Double-rotation (DOR) NMR spectroscopy: Progress and perspectives

Double-rotation (DOR) solid-state NMR spectroscopy is a high-resolution technique developed in the late 1980s. Although multiple-quantum magic-angle spinning (MQMAS) became the most widely used high-resolution method for half-integer spin quadrupoles after 1995, development and application of DOR NMR to a variety of chemical and materials science problems has endured. This Trend article recapitulates the development of DOR NMR, discusses various applications, and describes possible future directions. The main technical limitations specific to DOR NMR are simply related to the size of the double rotor system. The relatively large outer rotor (and thus coil) used for most applications over the past 35 years translates into relatively low rotor spinning frequencies, a low filling factor, and weak radiofrequency powers available for excitation and for proton decoupling. Ongoing developments in NMR instrumentation, including ever-shrinking MAS rotors and spherical NMR rotors, could solve many of these problems and may augur a renaissance for DOR NMR.

A toolbox for improving the workflow of NMR crystallography

NMR crystallography is a powerful tool with applications in structural characterization and crystal structure verification, to name two. However, applying this tool presents several challenges, especially for industrial users, in terms of consistency, workflow, time consumption, and the requirement for a high level of understanding of experimental solid-state NMR and GIPAW-DFT calculations. Here, we have developed a series of fully parameterized scripts for use in Materials Studio and TopSpin, based on the .magres file format, with a focus on organic molecules (e.g. pharmaceuticals), improving efficiency, robustness, and workflow. We separate these tools into three major categories: performing the DFT calculations, extracting & visualizing the results, and crystallographic modelling. These scripts will rapidly submit fully parameterized CASTEP jobs, extract data from the calculations, assist in visualizing the results, and expedite the process of structural modelling. Accompanied with these tools is a description on their functionality, documentation on how to get started and use the scripts, and links to video tutorials for guiding new users. Through the use of these tools, we hope to facilitate NMR crystallography and to harmonize the process across users.

Refining crystal structures using 13C NMR chemical shift tensors as a target function

A two-step process is described for refining crystal structures from any source.

Site-Specific Sodiation Mechanisms of Selenium in Microporous Carbon Host

We combined advanced TEM (HRTEM, HAADF, EELS) with solid-state (SS)MAS NMR and electroanalytical techniques (GITT, etc.) to understand the site-specific sodiation of selenium (Se) encapsulated in a nanoporous carbon host. The architecture employed is representative of a wide number of electrochemically stable and rate-capable Se-based sodium metal battery (SMB) cathodes. SSNMR demonstrates that during the first sodiation, the Se chains are progressively cut to form an amorphous mixture of polyselenides of varying lengths, with no evidence for discrete phase transitions during sodiation. It also shows that Se nearest the carbon pore surface is sodiated first, leading to the formation of a core-shell compositional profile. HRTEM indicates that the vast majority of the pore-confined Se is amorphous, with the only localized presence of nanocrystalline equilibrium Na₂Se₂ (hcp) and Na₂Se (fcc). A nanoscale fracture of terminally sodiated Na-Se is observed by HAADF, with SSNMR, indicating a physical separation of some Se from the carbon host after the first cycle. GITT reveals a 3-fold increase in Na⁺ diffusivity at cycle 2, which may be explained by the creation of extra interfaces. These combined findings highlight the complex phenomenology of electrochemical phase transformations in nanoconfined materials, which may profoundly differ from their "free" counterparts.

The Sodium Anion Is Strongly Perturbed in the Condensed Phase Even Though It Appears Like a Free Ion in Nuclear Magnetic Resonance Experiments

Solvated sodium anions (Na^-) were thought to behave essentially like isolated gas-phase ions that interact only weakly with their environments. For example, ²³Na NMR signals for solvated Na^- are very sharp, despite the potential for strong quadrupolar broadening. The sharp NMR signals appear to indicate a nearly spherical electron density of the ion. For the present study, ab initio molecular dynamics simulations and quadrupolar relaxation rate calculations were carried out for the Na^-/Na⁺ [2.2.2]cryptand system solvated in methylamine, followed by detailed analyses of the electric field gradient at the sodium nuclei. It is found that Na^- does not behave like a quasi-free ion interacting only weakly with its environment. Rather, the filled 3s shell of Na^- interacts weakly with the ion's own core and the nucleus, causing Na^- to appear in NMR experiments like a free ion.

Linear-scaling ab initio simulations of spin diffusion in rotating solids

We investigated the utility of locally restricting the basis sets involved in low-order correlations in Liouville space (LCL) calculations of spin diffusion. Using well-known classical models of spin diffusion, we describe a rationale for selecting the optimal basis set for such calculations. We then show that the use of these locally restricted basis sets provides the same computational accuracy as the full LCL set while reducing the computational time by several orders of magnitude. Speeding up the calculations also enables us to use higher maximum spin orders and increase the computational accuracy. Furthermore, unlike exact and full LCL calculations, locally restricted LCL calculations scale linearly with the system size and should thus enable the ab initio study of spin diffusion in spin systems containing several thousand spins.

NMR crystallography: structure and properties of materials from solid-state nuclear magnetic resonance observables

This topical review provides a brief overview of recent developments in NMR crystallography and related NMR approaches to studying the properties of molecular and ionic solids. Areas of complementarity with diffraction-based methods are underscored. These include the study of disordered systems, of dynamic systems, and other selected examples where NMR can provide unique insights. Highlights from the literature as well as recent work from my own group are discussed.

Investigating FAM-N pulses for signal enhancement in MQMAS NMR of quadrupolar nuclei

Although a popular choice for obtaining high-resolution solid-state NMR spectra of quadrupolar nuclei, the inherently low sensitivity of the multiple-quantum magic-angle spinning (MQMAS) experiment has limited its application for nuclei with low receptivity or when the available sample volume is limited. A number of methods have been introduced in the literature to attempt to address this problem. Recently, we have introduced an alternative, automated approach, based on numerical simulations, for generating amplitude-modulated pulses (termed FAM-N pulses) to enhance the efficiency of the triple- to single-quantum conversion step within MQMAS. This results in efficient pulses that can be used without experimental reoptimisation, ensuring that this method is particularly suitable for challenging nuclei and systems. In this work, we investigate the applicability of FAM-N pulses to a wider variety of systems, and their robustness under more challenging experimental conditions. These include experiments performed under fast MAS, nuclei with higher spin quantum numbers, samples with multiple distinct sites, low-γ nuclei and nuclei subject to large quadrupolar interactions.

13C and 19F solid-state NMR and X-ray crystallographic study of halogen-bonded frameworks featuring nitrogen-containing heterocycles

Halogen bonding is a noncovalent interaction between the electrophilic region of a halogen (σ-hole) and an electron donor. We report a crystallographic and structural analysis of halogen-bonded compounds by applying a combined X-ray diffraction (XRD) and solid-state nuclear magnetic resonance (SSNMR) approach. Single-crystal XRD was first used to characterize the halogen-bonded cocrystals formed between two fluorinated halogen-bond donors (1,4-diiodotetrafluorobenzene and 1,3,5-trifluoro-2,4,6-triiodobenzene) and several nitrogen-containing heterocycles (acridine, 1,10-phenanthroline, 2,3,5,6-tetramethylpyrazine, and hexamethylenetetramine). New structures are reported for the following three cocrystals, all in the P2₁/c space group: acridine-1,3,5-trifluoro-2,4,6-triiodobenzene (1/1), C₆F₃I₃·C₁₃H₉N, 1,10-phenanthroline-1,3,5-trifluoro-2,4,6-triiodobenzene (1/1), C₆F₃I₃·C₁₂H₈N₂, and 2,3,5,6-tetramethylpyrazine-1,3,5-trifluoro-2,4,6-triiodobenzene (1/1), C₆F₃I₃·C₈H₁₂N₂. ¹³C and ¹⁹F solid-state magic-angle spinning (MAS) NMR is shown to be a convenient method to characterize the structural features of the halogen-bond donor and acceptor, with chemical shifts attributable to cocrystal formation observed in the spectra of both nuclides. Cross polarization (CP) from ¹⁹F to ¹³C results in improved spectral sensitivity in characterizing the perfluorinated halogen-bond donor when compared to conventional ¹H CP. Gauge-including projector-augmented wave density functional theory (GIPAW DFT) calculations of magnetic shielding constants, along with optimization of the XRD structures, provide a final set of structures in best agreement with the experimental ¹³C and ¹⁹F chemical shifts. Data for carbons bonded to iodine remain outliers due to well-known relativistic effects.

Quantitative structure parameters from the NMR spectroscopy of quadrupolar nuclei

Nuclear magnetic resonance (NMR) spectroscopy is one of the most important characterization tools in chemistry, however, 3/4 of the NMR active nuclei are underutilized due to their quadrupolar nature. This short review centers on the development of methods that use solid-state NMR of quadrupolar nuclei for obtaining quantitative structural information. Namely, techniques using dipolar recoupling as well as the resolution afforded by double-rotation are presented for the measurement of spin–spin coupling between quadrupoles, enabling the measurement of internuclear distances and connectivities. Two-dimensional J-resolved-type experiments are then presented for the measurement of dipolar and J coupling, between spin-1/2 and quadrupolar nuclei as well as in pairs of quadrupolar nuclei. Select examples utilizing these techniques for the extraction of structural information are given. Techniques are then described that enable the fine refinement of crystalline structures using solely the electric field gradient tensor, measured using NMR, as a constraint. These approaches enable the solution of crystal structures, from polycrystalline compounds, that are of comparable quality to those solved using single-crystal diffraction.

Solid-state (185/187)Re NMR and GIPAW DFT study of perrhenates and Re2(CO)10: chemical shift anisotropy, NMR crystallography, and a metal-metal bond

Advances in solid-state nuclear magnetic resonance (SSNMR) methods, such as dynamic nuclear polarization (DNP), intricate pulse sequences, and increased applied magnetic fields, allow for the study of systems which even very recently would be impractical. However, SSNMR methods using certain quadrupolar probe nuclei (i.e., I > 1/2), such as (185/187)Re remain far from fully developed due to the exceedingly strong interaction between the quadrupole moment of these nuclei and local electric field gradients (EFGs). We present a detailed high-field (B0 = 21.1 T) experimental SSNMR study on several perrhenates (KReO4, AgReO4, Ca(ReO4)2·2H2O), as well as ReO3 and Re2(CO)10. We propose solid ReO3 as a new rhenium SSNMR chemical shift standard due to its reproducible and sharp (185/187)Re NMR resonances. We show that for KReO4, previously poorly understood high-order quadrupole-induced effects (HOQIE) on the satellite transitions can be used to measure the EFG tensor asymmetry (i.e., ηQ) to nearly an order-of-magnitude greater precision than competing SSNMR and nuclear quadrupole resonance (NQR) approaches. Samples of AgReO4 and Ca(ReO4)2·2H2O enable us to comment on the effects of counter-ions and hydration upon Re(vii) chemical shifts. Calcium-43 and (185/187)Re NMR tensor parameters allow us to conclude that two proposed crystal structures for Ca(ReO4)2·2H2O, which would be considered as distinct, are in fact the same structure. Study of Re2(CO)10 provides insights into the effects of Re-Re bonding on the rhenium NMR tensor parameters and rhenium oxidation state on the Re chemical shift value. As overtone NQR experiments allowed us to precisely measure the (185/187)Re EFG tensor of Re2(CO)10, we were able to measure rhenium chemical shift anisotropy (CSA) for the first time in a powdered sample. Experimental observations are supported by gauge-including projector augmented-wave (GIPAW) density functional theory (DFT) calculations, with NMR tensor calculations also provided for NH4ReO4, NaReO4 and RbReO4. These calculations are able to reproduce many of the experimental trends in rhenium δiso values and EFG tensor magnitudes. Using KReO4 as a prototypical perrhenate-containing system, we establish a correlation between the tetrahedral shear strain parameter (|ψ|) and the nuclear electric quadrupolar coupling constant (CQ), which enables the refinement of the structure of ND4ReO4. Shortcomings in traditional DFT approaches, even when including relativistic effects via the zeroth-order regular approximation (ZORA), for calculating rhenium NMR tensor parameters are identified for Re2(CO)10.

NMR crystallography: Applications to inorganic materials

Current developments of NMR crystallography as well as some recent applications to diamagnetic inorganic solids are presented. First, we illustrate how solid-state NMR data can be used in combination with diffraction data for the determination of the periodic part of the crystal structures, from the space group selection, to the structure determination over the refinement and validation processes. As ss-NMR, contrary to diffraction (powder and single-crystal), is not restricted to periodic boundary conditions, ss-NMR data can be used to further complete the structural description of materials, including studies of local order/disorder, etc. This illustrated through examples, which are shown and discussed in the second part of this review.

23Na magic-angle spinning and double-rotation NMR study of solid forms of sodium valproate

Sodium valproate is a pharmaceutical with applications in the treatment of epilepsy, bipolar disorder, and other ailments. Sodium valproate can exist in many hydrated and acid-stabilized forms in the solid state, and it can be difficult to obtain precise structural information about many of these. Here, we present a 13C and 23Na solid-state NMR study of several forms of sodium valproate, only one of which has been previously structurally characterized by single-crystal X-ray diffraction. 23Na magic-angle spinning (MAS), double-rotation (DOR), and multiple-quantum magic-angle spinning (MQMAS) NMR spectra are shown to provide useful information on the number of molecules in the asymmetric unit, the local coordination geometry of the sodium cations, and the presence of amorphous phases. Two previously identified forms are shown to be highly similar, or identical, according to the 23Na NMR data. The utility of carrying out both DOR and MQMAS NMR experiments to identify all crystallographically unique sites is demonstrated. 13C cross-polarization MAS NMR spectra also provide complementary information on the number of molecules in the asymmetric unit and the crystallinity of the sample.

Central-transition double-quantum sideband NMR spectroscopy of half-integer quadrupolar nuclei: estimating internuclear distances and probing clusters within multi-spin networks

Clusters within quadrupolar spin networks are probed and internuclear distances between quadrupolar nuclei are estimated by central-transition double-quantum sideband NMR spectroscopy.