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Updated: Aug 29, 2025
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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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Chirality in the Solid State: Chiral Crystal Structures in Chiral and Achiral Space Groups
Gerhard H Fecher1, Jürgen Kübler2, Claudia Felser1
1Max Planck Institute for Chemical Physics of Solids, D-01187 Dresden, Germany.
Materials (Basel, Switzerland)
|September 9, 2022
Summary
This study classifies chiral crystal structures and quantifies their chirality. It proposes using circular dichroism in photoelectron angular distributions to distinguish the handedness of chiral solids and surfaces.
Area of Science:
- Crystallography
- Solid-state physics
- Quantum chemistry
Background:
- Chirality in crystal structures is defined by the absence of mirror planes and inversion centers, allowing only rotations as symmetry elements.
- Chiral space groups exhibit further restrictions on screw rotations, appearing as enantiomorphous pairs.
- Understanding and quantifying chirality in solids and surfaces is crucial for materials science and condensed matter physics.
Purpose of the Study:
- To classify and distinguish chiral crystal structures and space groups.
- To quantify chirality using Hausdorff distances and continuous chirality measures.
- To explore the relationship between chirality and electronic band structure properties.
Main Methods:
- Classification of chiral structures and space groups.
- Quantification of chirality using Hausdorff distances and continuous chirality measures.
- Analysis of band structure, density of states, and Berry curvature in relation to chirality.
Main Results:
- Chirality is quantified for selected crystal structures.
- Band structure and density of states are influenced by crystal parameters related to chirality but not handedness.
- Berry curvature depends on handedness but is not a definitive proof of chirality due to its response to inversion.
Conclusions:
- A method is proposed to quantify and distinguish chiral solids and surfaces.
- Circular dichroism in the angular distribution of photoelectrons is suggested as a tool to determine the handedness of chiral solids and surfaces.
- The study links crystallographic chirality to electronic properties and proposes an experimental method for characterization.
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