Carbocations

Carbocations are ions of organic molecules that carry a positive charge on the carbon atom; these carbons atom are sp2 hybridized (three orbital sp2  and one p empty orbital, perpendicular to the plane made by the sp2 orbitals.

carbocationeConsidering the substituents of the carbon which carries the positive charge, we can distinguish between different classes of carbocations:

classificazione-carbocationiIt was experimentally verified that the order of carbocation stability is, as follows:

carbocations-stability-orderThis stability scale can be explained reffering to the hyperconjugation, inductive effect and relocation concepts:

  • hyperconjugation

The hyperconjugation is the interaction between a σ bonding orbital  (typically C-C and C-H ) and other orbitals, usually p orbitals (which is the case, for example, of carbocations) or empty adjacent π orbitals. This type of interaction allows to distribute the electronic density, obtaining more stable forms.

Let's consider the specific case of the carbocation . Recalling, once again, that is sp2 hybridized , it has trigonal planar structure with an empty perpendicular p orbital, which, besides, carries the positive charge. If there's another adjacent carbon to this (ie in position β ) it is realized a partial overlap between carbon's σ  bonding orbital in β , and the empty p orbital of the positively charged carbon (carbocation).

hyperconjugationThe spatial arrangement of these orbitals allows the partial delocalization of the electron density in the free p orbital, something that cannot happen, for example, in the methyl carbocation:

methyl carbocationpurely for geometric reasons.

The interaction between p and σ orbitals leads to a real new molecular orbital, whose gain in terms of energy can be easily illustrated with a diagram:

hyperconjugation-diagraminductive effect

The inductive effect is the effect performed  by atoms and functional groups in respect of an adjacent atom, by virtue of the electronegativity difference with the latter. Take for example a tertiary carbocation:

tertiary-carbocationThe central carbon, who carries the positive charge, is more electronegative than surrounding sphybridized carbons . It follows that the bonds between spcarbons and the sp2 carbons are shifted in favor of the latter. The electron density is therefore delocalized from the alkyl group (-CH3 in this case) to the central carbon, with a complexive stabilizing effect on the carbocation, as if the positive charge of the carbon sp2 was dampened by the electron density from the adjacent groups.

inductive effect

This effect is obviously not exclusive prerogative of alkyl groups, and may also be either stabilizing or destabilizing . For example, an "electron-withdrawing group" as  -NO2 , would have a destabilizing effect on the carbocation, because it would tend to "attract" the electron density, and not to give it, further accentuating the unstable state of the spcarbon.

carbocatione-destabilizzato

The hyperconjugation and inductive effect concepts allow us to effectively explain the different stability of the simplest carbocations, therefore primary, secondary and tertiary.

  • Delocalization

Is the condition in which π electrons are free to move within a conjugated system of orbitals of adjacent atoms. Usually in organic chemistry to graphically represent the electron delocalization we resort to the artifice of resonance formulas. Is the case, for example, of the allylic carbocation :

carbocatione allilicothe resonance formulas don't describe a static structure, rather a dynamic system where charges spontaneously moves one towards the other. For this reason, sometimes the electrons of the π bonding-orbital flock in an empty p orbital of a carbocation causing the displacement of the positive charge on another carbon, while the next moment it's exactly the opposite, so that is almost totally unpredictable .

For a specific molecule I can often write different resonance formulas, all of which contribute to its comprehensive description; on the other hand not all of them do it significantly. I'll explain better. The delocalization of the charge lowers the energy of carbocations (highly unstable species). It lowers the energy because it allows the partial distribution of the electric charge over several atoms (not necessarily only C), as if the unit charge was smeared in smaller fractions on different atoms. Since the delocalization lowers the total energy of the carbocation, the most describing resonance formulas are those with the lowest energy. For example, in the case of allylic carbocation:

formule-di-risonanzaThe resonance formula that best describes the carbocation is the left, since the secondary carbocation is MUCH more stable than the primary one.

Another example is the benzyl carbocation , particularly stable since the charge is delocalized throughout the whole aromatic ring:

carbocatione benzilicoIn general, the more are the resonance formulas with which a molecule or ion can be described, the lower is the overall energy, since the charge is highly delocalized.

Finally, are particularly stable those carbocations which have a heteroatom (N, S, O etc.) with an electron pair adjacent to the carbon that bears the positive charge:

carbocatione eteroatomicoIn this case the more stable resonance formula is the one that bears the positive charge on the oxygen. The atoms that have electronic doublets bears better than carbon a positive charge (the lowest energy of the true carbocation and right).

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