Chapter 20, Problem 20.112SP

Interpretation Introduction

Interpretation:

The energy level diagram for 3d-orbitals of titanium in ${[Ti{(H_{2}O)}_6]}^{3+}$ should be dawn and its crystal field splitting should be explained along with the reason for its coloured properties.

Concept introduction:

In ground state all the five d-orbitals are degenerate and have similar energy but as soon as the ligand approaches to them, the energy levels split.
The difference in energies of all the five d-orbitals is explained on the basis of crystal field theory and its splitting energy.
Actually, the d-orbitals have five energy levels which are degenerate in ground state. But, the energy levels have differently oriented lobes as follows:
The $d_{xy}$ -orbital has its lobes in between X-Y axes.
The $d_{xz}$ -orbital has its lobes in X-Z axes.
The $d_{yz}$ -orbital has its lobes in Y-Z axes.
The $d_{Z^2}$ -orbital has its two lobes in Z- axis while a donut shaped ring cloud is found along XY-plane.
The $d_{x^2-y^2}$ -orbital has its lobes on the X-axis and Y-axis.
Hence, it creates set of two types of orbitals; first is orbitals in plane and second is orbitals along axes.
Orbitals in planes give t₂ set ( $d_{xy}$ , $d_{xz}$ and $d_{yz}$ ) while the orbitals along axes give e-set ( $d_{Z^2}$ and $d_{x^2-y^2}$ ). Initially, all these orbitals have same energy but the difference and splitting starts as per the approach of ligands and the electrostatic attraction between the d-orbital lobes and electrons of ligands.