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Related Concept Videos

Chirality02:25

Chirality

24.4K
Chirality is a term that describes the lack of mirror symmetry in an object. In other words, chiral objects cannot be superposed on their mirror images. For example, our feet are chiral, as the mirror image of the left foot, the right foot, cannot be superposed on the left foot.
Chiral objects exhibit a sense of handedness when they interact with another chiral object. For example, our left foot can only fit in the left shoe and not in the right shoe. Achiral objects — objects that have...
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Lattice Centering and Coordination Number02:33

Lattice Centering and Coordination Number

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The structure of a crystalline solid, whether a metal or not, is best described by considering its simplest repeating unit, which is referred to as its unit cell. The unit cell consists of lattice points that represent the locations of atoms or ions. The entire structure then consists of this unit cell repeating in three dimensions. The three different types of unit cells present in the cubic lattice are illustrated in Figure 1.
Types of Unit Cells
Imagine taking a large number of identical...
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Trends in Lattice Energy: Ion Size and Charge02:54

Trends in Lattice Energy: Ion Size and Charge

24.0K
An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure of the strength of this attraction. The lattice energy (ΔHlattice) of an ionic compound is defined as the energy required to separate one mole of the solid into its component gaseous ions. For the ionic solid sodium chloride, the lattice energy is the enthalpy change of the process:
24.0K
Molecules with Multiple Chiral Centers02:25

Molecules with Multiple Chiral Centers

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Molecules that possess multiple chiral centers can afford a large number of stereoisomers. For instance, while some molecules like 2-butanol have one chiral center, defined as a tetrahedral carbon atom with four different substituents attached, several molecules like butane-2,3-diol have multiple chiral centers. A simple formula to predict the number of stereoisomers possible for a molecule with n chiral centers is 2n. However, there can be a lower number where some of the stereoisomers are...
11.8K
Stereoisomerism of Cyclic Compounds02:33

Stereoisomerism of Cyclic Compounds

9.0K
In this lesson, we delve into the role of ring conformation and its stability, which determines the spatial arrangement and, consequently, the molecular symmetry and stereoisomerism of cyclic compounds. 1,2-Dimethylcyclohexane is used as a case study to evaluate the possible number of stereoisomers. Here, given the multiple (n = 2) chiral centers, there are 2n = 4 possible configurations that lack a plane of symmetry, as the ring skeleton exists in a non-planar chair conformation. In addition,...
9.0K
Fischer Projections02:18

Fischer Projections

13.5K
Learning to draw Fischer projections of molecules and understanding their relevance plays a crucial role in the visual depiction of organic molecules. A Fischer projection is a two-dimensional projection on a planar surface to simplify the three-dimensional wedge–dash representation of molecules. This is especially helpful in the case of molecules with multiple chiral centers that can be difficult to draw. Here, all the bonds of interest are represented as horizontal or vertical lines.
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Related Experiment Video

Updated: Jul 26, 2025

Construction and Systematical Symmetric Studies of a Series of Supramolecular Clusters with Binary or Ternary Ammonium Triphenylacetates
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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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Continuous chiral distances for two-dimensional lattices.

Matthew J Bright1, Andrew I Cooper1, Vitaliy A Kurlin1

  • 1Computer Science Department and Materials Innovation Factory, University of Liverpool, Liverpool, UK.

Chirality
|June 21, 2023
PubMed
Summary
This summary is machine-generated.

Chirality in 2D lattices is now a continuous property, not just binary. New distance metrics quantify deviations from higher symmetry, analyzing millions of real-world crystal structures.

Keywords:
chiral distancecontinuous metricisometryrigid motiontwo-dimensional material

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Area of Science:

  • Crystallography
  • Materials Science
  • Geometry

Background:

  • Chirality in periodic lattices was traditionally viewed as a binary, on/off property.
  • Recent work parametrized two-dimensional (2D) lattice classes as a continuous space using geographic-style coordinates.
  • Four non-oblique Bravais classes represent singular subspaces within this continuous space.

Purpose of the Study:

  • To continuously quantify lattice deviations from higher symmetry neighbors.
  • To analyze newly developed G-chiral distances for 2D lattices.
  • To apply these metrics to a large dataset of real 2D materials and crystal structures.

Main Methods:

  • Parametrization of 2D lattice classes in a continuous space.
  • Development and application of real-valued distance metrics satisfying metric axioms.
  • Analysis of millions of 2D lattices from the Cambridge Structural Database.

Main Results:

  • Lattice deviations from higher symmetry can be continuously measured using real-valued distances.
  • New G-chiral distances provide a quantitative measure for lattice chirality.
  • The study analyzed millions of 2D lattices from diverse material and crystal structures.

Conclusions:

  • Chirality in 2D lattices can be treated as a continuous variable, extending beyond the traditional binary classification.
  • Quantitative distance metrics offer a powerful tool for analyzing subtle variations in lattice structures.
  • The findings have implications for understanding and classifying complex 2D materials.