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

Quantifying the quadrupolar interaction by 45Sc-NMR spectroscopy of single crystals

Single crystals of the compound [ [Formula: see text] ]Cl₄ ⋅ 2H₂O were studied by ⁴⁵Sc-NMR, with the effect of the quadrupolar coupling interaction on the spectra of the spin-7/2 nucleus analysed in the hierarchical framework of perturbation theory. Orientation-dependent spectra acquired at B₀ = 17.6 T showed strong second-order effects due to the comparatively large coupling constant of χ = |14.613 ± 0.006| MHz, with an associated asymmetry parameter of η_Q = 0.540 9 ± 0.000 4. By analysing the splittings of the ±3/2 satellites, which in good approximation are subjected to first-order effects only, the full quadrupolar coupling tensor could be determined. The second-order effects caused by this tensor were calculated according to theoretical predictions for all orientations, and subtracted from both the centres of gravity of the satellites, and the central transitions. This allowed extraction of the full chemical shift tensor, with the eigenvalues being δ₁₁ = (5.6 ± 0.9) ppm, δ₂₂ = (12.4 ± 0.9) ppm, and δ₃₃ = (38.5 ± 0.9) ppm. In spectra acquired at a lower magnetic field of B₀ = 9.4 T, third-order effects could be detected, and similarly quantified using analytical expressions.

Accurate fragment-based 51-V chemical shift predictions in molecular crystals

Nuclear magnetic resonance (NMR) spectroscopy plays a crucial role in determining molecular structure for complex biological and pharmaceutical compounds. NMR investigations are increasingly reliant on computation for mapping spectral features to chemical structures. Here we benchmark the accuracy of fragment-based ⁵¹V chemical shielding tensor calculations using a training set comprised of 10 biologically and pharmaceutically relevant oxovanadium complexes. Using our self-consistent reproduction of the Madelung potential (SCRMP) electrostatic embedding model, we demonstrate comparable performance between fragment methods and computationally demanding cluster-based techniques. Specifically, fragment methods employing hybrid density functionals are capable of reproducing the experimental ⁵¹V isotropic chemical shifts with a training set rms error of ~9 ​ppm, representing a 20% improvement over traditional plane wave techniques. We provide training set-derived linear regression models for mapping the absolute shieldings obtained from computation to the experimentally determined chemical shifts using four common density functionals; PBE0, B3LYP, PBE, and BLYP. Finally, we establish the utility of fragment methods and the reported regression parameters examining four oxovanadium structures excluded from the training set including the tetracoordinate oxovanadium silicate [Formula: see text] , VO¹⁵NGlySalbz which contains redox-active ligands, and the solid-state form of the common ⁵¹V NMR reference compound VOCl₃.

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.

Local Electronic Structure in AlN Studied by Single-Crystal 27Al and 14N NMR and DFT Calculations

Both the chemical shift and quadrupole coupling tensors for 14N and 27Al in the wurtzite structure of aluminum nitride have been determined to high precision by single-crystal NMR spectroscopy. A homoepitaxially grown AlN single crystal with known morphology was used, which allowed for optical alignment of the crystal on the goniometer axis. From the analysis of the rotation patterns of 14N (I=1) and 27Al (I=5/2), the quadrupolar coupling constants were determined to χ(14N)=(8.19±0.02) kHz, and χ(27Al)=(1.914±0.001) MHz. The chemical shift parameters obtained from the data fit were δiso=−(292.6±0.6) ppm and δΔ=−(1.9±1.1) ppm for 14N, and (after correcting for the second-order quadrupolar shift) δiso=(113.6±0.3) ppm and δΔ=(12.7±0.6) ppm for 27Al. DFT calculations of the NMR parameters for non-optimized crystal geometries of AlN generally did not match the experimental values, whereas optimized geometries came close for 27Al with χ¯calc=(1.791±0.003) MHz, but not for 14N with χ¯calc=−(19.5±3.3) kHz.

Single-crystal 207Pb-NMR of wulfenite, PbMoO4, aided by simultaneous measurement of phosgenite, Pb2Cl2CO3

The effort for determining NMR interaction tensors from orientation-dependent spectra of single crystals may be greatly reduced by exploiting symmetry relations between atoms of the observed nuclide in the unit cell, as is well documented in the literature. In this work, we determined both the full chemical shift (CS) tensor of ²⁰⁷Pb and the unknown orientation of the rotation axis for the natural mineral phosgenite, Pb₂Cl₂CO₃, from a single rotation pattern, i.e. spectra of crystal orientations from 0 to 180°. In the tetragonal crystal structure of phosgenite, four symmetry-related, but magnetically inequivalent ²⁰⁷Pb are generated by the Wyckoff multiplicity. The mineral wulfenite, PbMoO₄, also crystallises in a tetragonal space group, but the site multiplicity for ²⁰⁷Pb generates only one magnetically inequivalent atom, thus not supplying sufficient experimental data to determine CS tensor and axis orientation from an arbitrary number of rotation patterns. One solution to this problem is to simultaneously acquire data of a known compound with high symmetry and Wyckoff multiplicity (here: phosgenite), which supplies additional constraints making the solution of the target compound (here: wulfenite) possible. The ²⁰⁷Pb CS tensors thus determined are characterised by the following eigenvalues in ppm: δ₁₁^PAS=(-2553±1), δ₂₂^PAS=(-1929±1), δ₃₃^PAS=(-1301±1) for phosgenite, and δ₁₁^PAS=(-2074±1), δ₂₂^PAS=(-2074±1), δ₃₃^PAS=(-1898±1) for wulfenite.

Determination of the Full 207Pb Chemical Shift Tensor of Anglesite, PbSO4, and Correlation of the Isotropic Shift to Lead–Oxygen Distance in Natural Minerals

The full 207 Pb chemical shift (CS) tensor of lead in the mineral anglesite, PbSO 4 , was determined from orientation-dependent nuclear magnetic resonance (NMR) spectra of a large natural single crystal, using a global fit over two rotation patterns. The resulting tensor is characterised by the reduced anisotropy Δ δ = ( - 327 ± 4 ) ppm, asymmetry η C S = 0 . 529 ± 0 . 002 , and δ i s o = ( - 3615 ± 3 ) ppm, with the isotropic chemical shift δ i s o also verified by magic-angle spinning NMR on a polycrystalline sample. The initially unknown orientation of the mounted single crystal was included in the global data fit as well, thus obtaining it from NMR data only. By use of internal crystal symmetries, the amount of data acquisition and processing for determination of the CS tensor and crystal orientation was reduced. Furthermore, a linear correlation between the 207 Pb isotropic chemical shift and the shortest Pb–O distance in the co-ordination sphere of Pb 2 + solely surrounded by oxygen has been established for a large database of lead-bearing natural minerals.