# What is the bond order?

Finds the bond order of a diatomic molecule or ion from H₂ to Ne₂ by filling its molecular orbitals, with its configuration and magnetism, or from counts of bonding and antibonding electrons.

- Page: https://www.acalculator.org/chemistry/bond-order-calculator
- JSON spec: https://www.acalculator.org/chemistry/bond-order-calculator.json
- Version: 3dd2e502a805

## Default answer

Example with the default inputs (From Diatomic molecule, Molecule O₂ (oxygen), Charge 0): Bond order = 2 for O₂.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| from | From | A diatomic molecule or ion of one element, or your own counts of bonding and antibonding electrons. |
| atom | Molecule | The two-atom molecule of one element, from H₂ to Ne₂. |
| q | Charge | The charge of the molecule: 0, or from −2 to +2 for an ion such as O₂⁻ or N₂⁺. |
| nb | Bonding electrons | Electrons in bonding molecular orbitals. |
| na | Antibonding electrons | Electrons in antibonding (starred) molecular orbitals. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| result | Bond order | Half the difference between bonding and antibonding electrons. |
| order | Bond order (number) | The bond order as a number. |
| bondingCount | Bonding electrons | Electrons in bonding orbitals. |
| antibondingCount | Antibonding electrons | Electrons in antibonding orbitals. |
| stability | Stability | A bond order above 0 means a stable bond is expected; 0 means none. |
| configuration | Molecular orbital configuration | The filled molecular orbitals and their electrons, lowest energy first. |
| unpaired | Unpaired electrons | Electrons alone in a molecular orbital, by Hund’s rule. |
| magnetism | Magnetism | Paramagnetic with any unpaired electron, diamagnetic with none. |
| subject | For | The molecule, or the electron counts the bond order is for. |

## Method

Bond order = (electrons in bonding orbitals − electrons in antibonding orbitals) ÷ 2. A diatomic molecule fills σ1s, σ*1s, σ2s, σ*2s, then π2p before σ2p for Li to N (σ2p before π2p for O, F, Ne), then π*2p and σ*2p.

## Assumptions

- Homonuclear diatomic molecules and ions from H₂ to Ne₂ with a charge from −2 to +2, in their ground state; 1 to 20 electrons.
- The two π2p orbitals and the two π*2p orbitals each fill one electron per orbital before pairing (Hund’s rule).
- A bond order above 0 means a stable bond is expected; 0 means none.

## Worked examples

1. from = molecule, atom = O, q = 0 gives order = 2, unpaired = 2, magnetism = Paramagnetic (2 unpaired electrons). Source: OpenStax, Chemistry 2e, §8.4 Molecular Orbital Theory (bond order = (bonding − antibonding electrons) ÷ 2), https://openstax.org/books/chemistry-2e/pages/8-4-molecular-orbital-theory, Example 8.6 (O₂): bond order 2, two unpaired electrons, paramagnetic.
2. from = molecule, atom = N, q = 0 gives order = 3, unpaired = 0, magnetism = Diamagnetic (all electrons paired). Source: OpenStax, Chemistry 2e, §8.4 Molecular Orbital Theory (bond order = (bonding − antibonding electrons) ÷ 2), https://openstax.org/books/chemistry-2e/pages/8-4-molecular-orbital-theory, Check Your Learning after Example 8.6 (N₂): bond order 3, diamagnetic.
3. from = molecule, atom = C, q = -2 gives order = 3, bondingCount = 10, antibondingCount = 4. Source: OpenStax, Chemistry 2e, §8.4 Molecular Orbital Theory (bond order = (bonding − antibonding electrons) ÷ 2), https://openstax.org/books/chemistry-2e/pages/8-4-molecular-orbital-theory, Example 8.7 (C₂²⁻): bond order 3, six more bonding than antibonding electrons.
4. from = molecule, atom = Be, q = -2 gives unpaired = 2, order = 1, configuration = (σ1s)² (σ*1s)² (σ2s)² (σ*2s)² (π2p)². Source: OpenStax, Chemistry 2e, §8.4 Molecular Orbital Theory (bond order = (bonding − antibonding electrons) ÷ 2), https://openstax.org/books/chemistry-2e/pages/8-4-molecular-orbital-theory, Check Your Learning after Example 8.7 (Be₂²⁻): two unpaired electrons, paramagnetic.
5. from = molecule, atom = Be, q = 0 gives order = 0, stability = Bond order 0: no stable bond is expected.. Source: OpenStax, Chemistry 2e, §8.4 Molecular Orbital Theory (bond order = (bonding − antibonding electrons) ÷ 2), https://openstax.org/books/chemistry-2e/pages/8-4-molecular-orbital-theory, Table 8.3: Be₂ bond order 0, unstable.
6. from = molecule, atom = F, q = 0 gives order = 1, unpaired = 0. Source: OpenStax, Chemistry 2e, §8.4 Molecular Orbital Theory (bond order = (bonding − antibonding electrons) ÷ 2), https://openstax.org/books/chemistry-2e/pages/8-4-molecular-orbital-theory, Table 8.3: F₂ bond order 1.
7. from = molecule, atom = H, q = 1 gives order = 0.5, result = Bond order = 0.5, unpaired = 1. Source: OpenStax, Chemistry 2e, §8.4 Molecular Orbital Theory (bond order = (bonding − antibonding electrons) ÷ 2), https://openstax.org/books/chemistry-2e/pages/8-4-molecular-orbital-theory (bond order formula).
8. from = counts, nb = 8, na = 2 gives order = 3, result = Bond order = 3. Source: OpenStax, Chemistry 2e, §8.4 Molecular Orbital Theory (bond order = (bonding − antibonding electrons) ÷ 2), https://openstax.org/books/chemistry-2e/pages/8-4-molecular-orbital-theory (bond order formula).

## FAQ

### How do I calculate bond order?

Bond order = (bonding electrons − antibonding electrons) ÷ 2. Fill the molecular orbitals from the lowest energy, count the electrons in bonding orbitals and in antibonding (starred) orbitals, then halve the difference. For N₂, 10 bonding and 4 antibonding electrons give (10 − 4) ÷ 2 = 3.

### What does the bond order tell me?

A bond order above 0 means the molecule should be stable, and a higher bond order means a stronger bond: N₂ (3) is stronger than O₂ (2), which is stronger than F₂ (1). A bond order of 0, as for He₂, Be₂ and Ne₂, means no stable bond forms.

### Why is O₂ paramagnetic?

Its last two electrons go into the two π*2p orbitals, one in each (Hund’s rule), so O₂ has 2 unpaired electrons and is attracted into a magnetic field. A Lewis structure with a double bond does not show this; the molecular orbital picture does.

### Why does the orbital order change between N₂ and O₂?

For Li₂ to N₂ the 2s and 2p orbitals are close in energy and mix (s-p mixing), which raises σ2p above the π2p pair. For O₂, F₂ and Ne₂ the mixing is negligible, so σ2p stays below π2p. The bond order is the same either way; the order changes which orbital a few electrons go into, and so the magnetism of B₂ and C₂.

### Can a bond order be a fraction?

Yes. An odd number of electrons gives a half: H₂⁺ has 1 electron in σ1s, so its bond order is (1 − 0) ÷ 2 = 0.5; O₂⁺ has 2.5. A half bond order still means a bond, weaker than the next whole one.

### Do the 1s electrons count?

They cancel. For Li₂ to Ne₂ the σ1s and σ*1s orbitals each hold 2 electrons, adding 2 bonding and 2 antibonding electrons, so leaving them out gives the same bond order. The page counts them so the configuration shows every electron.

## Sources

- OpenStax, Chemistry 2e, §8.4 Molecular Orbital Theory: bond order = (bonding − antibonding electrons) ÷ 2, the molecular orbital energy order for second-period diatomics with s-p mixing for Li₂ to N₂ and none for O₂, F₂ and Ne₂, Table 8.3 (bond orders Li₂ 1, Be₂ 0, B₂ 1, C₂ 2, N₂ 3, O₂ 2, F₂ 1, Ne₂ 0), Example 8.6 (O₂: bond order 2, paramagnetic) and its Check Your Learning (N₂: 3, diamagnetic), Example 8.7 (C₂²⁻: 3) and its Check Your Learning (Be₂²⁻: 2 unpaired electrons). https://openstax.org/books/chemistry-2e/pages/8-4-molecular-orbital-theory (retrieved 2026-10-19)