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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,...
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Isomerism in Complexes
Isomers are different chemical species that have the same chemical formula. Structural isomerism of coordination compounds can be divided into two subcategories, the linkage isomers and coordination-sphere isomers.
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On the basis of mirror symmetry, stereoisomers of an organic molecule can be further classified into diastereomers and enantiomers. Diastereomers are stereoisomers that are not mirror images of each other. Substituted alkenes, such as the cis and trans isomers of 2-butene, are diastereomers, as these molecules exhibit different spatial orientations of their constituent atoms, are not mirror images of each other, and do not interconvert. Here, the interconversion is suppressed due to...
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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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The Diels–Alder reaction is an example of a thermal pericyclic reaction between a conjugated diene and an alkene or alkyne, commonly referred to as a dienophile. The reaction involves a concerted movement of six π electrons, four from the diene and two from the dienophile, forming an unsaturated six-membered ring. As a result, these reactions are classified as [4+2] cycloadditions.
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A dynamic programming algorithm for generating chemical isomers based on frequency vectors.

Ryota Ido1, Naveed Ahmed Azam2,3, Jianshen Zhu1

  • 1Department of Applied Mathematics and Physics, Kyoto University, Yoshida Honmachi, Sakyo, 606-8501, Kyoto, Japan.

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|July 2, 2025
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Summary
This summary is machine-generated.

We developed a dynamic programming algorithm to generate chemical isomers using graph theory. This method efficiently counts and enumerates isomers, accelerating the discovery of novel molecular structures for drug discovery and material science.

Keywords:
Dynamic ProgrammingEnumeration of GraphsMolecular Design

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Area of Science:

  • Computational Chemistry
  • Graph Theory
  • Cheminformatics

Background:

  • Generating chemical isomers is crucial for exploring molecular diversity.
  • Existing methods can be computationally intensive for complex molecules.

Purpose of the Study:

  • To develop an efficient algorithm for generating and enumerating chemical isomers.
  • To create a compact representation for isomer enumeration.

Main Methods:

  • Representing chemical compounds as graphs with feature vectors.
  • Utilizing graph-theoretical descriptors, specifically "edge-configuration".
  • Applying dynamic programming for isomer generation.

Main Results:

  • A compact representation of all chemical isomers for a given graph.
  • Efficient counting of isomers without explicit generation.
  • Ability to enumerate any number of isomers, including random enumeration.

Conclusions:

  • The algorithm accelerates chemical compound exploration in drug discovery and material science.
  • Enhances search space exploration for novel molecular structures.
  • Facilitates advancements in molecular design through efficient isomer enumeration.