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Spin–Spin Coupling Constant: Overview01:08

Spin–Spin Coupling Constant: Overview

1.0K
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...
1.0K
Valence Bond Theory02:42

Valence Bond Theory

9.4K
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...
9.4K
Spin–Spin Coupling: One-Bond Coupling01:17

Spin–Spin Coupling: One-Bond Coupling

1.1K
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,...
1.1K
Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)01:20

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

1.1K
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...
1.1K
The Pauli Exclusion Principle03:06

The Pauli Exclusion Principle

49.9K
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:
49.9K
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

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Updated: Sep 10, 2025

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

9.1K

モジュール式テンソル図を用いたフェルミオンシステムのスピン固有関数の構築

Guohua Tao1

  • 1School of Advanced Materials, Peking University Shenzhen Graduate School, Shenzhen 518055, China.

The Journal of chemical physics
|August 27, 2025
PubMed
まとめ

新しいモジュール式テンソル図法により,複雑なフェルミオン系におけるスピン固有関数の構築が簡素化される. この方法は,状態空間を効率的に整理し,奇数のスピンを持つシステムに対して普遍的な再帰関係を生成します.

科学分野:

  • 量子力学について
  • 多体物理学
  • 計算物理

背景:

  • マルチスピンシステムのスピン固有関数の構築は,システムのサイズが増加するにつれて複雑になります.
  • 階層的な状態空間分解のために,モジュール式テンソール図アプローチが以前開発された.
  • このアプローチは,状態空間を整理し,対称性に適応した基本状態を効率的に構築します.

研究 の 目的:

  • 奇数回転を持つフェルミオン系に対するモジュールテンソール図のアプローチを一般化する.
  • 基本的なモジュールを分類し,幾何学的なブロックにマッピングします.
  • 任意の奇数回転系のためのスピン固有関数と普遍的な再帰関数を生成する.

主な方法:

  • 奇回転フェルミオン系に対するモジュラーテンソール図アプローチの一般化.
  • 基本モジュール (原始スピンペアモジュール + 奇数スピンタグモジュール) をモジュールクラスに分類する.
  • 空間構造と対称性を視覚化するために,モジュールを幾何学的なブロックにマッピングします.
  • タグ付けされた基本モジュールの対称性および正交性条件を使用してスピン固有関数を生成する.

主要な成果:

  • 奇回転フェルミオン系のための一般化されたモジュラーテンソール図法.

さらに関連する動画

Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser
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Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser

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Visualizing Uniaxial-strain Manipulation of Antiferromagnetic Domains in Fe1+YTe Using a Spin-polarized Scanning Tunneling Microscope
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Visualizing Uniaxial-strain Manipulation of Antiferromagnetic Domains in Fe1+YTe Using a Spin-polarized Scanning Tunneling Microscope

Published on: March 24, 2019

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関連する実験動画

Last Updated: Sep 10, 2025

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

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Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser
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Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser

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Visualizing Uniaxial-strain Manipulation of Antiferromagnetic Domains in Fe1+YTe Using a Spin-polarized Scanning Tunneling Microscope
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Visualizing Uniaxial-strain Manipulation of Antiferromagnetic Domains in Fe1+YTe Using a Spin-polarized Scanning Tunneling Microscope

Published on: March 24, 2019

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  • モジュールの分類と幾何学的な構造へのマッピング
  • スピンの固有関数と普遍的な再帰関数の効率的な生成
  • フェルミオンシステムの状態空間の構造と対称性の探求.
  • 結論:

    • 一般化されたアプローチは,奇回転フェルミオン系に効果的に組織された状態空間を提供します.
    • この方法は,対称性適応ベース状態とスピン固有関数の効率的な構築を可能にします.
    • この発見は量子多体システムとスピンダイナミクスに 新たな洞察をもたらします