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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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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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¹H NMR: Interpreting Distorted and Overlapping Signals01:02

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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.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are...
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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...
1.2K
The Quantum-Mechanical Model of an Atom02:45

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Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
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A quantum algorithm for spin chemistry: a Bayesian exchange coupling parameter calculator with broken-symmetry wave

Kenji Sugisaki1,2, Kazuo Toyota1, Kazunobu Sato1

  • 1Department of Chemistry and Molecular Materials Science, Graduate School of Science, Osaka City University 3-3-138 Sugimoto, Sumiyoshi-ku Osaka 558-8585 Japan sugisaki@sci.osaka-cu.ac.jp sato@sci.osaka-cu.ac.jp takui@sci.osaka-cu.ac.jp.

Chemical Science
|June 24, 2021
PubMed
Summary

A new quantum algorithm, Bayesian exchange coupling parameter calculator with broken-symmetry wave functions (BxB), directly computes magnetic interaction parameters (J). This method avoids calculating individual spin state energies, reducing computational costs.

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Area of Science:

  • Quantum computing
  • Quantum chemistry
  • Computational physics

Background:

  • The Heisenberg exchange coupling parameter (J) is crucial for understanding magnetic interactions in multi-spin systems.
  • Calculating J typically requires computing energies of individual spin states, which is computationally intensive.
  • Existing quantum chemical methods for J calculation are often resource-demanding.

Purpose of the Study:

  • To develop a novel quantum algorithm for directly calculating the Heisenberg exchange coupling parameter (J).
  • To reduce the computational cost associated with determining J values in quantum chemistry.
  • To bypass the need for calculating individual spin state energies.

Main Methods:

  • The proposed Bayesian exchange coupling parameter calculator with broken-symmetry wave functions (BxB) algorithm utilizes quantum simulations.
  • It involves simulating the time evolution of a broken-symmetry wave function under a modified Hamiltonian.
  • Key components include SWAP test for wave function overlap estimation and Bayesian optimization.

Main Results:

  • The BxB algorithm successfully computed J values with errors within 1 kcal mol⁻¹.
  • Numerical simulations were performed on various molecules, including H₂, O₂, and N₂.
  • The algorithm demonstrated lower computational costs compared to conventional quantum phase estimation methods.

Conclusions:

  • The BxB algorithm offers a more efficient quantum approach for calculating Heisenberg exchange coupling parameters.
  • This method provides a significant advantage in terms of computational resources.
  • BxB advances the capability of quantum computing for solving complex problems in quantum chemistry and materials science.