Question

Apply the crystal field theory to an octahedral complex.

Answer 1

Crystal Field Theory (CFT) is a model used to explain the color, magnetism, and stability of transition metal complexes. When applied to octahedral complexes, it describes how the d-orbitals of a central metal ion are affected by the approach of six ligands arranged at the corners of an octahedron. 

1. d-Orbital Splitting: In a free metal ion, the five d-orbitals are degenerate (i.e., have the same energy). In an octahedral field, six ligands approach along the x, y, and z axes. This causes the d-orbitals to split into two sets:
   • t₂g (lower energy): d_xy, d_yz, d_xz
   • e_g(higher energy): d_x²−y², d_z²
     The energy difference between these two sets is called the crystal field splitting energy (Δ_o).
2. Electron Configuration in Split Orbitals: Electrons fill the lower-energy t₂g orbitals first. Depending on the magnitude of Δ_o and the pairing energy, electrons may pair in t₂g or occupy the e_g orbitals (leading to either low-spin or high-spin configurations).
3. Factors Affecting Splitting: Nature of the metal ion (charge and size). Nature of the ligands (as explained by the spectrochemical series; e.g., CN⁻ > NH₃ > H₂O > F⁻ > Cl⁻). Oxidation state of the metal: Higher oxidation states lead to larger Δ_o.
4. Consequences of Splitting: The energy absorbed for electronic transitions (t₂g to e_g) often lies in the visible region, giving colored complexes. Magnetic properties depend on the number of unpaired electrons (predictable using CFT). Greater crystal field stabilization energy (CFSE) leads to more stable complexes.
5. Example: In [Fe(CN)₆]³⁻ (low-spin complex), Fe³⁺ has a 3d⁵ configuration. With strong-field ligands like CN⁻, electrons pair in t₂g orbitals, resulting in only one unpaired electron. In [FeF₆]³⁻ (high-spin complex), with weak-field ligands like F⁻, electrons occupy both t₂g and e_g, resulting in five unpaired electrons.