Bond Order Calculation by MOT

In the previous post you have seen how MOT helps us to guess the existence of a molecule. In this post we will explore some more applications of Molecular orbital theory. Let’s take O₂  molecule as an example and see what information can be drawn by MOT.

Oxygen ⁸O has 8 electrons. Its electronic configuration is 1s², 2s², 2p⁴. When two O atoms come closer to form O₂ molecule their atomic orbitals get overlapped and form molecular orbitals. Each O atom has 5 atomic orbitals thus they combine to form 10 MO. The energy order of these MO is as follows:

σ1s, σ*1s, σ2s, σ*2s, σ2p_x, {π2p_y, π2p_z}, {π*2p_y, π*2p_z}, σ*2p_x

This kind of energy order is usually applicable for Oxygen and other heavier elements.

O₂ molecule has got 16 electrons. When you fill these electrons in respective MOs you will get the following configuration:

σ1s², σ*1s², σ2s², σ*2s², σ2p_x², {π2p_y², π2p_z²}, {π*2p_y¹, π*2p_z¹}

By MOT we can calculate the bond order of the molecule. Bond order defines the number of bonds formed in between the bonded atoms in that molecule.

Bond Order = (Number of e^-occupying bonding MO) – (Number of e^- occupying antibonding MO)

         2

Let’s calculate it for O₂  molecule. It has 10 electrons in bonding MO and 6 electrons in antibonding MO. Thus its bond order will be (10-6)/2= 2, which corresponds to the double bond.

Now take another example of N₂ molecule. Nitrogen 7N has 7 electrons. Its electronic configuration is 1s², 2s², 2p³. When two N atoms come closer to form N₂ molecule their atomic orbitals get overlapped and form molecular orbitals. N₂ molecule has got 14 electrons, 7 electrons from each N atom. Each N atom has 5 atomic orbitals thus they combine to form 10 MO. The energy order of these MO is slightly different from the energy order given for O₂  molecule. This kind of energy order is applicable for the lighter elements like Nitrogen, Carbon and Boron:

σ1s, σ*1s, σ2s, σ*2s, {π2p_y, π2p_z}, σ2p_x, σ*2p_x, {π*2p_y, π*2p_z}

When we fill the electrons in MOs, we will get the following configuration:

σ1s², σ*1s², σ2s², σ*2s², {π2p_y², π2p_z²}, σ2p_x²

Let’s calculate its bond order; it has 10 electrons in bonding MO and 4 electrons in antibonding MO, so the bond order will be (10-4)/2 = 3, which corresponds to the triple bond.

Nitrogen and Oxygen both are gases but they behave differently when magnetic field is applied to them. I recommend you to see this video to understand what I am going to say. As you can see in the video that liquid Nitrogen is unaffected by external magnetic field and falls right through it while liquid Oxygen is affected by magnetic field and sort of dances between the poles and stays there for a while. This amazing nature of Oxygen can be explained by MOT, in the next post we will see how MOT reveals the secret of Oxygen. 

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