Crystal Field Splitting

d-Orbital Splitting in Transition Metal Complexes
15000 cm⁻¹

Crystal Field Theory

Octahedral: e_g (+0.6Δ), t₂g (-0.4Δ) — Δ_oct

Tetrahedral: e (-0.6Δ_tet), t₂ (+0.4Δ_tet) — Δ_tet ≈ (4/9)Δ_oct

Absorbed wavelength λ = hc/ΔE ↔ complementary color observed

Ligands split the 5-fold degenerate d-orbitals. The crystal field stabilization energy (CFSE) drives geometry preference. Strong field → low spin (pair electrons), weak field → high spin (Hund's rule). The absorption wavelength determines the metal complex color: Ti(H₂O)₆³⁺ absorbs green (Δ≈20,000 cm⁻¹) → appears violet-purple.