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Related Concept Videos

¹H NMR of Conformationally Flexible Molecules: Variable-Temperature NMR01:15

¹H NMR of Conformationally Flexible Molecules: Variable-Temperature NMR

The axial and equatorial protons in cyclohexane can be distinguished by performing a variable-temperature NMR experiment. In this process, except for one proton, the remaining eleven protons are replaced by deuterium. The deuterium substitution avoids the possible peak splitting caused by the spin-spin coupling between the adjacent protons. The remaining proton flips between the axial and equatorial positions.
Conformations of Cycloalkanes02:29

Conformations of Cycloalkanes

Adolf von Baeyer attempted to explain the instabilities of small and large cycloalkane rings using the concept of angle strain — the strain caused by the deviation of bond angles from the ideal 109.5° tetrahedral value for sp3  hybridized carbons. However, while cyclopropane and cyclobutane are strained, as expected from their highly compressed bond angles, cyclopentane is more strained than predicted, and cyclohexane is virtually strain-free. Hence, Baeyer’s theory that was based on the...
¹H NMR of Conformationally Flexible Molecules: Temporal Resolution00:52

¹H NMR of Conformationally Flexible Molecules: Temporal Resolution

At room temperature, the chair conformer of cyclohexane undergoes rapid ring flipping between two equivalent chair conformers at a rate of approximately 105 times per second. These two chair conformers are in equilibrium. The rapid ring flipping results in the interconversion of the axial proton to an equatorial proton and an equatorial to the axial proton. Such interconversions are too rapid and cannot be detected on the NMR timescale. Hence, the NMR spectrometer cannot distinguish between the...
Conformations of Cyclohexane02:11

Conformations of Cyclohexane

Cyclohexane does not exist in a planar form due to the high angle and torsional strain it would experience in the planar structure. Instead, it adopts non-planar chair and boat conformations.
The chair form is the most stable and derives its name from its resemblance to the “easy chair.” In the chair conformation, two carbon atoms are arranged out-of-plane — one above and one below, minimizing the torsional strain. In the chair form, the bond angle is very close to the ideal tetrahedral value,...
Conformations of Butane02:20

Conformations of Butane

Unlike ethane and propane that have only two major conformations, butane has more than two conformers. The staggered form of butane in which the bulky methyl groups on the two carbons are placed on opposite sides, that is, at a dihedral angle of 180°, is the lowest energy, most stable form — called the anti conformer. This conformation is stabilized due to the absence of steric repulsion between the largely spaced out methyl groups. The other two staggered conformations are degenerate and have...
Conformations of Ethane and Propane02:18

Conformations of Ethane and Propane

In an organic molecule, free rotation about the carbon-carbon single bond results in energetically different conformers of the molecule. Due to this rotation, called the internal rotation, ethane has two major conformations — staggered and eclipsed.
Staggered conformation is a low energy and more stable conformation with the C-H bonds on the front carbon placed at 60°dihedral angles relative to the C-H bonds on the back carbon, leading to a reduced torsional strain. In staggered ethane, the...

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Updated: May 18, 2026

Interactive Molecular Model Assembly with 3D Printing
06:15

Interactive Molecular Model Assembly with 3D Printing

Published on: August 13, 2020

Modularity optimization by conformational space annealing.

Juyong Lee1, Steven P Gross, Jooyoung Lee

  • 1School of Computational Sciences, Korea Institute of Advanced Study, Seoul, Korea. juyong@kias.re.kr

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 26, 2012
PubMed
Summary
This summary is machine-generated.

We introduce Mod-CSA, a novel modularity optimization method that outperforms simulated annealing in efficiency and accuracy. This approach finds superior graph partitions using fewer computational resources and scales to large networks.

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Area of Science:

  • Graph theory
  • Computational complexity
  • Network analysis

Background:

  • Community detection is crucial for understanding complex networks.
  • Existing methods like simulated annealing face limitations in efficiency and accuracy.
  • Optimizing graph modularity is a key challenge in network science.

Purpose of the Study:

  • To develop a superior modularity optimization method.
  • To enhance the efficiency and accuracy of community detection algorithms.
  • To provide a scalable solution for analyzing large-scale networks.

Main Methods:

  • Development of Mod-CSA, a modularity optimization technique.
  • Leveraging the conformational space annealing (CSA) stochastic global optimization algorithm.
  • Implementation of parallel processing for large graph analysis.

Main Results:

  • Mod-CSA demonstrates superior performance over simulated annealing in efficiency and accuracy.
  • Achieved higher modularity values than previously reported benchmarks.
  • Successfully applied to graphs exceeding 10,000 nodes.

Conclusions:

  • Mod-CSA offers a highly effective and efficient approach for graph modularity optimization.
  • The method's scalability and accuracy make it suitable for large, complex networks.
  • Mod-CSA can be integrated with other heuristic methods for broader applicability.