Crystal Field Theory: Splitting, CFSE and the Spectrochemical Series

The model in one paragraph

Crystal field theory treats ligands as point negative charges and asks what their electrostatic field does to the five d orbitals of the metal. In a free ion those five are degenerate. Bring ligands up along particular directions and the orbitals pointing at the ligands are destabilised more than those pointing between them. The degeneracy breaks, and almost every observable property of the complex follows from how it breaks.

Octahedral splitting

Six ligands approach along the ±x, ±y and ±z axes. The d_z² and d_x²−y² orbitals point directly at them and rise in energy; d_xy, d_yz and d_xz point between them and fall.

The weighted average is unchanged — 2(+0.6) + 3(−0.4) = 0 — which is the barycentre rule and is worth stating in a derivation answer.

High spin or low spin

For d⁴ to d⁷ configurations there is a genuine choice. Electrons can either occupy the upper e_g set, costing Δ_o, or pair in the lower t_2g set, costing the pairing energy P.

Tetrahedral complexes are essentially always high spin. The tetrahedral splitting is smaller — Δ_t ≈ (4/9)Δ_o — because there are only four ligands and none points directly at a d orbital. That splitting almost never exceeds the pairing energy, and stating this reasoning earns more than stating the fact.

Calculating CFSE

Crystal field stabilisation energy is the net energy gain from the splitting:

The high-spin d⁵ zero is worth noticing: a half-filled set spread evenly across both levels gains nothing from the splitting, which is part of why such complexes are labile.

The spectrochemical series

Ligands ordered by the size of Δ they produce:

Consequences you will be asked to derive

Colour

A d–d transition absorbs light of energy Δ, and the complex appears as the complementary colour. Larger Δ means absorption at shorter wavelength. A d⁰ or d¹⁰ complex has no d–d transition available and is typically colourless — a standard reasoning question.

Magnetic moment

The spin-only formula gives μ = √(n(n+2)) Bohr magnetons for n unpaired electrons. Measuring μ therefore tells you n, which tells you the spin state, which constrains Δ relative to P. Many questions run exactly this chain.

Jahn–Teller distortion

A non-linear complex in a degenerate electronic state distorts to remove that degeneracy. The effect is strong for unevenly occupied e_g sets — high-spin d⁴ and d⁹ are the standard examples — and weak for t_2g asymmetry, because those orbitals point away from the ligands.

Frequently asked questions

Why is tetrahedral splitting smaller than octahedral?

Two reasons together: fewer ligands, and no ligand points directly along a d-orbital lobe. The commonly quoted relationship is Δ_t ≈ (4/9)Δ_o for otherwise comparable systems.

Can CFSE alone predict which geometry forms?

It contributes but does not decide. Ligand size, metal ion charge and radius, and packing all matter. Answers that rest on CFSE alone are incomplete.

Where does crystal field theory fail?

It cannot explain the spectrochemical series, it ignores covalency entirely, and it cannot account for the intensity of charge-transfer bands. Ligand field and molecular orbital treatments address these.

How much of this is needed for IIT-JAM versus CSIR-NET?

JAM generally stays with splitting diagrams, CFSE and spin-only moments. CSIR-NET pushes into term symbols, Orgel and Tanabe–Sugano diagrams, and the π-bonding explanation of the series.