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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 Constant: Overview01:08

Spin–Spin Coupling Constant: Overview

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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...
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Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)01:22

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

1.0K
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...
1.0K
Spin–Spin Coupling: One-Bond Coupling01:17

Spin–Spin Coupling: One-Bond Coupling

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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,...
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¹H NMR: Long-Range Coupling01:27

¹H NMR: Long-Range Coupling

1.7K
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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NMR Spectroscopy: Spin–Spin Coupling01:08

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1.3K
The spin state of an NMR-active nucleus can have a slight effect on its immediate electronic environment. This effect propagates through the intervening bonds and affects the electronic environments of NMR-active nuclei up to three bonds away; occasionally, even farther. This phenomenon is called spin–spin coupling or J-coupling. Coupling interactions are mutual and result in small changes in the absorption frequencies of both nuclei involved. While nuclei of the same element are involved...
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Updated: Jun 10, 2025

Structure-Based Simulation and Sampling of Transcription Factor Protein Movements along DNA from Atomic-Scale Stepping to Coarse-Grained Diffusion
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Simulation of Spin Chains with Off-Diagonal Coupling Using the Inchworm Method.

Yixiao Sun1, Geshuo Wang1, Zhenning Cai1

  • 1Department of Mathematics, National University of Singapore, Block S17, 10 Lower Kent Ridge Road, Singapore 119076, Singapore.

Journal of Chemical Theory and Computation
|October 18, 2024
PubMed
Summary
This summary is machine-generated.

This study simulates open quantum spin chains coupled to harmonic baths. New methods extend path integrals to off-diagonal couplings, reducing computational costs for long-time simulations.

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Area of Science:

  • Quantum mechanics
  • Condensed matter physics
  • Computational chemistry

Background:

  • Investigating open quantum systems is crucial for understanding energy transfer and decoherence.
  • Previous work focused on diagonally coupled spin-bath interactions.

Purpose of the Study:

  • To extend dynamical simulation methods for open quantum spin chains.
  • To handle off-diagonal spin-bath couplings efficiently.
  • To reduce computational and memory costs in long-time simulations.

Main Methods:

  • Generalization of the inchworm method and modular path integrals to off-diagonal couplings.
  • Application of tensor-train representation for the reduced density matrix.
  • Utilizing the transfer tensor method (TTM) to manage computational complexity.

Main Results:

  • Successful generalization of the inchworm and modular path integral methods.
  • Efficient representation of the reduced density matrix using tensor trains.
  • Demonstrated reduction in computational cost for long-time dynamical simulations.

Conclusions:

  • The developed methods provide an efficient approach for simulating open quantum spin chains.
  • The combination of tensor-train representation and TTM significantly reduces resource requirements.
  • Validated through extensive numerical experiments, the method is robust and applicable.