Molecular Orbital Theory (MOT) is a modern theory of chemical bonding that describes electrons as occupying molecular orbitals spread over an entire molecule. Unlike the Valence Bond Theory and Lewis Structure, which postulate that electrons are confined between individual atoms, MOT treats electrons as delocalized over the entire molecule. Molecular orbitals are formed by combining atomic orbitals from the bonding atoms. ^[1-4]

Electrons fill the molecular orbitals according to their energy levels, similar to how they fill atomic orbitals in an atom. MOT explains important molecular properties such as bond order, stability, and magnetism more accurately than older models. 

Formation of Molecular Orbitals

When atoms come together to form a molecule, their atomic orbitals interact. This interaction leads to the formation of new orbitals called molecular orbitals. These orbitals extend across the entire molecule and accommodate electrons from both atoms. ^[1-6]

Molecular orbital formation takes place through a process called the Linear Combination of Atomic Orbitals (LCAO). It means that the wave functions of atomic orbitals are added to create molecular orbitals. Like waves in water, atomic orbitals can combine in different ways – sometimes reinforcing each other and sometimes canceling out.. Combining orbitals through LCAO helps to understand how molecules form and why some are stable while others are not.

Types of Molecular Orbitals ^[1-6]

1. Bonding Molecular Orbital: When two atomic orbitals combine so that their wave functions add up, constructive interference is achieved. This creates a bonding molecular orbital, with a high probability of finding electrons between the two nuclei. It helps hold the atoms together in a stable bond.

2. Anti-Bonding Molecular Orbital: When atomic orbitals combine to cancel each other out, it is called destructive interference. This leads to the formation of an anti-bonding molecular orbital, where the probability of finding electrons between the nuclei is very low. Instead, electrons are more likely to be found outside the bonding region, which reduces the molecule’s stability. Anti-bonding orbitals are denoted with an asterisk (*).

3. Non-bonding Orbital: Sometimes, atomic orbitals do not interact significantly. In such cases, they retain their original energy levels and shapes. These are called non-bonding orbitals. Electrons in non-bonding orbitals neither contribute to nor detract from the bond between atoms.

Molecular orbitals can also be classified based on their symmetry around the internuclear axis into sigma (σ) and pi (π) orbitals.

• A sigma (σ) orbital forms when two atomic orbitals overlap head-on along the axis connecting the nuclei. This strong, direct overlap leads to a symmetrical bonding orbital around the internuclear axis. For example, two s orbitals or an s and a p orbital overlapping end-to-end form a σ orbital. Electrons in a σ orbital are concentrated between the nuclei and help bond the atoms.

• A pi (π) orbital forms when two p orbitals overlap sideways, above and below the bond axis. This overlap is weaker than in σ orbitals, but electrons in π orbitals still contribute to molecular stability.

For both σ and π orbitals, anti-bonding counterparts also exist. These are labeled with an asterisk, such as σ* and π*. When occupied, these orbitals arise from destructive interference and tend to destabilize the molecule.

Rules of Molecular Orbital Theory

Electrons follow established rules when filling molecular orbitals: ^[1-6]

• Aufbau Principle: Electrons occupy the lowest energy molecular orbitals first, starting from the bottom up.
  
• Pauli Exclusion Principle: Each orbital can hold a maximum of two electrons with opposite spins.
  
• Hund’s Rule: When filling orbitals of equal energy, electrons are placed one per orbital with parallel spins before any pairing occurs. This minimizes electron-electron repulsion.

Molecular Orbital Energy Diagram

Molecular orbital (MO) energy diagrams visually represent how atomic orbitals from two atoms combine to form molecular orbitals. These diagrams help us understand electron arrangement and bond strength in a molecule. ^[1–6]

To construct an MO diagram:

1. Start with the atomic orbitals of each atom. Draw their energy levels (such as 2s and 2p) on the left and right sides of the diagram.
   
2. Combine atomic orbitals to form molecular orbitals. Show bonding and anti-bonding orbitals in the center of the diagram.
   
3. Label each orbital clearly – e.g., σ_2s, σ_2s*, π_2p, π_2p*.
   
4. Fill in the electrons using the rules above: start from the lowest energy level, place no more than two electrons per orbital, and follow Hund’s rule for degenerate orbitals.

Example

Consider the example of the oxygen molecule O₂. Its MO diagram shows two unpaired electrons in the π_2p* orbitals (specifically, π_2px* and π_2py*). These unpaired electrons make oxygen paramagnetic, meaning it is attracted to magnets – an observation that the Lewis Structure fails to predict.

Predicting Bond Order

In addition to electron configurations, MO diagrams allow us to calculate the bond order, which provides insight into bond strength and molecular stability.

Bond Order = (Number of electrons in bonding orbitals − Number in anti-bonding orbitals)/2

​For O₂, the bond order is 2, indicating a double bond and a relatively stable molecule.