Graduate
  1. Physical Chemistry  1.1. Thermodynamics  1.1.1. Laws of Thermodynamics  1.1.2. Enthalpy and heat capacity  1.1.3. Entropy and free energy  1.1.4. Phase Equilibrium  1.1.5. Statistical thermodynamics  1.1.6. Thermodynamic cycle  1.1.7. Fugacity and activity  1.2. Quantum Chemistry  1.2.1. Principles of quantum mechanics  1.2.2. Schrödinger Equation  1.2.3. Particle in a box  1.2.4. Operators and eigenvalues  1.2.5. Atomic orbitals  1.2.6. Molecular orbital theory  1.2.7. Perturbation theory  1.2.8. Valence bond theory  1.2.9. Hybridization and chemical bonding  1.3. Chemical kinetics  1.3.1. Rate laws and reaction mechanisms  1.3.2. Collision theory  1.3.3. Transition state theory  1.3.4. Enzyme Kinetics  1.3.5. Chain Reactions and Polymerization  1.3.6. Photochemical reactions  1.4. Statistical mechanics  1.4.1. Partitioning functions  1.4.2. Molecular distribution functions  1.4.3. Boltzmann Distribution  1.4.4. Bose–Einstein and Fermi–Dirac statistics  1.5. Spectroscopy  1.5.1. Rotational Spectroscopy  1.5.2. Vibrational Spectroscopy  1.5.3. Electronic Spectroscopy  1.5.4. Nuclear magnetic resonance spectroscopy  1.5.5. Mass Spectrometry  1.5.6. Raman Spectroscopy  1.5.7. Electron paramagnetic resonance spectroscopy  1.6. Surface and colloidal chemistry  1.6.1. Absorption isotherm  1.6.2. Surface tension and wetting  1.6.3. Colloidal Stability  1.6.4. Catalysis  1.6.5. Emulsions and micelles  1.7. Electrochemistry  1.7.1. Nernst equation  1.7.2. Electrochemical cells  1.7.3. Conductivity and mobility  1.7.4. War  1.7.5. Fuel cells  1.7.6. Electrolysis
  2. Organic chemistry  2.1. Reaction mechanism  2.1.1. Nucleophilic substitution reactions  2.1.2. Electrophilic addition reactions  2.1.3. Elimination reactions  2.1.4. Rearrangement reactions  2.1.5. Radical reactions  2.1.6. Pericyclic reactions  2.2. Spectroscopy and structural determination  2.2.1. UV-Vis Spectroscopy  2.2.2. IR Spectroscopy  2.2.3. NMR Spectroscopy  2.2.4. Mass Spectrometry  2.2.5. X-ray crystallography  2.3. Stereoscopic  2.3.1. Chirality and optical activity  2.3.2. Structural analysis  2.3.3. Geometrical isomerism  2.3.4. Dynamic Stereochemistry  2.4. Organometallic Chemistry  2.4.1. Organolithium and organomagnesium reagents  2.4.2. Palladium-catalyzed cross-coupling reactions  2.4.3. Transition Metal Complexes  2.4.4. Metal–carbon bond  2.5. Polymer chemistry  2.5.1. Polymerization mechanism  2.5.2. Polymer Characteristics  2.5.3. Biodegradable Polymer  2.5.4. Conducting polymer  2.5.5. Supramolecular polymers  2.6. Medicinal chemistry  2.6.1. Drug design and development  2.6.2. Pharmacokinetics and pharmacodynamics  2.6.3. Structure-activity relationships  2.6.4. Molecular docking and drug screening
  3. Inorganic chemistry  3.1. Coordination chemistry  3.1.1. Crystal field theory  3.1.2. Ligand field theory  3.1.3. Spectrochemical Series  3.1.4. Chelation and stability  3.2. Organometallic Chemistry  3.2.1. Metal Carbonyls  3.2.2. Catalysis by organometallic complexes  3.2.3. Metallocenes  3.3. Bio-inorganic chemistry  3.3.1. Metalloproteins and enzymes  3.3.2. The role of metals in biological systems  3.3.3. Metal ion transport and storage  3.4. Solid state chemistry  3.4.1. Crystal Structures  3.4.2. Band theory of solids  3.4.3. Superconductors  3.4.4. Defects in the crystal  3.5. Lanthanides and Actinides  3.5.1. Electronic configuration in lanthanides and actinides  3.5.2. Coordination chemistry of the lanthanides  3.5.3. Magnetic Properties of Lanthanides
  4. Analytical chemistry  4.1. Chromatography  4.1.1. Gas Chromatography  4.1.2. High Performance Liquid Chromatography  4.1.3. Thin Layer Chromatography  4.2. Spectroscopic Techniques  4.2.1. Atomic absorption spectroscopy  4.2.2. X-ray diffraction  4.2.3. Inductively coupled plasma spectroscopy  4.3. Electroanalytical methods  4.3.1. Potentiometry  4.3.2. Voltammetry  4.3.3. Colometry  4.4. Mass Spectrometry  4.4.1. Ionization Technique  4.4.2. Fragmentation Pattern  4.5. Chemometrics  4.5.1. Multidisciplinary analysis  4.5.2. Machine Learning in Chemistry
  5. Theoretical and Computational Chemistry  5.1. Molecular dynamics simulation  5.1.1. Force fields and energy minimization  5.1.2. Monte Carlo simulation in molecular dynamics simulations  5.2. Quantum chemical methods  5.2.1. Hartree–Fock theory  5.2.2. Density functional theory  5.2.3. Semi-empirical methods  5.3. Computational drug design  5.3.1. Molecular Docking  5.3.2. QSAR Modeling  5.3.3. Virtual Screening
  6. Biochemistry  6.1. Enzyme Kinetics  6.1.1. Michaelis-Menten kinetics  6.1.2. Inhibition mechanism  6.2. Metabolism and Bioenergetics  6.2.1. Glycolysis  6.2.2. Citric acid cycle  6.2.3. Electron transport chain  6.3. molecular Biology  6.3.1. DNA replication and repair  6.3.2. Protein synthesis  6.3.3. Gene Regulation  6.4. Structural Biochemistry  6.4.1. Protein Folding  6.4.2. Membrane Biophysics
  7. Environmental Chemistry  7.1. Atmospheric Chemistry  7.1.1. Greenhouse gases  7.1.2. Ozone depletion  7.1.3. Air pollutants and smoke  7.2. Water Chemistry  7.2.1. pH and water hardness  7.2.2. Wastewater treatment  7.2.3. Aquatic Chemistry  7.3. Soil Chemistry  7.3.1. Heavy metal contamination  7.3.2. Soil pH and Buffering  7.3.3. Nutrient cycling  7.4. Toxicology and Chemical Safety  7.4.1. Toxicokinetics  7.4.2. Risk Assessment in Toxicology and Chemical Safety in Environmental Chemistry  7.4.3. Effects of pollutants on the environment

Graduate → Inorganic chemistry → Coordination chemistry ↓


Ligand field theory


Ligand field theory (LFT) is a concept used in coordination chemistry to explain the behavior of metal complexes. It explores how different ligands affect the energy of d orbitals in transition metal ions, which in turn affects the properties of these complexes, such as their color and magnetic behavior. LFT is an extension of crystal field theory (CFT) that takes into account the covalent nature of metal-ligand bonds, while CFT is purely ionic in nature. Let's dive deeper into the details of ligand field theory.

Basic concepts of ligand field theory

The main idea of ligand field theory is to understand the splitting of the degenerate d orbitals of the transition metal when it is surrounded by ligands. This splitting is important for explaining the electronic and magnetic properties of the complex. The interaction between the electrons in the d orbitals of the metal and the electrons in the ligands causes the splitting.

d Orbitals: d xy, d yz, d zx, d x²-y², d z²

When a transition metal forms a complex with a ligand, the d orbitals are split into different energy levels. The pattern of this splitting depends on the geometry of the complex, i.e., the arrangement of the ligands around the metal ion. This can affect the colour of the complex, as different energy levels mean that different wavelengths of light are absorbed and thus different colours appear.

Energy level splitting

In an isolated metal ion, all five d orbitals are degenerate, meaning that they have the same energy. However, when ligands approach the metal ion, the electrostatic field created by them splits these orbitals. The nature and magnitude of this splitting depends on the symmetry and strength of the ligand's field.

Octahedral complex

Most transition metal complexes adopt octahedral geometry, where six ligands symmetrically surround the metal ion. In this configuration, the d orbitals are split into two different energy levels:

T2G e.g. d xy, d yz, d zx d x² - y², d z²

t 2g level consists of dxy, dyz and dzx orbitals. e g level consists of dx² -y² and dz² orbitals. The energy difference between these two sets of orbitals is called the crystal field splitting energy, represented by ∆ o.

Tetrahedral complex

In a tetrahedral complex, four ligands surround the metal ion. The splitting of the d orbitals in the tetrahedral field is the opposite of that in the octahedral field:

E T2 d x² - y², d z² d xy, d yz, d zx

Here, e set of orbitals (d x²-y² and d z²) is lower in energy than t 2 set (d xy, d yz, d zx). The energy difference is represented by ∆ t, and generally, ∆ t ≈ 4/9 ∆ o.

Role of ligands

The type of ligand can significantly affect the crystal field splitting energy. Ligands are arranged in a series known as the spectrochemical series, which ranks them according to their field strength:

I - < Br - < S 2- < SCN - < Cl - < NO 3 - < F - < OH - < H 2O < NH 3 < en < NO 2 - < CN - ≈ CO

Ligands located on the left side of the chain are called "weak field" ligands and generally result in lower splitting energies. In contrast, "strong field" ligands present on the right side of the chain cause larger splitting energies.

Electron configuration and spin states

The way in which the d electrons fill the split orbitals depends on the magnitude of the splitting energy relative to the electron pairing energy. This results in two possible configurations:

High spin complexes

In high spin complexes, the crystal field splitting energy is smaller than the pairing energy. Electrons will occupy higher energy orbitals to maximize the unpaired spin.

Low spin complex

For low spin complexes, the splitting energy is greater than the pairing energy, so fewer unpaired spins exist as the electrons pair up in lower energy orbitals.

Implications of ligand field theory

Ligand field theory explains a variety of complex properties:

  • Colours of complexes: Since different frequencies of light are absorbed to promote dd transitions within the split d orbitals, the complexes exhibit various colours.
  • Magnetic properties: The number of unpaired electrons obtained from the d orbital configuration affects the magnetic nature of the compound: paramagnetic if all are unpaired, and diamagnetic if all are paired.

Mathematical treatment

Ligand field theory can also be described quantitatively using mathematical models to calculate the energy of orbitals and the effects of ligand fields. These models use quantum mechanical principles and group theory.

Conclusion

Ligand field theory builds on crystal field theory by considering the covalent character of metal-ligand interactions. It provides a comprehensive framework for understanding the behavior of metal complexes, particularly with respect to their electronic structures and resulting properties such as color and magnetism. This understanding helps scientists and chemists optimize the properties of complexes for specific applications in areas such as materials science, catalysis, and bio-inorganic chemistry.


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Ligand field theory

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