Crystal Field Theory: Octahedral Complexes: Videos & Practice Problems

Crystal field splitting describes the division of five degenerate d orbitals into two energy levels due to the influence of ligand interactions in a complex ion. The pattern of splitting is determined by the geometry of the complex, with octahedral complexes featuring stronger interactions along the axes. This results in higher energy for the d orbitals oriented on the axes (d_x²-y² and d_z²), known as the E set, and lower energy for those between the axes, known as the T set. The energy difference between these sets is represented by:

$\Delta$

the crystal field splitting energy. Understanding this concept is crucial as it explains the electronic structure and properties of transition metal complexes.

The crystal field splitting pattern for octahedral complexes has the d orbitals on or along the axes as having the higher energy.

Crystal field splitting refers to the process where the five degenerate d orbitals, which initially possess the same energy, are separated into distinct energy levels due to the influence of surrounding ligands in a complex ion. The term "degenerate" indicates that these orbitals are initially at the same energy level. When ligands approach the metal ion, their interactions cause the d orbitals to split into two sets: one lower in energy and one higher in energy.

The specific pattern of this splitting is influenced by the geometry of the complex. In octahedral complexes, where six ligands are symmetrically arranged around a central metal ion, the interactions between the ligands and the d orbitals are strongest along the axes. This results in the d orbitals that align with the axes—specifically, the d_x²-y² and d_z² orbitals—experiencing a higher energy due to increased repulsion from the ligands. Consequently, these orbitals are positioned at a higher energy level.

In contrast, the remaining three d orbitals, which lie between the axes—namely, d_xz, d_yz, and d_xy—experience less interaction with the ligands and thus are lower in energy. This arrangement leads to the designation of the energy levels as follows: the higher energy set is referred to as t_2g (the two orbitals), while the lower energy set is called e_g (the three orbitals). The energy difference between these two sets is denoted as Δ, known as the crystal field splitting energy.

In summary, for octahedral complexes, the d orbitals split into two groups based on their orientation relative to the ligands, with the orbitals aligned along the axes having higher energy due to stronger interactions. This concept is crucial for understanding the electronic structure and properties of transition metal complexes.

Example

In coordination chemistry, the geometry of a complex ion significantly influences the energy levels of its d-orbitals. For octahedral complexes, the metal cation is surrounded by six ligands, leading to a specific arrangement of d-orbitals. In this geometry, the d-orbitals split into two energy levels: the lower-energy \( t_{2g} \) set, which consists of three orbitals, and the higher-energy \( e_g \) set, which consists of two orbitals.In the case of cobalt(III) ions (\( Co^{3+} \)), when coordinated with six water molecules, the resulting complex exhibits an octahedral geometry. This arrangement causes the \( t_{2g} \) orbitals to be lower in energy compared to the \( e_g \) orbitals. The stabilization of the \( t_{2g} \) orbitals occurs due to the ligand field created by the surrounding water molecules, which interact with the d-orbitals of the cobalt ion.Thus, for the complex where the \( t_{2g} \) set is lower in energy than the \( e_g \) set, the key factor is the octahedral coordination of the metal ion with six ligands. In this scenario, cobalt(III) with six water ligands is the only option that meets the criteria for an octahedral complex, confirming that the \( t_{2g} \) orbitals are indeed lower in energy than the \( e_g \) orbitals.

The following diagram shows crystal field splitting pattern for a complex. Which one of the complexes given below should best match the given diagram?

• A. [Ag(NH₃)₂]⁺
• B. [Cu(ox)₂]^2–
• C. [Cr(en)₃]³⁺
• D. [Fe(CO)₅]

Answer: (C)

Here’s what students ask on this topic:

According to crystal field theory, which orbitals in an octahedral complex would be higher in energy due to interaction with the ligands? Which ones should I check?

In crystal field theory, when considering an octahedral complex, the d-orbitals split into two different energy levels due to the interaction with the ligands. The five d-orbitals are divided into a set of three orbitals known as t_2g (d_xy, d_xz, d_yz) and a set of two orbitals called e_g (d_x²-y², d_z²).

In an octahedral field, the ligands approach the metal ion along the axes. This causes the d-orbitals that lie directly on these axes to experience a greater repulsion and thus, they are higher in energy. These are the e_g orbitals (d_x²-y² and d_z²). The t_2g orbitals (d_xy, d_xz, d_yz), which lie between the axes, experience less repulsion from the ligands and are therefore lower in energy.

So, when examining an octahedral complex in the context of crystal field theory, you should check the e_g orbitals (d_x²-y², d_z²) as they will be the ones higher in energy due to direct interaction with the ligands.

Which of the following orbitals belong to the higher energy group in crystal field theory, where octahedral metal orbitals are split into 2 groups of degenerate orbitals, one at lower energy, and one at higher energy? [Select all that apply]

In crystal field theory, when considering an octahedral metal complex, the five d orbitals split into two groups due to the electrostatic interactions between the metal ion and the ligands. The lower energy group consists of the d_xy, d_xz, and d_yz orbitals, which form the t_2g set. The higher energy group comprises the d_z² and d_x²-y² orbitals, which form the e_g set.

So, the orbitals that belong to the higher energy group in an octahedral crystal field are:

• d_z²
• d_x²-y²

These e_g orbitals experience a greater repulsion from the ligands that are positioned along the axes in an octahedral geometry, which results in their higher energy relative to the t_2g orbitals.