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Crystal Field Splitting Energy (CFSE)

Understanding d-orbital splitting in Octahedral and Tetrahedral Fields.

By chemca Team • Updated Jan 2026

Crystal Field Theory (CFT) explains the electronic structure of transition metal complexes. It considers the interaction between the metal ion and ligands as purely electrostatic. The approach of ligands causes the degeneracy of the d-orbitals to break.

1. Crystal Field Splitting in Octahedral Complexes ($\Delta_o$)

The $t_{2g}$ and $e_g$ Sets

In an octahedral field (6 ligands along the axes), the d-orbitals split into two sets:

• $e_g$ (Higher Energy): Orbitals along the axes ($d_{x^2-y^2}, d_{z^2}$). Repulsion is maximum. Energy rises by $+0.6 \Delta_o$.
• $t_{2g}$ (Lower Energy): Orbitals between the axes ($d_{xy}, d_{yz}, d_{zx}$). Repulsion is minimum. Energy drops by $-0.4 \Delta_o$.

CFSE Calculation Formula:

$$ CFSE = [-0.4(n_{t2g}) + 0.6(n_{eg})] \Delta_o + nP $$

Where $n_{t2g}, n_{eg}$ are number of electrons in respective orbitals, and $P$ is Pairing Energy.

2. High Spin vs Low Spin (The Condition)

For $d^1, d^2, d^3$, electrons simply fill $t_{2g}$. For $d^4$ to $d^7$, two possibilities exist depending on the ligand strength.

Strong Field Ligand (SFL)

Causes large splitting ($\Delta_o > P$).

Electrons pair up in $t_{2g}$ before going to $e_g$.

Result: Low Spin Complex.

Ex: $CN^-, CO, NH_3$ (usually)

Weak Field Ligand (WFL)

Causes small splitting ($\Delta_o < P$).

Electrons enter $e_g$ before pairing.

Result: High Spin Complex.

Ex: $F^-, Cl^-, H_2O$

Spectrochemical Series (Increasing Field Strength):
$I^- < Br^- < SCN^- < Cl^- < F^- < OH^- < H_2O < NCS^- < NH_3 < en < CN^- < CO$

3. Crystal Field Splitting in Tetrahedral Complexes ($\Delta_t$)

Inverted Splitting

In a tetrahedral field (4 ligands between axes), the splitting pattern is reversed:

• $t_2$ (Higher Energy): Energy rises by $+0.4 \Delta_t$.
• $e$ (Lower Energy): Energy drops by $-0.6 \Delta_t$.

Note: 'g' subscript is dropped because tetrahedral lacks center of symmetry.

Relationship: $$ \Delta_t = \frac{4}{9} \Delta_o $$

Important: Since $\Delta_t$ is small (always $\Delta_t < P$), tetrahedral complexes are Almost Always High Spin.

CFSE Formula:

$$ CFSE = [-0.6(n_e) + 0.4(n_{t2})] \Delta_t $$

4. Example Calculations

Example 1: $[Fe(CN)_6]^{4-}$ (Octahedral)
Fe is in +2 state ($3d^6$). $CN^-$ is SFL ($\Delta_o > P$).
Configuration: $t_{2g}^6 e_g^0$ (All paired).

$CFSE = [-0.4(6) + 0.6(0)]\Delta_o + 2P \text{ (extra pairs)}$
$= -2.4 \Delta_o + 2P$

Example 2: $[Fe(H_2O)_6]^{2+}$ (Octahedral)
Fe is in +2 state ($3d^6$). $H_2O$ is WFL ($\Delta_o < P$).
Configuration: $t_{2g}^4 e_g^2$ (High spin).

$CFSE = [-0.4(4) + 0.6(2)]\Delta_o = [-1.6 + 1.2]\Delta_o = -0.4 \Delta_o$

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