Spin-Transfer Pathways in Paramagnetic Lithium Transition-Metal Phosphates from Combined Broadband Isotropic Solid-State MAS NMR Spectroscopy and DFT Calculations

Strong Magnetic Exchange Interactions and Delocalized Mn-O States Enable High-Voltage Capacity in the Na-Ion Cathode P2-Na0.67[Mg0.28Mn0.72]O2

The increased capacity offered by oxygen-redox active cathode materials for rechargeable lithium- and sodium-ion batteries (LIBs and NIBs, respectively) offers a pathway to the next generation of high-gravimetric-capacity cathodes for use in devices, transportation and on the grid. Many of these materials, however, are plagued with voltage fade, voltage hysteresis and O2 loss, the origins of which can be traced back to changes in their electronic and chemical structures on cycling. Developing a detailed understanding of these changes is critical to mitigating these cathodes' poor performance. In this work, we present an analysis of the redox mechanism of P2-Na0.67[Mg0.28Mn0.72]O2, a layered NIB cathode whose high capacity has previously been attributed to trapped O2 molecules. We examine a variety of charge compensation scenarios, calculate their corresponding densities of states and spectroscopic properties, and systematically compare the results to experimental data: 25Mg and 17O nuclear magnetic resonance (NMR) spectroscopy, operando X-band and ex situ high-frequency electron paramagnetic resonance (EPR), ex situ magnetometry, and O and Mn K-edge X-ray Absorption Spectroscopy (XAS) and X-ray Absorption Near Edge Spectroscopy (XANES). Via a process of elimination, we suggest that the mechanism for O redox in this material is dominated by a process that involves the formation of strongly antiferromagnetic, delocalized Mn-O states which form after Mg2+ migration at high voltages. Our results primarily rely on noninvasive techniques that are vital to understanding the electronic structure of metastable cycled cathode samples.

A combined solid-state 1H, 13C, 17O NMR and periodic DFT study of hyperfine coupling tensors in paramagnetic copper(II) compounds

We report solid-state 1H, 13C, and 17O NMR determination of hyperfine coupling tensors (A-tensors) in several paramagnetic Cu(II) (d9, S = 1/2) complexes: trans-Cu(DL-Ala)2·H217O, Cu([1-13C]acetate)2·H2O, Cu([2-13C]acetate)2·H2O, and Cu(acetate)2·H217O. Using these new experimental results and some A-tensor data available in the literature for trans-Cu(L-Ala)2 and K2CuCl4·2H2O, we were able to examine the accuracy of A-tensor computation from a periodic DFT method implemented in the BAND program. We evaluated A-tensors on 1H (I = 1/2), 13C (I = 1/2), 14N (I = 1), 17O (I = 5/2), 39K (I = 3/2), 35Cl (I = 3/2), and 63Cu (I = 3/2) nuclei over a range spanning more than 3 orders of magnitude. We found that the BAND code can reproduce reasonably well the experimental results for both A-tensors and nuclear quadrupole coupling tensors.

Speciation of Lanthanide Metal Ion Dopants in Microcrystalline All-Inorganic Halide Perovskite CsPbCl3

Lanthanides are versatile modulators of optoelectronic properties owing to their narrow optical emission spectra across the visible and near-infrared range. Their use in metal halide perovskites (MHPs) has recently gained prominence, although their fate in these materials has not yet been established at the atomic level. We use cesium-133 solid-state NMR to establish the speciation of all nonradioactive lanthanide ions (La3+, Ce3+, Pr3+, Nd3+, Sm3+, Sm2+, Eu3+, Eu2+, Gd3+, Tb3+, Dy3+, Ho3+, Er3+, Tm3+, Yb3+, Lu3+) in microcrystalline CsPbCl3. Our results show that all lanthanides incorporate into the perovskite structure of CsPbCl3 regardless of their oxidation state (+2, +3).

Geometry and electronic structure of Yb(III)[CH(SiMe3)2]3 from EPR and solid-state NMR augmented by computations

Characterization of paramagnetic compounds, in particular regarding the detailed conformation and electronic structure, remains a challenge, and - still today it often relies solely on the use of X-ray crystallography, thus limiting the access to electronic structure information. This is particularly true for lanthanide elements that are often associated with peculiar structural and electronic features in relation to their partially filled f-shell. Here, we develop a methodology based on the combined use of state-of-the-art magnetic resonance spectroscopies (EPR and solid-state NMR) and computational approaches as well as magnetic susceptibility measurements to determine the electronic structure and geometry of a paramagnetic Yb(III) alkyl complex, Yb(III)[CH(SiMe3)2]3, a prototypical example, which contains notable structural features according to X-ray crystallography. Each of these techniques revealed specific information about the geometry and electronic structure of the complex. Taken together, both EPR and NMR, augmented by quantum chemical calculations, provide a detailed and complementary understanding of such paramagnetic compounds. In particular, the EPR and NMR signatures point to the presence of three-centre-two-electron Yb-γ-Me-β-Si secondary metal-ligand interactions in this otherwise tri-coordinate metal complex, similarly to its diamagnetic Lu analogues. The electronic structure of Yb(III) can be described as a single 4f13 configuration, while an unusually large crystal-field splitting results in a thermally isolated ground Kramers doublet. Furthermore, the computational data indicate that the Yb-carbon bond contains some π-character, reminiscent of the so-called α-H agostic interaction.

Superstructure and Correlated Na+ Hopping in a Layered Mg-Substituted Sodium Manganate Battery Cathode are Driven by Local Electroneutrality

In this work, we present a variable-temperature 23Na NMR and variable-temperature and variable-frequency electron paramagnetic resonance (EPR) analysis of the local structure of a layered P2 Na-ion battery cathode material, Na0.67[Mg0.28Mn0.72]O2 (NMMO). For the first time, we elucidate the superstructure in this material by using synchrotron X-ray diffraction and total neutron scattering and show that this superstructure is consistent with NMR and EPR spectra. To complement our experimental data, we carry out ab initio calculations of the quadrupolar and hyperfine 23Na NMR shifts, the Na+ ion hopping energy barriers, and the EPR g-tensors. We also describe an in-house simulation script for modeling the effects of ionic mobility on variable-temperature NMR spectra and use our simulations to interpret the experimental spectra, available upon request. We find long-zigzag-type Na ordering with two different types of Na sites, one with high mobility and the other with low mobility, and reconcile the tendency toward Na+/vacancy ordering to the preservation of local electroneutrality. The combined magnetic resonance methodology for studying local paramagnetic environments from the perspective of electron and nuclear spins will be useful for examining the local structures of materials for devices.

Pushing the Detection Limit of Static Wideline NMR Spectroscopy Using Ultrafast Frequency-Swept Pulses

We report a simple design strategy for wideband uniform-rate smooth truncation (WURST) pulses that enables ultrafast frequency sweeps to maximize the sensitivity of Carr-Purcell-Meiboom-Gill (CPMG) acquisition in static wideline nuclear magnetic resonance (NMR). Three compelling examples showcase the advantage of ultrafast frequency sweeps over currently employed WURST-CPMG protocols, demonstrating the potential of investigating materials that are typically inaccessible to static wideline NMR techniques, e.g., paramagnetic solids with short homogeneous transverse relaxation times.

Structural characterization of tin in toothpaste by dynamic nuclear polarization enhanced 119Sn solid-state NMR spectroscopy

Stannous fluoride (SnF2) is an effective fluoride source and antimicrobial agent that is widely used in commercial toothpaste formulations. The antimicrobial activity of SnF2 is partly attributed to the presence of Sn(II) ions. However, it is challenging to directly determine the Sn speciation and oxidation state within commercially available toothpaste products due to the low weight loading of SnF2 (0.454 wt% SnF2, 0.34 wt% Sn) and the amorphous, semi-solid nature of the toothpaste. Here, we show that dynamic nuclear polarization (DNP) enables 119Sn solid-state NMR experiments that can probe the Sn speciation within commercially available toothpaste. Solid-state NMR experiments on SnF2 and SnF4 show that 19F isotropic chemical shift and 119Sn chemical shift anisotropy (CSA) are highly sensitive to the Sn oxidation state. DNP-enhanced 119Sn magic-angle turning (MAT) 2D NMR spectra of toothpastes resolve Sn(II) and Sn(IV) by their 119Sn chemical shift tensor parameters. Fits of DNP-enhanced 1D 1H → 119Sn solid-state NMR spectra allow the populations of Sn(II) and Sn(IV) within the toothpastes to be estimated. This analysis reveals that three of the four commercially available toothpastes contained at least 80% Sn(II), whereas one of the toothpaste contained a significantly higher amount of Sn(IV).

Structure Determination and Refinement of Paramagnetic Materials by Solid-State NMR

Paramagnetism in solid-state materials has long been considered an additional challenge for structural investigations by using solid-state nuclear magnetic resonance spectroscopy (ssNMR). The strong interactions between unpaired electrons and the surrounding atomic nuclei, on the one hand, are complex to describe, and on the other hand can cause fast decaying signals and extremely broad resonances. However, significant progress has been made over the recent years in developing both theoretical models to understand and calculate the frequency shifts due to paramagnetism and also more sophisticated experimental protocols for obtaining high-resolution ssNMR spectra. While the field is continuously moving forward, to date, the combination of state-of-the-art numerical and experimental techniques enables us to obtain high-quality data for a variety of systems. This involves the determination of several ssNMR parameters that represent different contributions to the frequency shift in paramagnetic solids. These contributions encode structural information on the studied material on various length scales, ranging from crystal morphologies, to the mid- and long-range order, down to the local atomic bonding environment. In this perspective, the different ssNMR parameters characteristic for paramagnetic materials are discussed with a focus on their interpretation in terms of structure. This includes a summary of studies that have explored the information content of these ssNMR parameters, mostly to complement experimental data from other methods, e.g., X-ray diffraction. The presented overview aims to demonstrate how far ssNMR has hitherto been able to determine and refine the structures of materials and to discuss where it currently falls short of its full potential. We attempt to highlight how much further ssNMR can be pushed to determine and refine structure to deliver a comprehensive structural characterization of paramagnetic materials comparable to what is to date achieved by the combined effort of electron microscopy, diffraction, and spectroscopy.

Determining Local Magnetic Susceptibility Tensors in Paramagnetic Lanthanide Crystalline Powders from Solid-State NMR Chemical Shift Anisotropies

Exploring magnetic properties at the molecular level is a challenge that has been met by developing many experimental and theoretical solutions, such as polarized neutron diffraction (PND), muon-spin rotation (μ-SR), electron paramagnetic resonance (EPR), SQUID-based magnetometry measurements, and advanced modeling on open-shell systems and relativistic calculations. These methods are powerful tools that shed light on the local magnetic response in specifically designed magnetic materials such as contrast agents, for MRI, molecular magnets, magnetic tags for biological NMR, etc. All of these methods have their advantages and disadvantages. In order to complement the possibilities offered by these methods, we propose a new tool that implements a new approach combining simulation and fitting for high-resolution solid-state NMR spectra of lanthanide-based paramagnetic species. This method relies on a rigorous acquisition thanks to short high-power adiabatic pulses (SHAP) of high-resolution solid-state NMR isotropic and anisotropic data on a powdered magnetic material. It is also based on an efficient modeling of this data thanks to a semiempirical model based on a parametrization of the local magnetism and the crystal structure provided by diffraction methods. The efficiency of the calculation relies on a thorough simplification of the electron-nucleus interactions (point-dipole interaction, no Fermi contact) which is validated by experimental analysis. By taking advantage of the efficient calculation possibilities offered by our method, we can compare a great number of simulated spectra to experimental data and find the best-matching local magnetic susceptibility tensor. This method was applied to a series of isostructural lanthanide oxalates which are used as a benchmark system for many analytical methods. We present the results of thorough solid-state NMR and extensive modeling of the hyperfine interaction (including up to 400 paramagnetic centers) that yield local magnetic susceptibility tensor measurements that are self-consistent as well as consistent with bulk susceptibility measurements.

Deconvolution of metal apportionment in bulk metal-organic frameworks

We report a general route to decipher the apportionment of metal ions in bulk metal-organic frameworks (MOFs) by solid-state nuclear magnetic resonance spectroscopy. We demonstrate this route in Mg_1-xNi_x-MOF-74, where we uncover all eight possible atomic-scale Mg/Ni arrangements through identification and quantification of the distinct chemical environments of ¹³C-labeled carboxylates as a function of the Ni content. Here, we use magnetic susceptibility, bond pathway, and density functional theory calculations to identify local metal bonding configurations. The results refute the notion of random apportionment from solution synthesis; rather, we reveal that only two of eight Mg/Ni arrangements are preferred in the Ni-incorporated MOFs. These preferred structural arrangements manifest themselves in macroscopic adsorption phenomena as illustrated by CO/CO₂ breakthrough curves. We envision that this nondestructive methodology can be further applied to analyze bulk assembly of other mixed-metal MOFs, greatly extending the knowledge on structure-property relationships of MOFs and their derived materials.

17O NMR Spectroscopy in Lithium-Ion Battery Cathode Materials: Challenges and Interpretation

Modern studies of lithium-ion battery (LIB) cathode materials employ a large range of experimental and theoretical techniques to understand the changes in bulk and local chemical and electronic structures during electrochemical cycling (charge and discharge). Despite its being rich in useful chemical information, few studies to date have used ¹⁷O NMR spectroscopy. Many LIB cathode materials contain paramagnetic ions, and their NMR spectra are dominated by hyperfine and quadrupolar interactions, giving rise to broad resonances with extensive spinning sideband manifolds. In principle, careful analysis of these spectra can reveal information about local structural distortions, magnetic exchange interactions, structural inhomogeneities (Li⁺ concentration gradients), and even the presence of redox-active O anions. In this Perspective, we examine the primary interactions governing ¹⁷O NMR spectroscopy of LIB cathodes and outline how ¹⁷O NMR may be used to elucidate the structure of pristine cathodes and their structural evolution on cycling, providing insight into the challenges in obtaining and interpreting the spectra. We also discuss the use of ¹⁷O NMR in the context of anionic redox and the role this technique may play in understanding the charge compensation mechanisms in high-capacity cathodes, and we provide suggestions for employing ¹⁷O NMR in future avenues of research.

A machine learning protocol for revealing ion transport mechanisms from dynamic NMR shifts in paramagnetic battery materials

Solid-state nuclear magnetic resonance (ssNMR) provides local environments and dynamic fingerprints of alkali ions in paramagnetic battery materials. Linking the local ionic environments and NMR signals requires expensive first-principles computational tools that have been developed for over a decade. Nevertheless, the assignment of the dynamic NMR spectra of high-rate battery materials is still challenging because the local structures and dynamic information of alkali ions are highly correlated and difficult to acquire. Herein, we develop a novel machine learning (ML) protocol that could not only quickly sample atomic configurations but also predict chemical shifts efficiently, which enables us to calculate dynamic NMR shifts with the accuracy of density functional theory (DFT). Using structurally well-defined P2-type Na_2/3(Mg_1/3Mn_2/3)O₂ as an example, we validate the ML protocol and show the significance of dynamic effects on chemical shifts. Moreover, with the protocol, it is demonstrated that the two experimental ²³Na shifts (1406 and 1493 ppm) of P2-type Na_2/3(Ni_1/3Mn_2/3)O₂ originate from two stacking sequences of transition metal (TM) layers for the first time, which correspond to space groups P6₃/mcm and P6₃22, respectively. This ML protocol could help to correlate dynamic ssNMR spectra with the local structures and fast transport of alkali ions and is expected to be applicable to a wide range of fast dynamic systems.

We developed a widely applicable machine learning (ML) method that can help to correlate dynamic ssNMR spectra with the local structures and transport of ions and thus expands the ssNMR application to fast chemically exchanged material systems.

Monitoring electron spin fluctuations with paramagnetic relaxation enhancement

The magnetic interactions between the spin of an unpaired electron and the surrounding nuclear spins can be exploited to gain structural information, to reduce nuclear relaxation times as well as to create nuclear hyperpolarization via dynamic nuclear polarization (DNP). A central aspect that determines how these interactions manifest from the point of view of NMR is the timescale of the fluctuations of the magnetic moment of the electron spins. These fluctuations, however, are elusive, particularly when electron relaxation times are short or interactions among electronic spins are strong. Here we map the fluctuations by analyzing the ratio between longitudinal and transverse nuclear relaxation times T₁/T₂, a quantity which depends uniquely on the rate of the electron fluctuations and the Larmor frequency of the involved nuclei. This analysis enables rationalizing the evolution of NMR lineshapes, signal quenching as well as DNP enhancements as a function of the concentration of the paramagnetic species and the temperature, demonstrated here for LiMg_1-xMn_xPO₄ and Fe(III) doped Li₄Ti₅O₁₂, respectively. For the latter, we observe a linear dependence of the DNP enhancement and the electron relaxation time within a temperature range between 100 and 300 K.

Dynamic Nuclear Polarization in battery materials

The increasing need for portable and large-scale energy storage systems requires development of new, long lasting and highly efficient battery systems. Solid state NMR spectroscopy has emerged as an excellent method for characterizing battery materials. Yet, it is limited when it comes to probing thin interfacial layers which play a central role in the performance and lifetime of battery cells. Here we review how Dynamic Nuclear Polarization (DNP) can lift the sensitivity limitation and enable detection of the electrode-electrolyte interface, as well as the bulk of some electrode and electrolyte systems. We describe the current challenges from the point of view of materials development; considering how the unique electronic, magnetic and chemical properties differentiate battery materials from other applications of DNP in materials science. We review the current applications of exogenous and endogenous DNP from radicals, conduction electrons and paramagnetic metal ions. Finally, we provide our perspective on the opportunities and directions where battery materials can benefit from current DNP methodologies as well as project on future developments that will enable NMR investigation of battery materials with sensitivity and selectivity under ambient conditions.

Paramagnetic 7Li NMR Shifts and Magnetic Properties of Divalent Transition Metal Silylamide Ate Complexes [LiM{N(SiMe3)2}3] (M2+ = Mn, Fe, Co)

⁷Li NMR shifts and magnetic properties have been determined for three so-called ate complexes [LiM{N(SiMe₃)₂}₃] (M²⁺ = Mn, Fe, Co; e.g., named lithium-tris(bis(trimethylsilylamide))-manganate(II) in accordance with a formally negative charge assigned to the complex fragment [M{N(SiMe₃)₂}₃]^-, which comprises the transition metal). They are formed by addition reactions of LiN(SiMe₃)₂ and [M{N(SiMe₃)₂}₂] and stabilized by Lewis base/Lewis acid interactions. The results are compared to those of the related "ion-separated" complexes [Li(15-crown-5)][M{N(SiMe₃)₂}₃]. The ate complexes with the lithium atoms connected to the 3d metal atoms manganese, iron, or cobalt via μ₂ nitrogen bridges reveal strong ⁷Li NMR paramagnetic shifts of about -75, 125, and 171 ppm, respectively, whereas the shifts for the lithium ions coordinated by the 15-crown-5 ether are close to zero. The observed trends of the ⁷Li NMR shifts are confirmed by density-functional theory calculations. The magnetic dc and ac properties display distinct differences for the six compounds under investigation. Both manganese compounds, [LiMn{N(SiMe₃)₂}₃] and [Li(15-crown-5)][Mn{N(SiMe₃)₂}₃], display almost pure and ideal spin-only paramagnetic behavior of a 3d⁵ high-spin complex. In this respect slightly unexpected, both complexes show slow relaxation behavior at low temperatures under applied dc fields, which is especially pronounced for the ate complex [LiMn{N(SiMe₃)₂}₃]. Dc magnetic properties of the iron complexes reveal moderate g-factor anisotropies with small values of the axial magnetic anisotropy parameter D and a larger E (transversal anisotropy). Both complexes display at low temperatures and, under external dc fields of up to 5000 Oe, only weak ac signals with no maxima in the frequency range from 1 to 1500 s^-1. In contrast, the two cobalt complexes display strong g-factor anisotropies with large values of D and E. In addition, in both cases, the ac measurements at low temperatures and applied dc fields reveal two, in terms of their frequency range, well separated relaxation processes with maxima lying for the most part outside of the measurement range between 1 and 1500 s^-1.

Monitoring Dynamics, Structure, and Magnetism of Switchable Metal-Organic Frameworks via 1 H-Detected MAS NMR

We present a toolbox for the rapid characterisation of powdered samples of paramagnetic metal-organic frameworks at natural abundance by 1 H-detected solid-state NMR. Very fast MAS rates at room and cryogenic temperatures and a set of tailored radiofrequency irradiation schemes help overcome the sensitivity and resolution limits often associated with the characterisation of MOF materials. We demonstrate the approach on DUT-8(Ni), a framework containing Ni2+ paddle-wheel units which can exist in two markedly different architectures. Resolved 1 H and 13 C resonances of organic linkers are detected and assigned in few hours with only 1-2 mg of sample at natural isotopic abundance, and used to rapidly extract information on structure and local internal dynamics of the assemblies, as well as to elucidate the metal electronic properties over an extended temperature range. The experiments disclose new possibilities for describing local and global structural changes and correlating them to electronic and magnetic properties of the assemblies.

Solid-State Nuclear Magnetic Resonance Techniques for the Structural Characterization of Geminal Alane-Phosphane Frustrated Lewis Pairs and Secondary Adducts

The first comprehensive solid-state nuclear magnetic resonance (NMR) characterization of geminal alane-phosphane frustrated Lewis pairs (Al/P FLPs) is reported. Their relevant NMR parameters (isotropic chemical shifts, direct and indirect 27 Al-31 P spin-spin coupling constants, and 27 Al nuclear electric quadrupole coupling tensor components) have been determined by numerical analysis of the experimental NMR line shapes and compared with values computed from the known crystal structures by using density functional theory (DFT) methods. Our work demonstrates that the 31 P NMR chemical shifts for the studied Al/P FLPs are very sensitive to slight structural inequivalences. The 27 Al NMR central transition signals are spread out over a broad frequency range (>200 kHz), owing to the presence of strong nuclear electric quadrupolar interactions that can be well-reproduced by the static 27 Al wideband uniform rate smooth truncation (WURST) Carr-Purcell-Meiboom-Gill (WCPMG) NMR experiment. 27 Al chemical shifts and quadrupole tensor components offer a facile and clear distinction between three- and four-coordinate aluminum environments. For measuring internuclear Al⋅⋅⋅P distances a new resonance-echo saturation-pulse double-resonance (RESPDOR) experiment was developed by using efficient saturation via frequency-swept WURST pulses. The successful implementation of this widely applicable technique indicates that internuclear Al⋅⋅⋅P distances in these compounds can be measured within a precision of ±0.1 Å.

Proton-detected fast-magic-angle spinning NMR of paramagnetic inorganic solids

Fast (60 kHz) magic angle spinning solid-state NMR allows very sensitive proton detection in highly paramagnetic organometallic powders. We showcase this technique with the complete assignment of 1H and 13C resonances in a high-spin Fe(ii) polymerisation catalyst with less than 2 mg of sample at natural abundance.

Modes of Disorder in Poly(carbon monofluoride)

Poly(carbon monofluoride), or (CF)_n, is a layered fluorinated graphite material consisting of nanosized platelets. Here, we present experimental multidimensional solid-state NMR spectra of (CF)_n, supported by density functional theory (DFT) calculations of NMR parameters, which overhauls our understanding of structure and bonding in the material by elucidating many ways in which disorder manifests. We observe strong ¹⁹F NMR signals conventionally assigned to elongated or "semi-ionic" C-F bonds and find that these signals are in fact due to domains where the framework locally adopts boat-like cyclohexane conformations. We calculate that C-F bonds are weakened but are not elongated by this conformational disorder. Exchange NMR suggests that conformational disorder avoids platelet edges. We also use a new J-resolved NMR method for disordered solids, which provides molecular-level resolution of highly fluorinated edge states. The strings of consecutive difluoromethylene groups at edges are relatively mobile. Topologically distinct edge features, including zigzag edges, crenellated edges, and coves, are resolved in our samples by solid-state NMR. Disorder should be controllable in a manner dependent on synthesis, affording new opportunities for tuning the properties of graphite fluorides.

Structural Origins of Voltage Hysteresis in the Na-Ion Cathode P2-Na0.67[Mg0.28Mn0.72]O2: A Combined Spectroscopic and Density Functional Theory Study

P2-layered sodium-ion battery (NIB) cathodes are a promising class of Na-ion electrode materials with high Na+ mobility and relatively high capacities. In this work, we report the structural changes that take place in P2-Na0.67[Mg0.28Mn0.72]O2. Using ex situ X-ray diffraction, Mn K-edge extended X-ray absorption fine structure, and 23Na NMR spectroscopy, we identify the bulk phase changes along the first electrochemical charge-discharge cycle-including the formation of a high-voltage "Z phase", an intergrowth of the OP4 and O2 phases. Our ab initio transition state searches reveal that reversible Mg2+ migration in the Z phase is both kinetically and thermodynamically favorable at high voltages. We propose that Mg2+ migration is a significant contributor to the observed voltage hysteresis in Na0.67[Mg0.28Mn0.72]O2 and identify qualitative changes in the Na+ ion mobility.

Frequency-Swept Ultra-Wideline Magic-Angle Spinning NMR Spectroscopy

Recent years have witnessed the development of solid-state NMR techniques that allow the direct investigation of extremely wide inhomogeneously broadened resonance lines. To date, this typically involves the application of frequency sweeps as offered by wideband uniform rate smooth truncation (WURST) pulses. While the effects of such advanced irradiation schemes on static samples are well understood, the interference between the varying carrier frequency and the time-dependent evolution of the spin system under magic-angle spinning (MAS) conditions is more complex. Herein, we introduce the well-known WURST-Carr-Purcell-Meiboom-Gill (WCPMG) pulse sequence for spinning samples. Using numerical spin-density matrix analysis, an ideal design based on fast frequency sweeps and high truncation of the incorporated WURST pulses is presented that enables uniform excitation/refocusing under MAS conditions with low-to-moderate radio-frequency power requirements. This permits the acquisition of ultra-wideline MAS NMR lines exceeding 500 kHz with chemical shift resolution in a single transmitter step.

Proton-detected solid-state NMR spectroscopy of spin-1/2 nuclei with large chemical shift anisotropy

Constant-time (CT) dipolar heteronuclear multiple quantum coherence (D-HMQC) has previously been demonstrated as a method for proton detection of high-resolution wideline NMR spectra of spin-1/2 nuclei with large chemical shift anisotropy (CSA). However, ¹H transverse relaxation and t₁-noise often reduce the sensitivity of D-HMQC experiments, preventing the theoretical gains in sensitivity provided by ¹H detection from being realized. Here we demonstrate a series of improved pulse sequences for ¹H detection of spin-1/2 nuclei under fast MAS, with ¹⁹⁵Pt SSNMR experiments on cisplatin as an example. First, a t₁-incrementation protocol for D-HMQC dubbed Arbitrary Indirect Dwell (AID) is demonstrated. AID allows the use of arbitrary, rotor asynchronous t₁-increments, but removes the constant time period from CT D-HMQC, resulting in improved sensitivity by reducing transverse relaxation losses. Next, we show that short high-power adiabatic pulses (SHAPs), which efficiently invert broad MAS sideband manifolds, can be effectively incorporated into ¹H detected symmetry-based resonance echo double resonance (S-REDOR) and t₁-noise eliminated (TONE) D-HMQC experiments. The S-REDOR experiments with SHAPs provide approximately double the dipolar dephasing, as compared to experiments with rectangular inversion pulses. We lastly show that sensitivity and resolution can be further enhanced with the use of swept excitation pulses as well as adiabatic magic angle turning (aMAT).

A method to calculate the NMR spectra of paramagnetic species using thermalized electronic relaxation

For paramagnetic species, it has been long understood that the hyperfine interaction between the unpaired electrons and the nucleus results in a nuclear magnetic resonance (NMR) peak that is shifted by a paramagnetic shift, rather than split by the coupling, due to an averaging of the electronic magnetic moment caused by electronic relaxation that is fast in comparison to the hyperfine coupling constant. However, although this feature of paramagnetic NMR has formed the basis of all theories of the paramagnetic shift, the precise theory and mechanism of the electronic relaxation required to predict this result has never been discussed, nor has the assertion been tested. In this paper, we show that the standard semi-classical Redfield theory of relaxation fails to predict a paramagnetic shift, as does any attempt to correct for the semi-classical theory using modifications such as the inhomogeneous master equation or Levitt-di Bari thermalization. In fact, only the recently-introduced Lindbladian theory of relaxation in magnetic resonance [J.Magn.Reson., 310, 106645 (2019)] is able to correctly predict the paramagnetic shift tensor and relaxation-induced linewidth in pNMR. Furthermore, this new formalism is able to predict the NMR spectra of paramagnetic species outside the high-temperature and weak-order limits, and is therefore also applicable to dynamic nuclear polarization. The formalism is tested by simulations of five case studies, which include Fermi-contact and spin-dipolar hyperfine couplings, g-anisotropy, zero-field splitting, high and low temperatures, and fast and slow electronic relaxation.

Unravelling the Fast Alkali-Ion Dynamics in Paramagnetic Battery Materials Combined with NMR and Deep-Potential Molecular Dynamics Simulation

Solid-state nuclear magnetic resonance (ssNMR) has received extensive attention in characterizing alkali-ion battery materials because it is highly sensitive for probing the local environment and dynamic information of atoms/ions. However, precise spectral assignment cannot be carried out by conventional DFT for high-rate battery materials at room temperature. Herein, combining DFT calculation of paramagnetic shift and deep potential molecular dynamics (DPMD) simulation to achieve the converged Na⁺ distribution at hundreds of nanoseconds, we obtain the statistically averaged paramagnetic shift, which is in excellent agreement with ssNMR measurements. Two ²³ Na shifts induced by different stacking sequences of transition metal layers are revealed in the fast chemically exchanged NMR spectra of P2-type Na_2/3 (Mg_1/3 Mn_2/3 )O₂ for the first time. This DPMD simulation auxiliary protocol can be beneficial to a wide range of ssNMR analysis in fast chemically exchanged material systems.

Frequency-swept adiabatic pulses for broadband solid-state MAS NMR

We present a complete description of frequency-swept adiabatic pulses applied to isolated spin-1/2 nuclei with a shift anisotropy in solid materials under magic-angle spinning. Our theoretical framework unifies the existing descriptions of adiabatic pulses in the high-power regime, where the radiofrequency (RF) amplitude is greater than twice the spinning frequency, and the low-power regime, where the RF power is less than the spinning frequency, and so links the short high-powered adiabatic pulse (SHAP) and single-sideband-selective adiabatic pulses (S³AP) schemes used in paramagnetic solid-state NMR. We also identify a hitherto unidentified third regime intermediate between the low- and high-power regimes, and separated from them by rotary resonance conditions. We show that the prevailing benchmark of inversion performance based on (super) adiabatic factors is only applicable in the high- and intermediate-power regimes, but fails to account both for the poor performance at rotary resonance, and the impressive inversion seen in the low-power regime. For low-power pulses, which are non-adiabatic according to this definition of (super) adiabaticity, the effective Floquet Hamiltonian in the jolting frame reveals "hidden" (super) adiabaticity. The theory is demonstrated using a combination of simulation and experiment, and is used to refine the practical recommendations for the experimentalist who wishes to use these pulses.

Picometer Resolution Structure of the Coordination Sphere in the Metal-Binding Site in a Metalloprotein by NMR

Most of our understanding of chemistry derives from atomic-level structures obtained with single-crystal X-ray diffraction. Metal centers in X-ray structures of small organometallic or coordination complexes are often extremely well-defined, with errors in the positions on the order of 10^-4-10^-5 Å. Determining the metal coordination geometry to high accuracy is essential for understanding metal center reactivity, as even small structural changes can dramatically alter the metal activity. In contrast, the resolution of X-ray structures in proteins is limited typically to the order of 10^-1 Å. This resolution is often not sufficient to develop precise structure-activity relations for the metal sites in proteins, because the uncertainty in positions can cover all of the known ranges of bond lengths and bond angles for a given type of metal complex. Here we introduce a new approach that enables the determination of a high-definition structure of the active site of a metalloprotein from a powder sample, by combining magic-angle spinning (MAS) nuclear magnetic resonance (NMR) spectroscopy, tailored radio frequency (RF) irradiation schemes, and computational approaches. This allows us to overcome the "blind sphere" in paramagnetic proteins, and to observe and assign ¹H, ¹³C, and ¹⁵N resonances for the ligands directly coordinating the metal center. We illustrate the method by determining the bond lengths in the structure of the Co^II coordination sphere at the core of human superoxide dismutase 1 (SOD) with 0.7 pm precision. The coordination geometry of the resulting structure explains the nonreactive nature of the Co^II/Zn^II centers in these proteins, which allows them to play a purely structural role.

Resolving Dirac electrons with broadband high-resolution NMR

Detecting the metallic Dirac electronic states on the surface of Topological Insulators (TIs) is critical for the study of important surface quantum properties (SQPs), such as Majorana zero modes, where simultaneous probing of the bulk and edge electron states is required. However, there is a particular shortage of experimental methods, showing at atomic resolution how Dirac electrons extend and interact with the bulk interior of nanoscaled TI systems. Herein, by applying advanced broadband solid-state ¹²⁵Te nuclear magnetic resonance (NMR) methods on Bi₂Te₃ nanoplatelets, we succeeded in uncovering the hitherto invisible NMR signals with magnetic shielding that is influenced by the Dirac electrons, and we subsequently showed how the Dirac electrons spread inside the nanoplatelets. In this way, the spin and orbital magnetic susceptibilities induced by the bulk and edge electron states were simultaneously measured at atomic scale resolution, providing a pertinent experimental approach in the study of SQPs.

The detection of topological states is restricted to limited experimental tools. Here, the authors apply broadband solid-state ¹²⁵Te nuclear magnetic resonance on Bi₂Te₃ nanoplatelets uncovering signals distinguishing edge Dirac electrons and bulk electrons.

Combining density functional theory and 23Na NMR to characterize Na2FePO4F as a potential sodium ion battery cathode

Sodium ion batteries offer an inexpensive alternative to lithium ion batteries, particularly for large-scale applications such as grid storage that do not require fast charging rates and high power output. Moreover, the use of polyanionic structures as cathode materials afford incredibly high structural stability relative to layered transition metal oxides that can undergo a structural collapse upon full removal of the charge carrying ions. Sodium iron fluorophosphate, Na₂FePO₄F, has demonstrated its viability as a potential cathode material for sodium ion batteries, having a robust framework even after multiple charge-discharge cycles. Although solid-state NMR has traditionally been an excellent method for the determination of local structure and dynamic properties of cathode materials during the electrochemical cycling process, reliable assignment of the ²³Na chemical shifts resulting from the paramagnetic hyperfine interaction can be difficult when using only empirical rules. Here we present the use of density functional theory calculations to assign the experimentally observed NMR shifts to the crystallographic sites in Na₂FePO₄F, where it is found that the results do not agree with the previously reported assignment based upon simple geometry arguments. Furthermore, we report the justification of the proposed desodiation mechanism in Na₂FePO₄F on the basis of theoretical arguments, in good agreement with experimental NMR results reported previously.

A 17O paramagnetic NMR study of Sm2O3, Eu2O3, and Sm/Eu-substituted CeO2

Paramagnetic solid-state NMR of lanthanide (Ln) containing materials can be challenging due to the high electron spin states possible for the Ln f electrons, which result in large paramagnetic shifts, and these difficulties are compounded for ¹⁷O due to the low natural abundance and quadrupolar character. In this work, we present examples of ¹⁷O NMR experiments for lanthanide oxides and strategies to overcome these difficulties. In particular, we record and assign the ¹⁷O NMR spectra of monoclinic Sm₂O₃ and Eu₂O₃ for the first time, as well as performing density functional theory (DFT) calculations to gain further insight into the spectra. The temperature dependence of the Sm³⁺ and Eu³⁺ magnetic susceptibilities are investigated by measuring the ¹⁷O shift of the cubic sesquioxides over a wide temperature range, which reveal non-Curie temperature dependence due to the presence of low-lying electronic states. This behaviour is reproduced by calculating the electron spin as a function of temperature, yielding shifts which agree well with the experimental values. Using the understanding of the magnetic behaviour gained from the sesquioxides, we then explore the local oxygen environments in 15 at% Sm- and Eu-substituted CeO₂, with the ¹⁷O NMR spectrum exhibiting signals due to environments with zero, one and two nearest neighbour Ln ions, as well as further splitting due to oxygen vacancies. Finally, we extract an activation energy for oxygen vacancy motion in these systems of 0.35 ± 0.02 eV from the Arrhenius temperature dependence of the ¹⁷O T₁ relaxation constants, which is found to be independent of the Ln ion within error. The relation of this activation energy to literature values for oxygen diffusion in Ln-substituted CeO₂ is discussed to infer mechanistic information which can be applied to further develop these materials as solid-state oxide-ion conductors.

Artefact-free broadband 2D NMR for separation of quadrupolar and paramagnetic shift interactions

Two new two-dimensional, broadband, solid-state NMR experiments for separating and correlating the quadrupolar and shift interactions of spin I=1 nuclei in paramagnetic systems are proposed. The new pulse sequences incorporate the short, high-power adiabatic pulses (SHAPs) into the shifting d-echo experiment of Walder et al. [J. Chem. Phys., 142, 014201 (2015)], in two different ways, giving double and quadruple adiabatic shifting d-echo sequences. These new experiments have the advantage over previous methods of both suppressing spectral artefacts due to pulse imperfections, and exhibiting a broader excitation bandwidth. Both experiments are analysed with theoretical calculations and simulations, and are applied experimentally to the ²H NMR of deuterated CuCl₂ ⋅2H₂O, and two deuterated samples of the ion conductor oxyhydride BaTiO_3-xH_y prepared using two different methods. For the CuCl₂ ⋅2H₂O sample, both new methods obtain very high-quality spectra from which the parameters describing the shift and quadrupolar interaction tensors, and their relative orientation, were extracted. The two BaTiO_3-xH_y samples exhibited different local hydride environments with different tensor parameters. The ²H spectra of these oxyhydrides exhibit inhomogeneous broadening of the ²H shifts, and so whilst the quadrupolar interaction parameters were easily extracted, the measurement of the shift parameters was more complex. However, effective shift parameters were extracted, which combine the effects of both the paramagnetic shift tensor and the inhomogeneous broadening.

Quantum-chemical study of 7Li NMR shifts in the context of delithiation of paramagnetic lithium vanadium phosphate, Li3V2(PO4)3 (LVP)

The lithium NMR shifts of three paramagnetic materials important in the charging/discharging processes of lithium vanadium phosphate cathode materials have been studied by large-scale quantum-chemical methodology. Namely, the ⁷Li NMR shifts of the fully lithiated Li₃V₂(PO₄)₃ (LVP3.0), and of the partly delithiated Li_2.5V₂(PO₄)₃ (LVP2.5) and Li₂V₂(PO₄)₃ (LVP2.0), have been computed and analyzed using a recently proposed approach (A. Mondal, M. Kaupp J. Phys. Chem. C 123 (2019) 8387-8405) that accounts for the Fermi-contact, pseudo-contact, as well as orbital shifts, combining periodic computations with an incremental cluster model. LVP3.0 and LVP2.0 exhibit three and two unique Li sites, respectively, which could be assigned to their experimental ⁷Li NMR signals. In case of LVP2.0, the computations clearly assigned the signals at 143 ppm and 77 ppm to the Li(1) and Li(2) sites, respectively, even though the latter is connected to V_b^(+III d² sites and the former to V_a^(+IV) d¹ sites. LVP2.5 is the most complex of these three materials, exhibiting a 50% occupation of Li(3) sites, which generates much more complicated Li NMR spectra with seven peaks that partly are closely spaced. Exploring three different occupation patterns, the computations can clearly assign five of the seven signals to one type of Li site and give most probable assignments for the two remaining signals. Notably, the calculations support seven signals to be assigned to LVP2.5, while previous interpretations took two of the signals as being entirely due to contamination by LVP2.0. The accuracy of the computations could probably be improved further by full DFT optimization of large super-cell structures. This work suggests that first-principles computations of NMR shifts of extended paramagnetic solids provide an important tool for the analysis of even rather complex NMR spectra.

Paramagnetic NMR in solution and the solid state

The field of paramagnetic NMR has expanded considerably in recent years. This review addresses both the theoretical description of paramagnetic NMR, and the way in which it is currently practised. We provide a review of the theory of the NMR parameters of systems in both solution and the solid state. Here we unify the different languages used by the NMR, EPR, quantum chemistry/DFT, and magnetism communities to provide a comprehensive and coherent theoretical description. We cover the theory of the paramagnetic shift and shift anisotropy in solution both in the traditional formalism in terms of the magnetic susceptibility tensor, and using a more modern formalism employing the relevant EPR parameters, such as are used in first-principles calculations. In addition we examine the theory first in the simple non-relativistic picture, and then in the presence of spin-orbit coupling. These ideas are then extended to a description of the paramagnetic shift in periodic solids, where it is necessary to include the bulk magnetic properties, such as magnetic ordering at low temperatures. The description of the paramagnetic shift is completed by describing the current understanding of such shifts due to lanthanide and actinide ions. We then examine the paramagnetic relaxation enhancement, using a simple model employing a phenomenological picture of the electronic relaxation, and again using a more complex state-of-the-art theory which incorporates electronic relaxation explicitly. An additional important consideration in the solid state is the impact of bulk magnetic susceptibility effects on the form of the spectrum, where we include some ideas from the field of classical electrodynamics. We then continue by describing in detail the solution and solid-state NMR methods that have been deployed in the study of paramagnetic systems in chemistry, biology, and the materials sciences. Finally we describe a number of case studies in paramagnetic NMR that have been specifically chosen to highlight how the theory in part one, and the methods in part two, can be used in practice. The systems chosen include small organometallic complexes in solution, solid battery electrode materials, metalloproteins in both solution and the solid state, systems containing lanthanide ions, and multi-component materials used in pharmaceutical controlled-release formulations that have been doped with paramagnetic species to measure the component domain sizes.

Chemical exchange at the ferroelectric phase transition of lead germanate revealed by solid state 207Pb nuclear magnetic resonance

Multi-dimensional NMR is used to quantitatively identify a mixed order–disorder and displacive mechanism for the ferroelectric phase transition of lead germanate.

To Which Extent Is Paramagnetic Solid-State NMR Able To Address Polymorphism in Complex Transition-Metal Oxides?

A detailed characterization of the polymorphs constituting cathode materials, both before and after cell cycling, is mandatory to develop more stable and powerful lithium batteries. In many cases, e.g., for transition metal lithium silicates, standard diffraction techniques cannot give a clear-cut response. Here we show that broadband adiabatic fast MAS NMR can give unique information in the case of model Li₂(Mn,Fe)SiO₄ high-capacity cathode materials. By coupling ⁷Li and ²⁹Si 1D and 2D spectra, we are able to address polymorphs speciation also in the mixed Mn/Fe compositions, which is a nearly impossible task for X-rays and neutrons diffraction. We finally discuss the conditions under which this approach is useful when applied to rare nuclei such as ²⁹Si.

Resolving the Core and the Surface of CdSe Quantum Dots and Nanoplatelets Using Dynamic Nuclear Polarization Enhanced PASS-PIETA NMR Spectroscopy

Understanding the surface of semiconductor nanocrystals (NCs) prepared using colloidal methods is a long-standing goal of paramount importance for all their potential optoelectronic applications, which remains unsolved largely because of the lack of site-specific physical techniques. Here, we show that multidimensional ¹¹³Cd dynamic nuclear polarization (DNP) enhanced NMR spectroscopy allows the resolution of signals originating from different atomic and magnetic surroundings in the NC cores and at the surfaces. This enables the determination of the structural perfection, and differentiation between the surface and core atoms in all major forms of size- and shape-engineered CdSe NCs: irregularly faceted quantum dots (QDs) and atomically flat nanoplatelets, including both dominant polymorphs (zinc-blende and wurtzite) and their epitaxial nanoheterostructures (CdSe/CdS core/shell quantum dots and CdSe/CdS core/crown nanoplatelets), as well as magic-sized CdSe clusters. Assignments of the NMR signals to specific crystal facets of oleate-terminated ZB structured CdSe NCs are proposed. Significantly, we discover far greater atomistic complexity of the surface structure and the species distribution in wurtzite as compared to zinc-blende CdSe QDs, despite an apparently identical optical quality of both QD polymorphs.

Indirect detection of broad spectra in solid-state NMR using interleaved DANTE trains

We analyze the performances and the optimization of ¹H-{I} HMQC experiments using basic and interleaved DANTE schemes for the indirect detection of nuclei I = 1/2 or 1 exhibiting wide lines dominated by chemical shift anisotropy (CSA) or quadrupole interaction, respectively. These sequences are first described using average Hamiltonian theory. Then, we analyze using numerical simulations (i) the optimal lengths of the DANTE train and the individual pulses, (ii) the robustness of these experiments to offset, and (iii) the optimal choice of the defocusing and refocusing times for both ¹H-{I} J- and D-HMQC sequences for ¹⁹⁵Pt (I = 1/2) and ¹⁴N (I = 1) nuclei subject to large CSA and quadrupole interaction, respectively. These simulations are compared to ¹H-{¹⁴N} D-HMQC experiments on γ-glycine and L-histidine.HCl at B₀ = 18.8 T and MAS frequency of 62.5 kHz. The present study shows that (i) the optimal defocusing and refocusing times do not depend on the chosen DANTE scheme, (ii) the DANTE trains must be applied with the highest rf-field compatible with the probe specifications and the stability of the sample, (iii) the excitation bandwidth along the indirect dimension of HMQC sequence using DANTE trains is inversely proportional to their length, (iv) interleaved DANTE trains increase the excitation bandwidth of these sequences, and (v) dephasing under residual ¹H-¹H and ¹H-I dipolar couplings, as well as ¹⁴N second-order quadrupole interaction, during the length of the DANTE scheme attenuate the transfer efficiency.

Low-power broadband solid-state MAS NMR of 14N

We propose two broadband pulse schemes for ¹⁴N solid-state magic-angle-spinning (MAS) nuclear magnetic resonance (NMR) that achieves (i) complete population inversion and (ii) efficient excitation of the double-quantum spectrum using low-power single-sideband-selective pulses. We give a comprehensive theoretical description of both schemes using a common framework that is based on the jolting-frame formalism of Caravatti et al. [J. Magn. Reson. 55, 88 (1983)]. This formalism is used to determine for the first time that we can obtain complete population inversion of ¹⁴N under low-power conditions, which we do here using single-sideband-selective adiabatic pulses. It is then used to predict that double-quantum coherences can be excited using low-power single-sideband-selective pulses. We then proceed to design a new experimental scheme for double-quantum excitation. The final double-quantum excitation pulse scheme is easily incorporated into other NMR experiments, as demonstrated here for double quantum-single quantum ¹⁴N correlation spectroscopy, and ¹H-¹⁴N dipolar heteronuclear multiple-quantum correlation experiments. These pulses and irradiation schemes are evaluated numerically using simulations on single crystals and full powders, as well as experimentally on ammonium oxalate ((NH₄)₂C₂O₄) at moderate MAS and glycine at ultra-fast MAS. The performance of these new NMR methods is found to be very high, with population inversion efficiencies of 100% and double-quantum excitation efficiencies of 30%-50%, which are hitherto unprecedented for the low radiofrequency field amplitudes, up to the spinning frequency, that are used here.

Assignment of solid-state 13C and 1H NMR spectra of paramagnetic Ni(II) acetylacetonate complexes aided by first-principles computations

Recent advances in computational methodology allowed for first-principles calculations of the nuclear shielding tensor for a series of paramagnetic nickel(II) acetylacetonate complexes, [Ni(acac)₂L₂] with L = H₂O, D₂O, NH₃, ND₃, and PMe₂Ph have provided detailed insight into the origin of the paramagnetic contributions to the total shift tensor. This was employed for the assignment of the solid-state ^1,2H and ¹³C MAS NMR spectra of these compounds. The two major contributions to the isotropic shifts are by orbital (diamagnetic-like) and contact mechanism. The orbital shielding, contact, as well as dipolar terms all contribute to the anisotropic component. The calculations suggest reassignment of the ¹³C methyl and carbonyl resonances in the acac ligand [Inorg. Chem.53, 2014, 399] leading to isotropic paramagnetic shifts of δ(¹³C) ≈ 800-1100 ppm and ≈180-300 ppm for ¹³C for the methyl and carbonyl carbons located three and two bonds away from the paramagnetic Ni(II) ion, respectively. Assignment using three different empirical correlations, i.e., paramagnetic shifts, shift anisotropy, and relaxation (T₁) were ambiguous, however the latter two support the computational results. Thus, solid-state NMR spectroscopy in combination with modern quantum-chemical calculations of paramagnetic shifts constitutes a promising tool for structural investigations of metal complexes and materials.

Modeling short-range substitution order and disorder in crystals: Application to the Ga/Si distribution in a natrolite zeolite

Atomic substitutions are a central feature of the physicochemical properties of an increasing number of solid-state materials. The complexity that this chemical disorder locally generates in otherwise crystalline solids poses a major challenge to the understanding of the relationships between the structure and properties of materials at the atomic and molecular level. Strategies designed to efficiently explore the ensemble of local chemical environments present in disordered crystals and predict their signatures in local spectroscopies such as solid-state nuclear magnetic resonance (NMR) are therefore essential. Focusing on the Ga/Si disorder in the framework of rubidium-exchanged gallosilicate natrolite zeolite (Rb-PST-1) with a high Ga content (SiGa=1.28), we show how the structure-generation approach implemented in the new program supercell (Okhotnikov et al. [26]) provides an excellent basis for the understanding of complex experimental spectroscopic data. Furthermore, we describe how exhaustive explorations of atomic configurations can be performed to seek local structural ordering and/or disordering factors. In the case of Rb-PST-1, we more specifically explore the possibility to form and to detect the presence of thermodynamically unfavorable Ga-O-Ga connectivities. While particularly adapted to the description of dense materials, we demonstrate that this approach may successfully be used to reproduce and interpret the distributions of local structural distortions (i.e., the geometrical disorder) resulting from the chemical disorder in systems as complex as microporous zeolites.

Visualization of Electron Paramagnetic Resonance Hyperfine Structure Coupling Pathways

The close relation between the EPR hyperfine coupling constant and NMR indirect spin-spin coupling constant is well-known. For example, the Karplus-type dependence of hyperfine constants on the dihedral angle, originally proposed for NMR spin-spin coupling, is widely used in pNMR studies. In the present work we propose a new tool for visualization of hyperfine coupling pathways based on our experience with visualization of NMR indirect spin-spin couplings. The plotted 3D-function is the difference between the total electron densities when the magnetic moment of the nucleus of interest changes its sign and as such is an observable from the physical point of view. It has been shown that it is proportional to the linear response of the spin density to the nuclear spin (i.e., magnetic moment). In contrast to the widely used visualization of spin density, our new approach depicts only the part of the electron cloud of a molecule that is affected by the interaction of the unpaired electron(s) with the desired nuclear magnetic moment. Because visualization of NMR spin-spin couplings and hyperfine interaction is based on the same ideas and done using similar techniques, it allows a direct comparison of the corresponding pathways for the two phenomena so as to analyze their resemblance and/or dissimilarity.

Indirect detection of infinite-speed MAS solid-state NMR spectra

Heavy spin-1/2 nuclides are known to possess very large chemical shift anisotropies that can challenge even the most advanced magic-angle-spinning (MAS) techniques. Wide manifolds of overlapping spinning sidebands and insufficient excitation bandwidths often obfuscate meaningful spectral information and force the use of static, low-resolution solid-state (SS)NMR methods for the characterization of materials. To address these issues, we have merged fast-magic-angle-turning (MAT) and dipolar heteronuclear multiple-quantum coherence (D-HMQC) experiments to obtain D-HMQC-MAT pulse sequences which enable the rapid acquisition of 2D SSNMR spectra that correlate isotropic ¹H chemical shifts to the indirectly detected isotropic "infinite-MAS" spectra of heavy spin-1/2 nuclides. For these nuclides, the combination of fast MAS and ¹H detection provides a high sensitivity, which rivals the DNP-enhanced ultra-wideline SSNMR. The new pulse sequences were used to determine the Pt coordination environments in a complex mixture of decomposition products of transplatin and in a metal-organic framework with Pt ions coordinated to the linker ligands.

Solid-state NMR and short-range order in crystalline oxides and silicates: a new tool in paramagnetic resonances

Most applications of high-resolution NMR to questions of short-range order/disorder in inorganic materials have been made in systems where ions with unpaired electron spins are of negligible concentration, with structural information extracted primarily from chemical shifts, quadrupolar coupling parameters, and nuclear dipolar couplings. In some cases, however, the often-large additional resonance shifts caused by interactions between unpaired electron and nuclear spins can provide unique new structural information in materials with contents of paramagnetic cations ranging from hundreds of ppm to several per cent and even higher. In this brief review we focus on recent work on silicate, phosphate, and oxide materials with relatively low concentrations of paramagnetic ions, where spectral resolution can remain high enough to distinguish interactions between NMR-observed nuclides and one or more magnetic neighbors in different bonding configurations in the first, second, and even farther cation shells. We illustrate the types of information available, some of the limitations of this approach, and the great prospects for future experimental and theoretical work in this field. We give examples for the effects of paramagnetic transition metal, lanthanide, and actinide cation substitutions in simple oxides, pyrochlore, zircon, monazite, olivine, garnet, pyrochlores, and olivine structures.