in advance.

[kimyacı]

 order of stability of carbocations
 Allylic > Benzylic > tertiary > secondary > primary > methyl
 
 Cyclopropylmethyl carbocation is secondary (a)
 propylium carbocation is primary (b)
 tropylium carbocation is aromatic (c)
 tri-phenyl carbocation is tertiary (d)

 as far as I understand, order of stability of these carbocations : (c) > (d) > (a) > (b)
 
 

[aldoxime_amine]

I believe the cyclopropyl methyl carbocation is the most stable of all carbocations, the reason being unknown to me and I don't have any references to support my fact. Can someone provide a reference?

[Squirmy]

I agree that the cyclopropylmethyl cation is more stable than a standard secondary carbocation. I seem to remember it as a non-classical carbocation: http://en.wikipedia.org/wiki/Non-classical_ion

Still, I'd be surprised if it's more stable than a tropylium ion, which is aromatic and stable enough to put in a bottle. For that matter, I think the triphenylmethyl cation with its 10 resonance structures would also be more stable.

If I had to pick an order:

tropylium ion > triphenylmethyl cation > tricyclopropylmethyl cation > cyclopropylmethyl cation    >     propylium ion

Aromatic      Lots of resonance          Lot of sigma-bond donation   Some sigma-bond donation      Little sigma bond donation

[aldoxime_amine]

But how is it explained? Why do the sigma electrons leave their orbitals only in the case of this cyclopropyl-like structure, even in the norbornyl cation, a cyclo-propyl-like resonanating structure is obtained...

[Squirmy]

Honestly, it was a guess.

Clearly, there is more than one way to stabilize a carbocation. To know how well each feature stabilizes the cation, you'd have to look at some real data. One common set of data used for carbocation stability is gas phase, hydride ion affinity (HIA). 

[anirbanc4]

cyclopropyl methyl cation is the most stable carbocation and it is a unique case.. see March's Advanced Organic Chemistry SIXTH EDITION page 241

[PhDoc]

The cyclopropylmethyl cation is one of the strange ones, comparable to the cyclopropylcarbinyl cation. Use a standard model kit to construct a model of a cyclopropane. Odd's are, you'll break your kit.

While we're accustomed to tight directional sigma-sigma overlap in unstrained molecules, cyclopropyl moieties are unable to do this. Instead there's a slight "bend" in the bonds, or better phrased, the sigma orbitals are not co-linear with the bond axis, rather they're at an angle, placing the majority of electron density off-axis.

See here: http://isites.harvard.edu/fs/docs/icb.topic93502.files/Lectures_and_Handouts/06-Handouts/deMeijere.pdf

H.A. Hart provided a qualitative explanation of cyclopropyl delocalization, J. Am. Chem. Soc. 1962, 84, 2462; J. Am. Chem. Soc. 1964, 86, 2957.

In such a case, bond rotation can place a "bent" sigma orbital co-linear with the empty p-orbital of the cation in a manner supporting hyperconjugation, shared amongst three cyclopropyl groups. At the very least, this is a somewhat rational explanation taking physical organic chemistry into account.