What is Bond Order?
Bond order is a number that describes the stability and type of a chemical bond between two atoms. The higher the bond order, the stronger the bond, the higher its bond energy, and — for diatomic molecules — the shorter the bond length. A bond order of zero means no bond is formed and the molecule is unstable.
Bond Order Formula — Molecular Orbital Theory
According to molecular orbital (MO) theory, bond order is calculated as:
Bonding electrons occupy bonding molecular orbitals (σ, π) and stabilize the molecule. Antibonding electrons occupy antibonding molecular orbitals (σ*, π*) and destabilize it. Each bonding orbital and each antibonding orbital holds up to 2 electrons.
Bond Order Reference Table
| Bond Order | Bond Type | Example Molecules | Energy (kJ/mol) — metric | Energy (kcal/mol) — US | Length (pm) — metric | Length (Å) — US/imperial |
|---|---|---|---|---|---|---|
| 0 | No bond | He₂, Ne₂ | — | — | — | — |
| 0.5 | One-electron bond | H₂⁺ | 100–250 | 24–60 | 200–300 | 2.00–3.00 |
| 1 | Single bond | H₂, F₂, Cl₂ | 150–500 | 36–120 | 120–200 | 1.20–2.00 |
| 1.5 | Partial double bond | NO, O₂⁻ | 400–650 | 96–155 | 110–150 | 1.10–1.50 |
| 2 | Double bond | O₂, CO₂ | 500–750 | 120–179 | 110–140 | 1.10–1.40 |
| 2.5 | Partial triple bond | NO⁺, N₂⁺ | 700–900 | 167–215 | 100–130 | 1.00–1.30 |
| 3 | Triple bond | N₂, CO, C₂H₂ | 800–1075 | 191–257 | 100–125 | 1.00–1.25 |
How to Calculate Bond Order — Examples
Example 1: H₂ (Hydrogen)
Each hydrogen atom contributes 1 valence electron. When two H atoms bond, the 2 electrons fill the σ1s bonding orbital. No electrons go into antibonding orbitals.
Example 2: O₂ (Oxygen)
Oxygen has 8 electrons each. The 16 electrons fill orbitals: σ1s² σ*1s² σ2s² σ*2s² σ2p² π2p⁴ π*2p². Bonding electrons: 8, Antibonding electrons: 4.
Example 3: N₂ (Nitrogen)
Nitrogen has 7 electrons each. The 14 electrons fill: σ1s² σ*1s² σ2s² σ*2s² π2p⁴ σ2p². Bonding electrons: 8, Antibonding electrons: 2.
Example 4: CO (Carbon Monoxide)
Carbon (4 valence e⁻) and Oxygen (6 valence e⁻) form CO with 10 valence electrons. σ orbital: 2 bonding + 2 antibonding (cancel out). π orbitals: 6 bonding electrons. Net: 8 bonding − 2 antibonding = triple bond.
How to Find Bond Order — Valence Bond Theory
In valence bond (Lewis structure) theory, the bond order is simply the number of shared electron pairs between two atoms:
- 1 shared pair → single bond (bond order = 1)
- 2 shared pairs → double bond (bond order = 2)
- 3 shared pairs → triple bond (bond order = 3)
This approach is simpler but less accurate — it cannot account for molecules like O₂ (paramagnetic) or NO (bond order = 1.5), which require MO theory to explain correctly.
Bonding vs. Antibonding Electrons
Bonding orbitals (σ, π) form when atomic orbitals overlap constructively. Electrons in these orbitals hold atoms together and lower the system's energy.
Antibonding orbitals (σ*, π*) form when atomic orbitals overlap destructively. Electrons in these orbitals push atoms apart and raise the system's energy. Antibonding electrons are denoted with an asterisk (*).
The difference between bonding and antibonding electron counts — divided by 2 — gives the net bond order. This is why s-orbital electrons in inner shells often cancel out (equal bonding and antibonding contributions), and only valence-level electrons determine the actual bond order.
Metric vs. American Units for Bond Properties
Bond energies are measured in kJ/mol (metric/SI system) or kcal/mol (American/US customary system, common in biochemistry and organic chemistry). The conversion factor is: 1 kcal = 4.184 kJ.
Bond lengths are reported in picometers (pm) in the SI/metric system, or angstroms (Å) in the American convention. The relationship is: 1 Å = 100 pm = 0.1 nm.