Splitting of d Orbitals in Tetrahedral and Other Symmetries

Perhaps only slightly less common than octahedral symmetry is tetrahedral symmetry. We now examine the d orbital splitting in this environment. The story is much the same as above, except that it is now convenient to place the four point charges of the tetrahedron as shown in Fig. 3-6. Here ligands are put at alternate 

Note the absence of the g subscripts here. Although the d orbitals are still centro-symmetric, the tetrahedral environment lacks a centre of inversion. The d orbitals are therefore not classified with respect to a symmetry element which doesn t exist the absence of the g subscript does not imply the opposite - i.e. u (ungerade or odd). 

In practice, these conditions of radial waveforms and bond lengths will not be met exactly, so that a rough rule is that Ad 0.5 Act in real systems. Once again, only one electronic, d-d absorption is expected (and observed), although much shifted towards the red relative to that in an analogous octahedral complex. 

The discussion above might have pertained for example, to the energies and electronic spectra of titanium(iii) compounds. The same ideas can be applied with just one modification to the i/-electron properties of copper(ii) complexes and other 

Some prefer to write 4,ei = - % A ct in order to emphasize the inversion of t and e orbital subsets. However, if A and Z, e, are defined as the orbital splittings, it is probably best to omit the sign. 

---