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 ↓


Crystal field theory


Introduction

Crystal field theory (CFT) is a model that describes the electronic structure of transition metal complexes. This theory was developed to understand the behaviour, colour, magnetism and even stability of metal complexes. In CFT, the effect of the field created by the surrounding ligands on the d-orbitals of the transition metal is considered to predict the properties of the complex.

Fundamentals of crystal field theory

The basis of CFT lies in viewing the ligand as a point charge (especially applicable in ionic complexes such as [Ti(H 2 O) 6 ] 3+), applying an electric field to the d-orbitals of the metal ion. When the ligands approach the central metal atom, they interact with its d-electrons, causing a shift in energy levels. This results in the d-orbitals being split into different energy levels.

Splitting of d-orbitals

In an isolated metal atom, the energy levels of the five d-orbitals are the same (degenerate). However, due to the presence of ligands these orbitals get split into different energy levels. The pattern and extent of this splitting depends on the nature of the ligand and the geometry of the ligand arrangement.

Octahedral complex

Consider the general case of an octahedral complex where six ligands are arranged symmetrically around a central metal ion.

In the octahedral crystal region, the d-orbitals split into two groups:

  • t 2g: It contains d xy, d yz and d zx orbitals.
  • Example: It involves dx2 - y2 and dz2 orbitals.

This interaction results in a characteristic energy difference, usually denoted by the Greek letter Δ, often referred to as the crystal field splitting energy. In octahedral complexes, Δ oct is the energy difference between two orbitals.

2 orbitals (eg g) 3 orbitals (t 2g) Δ October

The above figure shows the splitting of d-orbitals in an octahedral field, where the t 2g orbitals have lower energy than the e g orbitals.

Tetrahedral complex

Unlike octahedral complexes, tetrahedral complexes involve four ligands arranged around the metal ion to form a tetrahedron.

For tetrahedral coordination, the d-orbitals split as follows:

  • e: Made up of d x 2 -y 2 and d z 2 orbitals.
  • t 2: Consists of d xy, d yz, and d zx orbitals.

Here, the energy gap between these orbitals, Δtet, is smaller than that typically observed in octahedral complexes, due to the less symmetric arrangement of the ligands.

3 orbitals (t 2) 2 orbitals (e) Δ Tet

The difference between octahedral and tetrahedral fission is clear: the order of the orbital energies is reversed, and tetrahedral fission is smaller.

Factors affecting crystal field splitting

The magnitude of the crystal field splitting energy (Δ) is affected by several factors:

Nature of metal ion

The oxidation state and principal quantum number of the metal ion directly affect Δ. Higher oxidation states generally increase Δ, due to increased electrostatic interactions between the metal ion and the ligand.

Nature of the ligand

Different ligands produce different crystal fields, as summarized by the "spectrochemical series", which orders ligands based on their ability to split d-orbitals: 

I - < Br - < S 2- < Cl - < F - < OH - < H 2 O < NH 3 < en < C 2 O 4 2- < CN - < CO
Ligands on the right, such as CO or CN -, produce greater splitting than ligands on the left, such as I - or Br -.

Complex geometry

As discussed, octahedral and tetrahedral geometries result in different splitting patterns and magnitudes. Square planar complexes exhibit higher Δ values than octahedral complexes due to increased asymmetry.

Applications and implications of crystal field theory

Understanding crystal field splitting helps explain many properties of transition metal complexes.

Colour

Transitions of electrons between split d-orbitals lead to the absorption of specific wavelengths of light. The color seen is the complementary color of the absorbed light. For example, a complex absorbing red light will appear green.

Magnetism

The electron arrangement in the split d-orbitals determines the magnetic behaviour of the complexes. Filled t 2g- orbitals and empty e g orbitals result in diamagnetic complexes, while unpaired electrons induce paramagnetism.

Stability

The stability of metal complexes can be predicted based on the splitting. Larger Δ values usually indicate greater stability due to the higher energy required to move electrons between orbitals.

Conclusion

Crystal field theory provides an important understanding of the behaviour of transition metal complexes. This theory provides insight into the effects of ligand arrangement and allows prediction of properties such as colour, magnetism and stability. Its applications extend to areas such as catalysis, materials science and bioinorganic chemistry, highlighting its importance and continued relevance in modern chemistry.


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Crystal field theory

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