The Lorentz sphere visualised

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.