Question

An octahedral vanadium(III) complex has d-d bands at 20000 and \(30000 \mathrm{~cm}^{-1}\). Interpret these data in terms of (a) the crystal field and (b) the ligand field models.

Short answer

The d-d bands observed can be explained in the context of both crystal field and ligand field theories. In terms of the crystal field model, the splitting of the metal d-orbitals due to the octahedral environment is responsible for these bands. The ligand field model could further explain the dissimilarity in energy levels, taking into account changes due to the nature of the ligands.

Step-by-step solution

Understanding the Crystal Field Theory

The crystal field theory describes the interaction between the ligands and the d-orbitals of the central metal ion. In octahedral complexes, the d-orbitals split into two different energy levels. These are the triply degenerate set \(t_{2g}\) (dxy, dyz, dxz) and the doubly degenerate set \(e_{g}\) (dx^2-y^2, dz^2). The \(t_{2g}\) set will be lower in energy while the \(e_{g}\) set will be higher in energy.

Applying the Crystal Field Theory to the Given Complex

Vanadium(III) has a d^2 configuration. Thus, we can predict that the two electrons will occupy the lower energy \(t_{2g}\) set. For transitions to occur, these electrons can be excited to the \(e_{g}\) level. This would give rise to two d-d transitions, correlating with the two bands observed at 20000 cm^-1 and 30000 cm^-1.

Understanding the Ligand Field Theory

While the crystal field theory ignores any covalent bonding between the metal and ligands, the ligand field theory takes this into account. It postulates that the nature of the ligands can further split the \(e_{g}\) and \(t_{2g}\) levels. This effect is most pronounced in a strong field or high spin complex.

Applying the Ligand Field Theory to the Given Complex

The ligand field theory may explain the difference in energy between the two transitions. Depending on the nature of the ligands, one of the \(e_{g}\) orbitals may be stabilized or the \(t_{2g}\) levels may be further split. This is very specific and would require further details to deduce.

Key concepts

Crystal Field Theory

Crystal Field Theory (CFT) offers a simple way to understand how metal-ligand interactions affect the energy of d-orbitals in transition metal complexes. In an octahedral arrangement, ligands approach the metal ion along the x, y, and z axes, influencing the distribution of the metal's d-orbitals. This interaction leads to the splitting of the d-orbitals into two sets:

• \(t_{2g}\): Consists of d_xy, d_yz, and d_xz orbitals, which are lower in energy.
• \(e_{g}\): Includes d_x^2-y^2 and d_z^2 orbitals, which are higher in energy.

This splitting explains the different colors and electronic absorption spectra observed for transition metal complexes. In the case of a vanadium(III) complex, electrons from the lower energy \(t_{2g}\) set can be excited to the higher energy \(e_{g}\) set, resulting in observable electronic transitions.

Ligand Field Theory

Ligand Field Theory (LFT) expands upon Crystal Field Theory by incorporating the covalent nature of metal-ligand interactions. While CFT mainly considers electrostatic forces, LFT also takes into account the bonding and antibonding molecular orbitals formed between the metal and its ligands.

This theory suggests that the strength and nature of ligands can further alter the splitting of the d-orbitals. Strong field ligands, like cyanide, can cause larger splits compared to weak field ligands, like iodide. This additional complex splitting is known as the ligand field splitting and is crucial to understanding the specific electronic transitions in a complex.

In vanadium(III) complexes, the type of ligand can influence how the d-d transitions are observed and their respective energies. By analyzing these transitions, scientists can infer the nature of ligands involved in the complex.

d-d Transitions

d-d Transitions occur when electrons are excited from one d-orbital level to another within the same metal ion. These transitions are responsible for the characteristic colors seen in many transition metal complexes. In the octahedral geometry of the vanadium(III) complex, you observe two main d-d transitions at energies of \(20000\, \text{cm}^{-1}\) and \(30000\, \text{cm}^{-1}\).

These values indicate the energy required to move electrons from lower energy \(t_{2g}\) orbitals to higher energy \(e_{g}\) orbitals. The magnitude of these transition energies reflects the splitting caused by the ligands, and therefore, offers insights into the strength and nature of the ligand field in the complex.

Understanding d-d transitions is key to interpreting the absorption spectra and identifying the electronic environment in transition metal complexes.

Octahedral Complexes

Octahedral complexes are one of the most common geometries found in coordination chemistry. In these structures, six ligands are symmetrically arranged around a central metal ion, forming an octahedron. The symmetry and orientation of the ligands significantly influence the metal's d-orbitals, leading to splitting as explained by Crystal Field Theory.

This geometry provides a simple model to understand the electronic structure and spectral properties of the complex. For a vanadium(III) complex with a \(d^{2}\) electron configuration, the octahedral field causes the \(t_{2g}\) and \(e_{g}\) levels to differ in energy, allowing for d-d transitions upon absorption of specific wavelengths of light.

The analysis of octahedral complexes is crucial for predicting the optical and magnetic properties of transition metal compounds, making it a fundamental concept in inorganic chemistry.