Integration of global ring currents using the Ampère-Maxwell law

Magnetically induced ring currents are calculated from the magnetic shielding tensor by employing the Ampère-Maxwell law. The feasibility of the method is demonstrated by integrating the zz component of the shielding tensor along the symmetry axis of highly symmetric ring-shaped aromatic, antiaromat...

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Bibliographic Details
Published in:Physical chemistry chemical physics : PCCP 2022-01, Vol.24 (2), p.624-628
Main Authors: Berger, Raphael J. F, Dimitrova, Maria, Nasibullin, Rinat T, Valiev, Rashid R, Sundholm, Dage
Format: Article
Language:English
Subjects:
Electronic structure
Magnetic shielding
Mathematical analysis
NMR
Nuclear magnetic resonance
Ring currents
Symmetry
Tensors
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Summary:Magnetically induced ring currents are calculated from the magnetic shielding tensor by employing the Ampère-Maxwell law. The feasibility of the method is demonstrated by integrating the zz component of the shielding tensor along the symmetry axis of highly symmetric ring-shaped aromatic, antiaromatic and nonaromatic molecules. The calculated ring-current strengths agree perfectly with the ones obtained by integrating the current-density flux passing through a plane cutting half the molecular ring. The method can be used in combination with all electronic structure codes capable of calculating nuclear magnetic resonance (NMR) shielding tensors in general points in space. We also show that nucleus independent chemical shifts (NICS) along the symmetry axis are related to the spatial derivative of the strength of the global ring-current along the z axis. We present a method based on Ampère-Maxwell's integral law for calculating strengths of magnetically induced ring currents.
ISSN:1463-9076
1463-9084
DOI:10.1039/d1cp05061c