PHD
  1. Inorganic chemistry  1.1. Coordination chemistry  1.1.1. Ligand field theory  1.1.2. Crystal field theory  1.1.3. Molecular Orbital Theory for Coordination Compounds  1.1.4. Stability of Coordination Compounds  1.1.5. Electronic spectra of coordination compounds  1.1.6. Isomerism in Coordination Compounds  1.1.7. Kinetics and mechanism of coordination reactions  1.2. Organometallic Chemistry  1.2.1. Metal Carbonyls  1.2.2. Metal alkyl and aryl  1.2.3. Fischer and Schrock carbonaceans  1.2.4. Oxidative Addition and Reductive Elimination  1.2.5. Metal Hydrides  1.2.6. Catalysis by organometallic compounds  1.2.7. Metallocenes and Sandwich Complexes  1.2.8. CH activation  1.3. Solid state chemistry  1.3.1. Crystal structures and lattices  1.3.2. Band theory and electrical properties  1.3.3. Defects in the crystal  1.3.4. Synthesis of solid state materials  1.3.5. Magnetic and optical properties of solids  1.3.6. Superconductivity  1.3.7. Solid state ionics  1.4. Bio-inorganic chemistry  1.4.1. Metalloproteins and enzymes  1.4.2. Metal ion transport and storage  1.4.3. The role of metals in medicine  1.4.4. Bioinspired catalysis  1.4.5. Metal–DNA interactions  1.4.6. Metal Complexes in Medical Science  1.5. Lanthanides and Actinides  1.5.1. Electronic configuration and oxidation states in lanthanides and actinides  1.5.2. Spectral and Magnetic Properties in Lanthanides and Actinides  1.5.3. Separation and Extraction of Lanthanides and Actinides  1.5.4. Coordination chemistry of f-block elements  1.6. Main Group Chemistry  1.6.1. Chemistry of boron compounds  1.6.2. Chemistry of Silicon and Germanium Compounds  1.6.3. Chemistry of Phosphorus and Sulfur Compounds  1.6.4. Organosilicon chemistry  1.6.5. Noble Gas Chemistry
  2. Organic chemistry  2.1. Reaction mechanism  2.1.1. Nucleophilic substitution reactions  2.1.2. Electrophilic addition and substitution reactions  2.1.3. Elimination reactions  2.1.4. Rearrangement reactions  2.1.5. Radical reactions  2.1.6. Pericyclic Reactions  2.1.7. Photochemical reactions  2.2. Stereoscopic  2.2.1. Chirality and optical activity  2.2.2. Structural analysis  2.2.3. Stereoelectronic effects  2.2.4. Asymmetric synthesis  2.2.5. Dynamic Stereochemistry  2.3. Organometallic Chemistry in Organic Synthesis  2.3.1. Organolithium and organomagnesium reagents  2.3.2. Transition metal catalyzed coupling reactions  2.3.3. Palladium-catalyzed reactions  2.3.4. Olefin Metathesis  2.3.5. Gold and silver catalysis  2.4. Natural products chemistry  2.4.1. Alkaloids and terpenoids  2.4.2. Steroids and Flavonoids  2.4.3. Total synthesis of natural products  2.4.4. Biosynthesis of natural products  2.5. Supramolecular Chemistry  2.5.1. Host-Guest Chemistry  2.5.2. Self-assembly and molecular recognition  2.5.3. Supramolecular Catalysis  2.5.4. Molecular Machines
  3. Physical Chemistry  3.1. Thermodynamics  3.1.1. Laws of Thermodynamics  3.1.2. Chemical Potential and Equilibrium  3.1.3. Statistical thermodynamics  3.1.4. Non-equilibrium thermodynamics  3.2. Quantum Chemistry  3.2.1. Schrödinger equation and its applications  3.2.2. Molecular orbital theory  3.2.3. Density functional theory  3.2.4. Post-Hartree–Fock methods  3.3. Chemical kinetics  3.3.1. Reaction rate theory  3.3.2. Mechanism and rate laws  3.3.3. Catalysis and enzyme kinetics  3.3.4. Reaction dynamics  3.4. Spectroscopy and molecular structure  3.4.1. Infrared Spectroscopy  3.4.2. UV-visible spectroscopy  3.4.3. Nuclear Magnetic Resonance Spectroscopy  3.4.4. Mass Spectrometry  3.4.5. Raman Spectroscopy  3.5. Surface and Colloid Chemistry  3.5.1. Absorption and Catalysis  3.5.2. Surfactants and micelles  3.5.3. Colloidal Stability  3.5.4. Nanomaterials and Interfaces
  4. Analytical chemistry  4.1. Chromatography  4.1.1. Gas Chromatography  4.1.2. High Performance Liquid Chromatography  4.1.3. Thin Layer Chromatography  4.1.4. Ion Chromatography  4.2. Electroanalytical techniques  4.2.1. Voltammetry and Polarography  4.2.2. Conductometry and potentiometry  4.2.3. Colometry  4.3. Spectroscopic Methods  4.3.1. Atomic absorption spectroscopy  4.3.2. Fluorescence Spectroscopy  4.3.3. X-ray diffraction  4.3.4. Electron paramagnetic resonance spectroscopy  4.4. Chemometrics  4.4.1. Data processing and statistical methods  4.4.2. Multidisciplinary analysis  4.4.3. Machine Learning in Analytical Chemistry
  5. Theoretical and Computational Chemistry  5.1. Molecular dynamics simulation  5.2. Quantum chemistry methods  5.3. Computational drug design  5.4. Machine Learning in Chemistry  5.5. Ab initio molecular dynamics
  6. Biophysics and Medicinal Chemistry  6.1. Drug discovery and design  6.2. Enzyme kinetics and inhibition  6.3. Chemical biology approach  6.4. Protein-ligand interactions  6.5. Bioorthogonal chemistry
  7. Materials chemistry  7.1. Polymer chemistry  7.1.1. Polymerization mechanism  7.1.2. Functional Polymers  7.1.3. Biodegradable Polymer  7.1.4. Conducting and semiconducting polymers  7.2. Nano Chemistry  7.2.1. Nanoparticles and nanostructures  7.2.2. Carbon-based nanomaterials  7.2.3. Quantum dots  7.3. Energy and Environmental Chemistry  7.3.1. Battery and Fuel Cell Chemistry  7.3.2. Green chemistry and sustainable materials  7.3.3. Photocatalysis

PHD → Inorganic chemistry → Coordination chemistry ↓


Ligand field theory


Ligand field theory (LFT) is a concept in coordination chemistry that helps explain the structure and properties of metal complexes. This theory is a modification of crystal field theory (CFT), which provides information about the magnetic properties, color, and structure of coordination complexes. Ligand field theory incorporates ideas from molecular orbital theory, which describe the bonding, structure, and energy levels of coordination compounds.

Background and development

The development of ligand field theory began as an extension and refinement of previously developed crystal field theory. CFT focused primarily on the effect of electrical charges of ligands (non-bonding electron pairs) on the d-orbitals of transition metal ions, leading to the splitting of d-orbital energy levels. However, LFT takes into account both ionic and covalent contributions to metal-ligand bonding.

Understanding crystal field theory

Before delving deeper into LFT, it is important to understand the basics of CFT. In CFT, ligands are approximated as point charges, and the central metal ion is viewed as a positive sphere. When ligands approach a metal ion, they affect the energy of the d-orbitals of the metal ion. This effect causes a splitting of the degenerate d-orbital energies, leading to two sets: t 2g and e g sets in an octahedral complex.

    eg ------ Higher energy d-orbitals (dx^2-y^2 and dz^2) ↑ | Δ ↓ t2g ------ Lower energy d-orbitals (dxy, dyz, dxz)

For tetrahedral complexes, the division is the opposite:

    t2 ------ Higher energy d-orbitals (dxy, dyz, dxz) ↑ | Δ ↓ e ------ Lower energy d-orbitals (dx^2-y^2, dz^2)

From crystal field to ligand field theory

While CFT provided a good explanation for many properties, it failed to address the covalent aspects of metal-ligand bonding. LFT emerged to bridge this gap by incorporating elements of molecular orbital theory, considering both sigma-bonding (σ-bonding) and pi-bonding (π-bonding) interactions between ligands and metal ions.

Molecular orbital framework

In LFT, molecular orbitals are formed by combining atomic orbitals from both the metal and its ligand. These can be visualized in the following steps:

  1. Construction of ligand group orbitals

    The atomic orbitals of the ligand that combine with the d-orbitals of the metal are considered as ligand group orbitals. These orbitals are built from ligand atomic orbitals that are symmetric about the metal-ligand axis.

  2. Formation of molecular orbitals

    Molecular orbitals are formed by the combination of these ligand group orbitals with metal ion orbitals. Generally, sigma and pi bonds are formed depending on the orientation and symmetry of the interacting orbitals.

  3. Energy and electron occupancy

    The energy levels of these molecular orbitals depend on the bond interaction strength. The filled molecular orbitals describe the bonding scenario, which affects the color and magnetic properties of the compound.

Sigma vs Pi Bonding in LFT

One of the important advancements of LFT is the inclusion of both sigma and pi interactions:

  • Sigma bonding - involves the overlap of ligand s or p orbitals with metal d orbitals. This mainly affects t 2g orbitals in octahedral complexes. Sigma donation usually results in an increase in orbital energy due to electrons being placed in anti-bonding orbitals.

  • Pi bonding - Pi interactions can involve pi donation or pi backbonding. In pi donation, filled ligand orbitals donate to empty metal d orbitals. In pi backbonding, filled metal d orbitals overlap with empty ligand pi* orbitals. These interactions have a profound effect on the properties of the complex, influencing the electron distribution and energy levels.

Examples of Different Coordination Complexes

To illustrate these concepts, consider the following examples, which highlight the effects of different partitioning patterns and ligand field interactions:

    [Cr(H2O)6]^{3+}: - Octahedral Complex - High Spin - Weak field ligands (H2O) - Occupation: t2g^3 eg^0 [Fe(CN)6]^{3-}: - Octahedral Complex - Low Spin - Strong field ligands (CN^-) - Occupation: t2g^5 eg^0

Impact on properties

With LFT, we gain a more comprehensive understanding of the various physical and chemical properties of coordination compounds:

Colour

The colours of coordination compounds arise from d-d transitions, which occur between split d-orbitals due to incident light absorption energy. The nature of the ligands strongly influences these transitions. In complex ions, strong field ligands usually absorb shorter wavelengths of light, resulting in the transmission of light in the red spectrum.

Magnetic Properties

The arrangement of metal ion electrons in low and high spin states directly affects the magnetic properties. High spin complexes (weak field ligands) show higher magnetic moments due to more unpaired electrons. In contrast, low spin complexes (strong field ligands) exhibit lower magnetic moments.

Spectrochemical Series

Spectrochemical series rank ligands based on their field strength (ability to split d-orbitals). Examples include:

    I^- < Br^- < S^2- < SCN^- < Cl^- < NO3^- < F^- < OH^- < C2O4^2- < H2O < NCS^- < py < NH3 < en < bipy < phen < NO2^- < PPh3 < CN^- < CO

The ligands on the left side produce weak fields and small splitting, while the ligands on the right side produce strong fields and large splitting.

Conclusion

Ligand field theory plays a vital role in advancing our understanding of coordination chemistry. By providing insight into both ionic and covalent contributions and improving simplified crystal field models, LFT explains a vast range of properties and phenomena related to metal complexes. This understanding enhances our ability to design and use metal complexes in a variety of applications ranging from catalysis to materials science.


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Ligand field theory

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