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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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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.
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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.
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Local Noncollinear Spin Analysis.

Bayileyegn A Abate1, Rajendra P Joshi1, Juan E Peralta1

  • 1Science of Advanced Materials and ‡Department of Physics, Central Michigan University , Mount Pleasant, Michigan 48859, United States.

Journal of Chemical Theory and Computation
|November 3, 2017
PubMed
Summary
This summary is machine-generated.

This study extends local spin analysis to noncollinear spin systems within density functional theory (DFT). The method aids in analyzing spin frustration and calculating magnetic exchange couplings without ad hoc spin values.

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Area of Science:

  • Quantum Chemistry
  • Computational Materials Science
  • Condensed Matter Physics

Background:

  • The local spin analysis by Clark and Davidson partitions the molecular spin square operator's expectation value into atomic contributions.
  • Extending this analysis to noncollinear spin systems is crucial for understanding complex magnetic phenomena.

Purpose of the Study:

  • Generalize the local spin analysis to noncollinear spin cases within Density Functional Theory (DFT).
  • Apply the generalized method to analyze spin-frustrated systems and calculate magnetic exchange couplings.

Main Methods:

  • Derivation of working equations for noncollinear local spin analysis in DFT.
  • Application to triangular H3He3 and Mn3 complexes for spin frustration analysis.
  • Extraction of interatomic spin interactions (⟨ŜA·ŜB⟩) as a function of spin orientation angle (θ).

Main Results:

  • The local spin analysis provides complementary information to standard spin population analysis for noncollinear spin solutions.
  • A novel methodology for calculating magnetic exchange couplings (JAB) from DFT is established.
  • This method avoids the need for arbitrary spin values (SA and SB) common in other approaches.

Conclusions:

  • The generalized local spin analysis offers a robust framework for studying noncollinear magnetism in DFT.
  • The developed methodology provides a more rigorous approach to calculating magnetic exchange couplings.
  • This work advances the understanding of spin frustration and magnetic interactions in complex materials.