DAT Organic Chemistry: Carbocation Rearrangements

DAT High-Yield Concept

Driving Force: Carbocation rearrangements occur spontaneously whenever a less stable intermediate ( $1^\circ$ or $2^\circ$ ) can transform into a more stable intermediate ( $3^\circ$ or resonance-stabilized) via a 1,2-shift.
Shift Preferences: Migratory aptitude follows the trend: hydride ( $\ce{H^-}$ ) > alkyl/methyl ( $\ce{CH3^-}$ ).
Ring Strain Relief: 4- and 5-membered rings with adjacent carbocations undergo ring expansion to form lower-strain 5- and 6-membered rings.
Reaction Scope: Rearrangements occur exclusively in stepwise mechanisms generating discrete carbocation intermediates ( $\text{S}_\text{N}1$ , $\text{E}1$ , electrophilic additions to alkenes), NOT in concerted reactions ( $\text{S}_\text{N}2$ , $\text{E}2$ ).

Fundamentals and General Mechanism

Carbocation Rearrangement: An intramolecular process in which an atom or group attached to an adjacent carbon (

\text{C}\beta

) migrates with its bonding pair of electrons to an electron-deficient carbocation carbon (

\text{C}\alpha

) to yield a more stable carbocation intermediate.

Carbocations are electron-deficient species with a vacant p orbital on an $sp^2$ -hybridized carbon. Relative stability follows the trend: tertiary ( $3^\circ$ ) > secondary ( $2^\circ$ ) > primary ( $1^\circ$ ) > methyl ( $\ce{CH3^+}$ ), with resonance-stabilized cations (allylic, benzylic) being exceptionally stable. Hyperconjugation and alkyl electron donation stabilize positive charge. When a carbocation forms adjacent to a carbon bearing a migratable group, a 1,2-shift can occur rapidly to lower the overall potential energy.

General mechanism for a carbocation rearrangement. (Source: FlyScienceGuy · CC BY-SA 4.0 · Wikimedia Commons)

1,2-Hydride Shifts

A 1,2-hydride shift involves the migration of a hydrogen atom with its pair of bonding electrons (a hydride ion, $\ce{H^-}$ ) from a neighboring carbon ( $\text{C}\beta$ ) into the empty p orbital of the positively charged carbon ( $\text{C}\alpha$ ). This shift occurs in a single concerted intramolecular step, converting a less stable secondary carbocation into a more stable tertiary or resonance-stabilized carbocation.

Worked Example: 1,2-Hydride Shift in Electrophilic Addition

Reaction: Treatment of 3-methyl-1-butene with hydrogen chloride ( $\ce{HCl}$ ).

Step 1 (Protonation): The alkene $\pi$ -bond attacks $\ce{HCl}$ according to Markovnikov's rule to yield a secondary carbocation intermediate:

\ce{CH2=CH-CH(CH3)2 + HCl -> CH3-CH^+-CH(CH3)2 + Cl^-}

Step 2 (Rearrangement): The secondary carbocation on C2 is adjacent to C3, which bears a tertiary hydrogen. A 1,2-hydride shift moves $\ce{H^-}$ from C3 to C2:

\ce{CH3-CH^+-CH(CH3)2 -> CH3-CH2-C^+(CH3)2}

This yields the thermodynamically preferred tertiary carbocation (2-methylbutan-2-yl cation).

Step 3 (Nucleophilic Attack): Chloride attacks the tertiary carbocation to form the major product:

\ce{CH3-CH2-C^+(CH3)2 + Cl^- -> CH3-CH2-CCl(CH3)2}

DAT Exam Trap: Expecting simple Markovnikov addition to yield 2-chloro-3-methylbutane. On the DAT, always check adjacent carbons for a hydrogen or alkyl group that can migrate to form a more stable $3^\circ$ carbocation.

1,2-Methyl and Alkyl Shifts

When a carbocation is adjacent to a quaternary carbon ( $4^\circ$ ) with no C–H bonds, a 1,2-hydride shift is impossible. Instead, an alkyl group (most commonly a methyl group, $\ce{CH3^-}$ ) migrates with its bonding pair of electrons to the carbocation center.

Worked Example: 1,2-Methyl Shift in Neopentyl Systems

Reaction: Reaction of neopentyl alcohol ( $\ce{(CH3)3C-CH2OH}$ ) with hydrobromic acid ( $\ce{HBr}$ ).

Step 1 (Protonation and Leaving Group Loss): Protonation of the hydroxyl group followed by water loss generates a primary neopentyl cation, which rearranges concurrently with leaving group departure to prevent high-energy primary carbocation formation:

\ce{(CH3)3C-CH2-OH2^+ -> CH3-CH2-C^+(CH3)2 + H2O}

Step 2 (Nucleophilic Capture): Bromide attacks the resulting tertiary carbocation:

\ce{CH3-CH2-C^+(CH3)2 + Br^- -> CH3-CH2-CBr(CH3)2}

The final product is 2-bromo-2-methylbutane, not 1-bromo-2,2-dimethylpropane.

DAT Exam Trap: Primary carbocations generally do not form as free intermediates; instead, neopentyl systems undergo concerted 1,2-methyl migration during leaving group departure.

Ring Expansions and Wagner-Meerwein Rearrangements

Ring expansion is a specialized 1,2-alkyl shift driven by the release of ring strain (angle strain and torsional strain). Small rings (cyclobutane and cyclopentane) with an adjacent exocyclic carbocation undergo migration of a ring C–C bond to expand the ring by one carbon (e.g., 4-membered ring to 5-membered ring, or 5-membered ring to 6-membered ring).

Worked Example: Ring Expansion Mechanism

Reaction: Acid-catalyzed dehydration of cyclobutylmethanol.

Protonation and water loss yield a cyclobutylmethyl carbocation. A C–C bond of the 4-membered ring migrates to the exocyclic carbocation carbon ( $\text{C}\alpha$ ), converting the strained 4-membered ring into a lower-strain 5-membered cyclopentyl cation. Elimination of a proton then yields cyclopentene as the major product.

Hydride versus Alkyl Migration Preference

When an adjacent carbon possesses both a hydrogen atom and an alkyl group, the hydride shift occurs exclusively over an alkyl shift.

Mnemonic — "Hydride Hops First": Hydride > Aryl > Alkyl. Hydrogen is smaller, experiences less steric hindrance, and breaking a C–H bond has a lower activation energy barrier than breaking a C–C bond.

Rearrangement Type	Migrating Group	Structural Prerequisite	Primary Driving Force
1,2-Hydride Shift	Hydride ( $\ce{H^-}$ )	Adjacent carbon with at least one C–H bond	Increase carbocation substitution ( $2^\circ \rightarrow 3^\circ$ ) or resonance
1,2-Methyl Shift	Methide / Methyl ( $\ce{CH3^-}$ )	Adjacent quaternary carbon ( $4^\circ$ ) with no hydrogens	Increase carbocation substitution ( $1^\circ/2^\circ \rightarrow 3^\circ$ )
Ring Expansion	Endocyclic C–C Bond	Strained ring (3-, 4-, or 5-membered) adjacent to cation	Relief of ring strain + carbocation stabilization

When Rearrangement is Impossible

Rearrangements do NOT occur under the following specific chemical conditions:

Concerted Reactions: Reactions that proceed without a carbocation intermediate (e.g., $\text{S}_\text{N}2$ , $\text{E}2$ , hydroboration-oxidation, oxymercuration-demercuration, halogenation with cyclic halonium ions) exhibit zero carbocation rearrangements.
No Thermodynamic Gain: If a shift would produce an equally stable carbocation without ring strain relief, the shift is non-productive and does not lead to a rearranged major product.
Bredt's Rule and Structural Constraints: Cations at bridgehead positions or rigid bicyclic systems cannot adopt the required planar $sp^2$ geometry or hyperconjugative orbital alignment needed for migration.
Non-Adjacent Positions: 1,3- or 1,4-shifts do not occur in a single step because the transition state orbital overlap over multi-bond distances is energetically unfavorable.

Critical Thinking Questions

Predict the major product formed when 3,3-dimethyl-2-butanol is heated with concentrated $\ce{H2SO4}$ . Identify the specific shift that occurs.
Why does oxymercuration-demercuration of 3-methyl-1-butene yield 3-methyl-2-butanol without rearrangement, whereas acid-catalyzed hydration yields 2-methyl-2-butanol?
In a cyclopentylmethyl system, why is ring expansion preferred over a 1,2-hydride shift from the adjacent tertiary ring carbon?

References

Sources returned by Google Search grounding during lesson verification.

Rearrangement Reactions (1): Hydride Shifts - Master Organic Chemistry — masterorganicchemistry.com
9.2: 1,2-Shifts in Carbocations - Chemistry LibreTexts — chem.libretexts.org

Carbocation Rearrangements

Summary

Practice Questions

AI Tutor