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Related Concept Videos

Atomic Nuclei: Nuclear Spin State Population Distribution01:14

Atomic Nuclei: Nuclear Spin State Population Distribution

Near absolute zero temperatures, in the presence of a magnetic field, the majority of nuclei prefer the lower energy spin-up state to the higher energy spin-down state. As temperatures increase, the energy from thermal collisions distributes the spins more equally between the two states. The Boltzmann distribution equation gives the ratio of the number of spins predicted in the spin −½ (N−) and spin +½ (N+) states.
Thermodynamic Potentials01:26

Thermodynamic Potentials

Thermodynamic potentials are state functions that are extremely useful in analyzing a thermodynamic system. They have dimensions of energy. The four important thermodynamic potentials are internal energy, enthalpy, Helmholtz free energy, and Gibbs free energy. These thermodynamic potentials can be expressed using two of the following variables: pressure, volume, temperature, and entropy. These two variables are expressed as the rate of change of the thermodynamic potential with respect to other...
Atomic Nuclei: Nuclear Spin State Overview01:03

Atomic Nuclei: Nuclear Spin State Overview

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 one, the...
Atomic Nuclei: Nuclear Spin01:08

Atomic Nuclei: Nuclear Spin

All atomic particles possess an intrinsic angular momentum, or 'spin'. Electrons, protons, and neutrons each have a spin value of ½, although protons and neutrons in nuclei may have higher half-integer spins owing to energetic factors.
Atomic nuclei have a net nuclear spin, , which can have an integer or half-integer value. In atomic nuclei, the spins of protons are paired against each other but not with neutrons, and vice versa. Consequently, an even number of protons does not contribute to...
Valence Bond Theory02:42

Valence Bond Theory

Coordination compounds and complexes exhibit different colors, geometries, and magnetic behavior, depending on the metal atom/ion and ligands from which they are composed. In an attempt to explain the bonding and structure of coordination complexes, Linus Pauling proposed the valence bond theory, or VBT, using the concepts of hybridization and the overlapping of the atomic orbitals. According to VBT, the central metal atom or ion (Lewis acid) hybridizes to provide empty orbitals of suitable...
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...

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Updated: May 14, 2026

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
12:11

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

Optimized unrestricted Kohn-Sham potentials from ab initio spin densities.

Katharina Boguslawski1, Christoph R Jacob, Markus Reiher

  • 1ETH Zurich, Laboratorium für Physikalische Chemie, Wolfgang-Pauli-Str. 10, CH-8093 Zurich, Switzerland.

The Journal of Chemical Physics
|February 8, 2013
PubMed
Summary
This summary is machine-generated.

Researchers accurately reconstructed spin exchange-correlation potentials from spin densities. This advancement in density-functional theory (DFT) helps improve approximations for open-shell systems.

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Area of Science:

  • Quantum Chemistry
  • Computational Physics
  • Materials Science

Background:

  • Density-functional theory (DFT) relies on approximations for exchange-correlation functionals.
  • Accurate electron densities can reveal limitations of current DFT approximations.
  • Spin density-functional theory (spin-DFT) extends DFT for open-shell systems.

Purpose of the Study:

  • To reconstruct unrestricted Kohn-Sham (KS) potentials from accurate ab initio spin densities.
  • To investigate the feasibility of reconstructing spin exchange-correlation potentials in spin-DFT.
  • To guide the development of improved DFT approximations for open-shell systems.

Main Methods:

  • Utilized a recently developed scheme for optimizing potentials.
  • Employed accurate ab initio spin densities as input.
  • Tested the method on the lithium atom and dioxygen molecule.

Main Results:

  • Successfully reconstructed spin exchange-correlation potentials.
  • Demonstrated the accuracy of the optimized potential scheme.
  • Validated results using high-level quantum chemical calculations (full configuration interaction and complete active space self-consistent field).

Conclusions:

  • The optimized potential scheme accurately reconstructs spin exchange-correlation potentials.
  • This method provides a pathway for developing better approximations in spin-DFT.
  • Insights gained can improve the treatment of open-shell systems in electronic structure calculations.