DAT Organic Chemistry: Curved Arrow Notation

DAT High-Yield Concept

Electron Movement, Not Atom Movement: Curved arrows exclusively track the movement of electron density. They never show the movement of atoms or positive charges.
Arrow Tail = Electron Source: The tail originates directly at an electron pair (lone pair or bond) or a single electron.
Arrow Head = Electron Sink: The head points directly to where electrons are moving (an atom or a bonding region).
Double-Headed vs. Single-Headed: Double-headed arrows represent the movement of an electron pair ( 2 e^-), whereas single-headed (fishhook) arrows represent a single electron (1 e^-).
Conservation of Mass and Charge: Formal charges and atom counts must balance perfectly across every elementary reaction step.

Core Principle: Tracking Electron Movement

Curved arrow notation (also known as electron pushing) is the formal accounting language of organic chemistry. On the DAT, understanding curved arrows allows you to predict reaction products, determine mechanism pathways, and evaluate resonance contributors. The fundamental rule of arrow pushing is that curved arrows represent the movement of electrons, not atoms or positive charges.

Fundamental Rule: Electrons carry negative charge and flow from regions of high electron density to regions of low electron density. Positive charges (such as protons or carbocations) never move; they change position only as a mathematical consequence of electron redistribution.

Anatomy of a Curved Arrow: Electron Source (Tail) and Electron Sink (Head)

Every curved arrow consists of two essential components: the tail and the head.

Arrow Tail (Electron Source): The tail must begin at the precise location where the electron density originates. A valid electron source is either a unshared lone pair on an atom or a covalent bond ( $\sigma$ or $\pi$ bond). Never begin an arrow tail on a positively charged atom or an atom lacking available valence electrons.
Arrow Head (Electron Sink): The head points to the exact location accepting electron density. A valid electron sink is either a specific atom (forming a new lone pair or accepting a leaving electron pair) or the space between two atoms (forming a new covalent bond).

Two electron-pair arrows in a single step. The arrow from hydroxide starts at its lone pair (the source) and ends at carbon (the sink). The second starts on the C-Br bond and ends on bromine, which leaves with both electrons.

When an electron pair moves from a bond to an atom, a bond breaks in a heterolytic process. Conversely, when an electron pair moves from an atom or bond toward an adjacent electron-deficient atom, a new bond is formed.

Double-Headed vs. Single-Headed (Fishhook) Arrows

The shape of the arrow head specifies the exact number of electrons being transferred during a step:

Double-Headed Curved Arrow: Features a standard two-barbed head. It represents the movement of an electron pair (2 e^-). This notation is used in polar reactions, ionic mechanisms (such as $\ce{S_N1}$ , $\ce{S_N2}$ , $\ce{E1}$ , and $\ce{E2}$ ), acid-base additions, and resonance structures.
Single-Headed (Fishhook) Arrow: Features a single barb. It represents the movement of a single electron (1 e^-). Fishhook arrows are exclusively used in radical mechanisms undergoing homolytic bond cleavage or radical addition steps.

DAT Mnemonic: "Double heads for Pairs in polar mechanisms; Fishhooks catch Single radicals!"

Feature	Double-Headed Curved Arrow	Single-Headed (Fishhook) Arrow
Electrons Moved	2 electrons (electron pair)	1 electron (single unshared electron)
Bond Cleavage Type	Heterolytic bond cleavage	Homolytic bond cleavage
Reaction Domain	Polar / Ionic reactions (acid-base, $\ce{S_N1}$ , $\ce{S_N2}$ , resonance)	Radical reactions (initiation, propagation, termination)
Tail Origin	Unshared lone pair or intact $\sigma$ / $\pi$ bond	Single radical electron or half of a breaking bond

Worked Examples and Exam Traps

Worked Example 1: Heterolytic Polar Attack ( $\ce{S_N2}$ Step)

Concrete Starting Point: Consider the reaction between hydroxide ion $\ce{OH-}$ and chloromethane $\ce{CH3Cl}$ .

Mechanism & Reasoning:

The electron-rich oxygen atom of $\ce{OH-}$ serves as the electron source. A double-headed curved arrow begins at a lone pair on oxygen (tail) and points directly to the electrophilic carbon atom of $\ce{CH3Cl}$ (sink) to form a new $\ce{C-O}$ $\sigma$ bond.
Because carbon cannot exceed an octet (second-row element limit), a simultaneous double-headed arrow must start at the $\ce{C-Cl}$ $\sigma$ bond (source) and point directly onto the chlorine atom (sink).

Products: Methanol $\ce{CH3OH}$ and chloride ion $\ce{Cl-}$ . Net charge is conserved ( $-1$ on reactants, $-1$ on products).

Common Exam Trap: Drawing an arrow from a positively charged carbon (carbocation) to an anion, or exceeding 8 valence electrons on a second-row atom (e.g., leaving 5 bonds on carbon without showing leaving group cleavage).

Worked Example 2: Homolytic Cleavage (Radical Initiation)

Concrete Starting Point: Di-tert-butyl peroxide $\ce{(CH3)3C-O-O-C(CH3)3}$ heated under thermal conditions ( $\Delta$ ).

Mechanism & Reasoning:

The weak $\ce{O-O}$ $\sigma$ bond breaks symmetrically.
Two single-headed fishhook arrows originate from the center of the $\ce{O-O}$ bond. One fishhook points to the left oxygen atom, and the second fishhook points to the right oxygen atom.

Products: Two tert-butoxy radicals $\ce{2 (CH3)3C-O\cdot}$ . Net charge remains neutral (0 on reactants, 0 on products).

Common Exam Trap: Using a full double-headed arrow for radical cleavage. A double-headed arrow implies heterolytic cleavage resulting in

\ce{RO+}

and

\ce{RO-}

, which is incorrect under radical conditions.

Critical Thinking Questions

Why is it mechanistically invalid on the DAT to draw a curved arrow starting from a carbocation ( $\ce{R3C+}$ )?
In the addition of $\ce{HBr}$ across an asymmetric alkene, why does the curved arrow originate at the $\pi$ bond rather than at the hydrogen atom?
How does drawing a double-headed arrow from a $\pi$ bond to an electronegative atom affect the formal charge bookkeeping of both atoms involved?
If a neutral molecule undergoes homolytic bond cleavage versus heterolytic bond cleavage, what are the resulting formal charge profiles of the products in each case?

References

Sources returned by Google Search grounding during lesson verification.

Curved Arrows (for reactions) - Master Organic Chemistry — masterorganicchemistry.com
6.6: Using Curved Arrows in Polar Reaction Mechanisms - Chemistry LibreTexts — chem.libretexts.org

Curved Arrow Notation

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