Stability of Carbocations

A carbocation is a carbon bearing only three bonds and a formal positive charge, with an empty $p$ orbital; it is $sp^2$-hybridised and planar at that carbon. Its relative stability governs how readily a haloalkane ionises in the rate-determining step of $S_N1$ (and the closely related E1 elimination), since a more stable carbocation corresponds to a lower-energy transition state for its formation.

Order of stability from alkyl substitution: $3^\circ > 2^\circ > 1^\circ > \text{methyl}$. Each alkyl group attached to the cationic carbon stabilises the positive charge in two ways: hyperconjugation, in which a $\text{C--H}$ (or $\text{C--C}$) sigma bond on an adjacent carbon partially overlaps with and donates electron density into the empty $p$ orbital (more adjacent bonds available means more hyperconjugative stabilisation, so more alkyl substitution helps), and the inductive effect, by which alkyl groups are weakly electron-donating relative to hydrogen and so partially offset the positive charge. A tertiary carbocation, flanked by three alkyl groups, therefore benefits from both effects the most and is the most stable of the simple alkyl cations; the methyl cation, with no adjacent carbon at all, is the least stable and essentially never forms under ordinary conditions.

Resonance stabilisation exceeds simple alkyl substitution. A carbocation adjacent to a $\pi$ system -- benzylic (next to an aromatic ring) or allylic (next to a $\text{C=C}$ double bond) -- is stabilised far more strongly than even a tertiary alkyl cation, because the positive charge can be delocalised by resonance over several atoms rather than merely offset inductively from adjacent bonds. …