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¹H NMR: Long-Range Coupling01:27

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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.
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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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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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The physical form of a substance changes on changing its temperature. For example, raising the temperature of a liquid causes the liquid to vaporize (convert into vapor). The process is called vaporization—a surface phenomenon. Vaporization occurs when the thermal motion of the molecules overcome the intermolecular forces, and the molecules (at the surface) escape into the gaseous state. When a liquid vaporizes in a closed container, gas molecules cannot escape. As these gas phase molecules...
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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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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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Area of Science:

  • Condensed Matter Physics
  • Quantum Liquids
  • Statistical Mechanics

Background:

  • Supercooled liquids exhibit complex dynamics near the glass transition.
  • Quantum mechanics introduces phenomena like tunneling, potentially altering classical dynamics.
  • Understanding quantum effects in supercooled liquids is crucial for materials science.

Purpose of the Study:

  • To investigate the dynamics of a supercooled quantum hard-sphere liquid.
  • To analyze the influence of quantum effects on relaxation times and glass transition density.
  • To explore the moderate quantum regime using a quantum mode-coupling formulation.

Main Methods:

  • Employed a quantum mode-coupling formulation for theoretical analysis.
  • Solved time-dependent quantum mode-coupling equations using a perturbative approach.
  • Studied the supercooled liquid dynamics in the moderate quantum regime.

Main Results:

  • Classical cage effects dominate in the moderate quantum regime, slowing dynamics.
  • Quantum tunneling in the strongly quantum regime leads to faster relaxation.
  • The glass transition critical density is higher in quantum liquids than classical ones.
  • Relaxation time exhibits a power-law increase with density, similar to classical liquids.
  • The power-law exponent depends linearly on quantumness in the moderate quantum regime.

Conclusions:

  • Quantum effects significantly modify supercooled liquid dynamics and glass transition properties.
  • The interplay between caging and tunneling determines relaxation behavior.
  • Quantum mode-coupling theory provides a valuable framework for studying these phenomena.