Bond Order Calculator (MO theory for H₂ to Ne₂ and ions, or your own electron counts)

Understanding the bond order calculator — concept and principle

Bond order tells you how many chemical bonds hold two atoms together. This calculator fills the molecular orbitals of diatomic molecules and ions made from hydrogen to neon, gives the bond order, counts unpaired electrons and predicts whether the molecule is paramagnetic.

How it is calculated

• Bond order = (bonding electrons − antibonding electrons) ÷ 2.
• Electrons fill σ1s, σ*1s, σ2s, σ*2s, then π2p and σ2p, then π*2p and σ*2p.
• Up to 14 electrons (B₂, C₂, N₂, CO) π2p lies below σ2p because of s–p mixing; from 15 electrons (O₂, F₂, NO) σ2p comes first.
• Degenerate π orbitals are half-filled before pairing (Hund's rule).
• Unpaired electrons > 0 means paramagnetic.

The principle

When atoms combine, their atomic orbitals mix into molecular orbitals. Bonding orbitals concentrate electrons between the nuclei and hold them together; antibonding orbitals push them apart. Each net pair of bonding electrons counts as one bond. MO theory explains things a simple Lewis structure cannot, most famously that O₂ has two unpaired electrons and is attracted to a magnet.

Worked example

Default inputs: O + O, charge 0.

1. Electrons counted = 8 + 8 = 16.
2. Configuration: (σ1s)² (σ*1s)² (σ2s)² (σ*2s)² (σ2p)² (π2p)⁴ (π*2p)².
3. Bonding electrons = 2 + 2 + 2 + 4 = 10; antibonding = 2 + 2 + 2 = 6.
4. Bond order = (10 − 6) ÷ 2 = 2, a double bond; expected to exist.
5. The two π* electrons occupy separate orbitals: 2 unpaired electrons, so O₂ is paramagnetic.

How to read the result

Higher bond order means a shorter, stronger bond: N₂ (bond order 3) is one of the strongest bonds known, while He₂ (bond order 0) does not form a stable molecule. Comparing ions shows trends: O₂⁺ has bond order 2.5 and a shorter bond than O₂, while O₂⁻ has 1.5.

Common mistakes

• Forgetting to add or remove electrons for the charge.
• Using the O₂-type ordering for N₂, or the reverse.
• Pairing electrons in π* orbitals before half-filling them.
• Treating heteronuclear molecules as exact; the shared level order is an approximation.

Frequently asked questions

What is the bond order of O₂?

2, with two unpaired electrons, which makes O₂ paramagnetic.

Why is N₂ so stable?

Its bond order is 3: a triple bond with all electrons paired.

Can bond order be a fraction?

Yes, for ions and radicals such as O₂⁺ (2.5) or H₂⁺ (0.5).

Sources: Atkins, P. & de Paula, J., Physical Chemistry (molecular orbital theory of diatomic molecules) · Housecroft, C. E. & Sharpe, A. G., Inorganic Chemistry, 5th ed. Pearson