The application of MAS recoupling methods in the intermediate motional regime

We present investigations concerning the effect of molecular motions on the experimental timescale upon the recoupling of anisotropic interactions under magic-angle spinning conditions. An approach for the efficient simulation of spin dynamics occurring during complex pulse sequences, based on a linearization of the general solution of the stochastic Liouville-von Neumann equation, was developed. Using (13)C CSA recoupling of the methyl carbon in dimethylsulfon as a sample interaction, we observed a characteristic signal decay under recoupling upon entering the intermediate motional regime, which can be well described by an apparent transverse relaxation time, T(2)(rcpl). This quantity does not depend on the spinning frequency to a first approximation. Specific recoupling experiments, namely the measurement of tensor parameters by spinning sideband analysis, and the determination of rate constants with the CODEX experiment, are discussed with respect to possibilities and limits of their application in the intermediate motional regime. Important conclusions are drawn with regards to the limited applicability of popular recoupling methods like REDOR to samples exhibiting intermediate mobility.     

Measurements of motionally averaged heteronuclear dipolar couplings in MAS NMR using R-type recoupling

A novel MAS NMR approach is presented for the determination of heteronuclear dipolar couplings in unoriented materials. The technique is based on the proton-detected local field (PDLF) protocol, and achieves dipolar recoupling by R-type radio-frequency irradiation. The experiment, which is called R-PDLF spectroscopy, is demonstrated on solid and liquid-crystalline systems. For mobile systems, it is shown that the R-PDLF scheme provides better dipolar resolution as compared to techniques combining conventional separated local field (SLF) spectroscopy with R-type recoupling.     

Sensitivity enhanced recoupling experiments in solid-state NMR by gamma preparation

In this paper, we introduce a class of dipolar recoupling experiments under magic angle spinning (MAS), which use gamma dependent antiphase polarization during the t1 evolution period. We show that this helps us to design dipolar recoupling experiments that transfer both components of the transverse magnetization of spin S to a coupled spin I in the mixing step of a 2D NMR experiment. We show that it is possible to design such transfer schemes and make them insensitive to the orientation dependency of the couplings in powders. This helps us to develop sensitivity enhanced 2D NMR experiments of powder samples under MAS.     

Low-power XiX decoupling in MAS NMR experiments

Low-power XiX proton decoupling under fast magic-angle spinning is introduced. The method is applicable if the MAS frequency exceeds the proton-proton interactions. For rigid organic solids this is the case for MAS frequencies above approximately 40 kHz. It is shown that the quality of the decoupling as well as the sensitivity to frequency offsets can be improved compared to low-power continuous-wave decoupling. The decoupling efficiency is somewhat reduced compared to optimized high-power decoupling: in a peptide sample investigated at an MAS frequency of 50 kHz a loss of about 10% in signal intensity for CH3 and CH groups, and of about 40% for CH2 groups was observed. Taking into consideration, that the rf amplitude in the low-power XiX was about 15 times lower than in high-power XiX decoupling, such a reduction in line intensity is sometimes tolerable.     

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.     

Characteristics of zero-quantum correlation spectroscopy in MAS NMR experiments

Zero-quantum coherence generation and reconversion in magic-angle spinning solid-state NMR is analyzed. Two methods are discussed based on implementations using symmetry-based pulse sequences that utilize either isotropic J couplings or dipolar couplings. In either case, the decoupling of abundant proton spins plays a crucial role for the efficiency of the zero-quantum generation. We present optimized sequences for measuring zero-quantum single-quantum correlation spectra in solids, achieving an efficiency of 50% in ubiquitin. The advantages and disadvantages of zero-quantum single-quantum over single-quantum single-quantum correlation spectroscopy are explored, and similarities and differences with double-quantum single-quantum correlation spectroscopy are discussed. Finally, possible application of zero-quantum single-quantum experiments to polypeptides, where it can lead to better spectral resolution is investigated using ubiquitin, where we find high efficiency and high selectivity, but also increased line widths in the MQ dimension.     

A standard for silver CP/MAS experiments

Silver methanesulfonate, AgSO3CH3, is a photo-stable, commercially available compound which is a superior 109Ag standard for setting up CP/MAS experiments. The 109Ag CP/MAS spectrum at moderate sample spinning speeds easily yields a single, relatively narrow peak with a single transient. The 109Ag chemical shift of solid AgSO3CH3 is 87.2 ppm with respect to a 9 M aqueous solution of AgNO3. The static spectrum yields chemical shift tensor components delta11=191 ppm, delta22=63 ppm and delta33=8 ppm. Therefore the span, Omega, is 183 ppm and the skew, kappa, is -0.39. These values are in accord with the known crystal structure.     

Enhanced resolution in proton solid-state NMR with very-fast MAS experiments

We present a new smooth amplitude-modulated (SAM) method that allows to observe highly resolved ¹H spectra in solid-state NMR. The method, which works mainly at fast or ultra-fast MAS speed (ν_R > 25 kHz) is complementary to previous methods, such as DUMBO, FSLG/PMLG or symmetry-based sequences. The method is very robust and efficient and does not present line-shape distortions or fake peaks. The main limitation of the method is that it requires a modern console with fast electronics that must be able to define the cosine line-shape in a smooth way, without any transient. However, this limitation mainly occurs at ultra-fast MAS where the rotation period is very short.     

Analysis of magnetization instability patterns in spin-transfer nano-oscillators

The stability of large precessional magnetization motions induced by spin-polarized currents in spin-transfer nano-oscillators is discussed. Quantitative analytical predictions are obtained for the critical values of spin-polarized injected current and external magnetic field at which the oscillator magnetization precession becomes unstable. It is shown that the mechanism leading to instability is parametric resonance of well-defined pairs of magnetostatically coupled perturbation modes. The amplitude of these modes grows to large non-thermal values when the oscillator frequency matches the mean of the natural frequencies of the two coupled modes. Analytical predictions are obtained for the space-time structure and symmetry of the magnetization patterns that are formed at the instability. Analytical results are compared with numerical simulations of spin-transfer-driven magnetization dynamics.     

Recoupling of chemical-shift anisotropy powder patterns in MAS NMR

A comparison of three different implementations of the chemical-shift recoupling experiment of Tycko et al. [R. Tycko, G. Dabbagh, P.A. Mirau, Determination of chemical-shift-anisotropy lineshapes in a two-dimensional magic-angle-spinning NMR experiment, J. Magn. Reson. 85 (1989) 265-274] is presented. The methods seek to reduce the effects of artefacts resulting from pulse imperfections and residual C-H dipolar coupling in organic solids. An optimised and constant time implementation are shown to give well-defined and artefact free powder pattern lineshapes in the indirectly observed dimension for both sp2 and sp3 carbon sites. Experimental setup is no more demanding than for the original experiment, and can be implemented using standard commercial hardware.     

Compound radiofrequency-driven recoupling pulse sequences for efficient magnetization transfer by homonuclear dipolar interaction under magic-angle spinning conditions

The maximum of the transferred magnetization in rotating powdered solids under the radiofrequency-driven recoupling (RFDR) pulse sequence is enhanced by reducing the orientation dependence of the effective recoupled homonuclear dipolar interaction. The compound RFDR (CRFDR) pulse sequence for this enhancement consists of RFDR pulse units (tau(i)-pi-tau(R)-pi-1171;tau(i)) with different tau(i), where tau(R) is the sample rotation period, tau(i) and 1171;tau(i) (=tau(R) - tau(i)) are delays, and pi is a 180 degrees pulse. The delay tau(i) modifies the zero-quantum spin operators and the sample rotation-angle dependence of the recoupled dipolar Hamiltonian. The CRFDR pulse sequences were optimized for mixing by varying tau(i). Numerical simulation for the two-spin system only with a dipolar interaction and isotropic chemical shifts indicates that the transfer efficiency of CRFDR averaged over the powder is about 70%, which is 30% higher than the efficiency of the RFDR pulse over a broad range of about 1/tau(R) in resonance frequency difference. The CRFDR sequences need about 60% longer mixing times to maximize the transferred magnetizaion in comparison with the original RFDR sequence. Chemical shift anisotropy, the other dipolar interactions, and relaxation generally reduce the enhancement by CRFDR. Experiments for fully (13)C-labeled alanine, however, show that the maximum of the magnetization transferred with CRFDR from the carboxyl to alpha carbon is about 15% greater than that with RFDR. Copyright 2000 Academic Press.     

Selective dephasing of OH and NH proton magnetization based on (1)H chemical-shift anisotropy recoupling

A method for selectively suppressing the signals of OH and NH protons in (1)H combined rotation and multiple-pulse spectroscopy (CRAMPS) and in (1)H-(13)C heteronuclear correlation (HETCOR) solid-state NMR spectra is presented. It permits distinction of overlapping CH and OH/NH proton signals, based on the selective dephasing of the magnetization of OH and NH protons by their relatively large (1)H chemical-shift anisotropies. For NH protons, the (14)N-(1)H dipolar coupling also contributes significantly to this dephasing. The dephasing is achieved by a new combination of heteronuclear recoupling of these anisotropies with (1)H homonuclear dipolar decoupling. Since the 180 degrees pulses traditionally used for heteronuclear dipolar and chemical-shift anisotropy recoupling would result in undesirable homonuclear dephasing of proton magnetization, instead the necessary inversion of the chemical-shift Hamiltonian every half rotation period is achieved by inverting the phases of all the pulses in the HW8 multiple-pulse sequence. In the HETCOR experiments, carefully timed (13)C 180 degrees pulses remove the strong dipolar coupling to the nearby (13)C spin. The suppression of NH and OH peaks is demonstrated on crystalline model compounds. The technique in combination with HETCOR NMR is applied to identify the CONH and NH-CH groups in chitin and to distinguish NH and aromatic proton peaks in a peat humin.     

Spatially varying steady state longitudinal magnetization in distant dipolar field-based sequences

Sequences based on the distant dipolar field (DDF) have shown great promise for novel spectroscopy and imaging. Unless spatial variation in the longitudinal magnetization, Mz(s), is eliminated by relaxation, diffusion, or spoiling techniques by the end of a single repetition, unexpected results can be obtained due to spatial harmonics in the steady state MzSS(s) profile. This is true even in a homogeneous single-component sample. We have developed an analytical expression for the MzSS(s) profile that occurs in DDF sequences when smearing by diffusion is negligible in the TR period. The expression has been verified by directly imaging the MzSS(s) profile after establishing the steady state.     

Long-term stability of rotor-controlled MAS frequencies to 0.1 Hz proved by 14N MAS NMR experiments and simulations

Experimental and simulated 14N MAS NMR spectra of the NH4+ ions in the two polymorphs, mS60 and mP60, of (NH4)2MoO4 are used to illustrate that a long-term stability of rotor-controlled MAS frequencies to 0.1 Hz can be achieved using commercial instrumentation (MAS speed controller and 7.5 mm MAS probe with a single marked rotor) attached to a highly pressure-stabilized air supply. A new modification of the STARS simulation software employs a Gaussian distribution for the experimental spinning frequency around the frequency set for the MAS speed controller. A simulated spectrum is then obtained by summation of several calculated spectra for evenly spaced spinning frequencies around the set frequency with relative weight factors corresponding to the Gaussian distribution.     

BaBa-xy16: robust and broadband homonuclear DQ recoupling for applications in rigid and soft solids up to the highest MAS frequencies

We here present a substantially improved version of the popular Back-to-Back (BaBa) homonuclear double-quantum (DQ) MAS recoupling pulse sequence. By combining the original pulse sequence with a virtual π pulse train with xy-16 phase cycling along with time-reversed DQ reconversion, a truly broadband and exceptionally robust pulse sequence is obtained. The sequence has moderate radio-frequency power requirements, amounting to only one 360° nutation per rotor cycle, it is robust with respect to rf power and tune-up errors, and its broadband performance increases with increasing spinning frequency, here tested up to 63 kHz. The experiment can be applied to many spin-1/2 nuclei in rigid solids with substantial frequency offsets and CSAs, which is demonstrated on the example of 31P NMR of a magnesium ultraphosphate, comparing experimental data with multi-spin simulations, and we also show simulations addressing the performance in 13C NMR of bio(macro)molecules. 1H-based studies of polymer dynamics are highlighted for the example of a rigid solid with strongly anisotropic mobility, represented by a polymer inclusion compound, and for the example of soft materials with weak residual dipole-dipole couplings, represented by homogeneous and inhomogeneous elastomers. We advocate the use of normalized (relaxation-corrected) DQ build-up curves for a quantitative assessment of weak average dipole-dipole couplings and even distributions thereof.     

Effects of L-spin longitudinal quadrupolar relaxation in heteronuclear recoupling and S-spin magic-angle spinning NMR

In experiments on S–L heteronuclear spin systems with evolution of the S-spin magnetization under the influence of a quadrupolar nucleus (L-spin), effects of longitudinal quadrupolar (T_1Q) relaxation of the L-spin coherence on the sub-millisecond time scale have been documented and explored, and methods for minimizing their effect have been demonstrated. The longitudinal relaxation results in heteronuclear dephasing even in the reference signal S₀ of S{L} REDOR, REAPDOR, RIDER, or SPIDER experiments, due to T_1Q-relaxation of the transiently generated S_yL_z coherence, reducing or even eliminating the observable dephasing ΔS. Pulse sequences for measuring an improved reference signal S₀₀ with minimal heteronuclear recoupling but the same number of pulses as for S₀ and S have been demonstrated. From the observed intensity ΔS₀ = S₀₀ − S₀ and the SPIDER signal ΔS/S₀, T_1Q can be estimated. Accelerated decays analogous to the dipolar S₀ curves will occur in T₂ measurements for J-coupled S–L spin pairs. Even in the absence of recoupling pulses, fast T_1Q relaxation of the unobserved nucleus shortens the transverse relaxation time T_2S,MAS of the observed nucleus, in particular at low spinning frequencies, due to unavoidable heteronuclear dipolar evolution during a rotation period. The observed spinning-frequency dependence of T_2S,MAS matches the theoretical prediction and may be used to estimate T_1Q. The effects are demonstrated on several ¹³C{¹⁴N} spin systems, including an arginine derivative, the natural N-acetylated polysaccharide chitin, and a model peptide, (POG)₁₀.     

31P and 13C chemical shielding tensors in the phosphoenolpyruvate moiety from rotary resonance recoupling 13C and 31P MAS and single crystal 31P NMR

A ³¹P and ¹³C NMR study of powder and single crystal samples of two phosphoenolpyruvate (PEP) compounds, the tris-ammonium salt monohydrate (NH₄)₃(PEP)·H₂O (1), and the mono-ammonium-salt (NH₄)(H₂PEP) (2) is presented. The P chemical shielding tensors in 1 are measured by ³¹P single crystal NMR on four minuscule samples and assigned without ambiguity by exploiting the orientation-dependent ³¹P-³¹p dipolar splittings of the resonance lines. The orientation of the ³¹P chemical shielding tensor is discussed in terms of the C_2v — and C₃-type distortions of the phosphate PO₄-coordination sphere. From ¹³C MAS NMR experiments with ³¹P rotary resonance recoupling on polycrystalline powder samples the orientations of the ³¹P chemical shielding tensors in 1 and 2 are obtained, for 1 in very good agreement with the ³¹P single crystal NMR results. Only some of the orientational parameters of the three ¹³C chemical shielding tensors in the PEP moiety of 1 could be derived from ¹³C MAS NMR experiments with ³¹P rotary resonance recoupling.     

Dissection of heteronuclear NMR experiments for studies of magnetization transfer efficiencies

Modern NMR experiments for applications with biological macromolecules in solution typically include multiple magnetization transfer steps. When working with large structures, a significant fraction of the magnetization is lost during these transfers. For the design and optimization of complex experimental schemes, the magnetization transfer efficiencies have therefore commonly been calculated from the spin relaxation times. This paper now suggests a new method for measurement of individual transfer efficiencies directly with the system of interest, using short, reliable experiments. Initial applications of this approach with a 110,000 Da protein indicate that there is a wide range of transfer efficiencies among individual spin pairs in a structure of this size, which leads to a correspondingly large variation of the individual signal intensities and the need for techniques to enhance the weak signals.