Pushing Electrons: Curved Arrows

The Grammar of Reactions

By now you have met the cast: a nucleophile is electron-rich and goes looking for positive charge, an electrophile is electron-poor and wants electrons, and an acid-base reaction is really a pair of electrons reaching out to grab a proton. What you have not yet seen is the notation that ties all of this into one running story. That notation is the curved arrow, and it is the single most important piece of bookkeeping in organic chemistry. Master it here, in the calm of acid-base chemistry, and every mechanism in the chapters ahead becomes a sentence you can read.

Here is the whole idea in one line: a curved arrow shows a pair of electrons moving from a SOURCE to a SINK. The tail of the arrow sits exactly where the electrons start — on a lone pair, or on a bond. The head points exactly where they end up — onto an atom, or between two atoms to make a new bond. Source means electron-rich (a lone pair, a pi bond, a negative charge); sink means electron-poor (a positive atom, the far end of a polar bond, an empty orbital). Read every arrow as one short clause: 'this pair goes there.'

Two Kinds of Arrow: Full Head and Fishhook

Arrows come in two shapes, and the shape tells you how many electrons move. A full-headed arrow — the ordinary kind, drawn with a complete arrowhead — moves a PAIR of electrons at once. This is the workhorse of the vast majority of reactions you will study: acid-base proton transfers, nucleophilic attacks, eliminations, almost everything. Whenever charges appear or disappear in a step, two-electron arrows are doing the work.

The other shape is the fishhook arrow, drawn with only HALF an arrowhead — like a barbless hook. It moves a SINGLE electron. You need it only for radical chemistry, where bonds split evenly and each fragment walks away with one unpaired electron, becoming a free radical. Because a single electron is being tracked, radical steps need two fishhooks where a polar step would need one full arrow. The shape is a promise: a full head says 'a pair travels together,' a half head says 'these two electrons are about to go their separate ways.'

full-headed arrow  ⇀⇀  moves 2 electrons (a pair)   -- polar reactions
fishhook arrow     ⇀    moves 1 electron (single)    -- radical reactions

rule of thumb: charges appear  ->  use full arrows
               radicals appear ->  use fishhooks

Breaking Bonds Two Ways: Heterolysis vs Homolysis

Why two kinds of arrow at all? Because a bond — a shared pair of electrons — can break in two fundamentally different ways, and these are the two halves of bond cleavage. In HETEROLYSIS ('uneven splitting'), both electrons leave together, going to one of the two atoms. That atom becomes negative; the one left behind, robbed of the pair, becomes positive. This is the world of curved full-headed arrows, of ions, and of polar reactions — the bread and butter of acid-base and nucleophile-electrophile chemistry. Break C-Br heterolytically and you can get a positively charged carbocation plus a bromide ion carrying the pair away.

In HOMOLYSIS ('even splitting'), the shared pair divides fairly: one electron to each atom. No ions form; instead each fragment leaves with one unpaired electron, becoming a neutral radical. This is the fishhook world. Homolysis usually needs heat or UV light to supply the energy and typically happens to nonpolar bonds like Cl-Cl or C-H, where neither atom is greedy enough to take both electrons. So the choice of arrow is not arbitrary decoration: a full-headed arrow IS heterolysis on paper, a fishhook pair IS homolysis on paper. The notation mirrors the physics.

Reading and Drawing a Mechanism Step

Let us walk one real step you already half-know: the simplest proton transfer, hydroxide grabbing a proton off water's cousin. Take hydroxide, HO with three lone pairs and a minus charge, meeting an acidic H on some molecule H-A. Two arrows tell the whole story. Arrow one: a lone pair on the oxygen of hydroxide reaches up to the proton — tail on the lone pair, head on the H. Arrow two: the electrons of the old H-A bond fall back onto A — tail on the H-A bond, head onto A. The proton has been handed over; A leaves with the pair and becomes a negative ion. That is acid-base chemistry drawn in its native language.

1. Find the source. Spot the electron-rich site that does the attacking — a lone pair, a negative charge, or a pi bond. Put the arrow's TAIL precisely there, on the electrons, not on the atom.
2. Find the sink. Spot the electron-poor target — a proton, a positive atom, or the partially positive end of a polar bond. The arrow's HEAD points there.
3. Make room. If forming the new bond would overstuff an atom past its octet, a second arrow must simultaneously break an old bond — its electrons fall onto the leaving atom. Electrons in, electrons out, in the same breath.
4. Balance the charges. Recount the formal charge on every atom that gained or lost electrons. The total charge must be the same before and after — arrows redistribute electrons, they never create or destroy them.

The Mistakes Everyone Makes (and How to Spot Them)

Almost every wrong mechanism fails one of a few honest checks. Backwards arrows: students often draw the arrow from the electrophile to the nucleophile, as if the positive site reaches out. It never does — electrons always flow FROM the rich source TO the poor sink, so the tail belongs on the electron-rich partner. Arrows starting on a positive charge: a tail must sit on electrons, and a plus charge marks a place that LACKS them, so an arrow can never begin there. And the cardinal sin — arrows that drag atoms around. If your arrow seems to move an H bodily across the page rather than tracking its electrons, you have written a fiction.

Two more guards worth keeping. First, no second-row atom (C, N, O, F) may ever exceed eight electrons — if forming a bond would give carbon five bonds, an arrow breaking an old bond MUST accompany it. This is exactly why a backside SN2 attack kicks out a leaving group in the same step the nucleophile arrives: the carbon can hold only four bonds at once. Second, count the total charge on both sides of the arrow; if it changed, you either added or lost electrons illegally. These two checks — octets and charge balance — catch the overwhelming majority of errors before they spread.

Keep one honest perspective on the whole device. Curved arrows are a model, a bookkeeping language — not a movie of where electrons literally are at each instant. Real electrons are smeared-out quantum waves, and a concerted step happens all at once, not as a neat sequence of separate arrows. But the model is astonishingly good: draw the arrows correctly and you almost always predict the right product, the right charges, and the right stereochemistry. That is why this notation, simple as it looks, is the backbone of every chapter still to come.