What is pairing energy $(P)$? Explain the distribution of $d^n$ ($n=1$ to $10$) electrons in high spin and low spin octahedral complexes.

(N/A) Pairing energy $(P)$ is the energy required to pair two electrons in a single orbital.
In an octahedral complex,the $d$-orbitals split into $t_{2g}$ (lower energy) and $e_g$ (higher energy) sets.
For $d^1, d^2, d^3$ configurations,electrons occupy $t_{2g}$ orbitals singly according to Hund's rule.
For $d^4$ to $d^7$ configurations,the distribution depends on the relative values of crystal field splitting energy $(\Delta_0)$ and pairing energy $(P)$:
$(i)$ If $\Delta_0 < P$ (weak field ligands),the energy required to pair is higher than the energy to promote an electron to the $e_g$ level. This results in high spin complexes (e.g.,$d^4$ is $t_{2g}^3 e_g^1$).
$(ii)$ If $\Delta_0 > P$ (strong field ligands),the energy required to pair is lower than the energy to promote an electron. This results in low spin complexes (e.g.,$d^4$ is $t_{2g}^4 e_g^0$).
For $d^8, d^9, d^{10}$ configurations,the $t_{2g}$ and $e_g$ orbitals are filled according to Hund's rule regardless of the ligand field strength.