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Related Concept Videos

Coordination Number and Geometry02:57

Coordination Number and Geometry

16.2K
For transition metal complexes, the coordination number determines the geometry around the central metal ion. Table 1 compares coordination numbers to molecular geometry. The most common structures of the complexes in coordination compounds are octahedral, tetrahedral, and square planar.
16.2K
Crystal Field Theory - Octahedral Complexes02:58

Crystal Field Theory - Octahedral Complexes

26.9K
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...
26.9K
Crystal Field Theory - Tetrahedral and Square Planar Complexes02:46

Crystal Field Theory - Tetrahedral and Square Planar Complexes

43.2K
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,...
43.2K
Metallic Solids02:37

Metallic Solids

18.5K
Metallic solids such as crystals of copper, aluminum, and iron are formed by metal atoms. The structure of metallic crystals is often described as a uniform distribution of atomic nuclei within a “sea” of delocalized electrons. The atoms within such a metallic solid are held together by a unique force known as metallic bonding that gives rise to many useful and varied bulk properties.
All metallic solids exhibit high thermal and electrical conductivity, metallic luster, and malleability....
18.5K
Valence Bond Theory02:42

Valence Bond Theory

8.8K
Coordination compounds and complexes exhibit different colors, geometries, and magnetic behavior, depending on the metal atom/ion and ligands from which they are composed. In an attempt to explain the bonding and structure of coordination complexes, Linus Pauling proposed the valence bond theory, or VBT, using the concepts of hybridization and the overlapping of the atomic orbitals. According to VBT, the central metal atom or ion (Lewis acid) hybridizes to provide empty orbitals of suitable...
8.8K
Molecular Shapes01:18

Molecular Shapes

57.0K
Molecules have characteristic shapes that are crucial for their function. The arrangement of various electron groups around the central atom dictates their molecular geometry. Electron pairs in the valence shell of a central atom will adopt an arrangement that minimizes repulsions between the electron pairs by maximizing the distance between them. The valence electrons form either bonding pairs, located primarily between bonded atoms, or lone pairs.
Two regions of electron density in a diatomic...
57.0K

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Updated: Jul 27, 2025

The Synthesis of [Sn10SiSiMe334]2- Using a Metastable SnI Halide Solution Synthesized via a Co-condensation Technique
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The Synthesis of [Sn10SiSiMe334]2- Using a Metastable SnI Halide Solution Synthesized via a Co-condensation Technique

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Mathematical Geometry and Groups for Low-Symmetry Metal Complex Systems.

Takashiro Akitsu1

  • 1Department of Chemistry, Faculty of Science, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan.

Molecules (Basel, Switzerland)
|June 10, 2023
PubMed
Summary

New mathematical approaches are needed for chemical research, especially for low-symmetry molecules. This will leverage advancements in computational chemistry and artificial intelligence for material design.

Keywords:
coordination chemistrycrystal structuregeometrygroup theorylow symmetry

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Construction and Systematical Symmetric Studies of a Series of Supramolecular Clusters with Binary or Ternary Ammonium Triphenylacetates
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Area of Science:

  • Chemistry, materials science, and crystallography utilize mathematical principles like geometry and symmetry for analyzing 3D structures.

Background:

  • Topology and differential geometry have found increasing applications in material design and chemistry.
  • Existing mathematical tools like group theory are effective for high-symmetry crystals but limited for low-symmetry molecules.
  • Crystal structure databases offer big data potential for computational chemistry methods like Hirshfeld surface analysis.

Purpose of the Study:

  • To highlight the limitations of current mathematical methods in chemistry for low-symmetry molecules.
  • To advocate for the development of novel mathematical approaches tailored for modern computational chemistry and AI.

Main Methods:

  • Review of existing mathematical applications in chemistry, materials science, and crystallography.
  • Analysis of the utility of topology, differential geometry, and group theory.
  • Consideration of big data from crystal structure databases for computational chemistry.

Main Results:

  • Traditional mathematical methods like group theory are insufficient for analyzing low-symmetry molecules.
  • The increasing role of computational chemistry and artificial intelligence necessitates new mathematical frameworks.
  • Emerging areas like topology and big data analysis offer new avenues for chemical research.

Conclusions:

  • There is a critical need for new mathematical strategies in chemical research.
  • These new methods must be compatible with computational chemistry and artificial intelligence.
  • Advancing material design and understanding molecular properties requires innovative mathematical tools.