How to Calculate Bond Order from Molecular Orbital Diagram?

The bond order from a molecular orbital diagram is calculated by determining the number of electrons in bonding and antibonding orbitals and then using a simple formula.

Steps to Calculate Bond Order

Here's a breakdown of the process:

1. Draw the Molecular Orbital (MO) Diagram: This diagram visually represents the relative energy levels of the molecular orbitals formed from atomic orbitals. For example, for a diatomic molecule, you'll typically have sigma (σ) and pi (π) bonding and antibonding orbitals (σ*, π*).

2. Fill the Molecular Orbitals with Electrons: Add the valence electrons of the atoms involved to the molecular orbitals, following the Aufbau principle (filling orbitals from lowest to highest energy), Hund's rule (maximizing unpaired electrons within a subshell), and the Pauli exclusion principle (each orbital can hold a maximum of two electrons with opposite spins).

3. Identify Bonding and Antibonding Orbitals:

   • Bonding Orbitals: These orbitals are lower in energy than the original atomic orbitals and contribute to the stability of the molecule. Examples include σ and π orbitals.
   • Antibonding Orbitals: These orbitals are higher in energy than the original atomic orbitals and decrease the stability of the molecule. They are typically denoted with an asterisk (e.g., σ* and π*).

4. Count the Number of Electrons in Bonding and Antibonding Orbitals: Determine the total number of electrons occupying bonding orbitals and the total number of electrons occupying antibonding orbitals.

5. Apply the Bond Order Formula: Calculate the bond order using the following formula:

   Bond Order = (Number of bonding electrons - Number of antibonding electrons) / 2

Example: Calculating the Bond Order of O₂

Let's calculate the bond order for diatomic oxygen (O₂):

1. Electronic Configuration of Oxygen: Each oxygen atom has 6 valence electrons. Therefore, O₂ has a total of 12 valence electrons.

2. MO Diagram for O₂ (simplified): The filling order is approximately (σ_2s) (σ_2s*) (σ_2p) (π_2p) (π_2p*) (σ_2p*).

3. Filling the Orbitals: Filling the 12 valence electrons into the MO diagram, we get the configuration: (σ_2s)² (σ_2s*)² (σ_2p)² (π_2p)⁴ (π_2p*)².

4. Identifying and Counting:

   • Bonding electrons: 2 (σ_2s) + 2 (σ_2p) + 4 (π_2p) = 8
   • Antibonding electrons: 2 (σ_2s*) + 2 (π_2p*) = 4

5. Calculating Bond Order:
   Bond Order = (8 - 4) / 2 = 2

Therefore, the bond order of O₂ is 2, indicating a double bond.

Significance of Bond Order

• Stability: Higher bond order generally indicates greater stability of the molecule.
• Bond Length: Higher bond order typically corresponds to shorter bond length.
• Bond Energy: Higher bond order usually implies higher bond energy (stronger bond).