Time Averaging of NMR Chemical Shifts in the MLF Peptide in the Solid State

Effect of Dynamical Motion in ab Initio Calculations of Solid-State Nuclear Magnetic and Nuclear Quadrupole Resonance Spectra

Solid-state nuclear magnetic resonance (SSNMR) and nuclear quadrupole resonance (NQR) spectra provide detailed information about the electronic and atomic structure of solids. Modern ab initio methods such as density functional theory (DFT) can be used to calculate NMR and NQR spectra from first-principles, providing a meaningful avenue to connect theory and experiment. Prediction of SSNMR and NQR spectra from DFT relies on accurate calculation of the electric field gradient (EFG) tensor associated with the potential of electrons at the nuclear centers. While static calculations of EFGs are commonly seen in the literature, the effects of dynamical motion of atoms in molecules and solids have been less explored. In this study, we develop a method to calculate EFGs of solids while taking into account the dynamics of atoms through DFT-based molecular dynamics simulations. The method we develop is general, in the sense that it can be applied to any material at any desired temperature and pressure. Here, we focus on application of the method to NaNO2 and study in detail the EFGs of 14N, 17O, and 23Na. We find in the cases of 14N and 17O that the dynamical motion of the atoms can be used to calculate mean EFGs that are in closer agreement with experiments than those of static calculations. For 23Na, we find a complex behavior of the EFGs when atomic motion is incorporated that is not at all captured in static calculations. In particular, we find a distribution of EFGs that is influenced strongly by the local (changing) bond environment, with a pattern that reflects the coordination structure of 23Na. We expect the methodology developed here to provide a path forward for understanding materials in which static EFG calculations do not align with experiments.

Posttranslational, site-directed photochemical fluorine editing of protein sidechains to probe residue oxidation state via 19F-nuclear magnetic resonance

The fluorination of amino acid residues represents a near-isosteric alteration with the potential to report on biological pathways, yet the site-directed editing of carbon-hydrogen (C-H) bonds in complex biomolecules to carbon-fluorine (C-F) bonds is challenging, resulting in its limited exploitation. Here, we describe a protocol for the posttranslational and site-directed alteration of native γCH₂ to γCF₂ in protein sidechains. This alteration allows the installation of difluorinated sidechain analogs of proteinogenic amino acids, in both native and modified states. This chemical editing is robust, mild, fast and highly efficient, exploiting photochemical- and radical-mediated C-C bonds grafted onto easy-to-access cysteine-derived dehydroalanine-containing proteins as starting materials. The heteroaryl-sulfonyl reagent required for generating the key carbon-centered C• radicals that install the sidechain can be synthesized in two to six steps from commercially available precursors. This workflow allows the nonexpert to create fluorinated proteins within 24 h, starting from a corresponding purified cysteine-containing protein precursor, without the need for bespoke biological systems. As an example, we readily introduce three γCF₂-containing methionines in all three progressive oxidation states (sulfide, sulfoxide and sulfone) as D-/L- forms into histone eH3.1 at site 4 (a relevant lysine to methionine oncomutation site), and each can be detected by ¹⁹F-nuclear magnetic resonance of the γCF₂ group, as well as the two diastereomers of the sulfoxide, even when found in a complex protein mixture of all three. The site-directed editing of C-H→C-F enables the use of γCF₂ as a highly sensitive, 'zero-size-zero-background' label in protein sidechains, which may be used to probe biological phenomena, protein structures and/or protein-ligand interactions by ¹⁹F-based detection methods.

Importance of Nuclear Quantum Effects for NMR Crystallography

The resolving power of solid-state nuclear magnetic resonance (NMR) crystallography depends heavily on the accuracy of computational predictions of NMR chemical shieldings of candidate structures, which are usually taken to be local minima in the potential energy. To test the limits of this approximation, we systematically study the importance of finite-temperature and quantum nuclear fluctuations for ¹H, ¹³C, and ¹⁵N shieldings in polymorphs of three paradigmatic molecular crystals: benzene, glycine, and succinic acid. The effect of quantum fluctuations is comparable to the typical errors of shielding predictions for static nuclei with respect to experiments, and their inclusion improves the agreement with measurements, translating to more reliable assignment of the NMR spectra to the correct candidate structure. The use of integrated machine-learning models, trained on first-principles energies and shieldings, renders rigorous sampling of nuclear fluctuations affordable, setting a new standard for the calculations underlying NMR structure determinations.

Investigating discrepancies between experimental solid-state NMR and GIPAW calculation: NC-N 13C and OH⋯O 1H chemical shifts in pyridinium fumarates and their cocrystals

An NMR crystallography analysis is presented for four solid-state structures of pyridine fumarates and their cocrystals, using crystal structures deposited in the Cambridge Crystallographic Data Centre, CCDC. Experimental one-dimensional one-pulse ¹H and ¹³C cross-polarisation (CP) magic-angle spinning (MAS) nuclear magnetic resonance (NMR) and two-dimensional ¹⁴N-¹H heteronuclear multiple-quantum coherence MAS NMR spectra are compared with gauge-including projector augmented wave (GIPAW) calculations of the ¹H and ¹³C chemical shifts and the ¹⁴N shifts that additionally depend on the quadrupolar interaction. Considering the high ppm (>10 ​ppm) ¹H resonances, while there is good agreement (within 0.4 ​ppm) between experiment and GIPAW calculation for the hydrogen-bonded NH moieties, the hydrogen-bonded fumaric acid OH resonances are 1.2-1.9 ​ppm higher in GIPAW calculation as compared to experiment. For the cocrystals of a salt and a salt formed by 2-amino-5-methylpyridinium and 2-amino-6-methylpyridinium ions, a large discrepancy of 4.2 and 5.9 ​ppm between experiment and GIPAW calculation is observed for the quaternary ring carbon ¹³C resonance that is directly bonded to two nitrogens (in the ring and in the amino group). By comparison, there is excellent agreement (within 0.2 ​ppm) for the quaternary ring carbon ¹³C resonance directly bonded to the ring nitrogen for the salt and cocrystal of a salt formed by 2,6-lutidinium and 2,5-lutidinium, respectively.

NMR crystallography of molecular organics

Developments of NMR methodology to characterise the structures of molecular organic structures are reviewed, concentrating on the previous decade of research in which density functional theory-based calculations of NMR parameters in periodic solids have become widespread. With a focus on demonstrating the new structural insights provided, it is shown how "NMR crystallography" has been used in a spectrum of applications from resolving ambiguities in diffraction-derived structures (such as hydrogen atom positioning) to deriving complete structures in the absence of diffraction data. As well as comprehensively reviewing applications, the different aspects of the experimental and computational techniques used in NMR crystallography are surveyed. NMR crystallography is seen to be a rapidly maturing subject area that is increasingly appreciated by the wider crystallographic community.

Improving the accuracy of solid-state nuclear magnetic resonance chemical shift prediction with a simple molecular correction

A fast, straightforward method for computing NMR chemical shieldings of crystalline solids is proposed. The method combines the advantages of both conventional approaches: periodic calculations using plane-wave basis sets and molecular computational approaches. The periodic calculations capture the periodic nature of crystalline solids, but the computational level of the electronic structure calculation is limited to general-gradient-approximation (GGA) density functionals. It is demonstrated that a correction to the GGA result calculated on an isolated molecule at a higher level of theory significantly improves the correlations between experimental and calculated chemical shifts while adding almost no additional computational cost. Corrections calculated with a hybrid density functional improved the accuracy of 13C, 15N and 17O chemical shift predictions significantly and allowed identifying errors in previously published experimental data. Applications of the approach to crystalline isocytosine, methacrylamide, and testosterone are presented.

Electron-phonon coupling from finite differences

The interaction between electrons and phonons underlies multiple phenomena in physics, chemistry, and materials science. Examples include superconductivity, electronic transport, and the temperature dependence of optical spectra. A first-principles description of electron-phonon coupling enables the study of the above phenomena with accuracy and material specificity, which can be used to understand experiments and to predict novel effects and functionality. In this topical review, we describe the first-principles calculation of electron-phonon coupling from finite differences. The finite differences approach provides several advantages compared to alternative methods, in particular (i) any underlying electronic structure method can be used, and (ii) terms beyond the lowest order in the electron-phonon interaction can be readily incorporated. But these advantages are associated with a large computational cost that has until recently prevented the widespread adoption of this method. We describe some recent advances, including nondiagonal supercells and thermal lines, that resolve these difficulties, and make the calculation of electron-phonon coupling from finite differences a powerful tool. We review multiple applications of the calculation of electron-phonon coupling from finite differences, including the temperature dependence of optical spectra, superconductivity, charge transport, and the role of defects in semiconductors. These examples illustrate the advantages of finite differences, with cases where semilocal density functional theory is not appropriate for the calculation of electron-phonon coupling and many-body methods such as the GW approximation are required, as well as examples in which higher-order terms in the electron-phonon interaction are essential for an accurate description of the relevant phenomena. We expect that the finite difference approach will play a central role in future studies of the electron-phonon interaction.

The application of tailor-made force fields and molecular dynamics for NMR crystallography: a case study of free base cocaine

Motional averaging has been proven to be significant in predicting the chemical shifts in ab initio solid-state NMR calculations, and the applicability of motional averaging with molecular dynamics has been shown to depend on the accuracy of the molecular mechanical force field. The performance of a fully automatically generated tailor-made force field (TMFF) for the dynamic aspects of NMR crystallography is evaluated and compared with existing benchmarks, including static dispersion-corrected density functional theory calculations and the COMPASS force field. The crystal structure of free base cocaine is used as an example. The results reveal that, even though the TMFF outperforms the COMPASS force field for representing the energies and conformations of predicted structures, it does not give significant improvement in the accuracy of NMR calculations. Further studies should direct more attention to anisotropic chemical shifts and development of the method of solid-state NMR calculations.

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.

Enhanced NMR Discrimination of Pharmaceutically Relevant Molecular Crystal Forms through Fragment-Based Ab Initio Chemical Shift Predictions

Chemical shift prediction plays an important role in the determination or validation of crystal structures with solid-state nuclear magnetic resonance (NMR) spectroscopy. One of the fundamental theoretical challenges lies in discriminating variations in chemical shifts resulting from different crystallographic environments. Fragment-based electronic structure methods provide an alternative to the widely used plane wave gauge-including projector augmented wave (GIPAW) density functional technique for chemical shift prediction. Fragment methods allow hybrid density functionals to be employed routinely in chemical shift prediction, and we have recently demonstrated appreciable improvements in the accuracy of the predicted shifts when using the hybrid PBE0 functional instead of generalized gradient approximation (GGA) functionals like PBE. Here, we investigate the solid-state ¹³C and ¹⁵N NMR spectra for multiple crystal forms of acetaminophen, phenobarbital, and testosterone. We demonstrate that the use of the hybrid density functional instead of a GGA provides both higher accuracy in the chemical shifts and increased discrimination among the different crystallographic environments. Finally, these results also provide compelling evidence for the transferability of the linear regression parameters mapping predicted chemical shieldings to chemical shifts that were derived in an earlier study.

Crystallographic and Dynamic Aspects of Solid-State NMR Calibration Compounds: Towards ab Initio NMR Crystallography

The excellent results of dispersion-corrected density functional theory (DFT-D) calculations for static systems have been well established over the past decade. The introduction of dynamics into DFT-D calculations is a target, especially for the field of molecular NMR crystallography. Four (13) C ss-NMR calibration compounds are investigated by single-crystal X-ray diffraction, molecular dynamics and DFT-D calculations. The crystal structure of 3-methylglutaric acid is reported. The rotator phases of adamantane and hexamethylbenzene at room temperature are successfully reproduced in the molecular dynamics simulations. The calculated (13) C chemical shifts of these compounds are in excellent agreement with experiment, with a root-mean-square deviation of 2.0 ppm. It is confirmed that a combination of classical molecular dynamics and DFT-D chemical shift calculation improves the accuracy of calculated chemical shifts.

Benchmark fragment-based (1)H, (13)C, (15)N and (17)O chemical shift predictions in molecular crystals

The performance of fragment-based ab initio(1)H, (13)C, (15)N and (17)O chemical shift predictions is assessed against experimental NMR chemical shift data in four benchmark sets of molecular crystals. Employing a variety of commonly used density functionals (PBE0, B3LYP, TPSSh, OPBE, PBE, TPSS), we explore the relative performance of cluster, two-body fragment, and combined cluster/fragment models. The hybrid density functionals (PBE0, B3LYP and TPSSh) generally out-perform their generalized gradient approximation (GGA)-based counterparts. (1)H, (13)C, (15)N, and (17)O isotropic chemical shifts can be predicted with root-mean-square errors of 0.3, 1.5, 4.2, and 9.8 ppm, respectively, using a computationally inexpensive electrostatically embedded two-body PBE0 fragment model. Oxygen chemical shieldings prove particularly sensitive to local many-body effects, and using a combined cluster/fragment model instead of the simple two-body fragment model decreases the root-mean-square errors to 7.6 ppm. These fragment-based model errors compare favorably with GIPAW PBE ones of 0.4, 2.2, 5.4, and 7.2 ppm for the same (1)H, (13)C, (15)N, and (17)O test sets. Using these benchmark calculations, a set of recommended linear regression parameters for mapping between calculated chemical shieldings and observed chemical shifts are provided and their robustness assessed using statistical cross-validation. We demonstrate the utility of these approaches and the reported scaling parameters on applications to 9-tert-butyl anthracene, several histidine co-crystals, benzoic acid and the C-nitrosoarene SnCl2(CH3)2(NODMA)2.

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.

Modeling Polymorphic Molecular Crystals with Electronic Structure Theory

Interest in molecular crystals has grown thanks to their relevance to pharmaceuticals, organic semiconductor materials, foods, and many other applications. Electronic structure methods have become an increasingly important tool for modeling molecular crystals and polymorphism. This article reviews electronic structure techniques used to model molecular crystals, including periodic density functional theory, periodic second-order Møller-Plesset perturbation theory, fragment-based electronic structure methods, and diffusion Monte Carlo. It also discusses the use of these models for predicting a variety of crystal properties that are relevant to the study of polymorphism, including lattice energies, structures, crystal structure prediction, polymorphism, phase diagrams, vibrational spectroscopies, and nuclear magnetic resonance spectroscopy. Finally, tools for analyzing crystal structures and intermolecular interactions are briefly discussed.

Comparing Vibrationally Averaged Nuclear Shielding Constants by Quantum Diffusion Monte Carlo and Second-Order Perturbation Theory

Using the method of modified Shepard's interpolation to construct potential energy surfaces of the H2O, O3, and HCOOH molecules, we compute vibrationally averaged isotropic nuclear shielding constants ⟨σ⟩ of the three molecules via quantum diffusion Monte Carlo (QDMC). The QDMC results are compared to that of second-order perturbation theory (PT), to see if second-order PT is adequate for obtaining accurate values of nuclear shielding constants of molecules with large amplitude motions. ⟨σ⟩ computed by the two approaches differ for the hydrogens and carbonyl oxygen of HCOOH, suggesting that for certain molecules such as HCOOH where big displacements away from equilibrium happen (internal OH rotation), ⟨σ⟩ of experimental quality may only be obtainable with the use of more sophisticated and accurate methods, such as quantum diffusion Monte Carlo. The approach of modified Shepard's interpolation is also extended to construct shielding constants σ surfaces of the three molecules. By using a σ surface with the equilibrium geometry as a single data point to compute isotropic nuclear shielding constants for each descendant in the QDMC ensemble representing the ground state wave function, we reproduce the results obtained through ab initio computed σ to within statistical noise. Development of such an approach could thereby alleviate the need for any future costly ab initio σ calculations.

Temperature Dependence of NMR Parameters Calculated from Path Integral Molecular Dynamics Simulations

The influence of temperature on NMR chemical shifts and quadrupolar couplings in model molecular organic solids is explored using path integral molecular dynamics (PIMD) and density functional theory (DFT) calculations of shielding and electric field gradient (EFG) tensors. An approach based on convoluting calculated shielding or EFG tensor components with probability distributions of selected bond distances and valence angles obtained from DFT-PIMD simulations at several temperatures is used to calculate the temperature effects. The probability distributions obtained from the quantum PIMD simulations, which includes nuclear quantum effects, are significantly broader and less temperature dependent than those obtained with conventional DFT molecular dynamics or with 1D scans through the potential energy surface. Predicted NMR observables for the model systems were in excellent agreement with experimental data.

Quantum calculation of protein NMR chemical shifts based on the automated fragmentation method

The performance of quantum mechanical methods on the calculation of protein NMR chemical shifts is reviewed based on the recently developed automatic fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) approach. By using the Poisson-Boltzmann (PB) model and first solvation water molecules, the influence of solvent effect is also discussed. Benefiting from the fragmentation algorithm, the AF-QM/MM approach is computationally efficient, linear-scaling with a low pre-factor, and thus can be applied to routinely calculate the ab initio NMR chemical shifts for proteins of any size. The results calculated using Density Functional Theory (DFT) show that when the solvent effect is included, this method can accurately reproduce the experimental ¹H NMR chemical shifts, while the ¹³C NMR chemical shifts are less affected by the solvent. However, although the inclusion of solvent effect shows significant improvement for ¹⁵N chemical shifts, the calculated values still have large deviations from the experimental observations. Our study further demonstrates that AF-QM/MM calculated results accurately reflect the dependence of ¹³C(α) NMR chemical shifts on the secondary structure of proteins, and the calculated ¹H chemical shift can be utilized to discriminate the native structure of proteins from decoys.

Extended Czjzek model applied to NMR parameter distributions in sodium metaphosphate glass

The extended Czjzek model (ECM) is applied to the distribution of NMR parameters of a simple glass model (sodium metaphosphate, NaPO3) obtained by molecular dynamics (MD) simulations. Accurate NMR tensors, electric field gradient (EFG) and chemical shift anisotropy (CSA) are calculated from density functional theory (DFT) within the well-established PAW/GIPAW framework. The theoretical results are compared to experimental high-resolution solid-state NMR data and are used to validate the considered structural model. The distributions of the calculated coupling constant C(Q) is proportional to |V(zz)| and the asymmetry parameter η(Q) that characterize the quadrupolar interaction are discussed in terms of structural considerations with the help of a simple point charge model. Finally, the ECM analysis is shown to be relevant for studying the distribution of CSA tensor parameters and gives new insight into the structural characterization of disordered systems by solid-state NMR.

Exploiting the Synergy of Powder X-ray Diffraction and Solid-State NMR Spectroscopy in Structure Determination of Organic Molecular Solids

We report a strategy for structure determination of organic materials in which complete solid-state nuclear magnetic resonance (NMR) spectral data is utilized within the context of structure determination from powder X-ray diffraction (XRD) data. Following determination of the crystal structure from powder XRD data, first-principles density functional theory-based techniques within the GIPAW approach are exploited to calculate the solid-state NMR data for the structure, followed by careful scrutiny of the agreement with experimental solid-state NMR data. The successful application of this approach is demonstrated by structure determination of the 1:1 cocrystal of indomethacin and nicotinamide. The ¹H and ¹³C chemical shifts calculated for the crystal structure determined from the powder XRD data are in excellent agreement with those measured experimentally, notably including the two-dimensional correlation of ¹H and ¹³C chemical shifts for directly bonded ¹³C-¹H moieties. The key feature of this combined approach is that the quality of the structure determined is assessed both against experimental powder XRD data and against experimental solid-state NMR data, thus providing a very robust validation of the veracity of the structure.

Contribution of high-energy conformations to NMR chemical shifts, a DFT-BOMD study

This paper highlights the relevance of including the high-energy conformational states sampled by Born-Oppenheimer molecular dynamics (BOMD) in the calculation of time-averaged NMR chemical shifts. Our case study is the very flexible glycerol molecule that undergoes interconversion between conformers in a nonrandom way. Along the sequence of structures from one backbone conformer to another, transition states have been identified. The three (13)C NMR chemical shifts of the molecule were estimated by averaging their calculated values over a large set of BOMD snapshots. The simulation time needed to obtain a good agreement with the two signals present in the experimental spectrum is shown to be dependent on the atomic orbital basis set used for the dynamics, with a necessary longer trajectory for the most extended basis sets. The large structural deformations with respect to the optimized conformer geometries that occur along the dynamics are related to a kinetically driven conformer distribution. Calculated conformer type populations are in good agreement with experimental gas phase microwave results.

Dynamic nuclear polarization-enhanced 13C NMR spectroscopy of static biological solids

We explore the possibility of using dynamic nuclear polarization (DNP) to enhance signals in structural studies of biological solids by solid state NMR without sample spinning. Specifically, we use 2D (13)C-(13)C exchange spectroscopy to probe the peptide backbone torsion angles (φ, ψ) in a series of selectively (13)C-labeled 40-residue β-amyloid (Aβ(1-40)) samples, in both fibrillar and non-fibrillar states. Experiments are carried out at 9.39 T and 8 K, using a static double-resonance NMR probe and low-power microwave irradiation at 264 GHz. In frozen solutions of Aβ(1-40) fibrils doped with DOTOPA-TEMPO, we observe DNP signal enhancement factors of 16-21. We show that the orientation- and frequency-dependent spin polarization exchange between sequential backbone carbonyl (13)C labels can be simulated accurately using a simple expression for the exchange rate, after experimentally determined homogeneous (13)C lineshapes are incorporated in the simulations. The experimental 2D (13)C-(13)C exchange spectra place constraints on the φ and ψ angles between the two carbonyl labels. Although the data are not sufficient to determine φ and ψ uniquely, the data do provide non-trivial constraints that could be included in structure calculations. With DNP at low temperatures, 2D (13)C-(13)C exchange spectra can be obtained from a 3.5 mg sample of Aβ(1-40) fibrils in 4 h or less, despite the broad (13)C chemical shift anisotropy line shapes that are observed in static samples.

β-hairpin-mediated nucleation of polyglutamine amyloid formation

The conformational preferences of polyglutamine (polyQ) sequences are of major interest because of their central importance in the expanded CAG repeat diseases that include Huntington's disease. Here, we explore the response of various biophysical parameters to the introduction of β-hairpin motifs within polyQ sequences. These motifs (tryptophan zipper, disulfide, d-Pro-Gly, Coulombic attraction, l-Pro-Gly) enhance formation rates and stabilities of amyloid fibrils with degrees of effectiveness well correlated with their known abilities to enhance β-hairpin formation in other peptides. These changes led to decreases in the critical nucleus for amyloid formation from a value of n=4 for a simple, unbroken Q23 sequence to approximate unitary n values for similar length polyQs containing β-hairpin motifs. At the same time, the morphologies, secondary structures, and bioactivities of the resulting fibrils were essentially unchanged from simple polyQ aggregates. In particular, the signature pattern of solid-state NMR (13)C Gln resonances that appears to be unique to polyQ amyloid is replicated exactly in fibrils from a β-hairpin polyQ. Importantly, while β-hairpin motifs do produce enhancements in the equilibrium constant for nucleation in aggregation reactions, these Kn values remain quite low (~10(-)(10)) and there is no evidence for significant enhancement of β-structure within the monomer ensemble. The results indicate an important role for β-turns in the nucleation mechanism and structure of polyQ amyloid and have implications for the nature of the toxic species in expanded CAG repeat diseases.

Applications of high-resolution 1H solid-state NMR

This article reviews the large increase in applications of high-resolution (1)H magic-angle spinning (MAS) solid-state NMR, in particular two-dimensional heteronuclear and homonuclear (double-quantum and spin-diffusion NOESY-like exchange) experiments, in the last five years. These applications benefit from faster MAS frequencies (up to 80 kHz), higher magnetic fields (up to 1 GHz) and pulse sequence developments (e.g., homonuclear decoupling sequences applicable under moderate and fast MAS). (1)H solid-state NMR techniques are shown to provide unique structural insight for a diverse range of systems including pharmaceuticals, self-assembled supramolecular structures and silica-based inorganic-organic materials, such as microporous and mesoporous materials and heterogeneous organometallic catalysts, for which single-crystal diffraction structures cannot be obtained. The power of NMR crystallography approaches that combine experiment with first-principles calculations of NMR parameters (notably using the GIPAW approach) are demonstrated, e.g., to yield quantitative insight into hydrogen-bonding and aromatic CH-π interactions, as well as to generate trial three-dimensional packing arrangements. It is shown how temperature-dependent changes in the (1)H chemical shift, linewidth and DQ-filtered signal intensity can be analysed to determine the thermodynamics and kinetics of molecular level processes, such as the making and breaking of hydrogen bonds, with particular application to proton-conducting materials. Other applications to polymers and biopolymers, inorganic compounds and bioinorganic systems, paramagnetic compounds and proteins are presented. The potential of new technological advances such as DNP methods and new microcoil designs is described.

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.

Structure-based prediction of methyl chemical shifts in proteins

Protein methyl groups have recently been the subject of much attention in NMR spectroscopy because of the opportunities that they provide to obtain information about the structure and dynamics of proteins and protein complexes. With the advent of selective labeling schemes, methyl groups are particularly interesting in the context of chemical shift based protein structure determination, an approach that to date has exploited primarily the mapping between protein structures and backbone chemical shifts. In order to extend the scope of chemical shifts for structure determination, we present here the CH3Shift method of performing structure-based predictions of methyl chemical shifts. The terms considered in the predictions take account of ring current, magnetic anisotropy, electric field, rotameric type, and dihedral angle effects, which are considered in conjunction with polynomial functions of interatomic distances. We show that the CH3Shift method achieves an accuracy in the predictions that ranges from 0.133 to 0.198 ppm for (1)H chemical shifts for Ala, Thr, Val, Leu and Ile methyl groups. We illustrate the use of the method by assessing the accuracy of side-chain structures in structural ensembles representing the dynamics of proteins.

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.

NMR crystallography of campho[2,3-c]pyrazole (Z' = 6): combining high-resolution 1H-13C solid-state MAS NMR spectroscopy and GIPAW chemical-shift calculations

(1)H-(13)C two-dimensional magic-angle spinning (MAS) solid-state NMR correlation spectra, recorded with the MAS-J-HMQC experiment, are presented for campho[2,3-c]pyrazole. For each (13)C moiety, there are six resonances associated with the six distinct molecules in the asymmetric unit cell (Z' = 6). The one-bond C-H correlations observed in the 2D (1)H-(13)C MAS-J-HMQC spectra allow the experimental determination of the (1)H and (13)C chemical shifts associated with the separate CH, CH(2), and CH(3) groups. (1)H and (13)C chemical shifts calculated by using the GIPAW (Gauge Including Projector Augmented Waves) plane-wave pseudopotential approach are presented. Calculations for the whole unit cell (12 × 29 = 348 atoms, with geometry optimization of all atoms) allow the assignment of the experimental (1)H and (13)C chemical shifts to the six distinct molecules. The calculated chemical shifts for the full crystal structure are compared with those for isolated molecules as extracted from the geometry-optimized crystal structure. In this way, the effect of intermolecular interactions on the observed chemical shifts is quantified. In particular, the calculations are sufficiently precise to differentiate the small (<1 ppm) differences between the (1)H chemical shifts of the six resonances associated with each distinct CH or CH(2) moiety.

Dynamical effects in ab initio NMR calculations: classical force fields fitted to quantum forces

NMR chemical shifts for an L-alanine molecular crystal are calculated using ab initio plane wave density functional theory. Dynamical effects including anharmonicity may be included by averaging chemical shifts over an ensemble of structural configurations generated using molecular dynamics (MD). The time scales required mean that ab initio MD is prohibitively expensive. Yet the sensitivity of chemical shifts to structural details requires that the methodologies for performing MD and calculating NMR shifts be consistent. This work resolves these previously competing requirements by fitting classical force fields to reproduce ab initio forces. This methodology is first validated by reproducing the averaged chemical shifts found using ab initio molecular dynamics. Study of a supercell of L-alanine demonstrates that finite size effects can be significant when accounting for dynamics.