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Related Concept Videos

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.
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...
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...
Spin–Spin Coupling: One-Bond Coupling01:17

Spin–Spin Coupling: One-Bond Coupling

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,...
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...
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.
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 involved orbitals. The...
Atomic Nuclei: Nuclear Spin State Overview01:03

Atomic Nuclei: Nuclear Spin State Overview

NMR-active nuclei have energy levels called 'spin states' that are associated with the orientations of their nuclear magnetic moments. In the absence of a magnetic field, the nuclear magnetic moments are randomly oriented, and the spin states are degenerate. When an external magnetic field is applied, the spin states have only 2 + 1 orientations available to them. A proton with = ½ has two available orientations. Similarly, for a quadrupolar nucleus with a nuclear spin value of one, the...

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Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser
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Two-component natural spinors from two-step spin-orbit coupled wave functions.

Tao Zeng1, Dmitri G Fedorov, Michael W Schmidt

  • 1Department of Chemistry, University of Alberta, Edmonton, Alberta T6G 2G2, Canada.

The Journal of Chemical Physics
|June 14, 2011
PubMed
Summary
This summary is machine-generated.

We developed a new algorithm to derive natural spinors from spin-orbit coupled wave functions. These natural spinors closely approximate j-j spinors, enabling similar wave function analyses.

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Area of Science:

  • Quantum Chemistry
  • Atomic Physics
  • Computational Chemistry

Background:

  • Spin-orbit coupling is crucial for understanding electronic structure in heavy atoms.
  • Accurate representation of electronic wave functions requires sophisticated computational methods.
  • j-j spinors are a standard representation in one-step spin-orbit coupling calculations.

Purpose of the Study:

  • To develop an algorithm for obtaining natural spinors from two-step spin-orbit coupled wave functions.
  • To assess the utility of natural spinors as an approximation to j-j spinors.
  • To enable wave function analysis using natural spinors.

Main Methods:

  • Developed a novel algorithm to compute natural spinors.
  • Utilized two-step spin-orbit coupled wave functions as input.
  • Compared natural spinors with j-j spinors for Tl, At, and Lu atoms.

Main Results:

  • Natural spinors were successfully derived from two-step spin-orbit coupled wave functions.
  • Natural spinors exhibit complex-valued properties and mix spin components.
  • Demonstrated close similarity between natural spinors and j-j spinors for Tl, At, and Lu.
  • Confirmed that natural spinors can approximate j-j spinors.

Conclusions:

  • The developed algorithm provides a new route to natural spinors.
  • Natural spinors offer a viable alternative to j-j spinors for wave function analysis.
  • This method enhances the analysis of electronic structures influenced by spin-orbit coupling.