CBSE · Class 12 · Chemistry · Coordination CompoundsExplain Crystal Field Theory (CFT) for octahedral coordination entities. How does crystal field splitting occur in octahedral complexes? Discuss the factors affecting the magnitude of crystal field splitting energy ($\Deltao$) and write the electronic configuration for $d^4$ ions when $\Deltao > P$ and $\Deltao

Crystal Field Theory (CFT) in Octahedral Complexes

\nCrystal Field Theory is an electrostatic model which considers the metal-ligand bond to be ionic arising from electrostatic forces between the positive metal ion and negative ligands (or negative ends of dipolar ligands like $NH_3$ and $H_2O$).

Crystal Field Splitting in Octahedral Complexes

1. In an octahedral complex, the metal ion is surrounded by six ligands at the vertices of an octahedron.
2. The five d-orbitals of the metal ion, which are degenerate in a free isolated metal ion, experience different electrostatic repulsions when approaching ligands.
3. The $d_{xy}$, $d_{yz}$, and $d_{xz}$ orbitals (collectively called $t_{2g}$ set) lie in between the coordinate axes, away from the approaching ligands. Thus, they experience lower repulsion and are lowered in energy.
4. The $d_{x^2-y^2}$ and $d_{z^2}$ orbitals (collectively called $e_g$ set) lie along the axes, directly in the path of the incoming ligands. Thus, they experience higher repulsion and are raised in energy.
5. This splitting of degenerate d-orbitals into two sets ($t_{2g}$ and $e_g$) under the influence of a ligand field is called Crystal Field Splitting, denoted by $\Delta_o$.
6. The energy of $t_{2g}$ orbitals decreases by $0.4\Delta_o$ (-$4q$), and the energy of $e_g$ orbitals increases by $0.6\Delta_o$ (+$6q$) relative to the barycenter.

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

• Nature of the ligand: Strong field ligands (e.g., $CN^-$, $CO$) cause large splitting, while weak field ligands (e.g., halides, $H_2O$) cause small splitting. This is arranged in the Spectrochemical Series.
• Oxidation state of the metal ion: Higher oxidation states result in a higher positive charge on the metal ion, attracting ligands more closely and increasing $\Delta_o$.
• Nature of the metal ion: Splitting increases down a group of transition elements due to the greater spatial extension of d-orbitals.
• Coordination number: The splitting is dependent on the geometry of the complex.

Electronic Configuration for $d^4$ Ions\nFor a $d^4$ system, the distribution of electrons in $t_{2g}$ and $e_g$ depends on the relative values of crystal field splitting energy ($\Delta_o$) and pairing energy ($P$):

1. When $\Delta_o > P$ (Strong field ligand): The energy required to pair electrons is less than the energy required to promote an electron to the $e_g$ orbital. Therefore, the fourth electron pairs up in the $t_{2g}$ orbital. Configuration: $t_{2g}^4 e_g^0$ (Low spin complex).
2. When $\Delta_o < P$ (Weak field ligand): The energy required to pair electrons is greater than the energy required to promote an electron. Therefore, the fourth electron enters the $e_g$ orbital. Configuration: $t_{2g}^3 e_g^1$ (High spin complex).