Organic Chemistry: Conjugated Unsaturated Systems

Chapter 13: Conjugated Unsaturated Systems Notes

Molecular Orbitals of Conjugated Systems

Conjugated Unsaturated Systems: Characterized by the presence of alternating single and double bonds, or a system where p-orbitals are aligned consecutively, allowing for the delocalization of $\pi$ (pi) electrons.
Examples:
- 1,3-Butadiene: A conjugated diene, $H2C=CH-CH=CH2$
- Allyl radical: $CH2=CH-CH2\cdot$ (with an unpaired electron)
- Allylic carbocation: $CH2=CH-CH2^+$ (with a positive charge)

Molecular Orbital View of Allyl Radical

Hybridization: All three carbon atoms in the allyl radical are $sp^2$ hybridized.
Formation: An allyl radical is formed, for example, via hydrogen abstraction from an allylic $sp^3$ hybridized carbon in propene, converting it to an $sp^2$ carbon.
Delocalization: The unpaired electron in the allyl radical is delocalized over the terminal carbon atoms, due to the overlap of three adjacent p-orbitals.

Orbital Energies of Allyl Radical

Atomic Orbitals: Three isolated p-orbitals, each containing one electron.
Molecular Orbitals: These three atomic p-orbitals combine to form three molecular orbitals:
- Bonding orbital ( $MO_1$ ): Lowest energy, no nodes between the carbons. Allows for maximum overlap and stabilization.
- Nonbonding orbital ( $MO_2$ ): Intermediate energy, has one node. The unpaired electron resides in this orbital.
- Antibonding orbital ( $MO_3^*$ ): Highest energy, has two nodes. Destabilizing.
Electron Configuration: The three $\pi$ electrons (one from each carbon) occupy these orbitals: two electrons in the bonding orbital ( $MO1$ ) and one electron in the nonbonding orbital ( $MO2$ ).

Allylic Radical Resonance

Representation: The allyl radical can be represented by two equivalent resonance structures where the double bond and the radical electron are shifted, indicating delocalization (e.g., $CH2=CH-\dot{C}H2 \leftrightarrow \dot{C}H2-CH=CH2$ ).
Proof of Resonance (Experimental Evidence): Reaction of propene with $Cl_2$ at high temperatures (radical conditions) leads to allylic chlorination. If the starting propene is radioactively labeled with $^{14}C$ at C1, the products formed (e.g., 3-chloro-1-propene) show $^{14}C$ distributed equally (50% at C1 and 50% at C3). This confirms the symmetrical nature of the allylic radical intermediate due to electron delocalization.

Relative Stability of Cations

Allylic Cations: Are exceptionally stable due to resonance delocalization of the positive charge.
Stability Order (Descending):
- Substituted allylic (e.g., $3^\circ$ allylic) > $3^\circ$ alkyl > Allyl > $2^\circ$ alkyl > Vinyl > $1^\circ$ alkyl

Orbital Energies of Allyl Cation

Similar to the allyl radical, three p-orbitals combine.
Electron Configuration: The allyl cation has only two $\pi$ electrons. Both electrons occupy the lowest energy bonding orbital ( $MO_1$ ). The nonbonding and antibonding orbitals remain empty.
This electron configuration accounts for the stability due to fully populating a bonding orbital.

Allylic Cation Resonance

Representation: The allylic cation can be represented by two equivalent resonance structures showing the positive charge delocalized over the two terminal carbon atoms (e.g., $CH2=CH-CH2^+ \leftrightarrow ^+CH2-CH=CH2$ ).
Hybrid Representation: The actual structure is a resonance hybrid with a partial positive charge ( $\delta+$ ) distributed over the two terminal carbons.

Rules for Resonance Structures

1. Resonance structures only exist on paper: They are theoretical constructs; the actual molecule is a hybrid, not rapidly interconverting between structures.
2. Atoms do not move in resonance: Only electrons ($\pi$ electrons and lone pairs) are delocalized. The connectivity of atoms remains the same.
3. Proper Lewis Structures are still required: Resonance structures must abide by Lewis structure rules, including octet rule (or duet for hydrogen) and formal charges. For example, a carbon cannot have 10 electrons.
4. Additional electron unpairing is forbidden: Electrons are simply de-localized; their pairing status (singlet, doublet, etc.) must be conserved.
5. Resonating groups must be coplanar: For effective overlap of p-orbitals, the atoms involved in resonance must lie in the same plane. Steric hindrance can prevent coplanarity and thus resonance (e.g., 2,3-di-tert-butyl-1,3-butadiene).
6. Resonance stabilizes: Delocalization of electrons leads to increased stability of the molecule or ion.
7. Equal resonance structures contribute equally: If two or more resonance structures are equivalent in energy and bonding, they contribute equally to the overall hybrid (e.g., benzene has two equal Kekulé structures).
8. Resonance structures need not be energetically equal: If structures are not equivalent, the more stable resonance structures contribute more to the overall hybrid representation.
9. More covalent bonds increase stability: Resonance structures with a greater number of covalent bonds are generally more stable and contribute more to the hybrid.
10. Full valence shells increase stability: Structures where all atoms (especially carbons) have complete octets are more stable and contribute more, even if they bear formal charges.
11. Charge separation decreases stability: Structures with separated charges (e.g., positive and negative charges on different atoms) are less stable than those without charge separation, provided all valencies are satisfied.

Polyunsaturated Hydrocarbons

Polyunsaturated hydrocarbons can be classified based on the arrangement of their double bonds:

1. Cumulated Dienes: Double bonds are adjacent to each other (e.g., $C=C=C$ ).
- Example: Allene (1,2-propadiene, $H2C=C=CH2$ ).
- The central carbon is $sp$ hybridized, and the terminal carbons are $sp^2$ hybridized.
- The p-orbitals on the central carbon overlap with p-orbitals on both adjacent carbons, but at 90-degree angles, leading to specific geometry.
2. Conjugated Dienes: Double bonds are separated by exactly one single bond (e.g., $C=C-C=C$ ).
- Example: 1,3-Butadiene ( $H2C=CH-CH=CH2$ ).
- All carbons involved are $sp^2$ hybridized, allowing for continuous overlap of p-orbitals across the entire system.
3. Isolated Dienes: Double bonds are separated by two or more single bonds (e.g., $C=C-(CH2)n-C=C$ where $n \ge 1$ ).
- Example: 1,4-Pentadiene ( $H2C=CH-CH2-CH=CH_2$ ).
- These double bonds behave independently as isolated alkenes; there is no significant conjugation.

Conjugation Shortens Bond Lengths

Bond Lengths: In 1,3-butadiene, the carbon-carbon double bonds are $1.34 \text{ Å}$ , which is typical for a double bond. However, the central single bond ( $C2-C3$ ) is $1.47 \text{ Å}$ , which is shorter than a typical $sp^3-sp^3$ single bond ( $1.54 \text{ Å}$ ) or even an $sp^2-sp^3$ single bond ( $1.50 \text{ Å}$ ).
Reason: This shortening indicates partial double bond character in the central single bond, further evidence of electron delocalization through resonance in conjugated systems.

Single Bond Lengths and Hybridization

Compound	Hybridization State	Bond Length (Å)
$H<em>3C-CH</em>3$	$sp^3-sp^3$	$1.54$
$H<em>2C=CH-CH</em>3$	$sp^2-sp^3$	$1.50$
$H<em>2C=CH-CH=CH</em>2$	$sp^2-sp^2$	$1.47$
$HC\equiv C-CH_3$	$sp-sp^3$	$1.46$
$HC\equiv C-CH=CH_2$	$sp-sp^2$	$1.43$
$HC\equiv C-C\equiv CH$	$sp-sp$	$1.37$

Trend: As the s-character in the hybridized orbitals increases (from $sp^3$ to $sp$ ), the bond length decreases. The $sp^2-sp^2$ single bond in 1,3-butadiene is shorter than expected due to conjugation.

Molecular Orbitals of 1,3-Butadiene

Four p-orbitals: The four contiguous $sp^2$ hybridized carbons in 1,3-butadiene contribute four atomic p-orbitals.
Four Molecular Orbitals: These combine to form four $\pi$ molecular orbitals ( $\pi1, \pi2, \pi3^, \pi4^$ ).
- $\pi_1$ (Bonding): Lowest energy, 0 nodes.
- $\pi_2$ (Bonding): Second lowest energy, 1 node. This is the Highest Occupied Molecular Orbital (HOMO).
- $\pi_3^*$ (Antibonding): Second highest energy, 2 nodes. This is the Lowest Unoccupied Molecular Orbital (LUMO).
- $\pi_4^*$ (Antibonding): Highest energy, 3 nodes.
Electron Configuration: 1,3-Butadiene has four $\pi$ electrons, which fill the two bonding orbitals ( $\pi1$ and $\pi2$ ) during ground state.

Stability of Conjugated Dienes: Heats of Hydrogenation

Definition: Heats of hydrogenation ( $\Delta H^\circ$ ) measure the stability of unsaturated compounds. A more negative (exothermic) value indicates a less stable starting material.
Prediction: For an isolated diene, the heat of hydrogenation is approximately the sum of two individual alkene hydrogenations.
- For example, if 1-butene has $\Delta H^\circ = -127 \text{ kJ mol}^{-1}$ , then a hypothetical non-conjugated butadiene (like 1,4-pentadiene) would have an estimated $\Delta H^\circ \approx 2 \times (-127 \text{ kJ mol}^{-1}) = -254 \text{ kJ mol}^{-1}$ .
Observation for Conjugated Dienes:
- 1,3-Butadiene has an observed $\Delta H^\circ = -239 \text{ kJ mol}^{-1}$ .
- The difference ( $|-254| - |-239| = 15 \text{ kJ mol}^{-1}$ ) indicates that 1,3-butadiene is $15 \text{ kJ mol}^{-1}$ more stable than a non-conjugated diene. This extra stability is known as resonance energy or conjugation energy.
Table of Heats of Hydrogenation:

Compound	$H_2$ (mol)	$\Delta H^\circ$ (kJ mol $^{-1}$ )
1-Butene	1	$-127$
1-Pentene	1	$-126$
trans-2-Pentene	1	$-115$
1,3-Butadiene	2	$-239$
trans-1,3-Pentadiene	2	$-226$
1,4-Pentadiene	2	$-254$
1,5-Hexadiene	2	$-253$

Conclusion: Conjugated dienes (e.g., 1,3-butadiene, trans-1,3-pentadiene) are significantly more stable (less negative $!\Delta H^\circ$ per double bond) than isolated dienes (e.g., 1,4-pentadiene, 1,5-hexadiene), demonstrating the stabilizing effect of conjugation.

UV-Visible Spectroscopy of Conjugated Systems

Electromagnetic Spectrum: UV-Vis spectroscopy utilizes energy in the ultraviolet (200-400 nm) and visible (400-700 nm) regions of the electromagnetic spectrum.
Mechanism: When a molecule absorbs UV-Vis light, an electron is promoted from a lower energy molecular orbital (typically the HOMO) to a higher energy molecular orbital (typically the LUMO). This is called a $\pi \to \pi^*$ transition for unsaturated systems.
Spectrophotometer: A UV-Vis spectrophotometer measures the absorbance of light by a sample at different wavelengths.
- Light passes through a diffraction grating to select specific wavelengths.
- The sample cuvette and a reference cuvette are illuminated.
- Detectors measure the transmitted light intensity.
Typical Diene UV Absorption Spectrum: Shows an absorbance peak at a specific wavelength, known as the absorption maximum ( $\lambda_{max}$ ).
Beer's Law: Relates absorbance to concentration and path length:
- $A = \epsilon \cdot C \cdot l$
- Where:
  - $A$ = Absorbance (unitless)
  - $\epsilon$ = Molar absorptivity (or extinction coefficient) in $M^{-1} \text{ cm}^{-1}$ (a constant for a given substance at a specific $\lambda_{max}$ )
  - $C$ = Concentration of the sample in molarity ( $\text{mol L}^{-1}$ )
  - $l$ = Path length of the sample cell in cm (usually $1 \text{ cm}$ )

Excitation Energy Gap and Conjugation

HOMO-LUMO Gap: The energy difference between the HOMO and LUMO determines the energy of light required for excitation.
- $E_{excitation} = h\nu = h \frac{c}{\lambda}$
- Where $h$ is Planck's constant, $\nu$ is frequency, $\text{c}$ is the speed of light, and $\lambda$ is wavelength.
Effect of Conjugation: As the extent of conjugation (number of alternating double and single bonds) increases, the HOMO-LUMO energy gap decreases.
- A smaller energy gap means longer wavelengths (lower energy) of light are absorbed.
- This shifts the absorption maximum ( $\lambda_{max}$ ) to longer wavelengths.
- Highly conjugated systems (like $\beta$-carotene with 11 conjugated double bonds) absorb in the visible region, making them colored.
**Table of Absorption Maxima ( $\lambda{max}$ ) and Molar Absorptivities ( $\epsilon{max}$ ):

Compound	Structure	$\lambda_{max}$ (nm)	$\epsilon_{max}$ ( $M^{-1} \text{ cm}^{-1}$ )
Ethene	$H<em>2C=CH</em>2$	$171$	$15,530$
1,3-Butadiene		$217$	$21,000$
trans-1,3,5-Hexatriene		$274$	$50,000$

Trend: Ethene (1 double bond) absorbs at $171 \text{ nm}$ . 1,3-Butadiene (2 conjugated double bonds) absorbs at $217 \text{ nm}$ . trans-1,3,5-Hexatriene (3 conjugated double bonds) absorbs at $274 \text{ nm}$ . This clearly illustrates the red-shift (shift to longer wavelength) with increasing conjugation.

Reactions of Conjugated Dienes: Electrophilic Addition

Conjugated dienes can undergo electrophilic addition reactions, leading to two types of products: 1,2-addition and 1,4-addition.
Example: Addition of HCl to 1,3-Butadiene at $25 \text{ °C}$
- 3-Chloro-1-butene (1,2-addition product): $78\%$ (major product at $25 \text{ °C}$ )
- 1-Chloro-2-butene (1,4-addition product): $22\%$ (primarily E isomer)

Mechanism for 1,2- and 1,4-Additions

Step 1: Protonation (Slow, Rate-determining Step)
- The electrophile ( $H^+$ ) adds to one of the terminal carbons of the diene.
- This always forms the more stable allylic carbocation intermediate.
- The allylic carbocation is resonance-stabilized, with the positive charge delocalized over the two terminal carbons.
Step 2: Nucleophilic Attack (Fast Step)
- The nucleophile ( $Cl^-$ from HCl, or another nucleophile) can attack either of the positively charged carbons of the allylic carbocation.
 - Attack at C2: Leads to the 1,2-addition product (e.g., 3-chloro-1-butene).
 - Attack at C4: Leads to the 1,4-addition product (e.g., 1-chloro-2-butene). The double bond in the 1,4-product shifts to the $C2-C3$ position.

The Cation Is Not the Sole Determinant

While the allylic cation intermediate dictates the possibilities, the final product ratio depends on kinetic vs. thermodynamic control.
For instance, in the addition of $Br_2$ to 1,3-butadiene, products differ depending on conditions:
- At $-15 \text{ °C}$ (kinetic control), the 1,2-addition product gives $80\%$ , and the 1,4-addition product gives $20\%$ .

1,6-Additions (When Possible)

If a conjugated system extends over more than four carbons, 1,6-addition (or even longer) can occur, yielding products from attack at the ends of the conjugated system where the positive charge is delocalized.

Kinetic Versus Thermodynamic Control

The relative amounts of 1,2- and 1,4-addition products are often temperature-dependent.
Kinetic Control (Low Temperature, e.g., $-80 \text{ °C}$ with HBr):
- The major product is the one formed fastest. This is the kinetic product.
- It typically arises from the electrophilic attack that has the lower activation energy.
- For HBr addition to 1,3-butadiene at $-80 \text{ °C}$ (kinetic conditions), the 1,2-addition product is $80\%$ and the 1,4-addition product is $20\%$ . The 1,2-addition product's formation has a lower activation energy.
Thermodynamic Control (High Temperature, e.g., $40 \text{ °C}$ with HBr):
- The major product is the most stable product. This is the thermodynamic product.
- At higher temperatures, the reaction is reversible, and the system reaches equilibrium, favoring the most stable product.
- For HBr addition to 1,3-butadiene at $40 \text{ °C}$ (thermodynamic conditions), the 1,2-addition product is $20\%$ and the 1,4-addition product is $80\%$ . The 1,4-addition product is generally more stable because its double bond is more substituted (internal vs. terminal) and often has more stable stereochemistry (e.g., trans).

Energy Diagram for 1,2- and 1,4-Additions

Reactants: 1,3-Butadiene + HX (e.g., HBr)
Intermediate: Allylic carbocation.
Transition State $TS{1,2}$ : Leads to the 1,2-addition product. It has a lower activation energy ( $\Delta G^\ddagger{1,2}$ ) than $TS_{1,4}$ (for the 1,4-addition product).
Transition State $TS{1,4}$ : Leads to the 1,4-addition product. It has a higher activation energy ( $\Delta G^\ddagger{1,4}$ ) than $TS_{1,2}$ but often leads to a more stable product.
Products:
- 1,2-addition product: Formed faster (kinetic product), generally less stable.
- 1,4-addition product: Formed slower but is generally more stable (thermodynamic product).
Conclusion: The 1,2-addition product is favored at low temperatures because it forms fastest (kinetic control). The 1,4-addition product is favored at high temperatures because it is the most stable product (thermodynamic control).

Diels-Alder Cycloaddition

Definition: A pericyclic reaction involving a conjugated diene and a dienophile (an alkene or alkyne with electron-withdrawing groups) to form a cyclohexene ring. It is a [4+2] cycloaddition.
Example: 1,3-Butadiene (diene) + Maleic anhydride (dienophile) combines to form an adduct (a substituted cyclohexene) upon heating in benzene at $100 \text{ °C}$ .
Mechanism: The reaction proceeds in a concerted manner, meaning all bond-forming and bond-breaking steps occur simultaneously in a single transition state. The electrons move in a cyclic fashion.
Unactivated Diels-Alder: Can occur without specific activating groups but requires much higher temperatures (e.g., $200 \text{ °C}$ in a sealed tube) and often yields lower conversions.

Diene Conformations

s-cis conformation: The two double bonds are on the same side of the connecting single bond. This is the required conformation for the Diels-Alder reaction.
s-trans conformation: The two double bonds are on opposite sides of the connecting single bond. This is generally more stable due to less steric hindrance between hydrogen atoms at C1 and C4.
Conformational Stability: For 1,3-butadiene, the s-trans conformation is more stable than the s-cis conformation, but rotation about the $C2-C3$ single bond allows interconversion. The s-cis conformation is necessary for the $\pi$ systems to align for the cycloaddition.
Unreactive Diene Conformation: An s-trans diene cannot participate in the Diels-Alder reaction because the terminal carbons ( $C1$ and $C4$ ) are too far apart to form new bonds simultaneously with the dienophile.
Cyclic Dienes: Dienes that are conformationally locked in the s-cis form (e.g., cyclopentadiene) are exceptionally reactive in Diels-Alder reactions.

Effect of Substituents

Dienophile: Electron-withdrawing groups (EWGs) on the dienophile (e.g., $C=O$ , $CN$ , $NO2$ , $SO2$ ) enhance its reactivity by lowering its LUMO energy, making it a better electron acceptor.
Diene: Electron-donating groups (EDGs) on the diene (e.g., alkyl groups, $OR$ , $NR_2$ ) enhance its reactivity by raising its HOMO energy, making it a better electron donor.
Example: 2,3-Dimethyl-1,3-butadiene (EDGs on diene) + Propenal (EWG on dienophile) reacts readily at $30 \text{ °C}$ with $100\%$ yield.

Lewis Acid Catalysis

Lewis acids (e.g., $AlCl3$ , $SnCl4$ ) can catalyze Diels-Alder reactions, especially when the dienophile has electron-withdrawing carbonyl groups.
The Lewis acid complexes with the carbonyl oxygen, making the dienophile even more electron-deficient and thus more reactive.

Cyclopentadiene Reactivity

Always s-cis: Cyclopentadiene is a cyclic diene forced into an s-cis conformation, making it highly reactive in Diels-Alder reactions.
Dimerization: At room temperature, cyclopentadiene readily undergoes a Diels-Alder reaction with itself (acting as both diene and dienophile) to form dicyclopentadiene.

Stereochemistry in Diels-Alder Reactions

Endo Arrangement is Preferred (for Bicyclic Products):
- In reactions forming bicyclic adducts (e.g., from cyclic dienes), two stereoisomers are possible: endo and exo.
- Endo Product: The substituent on the dienophile is oriented closer to the longer bridge of the newly formed ring system. It is usually the major product due to secondary orbital interactions in the transition state.
- Exo Product: The substituent on the dienophile is oriented away from the longer bridge. It is usually the minor product.
Dienophile Stereochemistry is Preserved:
- If the dienophile is cis (e.g., dimethyl maleate), the substituents on the newly formed ring will be cis relative to each other.
- If the dienophile is trans (e.g., dimethyl fumarate), the substituents on the newly formed ring will be trans relative to each other.
Diene Stereochemistry is Preserved:
- Substituents on the diene (at C1 or C4) retain their relative stereochemistry (cis or trans) in the cyclohexene product.
Intramolecular Diels-Alder Reactions: When the diene and dienophile moieties are part of the same molecule, intramolecular Diels-Alder reactions can occur, often leading to complex polycyclic structures.

Conjugated Systems Summary

Definition: Conjugated unsaturated systems are $\pi$ (pi) electron systems resulting from the overlap of adjacent p-orbitals involving three or more atoms.
Key Feature: Delocalization of $\pi$ electrons, leading to enhanced stability.
Characterization: Can be represented by a resonance hybrid, which is a weighted average of contributing resonance structures.
Evidence: UV-Vis Spectroscopy, heats of hydrogenation, and bond length analysis.

Resonance Structures Rules:

Exist only on paper.
Atoms do not move.
Require proper Lewis structures.
Additional electron unpairing is forbidden.
Resonating groups must be coplanar.
Resonance stabilizes the molecule.
Equal structures contribute equally.
Structures need not be energetically equal.
More covalent bonds increase stability.
Full valence shells increase stability.
Charge separation decreases stability.

Examples of Conjugated Systems:

Allylic systems (e.g., allyl radical, allyl cation)
Conjugated alkenes (e.g., 1,3-dienes)

Reactions of Conjugated Systems:

Radical Allylic Substitution: Involving reagents like $X_2$ (low conc.), ROOR, heat, or hv; or NBS (for Br), ROOR, heat, or hv.
Addition Reactions to Conjugated Systems:
- Involve an electrophilic part ( $E$ ) and a nucleophilic part ( $Nu$ ) of the adding reagent.
- Produce either simple (1,2) addition products or conjugate (1,4) addition products.
- Product distribution depends on kinetic control (fastest formed, favored at low T) or thermodynamic control (most stable, favored at high T).
Diels-Alder Reactions:
- A cycloaddition between a 1,3-diene and a dienophile.
- Forms a cyclohexene adduct.
- Requires the diene to be in an s-cis conformation.
- Favored by EDGs on the diene and EWGs on the dienophile.
- Stereochemistry of both diene and dienophile is preserved.
- Often shows endo preference for bicyclic products.

UV-Vis Spectroscopy:

Involves the absorption of energy in the UV-Vis region of the electromagnetic spectrum.
Leads to the promotion of an electron from the HOMO (highest occupied molecular orbital) to the LUMO (lowest unoccupied molecular orbital).
Can be used for quantitative analysis (Beer's Law).
Increasing conjugation leads to absorption at longer wavelengths ( $\lambda_{max}$ ).