NEET Crash Course Module - 13

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NEET Crash Course • Module 13

Molecular Orbital Theory (MOT)

Move past the limitations of VBT. Master the quantum mechanics of bonding through LCAO, decode the magnetic nature of $O_2$, and learn the ultimate 14-electron shortcut for Bond Order.

By chemca Academic Team • Updated for NEET 2027

Module Focus

Valence Bond Theory (VBT) is an excellent model, but it spectacularly failed to explain the paramagnetic behavior of Liquid Oxygen ($O_2$) and the existence of fractional bond orders. Molecular Orbital Theory (MOT), developed by Hund and Mulliken, solves this by treating the entire molecule as a single entity with its own distinct energy levels (Molecular Orbitals) formed by the mixing of atomic orbitals.

1. Linear Combination of Atomic Orbitals (LCAO)

Atomic orbitals can be expressed by wave functions ($\psi$). When two atoms approach each other, their wave functions can either add up (constructive interference) or subtract (destructive interference).

Bonding Molecular Orbital (BMO)

Formed by the addition (constructive interference) of atomic wave functions: $\psi_{\text{MO}} = \psi_{\text{A}} + \psi_{\text{B}}$.

• Electron density is concentrated between the nuclei, shielding them from repelling each other.
• Possesses lower energy and greater stability than the combining atomic orbitals.

Antibonding Molecular Orbital (ABMO)

Formed by the subtraction (destructive interference) of atomic wave functions: $\psi^*_{\text{MO}} = \psi_{\text{A}} - \psi_{\text{B}}$.

• Electron density is pushed away from the internuclear region. A nodal plane exists between the nuclei.
• Possesses higher energy and lower stability than the combining atomic orbitals. Denoted with an asterisk (*).

2. Energy Level Diagrams & s-p Mixing

The order in which molecular orbitals are filled follows the Aufbau principle, Pauli's exclusion principle, and Hund's rule. However, the exact order of energy levels depends on whether the molecule experiences $s-p$ mixing.

A. Molecules WITH s-p Mixing (Up to Nitrogen, $N_2$)

Applies to $Li_2, Be_2, B_2, C_2, \text{and } N_2$. Because the 2s and 2p orbitals are close in energy, they mix and repel each other. This pushes the $\sigma_{\text{2pz}}$ orbital higher in energy than the $\pi_{\text{2px}}$ and $\pi_{\text{2py}}$ orbitals.

$\sigma_{\text{1s}} < \sigma^*_{\text{1s}} < \sigma_{\text{2s}} < \sigma^*_{\text{2s}} < \mathbf{(\pi_{\text{2px}} = \pi_{\text{2py}}) < \sigma_{\text{2pz}}} < (\pi^*_{\text{2px}} = \pi^*_{\text{2py}}) < \sigma^*_{\text{2pz}}$

B. Molecules WITHOUT s-p Mixing ($O_2 \text{ and } F_2$)

Applies to elements beyond Nitrogen ($O_2, F_2, Ne_2$). The energy gap between 2s and 2p is large enough that they do not mix. The $\sigma_{\text{2pz}}$ orbital fills normally (before the $\pi$ orbitals).

$\sigma_{\text{1s}} < \sigma^*_{\text{1s}} < \sigma_{\text{2s}} < \sigma^*_{\text{2s}} < \mathbf{\sigma_{\text{2pz}} < (\pi_{\text{2px}} = \pi_{\text{2py}})} < (\pi^*_{\text{2px}} = \pi^*_{\text{2py}}) < \sigma^*_{\text{2pz}}$

Why is $O_2$ Paramagnetic?

Oxygen ($O_2$) has 16 electrons. Filling them into the standard sequence: the last two electrons enter the degenerate antibonding orbitals $(\pi^*_{\text{2px}} \text{ and } \pi^*_{\text{2py}})$. According to Hund's rule, they remain unpaired ($\pi^*_{\text{2px}}^1 = \pi^*_{\text{2py}}^1$). These two unpaired electrons make liquid oxygen strongly attracted to a magnetic field (Paramagnetic).

3. Bond Order and Stability

Bond Order indicates the number of covalent bonds between two atoms in a molecule.

$\text{Bond Order (B.O.)} = \frac{N_{\text{bonding}} - N_{\text{antibonding}}}{2}$

• Stability: If $N_{\text{bonding}} > N_{\text{antibonding}}$ (Positive B.O.), the molecule is stable. If $N_{\text{bonding}} \le N_{\text{antibonding}}$ (B.O. is 0 or negative), the molecule is highly unstable and does not exist (e.g., $He_2$).
• Bond Dissociation Energy: Directly proportional to Bond Order. ($N_2 > O_2 > F_2$).
• Bond Length: Inversely proportional to Bond Order.

NEET Time-Saver

The 14-Electron Rule

Do not write the full electronic configuration in the exam. Count the total electrons and use this chart. It works for both homonuclear and heteronuclear diatomic molecules (like $CO, NO, CN^-$).

Total Electrons

Bond Order

10

1.0

11

1.5

12

2.0

13

2.5

14

3.0 (Max)

15

2.5

16

2.0

17

1.5

18

1.0

Notice the symmetry: For every electron added or removed from 14, the Bond Order decreases by 0.5.

Exception Warning ($CO^+$): Carbon Monoxide ($CO$) has 14e⁻ (B.O. = 3.0). When it loses an electron to form $CO^+$, the electron is removed from a slightly antibonding $\sigma$ orbital. Its Bond Order actually increases to 3.5. This is a famous advanced exception.

Magnetic Nature Hacks

• If total electrons are an ODD number $\rightarrow$ Always Paramagnetic.
• If total electrons are an EVEN number $\rightarrow$ Usually Diamagnetic.
• EXCEPTIONS (10 and 16 electrons): Molecules with exactly 10 electrons ($B_2$) or 16 electrons ($O_2$) are Paramagnetic because they have unpaired electrons in degenerate $\pi$ orbitals.

Target 180/180

NEET Grand Test: Molecular Orbital Theory

15 High-Order Thinking Questions testing BO shortcuts, HOMO/LUMO, and magnetic anomalies.

All Quizzes NEET Rapid Revision Series Video Lectures

🎯 NEET 2027 Target 180

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