key term - $t_{2g}$

Definition

$t_{2g}$ refers to the set of three degenerate d-orbitals in a transition metal complex that have lower energy compared to the $e_{g}$ set of d-orbitals. This term is particularly important in the context of understanding the spectroscopic and magnetic properties of coordination compounds.

5 Must Know Facts For Your Next Test

1. The $t_{2g}$ orbitals are lower in energy compared to the $e_{g}$ orbitals due to their different orientations relative to the ligands in the coordination complex.
2. The degree of crystal field splitting, and hence the energy difference between the $t_{2g}$ and $e_{g}$ sets, depends on the strength of the ligand field.
3. The occupation of the $t_{2g}$ and $e_{g}$ orbitals determines the magnetic properties of the coordination compound, such as its spin state and magnetic moment.
4. The electronic transitions between the $t_{2g}$ and $e_{g}$ orbitals give rise to characteristic absorption bands in the visible and near-infrared regions of the electromagnetic spectrum.
5. The $t_{2g}$ orbitals are more stabilized in octahedral complexes, while in tetrahedral complexes, the $e_{g}$ orbitals are more stabilized.

Review Questions

• Explain the relationship between the $t_{2g}$ orbitals and the electronic structure of transition metal complexes.
  • The $t_{2g}$ orbitals are a set of three degenerate d-orbitals in a transition metal complex that have lower energy compared to the $e_{g}$ set of d-orbitals. This energy splitting between the $t_{2g}$ and $e_{g}$ orbitals is a result of the crystal field splitting caused by the interaction between the metal d-orbitals and the ligands. The occupation of these orbitals determines the spin state and magnetic properties of the coordination compound, as well as the characteristic absorption bands observed in the electronic spectrum.
• Describe how the strength of the ligand field affects the energy difference between the $t_{2g}$ and $e_{g}$ orbitals.
  • The energy difference between the $t_{2g}$ and $e_{g}$ orbitals, known as the crystal field splitting energy (Δ), is directly related to the strength of the ligand field. In strong-field ligands, the crystal field splitting is large, and the $t_{2g}$ orbitals are stabilized to a greater extent compared to the $e_{g}$ orbitals. Conversely, in weak-field ligands, the crystal field splitting is smaller, and the energy difference between the $t_{2g}$ and $e_{g}$ orbitals is less pronounced. The magnitude of the crystal field splitting energy is a crucial factor in determining the electronic configuration and magnetic properties of transition metal complexes.
• Analyze the differences in the stabilization of the $t_{2g}$ and $e_{g}$ orbitals in octahedral and tetrahedral coordination complexes.
  • In octahedral coordination complexes, the $t_{2g}$ orbitals are more stabilized compared to the $e_{g}$ orbitals due to their specific orientations relative to the ligands. The $t_{2g}$ orbitals are directed between the ligands, resulting in less overlap and repulsion, while the $e_{g}$ orbitals are directed towards the ligands, leading to greater destabilization. In tetrahedral complexes, the situation is reversed, with the $e_{g}$ orbitals being more stabilized than the $t_{2g}$ orbitals. This difference in orbital stabilization between octahedral and tetrahedral complexes has significant implications for the electronic structure, spin state, and magnetic properties of the transition metal complexes.

Related terms

$e_{g}$: The set of two higher energy d-orbitals in a transition metal complex that are directed along the coordinate axes and interact more strongly with the ligands.

Crystal Field Splitting: The process by which the d-orbitals of a transition metal ion are split into the $t_{2g}$ and $e_{g}$ sets when the ion is placed in a coordinating environment.

Ligand Field Theory:

A model used to explain the electronic structure and properties of transition metal complexes based on the interactions between the metal d-orbitals and the ligands.