Question

Pentadiene, ${\mathrm{C}}_5{\mathrm{H}}_8,$ has three isomers, depending on the position of the two double bonds. Determine the shape of these isomers by using VSEPR theory. Describe the bonding in these molecules by using the valence-bond method. Do the shapes agree in the two theories? Use molecular orbital theory to decide which of these molecules has a delocalized $\pi$ system. Sketch the molecular orbital and an energy-level diagram.

Short answer

Using VSEPR theory, all isomers of pentadiene have a trigonal planar geometry. According to the valence bond method, each Carbon atom forms σ bonds with its neighboring atoms, with the fourth valence electron forming a π bond. The molecular shapes are consistent with both theories. However, only 1,3-pentadiene and 1,4-pentadiene have a delocalized pi system as per Molecular Orbital theory.

Step-by-step solution

Sketch Structures of Isomers

Identify the three isomers of pentadiene, which are 1,2-pentadiene, 1,3-pentadiene, and 1,4-pentadiene based on the different positions of two double bonds. In VSEPR model, atom with double or single bond is considered as one domain. Thus, each Carbon atom in pentadiene is surrounded by three electron domains and according to VSEPR theory, such molecules possess trigonal planar electron-domain geometry.

Describe Bonding Using Valence-Bond Method

For the second step, use the valence bond theory to analyze. Each Carbon atom uses three of its valence electrons to form sigma bonds with its neighboring atoms. The fourth valence electron in each Carbon atom of a double bond pairs up to form a pi bond, where the electron density lies above and below the plane of the molecule.

Check Agreement Between VSEPR and Valence-Bond Theory

The molecular shapes predicted by VSEPR theory for these molecules are in agreement with the molecular structure suggested by the valence-bond method.

Identify Delocalized Pi System Using Molecular Orbital Theory

1,2-pentadiene has two isolated double bonds. Therefore, there can be no delocalization of pi electrons. On the other hand, 1,3-pentadiene and 1,4-pentadiene both have a continuous system of parallel p orbitals. This suggests delocalization of pi-bonded electrons in them.

Sketch the Molecular Orbital and Energy-Level Diagram

Here we need to draw the energy level diagrams indicating the molecular orbitals of 1,3-pentadiene and 1,4-pentadiene, showing the occupied and vacant pi molecular orbitals.

Key concepts

VSEPR Theory

VSEPR Theory, or Valence Shell Electron Pair Repulsion theory, is a model used to predict the geometry of individual molecules. According to VSEPR, electron pairs around a central atom arrange themselves in order to minimize repulsion, leading to specific molecular shapes. For pentadiene isomers, each carbon atom is considered to have three electron domains as each is bonded to three other atoms or groups via single or double bonds.
The shape of these isomers can be predicted using VSEPR theory:

• The presence of double bonds in pentadiene results in certain rigidity due to the planar nature of the bonds. Each carbon in the double bond has a trigonal planar geometry.
• Thus, carbon atoms involved in double bonds in all pentadiene isomers show this planar geometry, and the resulting overall shape is influenced by the positioning of these double bonds.

This establishes that in the pentadiene isomers, the geometry is mainly planar, corresponding to the trigonal planar arrangement for the carbons with double bonds.

Valence-Bond Method

The Valence-Bond Method explains the bonding within a molecule by considering how atomic orbitals overlap to form bonds. In the case of pentadiene isomers, the method focuses on

• Sigma (σ) bonds: These are formed from the end-to-end overlap of atomic orbitals. In pentadiene, each carbon partly uses its sp² hybrid orbitals to form these sigma bonds with its neighboring atoms.
• Pi (π) bonds: These are the result of side-by-side overlap of unhybridized p-orbitals that are present perpendicularly to the sigma bonds. In pentadiene, each double bond contains one pi bond formed by this method.

This dual nature, with sigma and pi bonds creating double bonds, helps stabilize the structure while maintaining planarity due to the arrangement of atomic orbitals.

Molecular Orbital Theory

The Molecular Orbital Theory (MOT) offers a different perspective by considering electrons in molecular orbitals, which are spread over the entire molecule rather than localized between atoms. In pentadiene isomers, MOT is significant when we analyze the possibility of electron delocalization.
According to MOT:

• 1,2-Pentadiene has isolated double bonds, meaning electrons are localized in pi bonds with no overlap, resulting in no delocalization.
• 1,3-Pentadiene exhibits a pattern where the p orbitals across carbons are parallel, allowing for overlap of pi electrons. This creates an extended pi system where electrons can delocalize.
• Similarly, 1,4-Pentadiene also allows for the overlap and delocalization of pi electrons due to continuous parallel alignment of p orbitals.

Hence, molecular orbitals in 1,3- and 1,4-pentadienes facilitate electron delocalization, increasing the stability of these isomers.

Delocalized Pi System

A delocalized pi system occurs when pi electrons, rather than being confined between two atoms, extend across multiple atoms, stabilizing the molecule further. In pentadiene isomers, the differences in pi systems distinguish the stability and reactivity.
Consider the

• 1,3-Pentadiene, where the p orbitals form a continuous system, allowing pi electrons to roam across four carbon atoms. This delocalization results in resonance structures, enhancing stability.
• Similarly, 1,4-Pentadiene also forms resonance structures through pi electron delocalization across five carbon atoms, contributing to stability.

These resonant structures in 1,3- and 1,4-pentadienes are not present in 1,2-pentadiene due to isolated pi bonds, resulting in distinct chemical behaviors and stability patterns between different isomers.