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Related Concept Videos

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...
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...
2D NMR: Overview of Heteronuclear Correlation Techniques01:18

2D NMR: Overview of Heteronuclear Correlation Techniques

Heteronuclear correlation spectroscopy is an analytical technique that investigates the coupling between different types of nuclei, often a proton and an X-nucleus, such as carbon-13 or nitrogen-15. This method is commonly used in nuclear magnetic resonance (NMR) spectroscopy to gain insights into complex chemical compounds' structural and compositional aspects. A typical heteronuclear correlation spectrum displays X-nucleus chemical shifts on one axis and a proton spectrum on the other axis.
Two-Dimensional (2D) NMR: Overview01:12

Two-Dimensional (2D) NMR: Overview

The 1D NMR spectrum of large and complex molecules like natural products has complicated splitting patterns and overlapping signals, which can be easily interpreted using 2-dimensional (2D) NMR. Unlike 1D NMR, 2D NMR has two frequency axes that provide the coupling information between the nucleus A and nucleus B in a molecule. The process from which 2D spectra are obtained has four steps.
The first step is the preparation period, during which nucleus A is excited with a radiofrequency pulse.
NMR Spectroscopy: Spin–Spin Coupling01:08

NMR Spectroscopy: Spin–Spin Coupling

The spin state of an NMR-active nucleus can have a slight effect on its immediate electronic environment. This effect propagates through the intervening bonds and affects the electronic environments of NMR-active nuclei up to three bonds away; occasionally, even farther. This phenomenon is called spin–spin coupling or J-coupling. Coupling interactions are mutual and result in small changes in the absorption frequencies of both nuclei involved. While nuclei of the same element are involved in...
NMR Spectrometers: Overview01:20

NMR Spectrometers: Overview

NMR spectrometers consist of a strong magnet, a radiofrequency transmitter, and a detector attached to a computer console for recording spectra of samples containing NMR-active nuclei. In first-generation NMR instruments called continuous-wave spectrometers, the resonance frequencies of the nuclei are determined by frequency-sweep or field-sweep methods. The magnetic field strength is fixed and the rf signal is swept in the former, while the radiofrequency signal is fixed and the magnetic field...

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Atomic Scale Structural Studies of Macromolecular Assemblies by Solid-state Nuclear Magnetic Resonance Spectroscopy
14:55

Atomic Scale Structural Studies of Macromolecular Assemblies by Solid-state Nuclear Magnetic Resonance Spectroscopy

Published on: September 17, 2017

Operator-based Floquet theory in solid-state NMR.

Ingo Scholz1, Jacco D van Beek, Matthias Ernst

  • 1Physical Chemistry, ETH Zürich, Wolfgang-Pauli-Strasse 10, 8093 Zürich, Switzerland.

Solid State Nuclear Magnetic Resonance
|June 25, 2010
PubMed
Summary
This summary is machine-generated.

Operator-based Floquet theory provides a powerful method for calculating effective Hamiltonians in solid-state Nuclear Magnetic Resonance (NMR). This review covers its application to various resonant and non-resonant problems, enhancing NMR spectroscopy techniques.

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Area of Science:

  • Solid-state Nuclear Magnetic Resonance (NMR) spectroscopy.
  • Quantum mechanics and perturbation theory.

Background:

  • Operator-based Floquet theory is a theoretical framework used in NMR.
  • Solid-state NMR experiments often involve complex radio-frequency pulse sequences and spinning conditions.

Purpose of the Study:

  • To review the application of operator-based Floquet theory in solid-state NMR.
  • To provide basic expressions for calculating effective Hamiltonians using van Vleck perturbation theory.
  • To illustrate the theory with literature examples.

Main Methods:

  • Application of operator-based Floquet theory.
  • Utilizing van Vleck perturbation theory for effective Hamiltonian calculations.
  • Analysis of problems with single or multiple incommensurate frequencies.

Main Results:

  • Effective Hamiltonians can be calculated for both resonant and non-resonant problems.
  • The theory is applicable to single-mode to triple-mode Floquet problems.
  • Demonstrated applicability to magic-angle spinning and radio-frequency irradiation in solid-state NMR.

Conclusions:

  • Operator-based Floquet theory is a versatile tool for solid-state NMR.
  • The presented methods facilitate the analysis of complex NMR phenomena.
  • This approach broadens the scope of solvable problems in NMR spectroscopy.