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The Lorentz sphere visualised.

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  • 1Scientific Computing Department, UKRI, Rutherford Appleton Laboratory, Harwell, United Kingdom.

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Summary
This summary is machine-generated.

This study quantifies the Lorentz sphere in periodic systems using density functional theory. It defines its size and shows how chemical features like hydrogen bonds impact magnetic shielding convergence.

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Area of Science:

  • Solid-state NMR spectroscopy
  • Computational chemistry
  • Quantum mechanics

Background:

  • The local origin of chemical shifts in nuclear magnetic resonance (NMR) spectroscopy is crucial for understanding molecular structure.
  • The concept of the Lorentz sphere approximates the region around a nucleus where electronic currents significantly influence chemical shifts.
  • A quantitative understanding of the Lorentz sphere in periodic systems is needed for accurate NMR spectral analysis.

Purpose of the Study:

  • To quantitatively estimate the size of the Lorentz sphere in periodic systems using computational methods.
  • To develop a mathematical framework for calculating magnetic shielding buildup functions based on electronic currents.
  • To investigate the influence of chemical environments, such as hydrogen bonds, on the Lorentz sphere and magnetic shielding.

Main Methods:

  • Utilizing plane-wave density functional theory (DFT) calculations with the CASTEP code.
  • Developing a radial buildup function for magnetic shielding derived from electronic currents and periodicity.
  • Computing buildup functions for various sites within molecular crystals.

Main Results:

  • An approximate upper bound for the Lorentz sphere size in crystalline materials was determined.
  • Radial buildup functions were computed for specific sites in two molecular crystals.
  • The influence of hydrogen bonds on the convergence of magnetic shielding values was demonstrated.

Conclusions:

  • This work provides a quantitative method to estimate the Lorentz sphere in periodic systems.
  • The findings highlight the importance of local electronic structure and intermolecular interactions in determining magnetic shielding.
  • The developed approach aids in interpreting NMR chemical shifts in solid-state materials.