2 L. E. Orgel 



It is readily seen that the d^^ and dy^ orbitals have the same spatial relation- 

 ship to the ligands in their planes as does the d^y orbital to the ligands along 

 the X and y axes. It follows from the identity of their environments that the 

 d^y, d^g and dy^ orbitals have the same energy. Figure 1 also shows that the 

 d^2 orbital is directed straight at the ligands along the z axis, and hence it is 



0.0-' 



Fig. 1. The 5 d orbitals. 



plausible that it too is unstable. In fact calculation shows the d^i_y2 and d^i 

 orbitals to have the same energy. Thus we may draw the energy level diagram 

 of Fig. 2, which is the key to a great part of the ligand-field theory. 



Our approach so far has been electrostatic, but fortunately our conclusions 

 are not altered greatly when we come to take covalent bonding into account. 

 Just as Pauling showed for valence-bond theory, ligand field (molecular- 

 orbital) theory establishes that the 3d^i_yi . 3d^^, 4s and three 4p orbitals can 



