Construct and interpret diatomic MO diagrams, including HOMO and LUMO

A complete diatomic molecular-orbital diagram shows the parent atomic levels, the resulting molecular levels, the energy direction and the electrons. Interpretation comes only after the levels have been constructed and filled.

GCE A-Level H3 Chemistry 9813-2027

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Learning objectives

Construct and interpret diatomic MO diagrams, including HOMO and LUMO

Build the diagram before drawing conclusions

For H₂, O₂ and F₂, use the correct orbital count and energy order, then identify bond order, unpaired electrons, HOMO and LUMO.

The quantities read from an MO diagram

The HOMO is the highest occupied molecular orbital. The LUMO is the lowest unoccupied molecular orbital; if that energy is degenerate, the whole equal-energy set is the LUMO level.

Bond order = 1/2(number of bonding electrons − number of antibonding electrons). A positive bond order predicts net bonding, while unpaired electrons predict paramagnetism.

For O₂ and F₂, use σ2s < σ*2s < σ2p < π2p < π*2p < σ*2p. Fill degenerate π orbitals according to Hund's rule.

H₂, O₂ and F₂ side by side

H₂ places two electrons in σ(1s), giving bond order 1. Its HOMO is σ(1s), its LUMO is σ*(1s), and all electrons are paired, so H₂ is diamagnetic.

O₂ has twelve valence electrons. After filling through π(2p), its last two electrons occupy the degenerate π*(2p) orbitals singly. Bond order is 2 and the two unpaired electrons make O₂ paramagnetic.

F₂ has fourteen valence electrons. The π*(2p) pair becomes fully occupied, giving bond order 1 and no unpaired electrons. Its HOMO is π*(2p) and its LUMO is σ*(2p).

Worked example: explain O₂ paramagnetism

Count eight bonding electrons and four antibonding electrons in the O₂ valence diagram, so bond order = 1/2(8 − 4) = 2.

The two highest occupied electrons enter separate degenerate π*(2p) orbitals with parallel spins. Because they remain unpaired, O₂ is attracted into a magnetic field.

Try this

Use the O₂ diagram to state its bond order and magnetic behaviour.

Check your answer

Bond order is 2. O₂ is paramagnetic because it has two unpaired electrons in the degenerate π*(2p) orbitals.

Construct F₂ carefully

Write fourteen valence electrons and fill the same O₂/F₂ ordering from the bottom. Pair only after placing one electron in each member of a degenerate set.

Then count bonding and antibonding electrons rather than inferring bond order from the position of the HOMO alone.

Try this

Find the bond order, HOMO and LUMO of F₂.

Check your answer

Bond order = 1/2(8 − 6) = 1. The HOMO is the occupied π*(2p) degenerate set and the LUMO is σ*(2p).

Compare H₂ and F₂

Both H₂ and F₂ have bond order 1, but their diagrams are not interchangeable. They use different parent shells and have different HOMO and LUMO symmetries.

When comparing bond properties, base every conclusion on the filled diagram and state any additional factors you would need before predicting an exact bond energy or length.

Try this

Why does equal bond order not mean H₂ and F₂ have identical bonds?

Check your answer

Bond order is only one feature. The molecules use different orbitals, atoms, sizes and energy levels, so exact bond length and strength need more than bond order alone.

Common mistake: pairing O₂ too early

Putting both final O₂ electrons into one π* orbital breaks Hund's rule and incorrectly predicts diamagnetism.

Another mistake is to call the highest empty orbital the LUMO. LUMO means lowest unoccupied, so always scan upward from the occupied levels.

Try this

Correct a diagram that pairs both final O₂ electrons in one π* orbital.

Check your answer

Place one electron in each equal-energy π* orbital with parallel spins. The corrected diagram has two unpaired electrons.

Check your understanding

A full response should show the energy order, correct electron count, Hund filling, bond-order working, magnetic behaviour and the HOMO/LUMO labels.

Next, construct and interpret the corresponding π-molecular-orbital diagrams for benzene and linear polyenes.

Try this

What are the two quickest checks that catch most diatomic MO-diagram errors?

Check your answer

Check that the number of molecular orbitals matches the parent atomic orbitals, then check that the total number of electrons and Hund filling are correct.