REDOR-based heteronuclear dipolar correlation experiments in multi-spin systems: rotor-encoding, directing, and multiple distance and angle determination

Measuring Dipolar Order Parameters in Nondeuterated Proteins Using Solid-State NMR at the Magic-Angle-Spinning Frequency of 100 kHz

Proteins are dynamic molecules, relying on conformational changes to carry out function. Measurement of these conformational changes can provide insight into how function is achieved. For proteins in the solid state, this can be done by measuring the decrease in the strength of anisotropic interactions due to motion-induced fluctuations. The measurement of one-bond heteronuclear dipole-dipole coupling at magic-angle-spinning (MAS) frequencies >60 kHz is ideal for this purpose. However, rotational-echo double resonance (REDOR), an otherwise gold-standard technique for the quantitative measurement of these couplings, is difficult to implement under these conditions, especially in nondeuterated samples. We present here a combination of strategies based on REDOR variants ϵ-REDOR and DEDOR (deferred REDOR) and simultaneously measure residue-specific ¹⁵N-¹H and ¹³C_α-¹H_α dipole-dipole couplings in nondeuterated systems at the MAS frequency of 100 kHz. These strategies open up avenues to access dipolar order parameters in a variety of systems at the increasingly fast MAS frequencies that are now available.

Determination of Long-Range Distances by Fast Magic-Angle-Spinning Radiofrequency-Driven 19F-19F Dipolar Recoupling NMR

Nanometer-range distances are important for restraining the three-dimensional structure and oligomeric assembly of proteins and other biological molecules. Solid-state NMR determination of protein structures typically utilizes ¹³C-¹³C and ¹³C-¹⁵N distance restraints, which can only be measured up to ∼7 Å because of the low gyromagnetic ratios of these nuclear spins. To extend the distance reach of NMR, one can harvest the power of ¹⁹F, whose large gyromagnetic ratio in principle allows distances up to 2 nm to be measured. However, ¹⁹F possesses large chemical shift anisotropies (CSAs) as well as large isotropic chemical shift dispersions, which pose challenges to dipolar coupling measurements. Here, we demonstrate ¹⁹F-¹⁹F distance measurements at high magnetic fields under fast magic-angle spinning (MAS) using radiofrequency-driven dipolar recoupling (RFDR). We show that ¹⁹F-¹⁹F cross-peaks for distances up to 1 nm can be readily observed in two-dimensional ¹⁹F-¹⁹F correlation spectra using less than 5 ms of RFDR mixing. This efficient ¹⁹F-¹⁹F dipolar recoupling is achieved using practically accessible MAS frequencies of 15-55 kHz, moderate ¹⁹F radio frequency field strengths, and no ¹H decoupling. Experiments and simulations show that the fastest polarization transfer for aromatic fluorines with the highest distance accuracy is achieved using either fast MAS (e.g., 60 kHz) with large pulse duty cycles (>50%) or slow MAS with strong ¹⁹F pulses. Fast MAS considerably reduces relaxation losses during the RFDR π-pulse train, making finite-pulse RFDR under fast-MAS the method of choice. Under intermediate MAS frequencies (25-40 kHz) and intermediate pulse duty cycles (15-30%), the ¹⁹F CSA tensor orientation has a quantifiable effect on the polarization transfer rate; thus, the RFDR buildup curves encode both distance and orientation information. At fast MAS, the impact of CSA orientation is minimized, allowing pure distance restraints to be extracted. We further investigate how relayed transfer and dipolar truncation in multifluorine environments affect polarization transfer. This fast-MAS ¹⁹F RFDR approach is complementary to ¹⁹F spin diffusion for distance measurements and will be the method of choice under high-field fast-MAS conditions that are increasingly important for protein structure determination by solid-state NMR.

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.

Macroscopic Structural Compositions of π-Conjugated Polymers: Combined Insights from Solid-State NMR and Molecular Dynamics Simulations

Molecular dynamics simulations are combined with solid-state NMR measurements to gain insight into the macroscopic structural composition of the π-conjugated polymer poly(2,5-bis(3-tetradecyl-thiophen-2-yl)thieno[3,2-b]thiophene) (PBTTT). The structural and dynamical properties, as established by the NMR analyses, were used to test the local structure of three constitutient mesophases with (i) crystalline backbones and side chains, (ii) lamellar backbones and disordered side chains, or (iii) amorphous backbones and side chains. The relative compositions of these mesophases were then determined from the deconvolution of the ¹H and ¹³C solid-state NMR spectra and dynamic order parameters. Surprisingly, on the basis of molecular dynamics simulations, the powder composition consisted of only 28% of the completely crystalline mesophase, while 23% was lamellar with disordered side chains and 49% amorphous. The protocol presented in this work is a general approach and can be used for elucidating the relative compositions of mesophases in π-conjugated polymers.

Composite Polymer Electrolytes: Nanoparticles Affect Structure and Properties

Composite polymer electrolytes (CPEs) can significantly improve the performance in electrochemical devices such as lithium-ion batteries. This review summarizes property/performance relationships in the case where nanoparticles are introduced to polymer electrolytes. It is the aim of this review to provide a knowledge network that elucidates the role of nano-additives in the CPEs. Central to the discussion is the impact on the CPE performance of properties such as crystalline/amorphous structure, dielectric behavior, and interactions within the CPE. The amorphous domains of semi-crystalline polymer facilitate the ion transport, while an enhanced mobility of polymer chains contributes to high ionic conductivity. Dielectric properties reflect the relaxation behavior of polymer chains as an important factor in ion conduction. Further, the dielectric constant (ε) determines the capability of the polymer to dissolve salt. The atom/ion/nanoparticle interactions within CPEs suggest ways to enhance the CPE conductivity by generating more free lithium ions. Certain properties can be improved simultaneously by nanoparticle addition in order to optimize the overall performance of the electrolyte. The effects of nano-additives on thermal and mechanical properties of CPEs are also presented in order to evaluate the electrolyte competence for lithium-ion battery applications.

Bottom-up synthesis of liquid-phase-processable graphene nanoribbons with near-infrared absorption

Structurally defined, long (>100 nm), and low-band-gap (∼1.2 eV) graphene nanoribbons (GNRs) were synthesized through a bottom-up approach, enabling GNRs with a broad absorption spanning into the near-infrared (NIR) region. The chemical identity of GNRs was validated by IR, Raman, solid-state NMR, and UV-vis-NIR absorption spectroscopy. Atomic force microscopy revealed well-ordered self-assembled monolayers of uniform GNRs on a graphite surface upon deposition from the liquid phase. The broad absorption of the low-band-gap GNRs enables their detailed characterization by Raman and time-resolved terahertz photoconductivity spectroscopy with excitation at multiple wavelengths, including the NIR region, which provides further insights into the fundamental physical properties of such graphene nanostructures.

Coexistence of helical morphologies in columnar stacks of star-shaped discotic hydrazones

Discotic hydrazone molecules are of particular interest as they form discotic phases where the discs are rigidified by intramolecular hydrogen bonds. Here, we investigate the thermotropic behavior and solid-state organizations of three discotic hydrazone derivatives with dendritic groups attached to their outer peripheries, containing six, eight, and ten carbons of linear alkoxy chains. On the basis of two-dimensional wide angle X-ray scattering (2DWAXS), the elevated temperature liquid crystalline (LC) phases were assigned to a hexagonal columnar (Colh) organization with nontilted hydrazone discs for all three compounds. With WAXS, advanced solid-state nuclear magnetic resonance (SSNMR) techniques, and ab initio computations, the compounds with six and ten carbons of achiral alkoxy side chains were further subjected to studies at 25 °C, revealing complex crystalline phases with rigid columns and flexible side chains. This combined approach led to models of coexisting helical columnar stacking morphologies for both systems with two different tilt/pitch angles between successive hydrazone molecules. The differences in tilt/pitch angles between the two compounds illustrate that the columns with short alkoxy chains (six carbons) are more influenced by the presence of other stacks in their vicinity, while those with long side chains are less tilted due to a larger alkoxy (ten carbons) buffer zone. The formation of different packing morphologies in the crystalline phase of a columnar LC has rarely been reported so far, which suggests the possibility of complex stacking structures of similar organic LC systems, utilizing small molecules as potential materials for applications in organic electronics.

C-REDOR curves of extended spin systems

The convergence of simulated C-REDOR curves of (infinitely) large spin systems is investigated with respect to the number of spins considered in the calculations. Taking a sufficiently large number of spins (>20,000 spins) into account enables the simulation of converged C-REDOR curves over the entire time period and not only the initial regime. The calculations are based on an existing approximation within first order average Hamiltonian theory (AHT), which assumes the absence of homonuclear dipole-dipole interactions. The C-REDOR experiment generates an average Hamiltonian close to the idealized AHT behavior even for multiple spin systems including multiple homonuclear dipole-dipole interactions which is shown from numerically exact calculations of the spin dynamics. Experimentally it is shown that calculations accurately predict the full, experimental C-REDOR curves of the multi-spin systems (31)P-(19)F in apatite, (31)P-(1)H in potassium trimetaphosphimate and (1)H-(31)P in potassium dihydrogen phosphate. We also present (13)C-(1)H and (15)N-(1)H data for the organic compounds glycine, l-alanine and l-histidine hydrochloride monohydrate which require consideration of molecular motion. Furthermore, we investigated the current limits of the method from systematic errors and we suggest a simple way to calculate errors for homogeneous and heterogeneous samples from experimental data.

Constant time tensor correlation experiments by non-gamma-encoded recoupling pulse sequences

Constant-time tensor correlation under magic-angle spinning conditions is an important technique in solid-state nuclear magnetic resonance spectroscopy for the measurements of backbone or side-chain torsion angles of polypeptides and proteins. We introduce a general method for the design of constant-time tensor correlation experiments under magic-angle spinning. Our method requires that the amplitude of the average Hamiltonian must depend on all the three Euler angles bringing the principal axis system to the rotor-fixed frame, which is commonly referred to as non-gamma encoding. We abbreviate this novel approach as COrrelation of Non-Gamma-Encoded Experiment (CONGEE), which exploits the orientation-dependence of non-gamma-encoded sequences with respect to the magic-angle rotation axis. By manipulating the relative orientation of the average Hamiltonians created by two non-gamma-encoded sequences, one can obtain a modulation of the detected signal, from which the structural information can be extracted when the tensor orientations relative to the molecular frame are known. CONGEE has a prominent feature that the number of rf pulses and the total pulse sequence duration can be maintained to be constant so that for torsion angle determination the effects of systematic errors owing to the experimental imperfections and/or T(2) effects could be minimized. As a proof of concept, we illustrate the utility of CONGEE in the correlation between the C' chemical shift tensor and the C(α)-H(α) dipolar tensor for the backbone psi angle determination. In addition to a detailed theoretical analysis, numerical simulations and experiments measured for [U-(13)C, (15)N]-L-alanine and N-acetyl-[U-(13)C, (15)N]-D,L-valine are used to validate our approach at a spinning frequency of 20 kHz.

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.

Time displacement rotational echo double resonance: heteronuclear dipolar recoupling with suppression of homonuclear interaction under fast magic-angle spinning

We have developed a novel variant of REDOR which is applicable to multiple-spin systems without proton decoupling. The pulse sequence is constructed based on a systematic time displacement of the pi pulses of the conventional REDOR sequence. This so-called time displacement REDOR (td-REDOR) is insensitive to the effect of homonuclear dipole-dipole interaction when the higher order effects are negligible. The validity of td-REDOR has been verified experimentally by the P-31{C-13} measurements on glyphosate at a spinning frequency of 25 kHz. The experimental dephasing curve is in favorable agreement with the simulation data without considering the homonuclear dipole-dipole interactions.

Fast and slow dynamics in a discotic liquid crystal with regions of columnar order and disorder

Aromatic disk-shaped molecules tend to self-organize into a herringbone packing where the disks are inclined at angles ±θ with respect to the axis of the column. In discotic liquid crystals this can introduce defects between stacks of limited length. In a C(3)-symmetric hexa-peri-hexabenzocoronene, solid-state NMR, x-ray scattering, and rheology identifies such a packing with θ=43° and stacks of about seven disks. Disordered regions containing defects fill the space in between the ordered stacks. Biaxial intra- and intercolumnar dynamics differing by eight decades are identified.

Rotational echo double resonance without proton decoupling under fast spinning condition

We show that rotational echo double resonance (REDOR) experiments can be carried out without proton decoupling under the conditions of fast spinning and strong rf field. Numerical simulations on a five-spin systems show that no significant attenuation of the reference signal (S(0)) is observed at a spin rate of 25 kHz, provided that the rf power is larger than 100 kHz. This approach has been validated by (31)P{(13)C} REDOR measurements on isotopically labeled glyphosate. The obtained van Vleck's second moment is in favorable agreement with the value calculated based on the crystal structure.

Columnar packing motifs of functionalized perylene derivatives: local molecular order despite long-range disorder

We elucidate local packing motifs and dynamical order parameters in a perylene tetracarboxydiimide derivative (C(8,7)-PDI), one of the most promising candidates for rationally designed, self-assembling, and self-healing molecular wires. Spectroscopic fingerprints obtained from solid-state NMR spectroscopy are interpreted by means of first-principles calculations and molecular dynamics simulations. The interplay of steric repulsion, H bonding, and pi-pi packing effects leads to a specific relative molecular pitch angle of approximately 35 +/- 10 degrees between successive molecules in the stack. Dynamical order parameters, determined from NMR sideband patterns as a measure of molecular motion, yield values of S approximately = 1.0 in the core of the columnar stack, corresponding to an almost frozen molecular dynamics at ambient temperature. This rigidity is compatible with characteristic intermolecular distances obtained from dipolar couplings between specific hydrogens via double-quantum NMR experiments and further supported by ab initio calculations.

Analytical solutions to several magic-angle spinning NMR experiments

Using the Anderson-Weiss (AW) formalism, analytical expressions of the NMR signal are obtained for the following magic-angle spinning (MAS) experiments: total suppression of sidebands (TOSS); phase adjusted spinning sidebands (PASS); rotational-echo double-resonance (REDOR); rotor-encoded REDOR (REREDOR); cross-polarization magic-angle spinning (CPMAS); exchange induced sidebands (EIS); one-dimensional exchange spectroscopy by sideband alternation (ODESSA); time-reverse ODESSA (trODESSA); centerband-only detection of exchange (CODEX). In order to test the validity of the AW approach, the Gaussian powder approximation is compared with exact powder calculations. A quantitative study of the effect of molecular dynamics on the efficiency of the TOSS and REDOR pulse sequences is then presented.

Origin of the complex molecular dynamics in functionalized discotic liquid crystals

The molecular dynamics of three dipole functionalized hexa-peri-hexabenzocoronenes have been studied using site-specific NMR techniques and dielectric spectroscopy as a function of temperature and pressure. These probes (i) suggest that the thermodynamic state completely controls the dynamic response, (ii) clarify the origin of two dynamic processes associated with the presence of two glass temperatures, and (iii) provide the first phase diagram for substances of this kind.

Morphological differences in semicrystalline polymers: Implications for local dynamics and chain diffusion

Morphological differences in semicrystalline polymers due to different crystallization conditions have implications for the chain motion. The local dynamics in the noncrystalline regions of solution-crystallized linear polyethylene is lower than in a melt-crystallized sample, but the opposite is observed for chain diffusion between noncrystalline and crystalline regions. The activation enthalpy for chain diffusion, however, is the same, indicating that entropic differences in the noncrystalline regions strongly influence the chain diffusion of the same polymer in different morphologies.

Molecular motion of isolated linear alkanes in nanochannels

The mobility of a series of linear alkanes in their inclusion compound with tris(o-phenylenedioxy)spirotriphosphazene is studied by high-resolution carbon-proton magic-angle spinning solid-state NMR spectroscopy. Two different carbon-proton dipolar recoupling experiments are compared with respect to their ability to yield precise site-specific, motion-averaged dipolar coupling constants. The most accurate results are obtained by analysis of extrema positions in Lee-Goldburg cross-polarization build-up curves. We present a comprehensive collection of coupling constants, which evidence a rotational motion of the all-trans chains around the channel axis, with some further averaging due to additional fluctuations, as previously found for alkanes in other host matrices such as urea. The order parameter increases toward the inner parts of the chains, and is largely independent of chain length. Notably, chains in a TPP host are not more ordered than in urea, even though the average TPP channel diameter is reported to be smaller. Significantly decreased order is found for highly filled short-alkane samples, which is interpreted in terms of an increased rate of mutual collisions. From residual dipolar couplings as well as carbon chemical shifts, we derive similar amounts of gauche conformers. Translational motions along the channels are further studied by proton double-quantum spectroscopy, which probes guest-host dipolar couplings. The extent of local-scale lateral motion is again correlated with the sample filling, and is a weak function of temperature, as expected from a case in which highly restricted single-file diffusion should dominate the mobility. Characteristic effects of sample aging are apparent in all our experiments.

Template-Aluminosilicate Structures at the Early Stages of Zeolite ZSM-5 Formation. A Combined Preparative, Solid-state NMR, and Computational Study

Species at three stages in the self-assembly of zeolite ZSM-5 have been studied with one- and two-dimensional magic-angle-spinning 13C, 27Al, 29Si, and 1H NMR spectroscopy and compared with the earlier proposed structures: (1) precursor species containing 33-36 T sites around a tetrapropylammonium (TPA) cation, (2) nanoslabs consisting of a flat 4 x 3 array of such precursors, and (3) the final TPA-ZSM-5 zeolite. Synthesis was carried out in D2O to suppress the water and silanol protons. Under such conditions, the effective Si-H and Al-H distances measured with 29Si-{1H} and 27Al-{1H} rotational echo double resonance (REDOR) reflect the interactions between TPA cations and the surrounding aluminosilica. The 29Si-{1H} REDOR curves for Q4-type silicon atoms at the three mentioned stages are closely similar, as well as the observed 27Al-1H REDOR curve for the precursor species compared to that for the TPA-ZSM-5. This indicates that in addition to externally attached TPA, there is also internal TPA already incorporated at an early stage into the aluminosilicate in a similar way as in the final zeolite, in accordance with the earlier proposed MFI self-assembly pathway (Kirschhock et al. Angew. Chem. Int. Ed. 2001, 40, 2637). However, the effective distances extracted from the initial REDOR curvatures are significantly (10-15%) larger than those computed for the model. Since there is no temperature effect, we tentatively assign this difference to a reduction of the 29Si-1H and 27Al-1H interactions by multispin decoherence effects or self-decoupling caused by proton spin diffusion. By assuming the computed model distances and fitting Anderson-Weiss curves to the observed REDOR data, we obtain similar "decoherence times" in the order of 0.1 ms. The observed 29Si-{1H} REDOR dephasing for the Q3 sites in the precursors is significantly faster than that for the Q4 sites. This is tentatively ascribed to a partial deuteron-proton back exchange at the silanol positions.

Determining the Geometry of Hydrogen Bonds in Solids with Picometer Accuracy by Quantum-Chemical Calculations and NMR Spectroscopy

The structure of multiply hydrogen-bonded systems is determined with picometer accuracy by a combined solid-state NMR and quantum-chemical approach. On the experimental side, advanced 1H-15N dipolar recoupling NMR techniques are capable of providing proton-nitrogen distances of up to about 250 pm with an accuracy level of +/-1 pm for short distances (i.e., around 100 pm) and +/-5 pm for longer ones (i.e., 180 to 250 pm). The experiments were performed under fast magic-angle spinning, which ensures sufficient dipolar decoupling and spectral resolution of the 1H resonance lines. On the quantum-chemical side, the structures of the hydrogen-bonded systems were computationally optimised, yielding complete sets of nitrogen-proton and proton-proton distances, which are essential for correctly interpreting the experimental NMR data. In this way, nitrogen-proton distances were determined with picometer accuracy, so that vibrational averaging effects on dipole-dipole couplings need to be considered. The obtained structures were finally confirmed by the complete agreement of computed and experimental 'H and '5N chemical shifts. This demonstrates that solid-state NMR and quantum-chemical methods ideally complement each other and, in a combined manner, represent a powerful approach for reliable, high-precision structure determination whenever scattering techniques are inapplicable.

Shape-persistent macrocycles with intraannular polar groups: synthesis, liquid crystallinity, and 2D organization

The synthesis of macrocycles with intraannular polar ester groups and extraannular oligo-alkyl groups is described. The compounds exhibit stable liquid crystalline phases showing fan-shaped textures under the polarizing microscope, typical for a columnar order of the molecules. X-ray powder diffraction data of the LC phase indicate that the unit cell contains two symmetry-related units, a feature pointing most probably to a restricted rotation of the macrocycles within a stack. The X-ray data were further supported by solid-state NMR experiments, showing that the rigid core of the compounds does not rotate with kHz or higher frequencies within the column in the LC phase. Apart from the organization of the molecules in the LC phase, the 2D organization of the macrocycles at the solvent-highly oriented pyrolytic graphite (HOPG) interface was investigated and showed that these compounds are capable of nanofunctionalizing the HOPG surface in the multinanometer regime.