A robust pulse sequence for the determination of small homonuclear dipolar couplings in magic-angle spinning NMR

Solid-State NMR Double-Quantum Dipolar Recoupling Enhanced by Additional Phase Modulation

Additional phase modulation (APM) is proposed to generally enhance the theoretical efficiency of homonuclear double-quantum (DQ) recoupling in solid-state NMR. APM applies an additional phase list to DQ recoupling in steps of an entire block. The sine-based phase list can enhance the theoretical efficiency by 15-30 %, from 0.52 to 0.68 (non-γ-encoded recoupling) or from 0.73 to 0.84 (γ-encoded recoupling), with doubled recoupling time. The genetic-algorithm (GA) optimized APM can adiabatically enhance the efficiency to ∼1.0 at longer times. The concept of APM has been tested on SPR-51 , BaBa, and SPR-31 , which represent γ-encoded recoupling, non-γ-encoded recoupling, and another kind beyond the former two, respectively. Simulations reveal that enhancements from APM are due to the activation of more crystallites in the powder. Experiments on 2,3-13 C labeled alanine are used to validate the APM recoupling. This new concept shall shed light on developing more efficient homonuclear recoupling methods.

Theory of frequency-selective homonuclear dipolar recoupling in solid-state NMR

In solid-state nuclear magnetic resonance, frequency-selective homonuclear dipolar recoupling is key to quantitative distance measurement or selective enhancement of correlations between atoms of interest in multiple-spin systems, which are not amenable to band-selective or broadband recoupling. Previous frequency-selective recoupling is mostly based on the so-called rotational resonance (R²) condition that restricts the application to spin pairs with resonance frequencies differing in integral multiples of the magic-angle spinning (MAS) frequency. Recently, we have proposed a series of frequency-selective homonuclear recoupling sequences called SPR (short for Selective Phase-optimized Recoupling), which have been successfully applied for selective ¹H-¹H or ¹³C-¹³C recoupling under from moderate (∼10 kHz) to ultra-fast (150 kHz) MAS frequencies. In this study, we fully analyze the average Hamiltonian theory of SPR sequences and reveal the origin of frequency selectivity in recoupling. The theoretical description, as well as numerical simulations and experiments, demonstrates that the frequency selectivity can be easily controlled by the flip angle (p) in the (p)_ϕk(p)_ϕk+π unit in the pSPR-N_n sequences. Small flip angles lead to frequency-selective recoupling, while large flip angles may lead to broadband recoupling in principle. The result shall shed new light on the design of homonuclear recoupling sequences with arbitrary frequency bandwidths.

Efficient symmetry-based γ-encoded DQ recoupling sequences for suppression of t1-noise in solid-state NMR spectroscopy at fast MAS

Solid-state NMR spectroscopy has played a significant role in elucidating the structure and dynamics of materials and biological solids at a molecular level for decades. In particular, the ¹H double-quantum/single-quantum (DQ/SQ) chemical shift correlation experiment is widely used for probing the proximity of protons, rendering it a powerful tool for elucidating the hydrogen-bonding interactions and molecular packing of various complex molecular systems. Two factors, namely, the DQ filtering efficiency and t₁-noise, dictate the quality of the 2D ¹H DQ/SQ spectra. Experimentally different recoupling sequences show varied DQ filtering efficiencies and t₁-noise. Herein, after a systematic search of symmetry-based DQ recoupling sequences, we report that the symmetry-based γ-encoded RN_n^ν sequences show superior performance to other DQ recoupling sequences, which not only have a higher DQ recoupling efficiency but can also significantly reduce t₁-noise. The origin of t₁-noise is further discussed in detail via extensive numerical simulations. We envisage that such γ-encoded RN_n^ν sequences are superior candidates for DQ recoupling in proton-based solid-state NMR spectroscopy due to its capability of efficiently exciting DQ coherences and suppressing t₁-noise.

The Desensitized Channelrhodopsin-2 Photointermediate Contains 13 -cis, 15 -syn Retinal Schiff Base

Channelrhodopsin‐2 (ChR2) is a light‐gated cation channel and was used to lay the foundations of optogenetics. Its dark state X‐ray structure has been determined in 2017 for the wild‐type, which is the prototype for all other ChR variants. However, the mechanistic understanding of the channel function is still incomplete in terms of structural changes after photon absorption by the retinal chromophore and in the framework of functional models. Hence, detailed information needs to be collected on the dark state as well as on the different photointermediates. For ChR2 detailed knowledge on the chromophore configuration in the different states is still missing and a consensus has not been achieved. Using DNP‐enhanced solid‐state MAS NMR spectroscopy on proteoliposome samples, we unambiguously determined the chromophore configuration in the desensitized state, and we show that this state occurs towards the end of the photocycle.

Natural Isotopic Abundance 13C and 15N Multidimensional Solid-State NMR Enabled by Dynamic Nuclear Polarization

Dynamic nuclear polarization (DNP) has made feasible solid-state NMR experiments that were previously thought impractical due to sensitivity limitations. One such class of experiments is the structural characterization of organic and biological samples at natural isotopic abundance (NA). Herein, we describe the many advantages of DNP-enabled ssNMR at NA, including the extraction of long-range distance constraints using dipolar recoupling pulse sequences without the deleterious effects of dipolar truncation. In addition to the theoretical underpinnings in the analysis of these types of experiments, numerous applications of DNP-enabled ssNMR at NA are discussed.

Studying hydrogen bonding and dynamics of the acetylate groups of the Special Pair of Rhodobacter sphaeroides WT

Although the cofactors in the bacterial reaction centre of Rhodobacter sphaeroides wild type (WT) are arranged almost symmetrically in two branches, the light-induced electron transfer occurs selectively in one branch. As origin of this functional symmetry break, a hydrogen bond between the acetyl group of P_L in the primary donor and His-L168 has been discussed. In this study, we investigate the existence and rigidity of this hydrogen bond with solid-state photo-CIDNP MAS NMR methods offering information on the local electronic structure due to highly sensitive and selective NMR experiments. On the time scale of the experiment, the hydrogen bond between P_L and His-L168 appears to be stable and not to be affected by illumination confirming a structural asymmetry within the Special Pair.

Solid-state NMR tools for the structural characterization of POSiSils: 29 Si sensitivity improvement with MC-CP and 2D 29 Si-29 Si DQ-SQ at natural abundance

The ¹ H-²⁹ Si multiple-contact cross polarization (MC-CP) MAS NMR experiment is evaluated for the class of silicate-siloxane copolymers called POSiSils, that is, polyoligosiloxysilicones. It proves a reasonably good solution to tackle the challenge of recording quantitative ²⁹ Si NMR data in experimental time much reduced compared with single pulse acquisition. In a second time, we report ²⁹ Si-²⁹ Si MC-CP double-quantum single-quantum (MC-CP-DQ-SQ) NMR experiment, which provides information about the through-space proximities between all silicon species despite the high degree of heterogeneity of this material. This work furthers the NMR tools for NMR crystallography for inorganic polymers, as it covers flexible polymers with different dimensionalities and long or heterogeneous relaxation characteristics at low ²⁹ Si natural abundance.

NMR crystallography of zeolites: How far can we go without diffraction data?

Nuclear magnetic resonance (NMR) crystallography-an approach to structure determination that seeks to integrate solid-state NMR spectroscopy, diffraction, and computation methods-has emerged as an effective strategy to determine structures of difficult-to-characterize materials, including zeolites and related network materials. This paper explores how far it is possible to go in determining the structure of a zeolite framework from a minimal amount of input information derived only from solid-state NMR spectroscopy. It is shown that the framework structure of the fluoride-containing and tetramethylammonium-templated octadecasil clathrasil material can be solved from the 1D ²⁹ Si NMR spectrum and a single 2D ²⁹ Si NMR correlation spectrum alone, without the space group and unit cell parameters normally obtained from diffraction data. The resulting NMR-solved structure is in excellent agreement with the structures determined previously by diffraction methods. It is anticipated that NMR crystallography strategies like this will be useful for structure determination of other materials, which cannot be solved from diffraction methods alone.

Enhanced 1H-X D-HMQC performance through improved 1H homonuclear decoupling

The sensitivity of solid-state NMR experiments that utilize ¹H zero-quantum heteronuclear dipolar recoupling, such as D-HMQC, is compromised by poor homonuclear decoupling. This leads to a rapid decay of recoupled magnetization and an inefficient recoupling of long-range dipolar interactions, especially for nuclides with low gyromagnetic ratios. We investigated the use, in symmetry-based ¹H heteronuclear recoupling sequences, of a basic R element that was principally designed for efficient homonuclear decoupling. By shortening the time required to suppress the effects of homonuclear dipolar interactions to the duration of a single inversion pulse, spin diffusion was effectively quenched and long-lived recoupled coherence lifetimes could be obtained. We show, both theoretically and experimentally, that these modified sequences can yield considerable sensitivity improvements over the current state-of-the-art methods and applied them to the indirect detection of ⁸⁹Y in a metal-organic framework.

29Si NMR and SAXS investigation of the hybrid organic-inorganic glasses obtained by consolidation of the melting gels

This study is focused on structural characterization of hybrid glasses obtained by consolidation of melting gels. The melting gels were prepared in molar ratios of methyltriethoxysilane (MTES) and dimethyldiethoxysilane (DMDES) of 75%MTES-25%DMDES and 65%MTES-35%DMDES. Following consolidation, the hybrid glasses were characterized using Raman, ²⁹Si and ¹³C Nuclear Magnetic Resonance (NMR) spectroscopies, synchrotron Small Angle X-Ray Scattering (SAXS) and scanning electron microscopy (SEM). Raman spectroscopy revealed the presence of Si-C bonds in the hybrid glasses and 8-membered ring structures in the Si-O-Si network. Qualitative NMR spectroscopy identified the main molecular species, while quantitative NMR data showed that the ratio of trimers (T) to dimers (D) varied between 4.6 and 3.8. Two-dimensional ²⁹Si NMR data were used to identify two distinct types of T³ environments. SAXS data showed that the glasses are homogeneous across the nm to micrometer length scales. The scattering cross section was one thousand times lower than what is expected when phase separation occurs. The SEM images show a uniform surface without defects, in agreement with the SAXS results, which further supports that the hybrid glasses are nonporous.

Transient effects in π-pulse sequences in MAS solid-state NMR

Dipolar recoupling techniques that use isolated rotor-synchronized π pulses are commonly used in solid-state NMR spectroscopy to gain insight into the structure of biological molecules. These sequences excel through their simplicity, stability towards radio-frequency (rf) inhomogeneity, and low rf requirements. For a theoretical understanding of such sequences, we present a Floquet treatment based on an interaction-frame transformation including the chemical-shift offset dependence. This approach is applied to the homonuclear dipolar-recoupling sequence Radio-Frequency Driven Recoupling (RFDR) and the heteronuclear recoupling sequence Rotational Echo Double Resonance (REDOR). Based on the Floquet approach, we show the influence of effective fields caused by pulse transients and discuss the advantages of pulse-transient compensation. We demonstrate experimentally that the transfer efficiency for homonuclear recoupling can be doubled in some cases in model compounds as well as in simple peptides if pulse-transient compensation is applied to the π pulses. Additionally, we discuss the influence of various phase cycles on the recoupling efficiency in order to reduce the magnitude of effective fields. Based on the findings from RFDR, we are able to explain why the REDOR sequence does not suffer in the recoupling efficiency despite the presence of effective fields.

Analysis of the Electronic Structure of the Special Pair of a Bacterial Photosynthetic Reaction Center by 13 C Photochemically Induced Dynamic Nuclear Polarization Magic-Angle Spinning NMR Using a Double-Quantum Axis

The origin of the functional symmetry break in bacterial photosynthesis challenges since several decades. Although structurally very similar, the two branches of cofactors in the reaction center (RC) protein complex act very differently. Upon photochemical excitation, an electron is transported along one branch, while the other remains inactive. Photochemically induced dynamic nuclear polarization (photo-CIDNP) magic-angle spinning (MAS) ¹³ C NMR revealed that the two bacteriochlorophyll cofactors forming the "Special Pair" donor dimer are already well distinguished in the electronic ground state. These previous studies are relying solely on ¹³ C-¹³ C correlation experiments as radio-frequency-driven recoupling (RFDR) and dipolar-assisted rotational resonance (DARR). Obviously, the chemical-shift assignment is difficult in a dimer of tetrapyrrole macrocycles, having eight pyrrole rings of similar chemical shifts. To overcome this problem, an INADEQUATE type of experiment using a POST C7 symmetry-based approach is applied to selectively isotope-labeled bacterial RC of Rhodobacter (R.) sphaeroides wild type (WT). We, therefore, were able to distinguish unresolved sites of the macromolecular dimer. The obtained chemical-shift pattern is in-line with a concentric assembly of negative charge within the common center of the Special Pair supermolecule in the electronic ground state.

Optimizing symmetry-based recoupling sequences in solid-state NMR by pulse-transient compensation and asynchronous implementation

Pulse imperfections like pulse transients and radio-frequency field maladjustment or inhomogeneity are the main sources of performance degradation and limited reproducibility in solid-state nuclear magnetic resonance experiments. We quantitatively analyze the influence of such imperfections on the performance of symmetry-based pulse sequences and describe how they can be compensated. Based on a triple-mode Floquet analysis, we develop a theoretical description of symmetry-based dipolar recoupling sequences, in particular, R26₄¹¹, calculating first- and second-order effective Hamiltonians using real pulse shapes. We discuss the various origins of effective fields, namely, pulse transients, deviation from the ideal flip angle, and fictitious fields, and develop strategies to counteract them for the restoration of full transfer efficiency. We compare experimental applications of transient-compensated pulses and an asynchronous implementation of the sequence to a supercycle, SR26, which is known to be efficient in compensating higher-order error terms. We are able to show the superiority of R26 compared to the supercycle, SR26, given the ability to reduce experimental error on the pulse sequence by pulse-transient compensation and a complete theoretical understanding of the sequence.

Structure determination of a partially ordered layered silicate material with an NMR crystallography approach

Structure determination of layered materials can present challenges for conventional diffraction methods due to the fact that such materials often lack full three-dimensional periodicity since adjacent layers may not stack in an orderly and regular fashion. In such cases, NMR crystallography strategies involving a combination of solid-state NMR spectroscopy, powder X-ray diffraction, and computational chemistry methods can often reveal structural details that cannot be acquired from diffraction alone. We present here the structure determination of a surfactant-templated layered silicate material that lacks full three-dimensional crystallinity using such an NMR crystallography approach. Through a combination of powder X-ray diffraction and advanced ²⁹Si solid-state NMR spectroscopy, it is revealed that the structure of the silicate layer of this layered silicate material templated with cetyltrimethylammonium surfactant cations is isostructural with the silicate layer of a previously reported material referred to as ilerite, octosilicate, or RUB-18. High-field ¹H NMR spectroscopy reveals differences between the materials in terms of the ordering of silanol groups on the surfaces of the layers, as well as the contents of the inter-layer space.

Efficient 2D double-quantum solid-state NMR spectroscopy with large spectral widths

STiC phase shifts enable the use of supercycled recoupling sequences for recording 2D DQ–SQ correlation spectra with arbitrary spectral widths.

Low-power broadband homonuclear dipolar recoupling in MAS NMR by two-fold symmetry pulse schemes for magnetization transfers and double-quantum excitation

We provide an experimental, numerical, and high-order average Hamiltonian evaluation of an open-ended series of homonuclear dipolar recoupling sequences, SR [Formula: see text] with p=1,2,3,…. While operating at a very low radio-frequency (rf) power, corresponding to a nutation frequency of 1/2 of the magic-angle spinning (MAS) rate (ωnut=ωr/2), these recursively generated double-quantum (2Q) dipolar recoupling schemes offer a progressively improved compensation to resonance offsets and rf inhomogeneity for increasing pulse-sequence order p. The excellent recoupling robustness to these experimental obstacles, as well as to CSA, is demonstrated for 2Q filtering (2QF) experiments and for driving magnetization transfers in 2D NMR correlation spectroscopy, where the sequences may provide either double or zero quantum dipolar Hamiltonians during mixing. Experimental and numerical demonstrations, which mostly target conditions of "ultra-fast" MAS (≳50kHz) and high magnetic fields, are provided for recoupling of (13)C across a wide range of isotropic and anisotropic chemical shifts, as well as dipolar coupling constants, encompassing [2,3-(13)C2]alanine, [1,3-(13)C2]alanine, diammonium [1,4-(13)C2]fumarate, and [U-(13)C]tyrosine. When compared at equal power levels, a superior performance is observed for the SR [Formula: see text] sequences with p⩾3 relative to existing and well-established 2Q recoupling techniques. At ultra-fast MAS, proton decoupling is redundant during the homonuclear dipolar recoupling of dilute spins in organic solids, which renders the family of SR [Formula: see text] schemes the first efficient 2Q recoupling option for general applications, such as 2Q-1Q correlation NMR and high-order multiple-quantum excitation, under truly low-power rf conditions.

Investigating adsorption of organic compounds in metal-organic framework MIL-53

Metal-organic frameworks (MOFs) are versatile materials that incorporate metal centers along with organic linkers in highly ordered, intricate structures. MIL-53 is a MOF that exhibits a “breathing effect,” where the pore size and MOF topology are profoundly influenced by the identity and binding mechanism of guest molecules. This phenomenon renders MIL-53 a promising candidate for sensing applications. In this report, the adsorption of various organic compounds within MIL-53 is investigated using a combination of complementary techniques. Thermal gravimetric analysis experiments confirm loading of the guest molecules and yield insight into adsorption interactions and strengths. Significant guest-induced changes in the crystal structure of MIL-53 are revealed by powder X-ray diffraction experiments; specific unique phases of MIL-53 are related to the identity of the guest molecule and its binding mechanism to the framework. 27Al and 13C solid-state NMR experiments probe the interaction between guest molecules and MIL-53. The relationship between the nature of the guest, the structure of MIL-53, and 27Al NMR parameters is explored. 27Al NMR parameters are sensitive to the host-guest binding mechanism (i.e., hydrogen-bonding or π–π stacking interactions) and yield valuable information regarding the influence of the adsorbates on the local aluminum environment. This combination of physical characterization techniques is a useful probe of guest adsorption and the breathing effect within MIL-53 and should prove useful for investigation of related MOFs.

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.

A simulated annealing approach for solving zeolite crystal structures from two-dimensional NMR correlation spectra

An improved NMR crystallography strategy is presented for determining the structures of network materials such as zeolites from just a single two-dimensional (2D) NMR correlation spectrum that probes nearest-neighbor interactions, combined with the unit cell parameters and space group information measured in a diffraction experiment. The correlation information contained within a 2D spectrum is converted into a "connectivity matrix" which is incorporated into a cost function whose minimum is searched for using a simulated annealing algorithm. The algorithm was extensively tested on over 150 zeolite frameworks from the International Zeolite Association database of zeolite structures and shown to be very robust and efficient in reconstructing the structures from connectivity information. The structure determination of the pure silica zeolites ITQ-4, Ferrierite, and Sigma-2 from experimental 2D (29)Si double-quantum NMR spectra and powder X-ray diffraction data using this improved approach is also presented.

Multiple-quantum spin counting in magic-angle-spinning NMR via low-power symmetry-based dipolar recoupling

By using a symmetry-based R2(8)(1)R2(8)(-1) double-quantum (2Q) dipolar recoupling sequence, we demonstrate high-order multiple-quantum coherence (MQC) excitation at fast magic-angle spinning (MAS) frequencies up to 34 kHz. This scheme combines several attractive features, such as a relatively high dipolar scaling factor, good compensation to rf-errors, isotropic and anisotropic chemical shifts, as well as an ultra-low radio-frequency (rf) power requirement. The latter translates into nutation frequencies below 30 kHz for MAS rates up to 60 kHz, thereby permitting rf application for very long excitation periods without risk of damaging the NMR probehead or sample, while the compensation to chemical shifts improves as the MAS rate increases. (31)P MQC spin counting is demonstrated on powders of calcium hydroxyapatite (Ca5(PO4)3OH) and anhydrous sodium diphosphate (Na4P2O7), from which all even coherence orders up to 30 and 14 were detected, respectively, over the respective MAS ranges of 15-24 kHz and 20-34 kHz. The amplitude distributions among the (31)P MQC orders depend on the precise nutation frequency during recoupling, despite that the highest detected order was relatively insensitive to this parameter. An observed gradual transition from a Gaussian to exponential functionality of the MQC amplitude-profile is discussed in relation to the prevailing approach to derive spin-cluster sizes by fitting the MQC amplitude-distribution to a Gaussian decay, where minor systematic deviations between the model and experimental data are frequently reported.

Anisotropic nuclear spin interactions in H₂O@C₆₀ determined by solid-state NMR

We report a solid-state NMR study of the anisotropic nuclear spin interactions in H₂O@C₆₀ at room temperature. We find evidence of significant dipole-dipole interactions between the water protons, and also a proton chemical shift anisotropy (CSA) interaction. The principal axes of these interaction tensors are found to be perpendicular. The magnitude of the CSA is too large to be explained by a model in which the water molecules are partially aligned with respect to an external axis. The evidence indicates that the observed CSA is caused by a distortion of the geometry or electronic structure of the fullerene cages, in response to the presence of the endohedral water.

A general protocol for determining the structures of molecularly ordered but noncrystalline silicate frameworks

A general protocol is demonstrated for determining the structures of molecularly ordered but noncrystalline solids, which combines constraints provided by X-ray diffraction (XRD), one- and two-dimensional solid-state nuclear magnetic resonance (NMR) spectroscopy, and first-principles quantum chemical calculations. The approach is used to determine the structure(s) of a surfactant-directed layered silicate with short-range order in two dimensions but without long-range periodicity in three-dimensions (3D). The absence of long-range 3D molecular order and corresponding indexable XRD reflections precludes determination of a space group for this layered silicate. Nevertheless, by combining structural constraints obtained from solid-state (29)Si NMR analyses, including the types and relative populations of distinct (29)Si sites, their respective (29)Si-O-(29)Si connectivities and separation distances, with unit cell parameters (though not space group symmetry) provided by XRD, a comprehensive search of candidate framework structures leads to the identification of a small number of candidate structures that are each compatible with all of the experimental data. Subsequent refinement of the candidate structures using density functional theory calculations allows their evaluation and identification of "best" framework representations, based on their respective lattice energies and quantitative comparisons between experimental and calculated (29)Si isotropic chemical shifts and (2)J((29)Si-O-(29)Si) scalar couplings. The comprehensive analysis identifies three closely related and topologically equivalent framework configurations that are in close agreement with all experimental and theoretical structural constraints. The subtle differences among such similar structural models embody the complexity of the actual framework(s), which likely contain coexisting or subtle distributions of structural order that are intrinsic to the material.

Structure solution of network materials by solid-state NMR without knowledge of the crystallographic space group

An algorithm is presented for solving the structures of silicate network materials such as zeolites or layered silicates from solid-state (29)Si double-quantum NMR data for situations in which the crystallographic space group is not known. The algorithm is explained and illustrated in detail using a hypothetical two-dimensional network structure as a working example. The algorithm involves an atom-by-atom structure building process in which candidate partial structures are evaluated according to their agreement with Si-O-Si connectivity information, symmetry restraints, and fits to (29)Si double quantum NMR curves followed by minimization of a cost function that incorporates connectivity, symmetry, and quality of fit to the double quantum curves. The two-dimensional network material is successfully reconstructed from hypothetical NMR data that can be reasonably expected to be obtained for real samples. This advance in "NMR crystallography" is expected to be important for structure determination of partially ordered silicate materials for which diffraction provides very limited structural information.

Genetic algorithms and solid state NMR pulse sequences

The use of genetic algorithms for the optimisation of magic angle spinning NMR pulse sequences is discussed. The discussion uses as an example the optimisation of the C7(2)(1) dipolar recoupling pulse sequence, aiming to achieve improved efficiency for spin systems characterised by large chemical shielding anisotropies and/or small dipolar coupling interactions. The optimised pulse sequence is found to be robust over a wide range of parameters, requires only minimal a priori knowledge of the spin system for experimental implementations with buildup rates being solely determined by the magnitude of the dipolar coupling interaction, but is found to be less broadbanded than the original C7(2)(1) pulse sequence. The optimised pulse sequence breaks the synchronicity between r.f. pulses and sample spinning.

Compensated second-order recoupling: application to third spin assisted recoupling

We consider the effect of phase shifts in the context of second-order recoupling techniques in solid-state NMR. Notably we highlight conditions leading to significant improvements for the Third Spin Assisted Recoupling (TSAR) mechanism and demonstrate the benefits of resulting techniques for detecting long-distance transfer in biomolecular systems. The modified pulse sequences of PAR and PAIN-CP, Phase-Shifted Proton Assisted Recoupling (AH-PS-PAR) and Phase-Shifted Proton-Assisted Insensitive Nuclei Cross Polarization (ABH-PS-PAIN-CP), still rely on cross terms between heteronuclear dipolar couplings involving assisting protons that mediate zero-quantum polarization transfer between low-γ nuclei ((13)C-(13)C, (15)N-(15)N, (15)N-(13)C polarization transfer). Using Average Hamiltonian Theory we show that phase inversion compensates off-resonance contributions and yields improved polarization transfer as well as substantial broadening of the matching conditions. PS-TSAR greatly improves on the standard TSAR based methods because it alleviates their sensitivity to precise RF settings which significantly enhances robustness of the experiments. We demonstrate these new methods on a 19.6 kDa protein (U-[(15)N, (13)C]-YajG) at high magnetic fields (up to 900 MHz (1)H frequency) and fast sample spinning (up to 65 kHz MAS frequency).

Pulse-transient adapted C-symmetry pulse sequences

In solid-state NMR, pulse sequences make often use of pulses which are short compared to the recovery time of the probe head. Especially, rotorsynchronized dipolar recoupling experiments under magic-angle-spinning conditions can profit from the use of very high pulse amplitudes which in turn will reduce the length of the individual pulses. In this contribution we show that C-symmetry based pulse sequences used for double-quantum filtering experiments can strongly be influenced by pulse transients. We analyze the origin of pulse transients and show that the quadrature component can be minimized by cable-length variation which causes a mutual cancellation of probe-external and internal contributions. We implement and test a model to investigate the influence of pulse-transients by numerically exact calculations of the spin-density matrix allowing for composite pulses consisting of slices which are short compared to the circuit recovery time-constant. Moreover we introduce a phase-tuned C-element, which can be applied to γ-encoded experiments from the C-symmetry class, to reconstitute an almost ideal performance of the sequence. We have validated the modified transient-adapted pulse sequences theoretically on the basis of numerically exact calculations of the spin-dynamics. While comparably easy to apply the scheme proved also robust in practical application to (15)N, (13)C and (31)P double-quantum filtered experiments and leads to a significantly increased conversion efficiency.

Solid state NMR of porous materials : zeolites and related materials

Solid state NMR spectroscopy applied to the science of crystalline micro- and mesoporous silica materials over the past 10 years is reviewed. A survey is provided of framework structure and connectivity analyses from chemical shift effects of various elements in zeolites including heteroatom substitutions, framework defects and pentacoordinated silicon for zeolites containing fluoride ions. New developments in the field of NMR crystallography are included. Spatial host-guest ordering and confinement effects of zeolite-sorbate complexes are outlined, with special emphasis on NMR applications utilizing the heteronuclear dipolar interaction. The characterization of zeolite acid sites and in situ NMR on catalytic conversions is also included. Finally, the motion of extra-framework cations is investigated in two tutorial cases of sodium hopping in sodalite and cancrinite.

Double-quantum NMR spectroscopy of 31P species submitted to very large CSAs

We introduce an original pulse sequence, BR2(2)(1)(taupitau), which is a block super-cycled R2(2)(1) sequence employing as basic element a pi pulse sandwiched by 'window' intervals. This homonuclear dipolar recoupling method allows the efficient excitation of double-quantum coherences between spin-1/2 nuclei submitted to very large chemical shift anisotropy. We demonstrate that this technique can be employed in double-quantum<-->single-quantum (31)P homonuclear correlation experiment at high magnetic field (B(0)>or=14 T) and high MAS frequencies (nu(R)>or=30 kHz). The performances of BR2(2)(1)(taupitau) are compared to those of the double-quantum recoupling methods, such as BABA and bracketed fp-RFDR, which were already employed at fast MAS rates. The BR2(2)(1)(taupitau) sequence displays a higher robustness to CSA and offset than the other existing techniques.

Supercycled symmetry-based double-quantum dipolar recoupling of quadrupolar spins in MAS NMR: I. Theory

Using average Hamiltonian (AH) theory, we analyze recently introduced homonuclear dipolar recoupling pulse sequences for exciting central-transition double-quantum coherences (2QC) between half-integer spin quadrupolar nuclei undergoing magic-angle-spinning. Several previously observed differences among the recoupling schemes concerning their compensation to resonance offsets and radio-frequency (rf) inhomogeneity may qualitatively be rationalized by an AH analysis up to third perturbation order, despite its omission of first-order quadrupolar interactions. General aspects of the engineering of 2Q-recoupling pulse sequences applicable to half-integer spins are discussed, emphasizing the improvements offered from a diversity of supercycles providing enhanced suppression of undesirable AH cross-terms between resonance offsets and rf amplitude errors.

Comparison of several hetero-nuclear dipolar recoupling NMR methods to be used in MAS HMQC/HSQC

We compare several hetero-nuclear dipolar recoupling sequences available for HMQC or HSQC experiments applied to spin-1/2 and quadrupolar nuclei. These sequences, which are applied to a single channel, are based either on the rotary resonance recoupling (R3) irradiation, or on two continuous rotor-synchronized modulations (SFAM1 and SFAM2), or on four symmetry-based sequences (R2(1)1,SR4(1)2,R12(3)5,R20(5)9), or on the REDOR scheme. We analyze systems exhibiting purely hetero-nuclear dipolar interactions as well as systems where homo-nuclear dipolar interactions need to be canceled. A special attention is given to the behavior of these sequences at very fast MAS. It is shown that R3 methods behave poorly due to the narrowness of their rf-matching curves, and that the best methods are SR4(1)2 and SFAM (SFAM1 or SFAM2 if homo-nuclear interactions are not negligible). REDOR can also recouple efficiently hetero-nuclear dipolar interactions, provided the sequence is sent on the non-observed channel and homo-nuclear dipolar interactions are negligible. We anticipate that at ultra-fast spinning speed, SFAM1 and SFAM2 will be the most efficient methods.

Analytical theory of gamma-encoded double-quantum recoupling sequences in solid-state nuclear magnetic resonance

Many important double-quantum recoupling techniques in solid-state NMR are classified as being gamma-encoded. This means that the phase of the double-quantum effective Hamiltonian, but not its amplitude, depends on the third Euler angle defining the orientation of the molecular spin system in the frame of the magic-angle-spinning rotor. In this paper, we provide closed analytical solutions for the dependence of the powder-average double-quantum-filtered signal on the recoupling times, within the average Hamiltonian approximation for gamma-encoded pulse sequences. The validity of the analytical solutions is tested by numerical simulations. The internuclear distance in a (13)C(2)-labelled retinal is estimated by fitting the analytical curves to experimental double-quantum data.

A double quantum (129)Xe NMR experiment for probing xenon in multiply-occupied cavities of solid-state inclusion compounds

A method is presented for detecting multiple xenon atoms in cavities of solid-state inclusion compounds using (129)Xe double quantum NMR spectroscopy. Double quantum filtered (129)Xe NMR spectra, performed on the xenon clathrate of Dianin's compound were obtained under high-resolution Magic-Angle Spinning (MAS) conditions, by recoupling the weak (129)Xe-(129)Xe dipole-dipole couplings that exist between xenon atoms in close spatial proximity. Because the (129)Xe-(129)Xe dipole-dipole couplings are generally weak due to dynamics of the atoms and to large internuclear separations, and since the (129)Xe Chemical Shift Anisotropy (CSA) tends to be relatively large, a very robust dipolar recoupling sequence was necessary, with the symmetry-based SR26 dipolar recoupling sequence proving appropriate. We have also attempted to measure the (129)Xe-(129)Xe dipole-dipole coupling constant between xenon atoms in the cavities of the xenon-Dianin's compound clathrate and have found that the dynamics of the xenon atoms (as investigated with molecular dynamics simulations) as well as (129)Xe multiple spin effects complicate the analysis. The double quantum NMR method is useful for peak assignment in (129)Xe NMR spectra because peaks arising from different types of absorption/inclusion sites or from different levels of occupancy of single sites can be distinguished. The method can also help resolve ambiguities in diffraction experiments concerning the order/disorder in a material.

Spherical tensor analysis of nuclear magnetic resonance signals

In a nuclear magnetic-resonance (NMR) experiment, the spin density operator may be regarded as a superposition of irreducible spherical tensor operators. Each of these spin operators evolves during the NMR experiment and may give rise to an NMR signal at a later time. The NMR signal at the end of a pulse sequence may, therefore, be regarded as a superposition of spherical components, each derived from a different spherical tensor operator. We describe an experimental method, called spherical tensor analysis (STA), which allows the complete resolution of the NMR signal into its individual spherical components. The method is demonstrated on a powder of a (13)C-labeled amino acid, exposed to a pulse sequence generating a double-quantum effective Hamiltonian. The propagation of spin order through the space of spherical tensor operators is revealed by the STA procedure, both in static and rotating solids. Possible applications of STA to the NMR of liquids, liquid crystals, and solids are discussed.

Solid-state NMR of endohedral hydrogen–fullerene complexes

We present an overview of solid-state NMR studies of endohedral H(2)-fullerene complexes, including (1)H and (13)C NMR spectra, (1)H and (13)C spin relaxation studies, and the results of (1)H dipole-dipole recoupling experiments. The available data involves three different endohedral H(2)-fullerene complexes, studied over a wide range of temperatures and applied magnetic fields. The symmetry of the cage influences strongly the motionally-averaged nuclear spin interactions of the endohedral H(2) species, as well as its spin relaxation behaviour. In addition, the non-bonding interactions between fullerene cages are influenced by the presence of endohedral hydrogen molecules. The review also presents several pieces of experimental data which are not yet understood, one example being the structured (1)H NMR lineshapes of endohedral H(2) molecules trapped in highly symmetric cages at cryogenic temperatures. This review demonstrates the richness of NMR phenomena displayed by H(2)-fullerene complexes, especially in the cryogenic regime.

Sensitivity Enhancement and Heteronuclear Distance Measurements in Biological 17O Solid-State NMR

In this contribution we present a comprehensive approach to study hydrogen bonding in biological and biomimetic systems through 17O and 17O-1H solid-state NMR combined with density functional theory calculations of 17O and 1H NMR parameters. We explore the signal enhancement of 17O in L-tyrosine.HCl using repetitive double-frequency swept radio frequency pulses in solid-state NMR. The technique is compatible with high magnetic fields and fast magic-angle spinning of the sample. A maximum enhancement by a factor of 4.3 is obtained in the signal-to-noise ratio of the selectively excited 17O central transition in a powdered sample of 17Oeta-L-tyrosine.HCl at an external field of 14.1 T and a spinning frequency of 25 kHz. As little as 128 transients lead to meaningful 17O spectra of the same sample at an external field of 18.8 T and a spinning frequency of 50 kHz. Furthermore we employed supercycled symmetry-based pulse sequences on the protons to achieve heteronuclear longitudinal two-spin-order (IzSz) recoupling to determine 17O-1H distances. These sequences recouple the heteronuclear dipolar 17O-1H couplings, where dipolar truncation is absent, while decoupling the homonuclear proton dipolar interactions. They can be applied at fast magic-angle-spinning frequencies up and beyond 50 kHz and are very robust with respect to 17O quadrupolar couplings and both 17O and 1H chemical shift anisotropies, which makes them suitable for the use at high external magnetic fields. The method is demonstrated by determining the 17Oeta-1H distance in L-tyrosine.HCl at a spinning frequency of 50 kHz and an external field of 18.8 T.

Theory and applications of supercycled symmetry-based recoupling sequences in solid-state nuclear magnetic resonance

We present the theoretical principles of supercycled symmetry-based recoupling sequences in solid-state magic-angle-spinning NMR. We discuss the construction procedure of the SR26 pulse sequence, which is a particularly robust sequence for double-quantum homonuclear dipole-dipole recoupling. The supercycle removes destructive higher-order average Hamiltonian terms and renders the sequence robust over long time intervals. We demonstrate applications of the SR26 sequence to double-quantum spectroscopy, homonuclear spin counting, and determination of the relative orientations of chemical shift anisotropy tensors.