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I have checked the internet and read quite a few books, but I still am not able to understand why vinylic and arylic carbocations are highly unstable.

What I found while surfing the internet is: For arylic carbocation, the carbon bearing postive charge cannot participate in resonance with adjacent carbons because it's p orbital is perpendicular to the other orbitals. But, I didn't really understand what this means.

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Background

S-orbitals are lower in energy than p-orbitals, therefore the more s-character in an orbital, the lower its energy and the more stable any electrons occupying the orbital. In other words, electrons will be more stable (lower in energy) in an $\ce{sp}$ orbital than an $\ce{sp^2}$ orbital, and electrons in an $\ce{sp^2}$ orbital will be lower in energy than those in an $\ce{sp^3}$ orbital.

This is the basis of the inductive effect. For example, it explains why the electrons in an $\ce{sp^3}$ methyl group will be drawn towards a connected $\ce{sp^2}$ carbon in an aromatic ring - the methyl group is inductively electron donating to the aromatic ring as its $\ce{sp^3}$ electrons drift towards the lower energy $\ce{sp^2}$ aromatic carbon.

What we're really saying is that an $\ce{sp}$ hybridized carbon atom is more electronegative (it's lower in energy and the electrons prefer to move towards it) than an $\ce{sp^2}$ hybridized carbon atom, which in turn is more electronegative than an $\ce{sp^3}$ hybridized carbon atom.

Answer

Look at the figure below, notice that in the alkyl carbocation on the left the cationic center is attached to an $\ce{sp^3}$ carbon, whereas in the vinylic cation in the middle, the cationic center is attached to a more electronegative $\ce{sp^2}$ carbon. For a positive center to be attached to a more electronegative group is destabilizing. Hence the vinylic cation is less stable than a typical alkyl cation.

Things are even worse with the aryl carbocation on the right. Here the positive carbon is attached to 2 $\ce{sp^2}$ carbons. Destabilizing the aryl cation even further is its geometry. A vinyl cation prefers to be linear, but due to geometrical constraints imposed by the aromatic ring the aryl cation must be bent and the empty orbital is forced to be $\ce{sp^2}$ rather than $\ce{p}$. These three factors combine to make the aryl carbocation even higher in energy than the vinyl cation.

enter image description here

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  • $\begingroup$ I was taught that electrons from an sp3 carbon move to an sp2 carbon due to hyperconjugation, that is: the shift of a bonded electron into the unhybridised p orbital of the sp2 carbon. Is the shift of electrons due to a combination of both this and inductive effect? $\endgroup$ – Mahathi Vempati Feb 20 '16 at 1:55
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    $\begingroup$ Yes, that's how I see it, a mix of resonance and inductive effects. $\endgroup$ – ron Feb 20 '16 at 3:58
  • $\begingroup$ @ron for hyperconjugation to occur, must the orbitals hyperconjugating be in the same plane? $\endgroup$ – Mason Feb 9 at 13:44
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in the vinylic and arylic carbocation both are in sp2 hybrid orbital... we know higher the s character closer to the nueclus ..So plus charge closer to the nueclus will feel strong replulsion In arylic position same thing happen..and there it cant b also stabilized by the pi conjugation of benzene as sp2 hybrid orbital and p are orthogonal

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