Crystal Field Theory (CFT)
Short Note – CFT explains how the degeneracy of transition‑metal d‑orbitals is lifted when a metal ion is surrounded by ligands.
1. Simple Explanation
| Concept | What it means |
|---|---|
| Crystal field | The electrostatic field produced by the surrounding ligands (treated as point charges or dipoles). |
| d‑orbital splitting | In a free ion all five d‑orbitals have the same energy. In a ligand field, the spatial orientation of the orbitals relative to the ligands causes different repulsions → different energies. |
| Assumptions | • Metal–ligand bond is purely ionic, no covalency. • Ligands are point charges/dipoles. • Metal ion remains spherical. |
| Result | Energy diagram of d‑orbitals (split into groups), crystal‑field splitting parameter Δ (Δo, Δt, Δe, …). |
2. Key Points
| Topic | Details |
|---|---|
| Geometry‑dependent splitting | <ul><li>Octahedral (O<sub>h</sub>) → t<sub>2g</sub> (lower) + e<sub>g</sub> (higher). </li> <li>Tetrahedral (T<sub>d</sub>) → e (lower) + t<sub>2</sub> (higher). </li> <li>Square‑planar → d<sub>xy</sub>, d<sub>x²–y²</sub>, d<sub>z²</sub>, d<sub>yz</sub>, d<sub>xz</sub> (in order d<sub>xy</sub> < d<sub>xz</sub> = d<sub>yz</sub> < d<sub>z²</sub> < d<sub>x²–y²</sub>). </li></ul> |
| Δ notation | Δo = 10 Dq (octahedral) Δt = 4/9 Δo ≈ 0.44 Δo (tetrahedral) Δe = 4/5 Δo ≈ 0.80 Δo (square‑planar) |
| Spectrochemical series (strong → weak field) | [F⁻ < Cl⁻ < Br⁻ < NO₃⁻ < H₂O < NCS⁻ < py < NH₃ < en < phen < NO₂⁻ < CN⁻ < CO] |
| Spin pairing energy (P) | Energy cost of pairing two electrons in the same orbital. |
| High‑spin vs Low‑spin | If Δ < P → high‑spin (maximise unpaired electrons). If Δ > P → low‑spin (minimise unpaired electrons). |
| Magnetic moment (µ<sub>eff</sub>) | µ = √(n(n+2)) BM, where n = # of unpaired electrons. |
| Ligand‑field stabilization energy (LFSE) | <ul><li>Octahedral: LFSE = (n<sub>t2g</sub> × –0.4Δo + n<sub>eg</sub> × +0.6Δo) – (P × #pairings)</li><li>Tetrahedral: LFSE = (n<sub>e</sub> × –0.6Δt + n<sub>t2</sub> × +0.4Δt) – (P × #pairings)</li></ul> |
| Colour & absorption | The electronic transition d<sub>t2g</sub> → d<sub>eg</sub> (octahedral) or d<sub>e</sub> → d<sub>t2</sub> (tetrahedral) gives Δ energy; λ = hc/Δ. |
| Limitations of CFT | • Ignores covalent character |