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Spin–Spin Coupling: One-Bond Coupling01:17

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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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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.
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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.
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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.
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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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Coordination compounds and complexes exhibit different colors, geometries, and magnetic behavior, depending on the metal atom/ion and ligands from which they are composed. In an attempt to explain the bonding and structure of coordination complexes, Linus Pauling proposed the valence bond theory, or VBT, using the concepts of hybridization and the overlapping of the atomic orbitals. According to VBT, the central metal atom or ion (Lewis acid) hybridizes to provide empty orbitals of suitable...
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Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser
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Sub-Ohmic spin-boson model with off-diagonal coupling: ground state properties.

Zhiguo Lü1, Liwei Duan, Xin Li

  • 1Division of Materials Science, Nanyang Technological University, Singapore 639798, Singapore.

The Journal of Chemical Physics
|November 5, 2013
PubMed
Summary
This summary is machine-generated.

We studied the spin-boson model, finding that adding off-diagonal coupling causes a sudden first-order phase transition, unlike the usual gradual second-order transition. This impacts quantum system behavior.

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Area of Science:

  • Quantum Mechanics
  • Condensed Matter Physics

Background:

  • The spin-boson model describes quantum systems interacting with their environment.
  • Previous studies focused on diagonal coupling, showing second-order phase transitions.

Purpose of the Study:

  • To investigate the spin-boson model in the sub-ohmic regime.
  • To analyze the impact of both diagonal and off-diagonal couplings on phase transitions.

Main Methods:

  • Analytical and numerical studies were performed.
  • The Davydov D1 variational ansatz was employed.
  • Canonical transformation approach was used for specific cases.

Main Results:

  • Off-diagonal coupling introduces a discontinuous first-order phase transition.
  • Ground state energy and magnetization plots reveal a transition between isotropic and nematic phases.
  • Entanglement entropy shows a discontinuity supporting the first-order transition.

Conclusions:

  • Off-diagonal coupling fundamentally alters the nature of phase transitions in the spin-boson model.
  • A continuous crossover to doubly degenerate localized phases occurs under specific coupling conditions.