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Chirality

Chirality

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...

Prochirality

Prochirality

The concept of prochirality leads to the nomenclature of the individual faces of a molecule and plays a crucial role in the enantioselective reaction. It is a concept where two or more achiral molecules react to produce chiral products. A typical process is the reaction of an achiral ketone to generate a chiral alcohol. Here, the achiral reactant reacts with an achiral reducing agent, sodium borohydride, to generate an equimolar mixture of the chiral enantiomers of the product. For example, an...

Molecules with Multiple Chiral Centers

Molecules with Multiple Chiral Centers

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...

Radicals: Electronic Structure and Geometry

Radicals: Electronic Structure and Geometry

This lesson delves into the geometry of a radical, which is influenced by the electronic structure of the molecule. The principle is similar to that of a lone pair, where the unpaired electron influences the geometry at the radical center.
Accordingly, the structure of a trivalent radical lies between the geometries of carbocations and carbanions. An sp2-hybridized carbocation is trigonal planar, while an sp3-hybridized carbanion is trigonal pyramidal. Here, the difference in geometry is...

Chirality in Nature

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Chirality is the most intriguing yet essential facet of nature, governing life’s biochemical processes and precision. It can be observed from a snail shell pattern in a macroscopic world to an amino acid, the minutest building block of life. Most of the snails around the world have right-coiled shells because of the intrinsic chirality in their genes. All the amino acids present in the human body exist in an enantiomerically pure state, except for glycine - the sole achiral amino acid. The...

Chirality at Nitrogen, Phosphorus, and Sulfur

Chirality at Nitrogen, Phosphorus, and Sulfur

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A consequence of chirality is the need for enantiomeric resolution. While this is theoretically possible for all...

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Related Experiment Video

Updated: May 13, 2026

Coulomb Explosion Imaging as a Tool to Distinguish Between Stereoisomers

Coulomb Explosion Imaging as a Tool to Distinguish Between Stereoisomers

Published on: August 18, 2017

Chiral scars in chaotic Dirac fermion systems.

Hongya Xu¹, Liang Huang, Ying-Cheng Lai

¹Institute of Computational Physics and Complex Systems and Key Laboratory for Magnetism and Magnetic Materials of MOE, Lanzhou University, Lanzhou, Gansu 730000, China.

Physical Review Letters

|February 26, 2013

Summary

Researchers discovered unique relativistic quantum scars, termed chiral scars, in massless Dirac fermion systems. These scars exhibit distinct phase behaviors around classical orbits, differing from nonrelativistic quantum scars.

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Last Updated: May 13, 2026

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Line Shape Analysis of Dynamic NMR Spectra for Characterizing Coordination Sphere Rearrangements at a Chiral Rhenium Polyhydride Complex

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Area of Science:

Quantum physics
Relativistic quantum mechanics
Chaos theory

Background:

Quantum scars are non-trivial wavefunction localizations in classically chaotic systems.
Relativistic quantum mechanics describes particles at high speeds, incorporating quantum mechanics and special relativity.

Purpose of the Study:

To investigate unique features of relativistic quantum scars in classically chaotic systems.
To identify and characterize relativistic quantum scars in massless Dirac fermion systems.

Main Methods:

Development of an analytic, conformal-mapping-based method.
Calculation of a large number of eigenstates with high accuracy.
Application of semiclassical theory.

Main Results:

Identification of a class of relativistic quantum scars named chiral scars.
Chiral scars exhibit phase returns or 2π changes only after two circulations around classical unstable periodic orbits.
The study found these scars in massless Dirac fermion systems.

Conclusions:

Chiral scars possess unique properties not found in nonrelativistic quantum scars.
The origin of chiral scars is attributed to the combined effects of intrinsic chirality and classical orbit geometry.
The developed analytic method enables accurate calculation of numerous eigenstates for identifying quantum phenomena.