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

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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

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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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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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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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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.
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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Competing interactions in a long-range spin-lattice coupled model and tricriticality.

Rohit Singh1, Kishore Dutta2

  • 1Department of Physics, Indian Institute of Technology Bombay, Mumbai 400 076, India.

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|May 21, 2019
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Summary

This study explores magnetic phase transitions in strongly correlated systems using a model Hamiltonian. It reveals novel critical behaviors influenced by long-range strain interactions and competing short-range forces.

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Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics
  • Materials Science

Background:

  • Strongly correlated systems exhibit complex critical behavior during magnetic phase transitions.
  • The interplay between spin and lattice degrees of freedom is crucial for understanding these transitions.
  • Analytical methods are needed to model these phenomena effectively.

Purpose of the Study:

  • To construct an effective model Hamiltonian for studying magnetic phase transitions.
  • To investigate the role of order parameter-strain field coupling.
  • To analyze the impact of long-range (LR) and short-range interactions on critical behavior.

Main Methods:

  • Development of a C-type model Hamiltonian.
  • Renormalization-group analysis at one-loop order.
  • Investigation of competing short-range interactions and nonlocal theories.

Main Results:

  • Identification of non-trivial critical behavior governed by an LR fixed point.
  • Demonstration of differing critical behavior with competing short-range interactions.
  • Observation of first-order instability signatures in purely nonlocal theories.

Conclusions:

  • The model effectively captures critical phenomena in strongly correlated systems.
  • Long-range strain interactions significantly influence magnetic phase transitions.
  • Further applicability in explaining experimental results is discussed.