[Gläzküll]

I'm revisiting some of my old homework and on a powerpoint slide with practices for resonance structures I found this molecule: The only thing I can think of is ring closure, but I'm not sure if it's correct. It's entirely possible that my teachers made a mistake. I'd like to hear your thoughts.

[pgk]

Why not, a neighboring migration of the double bond, in order to be closer and conjugated with the carbocation?

[Gläzküll]

Why not, a neighboring migration of the double bond, in order to be closer and conjugated with the carbocation?

I'm sorry, but not sure what you mean

[pgk]

(CH3)2C(+)CH2CH=CH2  ↔ (CH3)2C(+)CH=CHCH3 ↔ …….

Resonance structures that contain a cyclopropane ring, are also possible:

(CH3)2C(+)CH2CH=CH2  ↔ (CH3)2C(CH2)CHCH2(+)  ↔ ……

[clarkstill]

(CH3)2C(+)CH2CH=CH2  ↔ (CH3)2C(+)CH=CHCH3 ↔ …….

Those are structural isomers rather than resonance forms, aren't they? You would need to do a (forbidden) 1,3-hydride shift...

There is some discussion of this compound in Int J Quant Chem 1980,1479 (doi: 10.1002/qua.560180612). The authors consider whether this does behave as a non-classical carbocation (as implied by Gläzküll's proposal), and conclude that actually the cation is just stabilized by hyperconjugation, and there are no important resonance forms.

[pgk]

1). Yes, they are rather structural isomers and especially the cyclopropane ring containing ones. But in case of charged or radical structures, the borderlines between resonance structures and structural isomers, are very narrow.
2). Indeed, 1,3-hydride shift is thermodynamically permitted but geometrically forbidden, which can easily be concluded by drawing the molecular orbitals. But in presence of the carbocation all that change and 1,3-hydride shift can occur via two sequent 1,2-hydride shifts. In other words, the hereby carbocation behaves as an acidic catalyst of geometrical isomerization.
3). Hyperconjugation occurs between an empty orbital and an α-neighboring full one (e.g. (CH3)2C(+)CH=CHCH3 ). In contrast to “long distance conjugation” (often confused with hyperconjugation), which occurs between an empty orbital and a linearly away but geometrically close, full one (e.g. Z-(CH3)2C(+)CH2CH=CH2 ).   
4). In this case, hyperconjugation favors the formation of cyclopropane containing structures, while the “long distance conjugation” favors the formation of cyclobutane containing one. Please, note that cyclopropane and cyclobutane rings have similar ring strain, 27.5 and 26.3 kcal/mol respectively.
5). Actually, this is rather a non-classical carbocation that is stabilized by hyperconjugation (main resonance structure: (CH3)2C(+)CH=CHCH3), as concluded by the exclusive 1,4- polymerization of 2-methyl-1,3-pentadiene, under Lewis acid catalysis.
http://onlinelibrary.wiley.com/doi/10.1002/pola.26714
http://onlinelibrary.wiley.com/doi/10.1002/macp.200500135
http://www.sciencedirect.com/science/article/pii/S0166128097003266
US Patent 3476731 (1969)
US 2447610 (1948)
etc.

[clarkstill]

1). Yes, they are rather structural isomers and especially the cyclopropane ring containing ones. But in case of charged or radical structures, the borderlines between resonance structures and structural isomers, are very narrow.

I agree the lines can get blurred for non-classical carbocations.

2). Indeed, 1,3-hydride shift is thermodynamically permitted but geometrically forbidden, which can easily be concluded by drawing the molecular orbitals. But in presence of the carbocation all that change and 1,3-hydride shift can occur via two sequent 1,2-hydride shifts. In other words, the hereby carbocation behaves as an acidic catalyst of geometrical isomerization.

I also agree that 1,2-hydride (and carbon) shifts can occur in carbocations, but I disagree that we can call the isomers that arise from this 'resonance forms'. I'm also not sure about the first resonance you proposed - can you draw a mechanism for this? I can imagine a 1,2-hydride shift to form the allylic carbocation (although i'd contest that this isn't resonance), but I'm not sure how you're moving the hydride to the terminal carbon to get the structure you form.

3). Hyperconjugation occurs between an empty orbital and an α-neighboring full one (e.g. (CH3)2C(+)CH=CHCH3 ). In contrast to “long distance conjugation” (often confused with hyperconjugation), which occurs between an empty orbital and a linearly away but geometrically close, full one (e.g. Z-(CH3)2C(+)CH2CH=CH2 ).
4). In this case, hyperconjugation favors the formation of cyclopropane containing structures, while the “long distance conjugation” favors the formation of cyclobutane containing one. Please, note that cyclopropane and cyclobutane rings have similar ring strain, 27.5 and 26.3 kcal/mol respectively.

Hyperconjugation is between filled sigma and unfilled pi (or p-) orbitals, according to IUPAC. In (CH3)2C(+)CH=CHCH3 the primary stabilizing effect would be resonance with the pi bond, with some hyperconjugation from the CH3 groups flanking the cation. For (CH3)2C(+)CH2CH=CH2, however, there aren't any resonance forms of note. Neither potential structure involving the alkene stabilizing the cation (cyclopropane or cyclobutane) arises from hyperconjugation, since neither involves sigma electrons.

5). Actually, this is rather a non-classical carbocation that is stabilized by hyperconjugation (main resonance structure: (CH3)2C(+)CH=CHCH3), as concluded by the exclusive 1,4- polymerization of 2-methyl-1,3-pentadiene, under Lewis acid catalysis.
http://onlinelibrary.wiley.com/doi/10.1002/pola.26714
http://onlinelibrary.wiley.com/doi/10.1002/macp.200500135
http://www.sciencedirect.com/science/article/pii/S0166128097003266
US Patent 3476731 (1969)
US 2447610 (1948)
etc.

The examples you give all involve metal catalysts which fundamentally change the nature of the molecule, so I don't think you can extend any conclusions drawn to the behavior of the 'naked' carbocation in the absence of any metals. The paper I gave before specifically relates to the cation in question, and concludes that the interaction is classical in nature, involving several effects including an equilibrium (not resonance) between the open- and cyclobutane forms and hyperconjugative stabilization of the cation from the adjacent C-C sigma bond.

[pgk]

1). Thank you for the punctual remarks and corrections.
2). 1,2- Hydride shift to form the allylic carbocation that forms 2-methyl butadiene, followed by simultaneous trapping of the proton by the terminal double bond. The mechanism demands transposition of the proton that sounds more like tautomerism or isomerism. Nevertheless, isomerism is not a successful description for charged structures.
3). You are right, regarding hyperconjugation. It was a wrong expression from my part, due to the fast typing. The right is:
“Hyperconjugation occurs between a σ orbital and an α-neighboring full p/π one (e.g. (CH3)2C(+)CH=CHCH3 ). In contrast to “long distance conjugation” (often confused with hyperconjugation), which occurs between an empty orbital and a linearly away but geometrically close, full one.
In this case, conjugation/hyperconjugation favors the formation of cyclopropane containing structures ………………………”
4). Indeed, Lewis acids may change the geometry of butadienes and favor particular transition states but they cannot change the nature of the formed carbocations, nor totally eliminate the less favored transition states. Anyway, this is another long discussion.
5). All above give the chance of some clarifications:
- “The non-classical carbocation” hypothesis is proposed for the explanation of the stability of particular carbocations like the one hereby, the halogenation and hydrohalogenation products of bornene/norbornene, the extreme reactivity of triphenylmethylium with water, etc.
- The stability and the exotic chemical properties of non-classical carbocations are explained by their “homoaromaticity”, which denotes the conjugation of the carbocation’s empty σ orbital with distant full π orbitals, through space; like the hereby carbocation. However, “homoaromaticity” does not sound nice for non-cyclic system and therefore, “long distance conjugation” is a more successful description in non-cyclic compounds. As an indicative example, imagine a carbocation that participates in a protein or a polymer chain and conjugates with a double bond, dozens of amino acids or monomers away, due to their particular ternary structure.
- Besides, homoaromaticity of non-cyclic structures is often confused with hyperconjugation but thanks’ to clarkstill’s punctual remarks, the latter is fully clarified hereby.
6). As being an hypothesis, some examples of non-classical carbocations may be overcome by novel experimental data or advanced quantum mechanics calculations, like the described ones in the stated article.