28.3 Colour of Complexes
Learning outcomes
Candidates should be able to:
- define and use the terms degenerate and non-degenerate d orbitals
- describe the splitting of degenerate d orbitals into two non-degenerate sets of d orbitals of higher energy, and the use of ΔE in:
- (a) octahedral complexes, two higher and three lower d orbitals
- (b) tetrahedral complexes, three higher and two lower d orbitals
- explain why transition elements form coloured compounds in terms of the frequency of light absorbed as an electron is promoted between two non-degenerate d orbitals
- describe, in qualitative terms, the effects of different ligands on ΔE, frequency of light absorbed, and hence the complementary colour that is observed
- use the complexes of copper(II) ions and cobalt(II) ions with water and ammonia molecules and hydroxide and chloride ions as examples of ligand exchange affecting the colour observed
Why are complexes coloured?
White light contains all the wavelengths of the visible spectrum. When white light passes through a solution containing a transition-metal complex, part of the visible spectrum is absorbed.
The colour we see is the complementary colour — made up of the wavelengths that are not absorbed. For example, copper(II) ions absorb light from the red end of the spectrum, so the complementary colour seen is a pale blue (cyan).
a VO₂⁺
yellow
b VO²⁺
blue
c V³⁺
green
d V²⁺
violet
Here are some complementary pairs of colours:
| Colour absorbed | Colour seen (complementary) |
|---|---|
| red | cyan |
| yellow | blue |
| green | magenta |
To explain why transition-metal ions absorb part of the visible spectrum, we need to look more closely at the d orbitals themselves.
Degenerate and non-degenerate d orbitals
Splitting in octahedral complexes
In an octahedral complex, six ligands surround the metal ion along the x, y and z axes. The lone pairs donated by the ligands repel electrons in the dx²−y² and dz² orbitals more than those in the other three, because these two orbitals point directly along the metal–ligand bonds. The d orbitals therefore split, with dx²−y² and dz² at a slightly higher energy than dyz, dxz and dxy.
A Cu²⁺ ion has the configuration [Ar] 3d⁹. ΔE corresponds to part of the visible spectrum. When light shines on a solution of [Cu(H₂O)₆]²⁺, an electron absorbs this amount of energy and jumps to the higher non-degenerate level. The rest of the visible light passes through, making the solution appear blue.
Splitting in tetrahedral complexes
In a tetrahedral complex, such as [CoCl₄]²⁻, the splitting is different. The bonding pairs from the four ligands line up more closely with the dyz, dxz and dxy orbitals, which are pushed to a higher energy. The dx²−y² and dz² orbitals lie between the metal–ligand bonds, so they experience less repulsion and stay at lower energy — the opposite pattern to an octahedral complex.
Ligands, ΔE and colour
The size of ΔE depends on several factors, including which ligands surround the metal ion. A solution of [Cu(H₂O)₆]²⁺ is light blue, while [Cu(NH₃)₄(H₂O)₂]²⁺ is a much deeper blue. The ammonia ligands cause the d orbitals to split by a different amount of energy, so a different frequency of light is absorbed and a different colour is seen.
Smaller ΔE → lower frequency light absorbed.
Ligand exchange and the colour observed
| Metal ion + ligand | Complex formed | Colour observed |
|---|---|---|
| Cu²⁺ + H₂O | [Cu(H₂O)₆]²⁺ | pale blue solution |
| Cu²⁺ + NH₃ (excess) | [Cu(NH₃)₄(H₂O)₂]²⁺ | deep blue solution |
| Cu²⁺ + OH⁻ | Cu(OH)₂ | pale blue precipitate |
| Co²⁺ + H₂O | [Co(H₂O)₆]²⁺ | pink solution |
| Co²⁺ + Cl⁻ | [CoCl₄]²⁻ | blue solution |
| Co²⁺ + NH₃ | ammine complex | colour change |
| Co²⁺ + OH⁻ | Co(OH)₂ | blue precipitate |
Exam tips
- State the full causal chain for a “why coloured” question: d orbitals split → electron promoted/excited → light of frequency ΔE/h is absorbed → the colour seen is complementary to the colour absorbed.
- Know both splitting patterns and don’t mix them up: octahedral = 2 higher/3 lower; tetrahedral = 3 higher/2 lower.
- Changing the ligand changes ΔE, which changes the frequency of light absorbed and hence the colour seen — this is why ligand exchange causes a colour change.
Quick summary
- The colour of a complex is the complementary colour to the light it absorbs from the visible spectrum.
- Degenerate d orbitals (same energy) split into two non-degenerate sets when ligands bond to the metal ion.
- Octahedral: dx²−y², dz² higher; dxy, dyz, dxz lower. Tetrahedral: the reverse.
- An electron is promoted across the gap ΔE by absorbing light of frequency ν, where ΔE = hν.
- Different ligands give different ΔE, so ligand exchange (e.g. Cu²⁺ or Co²⁺ with H₂O, NH₃, OH⁻, Cl⁻) changes the colour observed.