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Related Concept Videos

The Periodic Table03:25

The Periodic Table

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As early chemists discovered more elements, they realized that various elements could be grouped by their similar chemical behaviors. One such grouping includes lithium (Li), sodium (Na), and potassium (K). All of these elements are shiny, conduct heat and electricity well, and have similar chemical properties. A second grouping includes calcium (Ca), strontium (Sr), and barium (Ba), which also are shiny, good conductors of heat and electricity, and have chemical properties in common. However,...
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Periodic Classification of the Elements04:00

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The periodic table arranges atoms based on increasing atomic number so that elements with the same chemical properties recur periodically. When their electron configurations are added to the table, a periodic recurrence of similar electron configurations in the outer shells of these elements is observed. Because they are in the outer shells of an atom, valence electrons play the most important role in chemical reactions. The outer electrons have the highest energy of the electrons in an atom...
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VSEPR Theory and the Basic Shapes02:52

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Overview of VSEPR Theory
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Electron Configurations02:46

Electron Configurations

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Electron configurations and orbital diagrams can be determined by applying the Aufbau principle (each added electron occupies the subshell of lowest energy available), Pauli exclusion principle (no two electrons can have the same set of four quantum numbers), and Hund’s rule of maximum multiplicity (whenever possible, electrons retain unpaired spins in degenerate orbitals).
The relative energies of the subshells determine the order in which atomic orbitals are filled (1s, 2s, 2p, 3s, 3p,...
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Atomic Orbitals02:44

Atomic Orbitals

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An atomic orbital represents the three-dimensional regions in an atom where an electron has the highest probability to reside. The radial distribution function indicates the total probability of finding an electron within the thin shell at a distance r from the nucleus. The atomic orbitals have distinct shapes which are determined by l, the angular momentum quantum number. The orbitals are often drawn with a boundary surface, enclosing densest regions of the cloud.
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Predicting Molecular Geometry02:27

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VSEPR Theory for Determination of Electron Pair Geometries
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X-ray Powder Diffraction in Conservation Science: Towards Routine Crystal Structure Determination of Corrosion Products on Heritage Art Objects
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A periodic-like table of space groups.

Bart Kahr1

  • 1Department of Chemistry and Molecular Design Institute, New York University, 29 Washington Place, New York City, NY 10003, USA.

Acta Crystallographica. Section E, Crystallographic Communications
|March 13, 2023
PubMed
Summary

A new periodic-like table organizes crystallographic space groups, making them accessible to a wider audience. This visualization aids in understanding solid-state structures and their symmetries.

Keywords:
BarlowFedorovSchoenfliesperiodic tablepoint groupsspace groupssymmorphic

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Area of Science:

  • Crystallography
  • Solid-state chemistry
  • Discrete mathematics

Background:

  • The 230 crystallographic space groups describe the symmetry of all possible crystals.
  • The periodic table of elements is a well-known organizational tool in chemistry.
  • Space groups are less accessible to non-specialists compared to chemical elements.

Purpose of the Study:

  • To create a novel, periodic table-like chart for organizing crystallographic space groups.
  • To enhance the accessibility and understanding of space groups for a broader scientific audience.
  • To inspire new designs and applications in solid-state science.

Main Methods:

  • Developing a two-dimensional chart using non-linear, non-orthogonal axes.
  • Organizing symmorphic space groups based on point group symmetry and order.
  • Representing non-symmorphic space groups as 'isotopes' of symmorphic groups via subscript notation.

Main Results:

  • A new periodic-like table for space groups has been designed.
  • The table visually organizes space groups, capturing their symmetry and multiplicity.
  • This approach simplifies the representation of complex crystallographic information.

Conclusions:

  • The designed table makes space groups more intuitive and accessible.
  • This visualization can foster wider interest and application of space group concepts.
  • The periodic-like structure aids in understanding the relationships between different space groups.