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.     

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.     

Efficient symmetry-based homonuclear dipolar recoupling of quadrupolar spins: double-quantum NMR correlations in amorphous solids

We report novel symmetry-based pulse sequences for exciting double-quantum (2Q) coherences between the central transitions of half-integer spin quadrupolar nuclei in the NMR of rotating solids. Compared to previous 2Q-recoupling techniques, numerical simulations and 23Na and 27Al NMR experiments on Na2SO4 and the open-framework aluminophosphate AlPO-CJ19 verify that the new dipolar recoupling schemes display higher robustness to both radio-frequency field inhomogeneity and to spreads in resonance frequencies. These advances allowed for the first demonstration of 2Q-recoupling in an amorphous solid for revealing its intermediate-range structural features, in the context of mapping 27Al-27Al connectivities between the aluminium polyhedra (AlO4, AlO5 and AlO6) of a lanthanum aluminate glass (La0.18Al0.82O1.5).     

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.     

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 29Si dipolar recoupling magic angle spinning NMR spectroscopy: a new method for investigating three-dimensional structures of zeolite frameworks

A new 29Si solid-state MAS NMR experiment is described for investigating the framework structures of pure silica zeolites. The symmetry-based homonuclear dipolar recoupling sequence SR26411 has been incorporated into a two-dimensional NMR experiment to probe the Si-O-Si bonding connectivities and long-range Si-Si distances in zeolite frameworks. This dipolar recoupling sequence is shown to have a number of advantages over the J-coupling-based INADEQUATE experiment. For the clathrasil Sigma-2, it is demonstrated that there is excellent agreement between experimental double-quantum build-up curves obtained from a series of two-dimensional double-quantum correlation spectra and simulated curves which consider all Si-Si distances out to 8 A. This result suggests that this experiment could be used to solve zeolite frameworks with unknown structures.     

Reintroducing anisotropic interactions in magic-angle-spinning NMR of half-integer quadrupolar nuclei: 3D MQMAS

Selective reintroduction of anisotropic interactions such as the chemical shift anisotropy (CSA) and homonucler dipolar (HMD) coupling were implemented in a high-resolution NMR spectroscopy for half-integer quadrupolar nuclei. Rotary resonance recoupling (R(3)) combined with the multiple-quantum magic-angle spinning (MQMAS) in a three-dimensional (3D) experiment provides not only site-specific high-resolution spectra to yield the quadrupolar interaction parameters but also the CSA or HMD interaction parameters. This 3D experiment provides an avenue for the complete local structural information of half-integer quadrupolar nuclei. Three-dimensional MQMAS experiments incorporating R(3) of HMD and CSA interactions were demonstrated on model compounds containing (11)B, (23)Na, and (87)Rb nuclei.     

Composite dipolar recoupling: anisotropy compensated coherence transfer in solid-state nuclear magnetic resonance

The efficiency of dipole-dipole coupling driven coherence transfer experiments in solid-state nuclear magnetic resonance (NMR) spectroscopy of powder samples is limited by dispersion of the orientation of the internuclear vectors relative to the external magnetic field. Here we introduce general design principles and resulting pulse sequences that approach full polarization transfer efficiency for all crystallite orientations in a powder in magic-angle-spinning experiments. The methods compensate for the defocusing of coherence due to orientation dependent dipolar coupling interactions and inhomogeneous radio-frequency fields. The compensation scheme is very simple to implement as a scaffold (comb) of compensating pulses in which the pulse sequence to be improved may be inserted. The degree of compensation can be adjusted and should be balanced as a compromise between efficiency and length of the overall pulse sequence. We show by numerical and experimental data that the presented compensation protocol significantly improves the efficiency of known dipolar recoupling solid-state NMR experiments.     

Heteronuclear recoupling in solid-state magic-angle-spinning NMR via overtone irradiation

A heteronuclear dipolar recoupling scheme applicable to I-S spin pairs undergoing magic-angle-spinning (MAS) is introduced, based on the overtone irradiation of one of the coupled nuclei. It is shown that when I is a quadrupole, for instance (14)N, irradiating this spin at a multiple of its Larmor frequency prevents the formation of MAS dipolar echoes. The ensuing S-spin signal dephasing is significant and dependent on a number of parameters, including the I-S dipolar coupling, the magnitude of I's quadrupolar coupling, and the relative orientations between these two coupling tensors. When applied to a spin-1 nucleus, this overtone recoupling method differs from hitherto proposed recoupling strategies in that it involves only the +/-1> I(z) eigenstates. Its dephasing efficiency becomes independent of first-order quadrupolar effects yet shows a high sensitivity to second-order offsets. A constant-time/variable-offset recoupling sequence thus provides a simple route to acquire, in an indirect fashion, (14)N overtone spectra from rotating powders. The principles underlying this kind of S-(14)N experiments and different applications involving S = (13)C, (59)Co sites are presented.     

Residual Dipolar Couplings in 31P MAS Spectra of P Ph 3 Substituted Cobalt Complexes

 Residual dipolar couplings between ³¹P–⁵⁹Co spin pairs were studied in ³¹P MAS spectra of mono- and dinuclear cobalt-triphenylphosphine complexes. These spectra can provide important informations such as the scalar coupling between the dipolar phosphorus and the quadrupolar cobalt nuclei normally not available from solution phase studies. In case of complementary (NQR or X-ray) data even the relative orientation of the interacting shielding, dipolar, scalar couplings, and electric field gradient tensors or internuclear distances can be determined. Examples are shown both for well resolved and practically unresolved cases, factors which possibly control the spectral resolution are discussed in detail.     

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.     

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.     

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.     

Spin diffusion between inequivalent quadrupolar nuclei by double-quantum flip-flops

A new mechanism for spin diffusion between quadrupolar nuclei whose NMR lines do not overlap is proposed. For spin-1 nuclei, double-quantum flip-flop transitions allow the diffusion of Zeeman order, but not quadrupolar order, without requiring an extraneous energy reservoir. The flip-flop rate is sensitive to the relative signs of the quadrupolar splittings.     

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.     

Residual Dipolar Couplings in 31P MAS Spectra of PPh 3 Substituted Cobalt Complexes

Summary.  Residual dipolar couplings between ³¹P–⁵⁹Co spin pairs were studied in ³¹P MAS spectra of mono- and dinuclear cobalt-triphenylphosphine complexes. These spectra can provide important informations such as the scalar coupling between the dipolar phosphorus and the quadrupolar cobalt nuclei normally not available from solution phase studies. In case of complementary (NQR or X-ray) data even the relative orientation of the interacting shielding, dipolar, scalar couplings, and electric field gradient tensors or internuclear distances can be determined. Examples are shown both for well resolved and practically unresolved cases, factors which possibly control the spectral resolution are discussed in detail. E-mail: gabor.szalontai@sparc4.mars.vein.hu Received June 7, 2002; accepted June 29, 2002     

Measurement of 13C-1H dipolar couplings in solids by using ultra-fast magic-angle spinning NMR spectroscopy with symmetry-based sequences

We show that (13)C-(1)H dipolar couplings in fully protonated organic solids can be measured by applying a Symmetry-based Resonance-Echo DOuble-Resonance (S-REDOR) experiment at ultra-fast Magic-Angle Spinning (MAS). The (13)C-(1)H dipolar couplings are recovered by using the R12 recoupling scheme, while the interference of (1)H-(1)H dipolar couplings are suppressed by the symmetry properties of this sequence and the use of high MAS frequency (65 kHz). The R12 method is especially advantageous for large (13)C-(1)H dipolar interactions, since the dipolar recoupling time can be incremented by steps as short as one rotor period. This allows a fine sampling for the rising part of the dipolar dephasing curve. We demonstrate experimentally that one-bond (13)C-(1)H dipolar coupling in the order of 22 kHz can be accurately determined. Furthermore, the proposed method allows a rapid evaluation of the dipolar coupling by fitting the S-REDOR dipolar dephasing curve with an analytical expression.     

Ishtar: An interactive system for quantitative investigation on dipolar and quadrupolar spin-lattice relaxation

Within the model of anisotropic rotational diffusion, the quantitative treatment of dipolar and quadrupolar spin-lattice relaxation provides valuable information about molecular structures and molecular associations. When quadrupolar relaxation is involved, the title program calculates: (1) the electric field gradient tensor (EFGT) which is diagonalized; (2) the assymetry parameter, the components of the principal axes of the EFGT in the molecular frame of reference and the quadrupole coupling constant; and (3) the rotational diffusion constants which are iteratively determined from the experimental quadrupolar relaxation times. Analogously, for dipolar relaxation ISHTAR calculates the tensor of inertia, the diagonalization of which leads to diffusion constants and free rotor correlation times and the rotational diffusion constants from the experimental spectral densities.     

Separate-local-field NMR spectroscopy on half-integer quadrupolar nuclei

New approaches to the characterization of resonances in the solid-state NMR spectroscopy of half-integer quadrupolar nuclei are explored, on the basis of the acquisition of heteronuclear separate-local-field spectra on rotating solids. In their two-dimensional version, these experiments correlate for each chemical site a second-order quadrupolar MAS powder pattern with the dipolar MAS sideband pattern to nearby heteronuclei. As 3D NMR sequences, such 2D anisotropic correlation spectra become separated for inequivalent chemical sites along a third, isotropic dimension. Extending in such manner separate-local-field NMR approaches to quadrupoles facilitates the assignment of inequivalent resonances to specific structural environments, and provides new tools for the investigation of dynamics in solids. Details about these 2D and 3D NMR experiments are given, and their application is illustrated with 1H-23Na recoupling experiments on mononucleotides possessing multiple bound cations.     

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.