The EFG Rosetta Stone: translating between DFT calculations and solid state NMR experiments

We present a comprehensive study on the best practices for integrating first principles simulations in experimental quadrupolar solid-state nuclear magnetic resonance (SS-NMR), exploiting the synergies between theory and experiment for achieving the optimal interpretation of both. Most high performance materials (HPMs), such as battery electrodes, exhibit complex SS-NMR spectra due to dynamic effects or amorphous phases. NMR crystallography for such challenging materials requires reliable, accurate, efficient computational methods for calculating NMR observables from first principles for the transfer between theoretical material structure models and the interpretation of their experimental SS-NMR spectra. NMR-active nuclei within HPMs are routinely probed by their chemical shielding anisotropy (CSA). However, several nuclear isotopes of interest, e.g.7Li and 27Al, have a nuclear quadrupole and experience additional interactions with the surrounding electric field gradient (EFG). The quadrupolar interaction is a valuable source of information about atomistic structure, and in particular, local symmetry, complementing the CSA. As such, there is a range of different methods and codes to choose from for calculating EFGs, from all-electron to plane wave methods. We benchmark the accuracy of different simulation strategies for computing the EFG tensor of quadrupolar nuclei with plane wave density functional theory (DFT) and study the impact of the material structure as well as the details of the simulation strategy. Especially for small nuclei with few electrons, such as 7Li, we show that the choice of physical approximations and simulation parameters has a large effect on the transferability of the simulation results. To the best of our knowledge, we present the first comprehensive reference scale and literature survey for 7Li quadrupolar couplings. The results allow us to establish practical guidelines for developing the best simulation strategy for correlating DFT to experimental data extracting the maximum benefit and information from both, thereby advancing further research into HPMs.

Nanosecond compressive fluorescence lifetime microscopy imaging via the RATS method with a direct reconstruction of lifetime maps

The RAndom Temporal Signals (RATS) method has proven to be a useful and versatile method for measuring photoluminescence (PL) dynamics and fluorescence lifetime imaging (FLIM). Here, we present two fundamental development steps in the method. First, we demonstrate that by using random digital laser modulation in RATS, it is possible to implement the measurement of PL dynamics with temporal resolution in units of nanoseconds. Secondly, we propose an alternative approach to evaluating FLIM measurements based on a single-pixel camera experiment. In contrast to the standard evaluation, which requires a lengthy iterative reconstruction of PL maps for each timepoint, here we use a limited set of predetermined PL lifetimes and calculate the amplitude maps corresponding to each lifetime. The alternative approach significantly saves post-processing time and, in addition, in a system with noise present, it shows better stability in terms of the accuracy of the FLIM spectrogram. Besides simulations that confirmed the functionality of the extension, we implemented the new advancements into a microscope optical setup for mapping PL dynamics on the micrometer scale. The presented principles were also verified experimentally by mapping a LuAG:Ce crystal surface.

Noise effect on 2D photoluminescence decay analysis using the RATS method in a single-pixel camera configuration

Using a random temporal signal for sample excitation (RATS method) is a new, capable approach to measuring photoluminescence (PL) dynamics. The method can be used in single-point measurement (0D), but also it can be converted to PL decay imaging (2D) using a single-pixel camera configuration. In both cases, the reconstruction of the PL decay and PL snapshot is affected by ubiquitous noise. This article provides a detailed analysis of the noise effect on the RATS method and possible strategies for its suppression. We carried out an extensive set of simulations focusing on the effect of noise introduced through the random excitation signal and the corresponding PL waveform. We show that the PL signal noise level is critical for the method. Furthermore, we analyze the role of acquisition time, where we demonstrate the need for a non-periodic excitation signal. We show that it is beneficial to increase the acquisition time and that increasing the number of measurements in the single-pixel camera configuration has a minimal effect above a certain threshold. Finally, we study the effect of a regularization parameter used in the deconvolution step, and we observe that there is an optimum value set by the noise present in the PL dataset. Our results provide a guideline for optimization of the RATS measurement, but we also study effects generally occurring in PL decay measurements methods relying on the deconvolution step.

Fluorescence lifetime imaging via spatio-temporal speckle patterns in a single-pixel camera configuration

Photoluminescence (PL) spectroscopy offers excellent methods for mapping the PL decay on the nanosecond time scale. However, capturing maps of emission dynamics on the microsecond timescale can be highly time-consuming. We present a new approach to fluorescence lifetime imaging (FLIM), which combines the concept of random temporal speckles excitation (RATS) with the concept of a single-pixel camera based on spatial speckles. The spatio-temporal speckle pattern makes it possible to map PL dynamics with unmatched simplicity. Moreover, the method can acquire all the data necessary to map PL decay on the microsecond timescale within minutes. We present proof-of-principle measurements for two samples and compare the reconstructed decays to the non-imaging measurements. Finally, we discuss the effect of the preprocessing routine and other factors on the reconstruction noise level. The presented method is suitable for lifetime imaging processes in several samples, including monitoring charge carrier dynamics in perovskites or monitoring solid-state luminophores with a long lifetime of PL.

Computational and Experimental 1H-NMR Study of Hydrated Mg-Based Minerals

Magnesium oxide (MgO) can convert to different magnesium-containing compounds depending on exposure and environmental conditions. Many MgO-based phases contain hydrated species allowing ¹H-nuclear magnetic resonance (NMR) spectroscopy to be used in the characterization and quantification of proton-containing phases; however, surprisingly limited examples have been reported. Here, ¹H-magic angle spinning (MAS) NMR spectra of select Mg-based minerals are presented and assigned. These experimental results are combined with computational NMR density functional theory (DFT) periodic calculations to calibrate the predicted chemical shielding results. This correlation is then used to predict the NMR shielding for a series of different MgO hydroxide, magnesium chloride hydrate, magnesium perchlorate, and magnesium cement compounds to aid in the future assignment of ¹H-NMR spectra for complex Mg phases.

Ionic and Electronic Conduction in TiNb2O7

TiNb₂O₇ is a Wadsley-Roth phase with a crystallographic shear structure and is a promising candidate for high-rate lithium ion energy storage. The fundamental aspects of the lithium insertion mechanism and conduction in TiNb₂O₇, however, are not well-characterized. Herein, experimental and computational insights are combined to understand the inherent properties of bulk TiNb₂O₇. The results show an increase in electronic conductivity of seven orders of magnitude upon lithiation and indicate that electrons exhibit both localized and delocalized character, with a maximum Curie constant and Li NMR paramagnetic shift near a composition of Li_0.60TiNb₂O₇. Square-planar or distorted-five-coordinate lithium sites are calculated to invert between thermodynamic minima or transition states. Lithium diffusion in the single-redox region (i.e., x ≤ 3 in Li_xTiNb₂O₇) is rapid with low activation barriers from NMR and D_Li = 10^-11 m² s^-1 at the temperature of the observed T₁ minima of 525-650 K for x ≥ 0.75. DFT calculations predict that ionic diffusion, like electronic conduction, is anisotropic with activation barriers for lithium hopping of 100-200 meV down the tunnels but ca. 700-1000 meV across the blocks. Lithium mobility is hindered in the multiredox region (i.e., x > 3 in Li_xTiNb₂O₇), related to a transition from interstitial-mediated to vacancy-mediated diffusion. Overall, lithium insertion leads to effective n-type self-doping of TiNb₂O₇ and high-rate conduction, while ionic motion is eventually hindered at high lithiation. Transition-state searching with beyond Li chemistries (Na⁺, K⁺, Mg²⁺) in TiNb₂O₇ reveals high diffusion barriers of 1-3 eV, indicating that this structure is specifically suited to Li⁺ mobility.

Recent Advances in Solid-State Nuclear Magnetic Resonance Spectroscopy

The sensitivity of nuclear magnetic resonance (NMR) spectroscopy to the local atomic-scale environment offers great potential for the characterization of a diverse range of solid materials. Despite offering more information than its solution-state counterpart, solid-state NMR has not yet achieved a similar level of recognition, owing to the anisotropic interactions that broaden the spectral lines and hinder the extraction of structural information. Here, we describe the methods available to improve the resolution of solid-state NMR spectra and the continuing research in this area. We also highlight areas of exciting new and future development, including recent interest in combining experiment with theoretical calculations, the rise of a range of polarization transfer techniques that provide significant sensitivity enhancements, and the progress of in situ measurements. We demonstrate the detailed information available when studying dynamic and disordered solids and discuss the future applications of solid-state NMR spectroscopy across the chemical sciences.

Combining solid-state NMR spectroscopy with first-principles calculations - a guide to NMR crystallography

Recent advances in the application of first-principles calculations of NMR parameters to periodic systems have resulted in widespread interest in their use to support experimental measurement. Such calculations often play an important role in the emerging field of "NMR crystallography", where NMR spectroscopy is combined with techniques such as diffraction, to aid structure determination. Here, we discuss the current state-of-the-art for combining experiment and calculation in NMR spectroscopy, considering the basic theory behind the computational approaches and their practical application. We consider the issues associated with geometry optimisation and how the effects of temperature may be included in the calculation. The automated prediction of structural candidates and the treatment of disordered and dynamic solids are discussed. Finally, we consider the areas where further development is needed in this field and its potential future impact.

The effect of a broad activation energy distribution on deuteron spin-lattice relaxation

Deuteron NMR spectra and spin-lattice relaxation were studied experimentally in zeolite NaY(2.4) samples containing 100% or 200% of CD3OH or CD3OD molecules of the total coverage of Na atoms in the temperature range 20-150K. The activation energies describing the methyl and hydroxyl motions show broad distributions. The relaxation data were interpreted by improving a recent model (Stoch et al., 2013 [16]) in which the nonexponential relaxation curves are at first described by a sum of three exponentials with adjustable relaxation rates and weights. Then a broad distribution of activation energies (the mean activation energy A0 and the width σ) was assumed for each essentially different methyl and hydroxyl position. The correlation times were calculated from the Arrhenius equation (containing the pre-exponential factor τ0), individual relaxation rates computed and classified into three classes, and finally initial relaxation rates and weights for each class formed. These were compared with experimental data, motional parameters changed slightly and new improved rates and weights for each class calculated, etc. This method was improved by deriving for the deuterons of the A and E species methyl groups relaxation rates, which depend explicitly on the tunnel frequency ωt. The temperature dependence of ωt and of the low-temperature correlation time were obtained by using the solutions of the Mathieu equation for a threefold potential. These dependencies were included in the simulations and as the result sets of A0, σ and τ0 obtained, which describe the methyl and hydroxyl motions in different positions in zeolite.

Comparison of various NMR methods for the indirect detection of nitrogen-14 nuclei via protons in solids

We present an experimental comparison of several through-space Hetero-nuclear Multiple-Quantum Correlation experiments, which allow the indirect observation of homo-nuclear single- (SQ) or double-quantum (DQ) (14)N coherences via spy (1)H nuclei. These (1)H-{(14)N} D-HMQC sequences differ not only by the order of (14)N coherences evolving during the indirect evolution, t1, but also by the radio-frequency (rf) scheme used to excite and reconvert these coherences under Magic-Angle Spinning (MAS). Here, the SQ coherences are created by the application of center-band frequency-selective pulses, i.e. long and low-power rectangular pulses at the (14)N Larmor frequency, ν0((14)N), whereas the DQ coherences are excited and reconverted using rf irradiation either at ν0((14)N) or at the (14)N overtone frequency, 2ν0((14)N). The overtone excitation is achieved either by constant frequency rectangular pulses or by frequency-swept pulses, specifically Wide-band, Uniform-Rate, and Smooth-Truncation (WURST) pulse shapes. The present article compares the performances of four different (1)H-{(14)N} D-HMQC sequences, including those with (14)N rectangular pulses at ν0((14)N) for the indirect detection of homo-nuclear (i) (14)N SQ or (ii) DQ coherences, as well as their overtone variants using (iii) rectangular or (iv) WURST pulses. The compared properties include: (i) the sensitivity, (ii) the spectral resolution in the (14)N dimension, (iii) the rf requirements (power and pulse length), as well as the robustness to (iv) rf offset and (v) MAS frequency instabilities. Such experimental comparisons are carried out for γ-glycine and l-histidine.HCl monohydrate, which contain (14)N sites subject to moderate quadrupole interactions. We demonstrate that the optimum choice of the (1)H-{(14)N} D-HMQC method depends on the experimental goal. When the sensitivity and/or the robustness to offset are the major concerns, the D-HMQC sequence allowing the indirect detection of (14)N SQ coherences should be employed. Conversely, when the highest resolution and/or adjusted indirect spectral width are needed, overtone experiments are the method of choice. The overtone scheme using WURST pulses results in broader excitation bandwidths than that using rectangular pulses, at the expense of reduced sensitivity. Numerically exact simulations also show that the sensitivity of the overtone (1)H-{(14)N} D-HMQC experiment increases for larger quadrupole interactions.

New methods and applications in solid-state NMR spectroscopy of quadrupolar nuclei

Solid-state nuclear magnetic resonance (NMR) spectroscopy has long been established as offering unique atomic-scale and element-specific insight into the structure, disorder, and dynamics of materials. NMR spectra of quadrupolar nuclei (I > (1)/2) are often perceived as being challenging to acquire and to interpret because of the presence of anisotropic broadening arising from the interaction of the electric field gradient and the nuclear electric quadrupole moment, which broadens the spectral lines, often over several megahertz. Despite the vast amount of information contained in the spectral line shapes, the problems with sensitivity and resolution have, until very recently, limited the application of NMR spectroscopy of quadrupolar nuclei in the solid state. In this Perspective, we provide a brief overview of the quadrupolar interaction, describe some of the basic experimental approaches used for acquiring high-resolution NMR spectra, and discuss the information that these spectra can provide. We then describe some interesting recent examples to showcase some of the more exciting and challenging new applications of NMR spectra of quadrupolar nuclei in the fields of energy materials, microporous materials, Earth sciences, and biomaterials. Finally, we consider the possible directions that this highly informative technique may take in the future.

Exploring the molecular structure of imidazolium-silica-based nanoparticle networks by combining solid-state NMR spectroscopy and first-principles calculations

A DFT-based molecular model for imidazolium-silica-based nanoparticle networks (INNs) is presented. The INNs were synthesized and characterized by using small-angle X-ray scattering (SAXS), NMR spectroscopy, and theoretical ab initio calculations. (11)B and (31)P HETCOR CP MAS experiments were recorded. Calculated (19)F NMR spectroscopy results, combined with the calculated anion-imidazolium (IM) distances, predicted the IM chain density in the INN, which was also confirmed from thermogravimetric analysis/mass spectrometry results. The presence of water molecules trapped between the nanoparticles is also suggested. First considerations on possible π-π stacking between the IM rings are presented. The predicted electronic properties confirm the photoluminescence emissions in the correct spectral domain.

Exploiting periodic first-principles calculations in NMR spectroscopy of disordered solids

Much of the information contained within solid-state nuclear magnetic resonance (NMR) spectra remains unexploited because of the challenges in obtaining high-resolution spectra and the difficulty in assigning those spectra. Recent advances that enable researchers to accurately and efficiently determine NMR parameters in periodic systems have revolutionized the application of density functional theory (DFT) calculations in solid-state NMR spectroscopy. These advances are particularly useful for experimentalists. The use of first-principles calculations aids in both the interpretation and assignment of the complex spectral line shapes observed for solids. Furthermore, calculations provide a method for evaluating potential structural models against experimental data for materials with poorly characterized structures. Determining the structure of well-ordered, periodic crystalline solids can be straightforward using methods that exploit Bragg diffraction. However, the deviations from periodicity, such as compositional, positional, or temporal disorder, often produce the physical properties (such as ferroelectricity or ionic conductivity) that may be of commercial interest. With its sensitivity to the atomic-scale environment, NMR provides a potentially useful tool for studying disordered materials, and the combination of experiment with first-principles calculations offers a particularly attractive approach. In this Account, we discuss some of the issues associated with the practical implementation of first-principles calculations of NMR parameters in solids. We then use two key examples to illustrate the structural insights that researchers can obtain when applying such calculations to disordered inorganic materials. First, we describe an investigation of cation disorder in Y2Ti(2-x)Sn(x)O7 pyrochlore ceramics using (89)Y and (119)Sn NMR. Researchers have proposed that these materials could serve as host phases for the encapsulation of lanthanide- and actinide-bearing radioactive waste. In a second example, we discuss how (17)O NMR can be used to probe the dynamic disorder of H in hydroxyl-humite minerals (nMg2SiO4·Mg(OH)2), and how (19)F NMR can be used to understand F substitution in these systems. The combination of first-principles calculations and multinuclear NMR spectroscopy facilitates the investigation of local structure, disorder, and dynamics in solids. We expect that applications will undoubtedly become more widespread with further advances in computational and experimental methods. Insight into the atomic-scale environment is a crucial first step in understanding the structure-property relationships in solids, and it enables the efficient design of future materials for a range of end uses.

Deuteron spin-lattice relaxation in the presence of an activation energy distribution: application to methanols in zeolite NaX

A new method is introduced for analyzing deuteron spin-lattice relaxation in molecular systems with a broad distribution of activation energies and correlation times. In such samples the magnetization recovery is strongly non-exponential but can be fitted quite accurately by three exponentials. The considered system may consist of molecular groups with different mobility. For each group a Gaussian distribution of the activation energy is introduced. By assuming for every subsystem three parameters: the mean activation energy E(0), the distribution width σ and the pre-exponential factor τ(0) for the Arrhenius equation defining the correlation time, the relaxation rate is calculated for every part of the distribution. Experiment-based limiting values allow the grouping of the rates into three classes. For each class the relaxation rate and weight is calculated and compared with experiment. The parameters E(0), σ and τ(0) are determined iteratively by repeating the whole cycle many times. The temperature dependence of the deuteron relaxation was observed in three samples containing CD(3)OH (200% and 100% loading) and CD(3)OD (200%) in NaX zeolite and analyzed by the described method between 20K and 170K. The obtained parameters, equal for all the three samples, characterize the methyl and hydroxyl mobilities of the methanol molecules at two different locations.

Investigation of the interface in silica-encapsulated liposomes by combining solid state NMR and first principles calculations

In the context of nanomedicine, liposils (liposomes and silica) have a strong potential for drug storage and release schemes: such materials combine the intrinsic properties of liposome (encapsulation) and silica (increased rigidity, protective coating, pH degradability). In this work, an original approach combining solid state NMR, molecular dynamics, first principles geometry optimization, and NMR parameters calculation allows the building of a precise representation of the organic/inorganic interface in liposils. {(1)H-(29)Si}(1)H and {(1)H-(31)P}(1)H Double Cross-Polarization (CP) MAS NMR experiments were implemented in order to explore the proton chemical environments around the silica and the phospholipids, respectively. Using VASP (Vienna Ab Initio Simulation Package), DFT calculations including molecular dynamics, and geometry optimization lead to the determination of energetically favorable configurations of a DPPC (dipalmitoylphosphatidylcholine) headgroup adsorbed onto a hydroxylated silica surface that corresponds to a realistic model of an amorphous silica slab. These data combined with first principles NMR parameters calculations by GIPAW (Gauge Included Projected Augmented Wave) show that the phosphate moieties are not directly interacting with silanols. The stabilization of the interface is achieved through the presence of water molecules located in-between the head groups of the phospholipids and the silica surface forming an interfacial H-bonded water layer. A detailed study of the (31)P chemical shift anisotropy (CSA) parameters allows us to interpret the local dynamics of DPPC in liposils. Finally, the VASP/solid state NMR/GIPAW combined approach can be extended to a large variety of organic-inorganic hybrid interfaces.

Observation of "hidden" magnesium: first-principles calculations and 25Mg solid-state NMR of enstatite

(25)Mg NMR parameters have been determined for two polymorphs of enstatite (MgSiO(3)), an important magnesium silicate phase present as a major component of the Earth's upper mantle. The crystal structures of both polymorphs contain two crystallographically distinct magnesium sites; however, only a single resonance is observed in (25)Mg MAS NMR spectra recorded at 14.1 and 20.0 T. First-principles calculations performed on geometry-optimised crystal structures reveal that the quadrupolar interaction for the second site is expected to be very large, resulting in extensive broadening of the spectral resonance, explaining its apparent absence in the NMR spectrum. (25)Mg QCPMG NMR experiments employing variable offset cumulative spectroscopy (VOCS) are used to observe the broadened site and enable measurement of NMR parameters. The large difference in quadrupolar interaction between the two crystallographic magnesium sites is rationalised qualitatively in terms of the distortion of the local coordination environment as well as longer-range effects using a simple point charge model.