Calculation, display, and analysis of the nature of nonsymmetric nuclear magnetic resonance shielding tensors: Application to three-membered rings

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Abstract
The components of the full nuclear shielding tensor are analyzed with particular regard to the origins of the antisymmetric component of the shielding of nuclei at low‐symmetry molecular sites. As an aid we propose the study and display of the shielding response vector, i.e., the nuclear shielding field per unit applied magnetic field. The analysis is based on ab initio calculations in the localized orbital‐local origin method for cyclopropane, cyclopropene, ethylene oxide, ethylene imine, and diazirine, and also includes a discussion of the mechanism for the large antisymmetric component predicted for the unsaturated nuclei in cyclopropene and diazirine, both in terms of bond and lone pair contributions and in terms of a decomposition of the dominant paramagnetic contributions into molecular point group species. Display of the component of the shielding vector parallel to the applied field is shown to be a valuable alternative to the common ellipsoid representations. Display of the components perpendicular to the applied field provides a picture of the relation of the antisymmetry to molecular structure and suggests its direct observation through monitoring the perpendicular response. Finally, we show that, contrary to a recent claim, the eigensolutions of the full tensor in the presence of antisymmetry play no role in the observed anisotropies.

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