Molecular Orbital Theory (MOT) | Chemical Bonding Class 11

Molecular Orbital Theory (MOT)

LCAO, Energy Diagrams & Bond Order | Chemical Bonding

1. Introduction to MOT

Developed by Mulliken and Hund (1932) to explain properties like the paramagnetic nature of Oxygen ($O_2$), which Valence Bond Theory could not explain.

                    Core Concept: Atomic orbitals combine to form Molecular Orbitals (MOs) which belong to the entire molecule rather than individual atoms. Electrons fill these MOs following Aufbau, Pauli, and Hund's rules.
                

2. Linear Combination of Atomic Orbitals (LCAO)

When two atomic orbitals combine, they form two molecular orbitals:

Bonding MO (BMO, $\sigma, \pi$): Formed by constructive interference ($\Psi_A + \Psi_B$). It has lower energy and greater stability.
Antibonding MO (ABMO, $\sigma^*, \pi^*$): Formed by destructive interference ($\Psi_A - \Psi_B$). It has higher energy and lesser stability. A node exists between nuclei.

3. Energy Level Diagrams

The order of energy levels depends on the total number of electrons.

Case A: Molecules with $\le 14$ electrons ($B_2, C_2, N_2$)

Due to s-p mixing, $\sigma_{2p_z}$ shifts to higher energy than $\pi_{2p}$.

$\sigma_{1s} < \sigma^*_{1s} < \sigma_{2s} < \sigma^*_{2s} < \pi_{2p_x} = \pi_{2p_y} < \sigma_{2p_z} < \pi^*_{2p_x} = \pi^*_{2p_y} < \sigma^*_{2p_z}$

Case B: Molecules with $> 14$ electrons ($O_2, F_2, Ne_2$)

Standard filling order (No significant s-p mixing).

$\sigma_{1s} < \sigma^*_{1s} < \sigma_{2s} < \sigma^*_{2s} < \sigma_{2p_z} < \pi_{2p_x} = \pi_{2p_y} < \pi^*_{2p_x} = \pi^*_{2p_y} < \sigma^*_{2p_z}$

4. Bond Order & Magnetic Character

Bond Order (B.O.)

$$ B.O. = \frac{1}{2} (N_b - N_a) $$

Where $N_b$ is electrons in BMO and $N_a$ is electrons in ABMO.

B.O. > 0: Molecule is stable.
B.O. $\le$ 0: Molecule does not exist (e.g., $He_2$).
Relation: Bond Order $\propto$ Stability $\propto$ Bond Energy $\propto \frac{1}{\text{Bond Length}}$.

Magnetic Nature

Diamagnetic: All electrons are paired. Repelled by magnetic field.
Paramagnetic: Contains unpaired electrons. Attracted by magnetic field.

5. Examples

Nitrogen ($N_2$, 14 electrons)

Configuration:

$$ \sigma_{1s}^{2} \sigma^{*}_{1s}{}^{2} \sigma_{2s}^{2} \sigma^{*}_{2s}{}^{2} (\pi_{2p_x}^{2} = \pi_{2p_y}^{2}) \sigma_{2p_z}^{2} $$

Analysis:
$N_b = 10$ (bonding), $N_a = 4$ (antibonding).
$$ B.O. = \frac{1}{2}(10 - 4) = 3 $$ Magnetic Nature: Diamagnetic (All electrons are paired).

Oxygen ($O_2$, 16 electrons)

Configuration:

$$ \sigma_{1s}^{2} \sigma^{*}_{1s}{}^{2} \sigma_{2s}^{2} \sigma^{*}_{2s}{}^{2} \sigma_{2p_z}^{2} (\pi_{2p_x}^{2} = \pi_{2p_y}^{2}) (\pi^{*}_{2p_x}{}^{1} = \pi^{*}_{2p_y}{}^{1}) $$

Analysis:
$N_b = 10$ (bonding), $N_a = 6$ (antibonding).
$$ B.O. = \frac{1}{2}(10 - 6) = 2 $$ Magnetic Nature: Paramagnetic (Due to 2 unpaired electrons in $\pi^*$ orbitals according to Hund's Rule).

Practice Quiz

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