🧪 SM-EDUCATE CHEMISTRY June 07, 2026

The Color of Coordination Complexes:
A Quantitative Dive into Crystal Field Theory

🎨 d-orbital splitting · Spectrochemical series · λ = hc / Δ · Why emeralds are green

Coordination Chemistry Crystal Field Theory d-d Transitions Spectrochemical Series Inorganic Chemistry Colour of Complexes

Why is [Ti(H₂O)₆]³⁺ violet? Why is [Cu(H₂O)₆]²⁺ blue? And why does [Ni(NH₃)₆]²⁺ look completely different from [Ni(H₂O)₆]²⁺? The answer lies in Crystal Field Theory (CFT) — a beautiful, quantitative model that explains how ligands split the d‑orbitals of transition metals, and how electrons jumping between those split levels absorb specific colours of light.

Octahedral Crystal Field Splitting (Δoct)

          High
            |
            |         eg (dx²−y², dz²)  ─────  higher energy
            |              ↑
            |              │
            |          Δoct
            |              │
            |              ↓
            |         t2g (dxy, dxz, dyz)  ─────  lower energy
            |
          Low
          
In an octahedral crystal field:
- Free ion (no ligands): five degenerate d-orbitals
- In an octahedral field, the five degenerate d-orbitals split into two sets:
  • t2g (dxy, dxz, dyz) – lower energy
  • eg (dx²−y², dz²) – higher energy

Energy of absorbed light:  E = hc / λ = Δoct
where λ = wavelength of absorbed light.

The energy gap between the two sets is Δoct.
Typical Δoct in the visible range: 1–4 eV.
      

In an octahedral field, the five degenerate d‑orbitals split into t_2g (lower) and e_g (higher). The splitting energy Δ_oct is typically in the visible range (1–4 eV).

1. The Origin of Colour: d‑d Transitions

When white light passes through a transition metal complex, certain wavelengths are absorbed to promote an electron from a lower d‑orbital (t_2g) to a higher d‑orbital (e_g). The complementary colour is transmitted. The energy of the absorbed photon equals Δ (the crystal field splitting energy).

Δ = hν = hc / λ

If Δ corresponds to a wavelength in the visible range (400–700 nm), the complex appears coloured. If Δ is too large (UV absorption) or too small (IR absorption), the complex is colourless or white.

🔬 Takeaway: Colour is not an intrinsic property of the metal — it depends on the ligand field. Changing the ligand changes Δ, which changes the colour.

2. The Spectrochemical Series: Ranking Ligands by Δ

Ligands are ranked by their ability to split d‑orbitals. The spectrochemical series (increasing Δ):

I⁻ < Br⁻ < Cl⁻ < F⁻ < OH⁻ < H₂O < NH₃ < en < NO₂⁻ < CN⁻ < CO

Weak‑field ligands (I⁻, Br⁻, Cl⁻) give small Δ → absorb long wavelengths (red) → complexes appear blue/green. Strong‑field ligands (CN⁻, CO) give large Δ → absorb short wavelengths (blue/violet) → complexes appear red/yellow. For example, [Ni(H₂O)₆]²⁺ is green, but [Ni(NH₃)₆]²⁺ is blue‑violet — because NH₃ is a stronger field ligand than H₂O.

   [Ni(H₂O)₆]²⁺          [Ni(NH₃)₆]²⁺
        🟢                     🟣
      Green                Blue-violet
   Weak field (H₂O)     Stronger field (NH₃)
   
   Larger Δ → shorter λ → colour shifts
      

The same Ni²⁺ ion with different ligands gives different colours because NH₃ causes a larger Δ than H₂O.

3. Quantitative Example: [Ti(H₂O)₆]³⁺

Titanium(III) has a d¹ configuration. The single electron occupies a t_2g orbital. When light is absorbed, the electron jumps to the e_g level. The absorption maximum for [Ti(H₂O)₆]³⁺ is at ~500 nm (green region). The complex appears violet (complementary colour). Calculate Δ:

Δ = hc / λ = (6.626 × 10⁻³⁴ J·s)(3.00 × 10⁸ m/s) / (500 × 10⁻⁹ m)
= 3.98 × 10⁻¹⁹ J per photon = 240 kJ/mol (since 1 mol = 6.022 × 10²³ photons)

This is typical for octahedral complexes. Weak‑field ligands give Δ ~100–200 kJ/mol; strong‑field ligands can exceed 300 kJ/mol (e.g., [Co(CN)₆]³⁻).

4. Beyond Octahedral: Tetrahedral and Square Planar

In tetrahedral complexes, the splitting pattern is inverted and smaller: e (higher) and t₂ (lower), with Δ_tet ≈ 4/9 Δ_oct. That's why tetrahedral complexes often have more intense colours (smaller Δ moves absorption into the visible) and sometimes appear differently. Square planar complexes (e.g., [PtCl₄]²⁻) have even more complex splitting patterns, often with a large Δ between the highest and lowest d‑orbitals, leading to yellow/red colours or even no colour if Δ is in the UV.

⚡ Takeaway: The colour of a coordination complex is a direct probe of the crystal field splitting. By measuring λ_max, we can calculate Δ and rank ligands quantitatively.

5. Why This Matters: Applications

Crystal field theory explains not just colour, but also magnetism, thermochromism, and catalytic activity. In biology, the colour of haemoglobin (red) and hemocyanin (blue) comes from different metal centres (Fe vs. Cu) and different ligand fields. In materials science, transition metal ions in gemstones (ruby: Cr³⁺ in Al₂O₃, emerald: Cr³⁺ in Be₃Al₂Si₆O₁₈) derive their colours from subtle changes in the crystal field environment.

   From colour to Δ: A quantitative relationship
   
   λ (nm) = hc / Δ   →   Δ (cm⁻¹) = 10⁷ / λ (nm)
   
   (Wavenumber ν̃ = 1/λ in cm⁻¹ is often used in spectroscopy)
      

The absorption maximum gives the splitting energy directly. This is the power of CFT: it turns colour into a quantitative measure of ligand field strength.

📚 Further Reading

• Figgis, B. N., & Hitchman, M. A. (1999). Ligand Field Theory and Its Applications. Wiley‑VCH.
• Orgel, L. E. (1966). An Introduction to Transition‑Metal Chemistry: Ligand Field Theory. Methuen.
• Shriver, D. F., & Atkins, P. W. (2010). Inorganic Chemistry (5th ed.). Oxford University Press. (Chapter on crystal field theory)
• Lever, A. B. P. (1984). Inorganic Electronic Spectroscopy. Elsevier.

SM-EDUCATE CHEMISTRY — Where colour meets quantum mechanics