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Molecular Orbital Diagram Generator
In short: Molecular orbital diagram generator for diatomic molecules and ions from H₂ to Ne₂, plus CO, NO, CN⁻ and HF. It uses the right orbital order (with or without s–p mixing), fills electrons by Hund's rule and gives the bond order, magnetism, HOMO, LUMO and MO configuration. It is free, works in your web browser and needs no download.
Pick a diatomic molecule or ion to see its MO energy diagram with atomic orbitals on both sides, molecular orbitals in the middle and every electron drawn as an arrow. The result box explains the bond order and magnetism step by step.
Type O2, N2+, O2 2-, NO, CO, CN- or HF, or pick the atoms below.
Examples
Bonding orbitals are teal, antibonding orbitals red and nonbonding orbitals grey. Dashed lines show which atomic orbitals combine. The energy scale is schematic.
How to use the MO diagram generator
- Type a diatomic molecule or ion in Molecule or ion, for example
O2,N2+,O2 2-orCN-. You can also choose Atom 1, Atom 2 and Charge, or press an example button. - Leave Orbital order on Automatic to use the textbook rule, or force the order with or without s–p mixing to compare.
- Read the bond order, magnetism, HOMO, LUMO and the MO configuration in the result box. The diagram shows the electrons as arrows.
- Press Download SVG or Download PNG to save the diagram for notes, slides or worksheets.
How a molecular orbital diagram works
When two atoms bond, their atomic orbitals combine into molecular orbitals (MOs). Two atomic orbitals give one bonding MO (lower in energy, electron density between the nuclei) and one antibonding MO (higher in energy, marked with *). Head-on overlap gives σ orbitals; side-on overlap of p orbitals gives a pair of π orbitals.
Bond order = (electrons in bonding MOs − electrons in antibonding MOs) / 2
Orbital order for second-row diatomics
| Species | Order of valence MOs (low to high) |
|---|---|
| Li₂ to N₂, and any species with 14 or fewer electrons (CO, CN⁻, NO⁺, N₂⁺) | σ2s < σ*2s < π2p < σ2p < π*2p < σ*2p |
| O₂, F₂, Ne₂, and species with more than 14 electrons (O₂⁺, O₂⁻, NO) | σ2s < σ*2s < σ2p < π2p < π*2p < σ*2p |
The switch comes from s–p mixing. In B, C and N the 2s and 2p levels are close, so σ2s and σ2p interact and σ2p is pushed above π2p. In O and F the 2s–2p gap is large, the mixing is weak and σ2p stays below π2p. For species with 15 or more electrons both orders give the same electron count in each orbital, so the bond order and magnetism do not change.
Filling rules
- Aufbau: fill the lowest MO first. Each orbital holds two electrons with opposite spins (Pauli principle).
- Hund's rule: in a degenerate pair such as π*2p, put one electron in each orbital before pairing. This is why O₂ has two unpaired electrons.
- Magnetism: any unpaired electron makes the species paramagnetic (attracted by a magnet). All electrons paired means diamagnetic.
- HOMO and LUMO: the highest occupied and lowest unoccupied MOs. A half-filled HOMO is also called a SOMO (singly occupied MO).
Heteronuclear diatomics
In CO, NO and CN⁻ the more electronegative atom has lower-energy atomic orbitals, so it is drawn lower on the right. Bonding MOs lie closer to that atom; antibonding MOs lie closer to the less electronegative atom. In HF, the H 1s orbital overlaps only with the F 2p orbital along the bond. The F 2s and the two other F 2p orbitals stay nonbonding lone pairs, so HF has bond order 1.
Bond order, bond length and bond energy compared
Higher bond order means a shorter and stronger bond. Approximate bond lengths in pm and bond dissociation energies in kJ/mol:
| Species | Electrons | Bond order | Magnetism (unpaired) | Bond length (pm) | Bond energy (kJ/mol) |
|---|---|---|---|---|---|
| H₂⁺ | 1 | ½ | paramagnetic (1) | 106 | 256 |
| H₂ | 2 | 1 | diamagnetic | 74 | 436 |
| He₂⁺ | 3 | ½ | paramagnetic (1) | 108 | 230 |
| He₂ | 4 | 0 | diamagnetic | not bound | not bound |
| Li₂ | 6 | 1 | diamagnetic | 267 | 105 |
| Be₂ | 8 | 0 | diamagnetic | 245 | about 10 |
| B₂ | 10 | 1 | paramagnetic (2) | 159 | 290 |
| C₂ | 12 | 2 | diamagnetic | 124 | 599 |
| N₂ | 14 | 3 | diamagnetic | 110 | 945 |
| N₂⁺ | 13 | 2½ | paramagnetic (1) | 112 | 841 |
| O₂⁺ | 15 | 2½ | paramagnetic (1) | 112 | 643 |
| O₂ | 16 | 2 | paramagnetic (2) | 121 | 498 |
| O₂⁻ (superoxide) | 17 | 1½ | paramagnetic (1) | 133 | n/a |
| O₂²⁻ (peroxide) | 18 | 1 | diamagnetic | 149 | n/a |
| F₂ | 18 | 1 | diamagnetic | 142 | 159 |
| Ne₂ | 20 | 0 | diamagnetic | not bound | not bound |
| CO | 14 | 3 | diamagnetic | 113 | 1076 |
| NO⁺ | 14 | 3 | diamagnetic | 106 | 1050 |
| CN⁻ | 14 | 3 | diamagnetic | 116 | n/a |
| NO | 15 | 2½ | paramagnetic (1) | 115 | 631 |
| HF | 10 | 1 | diamagnetic | 92 | 570 |
Trend in the oxygen series: O₂⁺ (2½, 112 pm) > O₂ (2, 121 pm) > O₂⁻ (1½, 133 pm) > O₂²⁻ (1, 149 pm). Isoelectronic species (N₂, CO, CN⁻, NO⁺ with 14 electrons) all have bond order 3.
Worked examples
O₂: why liquid oxygen sticks to a magnet
16 electrons: KK σ2s² σ*2s² σ2p² π2p⁴ π*2p².
Bonding 10 (with σ1s), antibonding 6. The two π* electrons are unpaired by Hund's rule.
Bond order 2, paramagnetic, 2 unpaired
N₂: the triple bond
14 electrons, s–p mixing order: KK σ2s² σ*2s² π2p⁴ σ2p².
Bond order = (10 − 4)/2.
Bond order 3, diamagnetic, HOMO σ2p
B₂ and C₂ (JEE and NEET favourite)
B₂ (10 e): π2p¹ π2p¹ gives 2 unpaired electrons. C₂ (12 e): π2p⁴, all paired.
Without s–p mixing B₂ would be diamagnetic, which disagrees with experiment.
B₂ paramagnetic (BO 1); C₂ diamagnetic (BO 2)
NO, NO⁺ and NO⁻
NO has 15 electrons: one electron in π*2p. NO⁺ (14) loses it; NO⁻ (16) is like O₂.
BO = (10 − 5)/2 for NO.
NO 2½ (1 unpaired), NO⁺ 3, NO⁻ 2 (2 unpaired)
CO: HOMO and LUMO
14 electrons like N₂. The HOMO is σ2p (3σ), mostly a carbon lone pair; the LUMO is π*2p.
This is why CO binds metals through carbon and accepts back-bonding into π*.
Bond order 3, diamagnetic
He₂ and He₂⁺
He₂: σ1s² σ*1s², bonding = antibonding. He₂⁺: σ1s² σ*1s¹.
BO = (2 − 1)/2 for He₂⁺.
He₂ bond order 0 (not stable); He₂⁺ bond order ½
Common mistakes
- Wrong order for N₂ or B₂. Using the O₂ order for B₂ predicts a diamagnetic molecule. Up to 14 electrons, π2p comes before σ2p.
- Pairing too early. In a degenerate π or π* pair, the first two electrons go into separate orbitals with parallel spins.
- Forgetting the charge. A positive charge removes electrons (O₂⁺ has 15), a negative charge adds them (O₂²⁻ has 18).
- Mixing up core and valence counts. Counting all electrons or only valence electrons gives the same bond order, because the σ1s and σ*1s core pair cancels. Just be consistent.
- Calling bond order 0 a weak bond. Bond order 0 (He₂, Be₂, Ne₂) means no net covalent bond; the species is not expected to exist as a stable molecule.
- Thinking paramagnetism needs an odd electron count. O₂ has an even number of electrons and is still paramagnetic.
Drawing molecules for notes or exams? Draw Lewis structures, resonance and reaction mechanisms in MolDraw, a free online chemical structure editor.
Open MolDraw editorFrequently asked questions
What is the bond order of O₂?
O₂ has 16 electrons: KK σ2s² σ*2s² σ2p² π2p⁴ π*2p². Bonding electrons = 10 and antibonding = 6 (counting the 1s core), so bond order = (10 − 6)/2 = 2.
Why is O₂ paramagnetic?
The last two electrons go into the two degenerate π*2p orbitals. By Hund's rule they occupy separate orbitals with parallel spins, so O₂ has 2 unpaired electrons and is attracted into a magnetic field.
Why is the MO order different for N₂ and O₂?
In B, C and N the 2s and 2p levels are close, so s–p mixing pushes σ2p above π2p. In O and F the gap is large and σ2p stays below π2p. As a rule, species with 14 or fewer electrons use the mixed order.
Why is B₂ paramagnetic but C₂ diamagnetic?
With s–p mixing, π2p lies below σ2p. B₂ (10 electrons) puts one electron in each π2p orbital, giving 2 unpaired electrons. C₂ (12 electrons) fills both π2p orbitals, so all electrons are paired.
What is the bond order of NO, NO⁺ and NO⁻?
NO has 15 electrons with one unpaired electron in π*2p, so bond order 2.5. NO⁺ (14 electrons) has bond order 3 and is diamagnetic. NO⁻ (16 electrons) has bond order 2 and two unpaired electrons, like O₂.
Which orbital is the HOMO of CO?
The HOMO of CO is the σ2p orbital (also called 3σ), which is mostly a lone pair on carbon. The LUMO is π*2p. This explains why CO bonds to metals through carbon.
How does bond order relate to bond length and energy?
Higher bond order gives a shorter, stronger bond. For the oxygen series: O₂⁺ (2.5) 112 pm, O₂ (2) 121 pm, O₂⁻ (1.5) 133 pm and O₂²⁻ (1) 149 pm.
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