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The axial and equatorial protons in cyclohexane can be distinguished by performing a variable-temperature NMR experiment. In this process, except for one proton, the remaining eleven protons are replaced by deuterium. The deuterium substitution avoids the possible peak splitting caused by the spin-spin coupling between the adjacent protons. The remaining proton flips between the axial and equatorial positions.
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Hyperfine interactions and internal rotation in methanol.

Boy Lankhaar1, Gerrit C Groenenboom1, Ad van der Avoird1

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This study rigorously derives nuclear spin-rotation and spin-torsion coupling terms for molecules with internal rotation, improving upon previous formulas. Applying these to methanol, the research accurately predicts hyperfine spectra.

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Area of Science:

  • Molecular Spectroscopy
  • Quantum Chemistry
  • Physical Chemistry

Background:

  • Accurate hyperfine Hamiltonians are crucial for interpreting molecular spectra.
  • Existing formulas for nuclear spin-rotation and spin-torsion coupling have limitations.
  • Methanol serves as a key test case due to its internal rotation and available experimental data.

Purpose of the Study:

  • To derive and present rigorous theoretical formulas for nuclear spin-rotation and spin-torsion coupling terms.
  • To apply these novel formulas to methanol and accurately predict its hyperfine spectra.
  • To resolve discrepancies with previously published theoretical expressions.

Main Methods:

  • Derivation of nuclear spin-rotation and spin-torsion coupling terms in the hyperfine Hamiltonian.
  • Calculation of nuclear spin-spin magnetic dipole-dipole interactions and spin-torsion coupling vectors as functions of internal rotation angle (γ).
  • Ab initio electronic structure calculations for spin-rotation coupling tensors.
  • Fitting experimental spectra to determine electronic contributions to spin-torsion coupling.

Main Results:

  • A new, rigorous derivation of nuclear spin-rotation and spin-torsion coupling terms is presented.
  • Calculated hyperfine transition frequencies and intensities for twelve torsion-rotation transitions in methanol show good agreement with experimental data.
  • The derived formulas provide a more accurate interpretation of experimental hyperfine spectra compared to previous models.

Conclusions:

  • The rigorously derived hyperfine Hamiltonian accurately describes the spectra of molecules with internal rotation, using methanol as a case study.
  • The new theoretical framework resolves inconsistencies with prior derivations and improves spectral interpretation.
  • This work provides a robust foundation for analyzing complex molecular spectra in systems with internal dynamics.