Reaction Mechanisms

Definition 1 (S$\_\text{N}$2): Bimolecular nucleophilic substitution — a single concerted step with backside attack.

$\text{Nu}^- + \text{R–LG} \to [\text{Nu}\cdots\text{R}\cdots\text{LG}]^{\ddagger} \to \text{Nu–R} + \text{LG}^-$

Theorem 1 (SN2 Rate Law):

$v = k[\text{Nu}^-][\text{R–LG}]$

Features:

• Second-order kinetics (depends on both nucleophile and substrate).
• Walden inversion (complete inversion of stereochemistry).
• Rate: $\text{CH}_3 > \text{1°} > \text{2°} \gg \text{3°}$ (3° essentially inert to S$\_\text{N}$2).
• Transition state: trigonal bipyramidal; the nucleophile and leaving group are at 180°.

Definition 2 (S$\_\text{N}$1): Unimolecular nucleophilic substitution — two steps via a carbocation intermediate.

$\text{R–LG} \xrightarrow{k_1} \text{R}^+ + \text{LG}^- \quad \text{(rate-determining)}$ $\text{R}^+ + \text{Nu}^- \xrightarrow{k_2} \text{R–Nu}$

Theorem 2 (SN1 Rate Law):

$v = k[\text{R–LG}]$

Features:

• First-order kinetics (rate independent of nucleophile concentration).
• Racemization (with possible slight inversion due to ion pairing).
• Rate: $\text{3°} > \text{2°} \gg \text{1°} > \text{CH}_3$.
• Favored by polar protic solvents and good leaving groups.

Theorem 3 (Carbocation Stability Order):

$\text{3°} > \text{2°} > \text{1°} > \text{CH}_3^+$

Stabilized by:

• Hyperconjugation: More C–H bonds adjacent $\implies$ more stabilization.
• Resonance: Allylic ($\text{CH}_2=\text{CH}-\text{CH}_2^+$) and benzylic cations are especially stable.
• Inductive effects: Alkyl groups donate electron density.

Definition 3 (Nucleophilicity): The ability of a species to donate an electron pair to carbon (to form a new bond). Measured by S$\_\text{N}$2 rate constants.

Definition 4 (Basicity): The thermodynamic tendency to accept a proton. Measured by pK$_a$ of the conjugate acid.

Theorem 4: For the same atom, nucleophilicity roughly parallels basicity. Exceptions:

• $\text{I}^-$ is a better nucleophile than $\text{F}^-$ (polarizability outweighs basicity in protic solvents).
• $\text{HS}^-$ is a better nucleophile than $\text{HO}^-$ (larger, more polarizable).
• Sterically hindered bases (e.g., $t$-BuO$^-$) are strong bases but poor nucleophiles.

Theorem 5 (Leaving Group Ability): The weaker the base, the better the leaving group:

$\text{I}^- > \text{Br}^- > \text{Cl}^- > \text{F}^- > \text{OH}^- \gg \text{NH}_2^-$

Weak bases make good leaving groups because they can stabilize the negative charge after departure. $\text{H}_2\text{O}$ is a better leaving group than $\text{HO}^-$; protonating $\text{HO}^-$ makes it $\text{H}_2\text{O}$.

• Polar protic solvents (e.g., H$_2$O, ROH): Stabilize ions, favor S$_\text{N}$1 by stabilizing the carbocation. Solvate small anions strongly (reduce nucleophilicity of $\text{F}^-$).
• Polar aprotic solvents (e.g., DMSO, DMF, acetone): Do not hydrogen-bond to anions; enhance nucleophilicity of small anions. Favor S$\_\text{N}$2.

Definition 5 (E2): Bimolecular elimination — concerted removal of HX.

$\text{Base} + \text{H–C–C–LG} \to \text{alkene} + \text{Base-H}^+ + \text{LG}^-$

Features:

• Anti-periplanar geometry required (H and LG at 180° dihedral).
• Rate: $v = k[\text{base}][\text{substrate}]$.
• Strong bases favor E2; bulky bases (e.g., $t$-BuOK) favor E2 over S$\_\text{N}$2.
• Zaitsev”s rule: The more substituted alkene is the major product.

Definition 6 (E1): Unimolecular elimination — carbocation intermediate, then deprotonation.

$\text{R–LG} \to \text{R}^+ + \text{LG}^- \quad \text{(rate-determining)}$ $\text{R}^+ \to \text{alkene} + \text{H}^+$

Features:

• First-order kinetics: $v = k[\text{substrate}]$.
• Competes with S$\_\text{N}$1 (same carbocation intermediate).
• Often gives a mixture of substitution and elimination products.

Definition 7 (E1cB): Elimination, unimolecular, conjugate base — deprotonation first, then leaving group departs.

$\text{Base} + \text{H–C–C–LG} \to \text{C}^--\text{C–LG} \to \text{alkene} + \text{LG}^-$

Favored when the leaving group is poor but the $\alpha$-H is acidic (e.g., carbonyl compounds).

Theorem 6 (Markovnikov’s Rule): In electrophilic addition to an unsymmetrical alkene, the electrophile adds to the carbon with more hydrogen atoms (the less substituted carbon).

$\text{HBr} + \text{CH}_3\text{CH}=\text{CH}_2 \to \text{CH}_3\text{CHBrCH}_3 \quad (\text{major})$

Mechanism: $\pi$ bond attacks electrophile $\to$ carbocation $\to$ nucleophile attack.

Regiochemistry: More substituted carbocation is favored (Markovnikov).

With HBr and peroxides (radical mechanism):

$\text{HBr} + \text{ROOR} \to \text{radical chain} \to \text{anti-Markovnikov product}$

$\text{Br}^\bullet + \text{CH}_3\text{CH}=\text{CH}_2 \to \text{CH}_3\text{CHCH}_2\text{Br} \quad (\text{anti-Markovnikov})$

Nucleophilic addition to C=O:

$\text{Nu}^- + \text{R}_2\text{C}=O \to \text{R}_2\text{C(O}^-\text{)Nu} \xrightarrow{\text{H}^+} \text{R}_2\text{CH(OH)Nu}$

• The carbonyl carbon is electrophilic due to the polarized $\text{C}^\delta+=\text{O}^\delta-$ bond.
• Nucleophilicity at carbonyl: the addition is favored by good nucleophiles and less hindered carbonyls.

For $\alpha,\beta$-unsaturated carbonyls:

$\text{Nu}^- + \text{CH}_2=\text{CH}-\text{C}=O \to \begin{cases} \text{1,2-addition (direct)} \\ \text{1,4-addition (conjugate/Michael)} \end{cases}$

Theorem 7: Hard nucleophiles (e.g., $^-$OH, $^-$CN) favor 1,2-addition. Soft nucleophiles (e.g., enolates, thiols) favor 1,4-addition (Michael addition).

1. Initiation: Homolytic cleavage (heat, light, or initiator): $\text{R–R} \xrightarrow{\Delta \text{ or } h\nu} 2\,\text{R}^\bullet$

2. Propagation: Radical reacts with stable molecule to generate a new radical: $\text{R}^\bullet + \text{H–C} \to \text{R–H} + \text{C}^\bullet$

3. Termination: Two radicals combine: $\text{R}^\bullet + \text{R}^\bullet \to \text{R–R}$

$\text{3°} > \text{2°} > \text{1°} > \text{CH}_3^\bullet > \text{H}^\bullet$

Allylic and benzylic radicals are especially stable due to resonance.

$\text{RH} + \text{X}_2 \xrightarrow{h\nu} \text{RX} + \text{HX}$

Selectivity:

• Chlorination: $3°:2°:1° \approx 5:4:1$ (moderately selective).
• Bromination: $3°:2°:1° \approx 1600:82:1$ (highly selective, follows radical stability).

Definition 8 (Pericyclic Reactions): Concerted reactions that proceed through a cyclic transition state without intermediates. Three main types:

• Electrocyclic reactions: Ring opening/closing involving $\pi$ bonds and $\sigma$ bonds.
• Cycloadditions: Two $\pi$ systems combine to form rings (e.g., Diels-Alder).
• Sigmatropic rearrangements: $\sigma$ bond migrates across a $\pi$ system.

Theorem 8 (Woodward-Hoffmann Rules): Pericyclic reactions proceed via the symmetry-allowed pathway. The rule depends on:

• Number of $\pi$ electrons.
• Thermal vs photochemical conditions.

Electrocyclic reactions:

Theorem 9 (Diels-Alder Reaction): A $[4 + 2]$ cycloaddition between a diene and a dienophile:

$\text{diene} + \text{dienophile} \to \text{cyclohexene}$

Requirements:

• Diene must be in the $s$-cis conformation.
• The reaction is thermally allowed (suprafacial on both components).
• Endo rule: The transition state leading to the endo product is lower in energy due to secondary orbital interactions.

Stereospecificity:

• cis-Dienophile → cis-substituents in the product.
• trans-Dienophile → trans-substituents in the product.
• The relative stereochemistry of the diene is preserved.

Example 1: Reaction of 1,3-butadiene with maleic anhydride gives the endo adduct stereospecifically.

$\blacksquare$

Definition 9: A sigmatropic rearrangement $[i,j]$ involves the migration of a $\sigma$ bond across a conjugated system of $i$ and $j$ atoms.

Theorem 10 (Cope Rearrangement): A $[3,3]$ sigmatropic rearrangement of 1,5-dienes:

$\text{CH}_2=\text{CH}-\text{CH}_2-\text{CH}_2-\text{CH}=\text{CH}_2 \rightleftharpoons \text{CH}_2=\text{CH}-\text{CH}_2-\text{CH}_2-\text{CH}=\text{CH}_2$

Thermally allowed via a chair-like transition state.

Claisen rearrangement: $[3,3]$ sigmatropic rearrangement of allyl vinyl ethers: $\text{CH}_2=\text{CH}-\text{CH}_2-\text{O}-\text{CH}=\text{CH}_2 \to \text{CH}_2=\text{CH}-\text{CH}_2-\text{CH}_2-\text{CHO}$

• Cyclobutene → 1,3-butadiene: Thermally conrotatory ($4n$ $\pi$ electrons).
• 1,3,5-Hexatriene → cyclohexadiene: Thermally disrotatory ($4n + 2$ $\pi$ electrons).

1. Electrophilic attack: $\text{E}^+$ adds to the aromatic ring, forming a resonance-stabilized arenium ion (sigma complex).
2. Deprotonation: Loss of H$^+$ restores aromaticity.

$\text{ArH} + \text{E}^+ \to [\text{ArHE}]^+ \xrightarrow{-\text{H}^+} \text{ArE}$

• Nitration: $\text{HNO}_3/\text{H}_2\text{SO}_4 \to \text{NO}_2^+$
• Sulfonation: $\text{SO}_3/\text{H}_2\text{SO}_4$
• Halogenation: $\text{Cl}_2/\text{FeCl}_3$ or $\text{Br}_2/\text{FeBr}_3$
• Friedel-Crafts alkylation: $\text{RCl}/\text{AlCl}_3$
• Friedel-Crafts acylation: $\text{RCOCl}/\text{AlCl}_3$

Definition 10 (S$_\text{N}$Ar): Two-step mechanism requiring electron-withdrawing groups ortho and/or para to the leaving group:

1. Nucleophilic addition to the aromatic ring (forming a Meisenheimer complex).
2. Elimination of the leaving group, restoring aromaticity.

$\text{Ar-X} + \text{Nu}^- \to [\text{Ar(X)(Nu)}]^- \to \text{Ar-Nu} + \text{X}^-$

Favored by strong EWGs and good leaving groups.

Under extreme conditions (strong base, very high $T$), elimination via benzyne intermediate:

$\text{Ar-X} + \text{NH}_2^- \to \text{benzyne} \to \text{Ar-NH}_2$

No regioselectivity; products are in most cases mixtures.

1. Confusing S$_\text{N}$1 and S$\_\text{N}$2 stereochemistry. S$_\text{N}$2 gives inversion; S$_\text{N}$1 gives racemization (not retention). Fix: S$_\text{N}$1 proceeds through a planar carbocation attacked from both sides.
2. Wrong regiochemistry in E2 reactions. Bulky bases favor the less substituted alkene (Hofmann product) via abstraction of the less hindered H. Fix: $t$-BuOK favors Hofmann; smaller bases favor Zaitsev.
3. Ignoring the anti-periplanar requirement in E2. The H and leaving group must be at 180°. Fix: Cyclohexyl halides can only eliminate if both H and LG are diaxial.
4. Wrong pericyclic stereochemistry. Electrocyclic reactions depend on the number of $\pi$ electrons and thermal/photochemical conditions. Fix: Apply Woodward-Hoffmann rules systematically.
5. Assuming all aromatic substitutions are electrophilic. Electron-poor rings undergo nucleophilic aromatic substitution (S$_\text{N}$Ar). Fix: Check if the ring has strong EWGs; if so, S$_\text{N}$Ar is likely.
6. Misassigning directing effects. Halogens are deactivating but ortho/para-directing (resonance donation outweighs inductive withdrawal for directing). Fix: Memorize the directing/activating table; halogens are a special case.
7. Overlooking ion pairing in S$\_\text{N}$1. The “racemic” product from S$\_\text{N}$1 is often slightly inverted due to the leaving group partially blocking one face. Fix: Use the ion-pair model for accurate stereochemical predictions.

• S$\_\text{N}$2: Concerted, backside attack, inversion, $v = k[\text{Nu}][\text{RX}]$, 1°/CH$_3$ favored.
• S$\_\text{N}$1: Stepwise, carbocation intermediate, racemization, $v = k[\text{RX}]$, 3° favored.
• E2: Concerted elimination, anti-periplanar, $v = k[\text{base}][\text{RX}]$.
• E1: Stepwise via carbocation, competes with S$\_\text{N}$1.
• Carbocation stability: 3° > 2° > 1° > CH$_3^+$; enhanced by resonance and hyperconjugation.
• Pericyclic reactions: Diels-Alder, Cope, Claisen; governed by Woodward-Hoffmann rules.
• Electrophilic aromatic substitution: Activating/deactivating groups control rate and directing.

Problem: Predict the mechanism and product when (1-bromo-1-methylpropyl)benzene reacts with NaCN in ethanol. The substrate is a tertiary benzylic halide. Solution: The tertiary benzylic carbon stabilises the carbocation through resonance with the benzene ring. SN1 is strongly favoured over SN2 (steric hindrance from the benzene ring and three alkyl groups). The carbocation is stabilised, leading to a racemic product (if the nucleophile attacks from both faces). Product: (1-cyano-1-methylpropyl)benzene, formed as a racemic mixture.

Problem: Predict the product of the Diels-Alder reaction between 1,3-butadiene and methyl vinyl ketone (MVK). Include regiochemistry. Solution: MVK is an electron-deficient dienophile. The diene (butadiene) is electron-rich. The endo transition state is favoured (Alder endo rule). Regiochemistry: the carbonyl group ends up ortho to the newly formed double bond in the cyclohexene product. Product: 4-acetylcyclohexene (endo). The reaction proceeds thermally [4+2] suprafacially.