CFT — Octahedral vs Tetrahedral Splitting — Notes

Feature	Octahedral Complex	Tetrahedral Complex
Number of ligands	6	4
Lower energy set	t_{2}g (dxy, dxz, dyz)	e ( $dz^{2}$ , $dx^{2}$ - $y^{2}$ )
Higher energy set	eg ( $dz^{2}$ , $dx^{2}$ - $y^{2}$ )	t_{2} (dxy, dxz, dyz)
Splitting energy symbol	$\Delta o$	$\Delta t$
Relative magnitude	$\Delta o$ (reference)	$\Delta t$ ≈ 4/9 $\Delta o$
Order inversion	No	Yes — completely inverted
Typical spin state	Low or high spin (depends on ligand)	Almost always high spin
Pairing energy consideration	Relevant for $\Delta o$ vs P comparison	Usually $\Delta t$ < P, so no pairing
Example	[Fe(CN)_{6}]^{4-}	[ $NiCl_{4}$ ]^{2-}

Why $\Delta t$ < $\Delta o$ :

Tetrahedral has 4 ligands vs 6 in octahedral — fewer interactions.
In tetrahedral geometry, ligands do NOT approach along the d-orbital axes (they approach between axes), so the interaction is weaker.
The mathematical result: $\Delta_t = \frac{4}{9}\Delta_o$

Consequence: Tetrahedral complexes are almost exclusively high spin because $\Delta t$ is too small to force electron pairing.

d-orbital splitting diagram (Wikimedia):

Crystal Field Splitting — Octahedral Field

E Free Ion (no ligand field) d orbitals (all degenerate) Octahedral Field [$ML_{6}$] complex 6 ligands approach eg $dx^{2}$-$y^{2}$, $dz^{2}$ t2g dxy, dxz, dyz barycenter +0.6$\Delta$o −0.4$\Delta$o $\Delta$o (Crystal Field Splitting Energy) Octahedral: 6 ligands along ±x, ±y, ±z axes → eg destabilised, t2g stabilised