Crystal Field Theory (CFT)

 

Crystal Field Theory (CFT)

 As originally developed, crystal field theory was used to describe the electronic structure of metal ions in crystals, where they are surrounded by oxide ions or other anions that create an electrostatic field with symmetry dependent on the crystal structure. The energies of the d orbitals of the metal ions are split by the electrostatic field, and approximate values for these energies can be calculated.

CFT was developed in 1930 Shortly afterward, it was recognized that the same arrangement of charged or neutral electron pair donor species around a metal ion existed in crystals and coordination complexes. 

In order to understand clearly the interactions that are responsible for crystal or ligand field effects in transition metal complexes, it is necessary to know the geometrical relationships of the d orbitals. There are five wave functions that can be written for orbitals having the typical four-lobed form.

Crystal Field Effects in Octahedral Complexes

 When the d orbitals of a metal ion are placed in an octahedral field of ligand electron pairs,directed at the surrounding ligands, are raised in energy. The dxy, dxz, and dyz orbitals, which are directed between the surrounding ions, are relatively unaffected by the field. The resulting energy difference is identified as o( o for octahedral; some older references use the term 10Dq instead of o).

In case of free metal ion all the five d-orbitals are degenerate (these have the same energy).

Now consider an octahedral complex, [ML6]n+ in which the central metal cation, Mn+ is placed at the center of the octahedral and is surrounded by six ligands which reside at the six corners of the octahedral.

 Now suppose both the ligands on each of the three axes are allowed to approach towards the metal cation, Mn+ from both the ends of the axes. In this process the electrons in d-orbitals of the metal cation are repelled by the negative point charge or by the negative end of the dipole of the ligands. (Remember CFT the ionic ligands as negative point charges and neutral ligands as dipoles). This repulsion will raise the energy of all the five d-orbitals. Since the lobes of dz and d orbitals (eg orbitals) lie directly in the path of the approaching ligands, the electrons in these orbitals experience greater force of repulsion than those in dxy, dyz, and dzx orbitals (t2g orbitals) whose lobes are directed in space between the path of the approaching ligands (the energy of eg orbitals is increased while that of t2g is decreased (greater the repulsion, greater the increase in energy).

Thus we find that under the influence of approaching ligands, the five d-orbitals which were originally degenerate in free metallic cation are now split (or resolved) into two levels, t2g level which is triply degenerate and is of lower energy, and eg level which is doubly degenerate and is of higher energy.

The resulting energy difference is identified as o (o for octahedral) or 10Dq. This approach provides a simple means of identifying the d- orbital splitting found in coordination complexes and can be extended to include more quantitative calculations.




To gain some appreciation for the magnitude of△ o and how it may be measured,

let us consider the d1 complex, [Ti(H2O)6]3+. This ion exists in aqueous solution of Ti3+ and gives rise to a purple color. The single d electron in the complex will occupy the lowest energy orbital available to it (one of the three degenerate t2g orbitals). The purple color is the result of absorption of light and promotion of the t2g electron to the eg level.