Conjugated Systems, Orbital Symmetry, and Ultraviolet Spectroscopy (Chapter 15 Study Notes)

Conjugated Systems

Definition and Stability

Conjugated systems are a fundamental concept in organic chemistry, involving alternating single and double bonds that allow for electron delocalization. This delocalization imparts unique stability and reactivity to these molecules.

• Conjugated double bonds are separated by one single bond, allowing for overlap of p orbitals and electron delocalization.

• Isolated double bonds are separated by two or more single bonds, preventing such overlap.

• Conjugated double bonds are more stable than isolated double bonds due to resonance stabilization.

Diene Stability and Heats of Hydrogenation

The stability of alkenes and dienes can be compared using heats of hydrogenation, which measure the energy released when hydrogen is added across double bonds.

• Lower heat of hydrogenation indicates greater stability.

• For conjugated dienes, the heat of hydrogenation is less than the sum for the individual double bonds, reflecting extra stability.

Example:

• Pent-1-ene: $\Delta H^\circ = -126\ \text{kJ}$

• Trans-pent-2-ene: $\Delta H^\circ = -114\ \text{kJ}$

• Trans-penta-1,3-diene: $\Delta H^\circ = -225\ \text{kJ}$ (actual), more stable by $15\ \text{kJ}$ than predicted

Relative Stabilities

Stability increases in the order: cumulated diene < terminal alkyne < internal alkyne < isolated diene < conjugated diene.

Structure and Bonding in Conjugated Dienes

Structure of Buta-1,3-diene

• The C2—C3 single bond is shorter than a typical single bond (1.54 Å), indicating partial double bond character.

• Electrons are delocalized over the entire molecule, contributing to stability.

Molecular Orbitals (MOs)

All atoms in buta-1,3-diene are sp2 hybridized, with overlapping p orbitals forming molecular orbitals.

• Constructive overlap of p orbitals forms a pi bonding (π) MO.

• Destructive overlap forms a pi antibonding (π*) MO.

MO Diagrams for Ethylene and Buta-1,3-diene

• Ethylene: Two p orbitals combine to give two MOs (one bonding, one antibonding).

• Buta-1,3-diene: Four p orbitals combine to give four MOs (two bonding, two antibonding).

Key MOs for Buta-1,3-diene:

• $\pi_1$: Lowest energy, all bonding interactions, electrons delocalized over four nuclei.

• $\pi_2$: Two bonding, one antibonding interaction, higher energy than $\pi_1$.

• $\pi_3^*$: Two antibonding, one bonding interaction, vacant in ground state.

• $\pi_4^*$: Three nodes, strongly antibonding, highest energy, vacant in ground state.

Resonance Stabilization

• Buta-1,3-diene has lower energy than ethylene due to resonance stabilization.

Conformations of Buta-1,3-diene

• The s-trans conformer is more stable than the s-cis by 12 kJ/mol (2.8 kcal/mol).

• Conformers interconvert easily at room temperature.

The Allylic Position and Reactivity

Definition and Resonance

• The allylic carbon is directly attached to an sp2 carbon.

• Allylic cations are stabilized by resonance, with the positive charge delocalized over two carbons.

Stability of Carbocations

• Order of stability: $\ce{CH3+} < 1^\circ < 2^\circ,\ allyl < 3^\circ,\ substituted\ allylic$

• Stability of $1^\circ$ allylic ≈ $2^\circ$ carbocation; $2^\circ$ allylic ≈ $3^\circ$ carbocation.

Electrophilic Addition to Conjugated Dienes

1,2- and 1,4-Addition

Electrophilic addition to conjugated dienes can yield two products, depending on where the nucleophile adds.

• 1,2-addition: Nucleophile adds to carbon 2.

• 1,4-addition: Nucleophile adds to carbon 4.

• Intermediate is a resonance-stabilized allylic cation.

Example: Addition of HBr to buta-1,3-diene produces 3-bromobut-1-ene (1,2-addition) and 1-bromobut-2-ene (1,4-addition).

Mechanism

1. Protonation of one double bond forms a resonance-stabilized allylic cation.

2. Nucleophile attacks at either electrophilic carbon (C2 or C4).

Kinetic vs. Thermodynamic Control

• Kinetic control (low temperature, e.g., -80°C): Product that forms faster (1,2-addition) predominates.

• Thermodynamic control (higher temperature, e.g., 40°C): Most stable product (1,4-addition) predominates due to equilibrium.

Allylic Radicals and Bromination

Stability and Formation

• Allylic radicals are stabilized by resonance.

• Stability order: 1° < 2° < 3° < 1° allylic.

• Substitution at the allylic position can compete with addition to the double bond.

Mechanism of Allylic Bromination

• Initiation: $\ce{Br2} \xrightarrow{hv} 2\ \ce{Br.}$

• Propagation: Allylic hydrogen abstraction forms an allylic radical, which reacts with $\ce{Br2}$ to form allylic bromide and another $\ce{Br.}$

Bromination Using N-Bromosuccinimide (NBS)

• NBS provides a low, constant concentration of $\ce{Br2}$.

• NBS reacts with HBr by-product to produce $\ce{Br2}$ and prevent HBr addition across the double bond.

Molecular Orbitals of the Allylic System

Resonance Forms and MO Representation

• Allyl cation, radical, and anion have three p orbitals parallel, allowing extended overlap.

• Resonance forms show delocalization of charge or unpaired electron across the system.

• No resonance form has an independent existence; the true structure is a hybrid.

MO Diagram for Allylic Species

Species	Electrons	Occupied MOs
Allyl cation	2	$\pi_1$
Allyl radical	3	$\pi_1$, $\pi_2$ (nonbonding)
Allyl anion	4	$\pi_1$, $\pi_2$

SN2 Reactions of Allylic Halides and Tosylates

Allylic halides and tosylates react rapidly by the SN2 mechanism due to stabilization of the transition state by conjugation with the pi system.

• Lower activation energy explains enhanced reactivity.

Summary Table: Key Concepts in Conjugated Systems

Concept	Description
Conjugation	Alternating single and double bonds, electron delocalization
Stability	Conjugated > isolated > cumulated
MO Theory	Bonding and antibonding orbitals, delocalization
Allylic Reactivity	Resonance stabilization, SN2 reactivity, radical stability
Electrophilic Addition	1,2- and 1,4-addition, kinetic vs. thermodynamic control
Bromination	NBS as a selective brominating agent for allylic positions