Crystal Field Theory for JEE Main: Coordination Chemistry

Crystal field theory (CFT) explains the colour, magnetic properties, and stability of transition metal complexes by describing how ligands split the d-orbitals of the central metal ion. JEE Main tests CFT through identifying high-spin vs low-spin complexes, calculating crystal field stabilisation energy (CFSE), and predicting magnetic moments. The logic is systematic and the calculations are straightforward.

d-Orbital Splitting in an Octahedral Field

In a free metal ion, all five d-orbitals are degenerate. In an octahedral complex, six ligands along the ±x, ±y, ±z axes repel the d_z² and d_x²-y² orbitals more strongly (they point directly at ligands), raising them to the e_g set, while d_xy, d_xz, and d_yz (the t₂g set) are lowered. The splitting energy Δ₀ separates e_g from t₂g. Electrons in t₂g have energy −0.4Δ₀ each; in e_g +0.6Δ₀ each. CFSE = (−0.4 × n_t₂g + 0.6 × n_eg) × Δ₀. For the broader coordination context see our coordination chemistry guide.

High-Spin vs Low-Spin Complexes

Electrons fill the split d-orbitals under two competing energies: the crystal field splitting energy Δ₀ vs the pairing energy P. If Δ₀ > P (strong field ligands: CN⁻, CO, NO₂⁻): electrons pair in t₂g before entering e_g → low-spin complex, fewer unpaired electrons, often diamagnetic or weakly paramagnetic. If Δ₀ < P (weak field ligands: F⁻, Cl⁻, H₂O, OH⁻): electrons follow Hund's rule and fill all five d-orbitals singly first → high-spin complex, maximum unpaired electrons, strongly paramagnetic. The spectrochemical series orders ligands by their Δ₀: I⁻ < Br⁻ < Cl⁻ < F⁻ < OH⁻ < H₂O < NH₃ < en < CN⁻.

Calculating CFSE: Worked Example

For [Fe(CN)₆]³⁻: Fe³⁺ is d⁵, CN⁻ is strong field → low-spin. Configuration: t₂g⁵ e_g⁰. CFSE = 5 × (−0.4Δ₀) = −2.0Δ₀. For [FeF₆]³⁻: Fe³⁺ is d⁵, F⁻ is weak field → high-spin. Configuration: t₂g³ e_g². CFSE = 3(−0.4) + 2(0.6) = −1.2 + 1.2 = 0. High-spin d⁵ has zero CFSE — the octahedral site provides no extra stability. This explains why Mn²⁺ (d⁵) prefers weak-field ligands and has no site preference energy.

Magnetic Moment and Unpaired Electrons

Magnetic moment μ = √(n(n+2)) BM (spin-only formula), where n is the number of unpaired electrons. For a d⁶ low-spin complex (t₂g⁶ e_g⁰): n = 0, μ = 0 (diamagnetic). For d⁶ high-spin (t₂g⁴ e_g²): n = 4, μ = √24 ≈ 4.9 BM. JEE commonly gives the magnetic moment and asks you to identify the d-electron count and spin state. Work backwards: from μ, find n; from n and the electron count, determine high vs low spin.

Colour and d-d Transitions

Transition metal complexes are coloured because electrons absorb visible light and jump from t₂g to e_g (d-d transition). The absorbed colour is complementary to the observed colour. Complexes with strong-field ligands absorb higher-energy (shorter wavelength) light: [Fe(CN)₆]⁴⁻ appears yellow (absorbs violet). Complexes with weak-field ligands absorb lower-energy light. d⁰ and d¹⁰ complexes have no available d electrons for transitions and are colourless (e.g. Ti⁴⁺, Zn²⁺). After mastering CFT, take a free mock test on coordination chemistry.