Curved Arrow Notation

Introduction

Curved arrows are the grammar of polar organic mechanisms. A full-headed arrow moves an electron pair from a bond or lone pair to a new location. An arrow can describe a new bond, a broken bond, or a changed π bond, but its tail must sit on existing electrons. Learning to place arrows from electron sources prevents impossible structures and makes unfamiliar reactions solvable from first principles.

Core explanation

A lone pair on a nucleophile can move toward an electrophilic atom. In HO⁻ + CH₃Br, oxygen's lone pair points to the methyl carbon. Because carbon already has four bonds, a second arrow sends the C–Br bond pair to bromine. Product oxygen gains C–O and loses negative charge; bromine gains a lone pair and becomes Br⁻. The two arrows describe a concerted SN2 step. Drawing the first arrow without the second would give a pentavalent carbon in an ordinary organic representation.

A π bond can be an electron source. When ethene is protonated by H₃O⁺, draw an arrow from C=C π electrons to a hydrogen on hydronium, then an arrow from that O–H bond to oxygen. One alkene carbon gains H, and the other becomes positively charged in the carbocation intermediate. The exact carbon receiving H influences carbocation stability in an unsymmetrical alkene. The arrows move electron pairs; they do not depict a proton physically flying along the curved line.

Bond cleavage begins with the existing bond as arrow tail. For heterolytic R–Br cleavage, arrow from C–Br to Br gives R⁺ and Br⁻. Reverse direction would give a very different and usually implausible R⁻/Br⁺ pair. In a proton transfer, draw base lone pair to H and the donor X–H bond pair back to X. Omitting the second arrow can overfill hydrogen's valence or leave the donor atom's charge wrong.

Resonance arrows use the same electron-pair logic but connect alternative drawings of one delocalised species rather than stages of a chemical reaction. The atom positions do not change in legitimate resonance forms; only electrons and formal charges shift. A double-headed equilibrium arrow between resonance structures would imply two separable molecules, which is not the intended meaning. Use a resonance double-headed connector for contributors and ordinary reaction arrows for chemical steps.

Radical mechanisms need single-headed fishhook arrows, each representing one electron. Homolytic Cl–Cl cleavage needs two fishhooks, one electron to each chlorine. Replacing those with a full-headed arrow would imply ionic cleavage. A mechanism can include radical and ionic stages, but each transition needs chemically meaningful electron accounting.

After every arrow set, perform an audit: count bonds at carbon, oxygen, nitrogen, and hydrogen; calculate formal charges; check total charge before and after; and compare with the intended bond changes. This audit catches common errors such as neutral oxygen shown with three bonds and no positive charge. A neat product with wrong charge is not a valid electron-flow result.

Step-by-step reasoning

1. Find the occupied lone pair or bond that supplies electrons. 2. Place arrow tail there, not on a positive charge or empty orbital. 3. Point the head at the atom or bond position receiving the pair. 4. Add simultaneous arrows when another bond must break to preserve valence. 5. Redraw product and check formal charges and total charge.

Visual explanation

Draw three arrow patterns: lone pair to carbon, C–X bond to X, and π bond to H with O–H bond to O. Beneath each, show product charges generated by the arrows.

Real-world analogy

An accounting transfer records both the account losing funds and the account receiving them. Electron arrows need a real source and destination, and the balances must reconcile afterward.

Real-world example

In a carbonyl-addition problem, a student draws nucleophile attack but forgets C=O π electrons moving to oxygen. A valence check immediately reveals the missing arrow.

Why?

Why does a full-headed arrow represent a pair rather than an atom's path? Covalent bond formation and heterolytic cleavage redistribute paired electrons; atom positions are inferred from the resulting bonds.

Common misconception

“The arrow should point from the positive carbon to the nucleophile because carbon attracts it.” Electron-pair flow starts at the nucleophile and heads toward electron-poor carbon.

Worked example

Show water attacking a tertiary carbocation. A lone pair on H₂O oxygen points to C⁺, forming a C–O bond. Water oxygen now has three bonds and carries positive charge in an oxonium intermediate. A second water molecule may remove a proton: its lone pair points to oxonium H, while the O–H bond pair returns to the attached oxygen. The result is neutral alcohol plus hydronium. Tracking arrows explains why deprotonation is required.

Quick check

1. Where does the arrow start when a C–Br bond breaks heterolytically to Br⁻? Answer: At the C–Br bond, with the arrow head at bromine.

Exam focus

Place tails on actual electron pairs and redraw every charged intermediate. Use full-headed arrows for electron pairs and fishhooks for one-electron radical steps.

Advanced insight

Arrow notation encodes a proposed redistribution of electron density, not a literal observed trajectory. Mechanistic experiments are needed to judge whether the proposed sequence describes the dominant pathway.

Summary

Curved arrows move electron pairs from occupied sources to accepting destinations. Correct arrow sets preserve valence and charge, while fishhooks separately describe single-electron radical motion.

Practice questions

1. What arrow accompanies nucleophile attack on a C=O carbon? Answer: A second arrow moves the C=O π bond pair to oxygen. 2. What charge does oxygen usually have immediately after neutral water bonds to a carbocation? Answer: Positive, because it has three bonds in the oxonium species. 3. Should atoms move between resonance contributors? Answer: No. Only electrons and formal-charge placement change between contributors.