Degenerate and Non-Degenerate d Orbitals

· Degenerate d orbitals = d orbitals with the same energy.
· In an isolated transition metal ion, the five 3d orbitals are usually degenerate.
· Non-degenerate d orbitals = d orbitals split into different energy levels.
· When ligands approach a metal ion, repulsion between ligand lone pairs and d-orbital electrons causes the d orbitals to split.
· The energy gap between the split d-orbital sets is called ΔE.

This diagram shows how ligands split the five degenerate d orbitals into two non-degenerate sets. It is useful for visualising ΔE and why d electrons can absorb visible light. Source

Splitting in Octahedral Complexes

· Octahedral complex = central metal ion surrounded by 6 ligands.
· Ligands approach along the x, y and z axes, so orbitals pointing along these axes experience more repulsion.
· Higher energy set: 2 d orbitals: dₓ²₋ᵧ² and d𝓏².
· Lower energy set: 3 d orbitals: dₓᵧ, dₓ𝓏 and dᵧ𝓏.
· The energy difference between these two sets is ΔE.

This image explains why octahedral ligands split d orbitals into two higher-energy orbitals and three lower-energy orbitals. It links orbital orientation to electron-pair repulsion from ligands. Source

Splitting in Tetrahedral Complexes

· Tetrahedral complex = central metal ion surrounded by 4 ligands.
· The splitting pattern is the opposite of octahedral splitting.
· Higher energy set: 3 d orbitals: dₓᵧ, dₓ𝓏 and dᵧ𝓏.
· Lower energy set: 2 d orbitals: dₓ²₋ᵧ² and d𝓏².
· For the same metal and ligand, tetrahedral ΔE is usually smaller than octahedral ΔE.

Why Transition Metal Complexes Are Coloured

· Transition metal complexes are coloured because they often contain partially filled d orbitals.
· An electron can absorb visible light and be promoted from a lower-energy d orbital to a higher-energy d orbital.
· This promotion is called a d–d transition.
· Light is absorbed only if its energy matches ΔE.
· The colour observed is the complementary colour of the light absorbed.

ΔE, Frequency Absorbed and Complementary Colour

· Higher ΔE means the complex absorbs light of higher frequency.
· Lower ΔE means the complex absorbs light of lower frequency.
· Since E = hν, energy absorbed is directly proportional to frequency.
· Changing ΔE changes the frequency of light absorbed.
· Therefore, changing ΔE changes the complementary colour observed.

Effect of Different Ligands

· Different ligands cause different amounts of d-orbital splitting.
· Ligands that cause larger ΔE make the complex absorb higher-frequency light.
· Ligands that cause smaller ΔE make the complex absorb lower-frequency light.
· Therefore, ligand exchange can cause a visible colour change.
· In exam answers, link: different ligand → different ΔE → different frequency absorbed → different complementary colour observed.

Ligand Exchange Colour Examples: Copper(II)

· [Cu(H₂O)₆]²⁺ = pale blue solution.
· Addition of OH⁻ gives a pale blue precipitate of copper(II) hydroxide.
· Addition of excess NH₃ gives deep blue [Cu(NH₃)₄(H₂O)₂]²⁺.
· Addition of excess Cl⁻ gives yellow/green [CuCl₄]²⁻.
· Key exam idea: colour changes because the ligand changes from H₂O to NH₃, OH⁻ or Cl⁻, changing ΔE.

These images show copper(II) complexes changing colour as ligands are exchanged. They are especially useful for remembering the pale blue to deep blue change with excess ammonia. Source

Ligand Exchange Colour Examples: Cobalt(II)

· [Co(H₂O)₆]²⁺ = pink solution.
· Addition of OH⁻ gives a blue precipitate of cobalt(II) hydroxide.
· Addition of excess NH₃ can give a straw/brown solution due to ligand exchange and oxidation.
· Addition of excess Cl⁻ gives blue [CoCl₄]²⁻.
· Key exam idea: cobalt(II) complexes show colour changes because ligand identity and geometry affect ΔE.

These diagrams show how cobalt(II) complex colours change when ligands are exchanged. They support the key CIE idea that ligand exchange changes ΔE, so the observed colour changes. Source

Common Exam Explanation Structure

· State that ligands split degenerate d orbitals into non-degenerate d orbitals.
· State that the energy gap is ΔE.
· State that an electron absorbs visible light and is promoted between d-orbital levels.
· State that the frequency absorbed depends on ΔE.
· State that the observed colour is the complementary colour of the absorbed light.

Exam Traps to Avoid

· Do not say the complex “emits” the colour seen; it absorbs one colour and transmits/reflex the complementary colour.
· Do not just write “transition metals are coloured”; explain using d-orbital splitting and d–d transitions.
· Do not forget that octahedral and tetrahedral complexes have different splitting patterns.
· Do not say all transition metal ions are coloured; ions with empty or full d subshells often lack d–d transitions.
· Do not explain ligand exchange colour changes only by “new compound formed”; link it to different ΔE.