Now that we have seen the usefulness of MO theory over valence bond theory, let’s take a look at how we can use the theory by finding the bond order of a molecule.

Previously, we have learnt how to fill the molecular orbitals following the Aufbau’s principle, Hund’s Rule and the Pauli’s Exclusion Principle. Now, we are going to use that molecular orbitals diagram to find the bond order. Read on to find out how!

Bond order

The concept of bond order in layman terms can be described as the average number of electrons involved per bond in a molecule.

It is based on the formula, B.O. = ½ [ no. of bonding electrons – no. of anti-bonding electrons].

As an example, let’s look at oxygen below.

MO Diagram of Oxygen

Bond order in O2 = ½ [ no. of bonding electrons – no. of anti-bonding electrons] = ½ [ 10 – 4 ] = 2

Hence an average of 2 electrons are involved in a bond in O2.

In reality, the dot and cross diagram does prove that to be true, as shown below.

You may want to try calculating the bond order for other molecules.

Try the example below:

Fluorine MO Diagram

Remember, bond order in O2 = ½ [ no. of bonding electrons – no. of anti-bonding electrons]

Answer: B.O.= 1

The bond order generally tells us the strength of the bond. The higher the bond order, the stronger the bond. We may make use of bond strength to further discuss about the stability of a molecule or the melting/boiling point. Yep, it’s that useful! Let me know if you find another use for it, it might be unheard of!

Alright, now that we have grasped the concept of bond order, we shall move on to another important concept which will help us predict an important property of a molecule – its magnetic properties! Here are 2 terms describing the magnetic property of a molecule:

1. Diamagnetic – This occurs when a molecule possess no singly paired electrons, and thus is not attracted to magnetic fields.

2. Paramagnetic – This occurs when a molecule possess singly paired electrons and is will be attracted to magnetic fields.

Example:

Fluorine MO Diagram

Oxygen MO Diagram

As observed in the MO Diagrams of Oxygen and Fluorine, we note that Oxygen has 2 unpaired electrons whereas Fluorine has none. Hence we can conclude that Oxygen is Paramagnetic whereas Fluorine is Diamagnetic.

Heteronuclear diatomic molecules are composed of two atoms of two different elements. The same electronic shell of the two atoms may not be of the same energy. That being said, it is not necessary for the electronic orbitals of the same shell to interact to give molecular orbitals. In fact, it is not necessary for the two 1s orbitals to interact. the 1s orbital may interact with other electronic orbitals, for example, this can be seen in the MO diagram of HF, below.

Figure 1: Molecular orbital of HF (Courtesy of chemwiki.ucdavis.edu)

The 1s orbital of H is of much similar energy to that of 2p in F. Therefore, interaction between the 1s and 2p orbitals takes place to form the molecular orbital of HF. Such electronic orbital interactions is common in heteronuclear diatomic as the electronic orbitals usually differ in energy levels.

In the molecular orbitals formed, a bonding and an anti-bonding molecular is formed. The molecules, H and F, contribute differently to each of these molecular orbitals. H contributes more to the anti-bonding orbitals as it is closer in energy to it. Likewise, F contributes moreto the bonding molecular orbital. The unequal contribution means that the covalent bond has a certain degree of ionic character.

Yes, so.. Do not be surprised the next time you see a 1s interacting with another 2p, 3s, 3p, who knows what orbital!