(a) What is linear combination of atomic orbitals ?
(b) illustrate bonding and antibonding molecular orbitals based on homonuclear dihydrogen molecule.

Answer

### Step-by-Step Text Solution

#### (a) What is Linear Combination of Atomic Orbitals (LCAO)?

1. **Definition**: The Linear Combination of Atomic Orbitals (LCAO) is an approximate method used to describe molecular orbitals in terms of atomic orbitals.

2. **Superimposition**: This method involves the superimposition of atomic wave functions. In physics, the principle of superposition states that two or more overlapping waves can combine to form a new wave.

3. **Constructive and Destructive Interference**:
- **Constructive Interference**: When two atomic wave functions combine constructively, they enhance each other, leading to the formation of a bonding molecular orbital. This results in an increase in electron density between the nuclei of the bonded atoms.
- **Destructive Interference**: Conversely, when the wave functions interfere destructively, they cancel each other out, leading to the formation of an antibonding molecular orbital. This results in a decrease in electron density between the nuclei and often places electron density outside the region between the nuclei.

4. **Summary**: Thus, LCAO is a method that helps in understanding how atomic orbitals combine to form molecular orbitals, which can be bonding or antibonding based on the type of interference.

#### (b) Illustrate Bonding and Antibonding Molecular Orbitals Based on Homonuclear Dihydrogen Molecule (H₂)

1. **Bonding Molecular Orbital (σ)**:
- In the case of a homonuclear dihydrogen molecule (H₂), when the 1s atomic orbitals of two hydrogen atoms combine constructively, they form a bonding molecular orbital (σ).
- This bonding orbital has increased electron density between the two hydrogen nuclei, which stabilizes the molecule.

2. **Antibonding Molecular Orbital (σ*)**:
- When the same 1s atomic orbitals combine destructively, they form an antibonding molecular orbital (σ*).
- In this case, the electron density is concentrated outside the region between the two hydrogen nuclei, which destabilizes the molecule.

3. **Illustration**:
- **Bonding Orbital (σ)**: Represented by a region of high electron density between the two nuclei.
- **Antibonding Orbital (σ*)**: Represented by a node (a region of zero electron density) between the nuclei and regions of electron density on either side.

4. **Conclusion**: The bonding molecular orbital promotes stability in the H₂ molecule, while the antibonding molecular orbital does the opposite.