The pentadienyl radical, H₂C=CH–CH=CH–CH₂•, has its unpaired electron delocalized over three carbon atoms.
f. Show how your molecular orbital picture agrees with the resonance picture showing delocalization of the unpaired electron onto three carbon atoms.

Verified step by step guidance

1. Begin by identifying the structure of the pentadienyl radical, H₂C=CH-CH=CH-CH₂·. Note that the unpaired electron is located on the terminal carbon atom (CH₂·). This radical is conjugated because it contains alternating double bonds and a single electron, allowing for delocalization.
2. Draw the resonance structures for the pentadienyl radical. Start by moving the π-electrons of the double bonds to adjacent positions while shifting the unpaired electron. This will result in three resonance structures where the unpaired electron is delocalized over the first, third, and fifth carbon atoms.
3. Introduce the concept of molecular orbitals (MOs). In the pentadienyl radical, there are five p orbitals (one on each carbon atom) that overlap to form a conjugated π-system. These p orbitals combine to form five molecular orbitals: three bonding, one non-bonding, and one anti-bonding.
4. Explain that the unpaired electron occupies the non-bonding molecular orbital. This orbital has equal contributions from the p orbitals on the first, third, and fifth carbon atoms, which aligns with the resonance structures showing delocalization of the unpaired electron over these three carbons.
5. Conclude by emphasizing that the molecular orbital picture supports the resonance picture. The delocalization of the unpaired electron over three carbon atoms is a result of the conjugated π-system and the non-bonding molecular orbital, which is consistent with the resonance structures drawn earlier.

Key Concepts

Molecular Orbitals

Molecular orbitals (MOs) are formed by the combination of atomic orbitals when atoms bond together. In the case of the pentadienyl radical, the unpaired electron can occupy a molecular orbital that is delocalized over multiple carbon atoms, allowing for resonance stabilization. Understanding how these orbitals overlap helps visualize the distribution of the unpaired electron across the molecule.

Resonance Structures

Resonance structures are different Lewis structures that represent the same molecule, illustrating how electrons are distributed. For the pentadienyl radical, resonance structures show the delocalization of the unpaired electron across three carbon atoms, indicating that the actual structure is a hybrid of these forms. This concept is crucial for understanding the stability and reactivity of radicals.

Delocalization of Electrons

Delocalization refers to the spreading of electrons across multiple atoms rather than being localized between two. In the pentadienyl radical, the unpaired electron is delocalized over three carbon atoms, which lowers the energy of the system and increases stability. This phenomenon is key to understanding the behavior of radicals and their reactivity in organic chemistry.