Molecular Orbital Theory (MOT)

Full Notes

Introduction to Molecular Orbital Theory

Molecular Orbital Theory (MOT) was developed to address the limitations of Lewis structures and Valence Bond Theory – particularly their failure to explain phenomena such as the paramagnetism of oxygen or the non-existence of the He₂ molecule.

According to MOT, atomic orbitals combine to form molecular orbitals that are delocalised over the entire molecule, rather than remaining confined to individual atoms. These molecular orbitals are described using wavefunctions, in line with the Schrödinger equation.

However, because the Schrödinger equation can only be exactly solved for single-electron systems, we cannot use it directly to describe multi-electron molecular orbitals. Instead, we use an approximation called the Linear Combination of Atomic Orbitals (LCAO). This involves combining the wavefunctions of atomic orbitals mathematically – typically in a head-on orientation along the bonding axis.

4.7.1 Formation of Molecular Orbitals – LCAO

When two atomic orbitals approach and overlap head-on, their wavefunctions interact, much like waves. This interaction results in the formation of two types of molecular orbitals: bonding (lower energy) and antibonding (higher energy).

Constructive Interference (In-Phase Combination, ψ + ψ)

If the atomic orbitals combine in phase, their wavefunctions reinforce each other. This increases electron density between the nuclei, forming a bonding molecular orbital.

• Electrons in bonding orbitals are attracted to both nuclei.
• This dual attraction lowers their energy, making the molecule more stable than the individual atoms.

Destructive Interference (Out-of-Phase Combination, ψ − ψ)

If the orbitals combine out of phase, their wavefunctions cancel each other out in the region between the nuclei. This results in a node (a region of zero electron density) and forms an antibonding molecular orbital.

• Electrons in antibonding orbitals are less attracted to the nuclei.
• This increases their energy and destabilises the molecule compared to the separate atoms.

Key Points

• Bonding orbitals are formed by constructive interference and are stabilising (lower energy).
• Antibonding orbitals are formed by destructive interference and are destabilising (higher energy).
• Antibonding orbitals are marked with an asterisk: σ* or π*.
• The LCAO method is central to molecular orbital theory and provides a framework for predicting bonding behavior, stability, and magnetic properties of molecules.

4.7.2 Conditions for the Combination of Atomic Orbitals

For effective overlap and formation of molecular orbitals, the following conditions must be met:

1. Similar Energy: Only orbitals with comparable energy levels can combine (e.g., 1s with 1s or 2p with 2p).
2. Proper Orientation: Orbitals must have suitable alignment for maximum overlap.
3. Maximum Overlap: Greater overlap leads to stronger bonding and a greater energy difference between bonding and antibonding orbitals.

4.7.3 Types of Molecular Orbitals

The type of molecular orbital that forms depends on the orientation of overlap of atomic orbitals.

σ (Sigma) Orbitals

Formed by head-on (axial) overlap.

For Example Between s–s orbitals

For Example Between p–p orbitals

Electron density is concentrated along bond axis.

π (Pi) Orbitals

Formed by sideways (lateral) overlap of p-orbitals.

Electron density is above and below the bond axis.

Antibonding Orbitals

• Labeled as σ* or π*.
• Contain a node between the nuclei.
• Electron occupancy leads to destabilisation.

4.7.4 Energy Level Diagram for Molecular Orbitals

The relative energies of molecular orbitals differ for lighter and heavier elements:

For Elements with Atomic Number ≤ 7 (e.g., B₂, C₂, N₂):

σ(1s) < σ*(1s) < σ(2s) < σ*(2s) < π(2p_y) = π(2p_z) < σ(2p_x) < π*(2p_y) = π*(2p_z) < σ*(2p_x)

Due to s–p mixing, π(2p) orbitals are lower in energy than σ(2p) in these cases.

For Elements with Atomic Number ≥ 8 (e.g., O₂, F₂, Ne₂):

σ(1s) < σ*(1s) < σ(2s) < σ*(2s) < σ(2p_x) < π(2p_y) = π(2p_z) < π*(2p_y) = π*(2p_z) < σ*(2p_x)

In heavier atoms, s–p mixing is negligible, so the σ(2p_x) orbital is lower than the π(2p_y/z) orbitals.

4.7.5 Electronic Configuration and Molecular Behaviour

Molecular Orbital Filling Rules:

• Aufbau Principle: Orbitals filled in order of increasing energy.
• Pauli Exclusion Principle: Max 2 electrons per orbital, with opposite spins.
• Hund’s Rule: Degenerate orbitals are singly filled before pairing begins.

Bond Order Formula:

Stability of Molecules:

• Bond order > 0 → Molecule is stable.
• Bond order = 0 → Molecule is unstable.

Examples H₂, He₂ and O₂

• H₂: σ(1s)² → Bond order = 1/2 (2 − 0) = 1 → Stable.
• He₂: σ(1s)² σ*(1s)² → Bond order = 1/2 (2 − 2) = 0 → Unstable.
• O₂: σ(1s)² σ*(1s)² σ(2s)² σ*(2s)² σ(2p_x)² π(2p_y)² π(2p_z)² π*(2p_y)¹ π*(2p_z)¹ → Bond order = 1/2 (10 − 6) = 2 → Paramagnetic due to two unpaired electrons.

Bond length

The bond order between two atoms in a molecule can be used as an approximate measure of the bond length. Bond length decreases as bond order increases.

Magnetic nature

If all the molecular orbitals in a molecule are doubly occupied, the substance is diamagnetic (repelled by magnetic field). However if one or more molecular orbitals are singly occupied it is paramagnetic (attracted by magnetic field).

Summary

• Atomic orbitals combine to form molecular orbitals via the LCAO method.
• Bonding molecular orbitals lower energy and stabilise the molecule while antibonding molecular orbitals raise energy and destabilise it.
• Bond order quantifies stability and decreases bond length as it increases.
• Paramagnetism arises from unpaired electrons and diamagnetism occurs when all electrons are paired.