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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.
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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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In the late 1800s, the revelation that light extended beyond visible wavelengths led to the discovery of X-rays by Wilhelm Roentgen. Recognized as high-energy electromagnetic radiation with short wavelengths, X-rays prompted exploration into their interaction with crystals. Max von Laue proposed in 1912 that the periodic arrangement of atoms, ions, or molecules in crystals would cause them to diffract X-rays, a hypothesis confirmed through experiments with copper sulfate and zinc sulfide...
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Crystals with various point group symmetries belong to different crystal classes, which are synonymous terms. Despite being in the same class, crystals may have distinct shapes, like cubes and octahedra. There are 32 three-dimensional point groups, all of which are systematically divided into seven crystal systems.The basic cubic crystal system, exemplified by NaCl, features orthogonal vectors (α = β = �� = 90°) of equal lengths (a = b = c). When specific...
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Schottky defects arise when some lattice points in a crystal, such as those in NaCl, remain unoccupied, creating lattice vacancies without disturbing the overall electrical neutrality of the crystal. This defect is common in ionic crystals where the positive and negative ions are similar in size, as seen in sodium chloride and cesium chloride. The presence of Schottky defects enables the crystal to conduct electricity to a small extent through an ionic mechanism. Electric fields cause nearby...
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Crystallographic Point Groups01:29

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Crystallographic point groups represent the various symmetry operations that can occur within crystals. They are unique in that at least one point will always remain unchanged during these actions. For instance, consider the triclinic system. This system, devoid of any axis or plane of symmetry, aligns with the C1 and Ci point groups.where Cᵢ is characterized solely by a center of inversion.Contrastingly, the monoclinic system introduces an element of symmetry. This system with one plane...
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Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
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Organic crystal polymorphism: a benchmark for dispersion-corrected mean-field electronic structure methods.

Jan Gerit Brandenburg1, Stefan Grimme1

  • 1Mulliken Center for Theoretical Chemistry, University of Bonn, Beringstrasse 4-6, 53115 Bonn, Germany.

Acta Crystallographica Section B, Structural Science, Crystal Engineering and Materials
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PubMed
Summary

We evaluated quantum chemical methods for crystal structure prediction, finding that density functionals with D3 and many-body dispersion corrections accurately rank polymorphs. Low-cost methods offer reasonable performance with significant speed-up.

Keywords:
London dispersionbenchmarkcrystal structure predictiondensity functional theorypolymorphism

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Area of Science:

  • Computational Chemistry
  • Materials Science
  • Quantum Mechanics

Background:

  • Crystal structure prediction is crucial for materials design.
  • Accurate modeling of intermolecular forces, especially London dispersion, is challenging.
  • Existing benchmark sets are vital for evaluating quantum chemical methods.

Purpose of the Study:

  • To assess various quantum chemical methods for crystal structure prediction.
  • To introduce a new benchmark dataset (POLY59) for method evaluation.
  • To investigate the impact of different dispersion correction schemes within DFT.

Main Methods:

  • Analysis of first principles and semi-empirical quantum chemical methodologies.
  • Application of pairwise dispersion corrections (D2, TS, dDsC) and higher-order corrections (D3, MBD, vdW-DF2).
  • Testing of computationally inexpensive methods: minimal basis Hartree-Fock (HF-3c) and density functional tight-binding (DFTB).

Main Results:

  • Density functionals with D3 and MBD corrections achieved excellent agreement with experimental polymorph rankings.
  • TPSS-D3 demonstrated superior performance when comparing computed geometries with X-ray data.
  • Low-cost methods (HF-3c, DFTB) provided reasonable energy rankings with substantial computational savings.

Conclusions:

  • Advanced dispersion corrections (D3, MBD) are highly effective for crystal structure prediction.
  • Cost-effective methods can offer viable alternatives for large-scale screening.
  • Zero-point vibrational energy and thermal effects influence crystal densities.