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 → Organic chemistry → Spectroscopy and structural determination ↓


X-ray crystallography


X-ray crystallography is an important method in spectroscopy and structural determination, especially in the field of organic chemistry. It is a technique used to determine the atomic and molecular structure of crystals. In this essay, we will explore the fundamentals of X-ray crystallography, its history, underlying principles, methodology, and its applications in the structural determination of organic compounds.

What is X-ray crystallography?

X-ray crystallography is a powerful analytical technique used to elucidate the arrangement of atoms within crystalline solids. When X-rays enter a crystal, they are diffracted in specific directions. By measuring the angles and intensities of these diffracted rays, it is possible to create a three-dimensional picture of the electron density within the crystal. From this electron density map, the positions of the atoms in the crystal can be identified, along with the chemical bonds, their lengths and angles.

History of X-ray crystallography

The history of X-ray crystallography begins in 1895, when Wilhelm Conrad Röntgen discovered X-rays. In 1912, Max von Laue suggested that a crystal could be used as a diffraction grating for X-rays, leading to the first successful diffraction of X-rays by a crystal lattice. This groundbreaking experiment marked the birth of X-ray crystallography. In 1913, William Henry Bragg and his son, William Lawrence Bragg, developed Bragg's law, which provided the basis for interpreting X-ray diffraction patterns.

Bragg's Law: nλ = 2d sin θ

where n is an integer, λ is the wavelength of the X-ray, d is the distance between atomic layers in the crystal, and θ is the angle of incidence that produces diffraction.

Principles of X-ray crystallography

The principle behind X-ray crystallography is the diffraction of X-rays by the electron cloud around the atoms in a crystal. When X-rays strike a crystal, they are scattered by the electrons in the atoms. The recombination of these scattered waves creates an interference pattern, which can be measured and analyzed.

Constructive Interference occurs when: (Path difference = nλ) Destructive Interference occurs when: (Path difference = (n + 1/2)λ)

Through the use of Fourier transform mathematics, the diffraction data - intensity and angle - are converted into an electron density map. This map allows scientists to determine the spatial arrangement of atoms in the crystal.

Methodology in X-ray crystallography

The process of X-ray crystallography consists of several important steps:

  1. Sample preparation: The first step is to obtain a suitable crystal of the substance being studied. The crystal must be of high quality, as imperfections can affect the diffraction pattern.
  2. Data collection: The crystal is mounted on a goniometer in an X-ray diffractometer, which rotates it while exposing it to X-rays. The diffracted rays are detected and recorded as data.
  3. Data processing: The raw diffraction data are processed to produce a set of reflections, each of which has a set of intensities and indices (h, k, l) that correspond to the crystal planes involved.
  4. The phase problem: Since only the intensity of the diffracted waves can be measured, phase information is lost, leading to the 'phase problem' which must be solved to produce accurate electron density maps.
  5. Model building: With the phase information obtained, an electron density map is calculated. Scientists create an atomic model that fits the map, and they refine this model to obtain the best possible fit to the diffraction data.

Visualization of the crystal lattice

Consider a simple face-centered cubic (FCC) lattice structure. The arrangement of atoms in such a lattice can be visualized by depicting the unit cell. Here is a simplified visual example using HTML/SVG:

In this diagram, the red circles represent the positions of atoms at the corners and center of each face of the cubic cell.

X-ray sources and detectors

The quality of X-ray beams and detectors is paramount in crystallography. Modern X-ray sources include synchrotrons, which produce high-intensity beams, and rotating anode generators. Detectors such as charge-coupled devices (CCDs) or pixel array detectors (PADs) capture the diffracted X-rays with high precision.

Applications of X-ray crystallography in organic chemistry

X-ray crystallography has wide applications in organic chemistry, providing detailed information about complex molecular structures.

  • Determining molecular geometry: The precise geometry of organic molecules, including bond angles and bond lengths, is essential to understanding their chemical properties.
  • Study of reaction mechanisms: By observing structural changes in reactants and products, chemists can elucidate reaction mechanisms.
  • Drug design: In medicinal chemistry, crystallography helps understand the binding of drugs to their target proteins, and guides the rational design of new drugs.

Challenges and limitations of X-ray crystallography

Despite its power, X-ray crystallography faces challenges:

  1. Crystal quality: High quality single crystals are required, which may be difficult to grow for some compounds.
  2. Phase problem: As mentioned, phase information is lost internally, complicating the solution.
  3. Dynamics and dislocations: Crystallography provides a static picture, but it is difficult to analyze dynamic phenomena or dislocations in crystals.

Future prospects

The field of X-ray crystallography is constantly evolving. Advances in technology, such as cryo-crystallography and in situ methods, improve data quality and broaden the range of suitable samples. Computational advances in solving the phase problem and processing large datasets portend a promising future for structural determination in organic chemistry.

Conclusion

X-ray crystallography remains an indispensable tool in organic chemistry, providing unrivalled insight into the molecular world. Its contributions to science have been enormous, influencing countless fields from fundamental chemistry to advanced medical research. As the technology advances, X-ray crystallography will undoubtedly continue to unravel the intricacies of structural chemistry.


Graduate → 2.2.5


U
username
0%
completed in Graduate

← Prev (2.2.4)
Mass Spectrometry
Next (2.3) →
Stereoscopic

Comments 



X-ray crystallography

https://www.chemistryelite.com/g/2.2.5?ceal=en