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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...
¹H NMR: Interpreting Distorted and Overlapping Signals01:02

¹H NMR: Interpreting Distorted and Overlapping Signals

Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are slanted or...
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...
2D NMR: Overview of Homonuclear Correlation Techniques01:16

2D NMR: Overview of Homonuclear Correlation Techniques

Homonuclear correlation spectroscopy (COSY) is a powerful technique used in Nuclear Magnetic Resonance (NMR) spectroscopy to study the correlations between nuclei of the same type within a molecule. It provides information about scalar couplings between adjacent nuclei, which helps determine connectivity and structural information. There are several COSY variants, each with its unique strengths and experimental parameters.
COSY90 is the standard two-dimensional (2D) COSY experiment that...
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,...
Atomic Nuclei: Nuclear Spin State Population Distribution01:14

Atomic Nuclei: Nuclear Spin State Population Distribution

Near absolute zero temperatures, in the presence of a magnetic field, the majority of nuclei prefer the lower energy spin-up state to the higher energy spin-down state. As temperatures increase, the energy from thermal collisions distributes the spins more equally between the two states. The Boltzmann distribution equation gives the ratio of the number of spins predicted in the spin −½ (N−) and spin +½ (N+) states.

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Related Experiment Video

Updated: May 11, 2026

Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
08:55

Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses

Published on: June 7, 2018

Numerically exact correlations and sampling in the two-dimensional Ising spin glass.

Creighton K Thomas1, A Alan Middleton

  • 1Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208-3108, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 18, 2013
PubMed
Summary

This study introduces a fast computational method for two-dimensional Ising models using Pfaffian techniques. The developed computer code enables efficient calculation of partition functions, spin correlations, and exact sampling for various couplings.

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Area of Science:

  • Statistical Mechanics
  • Computational Physics

Background:

  • Two-dimensional Ising models are crucial for understanding magnetism and phase transitions.
  • Evaluating statistical mechanical quantities often involves complex matrix operations.

Purpose of the Study:

  • To develop an efficient computational method for analyzing two-dimensional Ising models.
  • To create computer code for fast calculations and exact sampling.

Main Methods:

  • Utilizing Pfaffian evaluation of matrices representing spin couplings.
  • Incorporating recent advancements in inverse matrix evaluation and exact sampling techniques.
  • Applying the method to Ising models with arbitrary nearest-neighbor couplings and general dimer models.

Main Results:

  • A convenient and fast formulation for computing partition functions and spin correlations.
  • Successful implementation for exact sampling of configurations based on the Boltzmann distribution.
  • Demonstrated applicability to various Ising and dimer models with example computations.

Conclusions:

  • The developed method offers a significant speed improvement for studying two-dimensional Ising models.
  • The computer code provides a versatile tool for both theoretical analysis and simulation.
  • The approach is extendable to related models in statistical mechanics.