The Jahn-Teller effect occurs in non-linear molecules where the electronic configuration creates degeneracy (unequal occupation of degenerate orbitals), leading to geometric distortion to lower symmetry and energy. It is observed when the $t_{2g}$ or $e_g$ orbitals are unsymmetrically filled.

1. Analyze High Spin Configurations (Octahedral Field):

• $d^4$: Configuration is $t_{2g}^3 e_g^1$. The $e_g$ level is unsymmetrically filled (1 electron in 2 orbitals). Shows strong Jahn-Teller distortion .
• $d^7$: Configuration is $t_{2g}^5 e_g^2$. The $t_{2g}$ level is unsymmetrically filled (5 electrons in 3 orbitals). Shows Jahn-Teller distortion.
• $d^9$: Configuration is $t_{2g}^6 e_g^3$. The $e_g$ level is unsymmetrically filled (3 electrons in 2 orbitals). Shows strong Jahn-Teller distortion .
• $d^8$: Configuration is $t_{2g}^6 e_g^2$. The lower $t_{2g}$ set is completely filled (symmetric), and the upper $e_g$ set is exactly half-filled (symmetric). Because both sets of orbitals are symmetrically occupied, there is no electronic degeneracy .

2. Conclusion: The $d^8$ high spin configuration does not exhibit the Jahn-Teller effect.