Bond order tells you how many chemical bonds hold two atoms together. In a Lewis structure it is simply the number of shared electron pairs: 1 for the single bond in F₂, 2 for the double bond in O₂, 3 for the triple bond in N₂. Molecular-orbital (MO) theory gives the same idea a sharper definition – half the difference between electrons in bonding orbitals, which pull the nuclei together, and electrons in antibonding orbitals, which push them apart.
The MO picture explains things Lewis structures cannot. It shows that O₂ has two unpaired electrons in π* orbitals and is therefore attracted by a magnet, that He₂ (bond order 0) does not exist, and that removing an electron from N₂ weakens the bond (3 → 2.5) while removing one from O₂ strengthens it (2 → 2.5). Bond orders can be fractions, as in H₂⁺ (0.5) or nitrate, where four bonds are shared by three N–O positions (4/3).
Higher bond order means a shorter, stronger bond: the C–C bond length drops from 154 pm (single) to 134 pm (double) and 120 pm (triple). Use the first mode if you already know the electron counts, the second to fill an MO diagram for any pair of atoms from the first two periods, and the third for delocalised bonds.
How to use the Bond Order Calculator
- Method
- Number of bonding electrons
- Number of antibonding electrons
- First atom
- Second atom
- Charge of the molecule or ion — O₂⁻ (superoxide) is −1, N₂⁺ is +1, CN⁻ is C + N with −1.
- Total bonds between the central atom and the equivalent atoms — Count a double bond as 2. Nitrate (one N=O and two N–O) has 4.
- Number of equivalent bond positions
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How it works
In MO mode the valence electrons of both atoms (minus the charge) are placed into the molecular orbitals in order of energy, two per orbital, with degenerate π orbitals filled singly first (Hund’s rule). For 10 or fewer valence electrons s–p mixing places π2p below σ2p; above that σ2p comes first. Bonding minus antibonding electrons, halved, is the bond order; the unpaired electrons decide whether the species is paramagnetic. Pairs of H or He with a second-period atom (HF, OH, NH, LiH) use a simplified hydride diagram with one σ/σ* pair and nonbonding lone-pair orbitals.
Worked example
Oxygen, O₂: each O atom brings six valence electrons, 12 in total. With more than ten valence electrons the order is σ2s, σ*2s, σ2p, π2p, π*2p, σ*2p. Filling gives σ2s² σ*2s² σ2p² π2p⁴ π*2p², so there are 2 + 2 + 4 = 8 bonding and 2 + 2 = 4 antibonding electrons. Bond order = (8 − 4)/2 = 2, and the two π* electrons sit in separate orbitals – O₂ is paramagnetic.
Adding one electron (superoxide, O₂⁻) puts a third electron into π*: (8 − 5)/2 = 1.5. Removing one (O₂⁺) leaves (8 − 3)/2 = 2.5, a stronger and shorter bond than in O₂.
Bond orders of second-period diatomics
| Molecule | Valence electrons | Bond order | Unpaired electrons |
|---|---|---|---|
| Li₂ | 2 | 1 | 0 |
| Be₂ | 4 | 0 | 0 |
| B₂ | 6 | 1 | 2 |
| C₂ | 8 | 2 | 0 |
| N₂ | 10 | 3 | 0 |
| O₂ | 12 | 2 | 2 |
| F₂ | 14 | 1 | 0 |
| Ne₂ | 16 | 0 | 0 |
| CO | 10 | 3 | 0 |
| NO | 11 | 2.5 | 1 |
Tips
- Type formulas with normal capitals and numbers, e.g. Ca(OH)2 or CuSO4·5H2O – brackets and hydrates work.
- Atomic masses are IUPAC standard atomic weights; radioactive elements use the mass number of their longest-lived isotope.
- Electronegativity values are on the Pauling scale.
- Everything is calculated in your browser.
Common mistakes to avoid
- Writing CO (carbon monoxide) when you mean Co (cobalt) – capitals matter.
- Forgetting to multiply the bracket contents by the subscript after the bracket.
- Mixing up atomic number (protons) and mass number (protons + neutrons).
Formula
Bond order = (bonding electrons − antibonding electrons) / 2Resonance: bond order = total bonds between the atoms / number of equivalent bond positionsWorked example
Inputs — Method: Molecular-orbital diagram of a diatomic; First atom: O – oxygen; Second atom: O – oxygen; Charge of the molecule or ion: 0.
Results — Bond order = 2; As a fraction = 2; Bonding electrons = 8; Antibonding electrons = 4; What it means = Double bond.; MO electron configuration = KK (σ2s)² (σ*2s)² (σ2p)² (π2p)⁴ (π*2p)².
Key terms
- Bonding orbital
- A molecular orbital with electron density between the nuclei; electrons in it hold the atoms together.
- Antibonding orbital
- A molecular orbital (marked *) with a node between the nuclei; electrons in it weaken the bond.
- Paramagnetic
- Containing unpaired electrons, and therefore attracted into a magnetic field.
- s–p mixing
- Interaction of 2s and 2p orbitals that raises σ2p above π2p in B₂, C₂ and N₂.
- Resonance
- Description of a molecule by several Lewis structures whose average is the real bonding.
Frequently asked questions
How do you calculate bond order?
Bond order = (bonding electrons − antibonding electrons) / 2. For O₂: (8 − 4)/2 = 2 counting valence electrons, or (10 − 6)/2 = 2 including the 1s core – the core always cancels.
What is the bond order of N₂?
3. Its ten valence electrons fill σ2s², σ*2s², π2p⁴ and σ2p², giving (8 − 2)/2 = 3 – the triple bond that makes N₂ so unreactive.
Why is O₂ paramagnetic?
Its last two electrons go into the two degenerate π*2p orbitals one each, with parallel spins. Two unpaired electrons make liquid oxygen stick between the poles of a magnet.
Can the bond order be a fraction?
Yes. H₂⁺ has one bonding electron (0.5), NO has 2.5, O₂⁻ has 1.5, and in nitrate or carbonate resonance gives 4/3 per bond.
What does a bond order of zero mean?
Bonding and antibonding effects cancel, so no stable bond forms. He₂ and Ne₂ have bond order 0 and are not stable molecules.
What is the bond order of CO?
3, the same as N₂, because CO has the same ten valence electrons (it is isoelectronic with N₂ and CN⁻).
How is bond order related to bond length and strength?
Higher bond order means a shorter and stronger bond. N≡N (order 3) is 110 pm long with a dissociation energy of about 945 kJ/mol, compared with 121 pm and about 498 kJ/mol for O=O (order 2).
What is the bond order in benzene?
Each C–C bond has order 1.5: nine bonds (six single plus three double in one Kekulé structure) shared over six positions.
What formula does the Bond Order Calculator use?
Bond order = (bonding electrons − antibonding electrons) / 2.