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

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.

Time‐Dependent Density Functional Theory for Calculating Origin‐Independent Optical Rotation and Rotatory Strength Tensors

“…Right: Calculated orientation-dependent OR parameter b n of 3 according to Equation (7). In both cases, polar plots [28,29] of the tensors were generated and scaled by 8 pm/10 À40 esu 2 cm 2 (left) and 30 pm/au (right), for the purpose of visualizing the tensor relative to the molecular coordinate frame in SO coordinates. Blue/orange indicates positive/negative values of the tensors.…”

“…A polar plot of b n , based on the tensorB, relative to the molecular reference frame reveals the directional dependence of the chiroptical response amplitude with respect to the beam direction. Hansen et al have previously developed this concept for NMR shielding tensors [28] and subsequently for rotatory strength tensors. [15] A similar visualization concept has been used by us for the visualization of NMR shielding tensors [29] and electric field gradient tensors at quadrupolar nuclei.…”

The shielding tensor. Part I: Understanding its symmetry properties

“…Many other papers appear to avoid the issue by using phrases such as "not symmetric." To avoid confusion, in the remainder of this article, we use the term "nonsymmetric" (22) rather than "asymmetric" to indicate a second-rank tensor that can be decomposed to give both symmetric and antisymmetric parts. The term "asymmetric" is used subsequently only in the phrases "axially asymmetric" and "asymmetry parameter," never alone.…”

“…There is also a large calculated contribution from omti to the shielding of ' ' N in diazirine (22), a three-membered ring molecule that is a dinitrogen analogue of cyclopropene. Significant contributions from a""" are found for 19F and "S in the nonlinear molecule thiazyl fluoride (NSF), according to IGLO (individual gauge for localized molecular orbitals) ab initio quantum mechanical calculations by Schindler (36).…”

Elucidação estrutural de substâncias orgânicas com auxílio de computador: evoluções recentes

“…Há ainda a técnica CSGT 41 ("Continuous Set of Gauge Transformations") que utiliza uma origem única para o campo vetorial magnético externo. Existem ainda outras técnicas, as quais utilizam orbitais localizados IGLO 42 ("Individual Gauge Localized Orbital") e LORG 43 ("Localized Orbital/Local Origin"), porém são menos indicadas por sua maior dependência com a função de base utilizada.…”