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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...
Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule01:10

Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule

In the AX proton spin system, proton A can sense the two spin states of a coupled proton X, resulting in a doublet NMR signal with two peaks of equal (1:1) intensity. When proton A is coupled to two equivalent protons (AX2 spin system), the spin states of each X can be aligned with or against the external field, creating three possible scenarios. This results in a 1:2:1  triplet signal, where the central peak corresponds to the chemical shift of A and is twice as large or intense as the others.
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.
¹H NMR Signal Multiplicity: Splitting Patterns01:13

¹H NMR Signal Multiplicity: Splitting Patterns

When protons A and X are coupled, their nuclear spin energy levels are slightly modified. This is because the energy required to excite proton A to a spin state parallel to proton X is slightly different from the energy required for it to become anti-parallel to spin X. Consequently, there are two possible excitation frequencies for A (A1 and A2), depending on the spin state of X, and vice versa. The mutual nature of coupling implies that the difference between frequencies A1 and A2, indicated...
¹H NMR: Complex Splitting01:13

¹H NMR: Complex Splitting

A proton M that is coupled to a proton X results in doublet signals for M. However, NMR-active nuclei can be simultaneously coupled to more than one nonequivalent nucleus. When M is coupled to a second proton A, such as in styrene oxide, each peak in the doublet is split into another doublet.
Splitting diagrams or splitting tree diagrams are routinely used to depict such complex couplings. While drawing splitting diagrams, the splitting with the larger coupling constant is usually applied first.

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Measuring Interactions of Globular and Filamentous Proteins by Nuclear Magnetic Resonance Spectroscopy (NMR) and Microscale Thermophoresis (MST)
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Formalism for hypercomplex multidimensional NMR employing partial-component subsampling.

Adam D Schuyler1, Mark W Maciejewski, Alan S Stern

  • 1Department of Molecular, Microbial and Structural Biology, University of Connecticut Health Center, Farmington, 06030-3305, USA. schuyler@uchc.edu

Journal of Magnetic Resonance (San Diego, Calif. : 1997)
|December 19, 2012
PubMed
Summary
This summary is machine-generated.

This study introduces a hypercomplex number algebra for multidimensional NMR spectroscopy. This framework optimizes nonuniform sampling, crucial for enhancing NMR experiment efficiency and data quality.

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Area of Science:

  • Nuclear Magnetic Resonance (NMR) Spectroscopy
  • Data Analysis and Signal Processing

Background:

  • Multidimensional NMR spectroscopy often uses phase-sensitive detection, generating hypercomplex data.
  • Nonuniform sampling is widely adopted in NMR to reduce experiment time and improve sensitivity/resolution.

Purpose of the Study:

  • To develop a mathematical framework for optimal utilization of nonuniform sampling in multidimensional NMR.
  • To characterize the relationship between uniformly and nonuniformly sampled NMR data.

Main Methods:

  • Construction of a hypercomplex number algebra for representing multidimensional NMR data.
  • Inclusion of partial-component nonuniform sampling within the algebraic formalism.
  • Development of a modified Discrete Fourier Transform (DFT)-Convolution relationship.

Main Results:

  • The proposed algebra effectively represents multidimensional NMR data with partial-component nonuniform sampling.
  • A modified DFT-Convolution relationship was derived, incorporating a partial-component, hypercomplex point-spread function set.
  • The framework provides a basis for understanding and characterizing partial-component nonuniform sampling.

Conclusions:

  • The developed hypercomplex algebra is essential for the optimal application and characterization of partial-component nonuniform sampling in NMR.
  • This work advances the understanding of nonuniform sampling strategies in multidimensional NMR spectroscopy.