3.10 Molecular Orbital Theory

This topic introduces Molecular Orbital Theory (MOT), which describes how atomic orbitals combine to form molecular orbitals. It explains bonding and antibonding molecular orbitals, bond order, and magnetic properties.

Definition

Molecular Orbital Theory (MOT): A theory proposed by Hund and Mullikan in 1932. According to this theory, linear combination of atomic orbitals forms new orbitals called molecular orbitals which are characteristics of the whole molecule.

Main Idea

According to Molecular Orbital Theory, atomic orbitals combine to form molecular orbitals that belong to the whole molecule, not just to individual atoms. During this process, the identity of both atomic orbitals is lost. The molecular orbitals formed differ in energy — one of lower energy is called the bonding molecular orbital (BMO), while the other of higher energy is called the antibonding molecular orbital (ABMO).

Core Concept

• Atomic orbitals combine to form molecular orbitals.
• The number of molecular orbitals formed equals the number of atomic orbitals combined.
• Bonding molecular orbitals (BMO) have lower energy and contribute to stability.
• Antibonding molecular orbitals (ABMO) have higher energy and contribute to repulsion.
• Electrons fill molecular orbitals according to Aufbau principle, Pauli's exclusion principle, and Hund's rule.
• MOT explains paramagnetic and diamagnetic nature of molecules.

Detailed Explanation

What is Molecular Orbital Theory?

• Proposed by Hund and Mullikan in 1932.
• According to this theory, linear combination of atomic orbitals forms new orbitals called molecular orbitals.
• These molecular orbitals are characteristic of the whole molecule.
• During this process, the identity of both atomic orbitals is lost.
• After the combination of atomic orbitals, different types of molecular orbitals are formed which differ in energy.

Bonding and Antibonding Molecular Orbitals

• Formed by the overlap of atomic orbitals.
• Has high electron density in the region between the two nuclei.
• This is responsible for the stability of the bond.
• Each electron in the BMO contributes to attraction between the two atoms.
• Designated as σ and π BMO.
• Lower in energy than the parent atomic orbitals.

• Formed by the subtraction overlap of atomic orbitals.
• Has zero electron density in between the two nuclei.
• The concentration of electron density is on the opposite side.
• Each electron in ABMO contributes to repulsion between two atoms.
• Designated as σ^* and π^* ABMO.
• Higher in energy than the parent atomic orbitals.

Key Points About Molecular Orbitals

• Aufbau Principle
• Pauli's Exclusion Principle
• Hund's Rule

Types of Overlapping in MOT

• Takes place by the combination of s-s, s-p, and p_x - p_x orbitals.
• When "s" atomic orbitals overlap with each other, two molecular orbitals are formed: σ s (low energy) and σ^* s (high energy).

• Takes place between p_y - p_y and p_z - p_z orbitals.
• When two p orbitals overlap, two molecular orbitals are formed: π p_y = π p_z (low energy) and π^* p_y = π^* p_z (high energy).

Molecular Orbitals from 2p Atomic Orbitals

• When three 2p atomic orbitals (p_x, p_y, p_z) of one atom overlap with three 2p atomic orbitals of another atom, six molecular orbitals (three bonding and three antibonding) are formed.
• These molecular orbitals according to energy are:

σ 2p_x < π 2p_y = π 2p_z < π^* 2p_y = π^* 2p_z < σ^* 2p_x

Paramagnetic and Diamagnetic Nature

• Paramagnetic: Molecules having unpaired electrons in the molecular orbitals are paramagnetic in nature and can be attracted by a magnetic field.
• Diamagnetic: Molecules having no unpaired electrons in the molecular orbitals are diamagnetic in nature and cannot be attracted by a magnetic field. They repel the magnetic field.

Bond Order (No. of Bonds)

• It is the total number of bonds formed when two atoms' atomic orbitals overlap with each other.
• It is half of the difference between the number of bonding electrons and antibonding electrons.

Bond order = No. of electrons in BMOs - No. of electrons in ABMOs2

• No. of electrons in bonding orbitals = 2
• No. of electrons in antibonding orbitals = 0

Bond order = 2 - 02 = 1

• If bond order is zero, the molecule is unstable, and it does not exist.
• A positive value of bond order reveals that the molecule exists and is stable.

Relative Energies of the Molecular Orbitals

Spectroscopic measurements determine the relative energies of the molecular orbitals formed from 2s and 2p atomic orbitals.

a) For diatomic molecules such as O₂, F₂, and their positive and negative ions:

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

b) For diatomic molecules such as H₂, He₂, B₂, C₂, and N₂ (lighter molecules):

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

Why the Order Differs for Lighter Molecules

• Elements of the second period having atomic number 3 to 7 (prior to oxygen) have a relatively small difference in energy between the 2s and 2p orbitals.
• As the energy difference between 2s and 2p atomic orbitals is small, as a result, σ 2s and σ^* 2s MO do not retain pure s-character (hybridization of A.O.).
• Mixing of 2s and 2p orbitals is the primary cause of the difference in the molecular orbitals of nitrogen and oxygen, which is influenced by the initial atomic orbital energies.
• Hence energy of σ 2p_x is greater than π 2p_y and π 2p_z.

Intermediate Level

Main Points of MOT

• Atomic orbitals combine to form molecular orbitals.
• Number of molecular orbitals = number of atomic orbitals combined.
• Bonding molecular orbitals (BMO) have lower energy.
• Antibonding molecular orbitals (ABMO) have higher energy.
• Electrons fill according to Aufbau, Pauli, and Hund's rules.
• MOT explains paramagnetic and diamagnetic nature.

Bonding and Antibonding Molecular Orbitals

Bond Order

Bond order = No. of electrons in BMOs - No. of electrons in ABMOs2

• Bond order = 0 → molecule unstable
• Bond order > 0 → molecule stable

Magnetic Properties

• Paramagnetic: Unpaired electrons → attracted by magnetic field.
• Diamagnetic: No unpaired electrons → not attracted by magnetic field.

Types of Overlapping

Energy Order for O₂, F₂

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

Energy Order for H₂, He₂, 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

Important Points

• 1. MOT proposed by Hund and Mullikan (1932).
• 2. Atomic orbitals combine to form molecular orbitals.
• 3. Number of MOs = number of AOs combined.
• 4. Bonding MO: Lower energy; Antibonding MO: Higher energy.
• 5. Electrons fill according to Aufbau, Pauli, and Hund's rules.
• 6. Bond order = bonding electrons − antibonding electrons2.
• 7. Bond order = 0 → unstable; > 0 → stable.
• 8. Paramagnetic: Unpaired electrons; Diamagnetic: No unpaired electrons.
• 9. Energy order differs for O₂F₂ vs. H₂/He₂/B₂C₂/N₂.

Remember

• - MOT: Atomic orbitals → Molecular orbitals
• - BMO: Lower energy, stable
• - ABMO: Higher energy, unstable
• - Bond order: N_b - N_a2
• - Paramagnetic: Unpaired electrons
• - Diamagnetic: No unpaired electrons
• - **Energy order:** O₂F₂ vs. lighter molecules

Common Mistakes

• 1. Confusing bonding and antibonding MOs: BMO = lower energy; ABMO = higher energy.
• 2. Forgetting the bond order formula: N_b - N_a2
• 3. Mixing up paramagnetic and diamagnetic: Paramagnetic = unpaired; Diamagnetic = paired.
• 4. Ignoring the energy order difference: O₂F₂ vs. lighter molecules have different orders.
• 5. Thinking MOT is the same as VBT: MOT considers the whole molecule, not just individual atoms.

Quick Revision

• MOT proposed by Hund and Mullikan (1932).
• Atomic orbitals combine to form molecular orbitals.
• Number of MOs = number of AOs combined.
• Bonding MO: Lower energy; Antibonding MO: Higher energy.
• Electrons fill according to Aufbau, Pauli, and Hund's rules.
• Bond order = bonding electrons − antibonding electrons2.
• Bond order = 0 → unstable; > 0 → stable.
• Paramagnetic: Unpaired electrons; Diamagnetic: No unpaired electrons.
• Energy order differs for O₂F₂ vs. H₂/He₂/B₂C₂/N₂.

60-Second Revision

• MOT: Atomic orbitals → Molecular orbitals
• BMO: Lower energy, stable
• ABMO: Higher energy, unstable
• Bond order: N_b - N_a2
• Paramagnetic: Unpaired electrons
• Diamagnetic: No unpaired electrons
• **Energy order:** O₂F₂ vs. lighter molecules

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• Chapter: 3 (Chemical Bonding)

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