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19.3 Crystal Field Theory

Jun 17, 2025

Overview

This lecture introduces crystal field theory as a model to explain the spectroscopic and magnetic properties of coordination compounds, focusing on d-orbital splitting, electron configurations, and how these relate to color and magnetism in transition metal complexes.

Crystal Field Theory (CFT)

  • CFT explains behaviors of transition metal complexes not described by valence bond theory, especially colors and magnetic properties.
  • CFT models ligands and metals as point charges, focusing on electrostatic interactions and ignoring covalent character.
  • In an uncomplexed metal ion, all five d orbitals are degenerate (same energy).
  • In octahedral complexes, ligands approach along axes, splitting d orbitals into higher-energy eg and lower-energy t2g sets.
  • Eg orbitals (dz², dx²-y²) point directly at ligands and are higher in energy; t2g orbitals (dxy, dxz, dyz) point between ligands.
  • The energy difference between eg and t2g is the crystal field splitting energy (Δoct).

Factors Affecting Crystal Field Splitting

  • Δoct depends on the metal's identity, charge, d orbital shell, and the type of ligands.
  • Ligands are ranked in the spectrochemical series from weak- to strong-field: I⁻ < Br⁻ < Cl⁻ < F⁻ < H₂O < NH₃ < en < NO₂⁻ < CN⁻.
  • Strong-field ligands (e.g., CN⁻) cause larger splitting, leading to low-spin complexes; weak-field ligands (e.g., H₂O) cause smaller splitting, leading to high-spin complexes.

Electron Configurations & Spin States

  • Electrons fill orbitals to minimize energy; pairing energy (P) also affects arrangement.
  • If Δoct > P, electrons pair in t2g (low spin); if Δoct < P, electrons singly occupy all orbitals first (high spin).
  • Examples: [Fe(CN)₆]⁴⁻ is low-spin (all electrons paired); [Fe(H₂O)₆]²⁺ is high-spin (four unpaired electrons).
  • High- vs. low-spin arrangements differ for d⁴, d⁵, d⁶, and d⁷ octahedral complexes.

Other Coordination Geometries

  • Tetrahedral complexes: Ligand arrangement leads to a different splitting pattern; usually all are high-spin because Δtet is small (~4/9 Δoct).
  • Square planar complexes: Removal of two ligands (z-axis) creates a unique orbital energy pattern, often favoring low-spin.

Magnetic Properties

  • Unpaired electrons make complexes paramagnetic (attracted to magnetic fields), while all paired electrons result in diamagnetic substances (repelled).
  • The number of unpaired electrons determines the size of the magnetic moment, verifiable by experimental measurement.

Color in Coordination Compounds

  • Color arises when d-d transitions absorb visible light; observed color is complementary to the absorbed wavelength.
  • Changing ligands or metal oxidation states alters Δoct, shifting which wavelengths are absorbed (and thus the color).
  • d¹⁰ complexes (e.g., Cu⁺) are often colorless; partially filled d orbitals (e.g., Cu²⁺) yield colored compounds.

Key Terms & Definitions

  • Crystal Field Theory (CFT) — model explaining properties of metal complexes by electrostatic ligand-metal interactions.
  • Crystal field splitting (Δoct) — energy gap between eg and t2g d orbitals in an octahedral field.
  • Spectrochemical series — order of ligands by their field strength effects.
  • High-spin complex — maximum unpaired electrons, occurs with weak-field ligands.
  • Low-spin complex — minimum unpaired electrons, occurs with strong-field ligands.
  • Pairing energy (P) — energy required to pair two electrons in one orbital.
  • Paramagnetic — substance with unpaired electrons, attracted to magnetic fields.
  • Diamagnetic — substance with all paired electrons, slightly repelled by magnetic fields.

Action Items / Next Steps

  • Practice predicting high/low-spin configurations with different ligands and d electron counts.
  • Review and apply the spectrochemical series to solve color and magnetism problems.
  • Complete any assigned problems on electron configurations of transition metal complexes.