Crystal Field Theory — Chemistry Mnemonic
Target: mnemonic for crystal field theory CFT d orbital splitting
Why is this hard to memorize?
Crystal Field Theory (CFT) explains the colours, magnetic properties, and stability of transition metal complexes. When ligands approach a metal ion, the five degenerate d-orbitals split into two groups. In an octahedral field: dxy, dyz, dxz (t₂g, lower energy) and dx²-y², dz² (eg, higher energy) with splitting energy Δ₀. In a tetrahedral field: splitting is reversed and Δt ≈ 4/9 Δ₀. Strong-field ligands (large Δ) → low-spin complexes; weak-field ligands (small Δ) → high-spin complexes. JEE tests splitting diagrams and spin state predictions.
Classic mnemonics you should know
"t₂g(3 orbitals, lower) and eg(2 orbitals, higher). Splitting energy = Δ₀. "t₂g = 3 orbitals at ground, eg = 2 excited""
In octahedral field, ligands approach along x, y, z axes. The d-orbitals pointing at ligands (dx²-y², dz²) are repelled more → higher energy (eg). Those between axes (dxy, dyz, dxz) are less repelled → lower energy (t₂g). Energy difference = Δ₀ (crystal field splitting energy).
"Weak field ligand → small Δ₀ → electrons spread out → HIGH spin (more unpaired e⁻). Strong field ligand → large Δ₀ → electrons pair up first → LOW spin (fewer unpaired e⁻)"
If Δ₀ > pairing energy: electrons fill t₂g first (pair up) before going to eg → low-spin. If Δ₀ < pairing energy: electrons go to eg rather than pairing → high-spin. The spectrochemical series ranks ligands by Δ₀: I⁻ < Br⁻ < Cl⁻ < F⁻ < OH⁻ < H₂O < NH₃ < en < NO₂⁻ < CN⁻ < CO.
"CFSE = (−0.4 × t₂g electrons + 0.6 × eg electrons) × Δ₀. Higher CFSE = more stable complex."
Each electron in t₂g stabilizes by −0.4Δ₀, each in eg destabilizes by +0.6Δ₀. CFSE measures net stabilization. d³ octahedral: 3(−0.4Δ₀) = −1.2Δ₀ (very stable — Cr³⁺ complexes are inert). d⁰ and d⁵(HS) and d¹⁰: CFSE = 0.
The complete list
- Octahedral: t₂g (lower, 3 orbitals) + eg (higher, 2)
- Tetrahedral: e (lower, 2) + t₂ (higher, 3) — reversed
- Δ₀ = octahedral splitting energy
- Δt ≈ 4/9 Δ₀ (tetrahedral is weaker)
- Strong field → low spin (paired e⁻)
- Weak field → high spin (max unpaired e⁻)
- Spectrochemical series ranks Δ₀
- CFSE = stabilization from d-orbital splitting
Frequently asked questions
How do I determine if a complex is high-spin or low-spin?
Step 1: Identify the metal ion and its d-electron count. Step 2: Identify the ligand and check the spectrochemical series (strong or weak field). Step 3: If strong-field ligand (CN⁻, CO, NH₃) → electrons fill t₂g first, pairing up → low-spin. If weak-field ligand (Cl⁻, Br⁻, I⁻, H₂O) → electrons spread to eg before pairing → high-spin. Note: d¹, d², d³, d⁸, d⁹, d¹⁰ configurations have the same electron arrangement in both high and low-spin. Only d⁴−d⁷ differ.
Why is Δt smaller than Δ₀?
In octahedral geometry, 6 ligands approach directly along the axes — maximum interaction with d-orbitals. In tetrahedral, only 4 ligands approach between the axes — less direct interaction. Quantitatively: Δt = 4/9 Δ₀. Because Δt is always small, the pairing energy usually exceeds Δt, so tetrahedral complexes are almost always high-spin.
How does CFT explain the colour of complexes?
When visible light hits a complex, an electron in t₂g can absorb a photon and jump to eg (d-d transition). The energy of absorbed light = Δ₀ = hν. The colour we observe is the complementary colour of what's absorbed. For example, [Ti(H₂O)₆]³⁺ absorbs green light (Δ₀ matches green photon energy) → appears purple. Changing the ligand changes Δ₀ → changes the absorbed wavelength → changes the colour.
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