First-principles calculations of solid-state17O and29Si NMR spectra of Mg2SiO4polymorphs

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.

Natural abundance 17O MAS NMR and DFT simulations: New insights into the atomic structure of designed micas

Combining ¹⁷O Magic-Angle Spinning (MAS) NMR at natural abundance with DFT calculations is a promising methodology to shed light on the structure and disorder in tetrahedral sheets of designed micas with enhanced properties. Among brittle micas, synthetic mica is an important alternative to natural ones with a swelling sheet-like structure that results in many applications, by exploiting unique characteristics. Lowenstein's rule is one of the main chemical factor that determines the atomic structure of aluminosilicates and furthermore their properties. In the present article, ¹⁷O MAS NMR spectroscopy is used to validate (or not) the agreement of the Lowenstein's rule with the distribution of Si and Al sites in the tetrahedral sheets of synthetic micas. ¹⁷O MAS spectra of synthetic high-charged micas exhibit two regions of signals that revealed two distinguishable oxygen environments, namely Si-O-X (with X = Si, Al^tet, Mg) and Al^tet-O-Y (Y=Mg or Al^tet). DFT calculations were also conducted to obtain the ¹⁷O chemical shift and other NMR features like the quadrupolar coupling constant, C_Q, for all of the oxygen environments encountered in the two model structures, one respecting the Lowenstein's rule and the other involving Al^tet-O-Al^tet and Si-O-Si environments. Our DFT calculations support the ¹⁷O assignment, by confirming that Al^tet-O-3Mg and Al^tet-O-Al^tet oxygen environments show chemical shifts under 30 ppm and more important, with quadrupolar coupling constants of about 1 MHz, in line with the spectral observation. By quantifying the ¹⁷O MAS NMR spectra at natural abundance, we demonstrate that one of the synthetic mica compositions does not meet the Lowenstein's rule.

Temperature dependence of X-ray absorption and nuclear magnetic resonance spectra: probing quantum vibrations of light elements in oxides

Probing the quantum thermal fluctuations of nuclei in light-element oxides using XANES and NMR spectroscopies.

Hunting for hydrogen: random structure searching and prediction of NMR parameters of hydrous wadsleyite

The structural chemistry of materials containing low levels of nonstoichiometric hydrogen is difficult to determine, and producing structural models is challenging where hydrogen has no fixed crystallographic site. Here we demonstrate a computational approach employing ab initio random structure searching (AIRSS) to generate a series of candidate structures for hydrous wadsleyite (β-Mg2SiO4 with 1.6 wt% H2O), a high-pressure mineral proposed as a repository for water in the Earth's transition zone. Aligning with previous experimental work, we solely consider models with Mg3 (over Mg1, Mg2 or Si) vacancies. We adapt the AIRSS method by starting with anhydrous wadsleyite, removing a single Mg(2+) and randomly placing two H(+) in a unit cell model, generating 819 candidate structures. 103 geometries were then subjected to more accurate optimisation under periodic DFT. Using this approach, we find the most favourable hydration mechanism involves protonation of two O1 sites around the Mg3 vacancy. The formation of silanol groups on O3 or O4 sites (with loss of stable O1-H hydroxyls) coincides with an increase in total enthalpy. Importantly, the approach we employ allows observables such as NMR parameters to be computed for each structure. We consider hydrous wadsleyite (∼1.6 wt%) to be dominated by protonated O1 sites, with O3/O4-H silanol groups present as defects, a model that maps well onto experimental studies at higher levels of hydration (J. M. Griffin et al., Chem. Sci., 2013, 4, 1523). The AIRSS approach adopted herein provides the crucial link between atomic-scale structure and experimental studies.

Hydrogen bonding induced distortion of CO3 units and kinetic stabilization of amorphous calcium carbonate: results from 2D 13C NMR spectroscopy

The structure of amorphous calcium carbonate consists of a uniform spatial disposition of H₂O molecules around the CO₃ units, forming a hydrogen-bonded amorphous network that is stabilized against crystallization by steric frustration.

The strengths and weaknesses of NMR spectroscopy and mass spectrometry with particular focus on metabolomics research

Mass spectrometry (MS) and nuclear magnetic resonance (NMR) have evolved as the most common techniques in metabolomics studies, and each brings its own advantages and limitations. Unlike MS spectrometry, NMR spectroscopy is quantitative and does not require extra steps for sample preparation, such as separation or derivatization. Although the sensitivity of NMR spectroscopy has increased enormously and improvements continue to emerge steadily, this remains a weak point for NMR compared with MS. MS-based metabolomics provides an excellent approach that can offer a combined sensitivity and selectivity platform for metabolomics research. Moreover, different MS approaches such as different ionization techniques and mass analyzer technology can be used in order to increase the number of metabolites that can be detected. In this chapter, the advantages, limitations, strengths, and weaknesses of NMR and MS as tools applicable to metabolomics research are highlighted.

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.

Oxygen K-edge electron energy loss spectra of hydrous and anhydrous compounds

First-principles calculations have been employed to examine the possible use of electron energy loss spectroscopy (EELS) as a tool for determining the presence of OH groups and hence hydrogen content in compounds. Our density functional theory (DFT) based calculations describe accurately the experimental EELS results for forsterite (Mg2SiO4), hambergite (Be2BO3(OH)), brucite (Mg(OH)2) and diaspore (α-AlOOH). DFT calculations were complemented by an experimental time resolved study of the oxygen K-edge in diaspore. The results show unambiguously that there is no connection between a pre-edge feature in the oxygen K-edge spectrum of diaspore and the presence of OH groups in the structure. Instead, the experimental study shows that the pre-edge feature in diaspore is transient. It can be explained by the presence of molecular O2, which is produced as a result of the electron irradiation.

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.

High-field multinuclear solid-state nuclear magnetic resonance (NMR) and first principle calculations in MgSO4 polymorphs

A combination of solid-state nuclear magnetic resonance (NMR) and first principles calculations was applied to obtain 17O, 25Mg, and 33S NMR parameters for two polymorphs of anhydrous magnesium sulfate. Working at the very high magnetic field of 21.14 T results in a dramatic improvement of resolution through a reduction of the effects of quadrupolar interactions and significant improvement in sensitivity. Experimental 25Mg and 33S spectra are dominated by quadrupolar interactions with quadrupolar parameters unique for each polymorph. In the case of 17O, there is a substantial contribution of the chemical shift anisotropy. The use of multiple-quantum magic-angle spinning (MQMAS) experiments allows the resolution of distinct oxygen species and assignment of signals in the experimental 17O spectrum. Chemical shielding constants and quadrupolar parameters for all three nuclei were calculated using plane wave pseudopotential density functional theory as implemented in the CASTEP computational package. The calculated NMR parameters are in very good agreement with the experimental results and help in signal assignment of the 17O spectrum. The results suggest applicability of such a combined computational and experimental solid-state NMR approach for the refinement of crystallographic data.

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.

Obtaining accurate chemical shifts for all magnetic nuclei (1H, 13C, 17O, and 27Al) in tris(2,4-pentanedionato-O,O′)aluminium(III) — A solid-state NMR case study

We report a complete set of high-resolution solid-state NMR spectra for all magnetic nuclei (1H, 13C, 17O, and 27Al) in the α-form of tris(2,4-pentanedionato-O,O′)aluminium(III), α-Al(acac)3. These high-resolution NMR spectra were obtained by using a host of solid-state NMR techniques: standard cross-polarization under the magic-angle spinning (CPMAS) method for 13C, 1-D homonuclear decoupling using the windowed DUMBO sequence for 1H, double-rotation (DOR) for 17O and 27Al, and multiple-quantum MAS for 27Al. Some experiments were performed at multiple magnetic fields. We show that the isotropic chemical shifts obtained for 1H, 13C, 17O, and 27Al nuclei in α-Al(acac)3 are highly resolved and accurate, regardless of the nature of the targeted nuclear spins (i.e., spin-1/2 or quadrupolar) and, as such, can be treated equally in comparison with computational chemical shifts obtained from a gauge-including projector-augmented wave (GIPAW) plane-wave pseudopotential DFT method.

The PAW/GIPAW approach for computing NMR parameters: a new dimension added to NMR study of solids

In 2001, Mauri and Pickard introduced the gauge including projected augmented wave (GIPAW) method that enabled for the first time the calculation of all-electron NMR parameters in solids, i.e. accounting for periodic boundary conditions. The GIPAW method roots in the plane wave pseudopotential formalism of the density functional theory (DFT), and avoids the use of the cluster approximation. This method has undoubtedly revitalized the interest in quantum chemical calculations in the solid-state NMR community. It has quickly evolved and improved so that the calculation of the key components of NMR interactions, namely the shielding and electric field gradient tensors, has now become a routine for most of the common nuclei studied in NMR. Availability of reliable implementations in several software packages (CASTEP, Quantum Espresso, PARATEC) make its usage more and more increasingly popular, maybe indispensable in near future for all material NMR studies. The majority of nuclei of the periodic table have already been investigated by GIPAW, and because of its high accuracy it is quickly becoming an essential tool for interpreting and understanding experimental NMR spectra, providing reliable assignments of the observed resonances to crystallographic sites or enabling a priori prediction of NMR data. The continuous increase of computing power makes ever larger (and thus more realistic) systems amenable to first-principles analysis. In the near future perspectives, as the incorporation of dynamical effects and/or disorder are still at their early developments, these areas will certainly be the prime target.

Contribution of first-principles calculations to multinuclear NMR analysis of borosilicate glasses

Boron-11 and silicon-29 NMR spectra of xSiO(2)-(1-x)B(2)O(3) glasses (x=0.40, 0.80 and 0.83) have been calculated using a combination of molecular dynamics (MD) simulations with density functional theory (DFT) calculations of NMR parameters. Structure models of 200 atoms have been generated using classical force fields and subsequently relaxed at the PBE-GGAlevel of DFT theory. The gauge including projector augmented wave (GIPAW) method is then employed for computing the shielding and electric field gradient tensors for each silicon and boron atom. Silicon-29 MAS and boron-11 MQMAS NMR spectra of two glasses (x=0.40 and 0.80) have been acquired and theoretical spectra are found to well agree with the experimental data. For boron-11, the NMR parameter distributions have been analysed using a Kernel density estimation (KDE) approach which is shown to highlight its main features. Accordingly, a new analytical model that incorporates the observed correlations between the NMR parameters is introduced. It significantly improves the fit of the (11)B MQMAS spectra and yields, therefore, more reliable NMR parameter distributions. A new analytical model for a quantitative description of the dependence of the silicon-29 and boron-11 isotropic chemical shift upon the bond angles is proposed, which incorporates possibly the effect of SiO(2)-B(2)O(3) intermixing. Combining all the above procedures, we show how distributions of Si-O-T and B-O-T (T=Si, B) bond angles can be estimated from the distribution of isotropic chemical shift of silicon-29 and boron-11, respectively.

First-principles calculations of NMR parameters for phosphate materials

In this short review, we discuss the ability to reproduce NMR parameters in the case of phosphates materials through electronic structure calculation within density functional theory linear response. Indeed, the gauge-including projector-augmented wave is today largely used by the solid-state NMR community as a tool for structural determination and it has been applied to a large variety of materials. We emphasise on the crucial points that should be taken into account to perform such calculations. In particular, we discuss the influence of the electronic structure and of the geometry on the calculation of NMR parameters. To illustrate the review, we present experimental and theoretical comparison of (31)P, (1)H and (23)Na NMR data on a series of sodium phosphate systems.