Double-quantum homonuclear correlation magic angle sample spinning nuclear magnetic resonance spectroscopy of dipolar-coupled quadrupolar nuclei

A double-quantum homonuclear correlation nuclear magnetic resonance experiment for dipolar-coupled half-integer quadrupolar nuclei in solids is presented. The experiment is based on rotary resonance dipolar recoupling and uses bracketed spin-lock pulses to excite double-quantum coherence and later to convert it to the zero-quantum one. A central-transition-selective pi pulse at the beginning of the t1 evolution period differentiates coherence transfer pathways of double-quantum coherences arising from coupled spins and from a single spin, so that the latter can be efficiently filtered out by phase cycling. The experiment was tested on an aluminophosphate molecular sieve AlPO4-14, a material with a variety of aluminum quadrupolar coupling constants, isotropic chemical shifts and homonuclear distances. In a two-dimensional spectrum aluminum dipolar couplings with internuclear distances between 2.9 and 5.5 A were resolved. Although the experiment requires an application of weak radio-frequency fields, frequency offsets did not affect its performance crucially.     

Triple oscillating field technique for accurate distance measurements by solid-state NMR

We present a new concept for homonuclear dipolar recoupling in magic-angle-spinning (MAS) solid-state NMR experiments which avoids the problem of dipolar truncation. This is accomplished through the introduction of a new NMR pulse sequence design principle: the triple oscillating field technique. We demonstrate this technique as an efficient means to accomplish broadband dipolar recoupling of homonuclear spins, while decoupling heteronuclear dipolar couplings and anisotropic chemicals shifts and retaining influence from isotropic chemical shifts. In this manner, it is possible to synthesize Ising interaction (2IzSz) Hamiltonians in homonuclear spin networks and thereby avoid dipolar truncation--a serious problem essentially all previous homonuclear dipolar recoupling experiments suffer from. Combination of this recoupling concept with rotor assisted dipolar refocusing enables easy readout of internuclear distances through comparison with analytical Fresnel curves. This forms the basis for a new class of solid-state NMR experiments with potential for structure analysis of uniformly 13C labeled proteins through accurate measurement of 13C-13C internuclear distances. The concept is demonstrated experimentally by measurement of C alpha-C', C beta-C', and C gamma-C' internuclear distances in powder samples of the amino acids L-alanine and L-threonine.     

1H and 19F ultra-fast MAS double-quantum single-quantum NMR correlation experiments using three-spin terms of the dipolar homonuclear Hamiltonian

Measuring internuclear distances through dipolar interaction is a major challenge for solid-state nuclear magnetic resonance (NMR) spectroscopy. Obtaining reliable interatomic distances provides an access to the local structure in ordered or disordered solids. We show that at magic angle spinning (MAS) frequencies larger than ca. 50 kHz, some of the three-spin terms of the homogeneous homonuclear dipolar Hamiltonian can be used to promote the creation of double-quantum coherences between neighbouring (1)H or (19)F spins without using dipolar recoupling pulse sequences in the Dipolar Homonuclear Homogeneous Hamiltonian (DH(3)) double-quantum/single-quantum correlation experiment. This makes it possible to probe inter-nuclear spatial proximity with limited risk of probe or sample damage from radio-frequency (RF) irradiation, and is fully appropriate for fast repetition rate offering sensitivity gains in favourable cases. Experimental demonstrations are supported by multi-spin numerical simulations, which points to new possibilities for the characterization of spin-system geometries.     

A solid-state NMR method for solution of zeolite crystal structures

Since zeolites are notoriously difficult to prepare as large single crystals, structure determination usually relies on powder X-ray diffraction (XRD). However, structure solution (i.e., deriving an initial structural model) directly from powder XRD data is often very difficult due to the diffraction phase problem and the high degree of overlap between the individual reflections, particularly for materials with the structural complexity of most zeolites. Here, we report a method for structure determination of zeolite crystal structures that combines powder XRD and nuclear magnetic resonance (NMR) spectroscopy in which the crucial step of structure solution is achieved using solid-state (29)Si double-quantum dipolar recoupling NMR, which probes the distance-dependent dipolar interactions between naturally abundant (29)Si nuclei in the zeolite framework. For two purely siliceous zeolite blind test samples, we demonstrate that the NMR data can be combined with the unit cell parameters and space group to solve structural models that refine successfully against the powder XRD data.     

Frequency-selective homonuclear dipolar recoupling in solid state NMR

We introduce a new approach to frequency-selective homonuclear dipolar recoupling in solid state nuclear magnetic resonance (NMR) with magic-angle spinning (MAS). This approach, to which we give the acronym SEASHORE, employs alternating periods of double-quantum recoupling and chemical shift evolution to produce phase modulations of the recoupled dipole-dipole interactions that average out undesired couplings, leaving only dipole-dipole couplings between nuclear spins with a selected pair of NMR frequencies. In principle, SEASHORE is applicable to systems with arbitrary coupling strengths and arbitrary sets of NMR frequencies. Arbitrary MAS frequencies are also possible, subject only to restrictions imposed by the pulse sequence chosen for double-quantum recoupling. We demonstrate the efficacy of SEASHORE in experimental (13)C NMR measurements of frequency-selective polarization transfer in uniformly (15)N, (13)C-labeled L-valine powder and frequency-selective intermolecular polarization transfer in amyloid fibrils formed by a synthetic decapeptide containing uniformly (15)N, (13)C-labeled residues.     

Measuring distances between half-integer quadrupolar nuclei and detecting relative orientations of quadrupolar and dipolar tensors by double-quantum homonuclear dipolar recoupling nuclear magnetic resonance experiments

We studied the possibility of using double-quantum homonuclear dipolar recoupling magic angle spinning nuclear magnetic resonance experiments for structural analysis of systems of half-integer quadrupolar nuclei. We investigated symmetry-based recoupling schemes R2(2) (1) and R2(2) (1)R2(2) (-1) and showed that the obtained double-quantum filtered signals depend substantially on magnitudes and relative orientations of dipolar and quadrupolar tensors. Experimental results measured on aluminophosphate molecular sieve AlPO(4)-14, containing dipolar-coupled spin-52 aluminum nuclei, were compared to results of time-consuming numerical simulations. The comparison for short mixing times allowed us to roughly measure internuclear Al-Al distances, if constraints about relative tensor orientations were available. Inspection of relative orientations of dipolar and quadrupolar tensors, using known distances between nuclei, required experimental and simulated data for long mixing times and yielded less accurate results. Two experimental protocols were employed for measuring double-quantum filtered curves, the symmetric protocol, in which excitation and reconversion periods are incremented simultaneously, and the asymmetric protocol, in which only the length of the excitation period is incremented and the length of the reconversion period is kept constant. The former experimental protocol was more convenient for the detection of internuclear distances, and the latter one was more appropriate for the inspection of relative orientations of interaction tensors.     

Solid-state NMR structural studies of peptides immobilized on gold nanoparticles

In this paper we describe solid-state NMR experiments that provide information on the structures of surface-immobilized peptides. The peptides are covalently bound to alkanethiolates that are self-assembled as monolayers on colloidal gold nanoparticles. The secondary structure of the immobilized peptides was characterized by quantifying the Ramachandran angles phi and psi. These angles were determined in turn from distances between backbone carbonyl 13C spins, measured with the double-quantum filtered dipolar recoupling with a windowless sequence experiment, and by determination of the mutual orientation of chemical shift anisotropy tensors of 13C carbonyl spins on adjacent peptide planes, obtained from the double-quantum cross-polarization magic-angle spinning spectrum. It was found that peptides composed of periodic sequences of leucines and lysines were bound along the length of the peptide sequence and displayed a tight alpha-helical secondary structure on the gold nanoparticles. These results are compared to similar studies of peptides immobilized on hydrophobic surfaces.     

A study of homonuclear dipolar recoupling pulse sequences in solid-state nuclear magnetic resonance

Dipolar recoupling pulse sequences are of great importance in magic angle spinning solid-state NMR. Recoupling sequences are used for excitation of double-quantum coherence, which, in turn, is employed in experiments to estimate internuclear distances and molecular torsion angles. Much effort is spent on the design of recoupling sequences that are able to produce double-quantum coherence with high efficiency in demanding spin systems, i.e., spin systems with small dipole-dipole couplings and large chemical-shift anisotropies (CSAs). The sequence should perform robustly under a variety of experimental conditions. This paper presents experiments and computer calculations that extend the theory of double-quantum coherence preparation from the strong coupling/small CSA limit to the weak coupling limit. The performance of several popular dipole-dipole recoupling sequences-DRAWS, POST-C7, SPC-5, R1, and R2-are compared. It is found that the optimum performance for several of these sequences, in the weak coupling/large CSA limit, varies dramatically, with respect to the sample spinning speed, the magnitude and orientation of the CSAs, and the magnitude of dipole-dipole couplings. It is found that the efficiency of double-quantum coherence preparation by gamma-encoded sequences departs from the predictions of first-order theory. The discussion is supported by density-matrix calculations.     

Effective Hamiltonians by optimal control: solid-state NMR double-quantum planar and isotropic dipolar recoupling

We report the use of optimal control algorithms for tailoring the effective Hamiltonians in nuclear magnetic resonance (NMR) spectroscopy through sophisticated radio-frequency (rf) pulse irradiation. Specifically, we address dipolar recoupling in solid-state NMR of powder samples for which case pulse sequences offering evolution under planar double-quantum and isotropic mixing dipolar coupling Hamiltonians are designed. The pulse sequences are constructed numerically to cope with a range of experimental conditions such as inhomogeneous rf fields, spread of chemical shifts, the intrinsic orientation dependencies of powder samples, and sample spinning. While the vast majority of previous dipolar recoupling sequences are operating through planar double-or zero-quantum effective Hamiltonians, we present here not only improved variants of such experiments but also for the first time homonuclear isotropic mixing sequences which transfers all I(x), I(y), and I(z) polarizations from one spin to the same operators on another spin simultaneously and with equal efficiency. This property may be exploited to increase the signal-to-noise ratio of two-dimensional experiments by a factor of square root 2 compared to conventional solid-state methods otherwise showing the same efficiency. The sequences are tested numerically and experimentally for a powder of (13)C(alpha),(13)C(beta)-L-alanine and demonstrate substantial sensitivity gains over previous dipolar recoupling experiments.     

Structure-directing roles and interactions of fluoride and organocations with siliceous zeolite frameworks

Interactions of fluoride anions and organocations with crystalline silicate frameworks are shown to depend subtly on the architectures of the organic species, which significantly influence the crystalline structures that result. One- and two-dimensional (2D) (1)H, (19)F, and (29)Si nuclear magnetic resonance (NMR) spectroscopy measurements establish distinct intermolecular interactions among F(-) anions, imidazolium structure-directing agents (SDA(+)), and crystalline silicate frameworks for as-synthesized siliceous zeolites ITW and MTT. Different types and positions of hydrophobic alkyl ligands on the imidazolium SDA(+) species under otherwise identical zeolite synthesis compositions and conditions lead to significantly different interactions between the F(-) and SDA(+) ions and the respective silicate frameworks. For as-synthesized zeolite ITW, F(-) anions are established to reside in the double-four-ring (D4R) cages and interact strongly and selectively with D4R silicate framework sites, as manifested by their strong (19)F-(29)Si dipolar couplings. By comparison, for as-synthesized zeolite MTT, F(-) anions reside within the 10-ring channels and interact relatively weakly with the silicate framework as ion pairs with the SDA(+) ions. Such differences manifest the importance of interactions between the imidazolium and F(-) ions, which account for their structure-directing influences on the topologies of the resulting silicate frameworks. Furthermore, 2D (29)Si{(29)Si} double-quantum NMR measurements establish (29)Si-O-(29)Si site connectivities within the as-synthesized zeolites ITW and MTT that, in conjunction with synchrotron X-ray diffraction analyses, establish insights on complicated order and disorder within their framework structures.     

Determination of peptide backbone torsion angles using double-quantum dipolar recoupling solid-state NMR spectroscopy

Several approaches for utilizing dipolar recoupling solid-state NMR (ssNMR) techniques to determine local structure at high resolution in peptides and proteins have been developed. However, many of these techniques measure only one torsion angle or are accurate for only certain classes of secondary structure. Additionally, the efficiency with which these dipolar recoupling experiments suppress the deleterious effects of chemical shift anisotropy (CSA) at high magnetic field strengths varies. Dipolar recoupling with a windowless sequence (DRAWS) has proven to be an effective pulse sequence for exciting double-quantum (DQ) coherences between adjacent carbonyl carbons along the peptide backbone. By allowing this DQ coherence to evolve, it is possible to measure the relative orientations of the CSA tensors and subsequently use this information to determine the Ramachandran torsion angles phi and psi. Here, we explore the accuracies of the assumptions made in interpreting DQ-DRAWS data and demonstrate their fidelity in measuring torsion angles corresponding to a variety of secondary structures irrespective of hydrogen-bonding patterns. It is shown how a simple choice of isotopic labels and experimental conditions allows accurate measurement of backbone secondary structures without any prior knowledge. This approach is considerably more sensitive for determining structure in helices and has comparable accuracy for beta-sheet and extended conformations relative to other methods. We also illustrate the ability of DQ-DRAWS to distinguish between structures in heterogeneous samples.     

Symmetry-based constant-time homonuclear dipolar recoupling in solid state NMR

Constant-time dipolar recoupling pulse sequences are advantageous in structural studies by solid state nuclear magnetic resonance (NMR) with magic-angle spinning (MAS) because they yield experimental data that are relatively insensitive to radio-frequency pulse imperfections and nuclear spin relaxation processes. A new approach to the construction of constant-time homonuclear dipolar recoupling sequences is described, based on symmetry properties of the recoupled dipole-dipole interaction Hamiltonian under cyclic displacements in time with respect to the MAS sample rotation period. A specific symmetry-based pulse sequence called PITHIRDS-CT is introduced and demonstrated experimentally. (13)C NMR data for singly-(13)C-labeled amino acid powders and amyloid fibrils indicate the effectiveness of PITHIRDS-CT in measurements of intermolecular distances in solids. (15)N-detected and (13)C-detected measurements of intramolecular (15)N-(15)N distances in peptides with alpha-helical and beta-sheet structures indicate the utility of PITHIRDS-CT in studies of molecular conformations, especially measurements of backbone psi torsion angles in peptides containing uniformly (15)N- and (13)C-labeled amino acids.     

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.     

Probing local structure in zeolite frameworks: ultrahigh-field NMR measurements and accurate first-principles calculations of zeolite 29Si magnetic shielding tensors

The principal components of zeolite 29Si magnetic shielding tensors have been accurately measured and calculated for the first time. The experiments were performed at an ultrahigh magnetic field of 21.1 T in order to observe the small anisotropies of the 29Si shielding interactions that arise for Si atoms in near-tetrahedral geometries. A robust two-dimensional (2D) chemical shift anisotropy (CSA) recoupling pulse sequence was employed that enables quasi-static powder patterns to be resolved according to the isotropic chemical shifts. For the zeolites Sigma-2 and ZSM-12, it is demonstrated that the 29Si chemical shift (CS) tensor components measured by the recoupling experiment are in excellent agreement with those determined from spinning sidebands in slow magic-angle spinning (MAS) experiments. For the zeolite ZSM-5, the principal components of the 29Si CS tensors of 15 of the 24 Si sites were measured using the 2D CSA recoupling experiment, a feat that would not be possible with a slow MAS experiment due to the complexity of the spectrum. A simple empirical relationship between the 29Si CS tensors and local structural parameters could not be established. However, the 29Si magnetic shielding tensors calculated using Hartree-Fock ab initio calculations on clusters derived from the crystal structures are in excellent agreement with the experimental results. The accuracy of the calculations is strongly dependent on the quality of the crystal structure used in the calculation, indicating that the 29Si magnetic shielding interaction is extremely sensitive to the local structure around each Si atom. It is anticipated that the measurement and calculation of 29Si shielding tensors could be incorporated into the "NMR crystallography" of zeolites and other related silicate materials, possibly being used for structure refinements that may lead to crystal structures with very accurate Si and O atomic coordinates.     

Structure resolution of Ba5Al3F19 and investigation of fluorine ion dynamics by synchrotron powder diffraction, variable-temperature solid-state NMR, and quantum computations

The room temperature structure of Ba(5)Al(3)F(19) has been solved using electron microscopy and synchrotron powder diffraction data. One-dimensional (1D) (27)Al and ultrafast magic-angle-spinning (MAS) (19)F NMR spectra have been recorded and are in agreement with the proposed structural model for Ba(5)Al(3)F(19). The (19)F isotropic chemical shift and (27)Al quadrupolar parameters have been calculated using the CASTEP code from the experimental and density functional theory geometry-optimized structures. After optimization, the calculated NMR parameters of both the (19)F and (27)Al nuclei show improved consistency with the experimental values, demonstrating that the geometry optimization step is necessary to obtain more accurate and reliable structural data. This also enables a complete and unambiguous assignment of the (19)F MAS NMR spectrum of Ba(5)Al(3)F(19). Variable-temperature 1D MAS (19)F NMR experiments have been carried out, showing the occurrence of fluorine ion mobility. Complementary insights were obtained from both two-dimensional (2D) exchange and 2D double-quantum dipolar recoupling NMR experiments, and a detailed analysis of the anionic motion in Ba(5)Al(3)F(19) is proposed, including the distinction between reorientational processes and chemical exchange involving bond breaking and re-formation.     

Determination of long-range distances and dynamic order parameters by dipolar recoupling in high-resolution magic-angle spinning NMR spectroscopy

By introducing dipolar recoupling methods to high-resolution magic-angle spinning (HRMAS) NMR spectroscopy, a class of experiments has been delevoped that allows the measurement of residual dipole-dipole couplings of approximately 1 Hz in weakly immobilized molecules. Using homonuclear 1H-1H recoupling, distances of up to approximately 8 A can be selectively determined, while heteronuclear 1H-13C recoupling provides access to dynamic order parameters of individual molecular segments on the order of approximately 10-3. The experiments are demonstrated on functionalized oligopeptides that are attached to polymer resins.     

Proton-selective 17O-1H distance measurements in fast magic-angle-spinning solid-state NMR spectroscopy for the determination of hydrogen bond lengths

We present a proton-selective method to determine 17O-1H distances in organic, biological, and biomimetic materials by fast magic-angle-spinning solid-state NMR spectroscopy. This method allows the determination of internuclear distances between specific (17O, 1H) spin pairs selectively. It enables the estimation of medium-range 17O...1H distances across hydrogen bonds in the presence of short-range 17O-1H contacts sharing the same 17O site. The method employs the newly developed symmetry-based radiofrequency pulse sequence SR%@mt;sys@%4%@sx@%1%@be@%2%@sxx@%%@mx@% applied to the protons to achieve heteronuclear dipolar recoupling, while simultaneously decoupling the homonuclear proton dipolar interactions. Fast MAS (50 kHz) and high static magnetic fields (18.8 T) achieve the required proton spectral resolution.     

Theory of stochastic dipolar recoupling in solid-state nuclear magnetic resonance

Dipolar recoupling techniques in solid-state nuclear magnetic resonance (NMR) consist of radio frequency (rf) pulse sequences applied in synchrony with magic-angle spinning (MAS) that create nonzero average magnetic dipole-dipole couplings under MAS. Stochastic dipolar recoupling (SDR) is a variant in which randomly chosen rf carrier frequency offsets are introduced to cause random phase modulations of individual pairwise couplings in the dipolar spin Hamiltonian. Several aspects of SDR are investigated through analytical theory and numerical simulations: (1) An analytical expression for the evolution of nuclear spin polarization under SDR in a two-spin system is derived and verified through simulations, which show a continuous evolution from coherent, oscillatory polarization exchange to incoherent, exponential approach to equilibrium as the range of random carrier offsets (controlled by a parameter f(max)) increases; (2) in a many-spin system, polarization transfers under SDR are shown to be described accurately by a rate matrix in the limit of large f(max), with pairwise transfer rates that are proportional to the inverse sixth power of pairwise internuclear distances; (3) quantum mechanical interferences among noncommuting pairwise dipole-dipole couplings, which are a complicating factor in solid-state NMR studies of molecular structures by traditional dipolar recoupling methods, are shown to be absent from SDR data in the limit of large f(max), provided that coupled nuclei have distinct NMR chemical shifts.     

Observing 13C-13C connectivities at high magnetic fields and very high spinning frequencies

We report the application of a dipolar recoupling sequence for the observation of (13)C-(13)C connectivities in biomolecules at high magnetic fields (B(0)≥ 21.1 T) and ultra-high magic angle spinning frequencies (ν(R) = 60 kHz). The efficiency and the robustness of this double-quantum technique are demonstrated on the YajG protein (19.6 kDa).     

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.