Satellite-transition MAS NMR of spin I = 3/2, 5/2, 7/2, and 9/2 nuclei: sensitivity,resolution, and practical implementation

The satellite-transition MAS (STMAS) experiment offers an alternative approach to established methods such as dynamic angle spinning (DAS), double rotation (DOR), and multiple-quantum MAS (MQMAS) for obtaining high-resolution NMR spectra of half-integer quadrupolar nuclei. Unlike the multiple-quantum experiment, STMAS involves two-dimensional correlation of purely single-quantum coherences; satellite transitions in t(1) (or F(1)) and the central transition in t(2) (or F(2)). To date, STMAS has primarily been demonstrated for nuclei with spin quantum numbers I = 3/2 and, to a lesser extent, I > 5/2. However, many chemically relevant nuclei possess I > 3/2, such as (17)O and (27)Al (both I = 5/2), (59)Co (I = 7/2), and (93)Nb (I = 9/2). Here, we discuss the application of STMAS to nuclei with spin quantum numbers from I = 3/2 to 9/2. First, we consider the practical implementation of the STMAS experiment using (87)Rb (I = 3/2) NMR as an example. We then extend the discussion to include nuclei with higher spin quantum numbers, demonstrating (27)Al, (45)Sc (I = 7/2), (59)Co, and (93)Nb STMAS experiments on both crystalline and amorphous samples. We also consider the possibility of experiments involving satellite transitions other than m(I) = +/- 1/2 <--> +/- 3/2 and, using (93)Nb NMR, demonstrate the correlation of all single-quantum satellite transitions up to and including m(I) = +/- 7/2 <--> +/- 9/2. The absolute chemical shift scaling factors in these experiments are discussed, as are the implications for isotropic resolution.     

Q-shear transformation for MQMAS and STMAS NMR spectra

The multiple-quantum magic-angle spinning (MQMAS) and satellite-transition magic-angle spinning (STMAS) experiments refocus second-order quadrupolar broadening of half-integer quadrupolar spins in the form of two-dimensional experiments. Isotropic shearing is usually applied along the indirect dimension of the 2D spectra such that an isotropic projection free of anisotropic quadrupolar broadening can be obtained. An alternative shear transformation by a factor equal to the coherence level (quantum number) selected during the evolution period is proposed. Such a transformation eliminates chemical shift along the indirect dimension leaving only the second-order quadrupolar-induced shift and anisotropic broadening, and is expected to be particularly useful for disordered systems. This transformation, dubbed Q-shearing, can help avoid aliasing problems due to large chemical shift ranges and spinning sidebands. It can also be used as an intermediate step to the isotropic representation for expanding the spectral window of rotor-synchronized experiments.     

SCAM-STMAS: satellite-transition MAS NMR of quadrupolar nuclei with self-compensation for magic-angle misset

Several methods are available for the acquisition of high-resolution solid-state NMR spectra of quadrupolar nuclei with half-integer spin quantum number. Satellite-transition MAS (STMAS) offers an approach that employs only conventional MAS hardware and can yield substantial signal enhancements over the widely used multiple-quantum MAS (MQMAS) experiment. However, the presence of the first-order quadrupolar interaction in the satellite transitions imposes the requirement of a high degree of accuracy in the setting of the magic angle on the NMR probehead. The first-order quadrupolar interaction is only fully removed if the sample spinning angle, chi, equals cos(-1)(1/3) exactly and rotor synchronization is performed. The required level of accuracy is difficult to achieve experimentally, particularly when the quadrupolar interaction is large. If the magic angle is not set correctly, the first-order splitting is reintroduced and the spectral resolution is severely compromised. Recently, we have demonstrated a novel STMAS method (SCAM-STMAS) that is self-compensated for angle missets of up to +/-1 degrees via coherence transfer between the two different satellite transitions ST(+)(m(I)=+3/2<-->+1/2) and ST(-)(m(I)=-1/2<-->-3/2) midway through the t(1) period. In this work we describe in more detail the implementation of SCAM-STMAS and demonstrate its wider utility through 23Na (I=3/2), 87 Rb (I=3/2), 27 Al (I=5/2), and 59 Co (I=7/2) NMR. We discuss linewidths in SCAM-STMAS and the limits over which angle-misset compensation is achieved and we demonstrate that SCAM-STMAS is more tolerant of temporary spinning rate fluctuations than STMAS, resulting in less "t(1) noise" in the two-dimensional spectrum. In addition, alternative correlation experiments, for example involving the use of double-quantum coherences, that similarly display self-compensation for angle misset are investigated. The use of SCAM-STMAS is also considered in systems where other high-order interactions, such as third-order quadrupolar effects or second-order quadrupole-CSA cross-terms, are present. Finally, we show that the sensitivity of the experiment can be improved through the use of amplitude-modulated pulses.     

Practical comparison of sensitivity and resolution between STMAS and MQMAS for Al

An experimental comparison of sensitivity and resolution of satellite transition (ST) MAS and multiple quantum (MQ) MAS was performed for ²⁷Al (I = 5/2) using several pulse sequences with a z-filter and SPAM, and two inorganic samples of kaolin (Al₂Si₂O₅(OH)₄) and glass (43.1CaO–12.5Al₂O₃–44.4SiO₂). Six pulse sequences of STMAS (double-quantum filter-soft pulse added mixing = DQF-SPAM, double-quantum filter = DQF, double-quantum = DQ) and MQMAS (3QMAS-z-filter = 3Qz, 3QMAS-SPAM = 3Q-SPAM, 5QMAS-z-filter = 5Qz) are employed. All experiments have been conducted utilizing a static field of 16.4 T (700 MHz for ¹H) and a rotor spinning frequency of 20 kHz. Dependence of S/N ratios as a function of radio frequency (r.f.) field strengths indicates that strong r.f. fields are essential to obtain a better S/N ratio in all experiments. High sensitivity is obtained in the following order: DQF-SPAM, DQF, DQ, 3QSPAM, and 3Qz, although the degree of sensitivity enhancement given by STMAS for glass is slightly smaller than that for kaolin. This might be due to the different excitation and conversion efficiencies of ST and MQ coherences as a function C_q values because quadrupolar interaction of the glass are widely distributed, or to motional broadening caused by framework flexibility in the structure of glass. With respect to resolution, the full widths at half maximum (FWHM) of F₁ projections of DQF-STMAS and 3QMAS spectra for kaolin are found to be comparable, which agrees with a simulated result reported in a literature. For glass, the STMAS possess slightly wider line widths than 3QMAS. However, because such a difference in line widths of STMAS and 3QMAS spectra is substantially small, we have concluded that STMAS and 3QMAS have comparable resolution for crystalline and non-crystalline materials.     

Implementing SPAM into STMAS: a net sensitivity improvement in high-resolution NMR of quadrupolar nuclei

Gan and Kwak recently introduced two new tools for high-resolution 2D NMR methods applied to quadrupolar nuclei: double-quantum filtering in STMAS (DQF-STMAS) and the soft-pulse added mixing (SPAM) idea. Double-quantum filtering suppresses all undesired signals in the STMAS method with limited loss in sensitivity. With SPAM, all pathways are added constructively after the second hard-pulse instead of using a single pathway as previously. Here, the sensitivity, advantages and drawbacks of DQF-STMAS are compared to 3QMAS. Additionally, SPAM can be included into DQF-STMAS method, resulting in a net sensitivity gain with respect to 3QMAS of ca. 10-15.     

Effective dipolar couplings determined by dipolar dephasing of double-quantum coherences

It is shown how homonuclear distances and homonuclear dipolar lattice sums between spin-1/2 nuclei can be measured by a pulsed solid-state NMR experiment under magic-angle spinning conditions. The presented technique is based on double-quantum coherence filtering. Instead of measuring a build-up of double-quantum coherence the pulse sequence is designed to dephase double-quantum coherence. This is achieved by exciting double-quantum coherence either with the help of the through-space dipolar coupling or the through-bond dipolar coupling while the dephasing relies on the through-space dipolar coupling as selected by a gamma-encoded pulse sequence from the C/R symmetry class. Since dephasing curves can be normalized on zero dephasing, it is possible to analyze the initial dephasing regime and hence determine dipolar lattice sums (effective dipolar couplings) in multiple-spin systems. A formula for the effective dipolar coupling is derived theoretically and validated by numerical calculations and experiments on crystalline model compounds for (13)C and (31)P spin systems. The double-quantum dephasing experiment can be combined with constant-time data sampling to compensate for relaxation effects, consequently only two experimental data points are necessary for a single distance measurement. The phase cycling overhead for the constant-time experiment is minimal because a short cogwheel phase cycle exists. A 2D implementation is demonstrated on [(13)C(3)]alanine.     

MAS, STMAS and DQMAS NMR Studies of the Thermal Transformation of Kaolinite

Thermal transformations of kaolinite at different temperatures were monitored using X-ray diffraction (XRD), high-resolution solid-state nuclear magnetic resonance (800 MHz for ¹H Larmor frequency) with single-pulse magic-angle spinning, double-quantum filter satellite-transition magic-angle spinning, and double-quantum homo-nuclear correlation under magic-angle spinning experiments. Results show that combined experiments clearly manifest the transitions of silicon and aluminum structures at different thermal treatment stages; and moreover, high magnetic field offers higher sensitivity and resolution, hereby the slim resonances are obtained successfully at less stringent conditions. The dehydroxylation process of kaolinite causes the presence of short-range order in metakaolinite, which is absence of XRD reflections. Particularly, the features of metakaolinite with high concentration of defects are found with dispersive aluminum coordinations; and further, the distorted tetrahedral aluminum is detected in kaolinite-derived mullite because of the locally disorganized structure. The framework structure of kaolinite-derived mullite is considered to be primarily formed by the tetrahedral aluminum bonding with octahedral aluminum. In addition, except for the primary limitation caused by potentially long relaxation time of sample, such approaches are applicable to obtain detailedly structural characteristics of aluminosilicate.     

Optimizing STMAS

The 2D satellite transition magic angle spinning (STMAS) experiment generates efficiently high-resolution isotropic NMR spectra of half-integer quadrupolar nuclei. The experiment involves excitation and coherence transfer of satellite transitions into the central transition. It requires efficient refocusing of satellite transitions and sample spinning at a very accurate magic angle to cancel the first-order quadrupolar interaction effect. A review of all parameters relevant to optimizing the STMAS experiment is presented, including pulse sequence calibration, regulating spinning speed, magic angle adjustment, optimization of satellite transition excitation, and coherence transfer for both I = 3/2 and I > or =5/2 nuclei.     

Rotor-synchronized acquisition of quadrupolar satellite-transition NMR spectra: practical aspects and double-quantum filtration

The very broad resonances of quadrupolar (spin I > 1/2) nuclei are resolved by magic angle spinning (MAS) into a large number of spinning sidebands, each of which often remains anisotropically broadened. The quadrupolar interaction can be removed to a first-order approximation if the MAS NMR spectrum is acquired in a rotor-synchronized fashion, aliasing the spinning sidebands onto a centreband and thereby increasing the signal-to-noise ratio in the resulting, possibly second-order broadened, spectrum. We discuss the practical aspects of this rotor-synchronization in the direct (t(2)) time domain, demonstrating that the audiofrequency filters in the receiver section of the spectrometer have a significant impact on the precise timings needed in the experiment. We also introduce a novel double-quantum filtered rotor-synchronized experiment for half-integer spin quadrupolar (spin I = 3/2, 5/2, etc.) nuclei that makes use of central-transition-selective inversion pulses to both excite and reconvert double-quantum coherences and yields a simplified spectrum containing only the ST(1) (m(I) = +/-1/2 <--> +/-3/2) satellite-transition lineshapes. For spin I = 5/2 nuclei, such as (17)O and (27)Al, this spectrum may exhibit a significant resolution increase over the conventional central-transition spectrum.     

Convection-compensating diffusion experiments with phase-sensitive double-quantum filtering

We present a design scheme for phase-sensitive, convection-compensating diffusion experiments with gradient-selected homonuclear double-quantum filtering. The scheme consists of three blocks: a 1/2J evolution period during which antiphase single-quantum coherences are created; a period of double-quantum evolution; and another 1/2J period, during which antiphase single-quantum coherences are converted back into an in-phase state. A single coherence transfer pathway is selected using an asymmetric set of gradient pulses, and both diffusion sensitization and convection compensation are built into the gradient coherence transfer pathway selection. Double-quantum filtering can be used either for solvent suppression or spectral editing, and we demonstrate examples of both applications. The new experiment performs well in the absence of a field-frequency lock and does not require magnitude Fourier transformation. The proposed scheme may offer advantages in diffusion measurements of spectrally crowded systems, particularly small molecules solubilized in colloidal solutions or bound to macromolecules.     

HMQC and refocused-INEPT experiments involving half-integer quadrupolar nuclei in solids

Hetero-nuclear coherence transfers in HMQC and refocused-INEPT experiments involving half-integer quadrupolar nuclei in solids are analyzed. 1D and 2D schemes are considered under MAS for the general case of multi-spin systems SI(n) (n4), where S is an observed nucleus. These results are also discussed in the context of high-resolution schemes featuring MQMAS or STMAS. The theoretical predictions are verified experimentally in a series of 1D and 2D experiments performed at 9.4 and 18.8T.     

Efficient double-quantum excitation in rotational resonance NMR

We present a new technique for double-quantum excitation in magic-angle-spinning solid-state NMR. The method involves (i) preparation of nonequilibrium longitudinal magnetization; (ii) mechanical excitation of zero-quantum coherence by spinning the sample at rotational resonance, and (iii) phase-coherent conversion of the zero-quantum coherence into double-quantum coherence by frequency-selective spin inversion. The double-quantum coherence is converted into observable magnetization by reversing the excitation process, followed by a pi/2 pulse. The method is technically simple, does not require strong RF fields, and is feasible at high spinning frequencies. In [(13)C(2),(15)N]-glycine, with an internuclear (13)C-(13)C distance of 0.153 nm, we achieve a double-quantum filtering efficiency of approximately 56%. In [11, 20-(13)C(2)]-all-E-retinal, with an internuclear (13)C-(13)C distance of 0.296 nm, we obtain approximately 45% double-quantum filtering efficiency.     

Double-quantum excitation in the NMR of spinning solids by pulse-assisted rotational resonance

We describe a new technique for double-quantum excitation in magic-angle-spinning NMR of powdered solids. The technique is designed to efficiently excite double-quantum coherence in the vicinity of a rotational resonance condition. The offset from rotational resonance allows the double-quantum filtered signals to be observed with high resolution and sensitivity. The method uses rotational excitation of zero-quantum coherence, assisted by radiofrequency pulse cycles. The zero-quantum coherence is converted into double-quantum coherence by a frequency-selective inversion sequence. Experiments on [(13)C(2), (15)N]-glycine demonstrate a double-quantum filtering efficiency of approximately 41% at a sample rotation frequency of 8.300 kHz, which is 1.600 kHz away from the n = 1 rotational resonance. We achieve 32% double-quantum filtering efficiency at a spinning frequency of 9.250 kHz, which is 2.550 kHz away from rotational resonance.     

自旋1/2-自旋1耦合系统的HSQC和HDQC实验的研究

对自旋1/2-自旋1耦合系统的单量子HSQC和双量子HDQC脉冲序列进行了理论和实验的探讨. 研究结果表明,文献提出的HDQC实验中实际上还发生了零量子跃迁,因此该实验应该是多量子HMQC实验. 研究结果还表明,HSQC有比HDQC更高的灵敏度.     

Double-quantum homonuclear correlations of spin I=5/2 nuclei

The challenges associated with acquiring double-quantum homonuclear Nuclear Magnetic Resonance correlation spectra of half-integer quadrupolar nuclei are described. In these experiments the radio-frequency irradiation amplitude is necessarily weak in order to selectively excite the central transition. In this limit only one out of the 25 double-quantum coherences possible for two coupled spin I=5/2 nuclei is excited. An investigation of all the 25 two spins double quantum transitions reveals interesting effects such as a compensation of the first-order quadrupolar interaction between the two single quantum transitions involved in the double quantum coherence. In this paper a full numerical study of a hypothetical two spin I=5/2 system is used to show what happens when the RF amplitude during recoupling is increased. In principle this is advantageous, since the required double quantum coherence should build up faster, but in practice it also induces adiabatic passage transfer of population and coherence which impedes any build up. Finally an optimized rotary resonance recoupling (oR(3)) sequence is introduced in order to decrease these transfers. This sequence consists of a spin locking irradiation whose amplitude is reduced four times during one rotor period, and allows higher RF powers to be used during recoupling. The sequence is used to measure (27)Al DQ dipolar correlation spectra of Y(3)Al(5)O(12) (YAG) and gamma alumina (γAl(2)O(3)). The results prove that aluminium vacancies in gamma alumina mainly occur in the tetrahedral sites.     

Homogeneous broadenings in 2D solid-state NMR of half-integer quadrupolar nuclei

The question of the homogeneous broadening that occurs in 2D solid-state NMR experiments is examined. This homogeneous broadening is mathematically introduced in a simple way, versus the irreversible decay rates related to the coherences that are involved during t1 and t2. We give the pulse sequences and coherence transfer pathways that are used to measure these decay rates. On AlPO4 berlinite, we have measured the 27Al echo-type relaxation times of the central and satellite transitions on 1Q levels, so that of coherences that are situated on 2Q, 3Q, and 5Q levels. We compare the broadenings that can be deduced from these relaxation times to those directly observed on the isotropic projection of berlinite with multiple-quantum magic-angle spinning (MAS), or satellite-transition MAS. We show that the choice of the high-resolution method, should be done according to the spin value and the corresponding homogeneous broadening.     

Calculation of coherence pathway selection and cogwheel cycles

The selection of proper coherence pathways is a very important aspect of the design of NMR pulse sequences. This article describes a C++ program for the calculation of coherence pathway selection via phase cycles, including a module to calculate cogwheel cycles. Cogwheel phase cycles shorter than the original ones [M.H. Levitt et al., J. Magn. Reson. 155 (2002) 300] are derived and experimentally tested for the MQMAS experiment for 3/2 spins. Some other cogwheel cycles are derived for the MQNQMAS, the STMAS experiment, and a PFG diffusion pulse sequence. This program is publicly available through our website http://www.nyu.edu/projects/jerschow with additional documentation and examples.     

弱耦合自旋1/2二核系统二维动态NMR谱

二维动态NMR谱通常可由三脉冲实验得到。但如果核系统有标量耦合,就有可能混淆实验所得的信息。本文在Liouvelle空间中求出二核弱耦合系统的二维理论动态谱,给出AX(I=1/2)系统中的密度矩阵的解析解。文中指出:(1)在梯度脉冲作用之后,密度矩阵将留下z分量、零量子相干和双量子相干。(2)标量耦合与交换作用、弛豫作用的影响不同。前者只对零量子相干及双量子相干有贡献。如果实验得当,有希望消除标量耦合对动态谱的干扰。 关键词：     

Apparent diffusion behaviour of intermolecular double-quantum coherence modulated by a distant dipolar field in solution NMR

A modified correlated spectroscopy (COSY) revamped with asymmetric Z-gradient echo detection sequence was designed to investigate the influence of diffusion behaviour on intermolecular double-quantum coherence signal attenuation during the pre-acquisition period. Theoretical formulas were deduced and experimental measurements and simulations were performed. It is found that the diffusion behaviour of intermolecular double-quantum coherence in the pre-acquisition period may be different from that of conventional single-quantum coherence, depending on the relative orientation of diffusion weighting gradients to coherence selection gradients. When the orientation of the diffusion weighting gradients is parallel or anti-parallel to the orientation of the coherence selection gradients, the diffusion is modulated by the distant dipolar field. This study is helpful for understanding the signal properties in intermolecular double-quantum coherence magnetic resonance imaging.     

High-resolution absorptive intermolecular multiple-quantum coherence NMR spectroscopy under inhomogeneous fields

Intermolecular multiple-quantum coherence (iMQC) is capable of improving NMR spectral resolution using a 2D shearing manipulation method. A pulse sequence termed CT-iDH, which combines intermolecular double-quantum filter (iDQF) with a modified constant-time (CT) scheme, is designed to achieve fast acquisition of high-resolution intermolecular zero-quantum coherences (iZQCs) and intermolecular double-quantum coherences (iDQCs) spectra without strong coupling artifacts. Furthermore, double-absorption lineshapes are first realized in 2D intermolecular multi-quantum coherences (iMQCs) spectra under inhomogeneous fields through a combination of iZQC and iDQC signals to double the resolution without loss of sensitivity. Theoretically the spectral linewidth can be further reduced by half compared to original iMQC high-resolution spectra. Several experiments were performed to test the feasibility of the new method and the improvements are evaluated quantitatively. The study suggests potential applications for in vivo spectroscopy.