Molecular Orbital Theory

Concept of Molecular Orbital Theory

Before diving into the Molecular Orbital Theory, let's review the basics of atomic orbitals and electron orbital diagrams based on electron configuration. Atomic orbitals are regions of space where electrons can be found.

Let's take a look at the s, p, and d atomic orbitals.

• s orbitals have a spherical shape, and only one s orbital exists in the s-subshell. These atomic orbitals contain no nodes.
• p orbitals are said to have a dumbbell shape, two phases, and one node. In the p-subshell, there are three p orbitals.
• d orbitals can either have a four-leafed clover shape or a toroidal shape and have a node. In the d-subshell, there are five d orbitals.

Remember that electrons are distributed (1s, 2s, 2p...) within orbitals using the Aufbau principle, which states that electrons fill orbitals with the lowest energy first. Other rules that are important when dealing with orbital diagrams are Hund's rule and the Pauli exclusion principle.

• Hund's rule states that the same energy (degenerate) orbitals are first half-filled before they are totally filled.
• Pauli Exclusion principle states an orbital can hold a maximum of two electrons that have opposite spin orientations, ↾ or ⇃.

Let's look at an example.

Molecular Orbital theory tends to be more complicated than drawing orbital diagrams, so let's take it slow. We can start looking at a theory called the valence bond theory.

For example, if you have two separate hydrogen (H) atoms, which have their unpaired electrons in a 1s orbital, and these two hydrogen atoms approach each other, then their orbitals will overlap and give rise to molecular orbitals!

Fig. 4: Molecular Orbital Diagram of H₂ molecule - Isadora Santos, StudySmarter Originals.

Molecular orbitals give rise to the Molecular Orbital (MO) theory, and the goal of this theory is to show the combination of atomic orbitals of elements into molecular orbitals.

Molecular Orbital Theory Diagrams

First, it's important to know that atomic orbitals are wave functions, and when these wave functions overlap, it simultaneously leads to the formation of two types of molecular orbitals: both bonding and anti-bonding (*) molecular orbitals.

Constructive overlap results in the formation of bonding molecular orbitals. For example, when two hydrogen atoms undergo constructive overlap (addition of the wave functions for their 1s orbital), a bonding molecular orbital (σ_1s) is formed. Bonding molecular orbitals have a high electron density concentration between nuclei.

Bonding molecular orbitals are lower in energy because they have a larger volume compared to anti-bonding molecular orbitals, and also to the original atomic orbitals.

Destructive overlap results in the formation of anti-bonding molecular orbitals. In the case of hydrogen, the destructive addition of the wave functions for their 1s orbital leads to the formation of a non-bonding molecular orbital (σ*_1s). This destructive overlap creates a node, referred to as a region of zero electron density between the two atoms.

Sigma (σ) and Pi (∏) Overlap

Understanding sigma and pi bonds are also important when dealing with molecular orbitals. All covalent bonds are either sigma (σ) or pi (∏) bonds.

• All single bonds are sigma (σ) bonds.
• Pi (∏) bonds only show up in double and triple bonds. Double bonds have a sigma and a pi bond, whereas triple bonds have one sigma and two pi bonds.

Fig. 8: Sigma and Pi bonds in the lewis structure of 2-Butynal, Isadora Santos - StudySmarter Original.

Sigma (σ) overlap is the end-to-end overlap of any type of atomic orbitals, resulting in sigma orbitals. For example, the overlap of two s orbitals in H₂ or the overlap of an s orbital and a p orbital in HF are considered sigma overlap. The end-to-end overlap of two p orbitals is also considered a sigma overlap.

Pi (∏) overlap is a special case, and it is the result of the sideways overlap of p orbitals. Pi overlap forms pi orbitals. Remember: Pi (∏) bonds are only seen when double or triple bonds are present.

When two sets of p orbitals combine, one sigma (σ) bonding and one sigma (σ*) anti-bonding molecular orbital are formed, along with two bonding pi ( ∏) molecular orbitals and two anti-bonding pi (∏*) molecular orbitals.

Further Molecular Orbital Theory Diagrams

Now that we know about the overlap of orbitals. Let's turn the page and look at some diagrams! There are some steps we can take to fill in a molecular orbital diagram:

1. Determine the electron configuration of both elements.
2. Construct a molecular orbital diagram for each element based on the location of the valence electrons (valence-electron orbitals). So, period 1 elements will start with 1s, period 2 elements will start with 2s, period 3 elements will start with 3s, and so on.
3. Fill in the molecular orbitals based on the Aufbau principle, Hund's rule, and the Pauli exclusion principle.

Let's look at the molecular orbital diagram for N_2. Nitrogen has an electron configuration of 1s²2s²2p³. Since Nitrogen is a period 2 element, we will start the molecular orbital diagram with 2s.

• First, fill in the atomic orbital diagram for both nitrogen atoms. Each nitrogen atom will have two electrons in the 2s, and then 1 electron in each 2p, as per instructed in the Aufbau principle.
• Then, we combine both atomic orbitals to fill in the molecular orbital diagram, shown in gray. Remember to always fill in the lowest energy orbitals first!

Now, due to a lack of sp mixing, O₂, F₂, and Ne₂ will have a different molecular orbital than other elements in period 2. In this case, the order of the molecular orbitals σ_2p and ∏_2p will be reversed. Let's look at the molecular orbital diagram for O₂. The electron configuration of an oxygen atom is 1s²2s²2p⁶. Since oxygen is a period 2 element, its molecular orbital diagram will start with 2s.

Bond Order Molecular Orbital Theory

To find out a molecule's bond order, we can use molecular orbital diagrams. Bond order corresponds to the number of bonds between atoms.

• A bond order equal to 1 means that the bond is a single bond.
• A bond order of 2 means the presence of a double bond.
• A bond order of 3 means the presence of a triple bond.
• If a bond order is equal to 0, then it means that bonds are impossible for that molecule.

Let's look at an example!

Features of Molecular Orbital Theory

Now that we are more familiar with what molecular orbital theory is and how to draw molecular orbital diagrams, let's make a table with the features of the molecular orbital theory that are significant.

Limitations of Molecular Orbital Theory

The main limitation of molecular orbital theory is that we can only use them to talk about diatomic molecules because it would get way more complex to use them to talk about polyatomic molecules. For example, the formula for bond order does not account for polyatomic molecules.

In your AP chemistry exam, you probably won't need to draw or fill in molecular orbital diagrams. But, knowing the MO theory will definitely give you a better understanding of bonding!