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An applied magnetic field causes the electrons present in the molecule to circulate, setting up a local diamagnetic current within the molecule. The local diamagnetic current arising from circulating sigma-bonding electrons induces a magnetic field, Blocal that opposes the applied magnetic field, B0. The effective magnetic field experienced by these nuclei is given by the difference between the applied and local magnetic fields in a phenomenon called local diamagnetic shielding. Essentially,...
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In aromatic compounds, such as benzene, the circulation of (4n + 2) π-electrons sets up a diamagnetic or diatropic ring current around the perimeter of the molecule. This current induces a magnetic field that opposes the external field inside the ring and reinforces it on the outside. The protons in benzene are deshielded and exhibit high chemical shifts in the range 6.5–8.5 ppm. The shielding effect at the center of the ring is evident in complex aromatic molecules, such as...
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Paramagnetic NMR Shielding Tensors and Ring Currents: Efficient Implementation and Application to Heavy Element

Sebastian Gillhuber1, Yannick J Franzke2, Florian Weigend2

  • 1Institute of Physical Chemistry, Karlsruhe Institute of Technology (KIT), 76131 Karlsruhe, Germany.

The Journal of Physical Chemistry. A
|November 1, 2021
PubMed
Summary

This study introduces an efficient computational method for calculating paramagnetic nuclear magnetic resonance (NMR) shielding tensors and shifts. The approach is applied to investigate magnetic currents in heavy-element clusters like [U@Bi12]3-. Keywords: paramagnetic NMR, shielding tensors, density functional theory, magnetic currents.

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Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Spectroscopy

Background:

  • Accurate calculation of nuclear magnetic resonance (NMR) properties is crucial for understanding molecular electronic structure.
  • Paramagnetic systems present unique challenges due to unpaired electrons, requiring specialized theoretical treatments.
  • Density functional theory (DFT) is a powerful tool for electronic structure calculations, but efficient methods for paramagnetic NMR are needed.

Purpose of the Study:

  • To develop and implement an efficient computational approach for paramagnetic NMR shielding tensors and shifts within DFT.
  • To extend the methodology to scalar-relativistic regimes using the exact two-component Hamiltonian.
  • To apply the developed method to investigate magnetic properties, specifically magnetically induced current densities and ring currents, in open-shell systems.

Main Methods:

  • Implementation of paramagnetic NMR shielding tensor and shift calculations in a nonrelativistic and scalar-relativistic DFT framework.
  • Utilized the scalar exact two-component (2c) Hamiltonian in its local approximation.
  • Employed the (multipole-accelerated) resolution of the identity (RI) approximation and the seminumerical exchange approximation for computational efficiency.

Main Results:

  • An efficient computational implementation for paramagnetic NMR shielding and shifts was successfully developed.
  • The perturbed density matrix was effectively used to study magnetically induced current densities in open-shell systems.
  • Calculations on [U@Bi12]3- revealed delocalized highest occupied molecular orbitals and a significant diatropic ring current (approx. 18 nA/T) through the Bi12 torus.

Conclusions:

  • The developed DFT approach provides an efficient means to compute paramagnetic NMR properties.
  • The study demonstrates the utility of the method in characterizing magnetic phenomena, such as ring currents, in complex heavy-element systems.
  • The findings for [U@Bi12]3- highlight similarities in aromaticity and electronic delocalization with all-metal aromatic clusters like [Th@Bi12]4-.