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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...

Fischer Projections

Fischer Projections

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.

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...

Stereoisomerism of Cyclic Compounds

Stereoisomerism of Cyclic Compounds

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,...

Chirality at Nitrogen, Phosphorus, and Sulfur

Chirality at Nitrogen, Phosphorus, and Sulfur

Chirality is most prevalent in carbon-based tetrahedral compounds, but this important facet of molecular symmetry extends to sp3-hybridized nitrogen, phosphorus and sulfur centers, including trivalent molecules with lone pairs. Here, the lone pair behaves as a functional group in addition to the other three substituents to form an analogous tetrahedral center that can be chiral.
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: Aug 6, 2025

Optimized Fabrication Procedure for High-Quality Graphene-based Moiré Superlattice Devices

Optimized Fabrication Procedure for High-Quality Graphene-based Moiré Superlattice Devices

Published on: July 11, 2025

Chiral Decomposition of Twisted Graphene Multilayers with Arbitrary Stacking.

ShengNan Zhang^1,2, Bo Xie³, QuanSheng Wu^1,2

¹Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland.

|March 20, 2023

Summary

We developed rules for twisted multilayer graphene electronic structures. At the magic angle, low-energy bands form entangled chiral pseudospin doublets and flat bands, enabling topological state design.

Keywords:

Chern number Dirac fermion chirality flat band moiré superlattice twisted multilayer graphene

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Last Updated: Aug 6, 2025

Optimized Fabrication Procedure for High-Quality Graphene-based Moiré Superlattice Devices

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Area of Science:

Condensed Matter Physics
Materials Science
Quantum Chemistry

Background:

Twisted multilayer graphene systems exhibit complex electronic properties due to moiré superlattices.
Understanding these properties is crucial for designing novel electronic and topological materials.

Purpose of the Study:

To formulate general chiral decomposition rules for twisted multilayer graphene.
To investigate the low-energy electronic structure at the magic angle.
To explore the role of displacement fields in tuning topological properties.

Main Methods:

Analytic construction of electronic band structures.
Numerical calculations using realistic parameterizations.
Investigation of systems with arbitrary stacking order and mutual twist.

Main Results:

Identified chiral pseudospin doublets and entangled flat bands at the magic angle in the chiral limit.
Demonstrated that displacement fields can open gaps and induce nonzero valley Chern numbers in flat bands.
Validated analytic predictions with explicit numerical computations.

Conclusions:

The derived rules provide a framework for understanding and designing electronic states in twisted graphene multilayers.
These findings offer guidelines for realizing topological and correlated states in these systems.
Highlights the potential of twisted graphene for advanced electronic applications.