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Related Concept Videos

Spin–Spin Coupling Constant: Overview01:08

Spin–Spin Coupling Constant: Overview

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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.
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...
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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: Three-Bond Coupling (Vicinal Coupling)01:22

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

Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)

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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.
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...
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Hybridization of Atomic Orbitals II03:35

Hybridization of Atomic Orbitals II

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sp3d and sp3d 2 Hybridization
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Hybridization of Atomic Orbitals I03:24

Hybridization of Atomic Orbitals I

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The mathematical expression known as the wave function, ψ, contains information about each orbital and the wavelike properties of electrons in an isolated atom. When atoms are bound together in a molecule, the wave functions combine to produce new mathematical descriptions that have different shapes. This process of combining the wave functions for atomic orbitals is called hybridization and is mathematically accomplished by the linear combination of atomic orbitals. The new orbitals that...
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Orbital-Optimized Unitary Coupled Cluster for Indirect Nuclear Spin-Spin Coupling Constants within a Quantum Linear

Juliane H Fuglsbjerg1, Peter Reinholdt2, Erik Kjellgren2

  • 1Department of Chemistry, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen Ø, Denmark.

Journal of Chemical Theory and Computation
|March 18, 2026
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Summary

We developed a quantum linear response (qLR) method using unitary coupled cluster (UCC) for predicting nuclear spin-spin coupling constants. Orbital optimization significantly improves accuracy, matching classical computational chemistry results.

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Area of Science:

  • Quantum chemistry
  • Computational spectroscopy
  • Nuclear Magnetic Resonance (NMR)

Background:

  • Indirect nuclear spin-spin coupling constants are crucial for interpreting NMR spectra.
  • Accurate prediction of these constants requires sophisticated quantum chemical methods.
  • Developing quantum computing-compatible methods is a key goal in computational chemistry.

Purpose of the Study:

  • To present a quantum linear response (qLR) approach for calculating nuclear spin-spin coupling constants.
  • To implement this approach using unitary coupled cluster (UCC) and orbital-optimized UCC (ooUCC) for quantum computing suitability.
  • To assess the accuracy and impact of orbital optimization on coupling constant predictions.

Main Methods:

  • Quantum linear response (qLR) theory applied within an active space framework.
  • Unitary Coupled Cluster (UCC) and its orbital-optimized variant (ooUCC) ansatz.
  • Comparison with established methods like CASCI, CASSCF, CCSD, and CC3.

Main Results:

  • The qLR approach with UCC/ooUCC successfully computes spin-spin coupling constants.
  • Results obtained are comparable to those from traditional classical methods.
  • Orbital optimization in ooUCC significantly impacts the computed couplings, enhancing agreement with CCSD and CC3.

Conclusions:

  • The qLR method with UCC/ooUCC is a viable approach for predicting NMR spin-spin coupling constants.
  • Orbital response is a critical factor for achieving high accuracy in these predictions.
  • The developed method shows promise for quantum computing applications in NMR spectroscopy.