Molecular Orbital Theory (MOT):LCAO, Molecular Orbital Diagram, and More

To understand MOT, we should dive into precursor theories a bit. The Valence Bond Theory (VBT) failed to explain a few key features, like paramagnetism in ${\mathrm{O}}_2$ , Delocalized bonding in Benzene, non-existence of He₂, and others. F. Hund and R.H. Mulliken proposed Molecular Orbital Theory, focusing on addressing all these issues with VBT.

As per the Molecular Orbital Theory," Atomic orbitals consisting of delocalized electrons combine to form new molecular orbitals. An electron in a molecular orbital is influenced by two or more nuclei, depending upon the
number of atoms in the molecule (Polycentric). When two atomic orbitals combine, they form two molecular orbitals: Bonding and Antibonding molecular orbitals(MO). When the number of bonding MOs is higher than the number of antibonding MOs, a stable chemical bond forms."

These key features(postulates) can help you get a complete picture of the MOT theory. Check the main features below.

To develop a good understanding, you need to learn a few major concepts of molecular orbital theory. We will discuss these topics in detail below. You can check the subtopics below.

• Formation of Molecular Orbitals
• Linear Combination of Atomic Orbitals (LCAO)
• Conditions for LCA
• Types of Molecular Orbitals
• Molecular Energy Diagrams
• Bond order calculation
• Prediction of Magnetic properties
• Difference between Bonding and Anti-bonding Molecular Orbitals

The molecular orbital theory opened the path to understand the chemical bonding in a more detailed and precise way. This is important to understand how MOT theory explains the formation of molecular orbitals and subsequently the chemical bond due to these molecular orbitals.

As per the quantum mechanical model of atoms, all subatomic particles of the atom including electrons, behave in duality. All these electrons in atomic orbitals, apart from being sub-atomic particles, also behave like waves. When these electron waves of two or more atomic orbitals superpose, they interact with each other. These waves can either have constructive or destructive interference based on the phase difference.

When there is constructive interference of atomic orbitals, bonding molecular orbitals are formed. On the other hand, if the interference is destructive, then antibonding molecular orbitals are formed. However, there may be certain cases where nothing happens between two or more atomic orbitals a non-bonding molecular orbitals are formed. Check the summarized table below.

Linear Combination of Atomic Orbitals (LCAO) is the method used to explain the formation of molecular orbitals (MOs) from individual atoms (Atomic orbitals). It is very similar to the superposition of waves to form a new wave.

 The Linear Combination of Atomic Orbitals (LCAOs) explains the formation of the molecular orbitals, which later on become the foundation of the chemical bonding between the atoms. The formation of molecular orbitals can be understood in terms of the constructive or destructive interference of the electron waves of the combining atoms. 

Conditions of LCAO

The LCAO, based on the conditions, is responsible for the formation of MOs. There are a few conditions of the LCAOs check below. These conditions are very useful for CBSE exams and other competitive exams. 

• 1Atomic orbitals must have the same or at least comparable energy.
• 2 Atomic orbitals must have the same symmetry around the molecular axis.
• 3Atomic orbitals should overlap to the maximum extent.

There are 4 major types of molecular orbitals classified based on their symmetry and overlapping extent. You can check the table below for detailed explanations and features of all these types of bonds.

Bond order measures bond strength and is calculated as: $\text{Bond Order}=\frac{1}{2}\times (\text{Bonding electrons}-\text{Antibonding electrons})$

Higher bond orders indicate stronger, shorter bonds.

Example: For ${\mathrm{N}}_2$ (14 electrons): - MO configuration: ${\left({\sigma }_{1s}\right)}^2{\left({\sigma }_{1s}^{\mathrm{*}}\right)}^2{\left({\sigma }_{2s}\right)}^2{\left({\sigma }_{2s}^{\mathrm{*}}\right)}^2{\left({\pi }_{2p_x}\right)}^2{\left({\pi }_{2p_y}\right)}^2{\left({\sigma }_{2p_z}\right)}^2$

${\left({\sigma }_{1s}\right)}^2{\left({\sigma }_{1s}^{\mathrm{*}}\right)}^2{\left({\sigma }_{2s}\right)}^2{\left({\sigma }_{2s}^{\mathrm{*}}\right)}^2{\left({\pi }_{2p_x}\right)}^2{\left({\pi }_{2p_y}\right)}^2{\left({\sigma }_{2p_z}\right)}^2$ - Bonding electrons: 10 ( 2 from ${\sigma }_{1s},2$ from ${\sigma }_{2s},2$ from ${\pi }_{2p_x},2$ from ${\pi }_{2p_y},2$ from ${\sigma }_{2p_z}$ )

Antibonding electrons: 4 (2 from ${\sigma }_{1s}^{\mathrm{*}},2$ from $\left.{\sigma }_{2s}^{\mathrm{*}}\right)$

Bond order: $\frac{1}{2}\times (10-4)=3$ (triple bond)

This explains ${\mathrm{N}}_2$ 's high stability (bond enthalpy  ).