Visual walkthrough — Reactive intermediates — carbocations (stability), carbanions, free radicals, carbenes, nitrenes; rearrangements (hydrid
We build everything: the empty orbital, why it is hungry, what "more stable" means as a picture, and finally the shift itself.
Step 1 — Draw the thing that is unhappy
WHAT. A carbocation is a carbon atom that is missing one pair of electrons. A neutral carbon normally owns 4 bonds (8 shared electrons around it, an octet). Take one bonding pair away and you leave carbon with only 6 electrons and a positive charge .
WHY draw the orbital. To predict behaviour we must see where the hole is. That carbon rearranges its three remaining bonds into a flat triangle (this shape is called sp² planar, borrowed from Hybridisation and s-character) and pushes the emptiness up into a clean, unused lobe sticking straight up and down — the empty p-orbital. Everything on this page is a story about filling that lobe.
PICTURE. Look at Step 1. The three bonds (magenta) lie flat at to each other. The violet lobes above and below are the empty p-orbital — that is the "hole."
Step 2 — Turn "stability" into a height on a picture
WHAT. "More stable" is not a vibe — it is a lower energy. We draw energy as height: high = shaky and eager to change, low = comfortable.
WHY a height. A reactive intermediate sits in a valley on the energy diagram (parent note). A shakier cation sits in a shallower, higher valley; a better cation sits in a deeper, lower one. Rearrangement is just a marble rolling downhill if a downhill path exists.
PICTURE. Step 2 shows two valleys. The left valley (orange marble) is higher — a poorly-stabilised cation. The right valley is lower — a well-stabilised one. The whole rest of the page answers: what makes the right valley lower, and is there a path from left to right?
Step 3 — What lowers the valley: count the donors (α C–H bonds)
WHAT. Neighbouring C–H bonds on the carbon next door can tilt and share their bonding electrons into the empty p-orbital. This sharing is called hyperconjugation (see Hyperconjugation). More such neighbouring C–H bonds = more sharing = lower valley.
WHY count them. We need a countable number to rank cations without measuring anything. The countable number is the α C–H bonds — the C–H bonds on the carbons directly attached to the positive carbon.
PICTURE. Step 3 counts by colour: green arrows are the α C–H bonds pointing their electrons at the violet hole. Left carbon (3°) fires 9 arrows; right (2°) fires 6. More arrows → deeper valley.
Recall Why is the term "α" and not "β" here?
α means directly attached to the positive carbon. Those are the only bonds close enough to overlap the empty p-orbital. (The β carbon matters later, for the shift — hold that thought.) ::: The α carbons touch the cation; their C–H bonds can align with the empty lobe and donate. β carbons are one step further and cannot reach the hole directly.
Step 4 — The setup: a shaky cation with a better neighbour
WHAT. Consider . The starred carbon is 2° (two carbons attached). Its β carbon — the one next door, one step past the cation — carries two methyls.
WHY this molecule. If the positive charge could somehow move onto that β carbon, that carbon would be attached to two methyls plus the rest of the chain = a 3° centre. Step 3 just told us 3° sits in a deeper valley. So a downhill path exists — we only need the vehicle.
PICTURE. Step 4 labels the cast: α carbon = current hole (violet, higher valley marker), β carbon = the promising site (orange), and the one H on the β carbon we are about to watch (magenta).
Step 5 — The move: hydride migrates with its electron pair
WHAT. One of the β carbon's C–H bonds swings the hydrogen together with the two electrons of that bond onto the empty p-orbital of the α carbon. Because the electrons travel with the H, this migrating H is a hydride ( — H plus a lone pair).
WHY this is the whole trick. Watch the bookkeeping, term by term:
The charge did not disappear; it slid over one carbon to a spot where it is happier. Net change: 2° cation 3° cation, a genuine roll downhill.
PICTURE. Step 5 is the money shot: a curved magenta arrow shows the H swinging left, dragging its electron pair (dot pair) into the violet hole. The hole (violet lobe) hops from the α carbon to the β carbon.
Step 6 — Edge case A: methyl/alkyl shift (when no good H is there)
WHAT. Sometimes the β carbon has no hydrogen to donate but does carry a methyl group. Then a whole migrates with its bonding pair instead — a 1,2-methyl shift. Same logic, different passenger.
WHY it still works. The rule is "move a group with its electron pair from β to α to reach a better cation." Nothing in that sentence requires the group to be H.
PICTURE. Step 6: the neopentyl cation (a dreadful 1° hole) fixes itself when a methyl (orange) slides from the β carbon into the hole, giving the 3° . The jump 1°→3° is huge, so this shift is almost unavoidable.
Step 7 — Edge case B: when NOTHING shifts (the degenerate/uphill cases)
WHAT. A shift happens only if it goes downhill (to an equal-or-better cation). Two cases where nothing moves:
- Already best. A cation with only or worse neighbours has nowhere better to go — it stays put.
- Uphill forbidden. A cation will not shift to become a less stable cation. does not happen spontaneously (that would be rolling up the valley).
WHY show this. Beginners over-apply shifts. The picture insurance: a shift needs a lower valley on the other side of a small bump. No lower valley ⇒ no shift.
PICTURE. Step 7 puts three marbles on three profiles: (i) 2°→3° downhill ✓ (shift), (ii) 3°→3° flat "degenerate" — the H hops back and forth but nothing net changes, (iii) 3°→2° uphill ✗ (no shift). Only the first two are allowed motions.
Recall When is a shift
forbidden? Whenever the product cation is less stable than the starting one — that is uphill. ::: A 1,2-shift only occurs toward an equal or more stable carbocation. Going to a less-substituted, higher-energy cation would require climbing the energy hill, so it does not happen on its own.
The one-picture summary
PICTURE. The final figure stitches the whole story onto a single energy landscape: on the left a high valley labelled 2° cation with its 6 α-H arrows; a curved magenta "shift" arrow (H + electron pair) crossing a low bump; and on the right a deep valley labelled 3° cation with 9 α-H arrows. Above the picture, the hole (violet lobe) is shown hopping from α to β. One glance = the entire derivation.
Recall Feynman retelling — say it to a friend in plain words
A carbocation is a carbon with a hole where a pair of electrons should be. Because the hole is empty, the carbon is uncomfortable — it sits high up on an energy hill. Nearby C–H bonds can lean in and share a little of their electrons into the hole; the more neighbours that can do this, the lower and comfier the carbon becomes. So a carbon with three neighbouring groups (3°) is comfier than one with two (2°). Now, if a shaky 2° carbon has a neighbour that would be a comfy 3° spot, the molecule does something clever: it lets a hydrogen (or a methyl) slide over, taking its electrons with it, into the hole. That fills the old hole and opens a new one — but the new hole is on the comfier carbon. So the whole molecule rolls downhill from a shaky cation to a stable one. It only ever does this downhill: if the move would make things worse, nothing happens. That single idea — the hole slides to wherever it's happiest — is the entire theory of carbocation rearrangements. ::: A rearrangement is the positive charge sliding one carbon over, carried by a migrating H or alkyl group with its electron pair, but only in the direction that lowers energy.