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Related Concept Videos

Spin–Spin Coupling Constant: Overview01:08

Spin–Spin Coupling Constant: Overview

932
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...
932
Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)01:22

Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)

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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.
The extent of coupling depends on the C‑C bond length, the two H‑C‑C angles, any electron-withdrawing substituents, and the dihedral angle between the...
1.1K
¹H NMR: Interpreting Distorted and Overlapping Signals01:02

¹H NMR: Interpreting Distorted and Overlapping Signals

1.0K
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...
1.0K
Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)01:20

Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)

1.0K
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...
1.0K
NMR Spectrometers: Resolution and Error Correction01:14

NMR Spectrometers: Resolution and Error Correction

700
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...
700
NMR Spectroscopy: Spin–Spin Coupling01:08

NMR Spectroscopy: Spin–Spin Coupling

1.4K
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...
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Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
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Self-interaction correction schemes for non-collinear spin-density-functional theory.

Nicolas Tancogne-Dejean1,2, Martin Lüders1, Carsten A Ullrich3

  • 1Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science, Luruper Chaussee 149, 22761 Hamburg, Germany.

The Journal of Chemical Physics
|December 12, 2023
PubMed
Summary
This summary is machine-generated.

We extended self-interaction correction (SIC) methods for density-functional theory to noncollinear magnetic systems. The averaged-density SIC improves ionization energies, while Perdew-Zunger SIC introduces an exchange-correlation torque.

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Area of Science:

  • Computational chemistry
  • Quantum mechanics
  • Materials science

Background:

  • Density-functional theory (DFT) is a powerful quantum mechanical method for electronic structure calculations.
  • Self-interaction error (SIE) is a known limitation of standard DFT approximations, affecting accuracy for certain properties.
  • Noncollinear magnetism involves magnetic moments not aligned with a specific axis, common in molecular magnets and clusters.

Purpose of the Study:

  • To extend established self-interaction correction (SIC) schemes, specifically Perdew-Zunger (PZ-SIC) and average-density SIC (AD-SIC), to handle systems with noncollinear magnetism.
  • To evaluate the performance of these extended SIC schemes in conjunction with the local spin-density approximation (LSDA) for molecular and metallic cluster systems.
  • To analyze the behavior of the exchange-correlation magnetic field generated by the extended PZ-SIC.

Main Methods:

  • Implementation of generalized Perdew-Zunger SIC and average-density SIC for noncollinear magnetic systems within a DFT framework.
  • Application of these extended SIC methods, combined with the local spin-density approximation (LSDA), to calculate electronic properties of selected molecules and metallic clusters.
  • Investigation of the exchange-correlation magnetic field and its alignment with the local total magnetization.

Main Results:

  • The extended AD-SIC scheme effectively improves calculated ionization energies, consistent with findings for collinear systems.
  • The extended AD-SIC scheme shows limitations in accurately predicting subtle properties such as dipole moments for polar molecules.
  • The exchange-correlation magnetic field arising from the extended PZ-SIC is found to be misaligned with the local total magnetization, leading to an exchange-correlation torque.

Conclusions:

  • The developed SIC schemes provide a viable approach for treating noncollinear magnetism in DFT.
  • AD-SIC is beneficial for improving ionization energies but requires further refinement for other properties.
  • The misalignment of the exchange-correlation magnetic field in PZ-SIC introduces a torque, offering new avenues for studying magnetic phenomena.