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Related Concept Videos

Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)01:20

Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)

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Two NMR-active nuclei bonded to a central atom can be involved in geminal or two-bond coupling. Geminal coupling is commonly seen between diastereotopic protons in chiral molecules and unsymmetrical alkenes, among others.
The central atom need not be NMR-active because its electrons are affected by the electron polarization of the spin-active atoms. However, spin information is transmitted less effectively than in one-bond coupling, and 2J values are usually weaker than 1J values. The energy of...
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Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)01:22

Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)

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Vicinal or three-bond coupling is commonly observed between protons attached to adjacent carbons. Here, nuclear spin information is primarily transferred via electron spin interactions between adjacent C‑H bond orbitals. This generally favors the antiparallel arrangement of spins, so 3J values are usually positive.
The extent of coupling depends on the C‑C bond length, the two H‑C‑C angles, any electron-withdrawing substituents, and the dihedral angle between the...
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Network Covalent Solids02:18

Network Covalent Solids

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Network covalent solids contain a three-dimensional network of covalently bonded atoms as found in the crystal structures of nonmetals like diamond, graphite, silicon, and some covalent compounds, such as silicon dioxide (sand) and silicon carbide (carborundum, the abrasive on sandpaper). Many minerals have networks of covalent bonds.
To break or to melt a covalent network solid, covalent bonds must be broken. Because covalent bonds are relatively strong, covalent network solids are typically...
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¹H NMR: Long-Range Coupling01:27

¹H NMR: Long-Range Coupling

2.4K
The coupling interactions of nuclei across four or more bonds are usually weak, with J values less than 1 Hz. While these are usually not observed in spectra, the presence of multiple bonds along the coupling pathway can result in observable long-range coupling.
In alkenes, spin information is communicated via σ–π overlap, as seen in allylic (four-bond) and homoallylic (five-bond) couplings. These coupling interactions are stronger when the σ bond is parallel to the alkene...
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Coordination Number and Geometry02:57

Coordination Number and Geometry

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For transition metal complexes, the coordination number determines the geometry around the central metal ion. Table 1 compares coordination numbers to molecular geometry. The most common structures of the complexes in coordination compounds are octahedral, tetrahedral, and square planar.
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Woodward–Hoffmann Selection Rules and Microscopic Reversibility01:34

Woodward–Hoffmann Selection Rules and Microscopic Reversibility

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Electrocyclic reactions, cycloadditions, and sigmatropic rearrangements are concerted pericyclic reactions that proceed via a cyclic transition state. These reactions are stereospecific and regioselective. The stereochemistry of the products depends on the symmetry characteristics of the interacting orbitals and the reaction conditions. Accordingly, pericyclic reactions are classified as either symmetry-allowed or symmetry-forbidden. Woodward and Hoffmann presented the selection criteria for...
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Generating Strictly Controlled Stimuli for Figure Recognition Experiments
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Data mechanics and coupling geometry on binary bipartite networks.

Hsieh Fushing1, Chen Chen1

  • 1Department of Statistics, University of California Davis, Davis, California, United States of America.

Plos One
|August 30, 2014
PubMed
Summary
This summary is machine-generated.

This study introduces Data Mechanics to discover patterns in binary bipartite networks by analyzing spin configurations. The approach reveals multiscale interactions, offering insights into community ecology and phylogenetics.

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Area of Science:

  • Network Science
  • Statistical Physics
  • Computational Biology

Background:

  • Discovering patterns in complex systems is challenging.
  • Binary bipartite networks represent intricate relationships.
  • Existing methods lack multiscale pattern identification capabilities.

Purpose of the Study:

  • To formalize pattern discovery in binary bipartite networks.
  • To develop a novel computational framework for identifying interrelated global interactions.
  • To reveal multiscale block patterns and nonparametric information content.

Main Methods:

  • Framing binary bipartite networks as thermodynamic systems with Ising model potentials.
  • Devising Data Mechanics, a computing paradigm for indirect macrostate searching.
  • Utilizing marginal ultrametrics and minimizing Gromov-Wasserstein distance for coupling geometry.

Main Results:

  • A macrostate congregates multiscale patterns within network data.
  • The coupling geometry reveals multiscale block patterns and interacting relationships.
  • This method quantifies nonparametric information content of networks.

Conclusions:

  • Data Mechanics provides a novel approach to pattern discovery in complex networks.
  • The coupling geometry offers new resolution for interaction issues in ecology and phylogenetics.
  • This framework has broad potential applications across scientific domains.