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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...
Derivatives of the Trigonometric Functions01:26

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The motion of a Ferris wheel rotating at a constant speed provides an intuitive model for understanding trigonometric functions and their derivatives. As a rider moves along the circular path, the vertical height above the ground changes smoothly and periodically over time. This vertical motion can be accurately represented by a sine function, reflecting the repeating pattern of ascent and descent inherent to circular motion.Height and Rate of ChangeIf the rider’s height is modeled by a sine...
Derivatives of Vector Functions01:17

Derivatives of Vector Functions

A vector-valued function describes position as a function of time. For example, in Cartesian coordinates, the position of a car moving along a curved road can be written as\begin{equation*}\textbf{r}(t)=\langle x(t),y(t),z(t)\rangle\end{equation*}Secant Vector and Average Velocity:This secant vector captures the overall change in position during the interval and provides a crude estimate of the direction of motion.At time t, the car is at point P, with position r(t). After a short interval h,...
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.
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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,...
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.
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New Features in Visual Dynamics 3.0
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Derivatives of spin dynamics simulations.

Ilya Kuprov1, Christopher T Rodgers

  • 1Oxford e-Research Centre, University of Oxford, 7 Keble Road, Oxford OX1 3QG, United Kingdom. ilya.kuprov@oerc.ox.ac.uk

The Journal of Chemical Physics
|December 23, 2009
PubMed
Summary

We developed analytical equations for spin dynamics simulations, offering faster, more accurate derivative calculations. These methods improve fitting, optimization, and stability analysis in magnetic resonance experiments.

Area of Science:

  • Magnetic Resonance
  • Computational Physics
  • Quantum Mechanics

Background:

  • Spin dynamics simulations are crucial for understanding magnetic resonance phenomena.
  • Current methods often rely on finite difference approximations, which can be slow and inaccurate.
  • Accurate derivatives are needed for advanced analysis and experimental design.

Purpose of the Study:

  • To derive analytical equations for the derivatives of spin dynamics simulations.
  • To provide a more efficient and reliable alternative to finite difference methods.
  • To enable enhanced fitting, optimization, and stability analysis.

Main Methods:

  • Developed analytical equations for calculating derivatives with respect to pulse sequence parameters.
  • Derived analytical equations for calculating derivatives with respect to spin system parameters.

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  • Validated the accuracy and speed of the analytical methods against numerical approximations.

    • Main Results:

    • The analytical methods are significantly faster than finite difference approximations.
    • The derived equations provide higher accuracy and reliability in derivative calculations.
    • Demonstrated the utility of the derivatives in various simulation and experimental analyses.

    Conclusions:

    • Analytical equations offer a superior approach for calculating spin dynamics derivatives.
    • These methods enhance the efficiency and precision of magnetic resonance data analysis.
    • The developed techniques will advance the capabilities of spin dynamics simulations and experiments.