Chapter 4: Problem 10

Discuss the splitting of \(d\) -orbitals in octahedral ligand field environment on the basis of group theory.

Short Answer

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Under an octahedral ligand field, due to the interaction between the ligands and the d-orbitals of the metal atom, the d-orbitals split into two energy levels. Subset \(d_{x^2-y^2}\) and \(d_{z^2}\) termed as \(e_g\) lie at a higher energy level, while \(d_{xz}, d_{yz}\), and \(d_{xy}\) termed as \(t_{2g}\) are at a lower energy level.

Step by step solution

Introduction to Ligand Field Theory

Ligand Field Theory (LFT) is a theory that describes the bonding, orbital arrangement, and other characteristics of coordination compounds. Essentially, LFT is used to understand the molecular structure and interpret the color and magnetism of metal complexes.

Understanding d-Orbitals

In an atom, there are 5 d-orbitals to which the electrons can be distributed. These include: \(d_{x^2-y^2}, d_{xz}, d_{yz}, d_{z^2}\), and \(d_{xy}\). According to the Shapes of Atomic Orbitals, d-orbitals are complex and often represented as four-leaf clovers or dumbbells with a ring.

Octahedral Ligand Field and its Geometry

An Octahedral Ligand field is one of the most common field in ligand field theory where a central metal atom is surrounded by six ligands, placed at the corners of an octahedron.

Splitting of d-Orbitals in Octahedral Ligand Field

When there is an interaction between the ligands and the d-orbitals of the central atom, the environment of the central atom changes. The metal d-orbitals split into two levels in an octahedral field, causing a difference in energy levels. Subset d-orbitals such as \(d_{x^2-y^2}\) and \(d_{z^2}\) – termed as \(e_g\) set – are on a higher energy level, while \(d_{xz}, d_{yz}\), and \(d_{xy}\) – termed as \(t_{2g}\) – lie lower. The ligands in the octahedral field interact strongest with the \(e_g\) set, causing them to be higher in energy.

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Discuss the splitting of \(d\) -orbitals in octahedral ligand field environment on the basis of group theory.

Short Answer

Step by step solution

Introduction to Ligand Field Theory

Understanding d-Orbitals

Octahedral Ligand Field and its Geometry

Splitting of d-Orbitals in Octahedral Ligand Field

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