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Related Concept Videos

Spin–Spin Coupling Constant: Overview01:08

Spin–Spin Coupling Constant: Overview

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 have a...
Spin–Spin Coupling: One-Bond Coupling01:17

Spin–Spin Coupling: One-Bond Coupling

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

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

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

Atomic Nuclei: Nuclear Spin State Overview

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 one, the...
The Pauli Exclusion Principle03:06

The Pauli Exclusion Principle

The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:
Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)01:22

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

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 involved orbitals. The...

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Related Experiment Video

Updated: May 16, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Criticality without frustration for quantum spin-1 chains.

Sergey Bravyi1, Libor Caha, Ramis Movassagh

  • 1IBM Watson Research Center, Yorktown Heights, New York 10598, USA.

Physical Review Letters
|December 11, 2012
PubMed
Summary
This summary is machine-generated.

Frustration-free spin chains with spin-1 exhibit highly entangled ground states, unlike their spin-1/2 counterparts. This unique state shows critical behavior and has entanglement entropy scaling with system size.

Related Experiment Videos

Last Updated: May 16, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Area of Science:

  • Quantum physics
  • Condensed matter theory
  • Quantum information science

Background:

  • Frustration-free (FF) spin chains possess ground states that minimize individual Hamiltonian terms.
  • While FF spin-1/2 chains have unentangled ground states, the entanglement properties of FF spin-1 chains are less understood.
  • Nearest-neighbor interactions are considered in these spin chains.

Purpose of the Study:

  • Investigate the entanglement properties of ground states in frustration-free quantum spin-s chains for small spin values (s).
  • Explore the less-studied case of spin-1 chains.
  • Introduce the first example of a translation-invariant FF spin-1 chain with a unique, highly entangled ground state.

Main Methods:

  • Analysis of the ground state properties of a novel frustration-free spin-1 chain model.
  • Characterization of the ground state as a uniform superposition of balanced bracket strings.
  • Calculation of entanglement entropy scaling.
  • Proof of polynomial energy gap scaling using Dyck path statistics.

Main Results:

  • A translation-invariant FF spin-1 chain with a unique, highly entangled ground state is proposed.
  • The ground state exhibits signatures of critical behavior.
  • Entanglement entropy for half the chain scales as 1/2 log n + O(1), where n is the number of spins.
  • The energy gap above the ground state is proven to scale polynomially with 1/n.

Conclusions:

  • The study presents the first example of a highly entangled ground state in a translation-invariant FF spin-1 chain.
  • This system demonstrates critical behavior and unique entanglement scaling.
  • The findings contribute to understanding entanglement in quantum many-body systems and introduce novel mathematical tools related to Dyck paths.