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Related Concept Videos

Spin–Spin Coupling Constant: Overview01:08

Spin–Spin Coupling Constant: Overview

982
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

Spin–Spin Coupling: One-Bond Coupling

1.0K
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,...
1.0K
Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)01:22

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

1.1K
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...
1.1K
Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)01:20

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

1.1K
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...
1.1K
Trends in Lattice Energy: Ion Size and Charge02:54

Trends in Lattice Energy: Ion Size and Charge

24.1K
An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure of the strength of this attraction. The lattice energy (ΔHlattice) of an ionic compound is defined as the energy required to separate one mole of the solid into its component gaseous ions. For the ionic solid sodium chloride, the lattice energy is the enthalpy change of the process:
24.1K
Boundary Conditions for Current Density01:25

Boundary Conditions for Current Density

942
Current density becomes discontinuous across an interface of materials with different electrical conductivities. The normal component of the current density is continuous across the boundary.
942

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Updated: Aug 19, 2025

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
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Current density functional framework for spin-orbit coupling.

Christof Holzer1, Yannick J Franzke2, Ansgar Pausch3

  • 1Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology (KIT), Wolfgang-Gaede-Straße 1, 76131 Karlsruhe, Germany.

The Journal of Chemical Physics
|December 1, 2022
PubMed
Summary
This summary is machine-generated.

Current density functional theory (CDFT) is essential for accurate relativistic calculations including spin-orbit coupling. This approach improves predictions for electron paramagnetic resonance (EPR) properties, especially with more unpaired electrons.

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Area of Science:

  • Quantum Chemistry
  • Computational Physics
  • Spectroscopy

Background:

  • Relativistic density functional theory (DFT) calculations are crucial for describing electronic structure, particularly spin-orbit interactions.
  • Non-relativistic DFT approximations do not account for the paramagnetic current density induced by spin-orbit coupling.

Purpose of the Study:

  • To develop and present a consistent current density functional theory (CDFT) approach for relativistic DFT that includes spin-orbit coupling.
  • To evaluate the impact of current density terms on various ground-state and response properties.

Main Methods:

  • Relativistic two-component density functional calculations in a non-collinear formalism.
  • Generalization of exchange-correlation functionals to include kinetic energy density dependence.
  • Consistent CDFT framework for relativistic DFT with spin-orbit coupling.

Main Results:

  • Spin-orbit coupling induces a non-vanishing paramagnetic current density, necessitating CDFT.
  • Current density terms significantly impact electron paramagnetic resonance (EPR) properties, especially with increasing numbers of unpaired electrons.
  • Notable changes observed for specific functionals (e.g., strongly constrained and appropriately normed, B97M, TASK), with less impact from exact exchange incorporation.

Conclusions:

  • CDFT is strongly recommended for self-consistent spin-orbit calculations due to its accurate treatment of current density effects.
  • The current-dependent kernel ensures the stability of response calculations, making CDFT a robust framework.