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

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

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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.
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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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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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Approximate Hamiltonians from a Linear Vibronic Coupling Model for Solution-Phase Spin Dynamics.

Toby R C Thompson1, Jakob K Staab1,2, Nicholas F Chilton1,3

  • 1Department of Chemistry, The University of Manchester, Manchester M13 9PL, U.K.

Journal of Chemical Theory and Computation
|January 17, 2025
PubMed
Summary
This summary is machine-generated.

The linear vibronic coupling (LVC) model approximates molecular Hamiltonians efficiently. Accurate spin dynamics simulations for lanthanide complexes require LVC re-parametrization every 10 fs.

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Area of Science:

  • Computational Chemistry
  • Quantum Mechanics
  • Spectroscopy

Background:

  • The linear vibronic coupling (LVC) model approximates molecular Hamiltonians for small geometric changes.
  • LVC offers a computationally efficient alternative to multiconfigurational ab initio calculations for specific applications.
  • Accurate modeling of spin dynamics in complex molecules is crucial for understanding their properties.

Purpose of the Study:

  • To investigate the application of the LVC model for projecting spin Hamiltonians of solvated lanthanide complexes.
  • To assess the accuracy of LVC-approximated spin Hamiltonians along a room-temperature molecular dynamics trajectory.
  • To determine the frequency of LVC re-parametrization needed for quantitatively accurate spin dynamics simulations.

Main Methods:

  • Utilized the linear vibronic coupling (LVC) model to approximate spin Hamiltonians.
  • Projected approximate spin Hamiltonians along a room-temperature molecular dynamics trajectory of a solvated lanthanide complex.
  • Performed time-dependent quantum simulations of spin dynamics using both LVC-projected and ab initio-projected Hamiltonians for comparison.

Main Results:

  • The accuracy of the LVC approximation decreases as molecular geometry diverges from the parametrization reference.
  • Quantitatively accurate spin dynamics are achieved when LVC parametrizations are performed at least every 10 femtoseconds (fs) during the trajectory.
  • Comparison with ab initio calculations validates the findings on LVC accuracy and re-parametrization requirements.

Conclusions:

  • The LVC model can be effectively used to approximate spin Hamiltonians for molecular dynamics simulations of lanthanide complexes.
  • Regular re-parametrization of the LVC model (every 10 fs) is essential for maintaining quantitative accuracy in spin dynamics simulations.
  • This approach provides a computationally feasible method for studying spin dynamics in complex molecular systems.