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Atomic Nuclei: Nuclear Spin State Overview01:03

Atomic Nuclei: Nuclear Spin State Overview

963
NMR-active nuclei have energy levels called 'spin states' that are associated with the orientations of their nuclear magnetic moments. In the absence of a magnetic field, the nuclear magnetic moments are randomly oriented, and the spin states are degenerate. When an external magnetic field is applied, the spin states have only 2 + 1 orientations available to them. A proton with = ½ has two available orientations. Similarly, for a quadrupolar nucleus with a nuclear spin value of...
963
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,...
985
Spin–Spin Coupling Constant: Overview01:08

Spin–Spin Coupling Constant: Overview

932
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...
932
Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)01:20

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

1.0K
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...
1.0K
The Pauli Exclusion Principle03:06

The Pauli Exclusion Principle

37.7K
The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:
37.7K
The Energies of Atomic Orbitals03:21

The Energies of Atomic Orbitals

24.0K
In an atom, the negatively charged electrons are attracted to the positively charged nucleus. In a multielectron atom, electron-electron repulsions are also observed. The attractive and repulsive forces are dependent on the distance between the particles, as well as the sign and magnitude of the charges on the individual particles. When the charges on the particles are opposite, they attract each other. If both particles have the same charge, they repel each other.
24.0K

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Related Experiment Video

Updated: Jul 8, 2025

Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser
09:00

Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser

Published on: June 28, 2018

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Mapping spin contamination-free potential energy surfaces using restricted open-shell methods with Grassmannians.

Jake A Tan1, Ka Un Lao2

  • 1Department of Chemistry, Gottwald Center for the Sciences, University of Richmond, Richmond, VA, USA. jake.tan@richmond.edu.

Physical Chemistry Chemical Physics : PCCP
|December 19, 2023
PubMed
Summary

The extended Lagrange-based Grassmann interpolation (G-Int) method accurately constructs potential energy surfaces for open-shell systems. This robust approach provides superior initial guesses for self-consistent field calculations, ensuring spin contamination-free results.

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Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Theoretical Chemistry

Background:

  • Accurate potential energy surfaces (PESs) are crucial for understanding chemical reactions and molecular properties.
  • Traditional methods for constructing PESs for open-shell systems often face challenges with accuracy and computational efficiency.
  • Developing robust initial guess schemes for self-consistent field (SCF) calculations is essential for open-shell systems.

Purpose of the Study:

  • To extend the Lagrange-based Grassmann interpolation (G-Int) method for open-shell systems using restricted open-shell (RO) methods.
  • To evaluate the performance of the extended G-Int method in constructing accurate PESs.
  • To assess the G-Int method's effectiveness as an initial guess scheme for SCF calculations.

Main Methods:

  • Extension of the Lagrange-based Grassmann interpolation (G-Int) method for open-shell systems.
  • Application of G-Int to construct PESs for vanadium(II) oxide, benzyl radical, and methanesulfenyl chloride radical cation.
  • Comparison of G-Int-generated density matrices with traditional SCF initial guess schemes (SADMO, GWH, CORE).
  • Investigation of grid sampling strategies (equally-spaced vs. unequally-spaced) to mitigate Runge's phenomenon.

Main Results:

  • The G-Int method successfully constructed accurate PESs for the studied open-shell systems.
  • Density matrices from G-Int significantly improved SCF convergence and accuracy compared to traditional schemes.
  • The G-Int energy satisfies the variational principle and outperforms direct energy-based interpolation.
  • Unequally-spaced grid sampling based on scaled Gauss-Chebyshev quadrature effectively resolved oscillations caused by Runge's phenomenon.

Conclusions:

  • The extended G-Int method is an efficient and robust strategy for constructing spin contamination-free PESs for open-shell systems.
  • G-Int provides superior initial guesses for SCF calculations, enhancing accuracy and convergence.
  • The combination of G-Int with appropriate grid sampling techniques offers a general approach for accurate PES construction.