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Related Concept Videos

Spin–Spin Coupling Constant: Overview01:08

Spin–Spin Coupling Constant: Overview

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 have a...
Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)01:22

Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)

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

Spin–Spin Coupling: One-Bond Coupling

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

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

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...
NMR Spectroscopy: Spin–Spin Coupling01:08

NMR Spectroscopy: Spin–Spin Coupling

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 in...
¹H NMR: Interpreting Distorted and Overlapping Signals01:02

¹H NMR: Interpreting Distorted and Overlapping Signals

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 slanted or...

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Related Experiment Video

Updated: May 12, 2026

Site Directed Spin Labeling and EPR Spectroscopic Studies of Pentameric Ligand-Gated Ion Channels
11:19

Site Directed Spin Labeling and EPR Spectroscopic Studies of Pentameric Ligand-Gated Ion Channels

Published on: July 4, 2016

Communication: An efficient algorithm for evaluating the Breit and spin-spin coupling integrals.

Toru Shiozaki1

  • 1Department of Chemistry, Northwestern University, 2145 Sheridan Rd., Evanston, Illinois 60208, USA. shiozaki@northwestern.edu

The Journal of Chemical Physics
|March 29, 2013
PubMed
Summary
This summary is machine-generated.

We developed an efficient algorithm for calculating two-electron integrals, crucial for relativistic quantum chemistry. This method significantly reduces computational cost compared to traditional techniques.

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Related Experiment Videos

Last Updated: May 12, 2026

Site Directed Spin Labeling and EPR Spectroscopic Studies of Pentameric Ligand-Gated Ion Channels
11:19

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Published on: July 4, 2016

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
08:04

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

Area of Science:

  • Quantum Chemistry
  • Computational Physics
  • Theoretical Chemistry

Background:

  • Evaluating two-electron integrals is computationally intensive in relativistic quantum chemistry.
  • Traditional methods for these integrals, like derivative techniques, are often inefficient.
  • Specific operators, such as the Breit interaction and spin-spin coupling, require specialized integral evaluation.

Purpose of the Study:

  • To present an efficient algorithm for evaluating a class of two-electron integrals.
  • To reduce the computational cost associated with relativistic quantum chemistry calculations.
  • To provide a faster alternative to conventional derivative techniques for specific operators.

Main Methods:

  • Developed a novel algorithm based on tailored Gaussian quadrature.
  • Employed horizontal recurrence relations to further optimize computational efficiency.
  • Algorithm is analogous to Rys quadrature used for electron repulsion integrals (ERIs).

Main Results:

  • The algorithm efficiently evaluates two-electron integrals of the form r12⊗r12/r12(n).
  • Computational cost for Breit or spin-spin coupling integrals is only 3-4 times that of ERI evaluation.
  • Demonstrated significant speed-up compared to expensive derivative techniques.

Conclusions:

  • The new algorithm offers a computationally efficient approach for evaluating key relativistic integrals.
  • This method can accelerate relativistic quantum chemistry calculations.
  • The tailored Gaussian quadrature and recurrence relations provide a practical solution for complex integral evaluations.