Unit 3: Unsaturated Hydrocarbons: Alkenes, Elimination Stereochemistry & Addition Mechanisms

Alkenes (olefins) are acyclic hydrocarbons containing at least one carbon-carbon double bond ($\text{C}=\text{C}$), corresponding to the general molecular formula $\text{C}_n\text{H}_{2n}$. Each double-bonded carbon is $sp^2$ hybridized, with three coplanar $sp^2$ hybrid orbitals forming strong $\sigma$ bonds at angles of approximately $120^\circ$ and one unhybridized $2p_z$ orbital oriented strictly perpendicular to the molecular plane. Parallel sideways overlap of the two $2p_z$ orbitals establishes a $\pi$ molecular bond.

The Index of Hydrogen Deficiency (IHD / Degree of Unsaturation)

The Degree of Unsaturation specifies the total sum of rings and $\pi$ bonds present in a molecule. For a general organic formula $\text{C}_c\text{H}_h\text{N}_n\text{O}_o\text{X}_x$ (where $\text{X} = \text{F, Cl, Br, I}$):

• Oxygen and sulfur atoms do not alter the saturated hydrogen count and are omitted from Eq. (3.1).
• Halogens replace one hydrogen atom (subtracted as $x/2$).
• Nitrogen atoms introduce an additional trivalent bond (added as $n/2$).
• An IHD of 1 corresponds to either one double bond or one ring; an IHD of 4 strongly suggests an aromatic benzene ring (3 $\pi$ bonds + 1 ring).

The Barrier to Rotation & Geometric Stereoisomerism

In alkanes, rotation about $\text{C}-\text{C}$ single $\sigma$ bonds is rapid under ambient conditions (torsional barrier in ethane is only $\sim 12\text{ kJ/mol}$). In alkenes, rotation about the $\text{C}=\text{C}$ double bond requires twisting the $2p_z$ orbitals out of parallel alignment, breaking the $\pi$ bond completely:

This colossal energy barrier prevents spontaneous rotation at temperatures below $400^\circ\text{C}$, freezing substituents into rigid, non-interconverting geometric stereoisomers.

The Cahn-Ingold-Prelog (CIP) $E/Z$ Priority Rules

While historical cis/trans terminology suffices for disubstituted alkenes, it fails for tri- and tetra-substituted systems. The CIP system assigns priority to the two substituents on each carbon:

1. Rule 1: Atomic Number: Higher atomic number takes precedence ($\text{I} > \text{Br} > \text{Cl} > \text{S} > \text{F} > \text{O} > \text{N} > \text{C} > \text{H} > \text{lone pair}$).

2. Rule 2: Subsequent Shells: If the bonded atoms are identical, compare the atoms attached to them in order of decreasing atomic number until a point of difference is reached.

3. Rule 3: Multiple Bonds: Multiply-bonded atoms are duplicated or triplicated (e.g., $-\text{CH}=\text{O}$ is treated as carbon bonded to $(\text{O, O, H})$).

• If the two highest-priority groups lie on the same side of the double bond: (Z) (from German zusammen = together).
• If the two highest-priority groups lie on opposite sides of the double bond: (E) (from German entgegen = opposite).

Cahn-Ingold-Prelog (CIP) Sequence Algorithm & Heats of Hydrogenation

The Cahn-Ingold-Prelog (CIP) priority rules establish an unambiguous, mathematical tree-traversal algorithm for assigning $(E)/(Z)$ descriptors to alkenes and $(R)/(S)$ descriptors to stereocenters:

1. CIP Hierarchical Tree Traversal Rules:

1. Rule 1 (Atomic Number): Higher atomic number precedes lower atomic number at the first point of difference along the ligand bond path:

2. Rule 2 (Isotopic Mass): If atomic numbers are identical, heavier isotopes precede lighter isotopes:

3. Rule 3 (Successive Sphere Comparison): If atoms at distance 1 are identical, construct an ordered list of atoms bonded to them in descending priority order. Compare the lists atom-by-atom at the first point of difference.

4. Rule 4 (Multiple Bonds - The Phantom Atom Rule): Multiply bonded atoms are duplicated by duplicating or triplicating them with phantom atoms (represented in parentheses with zero valence):

2. Heats of Hydrogenation & Thermodynamic Stability Benchmarks:

The catalytic addition of $\text{H}_2$ across an alkene to yield an alkane is strongly exothermic. Because all isomeric alkenes hydrogenate to the identical alkane, differences in standard heats of hydrogenation ($\Delta H_{\text{hydrog}}^\circ$) reflect the relative thermodynamic stability of the starting alkenes:

| Alkene Class | Example | Heats of Hydrogenation ($\Delta H_{\text{hydrog}}^\circ$) | Relative Thermodynamic Stability | | :---: | :---: | :---: | :---: | | Monosubstituted | 1-Butene | $\mathbf{-127\text{ kJ/mol}}$ ($-30.3\text{ kcal/mol}$) | Least stable | | gem-Disubstituted | 2-Methylpropene | $\mathbf{-119\text{ kJ/mol}}$ ($-28.4\text{ kcal/mol}$) | Intermediate | | cis-Disubstituted | cis-2-Butene | $\mathbf{-120\text{ kJ/mol}}$ ($-28.6\text{ kcal/mol}$) | Intermediate (steric clash) | | trans-Disubstituted | trans-2-Butene | $\mathbf{-115\text{ kJ/mol}}$ ($-27.6\text{ kcal/mol}$) | Stable | | Trisubstituted | 2-Methyl-2-butene | $\mathbf{-113\text{ kJ/mol}}$ ($-26.9\text{ kcal/mol}$) | Highly stable | | Tetrasubstituted | 2,3-Dimethyl-2-butene | $\mathbf{-111\text{ kJ/mol}}$ ($-26.6\text{ kcal/mol}$) | Most stable |

• Physical Origin of Stability: Increasing alkyl substitution stabilizes alkenes through:

1. Hyperconjugation: Overlap between filled $\sigma_{\text{C-H}}$ and $\sigma_{\text{C-C}}$ bonds of alkyl substituents and the empty $\pi^*$ antibonding orbital of the double bond ($\sigma \to \pi^*$).

2. Bond Strength: An $sp^2-sp^3$ $\text{C}-\text{C}$ single bond is shorter and stronger ($D \approx 360\text{ kJ/mol}$) than an $sp^3-sp^3$ single bond ($D \approx 347\text{ kJ/mol}$).

Alkenes are synthesized via $\beta$-elimination of alkyl halides or alcohols:

The Bimolecular Elimination ($E2$) Mechanism

The $E2$ pathway is a concerted, single-step bimolecular reaction exhibiting second-order kinetics:

The base abstracts the $\beta$-proton simultaneously with the expulsion of the leaving group and formation of the $\text{C}=\text{C}$ $\pi$ bond.

Strict Stereoelectronic Requirement: Anti-Periplanar Geometry

Quantum mechanical overlap requires that the $\text{C}_\beta-\text{H}$ $\sigma$ bonding orbital and the $\text{C}_\alpha-\text{X}$ $\sigma^*$ antibonding orbital lie in the same plane with a dihedral angle of $\phi = 180^\circ$ (anti-periplanar):

This allows smooth continuous electron flow from the breaking $\text{C}-\text{H}$ bond into the empty $\sigma^*$ orbital of the leaving group, transforming directly into the new $\pi$ bond with minimal electronic reorganization.

Regiochemical Control: Zaitsev vs Hofmann Elimination

1. Zaitsev's Rule (Thermodynamic Control):

When dehydrohalogenation is carried out with small, unhindered bases (such as $\text{NaOCH}_3, \text{NaOCH}_2\text{CH}_3, \text{NaOH}$), the major product is the most substituted, thermodynamically most stable alkene:

Stabilization originates from $\sigma_{\text{C}-\text{H}} \to \pi^*$ hyperconjugation and stronger $sp^2-sp^3$ $\sigma$ bonds.

2. Hofmann's Rule (Steric / Kinetic Control):

When dehydrohalogenation is carried out with sterically encumbered bases (such as potassium tert-butoxide, $\text{KO}t\text{-Bu}$, or lithium diisopropylamide, $\text{LDA}$), or with substrates bearing poor leaving groups (such as quaternary ammonium hydroxides $-\text{N}^+\text{R}_3$ or sulfonium $-\text{S}^+\text{R}_2$): Steric clash prevents the bulky base from accessing crowded interior $\beta$-hydrogens. The base abstracts the least hindered primary hydrogen, yielding the least substituted alkene as the major product.

Stereospecific Anti-Periplanar E2 Elimination in Cyclohexyl Systems

The base-promoted $E2$ elimination requires a strict anti-periplanar transition state ($\text{H}-\text{C}-\text{C}-\text{X}$ dihedral angle $\phi = 180^\circ$) to maximize overlap between the breaking $\sigma_{\text{C-H}}$ bonding orbital, the forming $\pi$ bond, and the departing $\sigma^*_{\text{C-X}}$ antibonding orbital.

Menthyl Chloride vs Neomenthyl Chloride:

This stereoelectronic requirement is demonstrated by the diastereomeric pair menthyl chloride and neomenthyl chloride:

1. Neomenthyl Chloride (Chlorine is Axial in Most Stable Chair):

• In its ground-state chair conformation, the bulky isopropyl group (A-value $= 2.15$) and methyl group (A-value $= 1.74$) occupy equatorial positions, placing the chlorine atom in the axial position at C3.
• The axial chlorine has two anti-periplanar axial hydrogens available on adjacent carbons: $\text{H}_{\text{ax}}$ at C2 (tertiary carbon) and $\text{H}_{\text{ax}}$ at C4 (secondary carbon).
• Elimination occurs rapidly upon treatment with ethoxide ($k_{\text{rel}} = 200$) to yield the more substituted, thermodynamic 3-menthene as the major Zaitsev product ($75\%$) alongside 2-menthene ($25\%$).

2. Menthyl Chloride (Chlorine is Equatorial in Most Stable Chair):

• In its ground-state chair conformation, chlorine is equatorial alongside isopropyl and methyl.
• In the equatorial position, chlorine has zero anti-periplanar hydrogens ($\phi \approx 60^\circ$).
• Elimination cannot occur from the ground state! The molecule must undergo an unfavorable chair-flip to a high-energy conformer where all three substituents become axial.
• In this diaxial conformer, the only available anti-periplanar hydrogen is at C4; the tertiary hydrogen at C2 is equatorial and cannot participate!
• Consequently, reaction rate is over 200 times slower, and the reaction exclusively produces the less-substituted 2-menthene ($100\%$), completely violating Zaitsev's rule due to absolute stereoelectronic anti-periplanar control!

The hallmark reaction of alkenes is electrophilic addition. Because the $\pi$ electron cloud lies above and below the nuclear plane and has a high-energy HOMO, it acts as an electron-rich Lewis base (nucleophile), reacting readily with electrophiles ($E^+$):

The Stepwise Carbocation Mechanism & Markovnikov's Rule

When a hydrogen halide ($HX$, where $X = \text{Cl, Br, I}$) adds across an unsymmetrical alkene:

1. Rate-Determining Step (RDS): The $\pi$ electrons attack the electrophilic proton ($H^+$), generating a carbocation intermediate:

2. Fast Trapping: The halide nucleophile ($X^-$) captures the carbocation:

Vladimir Markovnikov's Rule (1869)

In the addition of an unsymmetrical protic acid $HX$ to an unsymmetrical alkene, the acid hydrogen attaches to the carbon atom that already possesses the greater number of hydrogen atoms, while the halogen attaches to the more substituted carbon.

Modern Mechanistic Basis: Carbocation Stability

The reaction proceeds through the lowest activation energy barrier $\Delta G^\ddagger$, which by Hammond's postulate is governed by the relative thermodynamic stability of the carbocation intermediates:

• Hyperconjugation: Overlap of adjacent $\sigma_{\text{C}-\text{H}}$ and $\sigma_{\text{C}-\text{C}}$ bonds with the empty unhybridized $2p_z$ orbital of the cationic carbon delocalizes the positive charge. Each attached alkyl group contributes stabilizing hyperconjugative interactions.
• Inductive Electron Donation: Alkyl groups are polarizable and release electron density ($+I$) toward the electron-deficient positive center.

Carbocation Skeletal Rearrangements (1,2-Shifts)

Because carbocations are high-energy reactive intermediates with planar $sp^2$ geometry, they undergo rapid unimolecular isomerization whenever a 1,2-shift converts a less stable carbocation into a more stable one:

1. 1,2-Hydride Shift: A hydrogen atom migrates with its bonding pair of electrons:

2. 1,2-Alkyl (Methyl) Shift: A methyl or alkyl group migrates with its bonding pair:

These rearrangements frequently produce unexpected structural isomers in acid-catalyzed additions.

Wagner-Meerwein Rearrangements & The Peroxide Kharasch Effect

Electrophilic additions that generate open carbocation intermediates are subject to instantaneous 1,2-shifts if a more stable carbocation can be produced:

1. Wagner-Meerwein 1,2-Hydride & 1,2-Alkyl Shifts:

Consider the addition of $\text{HCl}$ to 3,3-dimethyl-1-butene (neopentylethylene):

• The secondary carbocation possesses an empty $p$-orbital adjacent to the bulky quaternary center.
• A methyl group migrates with its electron pair (1,2-methide shift) through a three-center two-electron bridge:

• Nucleophilic trapping by chloride yields 2-chloro-2,3-dimethylbutane as the major rearranged product ($85\%$) alongside unrearranged 3-chloro-2,2-dimethylbutane ($15\%$).

2. The Kharasch Peroxide Effect: Radical Mechanism of Anti-Markovnikov $\text{HBr}$ Addition:

In 1933, Morris Kharasch discovered that while addition of $\text{HBr}$ to alkenes in purified solvents gives Markovnikov products, traces of peroxides ($\text{ROOR}$) invert the regiochemistry to anti-Markovnikov:

1. Initiation: $\text{ROOR} \xrightarrow{\Delta \text{ or } h\nu} 2\,\text{RO}^\bullet \xrightarrow{+\text{HBr}} \text{ROH} + \mathbf{\text{Br}^\bullet}$

2. Propagation 1 (Regioselective Radical Attack):

• The bromine radical attacks the less substituted terminal carbon because this generates the significantly more stable secondary radical rather than an unstable primary radical ($E_a \approx 8\text{ kJ/mol}$).

3. Propagation 2 (Hydrogen Abstraction):

Why the Peroxide Effect is Strictly Unique to $\text{HBr}$:

• For $\text{HCl}$: Propagation 2 ($\text{R}^\bullet + \text{HCl} \to \text{RH} + \text{Cl}^\bullet$) is strongly endothermic ($\Delta H^\circ \approx +35\text{ kJ/mol}$) due to the high $\text{H}-\text{Cl}$ bond energy ($431\text{ kJ/mol}$), halting the chain.
• For $\text{HI}$: Propagation 1 ($\text{I}^\bullet + \text{alkene} \to \text{radical}$) is endothermic ($\Delta H^\circ \approx +22\text{ kJ/mol}$) due to the weak $\text{C}-\text{I}$ bond ($222\text{ kJ/mol}$), making addition reversible.
• Only for $\text{HBr}$ are both propagation steps exothermic ($\Delta H_1^\circ = -42\text{ kJ/mol}$, $\Delta H_2^\circ = -46\text{ kJ/mol}$), allowing self-sustaining radical chain catalysis!

When an alkene reacts with elemental bromine ($\text{Br}_2$) or chlorine ($\text{Cl}_2$) in non-nucleophilic solvents (such as $\text{CH}_2\text{Cl}_2$ or $\text{CCl}_4$), the reaction does not proceed through an open carbocation. Instead, it proceeds with strict stereospecific anti-addition.

The Cyclic Bromonium Ion Mechanism (Kimball & Roberts, 1937)

1. Electrophilic Attack & Ring Closure:

As the non-polar $\text{Br}_2$ molecule approaches the electron-rich alkene, its polarizable electron cloud is induced into a dipole ($^{\delta+}\text{Br}-\text{Br}^{\delta-}$). The $\pi$ electrons attack the electrophilic bromine atom while the bromine lone pair simultaneously back-donates into the developing empty orbital on carbon, displacing bromide ($\text{Br}^-$):

This generates a cyclic three-membered bromonium ion intermediate.

2. Stereospecific Backside Attack ($S_N2$):

The three-membered ring shields the face on which it formed. The liberated bromide ion ($\text{Br}^-$) can only attack from the opposite face (backside attack), opening the ring with complete inversion of configuration at the attacked carbon:

Proof of Stereospecificity:

• Addition of $\text{Br}_2$ to (E)-2-butene yields exclusively the optically inactive meso-2,3-dibromobutane.
• Addition of $\text{Br}_2$ to (Z)-2-butene yields exclusively the racemic pair $(\pm)$-2,3-dibromobutane ($50\% \; (2R,3R)$ and $50\% \; (2S,3S)$).

If an open carbocation were formed, free rotation about the $\text{C}-\text{C}$ single bond would have produced a mixture of meso and racemic diastereomers from both alkenes!

Quantum Nature of the Cyclic Bromonium Ion & Non-Classical Delocalization

The cyclic bromonium ion is an asymmetric three-membered ring whose electronic structure is best described as a closed three-center two-electron (3c-2e) $\sigma$ bonding system supplemented by back-donation from the bromine $4p$ lone pairs into the empty $p$-orbitals of the two carbons. The molecular orbital representation of the bromiranium ring consists of three orbitals formed by the linear combination of the two carbon $2p$ lobes and one bromine $4p$ orbital:

The two bonding electrons occupy $\Psi_1$, concentrating negative charge on bromine while spreading partial positive charge over the two carbon atoms. In an unsymmetrical alkene (such as propene or 2-methylpropene), the $\text{C}-\text{Br}$ bond to the more substituted carbon is significantly longer ($d \approx 2.25\text{ Å}$) than the bond to the primary carbon ($d \approx 2.05\text{ Å}$). Consequently, the more substituted carbon bears substantial partial positive charge ($^{\delta+}\text{C}$), which directs nucleophilic attack by external nucleophiles (such as water or alcohols in halohydrin synthesis) exclusively to the more substituted position with $100\%$ stereospecific inversion.

Stereochemical Outcomes of Bromination: Meso vs Racemic Mixtures

The electrophilic addition of bromine ($\text{Br}_2$) to alkenes proceeds via a three-membered cyclic bromonium ion intermediate, enforcing strict anti-stereospecificity:

Stereochemical Proof via (E)- and (Z)-2-Butene:

1. Addition to trans-2-Butene ((E)-isomer):

• Bromine attacks trans-2-butene to form an achiral meso-bromonium ion with a $C_{2v}$ plane of symmetry.
• Subsequent backside attack by bromide ion ($\text{Br}^-$) with equal probability at C2 or C3 produces:

2. Addition to cis-2-Butene ((Z)-isomer):

• Bromine attacks cis-2-butene to form a chiral pair of enantiomeric bromonium ions.
• Backside attack by bromide at either carbon inverts that center, yielding an equimolar mixture of $(2R, 3R)$ and $(2S, 3S)$ enantiomers:

Isolation of Stable Bromonium Ions:

In 1969, Strating, Bolster, and Wynne isolated and crystal-analyzed the first stable bromonium triflate salt using adamantylideneadamantane. The bulky adamantyl cages steric shield both faces of the three-membered ring, preventing nucleophilic attack by bromide and allowing single-crystal X-ray diffraction that conclusively proved the symmetric $\text{C}-\text{Br}-\text{C}$ three-membered ring geometry ($r_{\text{C}-\text{Br}} = 2.11\text{ \AA}$, $\angle \text{C}-\text{Br}-\text{C} = 65.8^\circ$)!

The addition of water across an alkene converts it into an alcohol. Modern organic chemistry possesses three complementary methods with distinct regiochemical and stereochemical controls:

1. Acid-Catalyzed Hydration

• Reagent: Dilute aqueous sulfuric acid ($\text{H}_2\text{SO}_4 / \text{H}_2\text{O}$).
• Mechanism: Stepwise addition via open carbocation intermediate.
• Regioselectivity: Markovnikov.
• Major Limitation: Severely prone to carbocation rearrangements (1,2-hydride and methyl shifts), giving low yields of the unrearranged product whenever branching is present.

2. Oxymercuration-Demercuration (Markovnikov without Rearrangement)

• Reagents:

1. Mercury(II) acetate in aqueous THF: $\text{Hg(OAc)}_2, \text{H}_2\text{O}$.
2. Sodium borohydride in basic media: $\text{NaBH}_4, \text{NaOH}$.

• Mechanism:
• Reaction of the alkene with $\text{Hg(OAc)}^+$ forms a stable, three-membered mercurinium ion intermediate, locking the carbon skeleton and completely preventing carbocation rearrangements.
• Water attacks the mercurinium ion at the more substituted, more electrophilic carbon (partial carbocation character).
• In step 2, $\text{NaBH}_4$ replaces the mercury moiety with hydrogen via radical demercuration.
• Outcome: Markovnikov alcohol in high yield without skeletal rearrangement.

3. Hydroboration-Oxidation (Herbert C. Brown, Nobel Prize 1979)

• Reagents:

1. Borane-THF complex: $\text{BH}_3 \cdot \text{THF}$.
2. Alkaline hydrogen peroxide: $\text{H}_2\text{O}_2, \text{NaOH}$.

• Mechanism:
• Boron is electron-deficient (empty $2p$ orbital) and acts as the electrophile. Borane adds to the alkene in a concerted, four-membered cyclic square transition state:

• Steric Factor: Boron ($-\text{BH}_2$) is sterically bulkier than hydrogen, attaching preferentially to the less crowded, less substituted terminal carbon.
• Electronic Factor: Partial positive charge develops on the more substituted carbon in the transition state, stabilizing the developing charge.
• Oxidation: Treatment with alkaline $\text{H}_2\text{O}_2$ oxidizes the trialkylborane via hydroperoxide anion addition and 1,2-alkyl migration with complete retention of stereochemical configuration.
• Outcome: Anti-Markovnikov, stereospecific syn-addition of water.

Stereochemical Retention in the Hydroboration-Oxidation Mechanism

The hydroboration-oxidation sequence converts alkenes into alcohols with anti-Markovnikov regiochemistry and syn-stereospecificity. The alkaline peroxide oxidation step demonstrates an extraordinary stereochemical phenomenon: complete retention of configuration at carbon:

Line-by-Line Mechanistic Sequence of Oxidation:

1. Nucleophilic Addition: The hydroperoxide anion ($\text{HOO}^-$, generated by $\text{H}_2\text{O}_2 + \text{OH}^-$) coordinates to the vacant $p$-orbital of boron, forming a tetrahedral borate complex.

2. 1,2-Alkyl Migration with Retention:

An alkyl group migrates with its bonding pair from boron to the adjacent oxygen atom, displacing hydroxide ion:

• Stereochemical Preservation: The migrating carbon atom interacts with oxygen from the same face as its bond to boron via a three-center two-electron $[B-C-O]$ transition state.
• The carbon center never becomes detached as a free carbocation or radical; therefore, its stereochemical configuration is preserved with $100\%$ retention!

3. Repeated Migration & Hydrolysis:

The migration repeats twice more until all three alkyl groups are converted to an orthoborate ester $\text{B}(\text{OR})_3$. Basic hydrolysis then quantitatively yields three equivalents of alcohol and sodium borate:

1. Ozonolysis (The Criegee Mechanism)

Ozone ($\text{O}_3$, a 1,3-dipole) oxidatively cleaves both the $\sigma$ and $\pi$ bonds of an alkene:

1. 1,3-Dipolar Cycloaddition: Ozone adds across the $\text{C}=\text{C}$ double bond to form an unstable primary ozonide (molozonide).

2. Retro-Cycloaddition: The molozonide fragments into a carbonyl compound and a carbonyl oxide zwitterion (Criegee intermediate).

3. Recombination: The fragments recombine to form a stable secondary ozonide (trioxolane).

4. Workup:

• Reductive Workup ($\text{Zn} / \text{CH}_3\text{COOH}$ or dimethyl sulfide, $\text{(CH}_3)_2\text{S}$): Cleaves the ozonide to aldehydes and ketones without further oxidation.
• Oxidative Workup ($\text{H}_2\text{O}_2$): Converts aldehydes into carboxylic acids.

2. Epoxidation (The Prilezhaev Reaction)

Peroxycarboxylic acids (such as meta-chloroperoxybenzoic acid, $m$CPBA) react with alkenes to form epoxides (oxiranes) via a concerted 'butterfly' transition state:

The reaction is strictly stereospecific syn-addition: a cis-alkene produces a cis-disubstituted epoxide, while a trans-alkene produces a trans-disubstituted epoxide.

3. Syn-Dihydroxylation: Potassium Permanganate & Osmium Tetroxide

Alkenes react with cold, dilute, alkaline $\text{KMnO}_4$ (Baeyer's Test) or catalytic $\text{OsO}_4$ with $N$-methylmorpholine $N$-oxide (NMO, Upjohn dihydroxylation) to form vicinal syn-diols (glycols):

Because both oxygen atoms are delivered simultaneously from the same face of the planar cyclic osmate ester intermediate, the addition is strictly stereospecific syn.

Isotopic $^{18}\text{O}$ Tracing & The Complete Criegee Mechanism of Ozonolysis

The mechanism of ozonolysis was definitively elucidated by Rudolf Criegee using oxygen-18 ($^{18}\text{O}$) isotopic labeling experiments:

1. Primary Cycloaddition: Ozone adds across the alkene double bond in a concerted $[3+2]$ cycloaddition to form the primary ozonide (1,2,3-trioxolane / molozonide).

2. Cycloreversion: The molozonide is thermodynamically unstable due to the weak $\text{O}-\text{O}$ peroxo linkages. It undergoes an immediate retro-$[3+2]$ cycloreversion, cleaving both the central $\text{C}-\text{C}$ $\sigma$ bond and an $\text{O}-\text{O}$ bond to generate:

• A neutral carbonyl compound (aldehyde or ketone).
• A zwitterionic carbonyl oxide (Criegee intermediate):

3. Recombination: In non-participating solvents, the carbonyl oxide flips orientation and undergoes a second $[3+2]$ cycloaddition with the carbonyl fragment, forming the secondary ozonide (1,2,4-trioxolane).

4. Isotopic Proof: When ozonolysis of an alkene is performed in the presence of an added aldehyde enriched with $^{18}\text{O}$ at the carbonyl oxygen, the resulting 1,2,4-trioxolane incorporates the $^{18}\text{O}$ label specifically into the ether bridge of the trioxolane ring. This confirmed that the original $\text{C}-\text{C}$ bond is completely severed during the cycloreversion step, ruling out any direct intramolecular migration!

Detailed Multistep Criegee Mechanism of Ozonolysis

Ozonolysis provides a diagnostic method for locating the position of double bonds through oxidative cleavage. The complete mechanism, elucidated by Rudolf Criegee in 1953, proceeds through three distinct pericyclic steps:

``` O O-O O-O || [3+2] / \ Retro-[3+2] / \ R2C = CR2 + O-O ------> R2C--CR2 -----------> R2C=O + R2C O (Molozonide) \_____/ (Criegee Zwitterion) | | [3+2] v O-O / \ R2C CR2 \ O / \___/ (Secondary Ozonide) ```

1. Step 1: 1,3-Dipolar Cycloaddition to Molozonide:

Ozone ($:\stackrel{-}{\text{O}}-\stackrel{+}{\text{O}}=\text{O}$) undergoes a concerted $[3+2]$ cycloaddition across the alkene $\pi$ bond to form an unstable primary ozonide (molozonide or 1,2,3-trioxolane).

2. Step 2: Retro-[3+2] Cycloaddition:

The weak $\text{O}-\text{O}$ single bonds and strained ring induce spontaneous cycloreversion, cleaving both the $\text{C}-\text{C}$ $\sigma$-bond and one $\text{O}-\text{O}$ bond to generate a carbonyl compound and a carbonyl oxide (Criegee zwitterion / 1,3-dipole):

3. Step 3: Recombination to Secondary Ozonide (1,2,4-Trioxolane):

The carbonyl oxide flips orientation and undergoes a second $[3+2]$ dipolar cycloaddition across the carbonyl group, forming the stable secondary ozonide (1,2,4-trioxolane).

4. Workup Regimes:

• Reductive Workup ($\text{Me}_2\text{S}$ or $\text{Zn} / \text{AcOH}$): Reduces the trioxolane to aldehydes and ketones without over-oxidation:

• Oxidative Workup ($\text{H}_2\text{O}_2 / \text{NaOH}$): Any aldehydes are oxidized to carboxylic acids:

Polymerization of alkenes converts thousands of monomeric units into high-molecular-weight macromolecules:

1. Free-Radical Polymerization

• Initiators: Organic peroxides (benzoyl peroxide, AIBN) that undergo homolytic cleavage.
• Propagation: Radicals add to the terminal methylene of alkene monomers.
• Consequence: Produces Low-Density Polyethylene (LDPE) containing extensive short- and long-chain branching caused by intramolecular 'backbiting' hydrogen abstraction.

2. Ionic Polymerization

• Cationic Polymerization: Initiated by Lewis acids ($\text{BF}_3, \text{AlCl}_3$ + traces of $\text{H}_2\text{O}$) for monomers with electron-donating groups (isobutylene $\to$ polyisobutylene / butyl rubber).
• Anionic Polymerization: Initiated by strong nucleophiles ($n\text{-BuLi}, \text{NaNH}_2$) for monomers bearing electron-withdrawing groups (acrylonitrile, methyl methacrylate). Operates as living polymerization with zero spontaneous chain termination.

3. Ziegler-Natta Coordination Polymerization (Nobel Prize 1963)

Karl Ziegler and Giulio Natta introduced heterogeneous catalysts consisting of titanium tetrachloride and triethylaluminum:

• Cossee-Arlman Mechanism: The alkene coordinates to an open coordination site on the octahedral titanium center and inserts into the titanium-carbon $\sigma$ bond.
• Stereochemical Control: Enables the synthesis of strictly linear High-Density Polyethylene (HDPE) and isotactic polypropylene (all methyl groups arranged on the identical side of the backbone), yielding polymers with superior tensile strength and high melting points.

The Chauvin Metallacyclobutane Mechanism of Olefin Metathesis

Awarded the 2005 Nobel Prize in Chemistry (Yves Chauvin, Robert Grubbs, Richard Schrock), olefin metathesis involves the redistribution of alkylidene fragments between alkenes through the catalytic cleavage and reformation of carbon-carbon double bonds:

``` R1-CH = CH-R1 R1-CH --- CH-R1 + [2+2] | | [M] = CH-R2 --------> [M] ----- CH-R2 (Transition Metal (Metallacyclobutane Alkylidene) Intermediate) | | Retro-[2+2] v R1-CH = CH-R2 (Crossed Alkene) + [M] = CH-R1 (Active Catalyst) ```

1. The Chauvin Mechanism:

1. [2+2] Cycloaddition: The active transition metal alkylidene ($[\text{M}]=\text{CHR}_2$) undergoes a concerted $[2+2]$ cycloaddition with an alkene $\pi$ bond to form a four-membered metallacyclobutane intermediate.

2. Retro-[2+2] Cleavage: The metallacyclobutane cleaves in the orthogonal direction, expelling a new alkene product ($\text{R}_1\text{CH}=\text{CHR}_2$) and generating a new propagating metal alkylidene ($[\text{M}]=\text{CHR}_1$).

3. Microscopic Reversibility: Because all steps are reversible, the equilibrium distribution is driven by thermodynamics or the irreversible removal of volatile byproducts:

• In Ring-Closing Metathesis (RCM): Formation of a cyclic alkene is entropically favored and driven by the irreversible escape of volatile ethylene gas ($\text{CH}_2=\text{CH}_2\uparrow$) from the reaction vessel!

2. Metathesis Catalysts:

• Schrock Catalysts: High-oxidation-state molybdenum(VI) and tungsten(VI) alkylidenes ($(\text{ArN})(\text{RO})_2\text{Mo}=\text{CHR}$). Extremely active, able to cleave sterically hindered and electron-deficient double bonds, but air- and moisture-sensitive.
• Grubbs 1st Generation Catalyst: Ruthenium(II) carbene complex $(\text{PCy}_3)_2\text{Cl}_2\text{Ru}=\text{CHPh}$. Exceptional functional group tolerance (compatible with alcohols, water, acids, esters).
• Grubbs 2nd Generation Catalyst: Replaces one tricyclohexylphosphine with an $N$-heterocyclic carbene (NHC, $\text{IMes}$ or $\text{SIMes}$). The strong $\sigma$-donor ability of the NHC ligand accelerates phosphine dissociation ($k_1$) and stabilizes the 14-electron catalytic intermediate, increasing catalytic activity by over $10^4$-fold!

Sharpless Asymmetric Epoxidation & Dihydroxylation

K. Barry Sharpless (2001 & 2022 Nobel Prize) developed catalytic asymmetric oxidations that achieve near-perfect enantioselectivity ($>98\%$ enantiomeric excess, $ee$):

1. Sharpless Asymmetric Epoxidation of Allylic Alcohols:

• Reagent System: Titanium(IV) tetraisopropoxide ($\text{Ti(O-}i\text{-Pr)}_4$), chiral diethyl tartrate (DET), and tert-butyl hydroperoxide ($t$-BuOOH) in dichloromethane at $-20^\circ\text{C}$.
• Active Catalyst: A dimeric titanium complex ($[\text{Ti}_2(\text{DET})_2(\text{O-}i\text{-Pr})_2]$) coordinates both the allylic alcohol's hydroxyl oxygen and the tert-butylperoxide group simultaneously.
• Enantioselection Rule (Sharpless Mnemonic):
• Draw the allylic alcohol with the $-\text{CH}_2\text{OH}$ group at the bottom right.
• Adding $(-)$-diethyl tartrate (D-tartrate) delivers oxygen exclusively to the top face ($\beta$-face).
• Adding $(+)$-diethyl tartrate (L-tartrate) delivers oxygen exclusively to the bottom face ($\alpha$-face).

2. Sharpless Asymmetric Dihydroxylation (AD):

• Ligands: Cinchona alkaloid derivatives anchored to a phthalazine core:
• AD-mix-$\alpha$ contains $(\text{DHQ})_2\text{PHAL}$ (dihydroquinine derivative) $\to$ attacks from the $\alpha$-face.
• AD-mix-$\beta$ contains $(\text{DHQD})_2\text{PHAL}$ (dihydroquinidine derivative) $\to$ attacks from the $\beta$-face.
• Potassium ferricyanide ($\text{K}_3\text{Fe(CN)}_6$) serves as the stoichiometric terminal co-oxidant in the aqueous phase, re-oxidizing the reduced osmium(VI) glycolate ester back to active osmium(VIII) without generating toxic volatile $\text{OsO}_4$ vapor!

High-Density vs Low-Density Polyethylene: Radical vs Ziegler-Natta Regimes

Polyethylene ($\text{PE}$) is the largest volume synthetic polymer globally, manufactured in two fundamentally distinct structural architectures:

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1. LOW-DENSITY POLYETHYLENE (LDPE):

• Process: Free-radical, 1000 - 3000 atm, 200 - 300 deg C
• Mechanism: Intramolecular 1,5-hydrogen shift ("Backbiting")
• Structure: Highly branched (butyl and ethyl short-chain branches)
• Properties: Low crystallinity (40 - 55%), Tm = 105 - 115 deg C, density = 0.91 - 0.93 g/cm3

1. HIGH-DENSITY POLYETHYLENE (HDPE):

• Process: Ziegler-Natta or Metallocene, 1 - 50 atm, 70 - 100 deg C
• Mechanism: Linear Cossee-Arlman migratory insertion
• Structure: Strictly linear, virtually unbranched polymer chains
• Properties: High crystallinity (70 - 85%), Tm = 130 - 137 deg C, density = 0.94 - 0.97 g/cm3

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1. The "Backbiting" Intramolecular Hydrogen Shift in LDPE:

During high-pressure free-radical polymerization, the propagating terminal secondary radical undergoes an intramolecular 1,5-hydrogen atom abstraction through a cyclic six-membered transition state:

• The newly generated internal secondary radical continues chain propagation by adding ethylene monomers, generating a butyl ($-\text{C}_4\text{H}_9$) branch.
• These branches disrupt regular chain folding into crystal lamellae, resulting in flexible, low-density material suitable for films and plastic bags.

2. Advanced Polymer Characterization: GPC & DSC:

1. Gel Permeation Chromatography (GPC / SEC): Measures molecular weight distributions:

• Number-average molecular weight: $\bar{M}_n = \frac{\sum N_i M_i}{\sum N_i}$
• Weight-average molecular weight: $\bar{M}_w = \frac{\sum N_i M_i^2}{\sum N_i M_i}$
• Polydispersity Index: $\text{PDI} = \frac{\bar{M}_w}{\bar{M}_n}$ (Metallocenes give narrow $\text{PDI} \approx 2.0$; classical heterogeneous Ziegler-Natta give broad $\text{PDI} \approx 4 - 8$).

2. Differential Scanning Calorimetry (DSC): Measures the glass transition temperature ($T_g$) and crystalline melting peak ($T_m$). The percentage crystallinity $X_c$ is quantified by integrating the melting endotherm:

where $\Delta H_m^\circ = 293\text{ J/g}$ for $100\%$ crystalline polyethylene.

Systematic Alkene Reaction Master Matrix

| Reaction Protocol | Reagents | Regiochemistry | Stereospecificity | Intermediate Species | Rearrangements? | | :---: | :---: | :---: | :---: | :---: | :---: | | Hydrohalogenation | $\text{HX}$ ($\text{X}=\text{Cl, Br, I}$) | Markovnikov | Non-stereospecific | Open carbocation | Yes (Hydride/Alkyl) | | Radical Addition | $\text{HBr} + \text{ROOR}$ | Anti-Markovnikov | Non-stereospecific | Carbon radical | No | | Halogenation | $\text{Br}_2 \text{ or } \text{Cl}_2$ | N/A | Strict Anti | Cyclic halonium ion | No | | Halohydrin | $\text{Br}_2 / \text{H}_2\text{O}$ | $\text{OH}$ at more subst. C | Strict Anti | Cyclic halonium ion | No | | Acid Hydration | $\text{H}_2\text{O} / \text{H}_2\text{SO}_4$ | Markovnikov | Non-stereospecific | Open carbocation | Yes | | Oxymercuration | $1.\;\text{Hg(OAc)}_2/\text{H}_2\text{O} \; 2.\;\text{NaBH}_4$ | Markovnikov | Anti (addition step) | Cyclic mercurinium ion | Strictly No | | Hydroboration | $1.\;\text{BH}_3\cdot\text{THF} \; 2.\;\text{H}_2\text{O}_2/\text{OH}^-$ | Anti-Markovnikov | Strict Syn | 4-membered cyclic TS | Strictly No | | Epoxidation | $m\text{CPBA}$ | N/A | Strict Syn | Butterfly transition state | No | | Syn-Dihydroxylation | $\text{OsO}_4 / \text{NMO}$ | N/A | Strict Syn | Cyclic osmate ester | No | | Ozonolysis | $1.\;\text{O}_3 \; 2.\;\text{Me}_2\text{S}$ | Cleavage | N/A | Molozonide $\to$ Trioxolane | No |