C‐13 Chemical‐Shift Tensors in Organic Materials

Abstract

The chemical‐shift tensor provides an exquisitely sensitive measure of the electronic environment around a nucleus. The tensor is defined by a real symmetric 3 × 3 matrix with six measurable components. Single crystals are usually required to measure all six components whereas three shifts per nucleus are measurable in powders. These powder data, known as principal values , are defined as δ 11 ≥ δ 22 ≥ δ 33 . Presently, most 2D experiments measuring tensor data display the 1D isotropic spectrum along one axis and the tensor patterns for each resonance along the second dimension. Experiments most frequently used are two‐dimensional phase‐adjusted spinning sideband (2D PASS), phase corrected magic angle turning (PHORMAT), FIREMAT (five π replicated magic angle turning), RAI (recoupling of anistropic information), SUPER (separation of undistorted powder patterns by effortless recoupling), and CSA (chemical shift anisotropy) amplification. Very few simple relationships exist between principal values and structure, thus comparison with model structures from computational methods has become important. Recently, these computational methods have been used to predict structure in solids that are intractable to traditional methods. Tensor data have also been found to be extremely sensitive to crystal structure and can therefore be used to further refine some structures, including single crystal structures. The prospect of predicting entire crystal structures from 13 C tensor data and computational methods is now realistic, and a few structures have recently been determined without diffraction data.

Chemical Shift Tensors of Cimetidine Form A Modeled with Density Functional Theory Calculations: Implications for NMR Crystallography

“…In such cases, one-dimensional NMR techniques that rely solely upon the measurement of isotropic chemical shifts can lead to incorrect peak assignments, even when conducted with a variety of double-resonance conditions aimed at site differentiation . Multidimensional NMR techniques can often resolve these ambiguities; however, measurements of the principal components of the chemical shift tensors provide a robust alternative for making assignments and also offer a data set rich in information on electronic structure and local symmetries that can be used for structural interpretation and enhanced NMR crystallographic modeling. − …”

Carbon‐13 chemical shift tensor measurements for nitrogen‐dense compounds

“…While measurement of the orientation of the chemical shift tensor in the molecular frame (or the six principal values within the icosahedral representation of the chemical shift tensor) 2 requires both a crystal of suitable size and quality and specialized single-crystal NMR probes and measurements, [3][4][5] the three principal values of the tensor can be extracted by fitting solid-state NMR (SSNMR) spectra from studies on powder samples (high-resolution magic-angle spinning [MAS] is by far the most common technique, although measurements can also be made on stationary samples). 6 Thus, measurement of the principal values of the chemical shift tensors for powder samples has far reaching applications, including the validation, refinement, and de novo determination of crystal structures, which is the focus of the field of NMR crystallography. [7][8][9][10][11] To aid NMR crystallographic investigations involving quantum chemical calculations, [12][13][14][15][16][17][18][19][20][21][22][23][24][25] NMR-guided crystal structure prediction, [26][27][28] NMR-guided Rietveld refinements of crystal structures, [29][30][31][32][33][34][35] machine learning, [36][37][38][39] and data-driven approaches, 40 a comprehensive da...…”

“…In the solid state, measurement of the symmetric second‐rank tensor that describes the chemical shift provides a detailed description of the electronic environment surrounding the atomic nucleus. While measurement of the orientation of the chemical shift tensor in the molecular frame (or the six principal values within the icosahedral representation of the chemical shift tensor) 2 requires both a crystal of suitable size and quality and specialized single‐crystal NMR probes and measurements, 3–5 the three principal values of the tensor can be extracted by fitting solid‐state NMR (SSNMR) spectra from studies on powder samples (high‐resolution magic‐angle spinning [MAS] is by far the most common technique, although measurements can also be made on stationary samples) 6 . Thus, measurement of the principal values of the chemical shift tensors for powder samples has far reaching applications, including the validation, refinement, and de novo determination of crystal structures, which is the focus of the field of NMR crystallography 7–11 …”