Molecular Orbital Theory: Bonding Made Simple

What is Molecular Orbital Theory? 🤔

This theory explains how atoms bond to form molecules. Think of it like mixing atomic orbitals (the “homes” of electrons in atoms) to create new “shared homes” called molecular orbitals (MOs) for electrons in molecules. Key ideas:

  • ✨ Electrons live in molecular orbitals, just like they live in atomic orbitals in atoms.
  • ✨ Atomic orbitals combine to form molecular orbitals.
  • ✨ Molecular orbitals spread over multiple nuclei (polycentric), while atomic orbitals center on one nucleus (monocentric).

How Are Molecular Orbitals Formed? 🧪

Atomic orbitals mix through Linear Combination of Atomic Orbitals (LCAO). For two hydrogen atoms (A and B):

  • Bonding MO (\(\sigma\)): Formed by adding wave functions: \[\sigma = \psi_A + \psi_B\] This orbital has lower energy and higher electron density between nuclei, stabilizing the molecule. 👍
  • Antibonding MO (\(\sigma^*\)): Formed by subtracting wave functions: \[\sigma^* = \psi_A – \psi_B\] This orbital has higher energy and a nodal plane (zero electron density) between nuclei, making the molecule unstable. 👎

Imagine electron waves: Bonding = waves adding up (constructive interference). Antibonding = waves canceling (destructive interference). 🌊

Rules for Mixing Atomic Orbitals ⚖️

Atomic orbitals can only combine if they:

  1. Have similar energy (e.g., 1s + 1s, not 1s + 2s).
  2. Have the same symmetry around the bond axis (e.g., \(2p_z + 2p_z\) works; \(2p_z + 2p_y\) doesn’t).
  3. Overlap as much as possible (more overlap = stronger bond!).

Types of Molecular Orbitals 🔣

  • σ (sigma) Orbitals:
    Symmetric around the bond axis. Formed by:
    • Combining s-orbitals (e.g., \(\sigma 1s\), \(\sigma^*1s\))
    • Combining \(p_z\)-orbitals head-on (e.g., \(\sigma 2p_z\), \(\sigma^*2p_z\))
  • π (pi) Orbitals:
    Not symmetric around the bond axis. Formed by combining \(p_x\) or \(p_y\) orbitals sideways:
    • Bonding: \(\pi 2p_x\), \(\pi 2p_y\) (electron density above/below bond axis).
    • Antibonding: \(\pi^* 2p_x\), \(\pi^* 2p_y\) (node between nuclei).

Energy Levels of Molecular Orbitals ⚡

Order of MO energies depends on the molecule:

  • For \(O_2\) and \(F_2\): \[\sigma 1s < \sigma^* 1s < \sigma 2s < \sigma^* 2s < \sigma 2p_z < (\pi 2p_x = \pi 2p_y) < (\pi^* 2p_x = \pi^* 2p_y) < \sigma^* 2p_z\]
  • For \(B_2\), \(C_2\), \(N_2\): \[\sigma 1s < \sigma^* 1s < \sigma 2s < \sigma^* 2s < (\pi 2p_x = \pi 2p_y) < \sigma 2p_z < (\pi^* 2p_x = \pi^* 2p_y) < \sigma^* 2p_z\] Note: For these, \(\sigma 2p_z\) is higher in energy than \(\pi 2p_x\)/\(\pi 2p_y\)!

What Electronic Configurations Tell Us 🧠

Fill MOs with electrons using Aufbau principle, Pauli exclusion, and Hund’s rule. Then calculate:

  • Stability:
    If electrons in bonding MOs (\(N_b\)) > electrons in antibonding MOs (\(N_a\)) → stable molecule. Otherwise, unstable.
  • Bond Order (B.O.): \[B.O. = \frac{1}{2} (N_b – N_a)\]
    • B.O. = 1, 2, 3 → single, double, triple bonds.
    • Higher B.O. = shorter bond length.
  • Magnetic Behavior:
    All electrons paired? → Diamagnetic (repels magnets).
    Unpaired electrons? → Paramagnetic (attracts magnets, e.g., O₂).

Example: Hydrogen Molecule (\(H_2\)) ⚛️

  • 2 electrons fill the \(\sigma 1s\) bonding orbital: (\(\sigma 1s)^2\).
  • Bond order: \(\frac{1}{2}(2 – 0) = 1\) (single bond).
  • Stable, diamagnetic, bond length = 74 pm.

NEET Super-Ready Concepts! 🚀

  1. Bond Order Formula: \[B.O. = \frac{1}{2}(N_b – N_a)\] (Calculate it for \(H_2\), O₂, N₂, etc.)
  2. Paramagnetism: O₂ is paramagnetic due to unpaired electrons (check its MO diagram!).
  3. Energy Level Order: Know the different sequences for O₂/F₂ vs. B₂/C₂/N₂.
  4. σ vs. π Orbitals: σ is symmetric (s/s or pz/pz); π is asymmetric (px/px or py/py).
  5. LCAO Method: Bonding (\(\sigma = \psi_A + \psi_B\)) and Antibonding (\(\sigma^* = \psi_A – \psi_B\)) MOs.

Keep practicing MO diagrams – you’ve got this! 💪