Hyperconjugation

Hyperconjugation is a further, genuinely PERMANENT electronic effect (unlike the electromeric effect, but like the inductive and resonance effects), and it specifically explains the observed relative STABILITY of a carbocation, a free radical, or an alkene. Formally, hyperconjugation is defined as the delocalisation of the SIGMA electrons of a C-H bond belonging to an alkyl group, specifically where that alkyl group is directly attached to a carbon atom that is ITSELF either part of an unsaturated (multiply-bonded) system, or carries a genuinely empty p-orbital, or carries a p-orbital holding a single unpaired electron. Working through the specific case of the ethyl cation, $CH_3{-}CH_2^{\oplus}$: the positively-charged carbon (carrying its own empty p-orbital) has an adjacent methyl group directly attached to it (called, in this context, the ALPHA methyl group); one particular C-H bond of that alpha methyl group happens to be geometrically aligned with the empty p-orbital on the cationic carbon, and it is specifically that C-H bond's own sigma electrons that delocalise sideways into the empty p-orbital, stabilising the cation as a result. Because this is fundamentally a delocalisation of SIGMA electrons into what is, in effect, a PI-type (p-orbital) system, hyperconjugation is described as a form of sigma-pi conjugation. Drawing out the full set of contributing ('no-bond resonance') structures for the ethyl cation makes this concrete: structure I shows the ordinary, intact C-H bond as normal, while three further structures (II, III, and IV) each instead show ONE of that methyl group's three individual C-H bonds as fully broken (i.e. no bond at all remaining between that particular carbon and that particular hydrogen), with that bond's electron pair now shown delocalised toward the cationic centre, and the hydrogen atom itself appearing, in effect, to have partially migrated away as if it were now a bare proton -- which is exactly why hyperconjugation earns the nickname 'no-bond resonance'. The general rule that follows directly from this picture is: the MORE alpha-hydrogens (i.e. hydrogens sitting on a carbon directly adjacent to the charged, radical, or unsaturated centre) a given species has available, the MORE such no-bond resonance structures can be drawn for it, and correspondingly the GREATER its overall stability -- which is precisely why carbocation stability decreases in the well-known order tert-butyl cation > isopropyl cation > ethyl cation > methyl cation, since these four cations carry 9, 6, 3, and 0 alpha-hydrogens respectively (with methyl cation, having no alpha-carbon at all, unable to be hyperconjugatively stabilised in this way whatsoever). The exact same underlying ide …