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Related Concept Videos

NMR Spectrometers: Resolution and Error Correction01:14

NMR Spectrometers: Resolution and Error Correction

When magnetic nuclei in a sample achieve resonance and undergo relaxation, the signal detected in NMR is an approximately exponential free induction decay. Fourier transform of an exponential decay yields a Lorentzian peak in the frequency domain. Lorentzian peaks in an NMR spectrum are defined by their amplitude, full width at half maximum, and position, where the peak width is governed by the spin-spin relaxation time alone. In real experiments, however, the applied magnetic field is rendered...
Double Resonance Techniques: Overview01:12

Double Resonance Techniques: Overview

Double resonance techniques in Nuclear Magnetic Resonance (NMR) spectroscopy involve the simultaneous application of two different frequencies or radiofrequency pulses to manipulate and observe two distinct nuclear spins. One important application of double resonance is spin decoupling, which selectively suppresses coupling with one type of nucleus while observing the NMR signal from another nucleus, simplifying the spectrum and enhancing resolution.
Spin decoupling is usually achieved by...
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...
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: Radiofrequency Pulses and Pulse Sequences01:17

NMR Spectrometers: Radiofrequency Pulses and Pulse Sequences

A pulse is a short burst of radio waves distributed over a range of frequencies that simultaneously excites all the nuclei in the sample. Upon passing a radio frequency pulse along the x-axis, the nuclei absorb energy corresponding to their Larmor frequencies and achieve resonance. This shifts the net magnetization vector from the z-axis toward the transverse plane. This angle of rotation of the magnetization vector, or the flip angle, is proportional to the duration and intensity of the pulse.
2D NMR: Homonuclear Correlation Spectroscopy (COSY)01:06

2D NMR: Homonuclear Correlation Spectroscopy (COSY)

Homonuclear correlation spectroscopy, or COSY, is a 2-dimensional NMR technique that provides information about coupled protons. Typically, the geminal and vicinal coupling are observed. For example, consider the COSY spectrum of ethyl acetate, where its 1D proton NMR spectrum is plotted along the vertical and horizontal axes with their corresponding chemical shift scale. Three spots on the diagonal corresponding to the three peaks in the 1D proton spectrum are called diagonal peaks. The COSY...

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Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser
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A new Lanczos-based algorithm for simulating high-frequency two-dimensional electron spin resonance spectra.

Yun-Wei Chiang1, Jack H Freed

  • 1Department of Chemistry, National Tsing Hua University, Hsinchu 30013, Taiwan. ywchiang@mx.nthu.edu.tw

The Journal of Chemical Physics
|January 26, 2011
PubMed
Summary
This summary is machine-generated.

The Lanczos algorithm combined with the quasi-minimal residual method (LA-QMR) improves convergence for large sparse matrix simulations. This enhanced LA-QMR approach enables accurate 2D-electron spin resonance (ESR) spectral simulations, outperforming the LA-conjugate gradient method.

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Area of Science:

  • Computational Physics
  • Quantum Chemistry
  • Spectroscopy

Background:

  • The Lanczos algorithm (LA) is efficient for reducing large matrices to tridiagonal form.
  • The quasi-minimal residual (QMR) method solves linear systems (Ax=b).
  • Accurate simulation of electron spin resonance (ESR) spectra requires orthogonal transformations of large sparse matrices.

Purpose of the Study:

  • To integrate the QMR method into the LA for monitoring convergence in large sparse matrix reduction.
  • To enhance the orthogonal transformation of sparse, complex, symmetric matrices for ESR spectral simulations.

Main Methods:

  • Incorporation of the QMR method into the Lanczos algorithm (LA-QMR).
  • Utilizing the QMR weight matrix to maintain orthogonality of Lanczos vectors during projections.
  • Comparison of LA-QMR with the LA-conjugate gradient (LA-CG) method for 2D-ESR simulations.

Main Results:

  • The LA-QMR method successfully mitigates the loss of orthogonality in Lanczos vectors.
  • LA-QMR enables more Lanczos projections, leading to improved accuracy in eigenvector and eigenvalue calculations.
  • LA-QMR reliably simulates challenging 2D-ESR spectra at W-band (95 GHz), unlike the LA-CG method.

Conclusions:

  • The LA-QMR method offers superior accuracy and convergence for large sparse matrix reduction compared to LA-CG.
  • LA-QMR is critical for simulating high-frequency 2D-ESR spectra with high resolution.
  • This advancement facilitates reliable simulations of very slow-motional 2D-ESR spectra.