Crystal Field Theory (CFT)
Exam-focused revision notes on Crystal Field Theory (CFT) for CSIR-NET Chemical Sciences, GATE Chemistry and IIT-JAM — the core concepts, the formulas worth memorising, the traps that cost marks, and a quick-recall table.
The core idea
A metal ion's five d orbitals are degenerate when free. Surround it with ligands and their lone pairs repel the d electrons — but unequally, because some d orbitals point at the ligands and some point between them. That unequal repulsion splits the d orbitals in energy. The pattern depends on geometry.
Octahedral field (most important)
- Ligands approach along the x, y, z axes.
- Orbitals pointing at the ligands — dz², dx²−y² — are raised: the eg set (higher).
- Orbitals pointing between — dxy, dxz, dyz — are lowered: the t2g set (lower).
- Energy gap = Δo (octahedral splitting).
- Barycentre rule: t2g at −0.4 Δo, eg at +0.6 Δo.
CFSE (crystal field stabilization energy)
Read it straight off the electron count. Example: low-spin d6 = t2g6eg0 → CFSE = 6(−0.4) = −2.4 Δo (plus pairing) — very stable, which is why [Co(NH3)6]3+ is inert.
High-spin vs low-spin (exam favourite)
- Compare Δo with the pairing energy P.
- Δo < P → electrons spread out first (Hund) → high-spin (weak-field ligands).
- Δo > P → electrons pair in t2g first → low-spin (strong-field ligands).
- Only d4–d7 octahedral can be high- or low-spin; d1–d3 and d8–d10 have only one option.
Spectrochemical series
Weak field → strong field:
Left = small Δo, high-spin. Right = large Δo, low-spin. CN−, CO, NO2− are strong-field π-acceptors.
Tetrahedral field
- Δt ≈ (4/9) Δo — always small → tetrahedral complexes are almost always high-spin.
- Splitting is inverted: e (lower) below t2 (higher).
What CFT explains (and gets asked)
- Magnetic moment: μ = √(n(n+2)) BM (n = unpaired e−). High-spin d5 = 5.92 BM; low-spin d6 = 0 (diamagnetic).
- Colour: d–d transitions absorb light of energy ≈ Δo; the complementary colour is seen. Larger Δo → absorbs shorter λ.
- Stability / CFSE trends and Jahn–Teller distortion (uneven eg occupancy, e.g. d9 Cu2+).
⚠️ Common traps students miss
- Tetrahedral is e below t2 (opposite of octahedral) — easy to flip and lose the mark.
- For tetrahedral, strong-field ligand ≠ low-spin (Δt too small — usually high-spin regardless).
- CFSE alone doesn't decide spin state — you compare Δ with P.
- The observed colour is the complement of what's absorbed.
30-second recall table
| d-count | Oct high-spin (unpaired e−) | Oct low-spin (unpaired e−) |
|---|---|---|
| d4 | 4 | 2 |
| d5 | 5 | 1 |
| d6 | 4 | 0 |
| d7 | 3 | 1 |
Practise this topic
ChemVidya has CSIR-NET Part-B and Part-C practice questions on this topic, each with a worked solution.
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