Electronic Structure and Electron Transport Properties of Metal Ions 



be used to form six bonds between the metal and ligands. In the language of 

 molecular-orbital theory six stable bonding orbitals may be formed by com- 

 bining these metal orbitals with a orbitals on the ligands, for example, with 

 the unshared pair orbitals on amines. There are, however, also six unstable 

 antibonding orbitals which are not considered in Pauling's theory, but to 



d,a.y2, di« 



<lxy. dxz , dyz 



Fig. 2. The energies of the d orbitals in an octahedral environment. 



which we attach considerable importance. In addition to these we must 

 consider also the d^y, d^^, dy^ orbitals which take no part in g bonding. 

 The energies of these orbitals are illustrated in Fig. 3. 



In almost all metal complexes each ligand supplies two o electrons. There 

 are then twelve ligand electrons which just fill up the bonding orbitals (forming 



4p 

 4s 



3d 



-< 



\ \ 

 \ \ 



\ 



\ \ 

 \ \ 

 \ \ 



•Metal orbitols Molecutar orbitals Ligand orbitols 



Fig. 3. Molecular orbital energies for an octahedral complex. 



six bonds), leaving the d^^, d^.^, dy^ orbitals and the antibonding d^i_y2 and 

 dg2 combinations to accommodate any extra electrons which come from the 

 metal ion, e.g. 5 and 6 from Fe+++ and Fe++ ions, respectively. Thus the 

 molecular-orbital theory supplements the electrostatic theory by showing that 

 the d^2^y2 and d^z orbitals become mixed with ligand orbitals by covalent 

 bonding, but it does not change the fundamental energy level scheme of 

 Fig. 2. 



Double bonding involving the d^y, d^^ and dy^ orbitals (Fig. 4) further 

 changes the gap between the d^y, d^^ and dy^ orbitals on the one hand and the 



