3.10.1 Bonding and Antibonding Molecular Orbitals

This topic explains the two types of molecular orbitals formed when atomic orbitals combine — bonding molecular orbitals (BMO) and antibonding molecular orbitals (ABMO).

Definition

Bonding Molecular Orbital (BMO): A molecular orbital formed by the overlap of atomic orbitals, having high electron density between the two nuclei, which is responsible for the stability of the bond.

Antibonding Molecular Orbital (ABMO): A molecular orbital formed by the subtraction overlap of atomic orbitals, having zero electron density between the two nuclei, with electron density concentrated on the opposite side.

Main Idea

• Bonding molecular orbital (BMO): Lower in energy, stable, contributes to attraction between atoms.
• Antibonding molecular orbital (ABMO): Higher in energy, unstable, contributes to repulsion between atoms.

The number of molecular orbitals formed is equal to the number of atomic orbitals combined.

Core Concept

• BMO: Formed by addition of atomic orbitals (constructive interference). Electron density is between the nuclei. Stabilizes the bond.
• ABMO: Formed by subtraction of atomic orbitals (destructive interference). Electron density is outside the nuclei. Destabilizes the bond.

Electrons in BMO contribute to attraction, while electrons in ABMO contribute to repulsion.

Detailed Explanation

Bonding Molecular Orbital (BMO)

• A bonding molecular orbital is formed by the overlap of atomic orbitals.
• BMO has high electron density in the region between the two nuclei.
• This high electron density is responsible for the stability of the bond.
• Each electron in the BMO contributes to attraction between the two atoms.
• They are designated as σ and π BMO.
• BMO is lower in energy than the parent atomic orbitals.

Example: In H₂, the two 1s atomic orbitals combine to form σ 1s (bonding) and σ^* 1s (antibonding). The two electrons occupy the lower energy σ 1s orbital, stabilizing the molecule.

Antibonding Molecular Orbital (ABMO)

• An antibonding molecular orbital is formed by the subtraction overlap of atomic orbitals.
• It 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 the two atoms.
• They are designated as σ^* and π^* ABMO.
• ABMO is higher in energy than the parent atomic orbitals.

Example: In He₂, the two 1s atomic orbitals combine to form σ 1s and σ^* 1s. The four electrons fill both orbitals, resulting in zero bond order and an unstable molecule.

Number of Molecular Orbitals

• The number of molecular orbitals formed is equal to the number of atomic orbitals that are combined.
• Example: Two 1s orbitals → two molecular orbitals (σ 1s and σ^* 1s).
• Example: Three 2p orbitals from each atom → six molecular orbitals (three bonding and three antibonding).

Electrons in Molecular Orbitals vs. Atomic Orbitals

• Electrons in the molecular orbitals are influenced by all nuclei.
• In an atomic orbital, an electron is influenced by one nucleus.

Filling of Electrons

The filling of electrons into the molecular orbitals occurs according to:

• Aufbau Principle: Electrons fill the lowest energy orbitals first.
• Pauli's Exclusion Principle: Maximum two electrons per orbital, with opposite spins.
• Hund's Rule: Electrons occupy degenerate orbitals singly first, with parallel spins.

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 of low energy (bonding)
• σ^* s of high energy (antibonding)

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

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

Bond Order

Bond order 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

Example: Hydrogen Molecule (H₂) - Bonding electrons = 2 - Antibonding electrons = 0 Bond order = 2 - 02 = 1

• If bond order = 0 → molecule unstable (does not exist).
• If bond order > 0 → molecule stable.

Paramagnetic and Diamagnetic Nature

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

Intermediate Level

Bonding vs. Antibonding Molecular Orbitals

Key Points

• Number of MOs = number of AOs combined.
• Electrons in MOs are influenced by all nuclei.
• Filling order: Aufbau, Pauli, Hund's rules.
• Bond order = N_b - N_a2.
• Bond order = 0 → unstable; > 0 → stable.
• Paramagnetic: Unpaired electrons.
• Diamagnetic: No unpaired electrons.

Types of Overlapping

Energy Order for 2p Orbitals

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

Important Points

• 1. BMO: Lower energy, stable, electron density between nuclei.
• 2. ABMO: Higher energy, unstable, electron density outside nuclei.
• 3. Number of MOs = number of AOs combined.
• 4. Electrons fill according to Aufbau, Pauli, and Hund's rules.
• 5. Bond order = N_b - N_a2.
• 6. Bond order = 0 → unstable; > 0 → stable.
• 7. Paramagnetic: Unpaired electrons; Diamagnetic: No unpaired electrons.
• 8. Energy order differs for O₂F₂ vs. lighter molecules.

Remember

• - BMO: Lower energy, stable, electron density between nuclei
• - ABMO: Higher energy, unstable, electron density outside nuclei
• - **Number of MOs = Number of AOs**
• - Bond order: N_b - N_a2
• - Paramagnetic: Unpaired electrons
• - Diamagnetic: No unpaired electrons

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

• BMO: Lower energy, stable, electron density between nuclei.
• ABMO: Higher energy, unstable, electron density outside nuclei.
• Number of MOs = number of AOs combined.
• Electrons fill according to Aufbau, Pauli, and Hund's rules.
• Bond order = N_b - N_a2.
• Bond order = 0 → unstable; > 0 → stable.
• Paramagnetic: Unpaired electrons; Diamagnetic: No unpaired electrons.
• Energy order differs for O₂F₂ vs. lighter molecules.

60-Second Revision

• BMO: Lower energy, stable, electron density between nuclei
• ABMO: Higher energy, unstable, electron density outside nuclei
• **Number of MOs = Number of AOs**
• Bond order: N_b - N_a2
• Paramagnetic: Unpaired electrons
• Diamagnetic: No unpaired electrons

QUALITY VALIDATION

• Topic: 3.10.1 Bonding and Antibonding Molecular Orbitals
• Chapter: 3 (Chemical Bonding)

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