3 .Crystal Field Splitting Energy

Crystal Field Splitting Energy

we know that an electron always prefers to occupy an orbital of a lower energy level. It is evident that if an octahedral complex contain one d electron, that electron will reside in one of the t2g orbitals. This orbital has an energy -4 Dq compared to the energy of the hypothetical degenerate orbitals of state II as shown in fig.. Thus, the complex will be 4 will be 4 Dq more stable than predicted by the pure electrostatic theory. Evidently, the energy of the complex would now be less the decrease in energy = 0- (- 4Dq) = 4Dq is called the Crystal Field Splitting Energy (CFSE) of the complex under consideration. So the CFSE can be defined as "The energy difference of the energy of orbital in which the d-block electron exist after splitting with the energy of the degenerated d orbitals." 

Calculation of  CFSE for octahedral compound

As above mentioned for the filling of first electron in the t2g is 4Dq. So for each electron entering into a t2g orbital, the CFSE is 4Dq. Hence, for each electron entering into an eg orbital the destabilistion energy would be 6Dq. Working on this bases, it is possible to calculate CFSE for various metal ions in octahedral complex. 

For example , for a d2 system, the two electrons will occupy t2g orbitals. The CFSE = 0 - 2(-4Dq) = 8Dq. Similarly, for a d3 system, CFSE= 0-3 (-4Dq) = 12Dq. 

However for the d4 system there are two possibilities :

1. All the four electrons may occupy t2g  orbitals. One electron obviously gets paired. The electronic configuration may be written as (t2g)4 
2. three electrons occupy t2g orbitals and one electron obviously gets paired . The electronic configuration may be written as (t2g)3(eg)1.

The actual configuration may be decided on the basis of 🔺0 and the pairing energy (P) i.e. the energy required to pair the electrons with one another. the configuration (1) is possible if 🔺0 > P. In this case, the complex has less number of unpaired electrons and is called low spin complex.

On the other hand, configuration (2) is possible if  🔺0 < P. In this case, the maximum number of electron remain unpaired and the complex is called high spin complex.

As shown above, a low spin  complex means in case first has an energy  = 4(-4Dq) = -16Dq. However, If we take into account the pairing energy (P)  also, the net energy becomes = -16Dq +P and in that case CFSE becomes = 0-(-16Dq + P) = 16Dq - P. On the other hand, for means in case second, the energy = 3(-Dq) + 1(6Dq) = - 6Dq and CFSE = 0-(-6Dq).

Calculation of  CFSE for Tetrahedral compound

The CFSE for tetrahedral complexes having different electronic configuration can also be calculated by the same procedure as for the octahedral complexes. But no tetrahedral complex with low spin configuration has been formed. This is due to the fact the crystal field splitting in tetrahedral field is quite small and it is always less than the pairing energy. Therefore, pairing does not occur and the complex are high spin complex.

Here we have not taken into account the inter electron repulsion between d electron of metal ion for calculating these CFSEs