Question

The Valence Bond Theory (VBT) explains the formation, magnetic behaviour and geometry of coordination compounds. The Crystal Field Theory (CFT) of coordination compounds is based on the effect of different crystal fields (provided by the ligands taken as point charges), on the degeneracy of d-orbital energies of the central metal atom/ion. The splitting of the d-orbitals provides different electronic arrangements in strong and weak crystal fields. Answer the following questione

29(a). In octahedral crystal field, energies of which d-orbitals will be raised when ligands approach? Give reason.

Hint:

Octahedral: $e_g$ is high energy. Tetrahedral: $t_2$ is high energy. They are essentially inverted because of ligand approach directions.

Answer 1

Step 1: Conceptual Overview:
Crystal field theory explains the behavior of transition metal complexes, particularly how the arrangement of ligands around the metal ion affects the energies of the metal's d-orbitals. Crystal field splitting occurs due to the interaction between the electric fields of the ligands and the metal's d-electrons. This phenomenon leads to the splitting of degenerate d-orbitals into sets with different energy levels.
Step 2: Detailed Explanation:
In an octahedral crystal field, six ligands approach the central metal ion symmetrically along the x, y, and z axes. The d-orbitals of the metal ion can be classified into two sets: \( e_g \) and \( t_{2g} \). The \( e_g \) set consists of the \( d_{x^2 - y^2} \) and \( d_{z^2} \) orbitals, which are oriented directly along the axes. On the other hand, the \( t_{2g} \) set consists of the \( d_{xy} \), \( d_{xz} \), and \( d_{yz} \) orbitals, which point between the axes.
Due to the electrostatic repulsion between the metal's d-electrons and the lone pairs on the ligands, the orbitals in the \( e_g \) set experience stronger repulsion than those in the \( t_{2g} \) set. This is because the ligands are positioned along the x, y, and z axes, where the \( e_g \) orbitals are located. Consequently, the repulsion between the ligands and the \( e_g \) orbitals increases their energy, raising it compared to the \( t_{2g} \) orbitals.
This results in crystal field splitting, where the \( e_g \) orbitals become higher in energy, and the \( t_{2g} \) orbitals remain lower in energy. This splitting is fundamental for understanding the color, magnetic properties, and stability of transition metal complexes, as the energy difference between the \( e_g \) and \( t_{2g} \) orbitals affects the absorption of light and electron transitions.
Step 3: Final Conclusion:
The energy of the \( e_g \) orbitals is increased due to the direct axial repulsion from the ligands in an octahedral field, making them higher in energy than the \( t_{2g} \) orbitals. This leads to crystal field splitting, which is a key factor in determining the properties of transition metal complexes.