Robust NMR Approaches for the Determination of Homonuclear Dipole-Dipole Coupling Constants in Studies of Solid Materials and Biomolecules

Great Offset Difference Internuclear Selective Transfer

Carbon-carbon dipolar recoupling sequences are frequently used building blocks in routine magic-angle spinning NMR experiments. While broadband homonuclear first-order dipolar recoupling sequences mainly excite intra-residue correlations, selective methods can detect inter-residue transfers and long-range correlations. Here, we present the great offset difference internuclear selective transfer (GODIST) pulse sequence optimized for selective carbonyl or aliphatic recoupling at fast magic-angle spinning, here, 55 kHz. We observe a 3- to 5-fold increase in intensities compared with broadband RFDR recoupling for perdeuterated microcrystalline SH3 and for the membrane protein influenza A M2 in lipid bilayers. In 3D (H)COCO(N)H and (H)CO(CO)NH spectra, inter-residue carbonyl-carbonyl correlations up to about 5 Å are observed in uniformly ¹³C-labeled proteins.

Disorder to order: how halide mixing in MAPbI3-xBrx perovskites restricts MA dynamics

Mixed-halide lead perovskites are of particular interest for the design of tandem solar cells currently reaching record efficiencies. While halide phase segregation upon illumination of mixed perovskites is extensively studied, the effect of halide disorder on A cation dynamics is not well understood, despite its importance for charge carrier diffusion and lifetime. Here, we study the methylammonium (MA) reorientational dynamics in mixed halide MAPbI_3-xBr_x perovskites by a combined approach of experimental solid-state NMR spectroscopy and molecular dynamics (MD) simulations based on machine-learning force-fields (MLFF). ²⁰⁷Pb NMR spectra indicate the halides are randomly distributed over their lattice positions, whereas PXRD measurements show that all mixed MAPbI_3-xBr_x samples are cubic. The experimental ¹⁴N spectra and ¹H double-quantum (DQ) NMR data reveal anisotropic MA reorientations depending on the halide composition and thus associated disorder in the inorganic sublattice. MD calculations allow us to correlate these experimental results to restrictions of MA dynamics due to preferred MA orientations in their local Pb₈I_12-nBr_n "cages". Based on the experimental and simulated results, we develop a phenomenological model that correlates the ¹H dipolar coupling and thus the MA dynamics with the local composition and reproduces the experimental data over the whole composition range. We show that the dominant interaction between the MA cations and the Pb-X lattice that influences the cation dynamics is the local electrostatic potential being inhomogeneous in mixed halide systems. As such, we generate a fundamental understanding of the predominant interaction between the MA cations and the inorganic sublattice, as well as MA dynamics in asymmetric halide coordinations.

Solid-State NMR Dipolar and Chemical Shift Anisotropy Recoupling Techniques for Structural and Dynamical Studies in Biological Systems

With the development of NMR methodology and technology during the past decades, solid-state NMR (ssNMR) has become a particularly important tool for investigating structure and dynamics at atomic scale in biological systems, where the recoupling techniques play pivotal roles in modern high-resolution MAS NMR. In this review, following a brief introduction on the basic theory of recoupling in ssNMR, we highlight the recent advances in dipolar and chemical shift anisotropy recoupling methods, as well as their applications in structural determination and dynamical characterization at multiple time scales (i.e., fast-, intermediate-, and slow-motion). The performances of these prevalent recoupling techniques are compared and discussed in multiple aspects, together with the representative applications in biomolecules. Given the recent emerging advances in NMR technology, new challenges for recoupling methodology development and potential opportunities for biological systems are also discussed.

Refined Structures of O-Phospho-l-serine and Its Calcium Salt by New Multinuclear Solid-State NMR Crystallography Methods

O-phospho-l-serine (Pser) and its Ca salt, Ca[O-phospho-l-serine]·H2O (CaPser), play important roles for bone mineralization and were recently also proposed to account for the markedly improved bone-adhesive properties of Pser-doped calcium phosphate-based cements for biomedical implants. However, the hitherto few proposed structural models of Pser and CaPser were obtained by X-ray diffraction, thereby leaving the proton positions poorly defined. Herein, we refine the Pser and CaPser structures by density functional theory (DFT) calculations and contrast them with direct interatomic-distance constraints from two-dimensional (2D) nuclear magnetic resonance (NMR) correlation experimentation at fast magic-angle spinning (MAS), encompassing double-quantum-single-quantum (2Q-1Q) 1H NMR along with heteronuclear 13C{1H} and 31P{1H} correlation NMR experiments. The Pser and CaPser structures before and after refinements by DFT were validated against sets of NMR-derived effective 1H-1H, 1H-31P, and 1H-13C distances, which confirmed the improved accuracy of the refined structures. Each distance set was derived from one sole 2D NMR experiment applied to a powder without isotopic enrichment. The distances were extracted without invoking numerical spin-dynamics simulations or approximate phenomenological models. We highlight the advantages and limitations of the new distance-extraction procedure. Isotropic 1H, 13C, and 31P chemical shifts obtained by DFT calculations using the gauge including projector augmented wave (GIPAW) method agreed very well with the experimental results. We discuss the isotropic and anisotropic 13C and 31P chemical-shift parameters in relation to the previous literature, where most data on CaPser are reported herein for the first time.

Heteronuclear and homonuclear radio-frequency-driven recoupling

The radio-frequency-driven recoupling (RFDR) pulse sequence is used in magic-angle spinning (MAS) NMR to recouple homonuclear dipolar interactions. Here we show simultaneous recoupling of both the heteronuclear and homonuclear dipolar interactions by applying RFDR pulses on two channels. We demonstrate the method, called HETeronuclear RFDR (HET-RFDR), on microcrystalline SH3 samples at 10 and 55.555 kHz MAS. Numerical simulations of both HET-RFDR and standard RFDR sequences allow for better understanding of the influence of offsets and paths of magnetization transfers for both HET-RFDR and RFDR experiments, as well as the crucial role of XY phase cycling.

Microscopic (Dis)order and Dynamics of Cations in Mixed FA/MA Lead Halide Perovskites

Recent developments in the field of high efficiency perovskite solar cells are based on stabilization of the perovskite crystal structure of FAPbI₃ while preserving its excellent optoelectronic properties. Compositional engineering of, for example, MA or Br mixed into FAPbI₃ results in the desired effects, but detailed knowledge of local structural features, such as local (dis)order or cation interactions of formamidinium (FA) and methylammonium (MA), is still limited. This knowledge is, however, crucial for their further development. Here, we shed light on the microscopic distribution of MA and FA in mixed perovskites MA_1-x FA _x PbI₃ and MA_0.15FA_0.85PbI_2.55Br_0.45 by combining high-resolution double-quantum ¹H solid-state nuclear magnetic resonance (NMR) spectroscopy with state-of-the-art near-first-principles accuracy molecular dynamics (MD) simulations using machine-learning force-fields (MLFFs). We show that on a small local scale, partial MA and FA clustering takes place over the whole MA/FA compositional range. A reasonable driving force for the clustering might be an increase of the dynamical freedom of FA cations in FA-rich regions. While MA_0.15FA_0.85PbI_2.55Br_0.45 displays similar MA and FA ordering as the MA_1-x FA _x PbI₃ systems, the average cation-cation interaction strength increased significantly in this double mixed material, indicating a restriction of the space accessible to the cations or their partial immobilization upon Br^- incorporation. Our results shed light on the heterogeneities in cation composition of mixed halide perovskites, helping to exploit their full optoelectronic potential.

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.

The Monetite Structure Probed by Advanced Solid-State NMR Experimentation at Fast Magic-Angle Spinning

We present a solid-state nuclear magnetic resonance (NMR) spectroscopy study of the local 31P and 1H environments in monetite [CaHPO4; dicalcium phosphate anhydrous (DCPA)], as well as their relative spatial proximities. Each of the three 1H NMR peaks was unambiguously assigned to its respective crystallographically unique H site of monetite, while their pairwise spatial proximities were probed by homonuclear 1H–1H double quantum–single quantum NMR experimentation under fast magic-angle spinning (MAS) of 66 kHz. We also examined the relative 1H–31P proximities among the inequivalent {P1, P2} and {H1, H2, H3} sites in monetite; the corresponding shortest internuclear 1H–31P distances accorded well with those of a previous neutron diffraction study. The NMR results from the monetite phase were also contrasted with those observed from the monetite component present in a pyrophosphate-bearing calcium phosphate cement, demonstrating that while the latter represents a disordered form of monetite, it shares all essential local features of the monetite structure.

Reducing the computational cost of NMR crystallography of organic powders at natural isotopic abundance with the help of 13 C-13 C dipolar couplings

Structure determination of functional organic compounds remains a formidable challenge when the sample exists as a powder. Nuclear magnetic resonance crystallography approaches based on the comparison of experimental and Density Functional Theory (DFT)-computed ¹ H chemical shifts have already demonstrated great potential for structure determination of organic powders, but limitations still persist. In this study, we discuss the possibility of using ¹³ C-¹³ C dipolar couplings quantified on powdered theophylline at natural isotopic abundance with the help of dynamic nuclear polarization, to realize a DFT-free, rapid screening of a pool of structures predicted by ab initio random structure search. We show that although ¹³ C-¹³ C dipolar couplings can identify structures possessing long range structural motifs and unit cell parameters close to those of the true structure, it must be complemented with other data to recover information about the presence and the chemical nature of the supramolecular interactions.

Optimization of band-selective homonuclear dipolar recoupling in solid-state NMR by a numerical phase search

Spin polarization transfers among aliphatic ¹³C nuclei, especially ¹³Cα-¹³Cβ transfers, permit correlations of their nuclear magnetic resonance (NMR) frequencies that are essential for signal assignments in multidimensional solid-state NMR of proteins. We derive and demonstrate a new radio-frequency (RF) excitation sequence for homonuclear dipolar recoupling that enhances spin polarization transfers among aliphatic ¹³C nuclei at moderate magic-angle spinning (MAS) frequencies. The phase-optimized recoupling sequence with five π pulses per MAS rotation period (denoted as PR5) is derived initially from systematic numerical simulations in which only the RF phases are varied. Subsequent theoretical analysis by average Hamiltonian theory explains the favorable properties of numerically optimized phase schemes. The high efficiency of spin polarization transfers in simulations is preserved in experiments, in part because the RF field amplitude in PR5 is only 2.5 times the MAS frequency so that relatively low ¹H decoupling powers are required. Experiments on a microcrystalline sample of the β1 immunoglobulin binding domain of protein G demonstrate an average enhancement factor of 1.6 for ¹³Cα → ¹³Cβ polarization transfers, compared to the standard ¹³C-¹³C spin-diffusion method, implying a two-fold time saving in relevant 2D and 3D experiments.

Quantitative description of 1H SQ and DQ coherences for the hydroxyl disorder within hydrous ringwoodite

Proton-containing point defects in solid materials are important for a variety of properties ranging from ionic transport over thermal conductivity up to compressibility. Ultrafast magic-angle spinning techniques nowadays offer high-resolution solid-state NMR spectra, even for 1H, and thus open up possibilities to study the underlying defect chemistry. Nevertheless, disorder within such defects again leads to heavy spectral overlap of 1H resonances, which prevents quantitative analysis of defect concentrations, if several defect types are present. Here, we present a strategy to overcome this limitation by simulating the 1H lineshape as well as 1H-1H double-quantum buildup curves, which we then validate against the experimental data in a joint cost function. To mimic the local structural disorder, we use molecular dynamics simulations at the DFT level. It turned out to be advantageous for the joint refinement to put the computational effort into the structural optimisation to derive accurate proton positions and to use empirical correlations for the relation between isotropic and anisotropic 1H chemical shifts and structural elements. The expressiveness of this approach is demonstrated on ringwoodite's (γ-Mg2SiO4) OH defect chemistry containing four different defect types in octahedral and tetrahedral voids with both pure Mg and mixed Si and Mg cation environments. Still, we determine the ratio for each defect type with an accuracy of about 5% as a result of the minimization of the joint cost function. We expect that our approach is generally applicable for local proton disorder and might prove to be a valuable alternative to the established AIRSS and Monte Carlo methods, respectively.

Fast Magic-Angle-Spinning 19F Spin Exchange NMR for Determining Nanometer 19F-19F Distances in Proteins and Pharmaceutical Compounds

Internuclear distances measured using NMR provide crucial constraints of three-dimensional structures but are often restricted to about 5 Å due to the weakness of nuclear-spin dipolar couplings. For studying macromolecular assemblies in biology and materials science, distance constraints beyond 1 nm will be extremely valuable. Here we present an extensive and quantitative analysis of the feasibility of 19F spin exchange NMR for precise and robust measurements of interatomic distances up to 1.6 nm at a magnetic field of 14.1 T, under 20-40 kHz magic-angle spinning (MAS). The measured distances are comparable to those achievable from paramagnetic relaxation enhancement but have higher precision, which is better than ±1 Å for short distances and ±2 Å for long distances. For 19F spins with the same isotropic chemical shift but different anisotropic chemical shifts, intermediate MAS frequencies of 15-25 kHz without 1H irradiation accelerate spin exchange. For spectrally resolved 19F-19F spin exchange, 1H-19F dipolar recoupling significantly speeds up 19F-19F spin exchange. On the basis of data from five fluorinated synthetic, pharmaceutical, and biological compounds, we obtained two general curves for spin exchange between CF groups and between CF3 and CF groups. These curves allow 19F-19F distances to be extracted from the measured spin exchange rates after taking into account 19F chemical shifts. These results demonstrate the robustness of 19F spin exchange NMR for distance measurements in a wide range of biological and chemical systems.

A magnetic resonance and electrochemical study of the role of polymer mobility in supporting hydrogen transport in perfluorosulfonic acid membranes

Perfluorosulfonic acid (PFSA) materials have been used in polymer electrolyte membrane fuel cells (PEMFCs) as electrolyte materials due to their mechanical durability and high proton conductivity.

Orientation-dependent proton double-quantum NMR build-up function for soft materials with anisotropic mobility

In recent years, the analysis of proton double-quantum NMR build-up curves has become an important tool to quantify anisotropic mobility in different kinds of soft materials such as polymer networks or liquid crystals. In the former case, such data provides a measure of orientation-dependent residual (time-averaged) dipolar couplings arising from anisotropic segmental motions, informing about the length and the state of local stretching of the network chains. Previous studies of macroscopically ordered, i.e. stretched, networks were subject to the limitation that a detailed build-up curve analysis on the basis of a universal "Abragam-like" (A-l) build-up function valid for a proton multi-spin system was only possible for an isotropic orientation-averaged response. This situation is here remedied by introducing a generic orientation-dependent build-up function for an anisotropically mobile protonated molecular segment. We discuss an application to the modeling of data for a stretched network measured at different orientations with respect to the magnetic field, and present a validation by fitting data of different liquid-crystal molecules oriented in the magnetic field.

Applications of Solid-State NMR Spectroscopy for the Study of Lipid Membranes with Polyphilic Guest (Macro)Molecules

The incorporation of polymers or smaller complex molecules into lipid membranes allows for property modifications or the introduction of new functional elements. The corresponding molecular-scale details, such as changes in dynamics or features of potential supramolecular structures, can be studied by a variety of solid-state NMR techniques. Here, we review various approaches to characterizing the structure and dynamics of the guest molecules as well as the lipid phase structure and dynamics by different high-resolution magic-angle spinning proton and 13C NMR experiments as well as static 31P NMR experiments. Special emphasis is placed upon the incorporation of novel synthetic polyphilic molecules such as shape-persistent T- and X-shaped molecules as well as di- and tri-block copolymers. Most of the systems studied feature dynamic heterogeneities, for instance those arising from the coexistence of different phases; possibilities for a quantitative assessment are of particular concern.

Self-Assembly of X-Shaped Bolapolyphiles in Lipid Membranes: Solid-State NMR Investigations

A novel class of rigid-rod bolapolyphilic molecules with three philicities (rigid aromatic core, mobile aliphatic side chains, polar end groups) has recently been demonstrated to incorporate into and span lipid membranes, and to exhibit a rich variety of self-organization modes, including macroscopically ordered snowflake structures with 6-fold symmetry. In order to support a structural model and to better understand the self-organization on a molecular scale, we here report on proton and carbon-13 high-resolution magic-angle spinning solid-state NMR investigations of two different bolapolyphiles (BPs) in model membranes of two different phospholipids (DPPC, DOPC). We elucidate the changes in molecular dynamics associated with three new phase transitions detected by calorimetry in composite membranes of different composition, namely, a change in π-π-packing, the melting of lipid tails associated with the superstructure, and the dissolution and onset of free rotation of the BPs. We derive dynamic order parameters associated with different H-H and C-H bond directions of the BPs, demonstrating that the aromatic cores are well packed below the final phase transition, showing only 180° flips of the phenyl ring, and that they perform free rotations with additional oscillations of the long axis when dissolved in the fluid membrane. Our data suggests that BPs not only form ordered superstructures, but also rather homogeneously dispersed π-packed filaments within the lipid gel phase, thus reducing the corrugation of large vesicles.

Dendritic domains with hexagonal symmetry formed by x-shaped bolapolyphiles in lipid membranes

A novel class of bolapolyphile (BP) molecules are shown to integrate into phospholipid bilayers and self-assemble into unique sixfold symmetric domains of snowflake-like dendritic shapes. The BPs comprise three philicities: a lipophilic, rigid, π–π stacking core; two flexible lipophilic side chains; and two hydrophilic, hydrogen-bonding head groups. Confocal microscopy, differential scanning calorimetry, XRD, and solid-state NMR spectroscopy confirm BP-rich domains with transmembrane-oriented BPs and three to four lipid molecules per BP. Both species remain well organized even above the main 1,2-dipalmitoyl-sn-glycero-3-phosphocholine transition. The BP molecules only dissolve in the fluid membrane above 70 °C. Structural variations of the BP demonstrate that head-group hydrogen bonding is a prerequisite for domain formation. Independent of the head group, the BPs reduce membrane corrugation. In conclusion, the BPs form nanofilaments by π stacking of aromatic cores, which reduce membrane corrugation and possibly fuse into a hexagonal network in the dendritic domains.

Quantitative structural constraints for organic powders at natural isotopic abundance using dynamic nuclear polarization solid-state NMR spectroscopy

A straightforward method is reported to quantitatively relate structural constraints based on (13)C-(13)C double-quantum build-up curves obtained by dynamic nuclear polarization (DNP) solid-state NMR to the crystal structure of organic powders at natural isotopic abundance. This method relies on the significant gain in NMR sensitivity provided by DNP (approximately 50-fold, lowering the experimental time from a few years to a few days), and is sensitive to the molecular conformation and crystal packing of the studied powder sample (in this case theophylline). This method allows trial crystal structures to be rapidly and effectively discriminated, and paves the way to three-dimensional structure elucidation of powders through combination with powder X-ray diffraction, crystal-structure prediction, and density functional theory computation of NMR chemical shifts.

Influence of proton coupling on symmetry-based homonuclear (19)F dipolar recoupling experiments

We study the efficiency of two symmetry based homonuclear (19)F double-quantum recoupling sequences for moderate (R142(6)) and ultra-fast (R144(5)) MAS under the influence of strong (1)H-(1)H and (1)H-(19)F dipolar interactions and (1)H continuous wave decoupling. Simulations based on various spin systems derived from the organic solid 1,3,5-tris(2-fluoro-2-methylpropionylamino)benzene (F-BTA), used as a model system, reveal that the strong-decoupling limit is not accessible even for moderate spinning speeds. Additionally, for the no-decoupling limit improved DQ efficiencies are predicted for both moderate and ultra-fast MAS. Strong perturbations of build-up curves can be avoided by additional stabilisation through supercycling. Additional (1)H cw decoupling during (19)F recoupling rapidly reduces the maximum DQ efficiency when deviating from the no-decoupling limit. These effects were confirmed by experimental data on F-BTA. For moderate spinning the influence of (1)H-(1)H and (1)H-(19)F couplings is markedly stronger compared to ultra-fast MAS. For the latter case those influences reduce to a constant scaling if only short excitation times up to the first minimum are taken into account. Based on this analysis the experimental build-up curves of 1,3,5-tris(2-fluoro-2-methylpropionylamino)benzene can be refined with homonuclear (19)F spin systems which allow to probe even subtle structural differences for the fluorine atoms of F-BTA.

Probing crystal packing of uniformly (13)C-enriched powder samples using homonuclear dipolar coupling measurements

The relationship between the crystal packing of powder samples and long-range (13)C-(13)C homonuclear dipolar couplings is presented and illustrated for the case of uniformly (13)C-enriched L-alanine and L-histidine·HCl·H2O. Dipolar coupling measurement is based on the partial reintroduction of dipolar interactions by spinning the sample slightly off-magic-angle, while the coupling of interest for a given spin pair is isolated with a frequency-selective pulse. A cost function is used to correlate the so-derived dipolar couplings to trial crystal structures of the samples under study. This procedure allowed for the investigation of the l-alanine space group and L-histidine·HCl·H2O space group and unit-cell parameters.

Comparison of double-quantum NMR normalization schemes to measure homonuclear dipole-dipole interactions

A recent implementation of a double-quantum (DQ) recoupling solid-state NMR experiment, dubbed DQ-DRENAR, provides a quantitative measure of homonuclear dipole-dipole coupling constants in multispin-1/2 systems. It was claimed to be more robust than another, previously known experiment relying on the recording of point-by-point normalized DQ build-up curves. Focusing on the POST-C7 and BaBa-xy16 DQ pulse sequences, I here present an in-depth comparison of both approaches based upon spin-dynamics simulations, stressing that they are based upon very similar principles and that they are largely equivalent when no imperfections are present. With imperfections, it is found that DQ-DRENAR/POST-C7 does not fully compensate for additional signal dephasing related to chemical shifts (CS) and their anisotropy (CSA), which over-compensates the intrinsic CS(A)-related efficiency loss of the DQ Hamiltonian and leads to an apparent cancellation effect. The simulations further show that the CS(A)-related dephasing in DQ-DRENAR can be removed by another phase cycle step or an improved super-cycled wideband version. Only the latter, or the normalized DQ build-up, are unaffected by CS(A)-related signal loss and yield clean pure dipolar-coupling information subject to unavoidable, pulse sequence specific performance reduction related to higher-order corrections of the dipolar DQ Hamiltonian. The intrinsically super-cycled BaBa-xy16 is shown to exhibit virtually no CS(A) related imperfection terms, but its dipolar performance is somewhat more challenged by CS(A) effects than POST-C7, which can however be compensated when applied at very fast MAS (>50 kHz). Practically, DQ-DRENAR uses a clever phase cycle separation to achieve a significantly shorter experimental time, which can also be beneficially employed in normalized DQ build-up experiments.

On the theory of double quantum NMR in polymer systems: the second cumulant approximation for many spin I = 1/2 systems

General analytical expressions for Double Quantum Nuclear Magnetic Resonance (DQ NMR) kinetic curves of many-spin I = 1∕2 systems are derived with an accuracy of the second cumulant approximation. The expressions obtained exactly describe the initial part of the kinetic curves and provide a reasonable approximation up to times of about the effective spin-relaxation time. For the case when the system contains two isolated spins, this result exactly reproduces known expressions. In the case of polymer melts, the intermolecular magnetic dipole-dipole interactions significantly influence the time dependence of the DQ NMR kinetic curves.