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

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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.
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Explicitly correlated RMP2 for high-spin open-shell reference states.

Gerald Knizia1, Hans-Joachim Werner

  • 1Institut für Theoretische Chemie, Universität Stuttgart, Stuttgart, Germany.

The Journal of Chemical Physics
|April 25, 2008
PubMed
Summary
This summary is machine-generated.

We developed an explicitly correlated RMP2-F12 method for high-spin open-shell systems. This advanced computational chemistry technique rapidly achieves basis set convergence, improving accuracy for electronic property predictions.

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Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Theoretical Chemistry

Background:

  • The resolution of the identity (RI) approximation is widely used in quantum chemistry to accelerate calculations.
  • Explicitly correlated methods, such as MP2-F12, significantly improve the convergence of calculations with respect to the basis set size.
  • Extending these benefits to open-shell systems remains an active area of research.

Purpose of the Study:

  • To develop and present an explicitly correlated version of the RMP2 (restricted Møller-Plesset perturbation theory of second order) method for high-spin open-shell systems, termed RMP2-F12.
  • To demonstrate that RMP2-F12 achieves rapid basis set convergence, similar to its closed-shell counterpart MP2-F12.
  • To evaluate the performance of the RMP2-F12 method through benchmark calculations of various electronic properties.

Main Methods:

  • The theoretical framework was derived in a unitarily invariant form, facilitating the incorporation of local approximations.
  • Efficient density fitting approximations were employed for integral computations.
  • Resolution of the identity approximations were utilized to circumvent the calculation of many-electron integrals.

Main Results:

  • The RMP2-F12 method exhibits rapid basis set convergence, comparable to MP2-F12.
  • Benchmark calculations on ionization potentials, electron affinities, and atomization energies demonstrate the method's efficacy.
  • RMP2-F12 calculations using triple-zeta basis sets produced results closer to the basis set limit than standard RMP2 with augmented quintuple-zeta basis sets.

Conclusions:

  • The developed RMP2-F12 method offers a computationally efficient and accurate approach for high-spin open-shell systems.
  • The method provides significant improvements in basis set convergence, reducing the need for very large basis sets.
  • Further investigations into perturbative corrections for open-shell Hartree-Fock treatments were explored and tested within this framework.