3.10.3 Relative Energies of the Molecular Orbitals

This topic explains the relative energies of molecular orbitals formed from 2s and 2p atomic orbitals. It describes why the energy order differs for different diatomic molecules.

Definition

Relative Energies of Molecular Orbitals: The order of molecular orbital energy levels based on spectroscopic measurements.

Main Idea

• For O₂, F₂, and their ions: σ 2p_x is lower in energy than π 2p_y and π 2p_z.
• For H₂, He₂, B₂, C₂, and N₂ (lighter molecules): π 2p_y and π 2p_z are lower in energy than σ 2p_x.

This difference is due to the mixing of 2s and 2p orbitals, which is influenced by the initial atomic orbital energies.

Core Concept

The relative energies of molecular orbitals depend on the energy difference between 2s and 2p atomic orbitals. For lighter elements (Z = 3 to 7), the energy difference is small, causing mixing of 2s and 2p orbitals. This mixing changes the energy order of the molecular orbitals.

Detailed Explanation

Relative Energies for O₂, F₂, and Their Ions

The following increasing order of energy shows the molecular orbitals of diatomic molecules such as O₂, F₂, and their positive and negative ions:

σ 1s < σ^* 1s < σ 2s < σ^* 2s < σ 2p_x < π 2p_y = π 2p_z < π^* 2p_y = π^* 2p_z < σ^* 2p_x

• σ 2p_x is lower in energy than π 2p_y and π 2p_z.
• The order is: σ 2p_x < π 2p_y = π 2p_z < π^* 2p_y = π^* 2p_z < σ^* 2p_x.

Relative Energies for H₂, He₂, B₂, C₂, and N₂

The diatomic molecules such as H₂, He₂, B₂, C₂, and N₂ (lighter molecules) show a slightly different energy order:

σ 1s < σ^* 1s < σ 2s < σ^* 2s < π 2p_y = π 2p_z < σ 2p_x < π^* 2p_y = π^* 2p_z < σ^* 2p_x

• π 2p_y and π 2p_z are lower in energy than σ 2p_x.
• The order is: π 2p_y = π 2p_z < σ 2p_x < π^* 2p_y = π^* 2p_z < σ^* 2p_x.

Reason for the Difference

• Elements of the second period having atomic number 3 to 7 (prior to oxygen) have a relatively small difference in energy between the 2s and 2p orbitals.
• As the energy difference between 2s and 2p atomic orbitals is small, as a result, σ 2s and σ^* 2s MO do not retain pure s-character (hybridization of A.O.).
• Mixing of 2s and 2p orbitals is the primary cause of the difference in the molecular orbitals of nitrogen and oxygen.
• This mixing is influenced by the initial atomic orbital energies.
• Hence, the energy of σ 2p_x is greater than π 2p_y and π 2p_z for lighter molecules.

Comparison Table

Why This Matters

• Molecular orbital diagrams: The correct energy order is essential for drawing MO diagrams.
• Bond order: The filling of electrons depends on the energy order.
• Magnetic properties: The energy order affects whether a molecule is paramagnetic or diamagnetic.
• Spectroscopy: Spectroscopic measurements confirm the energy order.

Intermediate Level

Energy Order for O₂, F₂

σ 1s < σ^* 1s < σ 2s < σ^* 2s < σ 2p_x < π 2p_y = π 2p_z < π^* 2p_y = π^* 2p_z < σ^* 2p_x

- σ 2p_x is lower than π 2p_y = π 2p_z.

Energy Order for H₂, He₂, B₂, C₂, N₂

σ 1s < σ^* 1s < σ 2s < σ^* 2s < π 2p_y = π 2p_z < σ 2p_x < π^* 2p_y = π^* 2p_z < σ^* 2p_x

- π 2p_y = π 2p_z is lower than σ 2p_x.

Reason for Difference

• Lighter elements (Z = 3 to 7) have a small energy difference between 2s and 2p orbitals.
• This causes mixing of 2s and 2p orbitals.
• As a result, σ 2p_x has greater energy than π 2p_y and π 2p_z.

Comparison Table

Important Points

• 1. Spectroscopic measurements determine relative energies of MOs.
• 2. For O₂, F₂: σ 2p_x < π 2p_y = π 2p_z.
• 3. For H₂, He₂, B₂, C₂, N₂: π 2p_y = π 2p_z < σ 2p_x.
• 4. Reason: Mixing of 2s and 2p orbitals in lighter elements.
• 5. Lighter elements (Z = 3 to 7) have a small energy difference between 2s and 2p.
• 6. This mixing is influenced by initial atomic orbital energies.

Remember

• - O₂, F₂: σ 2p_x lower
• - H₂, He₂, B₂, C₂, N₂: π 2p lower
• - Reason: Mixing of 2s and 2p orbitals
• - Lighter elements: Small energy difference between 2s and 2p

Common Mistakes

• 1. Using the same energy order for all molecules: O₂F₂ vs. lighter molecules have different orders.
• 2. Forgetting the reason for the difference: Mixing of 2s and 2p orbitals.
• 3. Mixing up the order: For O₂F₂, σ 2p_x is lower; for lighter molecules, π 2p is lower.
• 4. Ignoring spectroscopic evidence: The energy order is confirmed by spectroscopic measurements.

Quick Revision

• Spectroscopic measurements determine relative energies of MOs.
• For O₂, F₂: σ 2p_x < π 2p_y = π 2p_z.
• For H₂, He₂, B₂, C₂, N₂: π 2p_y = π 2p_z < σ 2p_x.
• Reason: Mixing of 2s and 2p orbitals in lighter elements.
• Lighter elements (Z = 3 to 7) have a small energy difference between 2s and 2p.
• This mixing is influenced by initial atomic orbital energies.

60-Second Revision

• O₂, F₂: σ 2p_x lower
• H₂, He₂, B₂, C₂, N₂: π 2p lower
• Reason: Mixing of 2s and 2p orbitals
• Lighter elements: Small energy difference between 2s and 2p

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• Topic: 3.10.3 Relative Energies of the Molecular Orbitals
• Chapter: 3 (Chemical Bonding)

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