Chapter 13: Conjugated Unsaturated Systems

.Chapter 13: Conjugated Unsaturated Systems Notes

Introduction

• Conjugated systems involve at least one atom with a p orbital adjacent to at least one $\pi$ bond.

  • Examples: conjugated diene, allylic radical, allylic cation, allylic anion, enone, and enyne.

The Stability of the Allyl Radical

Molecular Orbital Description

• Three isolated p orbitals combine to form three molecular orbitals: one bonding, one nonbonding, and one antibonding.

• The allyl radical has three $\pi$ electrons, filling the bonding and nonbonding orbitals.

Resonance Description

• The allyl radical can be represented by two resonance structures, showing delocalization of the unpaired electron.

The Allyl Cation

• The allyl cation is more stable than a typical secondary carbocation due to resonance stabilization.

• Relative order of carbocation stability: allyl > secondary alkyl

Resonance Theory Revisited

Proper Resonance Structures

• Resonance structures exist only on paper and are used to describe molecules for which a single Lewis structure is inadequate.

• Resonance structures are connected by double-headed arrows ($\leftrightarrow$).

• The hybrid of all resonance structures represents the real molecule.

• Only electrons can be moved when writing resonance structures.

• All resonance structures must be proper Lewis structures (obeying the octet rule).

• All resonance structures must have the same number of unpaired electrons.

• Atoms that are part of the delocalized $\pi$-electron system must lie in the same plane or be nearly planar.

• The energy of the actual molecule is lower than the energy estimated for any contributing structure.

• Equivalent resonance structures make equal contributions to the hybrid, leading to large resonance stabilization.

• The more stable a structure is, the greater its contribution to the hybrid.

  • Example: A tertiary allylic cation contributes more than a secondary allylic cation.

Estimating Relative Stability

• The more covalent bonds a structure has, the more stable it is.

• Structures with all atoms having a complete valence shell of electrons are especially stable.

• Charge separation decreases stability.

Alkadienes & Polyunsaturated Hydrocarbons

Types of Compounds

• Alkadienes (Dienes): molecules with two double bonds.

  • Examples: 1,3-Butadiene, (2E,4E)-2,4-Hexadiene, 1,3-Cyclohexadiene.

• Alkatrienes (Trienes): molecules with three double bonds.

  • Example: (2E,4E,6E)-Octa-2,4,6-triene.

• Alkadiynes (Diynes): molecules with two triple bonds.

• Alkenynes (Enynes): molecules with one double bond and one triple bond.

  • Examples: Hex-1-en-5-yne, (2E)-Oct-2-en-6-yne.

• Cumulenes: compounds with three or more cumulative double bonds (e.g., allene).

  • Allenes can exhibit chirality.

Conjugation

• Conjugated dienes: double bonds are separated by a single bond.

• Non-conjugated dienes: double bonds are separated by two or more single bonds (isolated alkenes).

1,3-Butadiene: Electron Delocalization

Bond Lengths

• The central C-C single bond in 1,3-butadiene (1.47 Å) is shorter than a typical C-C single bond (1.54 Å) due to partial double bond character.

• The C=C double bonds in 1,3-butadiene (1.34 Å) are slightly longer than typical C=C double bonds due to electron delocalization.

Conformations

• 1,3-Butadiene exists in two main conformations: s-cis and s-trans.

• The s-trans conformation is more stable due to reduced steric hindrance.

Molecular Orbitals

• Four p orbitals combine to form four molecular orbitals: two bonding ($\pi<em>1$ and $\,pi</em>2</p><p>.$) and two antibonding (\pi3^ and $\pi4^</em>$).

• The HOMO (highest occupied molecular orbital) is $\pi<em>2$, and the LUMO (lowest unoccupied molecular orbital) is $\pi</em>3^*$.

The Stability of Conjugated Dienes

• Conjugated alkadienes are thermodynamically more stable than isomeric isolated alkadienes.

• For example, hydrogenation of conjugated dienes releases less heat than hydrogenation of isolated dienes.

  • $\Delta H_o(kJmol^{-1}) = -239$ for conjugated diene vs $-254$ for isolated diene.

    • Difference: $15 kJ mol^{-1}$

Ultraviolet–Visible Spectroscopy

Basic Principle

• UV–Vis spectroscopy measures the absorption of UV–Vis radiation by molecules.

• Absorption occurs when electrons are excited to higher energy orbitals.

Electromagnetic Spectrum

• The UV–Vis region lies between 200 nm and 700 nm.

Spectrophotometer Components

• A UV-Vis spectrophotometer consists of a light source, monochromator, sample holder, and detector.

Beer’s Law

• Beer’s law relates absorbance to concentration and path length: $A = \epsilon \times c \times l$, where A is absorbance, $\epsilon$ is molar absorptivity, c is concentration, and l is path length.

• $\epsilon = A/(c \times l)$

• Example: 2,5-Dimethyl-2,4-hexadiene has $\lambda_{max}$ (methanol) at 242.5 nm with $\epsilon = 13,100$.

Absorption Maxima

• Conjugated dienes have different absorption maxima compared to non-conjugated dienes.

• Example: Acetone (non-conjugated) vs. conjugated enone.

  • Acetone: Ground state n to $\pi^*$, $\lambda<em>{max} = 280 nm$, $\epsilon</em>{max} = 15$

  • Enone: $\pi$ to $\pi^*$, $\lambda<em>{max} = 219 nm$, $\epsilon</em>{max} = 3600$

  • n to $\pi^*$, $\lambda<em>{max} = 324 nm$, $\epsilon</em>{max} = 24$

Analytical Uses

• UV–Vis spectroscopy can be used for structure elucidation to determine if conjugation is present.

• It is also widely used for quantitative analysis to determine the concentration of an unknown sample.

• It is commonly used in biochemical studies to measure the rates of enzymatic reactions.

Electrophilic Attack on Conjugated Dienes: 1,4-Addition

• Electrophilic attack on conjugated dienes can lead to 1,2-addition and 1,4-addition products.

  • Example: Reaction of 1,3-butadiene with HCl at 25°C gives 78% 1,2-addition and 22% 1,4-addition.

Mechanism

• The reaction proceeds through a resonance-stabilized allylic carbocation intermediate.

Kinetic Control vs. Thermodynamic Control

• At low temperatures, the 1,2-addition product is favored (kinetic control) because it forms faster.

  • Example: Reaction of a diene with HBr at -80°C gives 80% 1,2-addition and 20% 1,4-addition.

• At high temperatures, the 1,4-addition product is favored (thermodynamic control) because it is more stable.

  • Example: Reaction of a diene with HBr at 40°C gives 20% 1,2-addition and 80% 1,4-addition.

• The 1,4-addition product is more stable due to the more substituted alkene.

Free Energy Diagram

• The activation energy for 1,2-addition is lower than that for 1,4-addition, but the 1,4-addition product is more stable.