The Molecular Orbital Theory (MO Theory) is necessary as it presents some distinct advantages over the valence bond theory (VB Theory). Figure 4.1 below will detail the differences between MO theory and VB theory:

Figure 1.1: Table comparing VB theory to MO theory

As seen, the MO theory is much more effective in explaining formation of bonds between atoms than the VB theory.

It has been mentioned previously that the number of molecular orbitals formed is the same as the number of atomic orbitals involved in bonding. The total number of electrons in the molecular orbitals is therefore also the same as the number of electrons in the original atomic orbitals.

The filling of electrons into the molecular orbitals follow three basic rules:

1. The Aufbau principle: Electrons are filled from the lowest energy orbital to the highest energy orbital. For example, atomic orbitals in atoms are filled from lowest energy to highest energy according to this order: 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4f < 5d < 6p < 7s < 5f
2. The Pauli Exclusion principle:
   • No more than two electrons can occupy one orbital
   • The two electrons must be of different spins
3. Hund’s Rule: When there are degenerate orbitals, electrons will occupy empty orbitals before pairing up with another electron to minimize repulsion between particles of like charges

The following very interesting video will explain these three basic rules:

In the first post about atomic orbitals, it was mentioned that only atomic orbitals with the same symmetry can overlap to form molecular orbitals. For instance, s atomic orbitals form molecular orbitals with s atomic orbitals, p_x atomic orbitals with p_x atomic orbitals, and so on.

However, exceptions to this rule do exist.

MO diagram for nitrogen gas

Looking at the MO diagram above, Nitrogen gas obviously does not follow the rule because the 2s atomic orbitals are forming molecular orbitals with the 2p atomic orbitals. But how is this possible?? How come nitrogen gas can defy the basic rules of MO theory??

This is due to magical phenomena known as s-p mixing!

So, what is s-p mixing? This is a special process that only happen in elements where the s atomic orbital is very close in energy to the p atomic orbital. In this case, this usually happens to elements found before oxygen in the periodic table (hint: see nitrogen).

Diagram showing MO diagram before (a) and after (b) s-p mixing

The diagram above shows the MO diagram of a homonuclear diatomic compound before and after s-p mixing.

For S-P mixing to occur, the 2 interacting orbitals must be of the same symmetry and of similar energy. From the diagram above, we can see that the labelled orbitals are able to interact as they are of the same symmetry as labelled. Since they can interact, they must be of similar energy. A key point to note is that the greatest interaction occurs when the energy gap between the 2 interacting orbitals is the smallest.  Such an interaction occurs between 2σg and 3σg as they are closest in energy.

Comparing (a) and (b), it is evident that s-p mixing lowers the energy level of the 2σ orbitals, thereby stablising them. At the same time, the 3σ orbitals are raised in energy. This way, the 3σ bonding orbital is higher in energy than the 1π bonding orbital. Thus following the Aufbau principle, the 1π bonding orbitals are filled before the 3σ bonding orbital. Thus, s-p mixing can change the magnetism of a compound.

One example of a compound that changes magnetism after s-p mixing is B₂ as shown below:

MO diagram for B2 for no s-p mixing

MO diagram for B2 for s-p mixing

As seen, if s-p mixing occurs, B₂  will be paramagnetic. This is because the electrons fill the 2π bonding orbitals singly before pairing up. Whereas in the non s-p mixing state, there is only one σ bonding orbital created by the p atomic orbitals and that means that the electrons pair up to fill the σ bonding orbital up completely. Therefore, diamagnetism is observed.

S-p mixing might not be prevalent, however, it can be useful to explain why some elements do not follow the expected trend of magnetism.

Apart from the magical process of s-p mixing, another magical process happens during the formation of molecular orbitals – sp-hybridisation!

To summarise, there are three main types of s-p hybrids available and they are as follows:

• sp³
• sp²
• sp

The shapes and angles of the hybrid atomic orbitals formed from s-p hybridisation are summarised below.

Bond angle and shapes associates with sp, sp2 and sp3 hybridisation

Sp³ hybridisation

One s orbital and three p orbitals hybridise to form four degenerate sp³ hybrid atomic orbitals (HAOs). The HAOs point towards the corners of a tetrahedron, thus, forming tetrahedral shape upon forming molecular orbitals. The bond angle in compounds with sp³ hybridisation is 109.5^o, allowing the compound to be more stable.

One example of a sp³ hybridised compound is C₂H₆.

Atomic orbitals overlap in C2H6

Sp² hybridisation

Sp² hybridised compounds are planar with a bond angle of 120^o. This is because three degenerate sp² hybrid atomic orbitals are produced.

One of the sp² hybridised compounds are CH₂O.

Atomic orbitals overlap in CH2O

Sp hybridisation

Sp hybridised compounds are also planar, with a bond angle of 180^o that will keep bond pairs as far away from each as possible.

An example of a sp hybridised compound is a C₂H₂.

Atomic orbitals overlap in C2H2