Crystal field splitting patterns of the 4f orbitals

If we place six ligands at the centers of the faces of a cube, as shown in Fig. 8.11.3, it can be readily seen that the (2u orbitals (x3, y3, z3) have lobes pointing directly toward the ligands. Hence they have the highest energy. Also, 

Splitting pattern of the 4f orbitals in a tetrahedral crystal field. 

The splitting pattern of the 4f orbitals in a tetrahedral crystal field can be deduced in a similar manner. If we adopt the coordinate system shown in Fig. 8.11.4, we can obtain the splitting pattern shown in the same figure. As expected the 1 3 3 pattern for the tetrahedral crystal field is just the reverse of the 3 3 1 pattern of the octahedral field. Also, the symmetry classification of the orbitals in a tetrahedral complex can be readily obtained from the character table of the Td group. 

Cotton, G Wilkinson, C. A. Murillo and M. Bochmann, Advanced Inorganic Chemistry, 6th edn., Wiley, New York, 1999. 

Greenwood and A Earnshaw, Chemistry of the Elements, 2nd edn., Butterworth-Heinemann, Oxford, 1997. 

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