Crystal Field Theory Summary: Videos & Practice Problems

Crystal field theory explains the energy splitting of d orbitals in transition metal complexes based on geometry. Tetrahedral complexes exhibit the smallest crystal field splitting energy (Δ), octahedral complexes have a moderate Δ, and square planar complexes show the highest Δ. In tetrahedral geometry, orbitals d_xy, d_yz, and d_xz are higher in energy due to weaker ligand interactions, while in octahedral geometry, d_x²-y² and d_z² are higher due to stronger interactions. Square planar complexes have a complex splitting pattern with significant energy differences.

The greatest ligand-orbital interactions result in the greatest increase in energy.

In coordination chemistry, the splitting patterns of d orbitals in metal complexes are influenced by the geometry of the complex. The strength of interactions between the d orbitals and the surrounding ligands determines the energy levels of these orbitals, with the crystal field splitting energy, denoted as Δ, representing the energy difference between the higher and lower energy d orbitals.

For tetrahedral complexes, the crystal field splitting energy (Δ) is the smallest among the common geometries. In this arrangement, the d orbitals that experience the greatest interaction with ligands are those oriented between the axes: d_xy, d_yz, and d_xz. These orbitals are positioned at a higher energy level, while the orbitals aligned along the axes, d_x² - _y² and d_z², have lower energy due to reduced interactions.

In octahedral complexes, the situation is more balanced, with Δ being intermediate. Here, the orbitals that lie along the axes, d_x² - _y² and d_z², experience the strongest interactions, resulting in higher energy levels. The remaining three orbitals, d_xy, d_yz, and d_xz, are lower in energy due to their positioning between the axes.

Square planar complexes exhibit the most complex splitting pattern, characterized by a high Δ. In this geometry, the d_x² - _y² orbital has the highest energy due to its strong interactions along the axes, followed by d_xy, which retains some x and y characteristics. The d_z² orbital occupies a middle position, while d_yz and d_xz are at the lowest energy levels.

Understanding these differences in crystal field splitting energies across tetrahedral, octahedral, and square planar geometries is crucial for predicting the electronic properties and reactivity of metal complexes.

Example

In the context of crystal field theory, the crystal field splitting energy (Δ) is a crucial concept that describes the energy difference between the split d-orbitals in transition metal complexes. Tetrahedral complexes typically exhibit smaller crystal field splitting energy compared to octahedral or square planar complexes due to their geometric arrangement and the nature of the ligands involved.

To determine which complex has the smallest crystal field splitting energy, we first need to identify the complexes with tetrahedral geometry. Tetrahedral complexes require four ligands or donor atoms. In the given options:

Option A cannot be a tetrahedral complex because it contains ethylene diamine, which is a bidentate ligand, resulting in a total of six donor atoms.

Option B is a potential candidate as it consists of four fluoride ions coordinated to a copper ion, indicating a tetrahedral geometry.

Option C is also ruled out since it has six water molecules acting as ligands, leading to a total of six donor atoms.

Option D presents a complex with two ammonia molecules and two chloride ions, which totals four ligands, making it a possible tetrahedral complex as well.

Next, we analyze the oxidation states and electron configurations of the metal ions in options B and D. In option B, the copper ion is in the +1 oxidation state, resulting in an electron configuration of 3d¹⁰. This configuration is characteristic of tetrahedral complexes, which typically have lower crystal field splitting energy.

In contrast, option D features platinum in the +2 oxidation state, leading to an electron configuration of 4f¹⁴5d⁸. Complexes with a d⁸ configuration often adopt a square planar geometry, which is associated with higher crystal field splitting energy.

Given that tetrahedral complexes (like that in option B) have the smallest crystal field splitting energy compared to square planar complexes (like that in option D), we conclude that option B is the correct answer. Thus, the complex with the smallest crystal field splitting energy is the one with the tetrahedral geometry formed by the copper ion and four fluoride ligands.

What is the correct order when the following complexes are arranged in ascending order of the Δ values?
i) [Mn(NO₂)₆]^4–               ii) [Ni(CN)₄]^2–                 iii) [Zn(OH)₄]^2–

• A. i < ii < iii
• B. ii < i < iii
• C. ii < iii < i
• D. iii < i < ii

Answer: (D)

Here’s what students ask on this topic:

What is crystal field splitting energy (Δ) and how does it vary with different geometries?

Crystal field splitting energy (Δ) is the energy difference between higher and lower sets of d orbitals in a metal complex due to the presence of ligands. The value of Δ varies based on the geometry of the complex. In tetrahedral complexes, Δ is the smallest because the ligands interact less strongly with the d orbitals. In octahedral complexes, Δ is intermediate, with the orbitals along the axes (d_x²-y², d_z²) having higher energy. Square planar complexes have the highest Δ due to strong interactions on and between the x and y axes, with d_x²-y² and d_xy having the highest energy.

How do d orbitals split in a tetrahedral complex?

In a tetrahedral complex, the d orbitals split into two sets due to the interaction with ligands. The orbitals d_xy, d_yz, and d_xz experience greater interaction with the ligands and thus have higher energy. The orbitals that lie on or along the axis, d_x²-y² and d_z², have lower energy because they interact less with the ligands. This results in a smaller crystal field splitting energy (Δ) compared to other geometries.

What factors influence the magnitude of Δ in octahedral complexes?

The magnitude of Δ in octahedral complexes is influenced by several factors, including the nature of the ligands, the charge on the metal ion, and the position of the metal in the periodic table. Strong field ligands, such as CN^- and CO, cause a larger Δ, while weak field ligands, like I^- and Br^-, result in a smaller Δ. Higher oxidation states of the metal ion also increase Δ. Additionally, transition metals in the second and third rows of the periodic table generally have larger Δ values compared to those in the first row.

Why do square planar complexes have the highest crystal field splitting energy (Δ)?

Square planar complexes have the highest crystal field splitting energy (Δ) because of the strong interactions between the ligands and the d orbitals on and between the x and y axes. The d_x²-y² orbital experiences the greatest interaction and thus has the highest energy, followed by the d_xy orbital. The d_z² orbital is in the middle, while the d_yz and d_xz orbitals have the lowest energy. This significant difference in energy levels results in a high Δ for square planar complexes.

How do d orbitals split in an octahedral complex?

In an octahedral complex, the d orbitals split into two sets due to the interaction with ligands. The orbitals along the axes, d_x²-y² and d_z², experience greater interaction with the ligands and thus have higher energy. The orbitals that lie between the axes, d_xy, d_yz, and d_xz, have lower energy because they interact less with the ligands. This results in an intermediate crystal field splitting energy (Δ) compared to tetrahedral and square planar geometries.