Crystal Field Splitting — Ligand d-Orbital Theory

How ligand geometry splits degenerate d-orbitals and determines spin state & color

Energy level diagram

d-orbital geometry & ligand field

Geometry

d electrons (0–10) 5 (d⁵)

Δ (field strength) 50

Pairing energy P 35

Δ: —

CFSE: —

Spin state: —

μ (spin-only): —

Unpaired e⁻: —

Crystal field theory (Bethe 1929, Van Vleck 1932): ligands split d-orbitals via electrostatic repulsion. Octahedral: t₂g (dxy, dxz, dyz) lower by -0.4Δ; eg (dx²-y², dz²) higher by +0.6Δ. High vs low spin depends on Δ/P ratio. Color from d-d transitions (absorption spectrum).