# Why are vinylic and arylic carbocations highly unstable?

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.

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.

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.