Ch. 8 - Delocalized Electrons: Their Effect on Stability, pKa, and the Products of a Reaction • Aromaticity and Electronic Effects: An Introduction to the Reactions of Benzene

Bruice8th EditionOrganic ChemistryISBN: 9780135213711Not the one you use?Change textbook

Bruice 8th Edition

Ch. 8 - Delocalized Electrons: Their Effect on Stability, pKa, and the Products of a Reaction • Aromaticity and Electronic Effects: An Introduction to the Reactions of Benzene

Problem 86c

Chapter 9, Problem 86c

Answer the following questions for the molecular orbitals (MOs) of 1,3,5,7-octatetraene:
c. Which MOs are symmetric, and which are antisymmetric?

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Understand the molecular structure of 1,3,5,7-octatetraene: It is a conjugated system with 8 π-electrons distributed across 8 p-orbitals. These p-orbitals combine to form 8 molecular orbitals (MOs), which are either bonding, non-bonding, or anti-bonding.

Recall the symmetry properties of molecular orbitals: Symmetric MOs remain unchanged when reflected across a plane of symmetry (e.g., the molecular plane or a vertical plane passing through the molecule), while antisymmetric MOs change sign under such reflections.

Construct the molecular orbital diagram for 1,3,5,7-octatetraene: The MOs are formed by the linear combination of the 8 p-orbitals. Label the MOs as Ψ₁, Ψ₂, Ψ₃, ..., Ψ₈, where Ψ₁ is the lowest-energy bonding orbital and Ψ₈ is the highest-energy anti-bonding orbital.

Analyze the symmetry of each MO: Use the nodal patterns of the MOs to determine their symmetry. For example, Ψ₁ (the lowest-energy MO) has no nodes and is symmetric, while Ψ₂ (the next MO) has one node and is antisymmetric. Continue this analysis for all 8 MOs.

Summarize the results: Identify which MOs are symmetric and which are antisymmetric based on their nodal patterns and behavior under symmetry operations. Typically, bonding MOs with even numbers of nodes are symmetric, while those with odd numbers of nodes are antisymmetric.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Molecular Orbitals (MOs)

Molecular orbitals are formed by the linear combination of atomic orbitals (LCAO) when atoms bond together. They can be classified as bonding, antibonding, or non-bonding, depending on their energy levels and stability. In conjugated systems like 1,3,5,7-octatetraene, MOs play a crucial role in determining the molecule's electronic properties and reactivity.

Symmetry in Molecular Orbitals

Symmetry in molecular orbitals refers to how the wave functions of the orbitals behave under symmetry operations, such as rotation or reflection. Symmetric orbitals remain unchanged under these operations, while antisymmetric orbitals change sign. Understanding the symmetry of MOs is essential for predicting their behavior in chemical reactions and interactions.

Conjugation and its Effects

Conjugation occurs when alternating single and double bonds allow for the delocalization of π electrons across multiple adjacent atoms. This delocalization stabilizes the molecule and affects the energy levels of the MOs. In 1,3,5,7-octatetraene, the conjugated system leads to a specific arrangement of symmetric and antisymmetric MOs, influencing the molecule's optical and electronic properties.

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