Tetrahedron, crystal field splitting

We will briefly consider the crystal field splitting of the rf-orbitals in four-coordinate, tetrahedral complexes. The cube, octahedron and tetrahedron are related geometrically. Octahedral coordination results when ligands are placed in the centers of cube faces, while tetrahedral coordination results when ligands are placed on alternate comers of a cube, as shown in Fig. 10.9. 

When a transition metal ion is surrounded by a tetrahedron of oxygen ions (Figure S4.10), the crystal field splitting is reversed. In this case, the xy, d. z dyj, orbitals, now called the t2 group. 

Fig. 4. Geometric model illustrating the nature of the splitting of d levels of the central metal atom due to the effect of the crystal field of adjacent atoms a) tetrahedral surroundings b) distorted tetrahedron corresponding to the first coordination sphere of atoms in CrSi2.

The separation between the e and t2 levels in a tetrahedron is smaller than the separation between t2g and eg levels in an octahedron. Within the assumptions of crystal field theory the e-t2 splitting in a tetrahedron is 4/9 (44%) of the value of the t2g-eg splitting in an octahedron. While many assumptions used in simple crystal field theory are not completely valid, a value of 40 to 50% is a reasonable rough approximation. As an example the t2g-e. splitting in Ti(H20)4 is 1.1 eV. 

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