Last updated: 14 October 2026
A solution containing Cu²⁺ ions is often blue, while a solution containing Zn²⁺ ions is colourless. The difference does not simply come from one metal being a transition metal and the other not. To understand the colour, we need to look inside the complex and ask what has happened to the metal ion's d-orbitals.
The central idea is an energy-gap story. Ligands surrounding a metal ion cause its d-orbitals to split into different energy levels. If the energy gap corresponds to part of the visible spectrum, a d-electron can absorb that light and move to a higher-energy d-orbital. Once you can connect orbital splitting, light absorption and complementary colour, the colours of transition-metal complexes become much easier to explain.
Try these five questions before reading the chapter. Focus on the relationship between d-orbital energies, light absorption and the colour that we actually observe.
- 5 diagnostic questions
- Orbital and light-energy reasoning
- Instant explanation for every answer option
Why the five d-orbitals begin at the same energy
A transition-metal ion has five d-orbitals: dxy, dxz, dyz, dx²−y² and dz². These orbitals have different orientations in space, but for an isolated gaseous ion they are treated as having the same energy.
Orbitals that have the same energy are described as degenerate. At this stage there is therefore no energy gap between one d-orbital and another.
Degenerate orbitals are orbitals that have the same energy.
What changes when ligands approach?
A complex forms when ligands donate lone pairs of electrons towards a central metal ion. Those ligand electron pairs repel electrons already occupying the metal ion's d-orbitals.
The important point is that the five d-orbitals do not all point in the same directions. They therefore experience different amounts of repulsion when the ligands approach.
Before complex formation: the five d-orbitals are degenerate.
After ligands surround the metal ion: the d-orbitals may split into groups with different energies.
d-Orbital splitting in an octahedral complex
In an octahedral complex, six ligands approach the metal ion along the positive and negative x-, y- and z-directions. This geometry is important because two of the d-orbitals point directly along these axes, while the other three lie mainly between them.
The difference in energy between these two groups is the d-orbital splitting energy, represented by ΔE. For an octahedral complex, this splitting may also be written as Δo.
Which d-orbitals have the higher energy?
The dx²−y² and dz² orbitals point directly along the coordinate axes. Since the ligands also approach along these axes, electrons in these orbitals experience particularly strong repulsion from the ligand electron pairs.
Their energies therefore increase relative to the other three d-orbitals. The dxy, dxz and dyz orbitals point mainly between the axes, so they experience less direct repulsion and form the lower-energy group.
| Group | d-orbitals | Reason |
|---|---|---|
| Higher energy, eg | dx²−y² and dz² | Their lobes point directly towards the approaching ligands. |
| Lower energy, t2g | dxy, dxz and dyz | Their lobes point mainly between the approaching ligands. |
Imagine six people approaching you along the three coordinate axes. If you stretch your arms directly towards them, you experience more direct contact than if your arms point into the spaces between them. The d-orbitals pointing towards the ligands similarly experience greater electron–electron repulsion and become higher in energy.
How d–d transitions absorb visible light
Once the d-orbitals have split, an electron occupying one of the lower-energy d-orbitals may be promoted into a higher-energy d-orbital. The electron cannot gain an arbitrary amount of energy. It must absorb a photon whose energy corresponds to the energy gap between the two groups of d-orbitals.
Here, ΔE is the d-orbital splitting energy, h is Planck's constant, ν is the frequency of the absorbed light, c is the speed of light and λ is its wavelength.
What exactly is a d–d transition?
A d–d transition is the promotion of an electron from a lower-energy d-orbital to a higher-energy d-orbital after the complex absorbs electromagnetic radiation of the appropriate energy.
A complex can absorb visible light by a d–d transition when the photon energy corresponds to the energy separation between occupied and available d-orbitals.
How wavelength depends on the energy gap
Because ΔE = hc / λ, energy and wavelength are inversely related. A larger d-orbital splitting requires a higher-energy photon and therefore corresponds to a shorter wavelength.
Larger ΔE: higher frequency and shorter wavelength of light absorbed.
Smaller ΔE: lower frequency and longer wavelength of light absorbed.
Why the colour observed is not the colour absorbed
White light contains a range of visible wavelengths. If a complex absorbs one region of this spectrum, that part of the light is removed from the light reaching our eyes.
The remaining transmitted light therefore appears approximately as the complementary colour of the absorbed light. For a solution, it is mainly the transmitted light that we observe. For coloured solids, reflected light may also be important.
| Approximate colour absorbed | Approximate complementary colour observed | Reasoning |
|---|---|---|
| Orange | Blue | Orange wavelengths are selectively removed from white light. |
| Red | Blue-green | The remaining visible light is dominated by the complementary region. |
| Violet | Yellow | Violet absorption leaves its approximate complementary colour. |
Do not say that a blue complex absorbs blue light. A blue solution appears blue because blue wavelengths are among the wavelengths that reach our eyes.
Why some metal complexes are colourless
For the simple d–d transition model used at A-Level, the metal ion needs both an electron that can be promoted and an available higher-energy d-orbital into which that electron can move.
This is why complexes containing a metal ion with a completely empty d-subshell, d⁰, or a completely filled d-subshell, d¹⁰, do not undergo the usual d–d transition.
The d⁰ case
Sc³⁺ has the electronic configuration [Ar], corresponding to 3d⁰. There is no d-electron available to promote, so a d–d transition cannot take place.
The d¹⁰ case
Zn²⁺ has the electronic configuration [Ar]3d¹⁰. Its d-subshell is completely filled, so there is no suitable vacant higher-energy d-orbital available for the usual d–d excitation.
d⁰: no d-electron is available to be promoted.
d¹⁰: the d-subshell is full, so there is no suitable vacant d-orbital available for the d–d transition.
For the ordinary complexes considered using the simple d–d model, a partially filled d-subshell — generally d¹ to d⁹ — allows d–d transitions to occur.
Why different complexes have different colours
The colour does not depend simply on whether the metal ion has an incomplete d-subshell. The wavelength absorbed depends on the size of ΔE, and the size of ΔE depends on the environment of the d-electrons.
Consequently, changing the metal ion, its oxidation state or the ligands surrounding it can change the splitting and therefore change the wavelengths absorbed and the colour observed.
| Factor changed | What can change | Possible consequence |
|---|---|---|
| Identity of the metal ion | The energies and behaviour of the d-orbitals | A different ΔE and hence a different absorbed wavelength |
| Oxidation state of the metal | d-electron configuration and metal–ligand interaction | A different absorption spectrum and colour |
| Identity of the ligand | Magnitude of d-orbital splitting | A different wavelength of light may be absorbed |
| Geometry of the complex | How ligands interact with differently oriented d-orbitals | The pattern and magnitude of splitting may change |
Ligand exchange can therefore cause a colour change
Ligand exchange replaces one type of ligand around a metal ion with another. Because different ligands interact differently with the d-orbitals, changing the ligand can change ΔE.
If ΔE changes, the frequency and wavelength of light absorbed also change:
A familiar example: Cu²⁺ and aqueous ammonia
The hexaaquacopper(II) ion, [Cu(H₂O)₆]²⁺, gives a pale blue solution. When excess aqueous ammonia is added, ammonia ligands replace four of the water ligands and a deep blue ammine complex is formed.
Copper remains in the +2 oxidation state, so the dramatic colour change is not caused by an oxidation-state change. Instead, the ligand environment around Cu²⁺ has changed.
NH₃ and H₂O produce different d-orbital splitting energies. This changes the energy required for the d–d transition and hence the wavelengths of visible light absorbed. The transmitted colour consequently changes from pale blue to deep blue.
An examination explanation should therefore connect the whole chain: ligand exchange changes the d-orbital splitting, so ΔE changes; a different wavelength of visible light is absorbed, and the colour observed therefore changes.
Building a complete examination explanation
Questions about the colour of transition-metal complexes often require several connected ideas rather than a single sentence. A strong answer usually begins with d-orbital splitting and ends with the colour that reaches the observer.
Ligands cause the metal ion's d-orbitals to split into two energy levels. A d-electron absorbs visible light of energy ΔE = hν and is promoted from a lower-energy d-orbital to a higher-energy d-orbital. The unabsorbed light reaching the eye produces the observed colour, which is approximately complementary to the colour absorbed.
A useful reasoning sequence
| Step | What to explain | Key phrase |
|---|---|---|
| 1 | Ligands interact with the metal ion's d-orbitals. | d-orbital splitting |
| 2 | An energy gap is produced between the two groups. | ΔE |
| 3 | A d-electron absorbs a photon whose energy corresponds to the gap. | ΔE = hν |
| 4 | The electron is promoted to a higher-energy d-orbital. | d–d transition |
| 5 | The remaining light reaching the eye determines the observed colour. | complementary colour |
Common Mistakes
| Common mistake | Why it is wrong | Better approach |
|---|---|---|
| Saying that all five d-orbitals remain at the same energy in a complex | The ligand environment removes their degeneracy. | Explain that ligand–electron repulsion splits the d-orbitals into different energy levels. |
| Saying that a blue complex absorbs blue light | The colour absorbed is removed from the light reaching the eye. | State that the observed colour is approximately complementary to the principal colour absorbed. |
| Saying Zn²⁺ is colourless because it has no d-electrons | Zn²⁺ is 3d¹⁰, not d⁰. | State that its d-subshell is completely filled, so the ordinary d–d transition cannot occur. |
| Explaining a ligand-exchange colour change only by saying that “the ligand has changed” | This does not explain the electronic origin of the colour change. | Link ligand identity to a change in ΔE, then to a different absorbed wavelength and observed colour. |
What you should be able to do
Explain degeneracy
State what it means for the five d-orbitals of an isolated metal ion to have the same energy.
Explain octahedral splitting
Identify which d-orbitals lie higher and lower in energy and explain the difference using ligand–electron repulsion.
Explain a d–d transition
Relate absorption of visible light to promotion of a d-electron across ΔE.
Use ΔE = hν = hc / λ
Relate changes in d-orbital splitting to the frequency and wavelength of light absorbed.
Explain colourless d⁰ and d¹⁰ ions
Explain why Sc³⁺ and Zn²⁺ cannot undergo the ordinary d–d transitions responsible for colour in many complexes.
Explain colour changes
Connect a change in ligand, oxidation state or metal environment to a change in ΔE, absorbed wavelength and observed colour.
These ten questions test whether you can apply d-orbital splitting, d–d transitions and complementary-colour reasoning to unfamiliar situations.
- 10 mastery questions
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Frequently asked questions
Questions students often ask about the colour of complexes
Most difficulties with this topic come from mixing up the colour absorbed, the colour observed and the reason the d-orbitals split in the first place. These questions bring those ideas together.
Why are the five d-orbitals degenerate before ligands approach?
For an isolated gaseous metal ion, there is no surrounding ligand arrangement that distinguishes one spatial orientation of the d-orbitals from another. The five d-orbitals are therefore treated as having the same energy. When ligands approach in particular directions, the different orbital orientations experience different amounts of repulsion and the degeneracy is removed.
Why are dx²−y² and dz² higher in energy in an octahedral complex?
Six ligands approach along the x-, y- and z-axes. The lobes of the dx²−y² and dz² orbitals point directly along these axes, so electrons occupying these orbitals experience greater repulsion from the ligand electron pairs. The dxy, dxz and dyz orbitals point mainly between the axes and experience less direct repulsion.
Why are Sc³⁺ and Zn²⁺ usually colourless?
Sc³⁺ is d⁰, so it has no d-electron available to promote. Zn²⁺ is d¹⁰, so its d-subshell is completely filled and there is no suitable vacant higher-energy d-orbital for the ordinary d–d excitation. Neither therefore produces colour through the usual d–d transition model.
Why does changing the ligand change the colour even if the metal ion stays the same?
Different ligands interact differently with the metal ion's d-orbitals and therefore produce different splitting energies. Changing the ligand changes ΔE. Since ΔE = hν = hc / λ, a different wavelength of light is absorbed and a different complementary colour may be observed.
Does every coloured metal-containing species get its colour from a d–d transition?
No. The d–d model explains the colour of many familiar transition-metal complexes, but electronic transitions other than d–d transitions can also produce colour. At A-Level, when you are specifically asked to explain the colour of the usual transition-metal complexes using d-orbital splitting, focus on the splitting, ΔE, absorption of visible light and the resulting d–d transition.
The colour of a transition-metal complex is therefore a visible consequence of what is happening at the electronic level. Ligands split the metal ion's d-orbitals, the resulting ΔE determines which wavelengths can be absorbed, and the light that remains determines what we see. Changing the metal ion, oxidation state or ligand environment changes that energy picture — and can therefore change the colour.