Order of orbital energy levels in crystal field theory

For an octahedral or tetrahedral environment we have already seen that five, originally degenerate, d-orbitals are split into two sets which have different energies one set is dsi and (called eg or e orbitals, depending on the environment) and the other is dcyi dM, and dyt (called tt9 or t2 orbitals). To investigate the relative order of the two new energy levels, it is only necessary to look at the effect of the environment on one orbital of each set, say d i i and day. 

In crystal field theory each ligand is approximated as a point charge or a point dipole and each metal-ligand interaction is taken to be purely electrostatic. So our problem is reduced to one of investigating the effect of point charges (or point dipoles) arranged tetrahedrally or octahedrally about an electron in a dai y or a dXI orbital. 

The difference between the effect of a tetrahedral arrangement of ligands on an electron in a dai Fi (e-type) orbital and on an electron in a dm ( -type) orbital is perhaps not quite so obvious as the previous case. However, a study of Fig. 12-6.3 suggests that an electron in a 

The ligands which are directly above and below the origin of the axes are not shown. 

The black circles indicate ligands below the xy plane and the shaded circles indicate ligands above it. Sec Fig. 11 5.2 for the relations between the axe3 and the ligands. 

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Order of orbital energy levels in crystal field theory... 

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