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Spin–Spin Coupling: One-Bond Coupling01:17

Spin–Spin Coupling: One-Bond Coupling

957
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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Valence Bond Theory02:42

Valence Bond Theory

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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...
8.5K
Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)01:20

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

1.0K
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...
1.0K
Spin–Spin Coupling Constant: Overview01:08

Spin–Spin Coupling Constant: Overview

911
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...
911
Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)01:22

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

1.1K
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...
1.1K
Atomic Nuclei: Nuclear Spin State Overview01:03

Atomic Nuclei: Nuclear Spin State Overview

934
NMR-active nuclei have energy levels called 'spin states' that are associated with the orientations of their nuclear magnetic moments. In the absence of a magnetic field, the nuclear magnetic moments are randomly oriented, and the spin states are degenerate. When an external magnetic field is applied, the spin states have only 2 + 1 orientations available to them. A proton with = ½ has two available orientations. Similarly, for a quadrupolar nucleus with a nuclear spin value of...
934

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Related Experiment Video

Updated: Jun 26, 2025

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
05:39

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

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Conformally invariant free-parafermionic quantum chains with multispin interactions.

Francisco C Alcaraz1, Lucas M Ramos1

  • 1Instituto de Física de São Carlos, Universidade de São Paulo, Caixa Postal 369, 13560-970, São Carlos, SP, Brazil.

Physical Review. E
|May 17, 2024
PubMed
Summary
This summary is machine-generated.

We studied non-Hermitian quantum chains with multispin interactions, finding distinct conformal phases based on boundary conditions. These models exhibit conformal invariance and a multicritical point.

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Area of Science:

  • Quantum physics
  • Condensed matter theory
  • Statistical mechanics

Background:

  • Non-Hermitian quantum systems offer a unique framework to explore complex phenomena beyond traditional Hermitian theories.
  • Multispin interactions in quantum chains introduce rich collective behaviors and symmetries.

Purpose of the Study:

  • To investigate the spectral properties and conformal invariance of two related families of non-Hermitian free-particle quantum chains with N-multispin interactions.
  • To analyze the influence of boundary conditions (open vs. periodic) on the physics of these non-Hermitian models.

Main Methods:

  • Calculation of spectral properties for Z(N) symmetric (parafermionic) and U(1) symmetric (fermionic) quantum chains.
  • Analysis of finite-size behavior of eigenspectra and entanglement properties of ground-state wave functions.
  • Comparison of models with open and periodic boundary conditions.

Main Results:

  • Both families of quantum chains share the same pseudo-energies forming their eigenspectra.
  • A multicritical point with a dynamical critical exponent z=1 was identified.
  • Finite-size scaling and entanglement data indicate conformal invariance for both model families.
  • Distinct physical behaviors and conformal phases emerge for open versus periodic boundary conditions due to non-Hermiticity.

Conclusions:

  • The studied non-Hermitian quantum chains exhibit rich physics, including conformal invariance and multicriticality.
  • Boundary conditions play a crucial role in determining the phase structure and conformal properties of these systems.
  • The Z(N) and U(1) symmetric models provide a versatile platform for exploring non-Hermitian quantum phenomena.