Determination of the31P and207Pb Chemical Shift Tensors in Pyromorphite, Pb5(PO4)3Cl, by Single-Crystal NMR Measurements and DFT Calculations

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.

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.

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.

How does the NMR thermometer work? Application of combined quantum molecular dynamics and GIPAW calculations into the study of lead nitrate

Lead nitrate is an inorganic salt, commonly used for the accurate temperature determination in the solid state NMR spectroscopy, due to the strong temperature dependence of the ²⁰⁷ Pb chemical shift. As the reason for this phenomenon remained unknown, the main purpose of this study was to explain this temperature dependence at the molecular level. To achieve this, combined CASTEP geometry optimization, quantum molecular dynamics at chosen temperatures and GIPAW NMR computations were performed. Due to the previous literature reports on inaccuracy in the calculation of ²⁰⁷ Pb NMR parameters using GIPAW, a large emphasis was put on the optimization of computational method. The application of quantum molecular dynamics provided the simulation of the temperature-dependent vibrational motions and enabled to accurately compute the changes in the value of Pb δ_iso resulting from them. © 2018 Wiley Periodicals, Inc.