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Bond Order Calculator

Explains why O₂ is paramagnetic and He₂ does not exist.

Work out Bond Order. Explains why O₂ is paramagnetic and He₂ does not exist. Every constant is an input, not an assertion.

Written and maintained by Mohit PatelLast checked August 4, 2026How we build these

The starred orbitals — σ*, π*

O₂ has two, which is why it is paramagnetic

Bond order

2

paramagnetic

Bonding electrons10
Antibonding electrons6
Net bonding electrons4
Bond order — net ÷ 22
Magnetic behaviourparamagnetic

A higher bond order means a shorter, stronger bond. Molecular orbital theory predicts oxygen to be paramagnetic with a bond order of 2 — something the Lewis structure, which pairs every electron, cannot account for. It is the theory's most cited success.

How the Bond Order Calculator works

Bond order from bonding and antibonding electron counts, with the magnetic behaviour that follows from the unpaired electrons. These are the two predictions molecular orbital theory makes that Lewis structures cannot, so both are stated rather than just the number.

Also known as: bond order from a molecular orbital diagram · is it paramagnetic or diamagnetic · why does he2 not exist · bonding minus antibonding electrons

What molecular orbital theory buys over Lewis structures

Lewis structures are excellent bookkeeping and they make two predictions they cannot support. They say He₂ should exist — you can draw it — and they say O₂ has a double bond with every electron paired. One of those is wrong and the other is unfalsifiable as drawn.

Molecular orbital theory combines atomic orbitals into bonding and antibonding molecular orbitals spread over the whole molecule, then fills them by energy. Bond order is (bonding − antibonding)/2, and it can be zero, fractional, or anything in between rather than restricted to the integers a Lewis structure allows.

For He₂ the two bonding and two antibonding electrons cancel exactly, bond order zero, no molecule. For O₂ the count gives bond order 2 — agreeing with Lewis — but places the last two electrons in separate degenerate π* orbitals with parallel spins. That prediction of two unpaired electrons is the one Lewis cannot make and the one experiment confirms.

Paramagnetism as evidence

Liquid oxygen poured between the poles of a magnet sticks there. It is a lecture demonstration precisely because it is so hard to explain any other way: a substance whose accepted structure pairs every electron should be weakly repelled by a magnetic field, not attracted to it.

Unpaired electrons have magnetic moments that align with an applied field, which is paramagnetism. Paired electrons have opposing spins whose moments cancel, leaving only the weak repulsion of diamagnetism. Counting unpaired electrons therefore predicts magnetic behaviour directly, and the measurement — a Gouy or Evans balance — counts them back.

N₂ makes the contrast. Its molecular orbital filling leaves no unpaired electrons, and liquid nitrogen poured through the same magnet falls straight through. Same period, same kind of bond, opposite magnetic behaviour, and the electron count predicts both.

Fractional bond orders and what they mean physically

An odd electron count gives a half-integer bond order. Nitric oxide, NO, has 15 valence electrons and a bond order of 2.5. The superoxide ion O₂⁻ has 1.5, and the peroxide ion O₂²⁻ has 1. Each added electron goes into an antibonding orbital and takes half a bond with it.

The bond lengths follow exactly. O₂ at bond order 2 has a bond length of 121 pm; superoxide at 1.5 stretches to 133 pm; peroxide at 1 reaches 149 pm. Bond order is not an abstraction — it is a prediction about a measurable distance, and the measurement agrees.

Resonance produces fractional bond orders in a different way. Benzene's carbon–carbon bonds are all 1.5, intermediate between single and double, and all 140 pm — between the 154 pm of ethane and the 134 pm of ethene. The delocalised π system is a molecular orbital description of what resonance structures approximate.

Where to go next

The Bond Order question rarely arrives on its own. These are the ones that usually come with it:

Frequently asked questions

How is bond order calculated?

Subtract the antibonding electrons from the bonding electrons and divide by two. O₂ has 10 bonding and 6 antibonding electrons, giving a bond order of 2.

What does a bond order of zero mean?

The molecule does not form. He₂ has two bonding and two antibonding electrons, which cancel exactly — which is why helium exists as single atoms even though a Lewis structure for He₂ can be drawn.

Why is oxygen paramagnetic?

Its two highest electrons occupy separate π* antibonding orbitals with parallel spins, following Hund's rule. Those unpaired electrons make liquid oxygen stick to a magnet — something the Lewis structure, which pairs every electron, cannot explain.

Can bond order be a fraction?

Yes. Odd electron counts give half-integer bond orders: NO has a bond order of 2.5, and the O₂⁻ superoxide ion has 1.5. Resonance produces fractional bond orders too, as in benzene at 1.5.

How does bond order relate to bond length and strength?

Higher bond order means shorter and stronger. Across N₂, O₂ and F₂ the bond order falls from 3 to 2 to 1 and the bond length rises from 110 to 121 to 142 pm.

What is the difference between paramagnetic and diamagnetic?

Paramagnetic species have at least one unpaired electron and are drawn into a magnetic field. Diamagnetic species have all electrons paired and are weakly repelled by one.

How do I fill a molecular orbital diagram?

Lowest energy first, two electrons per orbital with opposite spins, and degenerate orbitals get one electron each before any pairs up. That last rule — Hund's — is what produces oxygen's two unpaired electrons and its paramagnetism.

Why do the σ and π orbital energies swap for lighter diatomics?

Because of s–p mixing, which pushes σ2p above π2p for B₂, C₂ and N₂. From O₂ onwards the 2s and 2p energies are far enough apart that mixing is negligible and the normal order returns. It is why B₂ is paramagnetic and C₂ is not.

Can bond order predict bond length?

It predicts the trend reliably within a series. Across N₂, O₂ and F₂ the bond order falls 3, 2, 1 and the length rises 110, 121, 142 pm. Comparing across different elements is less reliable, since atomic radius changes too.

What is bond order in a resonance structure?

The average across the contributing structures. Benzene's carbon–carbon bonds are all 1.5, and the measured length of 140 pm sits between ethane's 154 and ethene's 134 — exactly where an average predicts.

How is paramagnetism measured?

By weighing a sample in and out of a magnetic field — a Gouy balance — or by the NMR shift a paramagnetic sample produces in a reference, which is the Evans method. Both give the number of unpaired electrons back.

Does molecular orbital theory work for larger molecules?

Yes, and it is the foundation of computational chemistry. Hand-drawn diagrams stop being practical past diatomics and small symmetric molecules, so the same theory is applied numerically instead — which is what a DFT calculation is doing.

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