MP Board · Class 12 · Chemistry · Coordination CompoundsCalculate the crystal field stabilization energy (CFSE) for a $d^4$ octahedral coordination compound in terms of $\Deltao$ and pairing energy ($P$), considering both weak field (high spin) and strong field (low spin) cases. Also, explain the factors affecting crystal field splitting energy.

Crystal Field Stabilization Energy (CFSE) Calculation for $d^4$ Configuration\nIn an octahedral crystal field, the $d$-orbitals split into two sets: lower energy $t_{2g}$ orbitals (3 orbitals) and higher energy $e_g$ orbitals (2 orbitals).

• Energy of each $t_{2g}$ electron = $-0.4 \Delta_o$
• Energy of each $e_g$ electron = $+0.6 \Delta_o$
• CFSE formula: $\text{CFSE} = [-0.4(n_{t_{2g}}) + 0.6(n_{e_g})]\Delta_o + mP$\nwhere $n_{t_{2g}}$ and $n_{e_g}$ are the number of electrons in $t_{2g}$ and $e_g$ orbitals respectively, and $m$ is the number of pairing energy terms.

Case 1: Weak Field Ligand (High Spin, $\Delta_o < P$)

• Electrons enter according to Hund's rule. The fourth electron enters the $e_g$ level because pairing energy $P$ is greater than $\Delta_o$.
• Electron distribution: $t_{2g}^3 e_g^1$.
• Calculation: $$\text{CFSE} = [(-0.4 \times 3) + (0.6 \times 1)]\Delta_o + 0P$$ $$\text{CFSE} = [-1.2 + 0.6]\Delta_o = -0.6 \Delta_o$$

Case 2: Strong Field Ligand (Low Spin, $\Delta_o > P$)

• Pairing energy $P$ is less than $\Delta_o$, so pairing occurs in the lower $t_{2g}$ level before filling $e_g$.
• Electron distribution: $t_{2g}^4 e_g^0$.
• Calculation: $$\text{CFSE} = [(-0.4 \times 4) + (0.6 \times 0)]\Delta_o + 1P$$ $$\text{CFSE} = [-1.6]\Delta_o + 1P = -1.6 \Delta_o + P$$

Factors Affecting Crystal Field Splitting Energy ($\Delta_o$)

• Nature of the Ligand: Strong field ligands cause larger splitting than weak field ligands (Spectrochemical series).
• Charge on Metal Ion: Higher oxidation state of the metal ion leads to larger splitting due to stronger attraction for ligands.
• Size of Metal Orbital: Transition elements of 4d and 5d series show larger splitting values compared to 3d series elements because of larger spatial expansion of their $d$-orbitals.