Crystal Field Theory: Tetrahedral Complexes: Videos & Practice Problems

Tetrahedral complexes exhibit unique ligand orbital interactions, where the dxy, dyz, and dxz orbitals, which lie between the axes, have the highest energy due to stronger interactions. These orbitals are represented as t₂ in crystal field diagrams, while the dx²−y² and dz² orbitals, aligned with the axes, are lower in energy and denoted as e. The energy difference, known as crystal field splitting energy (Δ), is smallest in tetrahedral complexes compared to octahedral and square planar complexes.

The crystal field splitting pattern for tetrahedral complexes has the d orbitals in between the axes as having the higher energy.

Tetrahedral complexes exhibit unique ligand orbital interactions, where the strongest interactions occur between the axes. In the context of the five d orbitals, the orbitals that lie between the axes—specifically d_xy, d_yz, and d_xz—experience the highest energy due to these interactions. When constructing a crystal field diagram, these three orbitals are positioned at the top, collectively referred to as the t₂ set, indicating a triplet of orbitals.

Conversely, the orbitals that align along the axes, namely d_x²-y² and d_z², have reduced interactions and, consequently, lower energy levels. These two orbitals are represented in the diagram as the e set. The energy difference between these two groups of orbitals is denoted as Δ, known as the crystal field splitting energy.

It is important to note that tetrahedral complexes have the smallest Δ compared to octahedral and square planar complexes. This characteristic is crucial when analyzing the behavior and properties of different coordination complexes.

Example

In coordination chemistry, the energy gap between the e set and the t₂ set of orbitals, denoted as Δ (delta), is influenced by the geometry of the complex. Tetrahedral complexes typically exhibit the smallest energy gap due to their unique arrangement of ligands around the central metal cation. For a complex to be classified as tetrahedral, it must have a metal ion coordinated to four ligands.

Among the options provided, the complex that meets this criterion is option D, which features a copper(II) ion (Cu²⁺) coordinated to four bromide ions (Br^-). This arrangement results in a tetrahedral geometry, leading to a smaller Δ value compared to other geometries such as octahedral, which involves six ligands and generally has a larger energy gap.

In contrast, the other options either involve more than four ligands or do not conform to the tetrahedral structure. For instance, complexes with six ligands, such as octahedral complexes, will have a larger energy gap due to the increased splitting of the d-orbitals. Additionally, while EDTA is a polydentate ligand capable of coordinating multiple donor atoms, it typically forms octahedral complexes due to its six donor sites.

Thus, the tetrahedral complex with copper(II) and four bromide ligands is the only one that results in the smallest energy gap between the e set and the t₂ set of orbitals.

For which of the following complexes, the energies of the dx2−y2 and dz2 orbitals will be lower than the other three d orbitals?

• A. [Co(en)₃]³⁺
• B. [Ni(CN)₄]^2–
• C. [Zn(H₂O)₄]²⁺
• D. [AuCl₂]^–

Answer: (C)

Here’s what students ask on this topic:

What is the crystal field splitting energy (Δ) in tetrahedral complexes?

The crystal field splitting energy (Δ) in tetrahedral complexes is the energy difference between the two sets of d orbitals: the higher energy triplet (t_2g) consisting of d_xy, d_yz, and d_xz orbitals, and the lower energy pair (e) consisting of d_x²-y² and d_z² orbitals. In tetrahedral complexes, the ligand interactions are strongest between the axes, leading to higher energy for the t_2g orbitals. Tetrahedral complexes exhibit the smallest Δ compared to octahedral and square planar complexes, making the energy difference relatively small.

Why do tetrahedral complexes have the smallest crystal field splitting energy (Δ)?

Tetrahedral complexes have the smallest crystal field splitting energy (Δ) because the ligand interactions are not as strong as in other geometries like octahedral or square planar. In tetrahedral complexes, the ligands approach the metal ion between the axes, leading to weaker interactions with the d orbitals. This results in a smaller energy difference between the higher energy t_2g orbitals (d_xy, d_yz, d_xz) and the lower energy e orbitals (d_x²-y², d_z²).

How are the d orbitals split in a tetrahedral crystal field?

In a tetrahedral crystal field, the d orbitals are split into two sets based on their energy levels. The d_xy, d_yz, and d_xz orbitals experience stronger interactions with the ligands and are grouped together as a triplet (t_2g) with higher energy. The d_x²-y² and d_z² orbitals, which lie along the axes, experience weaker interactions and are grouped as a pair (e) with lower energy. The energy difference between these sets is the crystal field splitting energy (Δ).

What is the significance of the t_2g and e sets in tetrahedral complexes?

In tetrahedral complexes, the t_2g and e sets represent the different energy levels of the d orbitals due to ligand interactions. The t_2g set consists of the d_xy, d_yz, and d_xz orbitals, which have higher energy because they lie between the axes where ligand interactions are strongest. The e set consists of the d_x²-y² and d_z² orbitals, which have lower energy as they lie along the axes with weaker ligand interactions. This splitting is crucial for understanding the electronic structure and properties of tetrahedral complexes.

How does the crystal field splitting in tetrahedral complexes compare to octahedral and square planar complexes?

The crystal field splitting in tetrahedral complexes is smaller compared to octahedral and square planar complexes. In tetrahedral complexes, the ligands interact with the metal ion between the axes, leading to weaker interactions and a smaller energy difference (Δ) between the t_2g and e sets of d orbitals. In octahedral complexes, the ligands interact directly along the axes, resulting in stronger interactions and a larger Δ. Square planar complexes also have strong ligand interactions along the axes, leading to a significant splitting of the d orbitals. Thus, tetrahedral complexes exhibit the smallest Δ among these geometries.