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 86d

Chapter 9, Problem 86d

Answer the following questions for the molecular orbitals (MOs) of 1,3,5,7-octatetraene:
d. Which MO is the HOMO and which is the LUMO in the ground state?

Verified step by step guidance

Identify the total number of π-electrons in 1,3,5,7-octatetraene. Each double bond contributes 2 π-electrons, and there are 4 double bonds, so the molecule has 8 π-electrons.

Determine the number of molecular orbitals (MOs) formed. For a conjugated system with 8 π-electrons, there will be 8 π-MOs, labeled as ψ₁, ψ₂, ψ₃, ..., ψ₈, with increasing energy levels.

Fill the molecular orbitals with the 8 π-electrons according to the Aufbau principle, starting from the lowest energy orbital (ψ₁) and filling up to the highest occupied orbital. Each orbital can hold a maximum of 2 electrons with opposite spins.

The Highest Occupied Molecular Orbital (HOMO) is the highest energy orbital that contains electrons in the ground state. Based on the filling, this will be ψ₄.

The Lowest Unoccupied Molecular Orbital (LUMO) is the next higher energy orbital that does not contain electrons in the ground state. This will be ψ₅.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

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 combination of atomic orbitals when atoms bond together. They can be classified as bonding, antibonding, or non-bonding orbitals, and they play a crucial role in determining the electronic structure of molecules. In conjugated systems like octatetraene, MOs are filled according to the Aufbau principle, influencing the molecule's stability and reactivity.

HOMO and LUMO

The Highest Occupied Molecular Orbital (HOMO) is the molecular orbital that contains the highest energy electrons in a molecule, while the Lowest Unoccupied Molecular Orbital (LUMO) is the lowest energy orbital that is unoccupied. The energy gap between the HOMO and LUMO is critical for understanding a molecule's electronic transitions, reactivity, and optical properties, especially in conjugated systems like octatetraene.

Ground State Configuration

The ground state configuration of a molecule refers to the arrangement of electrons in its molecular orbitals at the lowest energy level. For octatetraene, this involves filling the MOs according to the Pauli exclusion principle and Hund's rule, which dictate how electrons occupy orbitals. Understanding the ground state is essential for identifying the HOMO and LUMO, as these orbitals are determined by the filled and unfilled states of the molecule.

Recommended video:

Guided course

03:08

Ground vs. Excited States

Related Practice

Textbook Question