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

Spin–Spin Coupling: One-Bond Coupling

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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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Double Resonance Techniques: Overview01:12

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Double resonance techniques in Nuclear Magnetic Resonance (NMR) spectroscopy involve the simultaneous application of two different frequencies or radiofrequency pulses to manipulate and observe two distinct nuclear spins. One important application of double resonance is spin decoupling, which selectively suppresses coupling with one type of nucleus while observing the NMR signal from another nucleus, simplifying the spectrum and enhancing resolution.
Spin decoupling is usually achieved by...
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Spin–Spin Coupling Constant: Overview01:08

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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: 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...
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Tensor-Hypercontracted MP2 First Derivatives: Runtime and Memory Efficient Computation of Hyperfine Coupling

Felix H Bangerter1, Michael Glasbrenner1, Christian Ochsenfeld1,2

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|August 9, 2022
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We present a new computational method for calculating hyperfine coupling constants (HFCCs) using tensor-hypercontracted (THC) second-order Møller-Plesset perturbation theory (MP2). This approach achieves significant speedups and reduced storage for complex molecular systems.

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Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Theoretical Chemistry

Background:

  • Accurate computation of hyperfine coupling constants (HFCCs) is crucial for understanding molecular properties and reaction mechanisms.
  • Traditional methods for calculating HFCCs often suffer from high computational complexity, limiting their application to larger systems.
  • Second-order Møller-Plesset perturbation theory (MP2) is a widely used method for electronic structure calculations.

Purpose of the Study:

  • To introduce and validate a novel tensor-hypercontracted (THC) MP2 method for efficient computation of HFCCs.
  • To demonstrate the scalability and performance of the THC-MP2 approach for large molecular systems, including DNA fragments.
  • To significantly reduce the computational cost and memory requirements compared to existing methods.

Main Methods:

  • Implementation of a tensor-hypercontracted (THC) factorized electron repulsion integrals within the MP2 framework.
  • Leveraging the tensor structure of THC integrals for efficient formation of integral-based intermediates.
  • Utilizing natural blocking and screening based on the exponential decay of coupling between tensor indices to achieve subquadratic scaling.

Main Results:

  • The developed THC-based AO-MP2 method exhibits effective subquadratic scaling with a low prefactor.
  • Accurate computation of isotropic HFCCs was achieved for DNA fragments up to 500 atoms and 5000 basis functions.
  • Speedups of 600-1000 times and reduced storage were observed compared to previous implementations for organic radicals.

Conclusions:

  • The THC-MP2 method provides a highly efficient and scalable approach for calculating HFCCs.
  • This method significantly advances the computational capabilities for studying electronic properties of large molecular systems.
  • The developed approach opens new avenues for theoretical investigations in various fields of chemistry and materials science.