Molecular Orbital Theory — MO Diagrams, Bond Order & Magnetism
The big idea. When atoms bond, their atomic orbitals combine (LCAO) into molecular orbitals that belong to the whole molecule. Each pair of atomic orbitals gives one bonding MO (lower energy, electron density between the nuclei) and one antibonding MO (higher energy, marked with a *). Fill these with the molecule's electrons, and you can read off its bond order, stability and — crucially — its magnetism.
The two orderings
For second-period homonuclear diatomics there are two energy orderings, because s–p mixing pushes the σ2p up:
- Li₂ through N₂ (≤ 14 valence e⁻) — s–p mixing order: σ2s, σ2s, (π2px = π2py), σ2pz, (π2px = π2py), σ2pz. Here the π2p bonding MOs sit below σ2pz.
- O₂, F₂, Ne₂ — normal order: σ2s, σ2s, σ2pz, (π2px = π2py), (π2px = π2py), σ2pz. Here σ2pz sits below the π2p.
Bond order
Bond order = ½ (N_bonding − N_antibonding).
Fill the MOs (Aufbau, Pauli, Hund) and count. Standard values:
| Species | e⁻ | Bond order | Unpaired e⁻ | Magnetism |
|---|
| H₂ | 2 | 1 | 0 | diamagnetic |
| He₂ | 4 | 0 | — | does not exist |
| Li₂ | 6 | 1 | 0 | diamagnetic |
| B₂ | 10 | 1 | 2 | paramagnetic |
| C₂ | 12 | 2 | 0 | diamagnetic |
| N₂ | 14 | 3 | 0 | diamagnetic |
| O₂ | 16 | 2 | 2 | paramagnetic |
| F₂ | 18 | 1 | 0 | diamagnetic |
Ions follow from adding/removing electrons: O₂⁺ 2.5, O₂⁻ (superoxide) 1.5, O₂²⁻ (peroxide) 1; N₂⁺ and N₂⁻ both 2.5; He₂⁺ 0.5; NO 2.5, NO⁺ 3, CN⁻ 3, CO 3.
Magnetism — MOT's triumph
A species is paramagnetic if it has unpaired electrons, diamagnetic if all are paired. MOT famously predicts that O₂ is paramagnetic — its last two electrons go singly into the degenerate π*2p orbitals (Hund's rule) — which the simple Lewis structure O=O cannot explain. B₂ is also paramagnetic (two electrons singly in π2p).
Bond order, length, energy — and adding/removing an electron
Higher bond order means a shorter bond and a higher dissociation energy. Whether ionisation raises or lowers the bond order depends on which MO the electron leaves or enters:
- O₂ → O₂⁺ removes an antibonding π* electron → bond order rises (2 → 2.5).
- O₂ → O₂⁻ adds an antibonding π* electron → bond order falls (2 → 1.5).
- N₂ → N₂⁺ removes a bonding σ2pz electron → bond order falls (3 → 2.5).
Species with the same electron count are isoelectronic and share a bond order: N₂, CO, CN⁻, NO⁺ and C₂²⁻ all have 14 electrons, bond order 3 and are diamagnetic.
Traps to avoid
- Forgetting O₂ is paramagnetic — the single most-tested MOT fact.
- Using the wrong ordering — σ2pz is below π2p only for O₂, F₂, Ne₂; for N₂ and lighter it is above.
- Assuming adding an electron always lowers the bond order — it raises it if the electron leaves an antibonding MO (O₂ → O₂⁺).
- Saying He₂ or Be₂ exists — their bond order is 0.
Concept-aligned original practice · not official past papers.
Molecular Orbital Theory is a key topic in the NCERT Class 11 Chemistry chapter on Chemical Bonding and Molecular Structure, and "MOT bond order formula" or "molecular orbital theory class 11 important questions" are frequently searched ahead of CBSE boards, JEE Main and NEET chemistry. The paramagnetism of O2 explained above is one of the most repeated JEE and NEET questions built directly on this NCERT Class 11 concept.