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Diamagnetic Shielding of Nuclei: Local Diamagnetic Current01:14

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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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Potential Due to a Polarized Object01:29

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A neutral atom consists of a positively charged nucleus surrounded by a negatively charged electron cloud. When placed in an external electric field, the external electric force pulls the electrons and nucleus apart, opposite to the intrinsic attraction between the nucleus and the electrons. The opposing forces balance each other with a slight shift between the center of masses of the nucleus and the electron cloud, resulting in a polarized atom. On the other hand, a few molecules, like water,...
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When placed in an external electric field, a dielectric material gets polarized. The charge density in the dielectric material is given by the sum of the bound and free charge densities, while the total charge density can also be written in terms of the total electric field. The bound charge density can be measured in terms of polarization, leading to the relationship between electric displacement and polarization.
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Atomic Nuclei: Nuclear Magnetic Moment00:59

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All atomic nuclei are positively charged. When they have a nonzero spin, they behave like rotating charges. As a consequence of their charge and spin, these nuclei generate a magnetic field (B). This, in turn, gives rise to a magnetic moment (μ), which is randomly oriented in the absence of an external magnetic field. When an external magnetic field (B0) is applied, the magnetic moment vectors can align with the field or against it in 2 + 1 orientations. A hydrogen nucleus, which is just a...
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Magnetic dipoles in magnetic materials are aligned when placed under an external magnetic field. For paramagnets and ferromagnets, dipole alignment occurs in the direction of the magnetic field. However, the dipoles align opposite to the field in the case of diamagnets. This state of magnetic polarization due to the external field is called magnetization. Magnetization is defined as the dipole moment per unit volume. It plays a similar role to polarization in electrostatics.
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Nuclear Magnetic Shielding Constants with the Polarizable Density Embedding Model.

Frederik Kamper Jørgensen1, Peter Reinholdt1, Erik Donovan Hedegård1

  • 1Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, Campusvej 55, DK-5230Odense M, Denmark.

Journal of Chemical Theory and Computation
|November 4, 2022
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The enhanced Polarizable Density Embedding (PDE) model accurately calculates nuclear magnetic resonance (NMR) shielding constants. This new method, using gauge-including atomic orbitals (GIAOs), outperforms older models, especially for systems with electron spill-out.

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Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Spectroscopy

Background:

  • Accurate calculation of nuclear magnetic resonance (NMR) shielding constants is crucial for molecular structure elucidation.
  • Existing computational models face challenges with accuracy, basis set convergence, and handling systems with electron spill-out.
  • The polarizable embedding (PE) model offers a computationally efficient approach but has limitations.

Purpose of the Study:

  • To extend the polarizable density embedding (PDE) model for calculating NMR shielding constants.
  • To incorporate gauge-including atomic orbitals (GIAOs) within a density functional theory (DFT) framework.
  • To assess the accuracy and performance of the enhanced PDE model compared to existing methods.

Main Methods:

  • Development of the PDE model to support GIAO-based NMR shielding constant calculations within DFT.
  • Implementation of two approaches (symmetrization and gauge transformation) to handle gauge dependency in the non-local operator.
  • Systematic evaluation of the PDE model's accuracy on various solutes in aqueous solutions and systems with electron spill-out.
  • Comparison with classical polarizable embedding (PE) and supermolecular reference calculations.

Main Results:

  • The extended PDE model successfully calculates NMR shielding constants using GIAOs.
  • The gauge transformation approach for the non-local operator demonstrated superior stability with increasing quantum mechanics (QM) region basis set size.
  • The PDE model generally outperformed the PE model, particularly for small QM region sizes and systems with significant electron spill-out.
  • Basis set convergence and QM region size requirements were analyzed, providing insights into optimal computational setups.

Conclusions:

  • The enhanced PDE model provides a robust and accurate method for calculating NMR shielding constants.
  • The PDE model offers a significant improvement over the PE model, especially in challenging chemical environments.
  • This development advances the capability of embedding models for accurate spectroscopic predictions in complex systems.