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Related Concept Videos

¹H NMR: Long-Range Coupling01:27

¹H NMR: Long-Range Coupling

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 π orbitals.
Spin–Spin Coupling Constant: Overview01:08

Spin–Spin Coupling Constant: Overview

In bromoethane, the three methyl protons are coupled to the two methylene protons that are three bonds away. In accordance with the n+1 rule, the signal from the methyl protons is split into three peaks with 1:2:1 relative intensities. The methylene protons appear as a quartet, with the relative intensities of 1:3:3:1.
Qualitatively, any spin plus-half nucleus polarizes the spins of its electrons to the minus-half state. Consequently, the paired electron in the hydrogen–carbon bond must have a...
Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)01:22

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

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 involved orbitals. The...
Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)01:20

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

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...
Spin–Spin Coupling: One-Bond Coupling01:17

Spin–Spin Coupling: One-Bond Coupling

Coupling interactions are strongest between NMR-active nuclei bonded to each other, where spin information can be transmitted directly through the pair of bonding electrons. While nuclei polarize their electrons to the opposite spins, the bonding electron pair has opposite spins. Configurations with antiparallel nuclear spins are expected to be lower in energy. When coupling makes antiparallel states more favorable, J is considered to have a positive value. The one-bond coupling constant, 1J,...
Debye–Huckel–Onsager Conductance Equation01:28

Debye–Huckel–Onsager Conductance Equation

The Debye-Hückel-Onsager equation is a cornerstone of physical chemistry, providing a method to determine the molar conductance (Λm) and molar conductance at infinite dilution (Λ°m) for uni-univalent electrolytes.Uni-univalent electrolytes are electrolytes that dissociate in solution to produce one cation with a +1 charge and one anion with a –1 charge per formula unit.This equation addresses two crucial phenomena: the asymmetry effect and the electrophoretic effect. According to this equation,...

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Related Experiment Video

Updated: Jun 6, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Wigner-distribution-function representation of the coupling coefficient.

D Dragoman

    Applied Optics
    |November 10, 2010
    PubMed
    Summary
    This summary is machine-generated.

    The Wigner-distribution function visualizes light fields, linking their symmetries to the efficiency of light coupling between optical components. This method quanties how much light is transferred.

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    Area of Science:

    • Optics and Photonics
    • Quantum Optics
    • Information Optics

    Background:

    • The Wigner-distribution function (WDF) is a powerful tool for representing quantum states and optical fields.
    • Understanding light field coupling is crucial for designing efficient optical systems and devices.
    • Symmetry properties of optical fields can offer insights into their propagation and interaction characteristics.

    Purpose of the Study:

    • To establish a method for quantifying light coupling efficiency using the Wigner-distribution function.
    • To explore the relationship between the symmetries of Wigner distribution graphical representations and the amount of coupled light.

    Main Methods:

    • Utilizing the Wigner-distribution function representation for both the source and receiver light fields.
    • Analyzing the symmetries present in the graphical representations of these Wigner distributions.
    • Developing a framework to correlate these symmetries with the calculated coupling efficiency.

    Main Results:

    • A direct correlation was found between the symmetries of the Wigner-distribution graphical representations and the amount of coupled light.
    • The WDF representation provides a clear visualization of how field symmetries influence coupling efficiency.
    • Quantified the relationship, showing that higher degrees of symmetry in the WDF correspond to greater light coupling.

    Conclusions:

    • The Wigner-distribution function offers an effective and intuitive approach to analyze and optimize light coupling efficiency.
    • Symmetry analysis of WDFs can serve as a predictive tool for the performance of optical systems.
    • This work provides a novel perspective on understanding light field interactions based on their phase-space characteristics.