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X-ray Crystallography02:18

X-ray Crystallography

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The size of the unit cell and the arrangement of atoms in a crystal may be determined from measurements of the diffraction of X-rays by the crystal, termed X-ray crystallography.
Diffraction
Diffraction is the change in the direction of travel experienced by an electromagnetic wave when it encounters a physical barrier whose dimensions are comparable to those of the wavelength of the light. X-rays are electromagnetic radiation with wavelengths about as long as the distance between neighboring...
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Crystal Field Theory - Octahedral Complexes02:58

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Crystal Field Theory
To explain the observed behavior of transition metal complexes (such as colors), a model involving electrostatic interactions between the electrons from the ligands and the electrons in the unhybridized d orbitals of the central metal atom has been developed. This electrostatic model is crystal field theory (CFT). It helps to understand, interpret, and predict the colors, magnetic behavior, and some structures of coordination compounds of transition metals.
CFT focuses on...
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Crystal Field Theory - Tetrahedral and Square Planar Complexes02:46

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Tetrahedral Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
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The Quantum-Mechanical Model of an Atom02:45

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Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
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In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...
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Molecular Orbital Theory I02:35

Molecular Orbital Theory I

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Overview of Molecular Orbital Theory
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Updated: Oct 24, 2025

Microcrystallography of Protein Crystals and In Cellulo Diffraction
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Microcrystallography of Protein Crystals and In Cellulo Diffraction

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Combining crystallography with quantum mechanics.

Justin Bergmann1, Esko Oksanen2, Ulf Ryde1

  • 1Department of Theoretical Chemistry, Lund University, Chemical Centre, P. O. Box 124, SE-221 00 Lund, Sweden.

Current Opinion in Structural Biology
|August 15, 2021
PubMed
Summary
This summary is machine-generated.

Quantum refinement uses quantum mechanical calculations to improve biomacromolecular crystal structures. This method enhances accuracy for ligands and metal sites, correcting errors and determining molecular states.

Keywords:
X-ray crystallographyligand strainprotonation statequantum refinementtautomeric state

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Area of Science:

  • Structural Biology
  • Computational Chemistry
  • Biochemistry

Background:

  • Standard crystallographic refinement relies on empirical restraints for biomacromolecules.
  • These restraints are less accurate for ligands, cofactors, and metal sites compared to amino acids and nucleic acids.

Purpose of the Study:

  • To introduce and evaluate quantum refinement as an alternative to empirical restraints in crystallographic refinement.
  • To improve the accuracy of biomacromolecular structures, particularly at sites with ligands or metal ions.

Main Methods:

  • Quantum refinement replaces empirical restraints with quantum mechanical (QM) calculations.
  • Implementations vary in QM level and application scope (entire structure vs. specific sites).

Main Results:

  • Quantum refinement has been shown to improve and correct errors in crystal structures.
  • The method accurately determines protonation and tautomeric states of various ligands.
  • It aids in resolving structural ambiguities by refining different interpretations.

Conclusions:

  • Quantum refinement offers a more accurate approach for crystallographic data analysis, especially for non-standard residues.
  • This method enhances the reliability of biomacromolecular structures and aids in understanding ligand interactions.