Accurate determination of chemical shift tensor orientations of single-crystals by solid-state magic angle spinning NMR

High-Precision Determination of NMR Interaction Parameters by Measurement of Single Crystals: A Review of Classical and Advanced Methods

In this review, the process of extracting precise values for NMR interaction tensors from single crystal samples is systematically explored. Starting with a description of the orientation dependence of the considered interactions, i.e., chemical shift, dipolar, and quadrupole interaction, the techniques for acquiring and analysing single-crystal spectra are outlined. This includes the 'classical' approach, which requires the acquisition of three rotation patterns around three rotation axes that are orthogonal to each other, as well as more recent strategies aimed at reducing the number of required NMR spectra. One such strategy is the 'single-rotation method', which exploits the symmetry relations between tensors in the crystal structure to reduce the necessary amount of orientation-dependent data. This concept may be extended to additionally include the orientation of the goniometer axis itself in the data fit, which may be termed the 'minimal-rotation method'. Other, more exotic schemes, such as the use of specialised probe designs or the investigation of single crystals under magic-angle-spinning, are also briefly discussed. Actual values of NMR interaction tensors as determined from the various single-crystal methods have been collected and are provided in tables for spin I=1/2, I=1, and half-integer spins with I>1/2.

NMR crystallography of amino acids

The development of NMR crystallography methods requires a reliable database of chemical shifts measured for systems with known crystal structure. We measured and assigned carbon and hydrogen chemical shifts of twenty solid natural amino acids of known polymorphic structure, meticulously determined using powder X-ray diffraction. We then correlated the experimental data with DFT-calculated isotropic shieldings. The small size of the unit cell of most amino acids allowed for advanced computations using various families of DFT functionals, including generalized gradient approximation (GGA), meta-GGA and hybrid DFT functionals. We tested several combinations of functionals for geometry optimizations and NMR calculations. For carbon shieldings, the widely used GGA functional PBE performed very well, although an improvement could be achieved by adding shielding corrections calculated for isolated molecules using a hybrid functional. For hydrogen nuclei, we observed the best performance for NMR calculations carried out with structures optimized at the hybrid DFT level. The high fidelity of the calculations made it possible to assign additional signals that could not be assigned based on experiments alone, for example signals of two non-equivalent molecules in the unit cell of some of the amino acids.

Stable magic angle spinning with Low-Cost 3D-Printed parts

A 3D-printed double-bearing magic angle spinning (MAS) system was developed with a home-built 4.0 mm MAS nuclear magnetic resonance (NMR) probe at 7 T. Various fused deposition modelling 3D printers were used to produce spinning modules of ignorable materials costs for rotors with a diameter of 7.0, 4.0, and 3.5 mm. High-performance MAS experiments on the 4.0 mm-diameter model using a pencil-type ceramic rotor and 3D-printed drive cap resulted in a high-resolution ¹H NMR signal of silicone grease. The 3.5 mm-diameter MAS system reached a spinning frequency of 23 kHz. Furthermore, 3D-printed inserts were designed for various rotor sizes which can isolate the sample from humidity for a duration of more than a week. Single crystal inserts for MAS rotors of commercial probes can readily be printed using two-color printers. Those developments enable customized low-cost MAS NMR for both adapting existing and manufacturing new probes, respectively.

Single-crystal NMR spectroscopy

Single-crystal (SC) NMR spectroscopy is a solid-state NMR method that has been used since the early days of NMR to study the magnitude and orientation of tensorial nuclear spin interactions in solids. This review first presents the field of SC NMR instrumentation, then provides a survey of software for analysis of SC NMR data, and finally it highlights selected applications of SC NMR in various fields of research. The aim of the last part is not to provide a complete review of all SC NMR literature but to provide examples that demonstrate interesting applications of SC NMR.

NMR interaction tensors of 51V and 207Pb in vanadinite, Pb5(VO4)3Cl, determined from DFT calculations and single-crystal NMR measurements, using only one general rotation axis

Orientation-dependent NMR spectra of a single crystal of the mineral vanadinite, Pb₅(VO₄)₃Cl, were acquired using only one rotation axis with a general orientation in the hexagonal crystal lattice (space group P6₃/m). The chemical shift (CS) tensors for the ²⁰⁷Pb on Wyckoff positions 6h and 4f, and both CS and quadrupole coupling tensor Q for ⁵¹V at the positions 6h were determined by including the NMR response of symmetry-related atoms in the unit cell (and in case of ²⁰⁷Pb at 4f, also the isotropic shift from MAS NMR spectra). This previously suggested 'single rotation method' greatly reduces the necessary amount of data acquisition and analysis. The precise orientation of the rotation axis could not be found by X-ray diffraction experiments because of the high linear absorption coefficient of vanadinite, which is chiefly due to its high lead content. The axis orientation was therefore included into the multi-parameter data fit routine. This NMR-based approach is widely applicable, and offers an alternative way of orienting single crystals. The NMR parameters derived from the tensor eigenvalues are δ_iso=(-1729±9) ppm, Δδ=(-1071±5) ppm, η_CS=0.362±0.008 for ²⁰⁷Pb at positions 6h, and δ_iso=(-1619±2) ppm, Δδ=(-780±58) ppm, η_CS=0.06±0.08 for positions 4f. For ⁵¹V, δ_iso=(-509±3) ppm, Δδ=(-37±2) ppm, η_CS=0.78±0.09, with the quadrupolar coupling described by χ=(2.52±0.01) MHz and η_Q=0.047±0.003. In contrast to the precisely determined tensor eigenvalues, the orientation of the eigenvectors in the crystal ab -plane of the vanadinite system could only be resolved by resorting to data obtained from density functional theory (DFT) calculations.