Question

In octahedral complexes, the choice between high-spin and low spin electron configurations arises only for \(d^{4}-d^{7}\) complexes. Explain.

Short answer

High-spin vs low-spin choice occurs in d4-d7 complexes because ligand field strength affects electron pairing only in this range.

Step-by-step solution

Understanding Octahedral Complexes

Octahedral complexes have six ligands surrounding a central metal ion. The metal ion's d-orbitals split into two sets - t2g (lower energy) and eg (higher energy) levels due to the ligand field.

Ligand Field Strength

In octahedral complexes, ligands can be either strong-field or weak-field. Strong-field ligands cause a large splitting of the d-orbitals, while weak-field ligands result in a small splitting.

Electron Configuration Impact

The electron configuration of the central metal ion determines the filling of d-orbitals. This is particularly significant for metal ions with d-electron counts in the range of d4 to d7.

High-Spin vs Low-Spin

High-spin and low-spin configurations depend on the strength of the ligand field splitting compared to the electron pairing energy. In high-spin complexes, electrons prefer to occupy higher energy orbitals singly before pairing, whereas in low-spin complexes, strong-field ligands cause electrons to pair in lower energy orbitals.

Critical Electron Range

For d1 to d3 and d8 to d10, the choice between high-spin and low-spin doesn't arise. In d4 to d7, whether a complex adopts a high-spin or low-spin configuration makes a significant difference in electron distribution and properties.

Key concepts

High-Spin vs Low-Spin Configurations

In octahedral complexes, the arrangement of electrons within the metal ion's d-orbitals can vary, leading to the terms high-spin and low-spin configurations.
High-spin and low-spin differences emerge when dealing with metal ions whose electron configuration falls within the range of d⁴ to d⁷. This is because, for these particular configurations, the energy difference between the t₂g and eg levels is comparable to the electron pairing energy.

• **High-spin configuration**: Electrons occupy higher energy eg orbitals singly before pairing occurs at lower energy t₂g orbitals. This configuration occurs in the presence of weak-field ligands, which cause minimal splitting of the d-orbitals.
• **Low-spin configuration**: Electrons fill lower energy t₂g orbitals first, with pairing taking place early. Strong-field ligands cause significant splitting, making it energetically favorable for electrons to pair in the lower energy set rather than occupying the higher energy eg orbitals singly.

In summary, the choice between high-spin and low-spin for d⁴ to d⁷ complexes changes the distribution of electrons and thus impacts the complex's properties.

Ligand Field Theory

Ligand field theory helps explain how the electronic arrangement within d-orbitals is influenced by surrounding ligands in a metal complex.
This theory is an evolution of crystal field theory, and it provides a more detailed understanding of how electronic energies are affected by the presence of ligands.
When ligands approach a metal ion, they interact with its d-electrons, causing the initially degenerate d-orbitals to split.

• The extent of this splitting is referred to as 'ligand field splitting' and is denoted by the symbol Δ (delta).
• The strength of the ligand field is determined by factors such as the nature of the ligand and the identity of the metal ion.

Ligand field theory not only explains the energy differences between orbitals but also helps predict coordination geometry, color, and magnetic behavior of complexes.

D-orbitals Splitting

In an octahedral complex, the metal ion is surrounded symmetrically by six ligands. This symmetrical arrangement causes the d-orbitals to experience different levels of repulsion from the ligand's electrons.
The d-orbitals split into two sets:

• **T₂g orbitals**: Consists of d_xy, d_xz, and d_yz. These orbitals are positioned between the axes and experience less repulsion, resulting in lower energy.
• **Eg orbitals**: Contains d_z² and d_x²-y² orbitals, which point along the axes. Consequently, they experience greater repulsion and are of higher energy.

The energy difference between these two sets, known as the crystal field splitting energy or Δ_oct, is crucial in determining whether a complex will be high-spin or low-spin.

Electron Configuration in Octahedral Complexes

Understanding the electron configuration of a metal ion in an octahedral complex is essential in predicting its magnetic and spectroscopic properties.
The electron configuration determines how electrons arrange themselves in the available d-orbitals. For metal ions in octahedral complexes, the specific electron configuration will decide how electrons fill the split t₂g and eg orbitals.

• **For d¹-d³ and d⁸-d¹⁰**: The choice between high-spin and low-spin is straightforward or non-existent, as the electron pairing energy doesn't have much influence.
• **For d⁴-d⁷**: It's complex because the energy difference between splitting (Δ) and pairing energy is comparable, causing electrons to either spread out in a high-spin state or pair up in a low-spin state.

Ultimately, the electron configuration helps determine the stability, color, and even reactivity of the complex. It is through understanding how electrons distribute themselves in these split orbitals that many properties of the complexes can be elucidated.