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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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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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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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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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This study presents a new method for deriving diabatic spin-orbit (SO) Hamiltonians, crucial for understanding molecular behavior. The approach utilizes symmetry properties for accurate multi-mode system analysis.

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Area of Science:

  • Quantum Chemistry
  • Molecular Spectroscopy
  • Theoretical Chemistry

Background:

  • Spin-orbit (SO) interactions are fundamental in molecular electronic structure.
  • Accurate theoretical models are needed for multi-mode systems with complex symmetries.
  • Previous methods often struggle with arbitrary orders of expansion and multiple modes of the same symmetry.

Purpose of the Study:

  • To develop a general and systematic method for deriving diabatic spin-orbit (SO) Hamiltonians.
  • To incorporate arbitrary orders of expansion in nuclear coordinates.
  • To handle multi-mode systems, including those with multiple modes of the same symmetry.

Main Methods:

  • Derivation based on the microscopic Breit-Pauli SO operator.
  • Utilizing time reversal and spatial symmetry transformation properties.
  • Expansion in terms of nuclear coordinates to arbitrary order.
  • Demonstration for C(3v)* symmetry using 3D and 9D cases.

Main Results:

  • A general structure for diabatic SO Hamiltonians is established, dependent only on basis states and time reversal symmetry.
  • The Hamiltonian matrix is expressible as a power series using parametrized structure matrices and symmetrized coordinates.
  • A full-dimensional diabatic SO model for methyl halide cations is provided as an explicit example.

Conclusions:

  • The presented method offers a robust framework for constructing diabatic SO Hamiltonians.
  • The approach is applicable to complex molecular systems with multiple vibrational modes.
  • This work lays the foundation for future theoretical studies of methyl halide cations.