Question

What is crystal field splitting energy? How does the magnitude of ${\Delta }_0$ decide the actual configuration of d orbitals in a coordination entity?

Answer 1

The crystal field stabilisation energy (CFSE) is the gain in the energy achieved by preferential filling up of orbitals by electrons. It is usually less than or equal to 0. When it is equal to 0, the complex is unstable. The magnitude of CFSE depends on the number and nature of ligands and the geometry of the complex.
Consider octahedral $d^4$ system. Three electrons are in lower $t_{2g}$ level. Fourth electron will enter into higher $e_g$ level if ${\Delta }_o<P$. Fourth electron will enter into lower $t_{2g}$ level if ${\Delta }_o>P$. Here, P is the pairing energy. It is the energy required to pair two electrons against electron electron repulsion in the same orbital.