Molecular Orbital Theory

The Molecular Orbital Theory (MOT) is a fundamental concept in chemistry, explaining how molecules form and behave based on the quantum mechanical behavior of electrons. It describes molecular structure and bonding by analyzing the interaction of atomic orbitals to form molecular orbitals.

1.0Introduction 

Molecular Orbital (MO) theory, created in 1932 by F. Hund and R.S. Mulliken, helps explain how electrons behave in molecules, offering insights into how molecules are formed and how they stick together.

Molecular Orbital Theory (MOT) was created to better understand how molecules form, bond, and behave, especially for complex cases that simpler theories, like Valence Bond Theory, couldn't fully explain. 

It helps us understand tricky structures like molecules with resonance and multiple equal bonds, giving a clearer view of how molecules behave and their properties.

The Valence Bond Theory (VBT) and other previous theories faced challenges in explaining certain features of atomic orbitals, such as:

Equivalent Bonds: Difficulty in elucidating molecules with multiple identical    bonds, like those found in certain organic compounds or resonance structures.

Complex Molecules: Inadequate explanation for intricate molecules, especially those with delocalized electrons or unconventional bonding patterns.

Predictive Ability: Limited predictive power in anticipating and describing the properties of molecules beyond simple structures.

Electron Behavior: Inability to fully describe electron behavior in molecules, especially in cases where electrons are spread across multiple atoms.

Molecular Geometry: Struggles in precisely defining and predicting the geometric arrangements of atoms in complex molecules.

Energy Levels: Insufficiency in providing an accurate depiction of energy levels and electron distributions in larger or more intricate molecular systems.

2.0The key features of Molecular Orbital Theory

(i) Electrons within a molecule occupy molecular orbitals, similar to how atomic orbitals host electrons in individual atoms.

(ii) Atomic orbitals of similar energies and appropriate symmetries combine to create molecular orbitals.

(iii) An electron in an atomic orbital is influenced by one nucleus, while in a molecular orbital, it's influenced by multiple nuclei from the molecule. This makes an atomic orbital "monocentric" and a molecular orbital "polycentric."

(iv) The number of molecular orbitals formed equals the number of combining atomic orbitals. When two atomic orbitals combine, they create two molecular orbitals: one bonding and one antibonding.

(v)The bonding molecular orbital, with lower energy, is more stable compared to the antibonding molecular orbital.

(vi) Similar to atomic orbitals describing electron distribution around a nucleus in an atom, molecular orbitals describe electron distribution around a group of nuclei in a molecule.

(vii) Molecular orbitals follow principles like aufbau, Pauli’s exclusion, and Hund’s rule when being filled, similar to atomic orbitals. 

3.0Comparison of Bonding molecular orbital & Antibonding molecular orbital

Further we will discuss Notations, Formation and special characteristics of Molecular orbitals. 

4.0Notation of molecular orbitals

As atomic orbitals are known by letters s, p, d and f depending on their shapes. Similarly, for molecular orbital

For bonding molecular orbital        -  𝛔 , π

For antibonding molecular orbital  -  𝛔  , π

are used for different shapes of electron cloud.

5.0Shapes and Formation of Molecular Orbitals (Linear Combination Atomic  Orbital Method)

The Linear Combination of Atomic Orbitals (LCAO) method is an approach used in Molecular Orbital Theory to construct molecular orbitals (MOs) by combining atomic orbitals (AOs) from individual atoms in a molecule.

(A) (𝛔 molecular orbital) :- It is formed by two ways

(i)   Combination of s-orbitals

𝛔* 1s have one nodal plane.

(ii)  Head on overlapping of p-orbitals

𝛔* p have one nodal plane

(B) π (pi) molecular orbitals

6.0Sequence of Filling of Electrons

The sequence of filling electrons in atomic orbitals follows the Aufbau principle, which states that electrons fill atomic orbitals of the lowest available energy levels before occupying higher levels. 

(i) Total electrons ≤ 14 (Atomic number ≤7) w(s-p mixing takes place)

σ1s, σ*1s, σ2s, σ*2s, [π2p_x = π2p_y], σ2p_Z, [π*2p_x = π*2p_y], σ*2p_Z

                                                            Degenerate Orbitals

(ii) Total electrons > 14 (Atomic number > 7)

        σ1s, σ*1s, σ2s, σ*2s, σ2p_z, [π2p_x = π2p_y], [π*2p_x = π*2p_y], σ*2p_Z

                                                              Degenerate orbitals 

7.0Applications of Molecular Orbital Theory

• Stability of molecule: If a molecule has '0' bond order then the molecule will not exist. Stability ∝ bond order

Note: If different molecular ions of a molecule having same bond order then the molecular ion having less no of electrons in ABMO will be more stable

• Magnetic property

(a) When electron in MO are paired — diamagnetic

(b) When electron in MO are unpaired — paramagnetic

• If bond order is fractional then the molecule will be paramagnetic.
• Hydrogen (H₂) and Nitrogen (N₂) like diatomic gasses are examples of Molecular orbital theory. As the theory explains the formation of bonding and antibonding molecular orbitals.