Glossary

8.3 Crystal field theory and magnetic properties

3 min read•july 22, 2024

explains how metal ions interact with ligands in coordination compounds. It predicts , which affects complex properties like color and magnetism. Understanding this theory helps us grasp why different metal complexes behave uniquely.

The theory explores how geometry and ligand strength influence electronic configurations. This impacts whether complexes are or , determining their magnetic properties. It also explains why coordination compounds have specific colors based on d-orbital energy gaps.

Crystal Field Theory

Principles of crystal field theory

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  • Electrostatic model explains electronic structure and properties of coordination compounds
  • Considers interactions between metal ion and ligands treated as point negative charges
  • Predicts d-orbital splitting in transition metal complexes based on complex geometry (, )
  • Splitting magnitude influenced by metal ion and ligand nature
  • Explains coordination compound properties
    • Color and absorption spectra
    • Magnetic properties
    • Stability and reactivity

D-orbital splitting in complexes

  • : d-orbitals split into two energy levels
    • ege_g set (dx2−y2d_{x^2-y^2} and dz2d_{z^2} orbitals) higher energy due to direct ligand pointing and greater electrostatic repulsion
    • t2gt_{2g} set (dxyd_{xy}, dxzd_{xz}, and dyzd_{yz} orbitals) lower energy due to pointing between ligands and less electrostatic repulsion
    • Energy difference between ege_g and t2gt_{2g} sets denoted as Δo\Delta_o (octahedral )
  • : d-orbitals split into two energy levels
    • t2t_2 set (dxyd_{xy}, dxzd_{xz}, and dyzd_{yz} orbitals) higher energy due to closer ligand pointing and greater electrostatic repulsion
    • ee set (dx2−y2d_{x^2-y^2} and dz2d_{z^2} orbitals) lower energy due to pointing away from ligands and less electrostatic repulsion
    • Energy difference between t2t_2 and ee sets denoted as Δt\Delta_t (tetrahedral crystal field splitting energy)
    • Δt\Delta_t typically smaller than Δo\Delta_o (approximately 4/9 of Δo\Delta_o)

Electronic configuration of coordination compounds

  • Electronic configuration depends on d-electron number and crystal field splitting energy
  • Electrons fill lower energy orbitals first following Hund's rule and Pauli exclusion principle
  • have smaller Δ\Delta compared to pairing energy
    • Electrons occupy all available orbitals before pairing maximizing
  • have larger Δ\Delta compared to pairing energy
    • Electrons pair up in lower energy orbitals before occupying higher energy orbitals minimizing unpaired electrons
  • Magnetic properties determined by unpaired electron number
    • Paramagnetic complexes have unpaired electrons attracted by magnetic field
    • Diamagnetic complexes have no unpaired electrons weakly repelled by magnetic field
    • Magnetic moment calculated using spin-only formula: μ=n(n+2)\mu = \sqrt{n(n+2)} μB\mu_B, where nn = unpaired electron number and μB\mu_B = Bohr magneton

Spectroscopic Properties

UV-visible spectra of coordination compounds

  • UV-visible spectroscopy probes electronic transitions between split d-orbitals
  • Light absorption causes electron excitation from lower to higher energy orbitals
  • Coordination compound color determined by non-absorbed wavelengths (transmitted or reflected)
  • Absorbed wavelengths correspond to energy difference between split d-orbitals
  • ranks ligands based on d-orbital splitting ability
    • (CN-, CO) cause larger splitting and absorb lower wavelengths (higher energy)
    • (I-, Br-) cause smaller splitting and absorb higher wavelengths (lower energy)
  • Selection rules govern allowed electronic transitions
    1. Laporte rule: Transitions between same parity orbitals (g → g or u → u) forbidden
      • In octahedral complexes, d-d transitions Laporte forbidden but become allowed due to vibronic coupling
    2. Spin rule: Transitions between different spin multiplicity states forbidden
      • Spin-allowed transitions (singlet → singlet) more intense than spin-forbidden transitions (singlet → triplet)

Key Terms to Review (30)

Cn⁻: The term cn⁻ refers to a specific ligand in coordination chemistry, known as the cyanide ion, which is a strong field ligand and has the chemical formula CN⁻. In the context of crystal field theory, it plays a significant role in determining the electronic structure and magnetic properties of metal complexes by influencing the splitting of d-orbitals.
Color of Complexes: The color of complexes refers to the specific wavelengths of light absorbed and transmitted by coordination compounds, which arise from electronic transitions in the d-orbitals of transition metal ions. This phenomenon is closely linked to crystal field theory, where the splitting of d-orbitals in the presence of ligands determines the energy levels involved in these transitions, ultimately influencing the observed color and magnetic properties of the complex.
Coordination Number 4: Coordination number 4 refers to the number of ligand atoms that are directly bonded to a central metal ion in a coordination complex. This geometric arrangement significantly influences the properties and behavior of the compound, including its stability, reactivity, and color. The coordination number also relates to the spatial arrangement of ligands around the central ion, which can lead to different shapes such as tetrahedral or square planar configurations.
Coordination Number 6: Coordination number 6 refers to the arrangement of six ligands surrounding a central metal ion in a coordination complex. This common geometry typically results in an octahedral shape, impacting the compound's properties, stability, and reactivity. Understanding coordination number 6 is crucial for grasping how ligands interact with metal ions and how these interactions influence crystal field theory and the nomenclature of coordination compounds.
Crystal field splitting energy: Crystal field splitting energy refers to the energy difference between two sets of d-orbitals in transition metal complexes when they are subjected to an electric field from surrounding ligands. This energy splitting occurs because the presence of ligands causes the degenerate d-orbitals to separate into groups with varying energy levels, significantly influencing the electronic structure, magnetic properties, and color of the complex.
Crystal Field Stabilization Energy: Crystal field stabilization energy (CFSE) is the energy difference between the energies of the electrons in a crystal field and those in an isolated atom. CFSE arises from the splitting of degenerate d-orbitals in transition metal complexes due to the presence of surrounding ligands, which affects the electronic configuration and stability of the complex. This concept is crucial for understanding the magnetic properties and color of coordination compounds, as it influences the arrangement of electrons in d-orbitals under varying ligand fields.
Crystal Field Theory: Crystal Field Theory (CFT) is a model that describes the electronic structure of transition metal complexes by considering the interaction between the metal ions and the surrounding ligands. It explains how these interactions lead to the splitting of d-orbitals in a metal ion, affecting the properties of the complex, including its magnetic behavior and color. CFT is crucial for understanding why some transition metal complexes are paramagnetic while others are diamagnetic.
D-orbital splitting: d-orbital splitting refers to the phenomenon where the five d-orbitals in transition metal complexes become energetically different when ligands approach the metal ion. This splitting occurs due to the electrostatic interactions between the incoming ligands and the d-electrons of the metal, leading to variations in energy levels. The pattern of this splitting is crucial for understanding the electronic structure, color, and magnetic properties of coordination compounds.
D-orbital splitting energy: D-orbital splitting energy refers to the energy difference between the split d-orbitals in transition metal complexes due to the interaction with surrounding ligands. This phenomenon occurs when a transition metal ion is surrounded by ligands, causing the degeneracy of the d-orbitals to be lifted and resulting in different energy levels. Understanding d-orbital splitting energy is crucial for explaining the magnetic properties and color of transition metal complexes, as it influences electron configurations and their transitions.
Degenerate Orbitals: Degenerate orbitals are orbitals that have the same energy level within a given electron shell and are often found in multi-electron atoms. These orbitals can hold a specific number of electrons but do not differentiate in energy when no external forces are applied, making them crucial in understanding electron configurations and chemical bonding, especially in transition metals.
Diamagnetism: Diamagnetism is a property of materials that causes them to create an opposing magnetic field when exposed to an external magnetic field, resulting in a repulsive effect. This phenomenon occurs in all materials but is particularly noticeable in those that have no unpaired electrons, making them non-magnetic under normal conditions. In the context of crystal field theory, diamagnetic substances exhibit specific behaviors and interactions with magnetic fields due to their electron configuration.
Electron pairing: Electron pairing refers to the phenomenon where two electrons occupy the same orbital within an atom or molecule, exhibiting opposite spins. This concept is essential in understanding how electrons interact within the context of crystal field theory, influencing the magnetic properties of transition metal complexes and their geometry. The arrangement and pairing of electrons play a critical role in determining a substance's reactivity, color, and magnetic behavior.
High-spin: High-spin refers to a specific electron arrangement in coordination complexes where the electrons occupy the highest energy orbitals available before pairing occurs. This arrangement is influenced by the strength of the ligand field, determining whether the electrons will fill lower-energy orbitals first or occupy higher-energy orbitals to minimize electron pairing. High-spin complexes typically exhibit weaker crystal field splitting and tend to be paramagnetic due to the presence of unpaired electrons.
High-spin complexes: High-spin complexes are coordination compounds where the arrangement of electrons in d-orbitals results in a larger number of unpaired electrons, leading to strong magnetic properties. This phenomenon occurs primarily due to weak field ligands that do not cause a significant energy difference between the split d-orbitals, allowing electrons to occupy higher energy levels before pairing up. As a result, high-spin complexes exhibit a range of magnetic behaviors and are crucial for understanding the electronic structure and reactivity of transition metal complexes.
Ligand Field Theory: Ligand Field Theory is a model that describes the electronic structure of transition metal complexes by focusing on the interactions between metal ions and surrounding ligands. It expands upon Crystal Field Theory by incorporating aspects of covalent bonding and the effects of ligand polarity, allowing for a more nuanced understanding of properties like color, magnetism, and stability in these complexes.
Low-spin: Low-spin refers to a situation in coordination chemistry where electrons occupy the lower energy d-orbitals before filling the higher energy d-orbitals, resulting in a configuration with fewer unpaired electrons. This phenomenon occurs in certain transition metal complexes, especially those with strong field ligands, and is essential for understanding the magnetic properties of these complexes.
Low-spin complexes: Low-spin complexes are coordination compounds where the energy difference between the lower and higher energy d-orbitals is significant enough that electrons tend to fill the lower energy orbitals first, resulting in fewer unpaired electrons. This phenomenon is a result of the splitting of d-orbitals in the presence of a ligand field, which influences the magnetic properties of the complex. Low-spin complexes are typically found with strong field ligands that create a larger crystal field splitting energy (Δ).
Octahedral: Octahedral refers to a geometric structure formed by eight faces, typically in a symmetrical arrangement. This shape is significant in chemistry as it relates to the spatial arrangement of ligands around a central metal atom in coordination complexes, influencing their properties and behavior in various chemical contexts.
Octahedral complexes: Octahedral complexes are coordination compounds where a central metal ion is surrounded by six ligands arranged at the corners of an octahedron. This geometry plays a significant role in determining the electronic structure, stability, and reactivity of these complexes, and it also influences their magnetic properties and types of isomerism.
Octahedral Field: An octahedral field refers to a specific arrangement of ligands around a central metal ion in a coordination complex, where six ligands are symmetrically positioned at the vertices of an octahedron. This geometric configuration plays a critical role in determining the electronic structure, stability, and magnetic properties of transition metal complexes, as described by crystal field theory.
Paramagnetism: Paramagnetism is a form of magnetism that occurs in materials with unpaired electrons, resulting in a weak attraction to an external magnetic field. This property is essential for understanding how certain transition metal complexes behave in the presence of magnetic fields, as the presence of unpaired electrons allows for these materials to align with magnetic fields, albeit weakly.
Spectrochemical series: The spectrochemical series is an arrangement of ligands based on their ability to split the degenerate d-orbitals of transition metal complexes. This series helps to predict the strength of the field created by different ligands and influences properties like color, magnetic behavior, and stability of coordination compounds. Ligands at the top of the series create a strong field, leading to larger energy differences between d-orbitals, while those at the bottom create a weak field with smaller energy differences.
Strong field ligands: Strong field ligands are molecules or ions that create a large splitting of the d-orbitals in transition metal complexes, leading to a greater energy difference between the lower and higher energy d-orbitals. These ligands favor low-spin configurations by causing electrons to pair up in the lower energy orbitals before occupying the higher ones. This behavior impacts the magnetic properties of the complex and plays a crucial role in understanding the colors and reactivity of coordination compounds.
Tetrahedral: Tetrahedral refers to a geometric shape formed by four points (atoms) that are arranged at the corners of a tetrahedron, with each bond angle measuring approximately 109.5 degrees. This shape is particularly important in the study of molecular geometry, especially when discussing the arrangement of ligands around a central atom in coordination compounds and how this arrangement influences properties such as magnetic behavior and crystal field splitting.
Tetrahedral Complexes: Tetrahedral complexes are coordination compounds where a central metal ion is surrounded by four ligands positioned at the corners of a tetrahedron. This geometry arises from the spatial arrangement of ligands in such a way that they minimize electron pair repulsions, leading to distinct magnetic properties and potential for isomerism based on ligand arrangements.
Tetrahedral field: A tetrahedral field refers to the arrangement of ligands around a central metal ion in a coordination complex, where the ligands are positioned at the corners of a tetrahedron. This spatial configuration influences the energy levels of the d-orbitals in transition metals, impacting their electronic structure, stability, and magnetic properties.
Unpaired Electrons: Unpaired electrons are electrons that occupy an orbital alone rather than being paired with another electron. This characteristic plays a crucial role in determining the magnetic properties of atoms and ions, as well as influencing their chemical behavior. The presence of unpaired electrons contributes to a material's paramagnetic or diamagnetic nature, and helps explain phenomena such as electron configuration and bonding in complex compounds.
Weak field ligands: Weak field ligands are molecules or ions that interact with a central metal atom or ion in a coordination complex, resulting in a smaller splitting of the d-orbitals compared to strong field ligands. These ligands tend to have lower electronegativity and produce a less pronounced crystal field splitting energy, which affects the electronic configuration of the metal complex and its magnetic properties. Understanding weak field ligands is crucial for predicting the behavior of transition metal complexes and their response to magnetic fields.
δo: δo, or the crystal field splitting energy, refers to the energy difference between the two sets of d-orbitals in a transition metal complex when subjected to an external electric field, typically from surrounding ligands. This splitting of the d-orbitals leads to variations in the electronic configurations of the metal ions, influencing their color, magnetism, and overall stability in different coordination environments.
δt: In the context of crystal field theory, δt refers to the crystal field splitting energy between the lower and higher energy d-orbitals of transition metal complexes. This energy difference is crucial for understanding the electronic structure of metal ions in different ligands and directly affects their magnetic properties. The value of δt influences whether a complex will exhibit paramagnetism or diamagnetism based on the arrangement of electrons in these orbitals.
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