How bond order is calculated
Fill the molecular orbitals from the bottom up, two electrons per orbital, and put one electron in each of the two π orbitals before pairing them (Hund's rule). Starred orbitals (σ*, π*) are antibonding.
The two energy orders
- Up to 14 electrons (B₂, C₂, N₂, CO): σ1s, σ*1s, σ2s, σ*2s, π2p, σ2p, π*2p, σ*2p.
- More than 14 electrons (O₂, F₂, NO): σ1s, σ*1s, σ2s, σ*2s, σ2p, π2p, π*2p, σ*2p.
The swap happens because the 2s and 2p orbitals are close in energy in the lighter atoms and mix, pushing σ2p up. It doesn't change the bond order, but it does change whether a molecule like B₂ is paramagnetic.
Paramagnetic or diamagnetic?
Count unpaired electrons in the diagram. Any unpaired electron makes the species paramagnetic (attracted to a magnet); if all are paired, it's diamagnetic.
Bond order, length and stability
A higher bond order means a shorter, stronger bond. The oxygen family is the most asked example:
- Bond order: O₂⁺ (2.5) > O₂ (2) > O₂⁻ (1.5) > O₂²⁻ (1).
- Bond length: O₂⁺ < O₂ < O₂⁻ < O₂²⁻, the reverse order.
- Bond order 0 (He₂, Be₂, Ne₂) means the molecule doesn't exist as a stable species.
Bond order of common species
| Species | Electrons | Bond order | Unpaired | Magnetic |
|---|---|---|---|---|
| H₂ | 2 | 1 | 0 | Diamagnetic |
| H₂⁺ | 1 | 0.5 | 1 | Paramagnetic |
| He₂ | 4 | 0 | 0 | Diamagnetic |
| He₂⁺ | 3 | 0.5 | 1 | Paramagnetic |
| Li₂ | 6 | 1 | 0 | Diamagnetic |
| Be₂ | 8 | 0 | 0 | Diamagnetic |
| B₂ | 10 | 1 | 2 | Paramagnetic |
| C₂ | 12 | 2 | 0 | Diamagnetic |
| N₂ | 14 | 3 | 0 | Diamagnetic |
| N₂⁺ | 13 | 2.5 | 1 | Paramagnetic |
| N₂⁻ | 15 | 2.5 | 1 | Paramagnetic |
| O₂ | 16 | 2 | 2 | Paramagnetic |
| O₂⁺ | 15 | 2.5 | 1 | Paramagnetic |
| O₂⁻ | 17 | 1.5 | 1 | Paramagnetic |
| O₂²⁻ | 18 | 1 | 0 | Diamagnetic |
| F₂ | 18 | 1 | 0 | Diamagnetic |
| Ne₂ | 20 | 0 | 0 | Diamagnetic |
| NO | 15 | 2.5 | 1 | Paramagnetic |
| NO⁺ | 14 | 3 | 0 | Diamagnetic |
| CO | 14 | 3 | 0 | Diamagnetic |
| CN⁻ | 14 | 3 | 0 | Diamagnetic |
For the shape and hybridization of molecules like XeF₄ and SF₄, use the hybridization calculator.
Questions students ask
What is the bond order of O₂?
2. O₂ has 10 bonding and 6 antibonding electrons, so ½ × (10 − 6) = 2. Two of the antibonding electrons are unpaired, so O₂ is paramagnetic.
What is the bond order of N₂?
3, a triple bond. N₂ has 10 bonding and 4 antibonding electrons.
Which has the highest bond order: O₂, O₂⁺, O₂⁻ or O₂²⁻?
O₂⁺, with 2.5. Then O₂ (2), O₂⁻ (1.5) and O₂²⁻ (1).
What does a bond order of zero mean?
Bonding and antibonding electrons cancel out, so there's no net bond. He₂, Be₂ and Ne₂ have bond order 0 and don't exist as stable molecules.