← Labs|Crystal Field Theory — Splitting, CFSE & Spin State
d-Electrons
Geometry
Spectrochemical Series
← weak field ···············strong field →
d6octahedral
High Spin
Ligand: H₂O
d-Orbital Energy Level Diagram
Energyd (free ion)dx²-y²dz²dxydxzdyzΔoeg (+0.6Δo)t2g (−0.4Δo)
CFSE-0.4 × Δo
Crystal Field Stabilisation Energy (octahedral)
Unpaired e⁻4
Paramagnetic
Spin-only μ4.90 BM
μ = √(n(n+2)) where n = unpaired electrons
Spin StateHigh Spin
Weak field: Δo < P — Hund's rule preferred
Octahedral CFSE (in Δo units)
d1
HS:-0.4
LS:-0.4
d2
HS:-0.8
LS:-0.8
d3
HS:-1.2
LS:-1.2
d4
HS:-0.6
LS:-1.6
d5
HS:0.0
LS:-2.0
d6
HS:-0.4
LS:-2.4
d7
HS:-0.8
LS:-1.8
d8
HS:-1.2
LS:-1.2
d9
HS:-0.6
LS:-0.6
d10
HS:0.0
LS:0.0
CFT Key Concepts
CFSE Formula (Oh)
CFSE = n_t2g × (−0.4Δo) + n_eg × (0.6Δo) High spin d⁵: CFSE = 0 (symmetric half-fill) Low spin d⁶: CFSE = −2.4Δo (most stable)
High vs Low Spin Rule
Δo > P → Low Spin (pair first) Δo < P → High Spin (Hund) Weak ligands (Cl⁻, H₂O) → HS Strong ligands (CN⁻, CO) → LS Tetrahedral: always HS (Δt too small)
Magnetic Moment
μ = √n(n+2) BM 0 unpaired: 0 (diamagnetic) 1: 1.73 BM 2: 2.83 BM 3: 3.87 BM 4: 4.90 BM 5: 5.92 BM (max)
Examples (JEE)
[Fe(CN)₆]³⁻: d⁵, LS, 1 unpaired [Fe(H₂O)₆]³⁺: d⁵, HS, 5 unpaired [CoF₆]³⁻: d⁶, HS, 4 unpaired [Co(NH₃)₆]³⁺: d⁶, LS, 0 unpaired K₂[NiF₄]: d⁸, 2 unpaired
Jahn-Teller Effect
d⁴, d⁹ in Oh: unequal occupation of eg → tetragonal distortion Strongest for Cu²⁺ (d⁹) Causes elongation along z-axis