MP Board · Class 12 · Chemistry · Coordination CompoundsDefine Crystal Field Splitting Energy ($\Deltao$) for octahedral complexes. Explain the factors affecting crystal field splitting and write the electronic configuration for $d^4$ ions in octahedral fields when $\Deltao > P$ and $\Deltao

Definition of Crystal Field Splitting Energy ($\Delta_o$)\nCrystal Field Splitting Energy ($\Delta_o$) in an octahedral coordination entity is defined as the energy difference between the two sets of $d$-orbitals ($t_{2g}$ and $e_g$) resulting from the splitting of degenerate $d$-orbitals under the influence of an octahedral ligand field. When ligands approach the central metal ion, the degeneracy of the five $d$-orbitals is lifted. The orbitals directed along the axes ($dx^2-y^2$ and $dz^2$, designated as $e_g$) experience greater electrostatic repulsion from the ligands and are raised in energy, whereas the orbitals directed between the axes ($dxy$, $dyz$, and $dxz$, designated as $t_{2g}$) are lowered in energy relative to the barycenter. The magnitude of this energy gap is denoted by $\Delta_o$.

Factors Affecting Crystal Field Splitting

• Nature of the Ligand: Ligands can be arranged in a series in order of increasing field strength, known as the Spectrochemical Series. Strong field ligands (e.g., $CO$, $CN^-$) cause a large splitting energy ($\Delta_o$), whereas weak field ligands (e.g., $I^-$, $Br^-$, $Cl^-$) cause a small splitting energy.
• Oxidation State of the Metal Ion: As the charge (oxidation state) on the metal ion increases, the ligands are attracted more strongly, leading to a smaller metal-ligand bond distance and consequently a larger value of $\Delta_o$.
• Nature of the Metal Ion: Splitting increases down a group of transition elements due to the greater spatial extension of $d$-orbitals in heavier transition metals.
• Coordination Number: For the same metal and ligand, the crystal field splitting in tetrahedral complexes ($\Delta_t$) is roughly equal to $4/9$ of that in octahedral complexes ($\Delta_o$).

Electronic Configuration for $d^4$ Ions in Octahedral Fields\nWhen filling the $d$-orbitals of a $d^4$ ion in an octahedral field, the occupation of $t_{2g}$ and $e_g$ orbitals depends on the relative values of crystal field splitting energy ($\Delta_o$) and pairing energy ($P$, the energy required to pair two electrons in an orbital):

1. When $\Delta_o > P$ (Strong Field Ligand):

   • The energy gap between $t_{2g}$ and $e_g$ is greater than the pairing energy.
   • It is energetically more favorable for the fourth electron to pair up in the lower energy $t_{2g}$ orbital rather than jump to the higher energy $e_g$ orbital.
   • Electronic Configuration: $t_{2g}^4 e_g^0$. This forms a low-spin complex.

2. When $\Delta_o < P$ (Weak Field Ligand):

   • The crystal field splitting energy is less than the pairing energy.
   • It requires less energy for the fourth electron to occupy one of the higher-energy $e_g$ orbitals than to overcome the electron-electron repulsion and pair up in a $t_{2g}$ orbital.
   • Electronic Configuration: $t_{2g}^3 e_g^1$. This forms a high-spin complex.