The tetrahedral crystal field

  So far we have restricted the discussion to octahedral complexes; we now turn to the tetrahedral crystal field. Figure 1.1 shows a convenient way of relating a tetrahedron to a Cartesian axis set. With the complex in this orientation, none of the metal d orbitals points exactly at the ligands, but the d_xy, d_yz and _dxz orbitals come nearer to doing so than the d_z² and d_x²_-y² orbitals. For a regular tetrahedron, the splitting of the d orbitals is inverted compared with that for a regular octahedral structure, and the energy difference (Δ_tet) is smaller.

Fig. 1.1 The relationship between a tetrahedral ML₄ complex and a cube; the cube is readily related to a Cartesian axis set. The ligands lie between the x, y and z axes; compare this with an octahedral complex, where the ligands lie on the axes.

   If all other things are equal (and of course, they never are), the relative splittings Δ_oct and Δ_tet are related by equation 1.1.

                          (1.1)

   Figure 1.2 compares crystal field splitting for octahedral and tetrahedral fields; remember, the subscript g in the symmetry labels  is not needed in the tetrahedral case.

   Since Δ_tet is significantly smaller than Δ_oct , tetrahedral complexes are high-spin. Also, since smaller amounts of energy are needed for an t₂←e transition (tetrahedral) than for an eg←t₂g transition (octahedral), corresponding octahedral and tetrahedral complexes often have different colours. Jahn–Teller effects in tetrahedral complexes are illustrated by distortions in d⁹ (e.g. [CuCl₄]^2-) and high-spin d⁴ complexes. A particularly strong structural distortion is observed in [FeO₄]^4-.

Fig. 1.2 Crystal field splitting diagrams for octahedral (left-hand side) and tetrahedral (right-hand side) fields.