Variable‐angle sample‐spinning high resolution NMR of solids

Fokker-Planck formalism in magnetic resonance simulations

This paper presents an overview of the Fokker-Planck formalism for non-biological magnetic resonance simulations, describes its existing applications and proposes some novel ones. The most attractive feature of Fokker-Planck theory compared to the commonly used Liouville - von Neumann equation is that, for all relevant types of spatial dynamics (spinning, diffusion, stationary flow, etc.), the corresponding Fokker-Planck Hamiltonian is time-independent. Many difficult NMR, EPR and MRI simulation problems (multiple rotation NMR, ultrafast NMR, gradient-based zero-quantum filters, diffusion and flow NMR, off-resonance soft microwave pulses in EPR, spin-spin coupling effects in MRI, etc.) are simplified significantly in Fokker-Planck space. The paper also summarises the author's experiences with writing and using the corresponding modules of the Spinach library - the methods described below have enabled a large variety of simulations previously considered too complicated for routine practical use.

Spatial reorientation experiments for NMR of solids and partially oriented liquids

Motional reorientation experiments are extensions of Magic Angle Spinning (MAS) where the rotor axis is changed in order to average out, reintroduce, or scale anisotropic interactions (e.g. dipolar couplings, quadrupolar interactions or chemical shift anisotropies). This review focuses on Variable Angle Spinning (VAS), Switched Angle Spinning (SAS), and Dynamic Angle Spinning (DAS), all of which involve spinning at two or more different angles sequentially, either in successive experiments or during a multidimensional experiment. In all of these experiments, anisotropic terms in the Hamiltonian are scaled by changing the orientation of the spinning sample relative to the static magnetic field. These experiments vary in experimental complexity and instrumentation requirements. In VAS, many one-dimensional spectra are collected as a function of spinning angle. In SAS, dipolar couplings and/or chemical shift anisotropies are reintroduced by switching the sample between two different angles, often 0° or 90° and the magic angle, yielding a two-dimensional isotropic-anisotropic correlation spectrum. Dynamic Angle Spinning (DAS) is a related experiment that is used to simultaneously average out the first- and second-order quadrupolar interactions, which cannot be accomplished by spinning at any unique rotor angle in physical space. Although motional reorientation experiments generally require specialized instrumentation and data analysis schemes, some are accessible with only minor modification of standard MAS probes. In this review, the mechanics of each type of experiment are described, with representative examples. Current and historical probe and coil designs are discussed from the standpoint of how each one accomplishes the particular objectives of the experiment(s) it was designed to perform. Finally, applications to inorganic materials and liquid crystals, which present very different experimental challenges, are discussed. The review concludes with perspectives on how motional reorientation experiments can be applied to current problems in chemistry, molecular biology, and materials science, given the many advances in high-field NMR magnets, fast spinning, and sample preparation realized in recent years.

Singularities in the lineshape of a second-order perturbed quadrupolar nucleus. The magic-angle spinning case

For a nucleus with a half-integral spin and a strong quadrupole coupling, the central transition (from magnetic quantum number -1/2 to +1/2) in the spectrum shows a characteristic lineshape. By strong coupling, we mean an interaction strong enough so that second-order perturbation theory is needed, yet still sufficient. The spectrum of a static sample is well-known and the magic-angle-spinning (MAS spectrum) is different, but still can be calculated. The important features of both these spectra are singularities and steps in the lineshape, since these are the main tools in fitting the calculated spectrum to experimental data. A useful tool in this investigation is a plot of the frequency as a function of orientation over the surface of the unit sphere. These plots have maxima, minima and saddle points, and these correspond to the features of the spectrum. We used these plots to define both the positions and derive new formulae for the heights of the features and we now extend this to the magic-angle spinning case. For the first time, we identify the orientations corresponding to the features of the MAS spectra and derive formulae for the heights. We then compare the static and MAS cases and show the relationships between the features in the two spectra.

51V NMR: A New Probe of Structure and Bonding in Catalysts

Solid State 51V NMR spectra are sensitive to changes In the surface structure of V2O5 dispersed on Al2O3 and TiO2 supports. For V2O5 supported on alumina, wideline and magic-angle spinning experiments at 4.7 and 7.0 T reveal the presence of two vanadium species with different bonding environments. The relative proportions of these species change monotonically as a function of the vanadium concentration. In contrast, supported vanadium oxide on TiO2 substrates show a much more V2O5-like environment. Structural inferences are discussed In connection with solid state 51V NMR studies on model compounds with known crystal structures and site symmetries.

Probing quadrupolar nuclei by solid-state NMR spectroscopy: recent advances

Solid-state nuclear magnetic resonance (NMR) of quadrupolar nuclei has recently undergone remarkable development of capabilities for obtaining structural and dynamic information at the molecular level. This review summarizes the key achievements attained during the last couple of decades in solid-state NMR of both integer spin and half-integer spin quadrupolar nuclei. We provide a concise description of the first- and second-order quadrupolar interactions, and their effect on the static and magic angle spinning (MAS) spectra. Methods are explained for efficient excitation of single- and multiple-quantum coherences, and acquisition of spectra under low- and high-resolution conditions. Most of all, we present a coherent, comparative description of the high-resolution methods for half-integer quadrupolar nuclei, including double rotation (DOR), dynamic angle spinning (DAS), multiple-quantum magic angle spinning (MQMAS), and satellite transition magic angle spinning (STMAS). Also highlighted are methods for processing and analysis of the spectra. Finally, we review methods for probing the heteronuclear and homonuclear correlations between the quadrupolar nuclei and their quadrupolar or spin-1/2 neighbors.

Design and construction of a contactless mobile RF coil for double resonance variable angle spinning NMR

Variable angle spinning (VAS) experiments can be used to measure long-range dipolar couplings and provide structural information about molecules in oriented media. We present a probe design for this type of experiment using a contactless resonator. In this circuit, RF power is transmitted wirelessly via coaxial capacitive coupling where the coupling efficiency is improved by replacing the ordinary sample coil with a double frequency resonator. Our probe constructed out of this design principle has shown favorable properties at variable angle conditions. Moreover, a switched angle spinning correlation experiment is performed to demonstrate the probe's capability to resolve dipolar couplings in strongly aligned molecules.

Solid-state 33S MAS NMR of inorganic sulfates

Solid-state (33)S MAS NMR spectra of a variety of inorganic sulfates have been obtained at magnetic field strengths of 4.7, 14.1, 17.6, and 18.8 T. Some of the difficulties associated with obtaining natural abundance (33)S NMR spectra have been overcome by using a high magnetic field strength and magic angle spinning (MAS). Multiple factors were considered when analyzing the spectral linewidths, including magnetic field inhomogeneity, dipolar coupling, chemical shift anisotropy, chemical shift dispersion, and quadrupolar coupling. In most of these sulfate samples, quadrupolar coupling was the dominant line broadening mechanism. Nuclear electric quadrupolar coupling constants (C(q)) as large as 2.05 MHz were calculated using spectral simulation software. Spectral information from these new data are compared with X-ray measurements and GAUSSIAN 98W calculations. A general correlation was observed between the magnitude of the C(q) and the increasing difference between S-O bond distances within the sulfate groups. Solid-state (33)S spin-lattice (T(1)) relaxation times were measured and show a significant reduction in T(1) for the hydrated sulfates. This is most likely the result of the modulation of the time-dependent electric field gradient at the nuclear site by motion of water molecules. This information will be useful in future efforts to use (33)S NMR in the compositional and structural analysis of sulfur containing materials.

High-Resolution 17O NMR Spectroscopy of Wadsleyite (β-Mg2SiO4)

The sensitivity of high-resolution 17O (I = 5/2) NMR spectroscopy of solids has advanced significantly in recent years. Here, we show that excellent results are now obtainable from milligram quantities of 17O-enriched materials, thereby allowing the technique to be applied to silicate phases synthesized under very high pressures in a multiple-anvil apparatus. We report the first 17O NMR study of beta-Mg2SiO4 (9.6 mg of 35% 17O-enriched material, synthesized at p = 16 GPa and T = 1873 K), a dense phase believed to have a significant role in the Earth's mantle. Using STMAS at magnetic fields of B0 = 9.4 and 11.7 T and MQMAS at B0 = 18.8 T, we have resolved and assigned all four crystallographically distinct O sites and determined their chemical shift and quadrupolar parameters.

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.

51V magic angle spinning NMR spectroscopy of six-coordinate Lindqvist oxoanions: a sensitive probe for the electronic environment in vanadium-containing polyoxometalates. Counterions dictate the 51V fine structure constants in polyoxometalate solids

Geometric and electronic environments of vanadium have been addressed by (51)V magic angle spinning NMR spectroscopy of six-coordinated polyoxometalate solids. (C(4)H(9))(4)N(+) and mixed Na(+)/Cs(+) salts of the Lindqvist-type mono- and divanadium-substituted oxotungstates, [VW(5)O(19)](3-) and [V(2)W(4)O(19)](4-), have been prepared as microcrystalline and crystalline solids. The solid-state NMR spectra reflect the details of the local environment of the vanadium site in these hexametalate solids via the anisotropic quadrupolar and chemical shielding interactions. Remarkably, these (51)V fine structure constants in the solid state are dictated by the nature and geometry of the countercations. Electrostatic calculations of the electric field gradients at the vanadium atoms have been performed. Experimental trends are well reproduced with the simple electrostatic model, and explain the sensitivity of the anisotropic NMR parameters to the changes in the cationic environment at the vanadium site.

Solid state 33S NMR of inorganic sulfides

Solid state 33S NMR spectra of a variety of inorganic sulfides have been obtained at magnetic field strengths of 4.7 and 17.6T. Spectra acquired with magic angle spinning show considerable improvements in sensitivity and resolution when compared with static spectra. Multiple factors are considered when analyzing the spectral line widths, including; magnetic field inhomogeneity, dipolar coupling, chemical shift anisotropy, chemical shift dispersion (CSD), T(2) relaxation, and quadrupolar coupling. Quadrupolar coupling was expected to be the dominant line broadening mechanism. However, for most of the samples CSD was the prevailing line broadening mechanism. Thus, for many of the metal sulfides studied at a high magnetic field strength, the line widths were actually larger than those observed in the spectra at low field. This is atypical in solid state 33S NMR. Solid state 33S spin-lattice (T(1)) and spin-spin (T(2)) relaxation rates were measured for the first time and are discussed. This information will be useful in future efforts to use 33S NMR in the compositional and structural analysis of sulfur containing materials.

Relaxation-assisted separation of chemical sites in NMR spectroscopy of static solids

We discuss the potential use of relaxation times toward the resolution of inequivalent chemical sites in the NMR spectroscopy of powdered or disordered samples. This proposal is motivated by the significant differences that can often be detected in the relaxation behavior of sites in solids, particularly when focusing on NMR observations of quadrupolar nuclei possessing different coordination and/or dynamic environments. It is shown that in these cases the implementation of a non-negative least-squares analysis on relaxation data sets enables the bidimensional resolution of overlapping powder line shapes, even when dealing with static samples. In combination with signal-enhancement methodologies such as the quadrupolar Carr-Purcell Meiboom-Gill train, such relaxation-assisted separations open up valuable routes toward the high-resolution characterization of systems involving insensitive (e.g., low-gamma) nuclei. The principles and limitations of the 2D NMR approach resulting from these considerations are discussed, and their potential is exemplified with a variety of static and spinning investigations. Their extension to other nuclear systems where spectral resolution is problematic, such as protons in organic solids, is also briefly considered.

51V solid-state magic angle spinning NMR spectroscopy and DFT studies of oxovanadium(V) complexes mimicking the active site of vanadium haloperoxidases

A series of 11 oxovanadium(V) complexes mimicking the active site of vanadium haloperoxidases have been investigated by (51)V magic angle spinning NMR spectroscopy and density functional theory (DFT). The MAS spectra are dominated by the anisotropic quadrupolar and chemical shielding interactions; for these compounds, C(Q) ranges from 3 to 8 MHz, and delta(sigma) is in the range 340-730 ppm. The quadrupolar coupling and chemical shielding tensors as well as their relative orientations have been determined by numerical simulations of the spectra. The spectroscopic NMR observables appear to be very sensitive to the details of the electronic and geometric environment of the vanadium center in these complexes. For the four crystallographically characterized compounds from the series, the quadrupolar and chemical shielding anisotropies were computed at the DFT level using two different basis sets, and the calculated tensors were in general agreement with the experimental solid-state NMR data. A combination of (51)V solid-state NMR and computational methods is thus beneficial for investigation of the electrostatic and geometric environment in diamagnetic vanadium systems with moderate quadrupolar anisotropies.

High-Resolution NMR Spectroscopy of Quadrupolar Nuclei in Solids: Satellite-Transition MAS with Self-Compensation for Magic-Angle Misset

Several methods are available for obtaining high-resolution NMR spectra of half-integer spin quadrupolar nuclei, such as (11)B, (23)Na (I = (3)/(2)) and (17)O, (27)Al (I = (5)/(2)), in powdered solids. Satellite-transition magic-angle spinning (STMAS) uses only conventional magic-angle spinning (MAS) hardware and, it has been claimed, improves significantly upon the signal-to-noise ratio obtained with the widely adopted multiple-quantum MAS (MQMAS) experiment. The STMAS technique, however, requires that the sample rotation axis be set to the magic angle (cos(-1)(1/ radical 3) = 54.736 degrees ) with respect to the magnetic field B(0) with an accuracy of better than +/-0.004 degrees, and this stringent requirement has severely limited the use of the method. Here, we propose a novel version of STMAS that self-compensates for magic-angle missets of up to +/-1.0 degrees and yet retains a sensitivity comparable with MQMAS. This SCAM-STMAS experiment is demonstrated on RbNO(3) using (87)Rb (I = (3)/(2)) NMR and on kyanite (Al(2)SiO(5)) using (27)Al (I = (5)/(2)) NMR.

Rotor-encoded heteronuclear MQ MAS NMR spectroscopy of half-integer quadrupolar and spin I=1/2 nuclei

A new two-dimensional heteronuclear multiple-quantum magic-angle spinning (MQ MAS) experiment is presented which combines high resolution for the half-integer quadrupolar nucleus with information about the dipolar coupling between the quadrupolar nucleus and a spin I=1/2 nucleus. Homonuclear MQ coherence is initially created for the half-integer quadrupolar nucleus by a single pulse as in a standard MQ MAS experiment. REDOR recoupling of the heteronuclear dipolar coupling then allows the creation of a heteronuclear multiple-quantum coherence comprising multiple- and single-quantum coherence of the quadrupolar and spin I=1/2 nucleus, respectively, which evolves during t1. Provided that the t1 increment is not rotor synchronized, rotor-encoded spinning-sideband patterns are observed in the indirect dimension. Simulated spectra for an isolated IS spin pair show that these patterns depend on the recoupling time, the magnitude of the dipolar coupling, the quadrupolar parameters, as well as the relative orientation of the quadrupolar and dipolar principal axes systems. Spectra are presented for Na2HPO4, with the heteronuclear 23Na-1HMQ MAS experiments beginning with the excitation of 23Na (spin I=3/2) three-quantum coherence. Coherence counting experiments demonstrate that four- and two-quantum coherences evolve during t1. The heteronuclear spinning-sideband patterns observed for the three-spin H-Na-H system associated with the Na(2) site are analyzed. For an IS2 system, simulated spectra show that, considering the free parameters, the spinning-sideband patterns are particularly sensitive to only, first, the angle between the two IS internuclear vectors and, second, the two heteronuclear dipolar couplings. It is demonstrated that the proton localization around the Na(2) site according to the literature crystal structure of Na2HPO4 is erroneous. Instead, the experimental data is consistent with two alternative different structural arrangements, whereby either there is a deviation of 10 degrees from linearity for the case of two identical Na-H distances, or there is a linear arrangement, but the two Na-H distances are different. Furthermore, the question of the origin of spinning-sidebands in the (homonuclear) MQ MAS experiment is revisited. It is shown that the asymmetric experimental MQ sideband pattern observed for the low-C(Q) Na(2) site in Na(2)HPO4 can only be explained by considering the 23Na chemical shift anisotropy.

Solid-state 29Si, 113Cd, 119Sn, and 31P NMR studies of II-IV-P2 semiconductors

Solid-state 29Si, 113Cd, 119Sn, and 31P MAS NMR spectra are reported on a series of II-IV-P2 compounds. In favorable cases (e.g., high degree of crystallinity, low concentration of unpaired electrons), well-defined spectra, with sharp lines for each specific nearest-neighbor configuration, are observed; in such cases, expected J coupling patterns are also seen. High-resolution solid-state NMR studies of this type provide useful information on structure (disorder), doping, and electron-mediated coupling in semiconductor systems.

27Al multiple-quantum MAS NMR of mechanically treated bayerite (alpha-Al(OH)3) and silica mixtures

Two-dimensional 27Al multiple-quantum magic angle spinning (MQMAS) NMR experiments are used to study mixtures of bayerite (alpha-Al(OH)3) with either silicic acid (SiO2.nH2O) or silica gel (SiO2) that have been ground together for varying lengths of time. This mechanical treatment produces changes in the 27Al MAS and MQMAS NMR spectra that correspond to the formation of new Al species. Mean values of the quadrupolar interaction (PQ) and isotropic chemical shift (deltacs) are extracted from the two-dimensional 27Al NMR spectra for each of these species. The presence of significant distributions of both 27Al quadrupolar and chemical shift parameters is demonstrated and the effect of grinding duration on the magnitudes of these distributions is discussed.

Multiple-quantum cross-polarization and two-dimensional MQMAS NMR of quadrupolar nuclei

Cross-polarization from (1)H to the multiple-quantum coherences of a quadrupolar nucleus is used in combination with the two-dimensional multiple-quantum magic angle spinning (MQMAS) NMR experiment in order to extract high-resolution CPMAS NMR spectra. The technique is demonstrated on (23)Na (S = 3/2), (17)O, (27)Al (both S = 5/2), and (45)Sc (S = 7/2) nuclei, showing the applicability of multiple-quantum cross-polarization to systems with differing spin quantum number, gyromagnetic ratio, and relative nuclide abundance. The utility of this two-dimensional MAS NMR experiment for spectral editing and site-specific measurement of cross-polarization intensities is demonstrated. The possibility of direct cross-polarization to higher order multiple-quantum coherences is also considered and three-, five-, and seven-quantum cross-polarized (45)Sc MAS NMR spectra are presented.

Influence of sodium ion dynamics on the 23Na quadrupolar interaction in sodalite: a high-temperature 23Na MAS NMR study

High-temperature 33Na MAS NMR experiments up to 873 K for a number of different sodalites (Na8[AlSiO4]6(NO3)2, Na8[AlSiO4]6(NO2)2, Na8[AlSiO4]6I2, Na7.9[AlSiO4]6(SCN)7.9 x 0.5H2O, Na8[AlGeO4]6(NO3)2, and Na7[AlSiO4]6(H3O2) x 4H2O) were carried out. The spectra of the first five sodalites consist of a quadrupolar MAS pattern with different quadrupolar coupling constants. The quadrupolar interaction for the thiocyanate sodalite, the nitrate aluminosilicate, and germanate sodalite decreases strongly passing a coalescence state on heating, while the quadrupolar interaction of the iodide and nitrite sample shows nearly no change. The basic hydrosodalite shows an asymmetric lineshape at room temperature and, between 350 and 370 K, a second line due to the evaporation of cage-water emerges. The linewidth increases with rising temperature. The temperature dependence of the quadrupolar interaction seems to be a function of the sodalite beta-cage expansion. Two conceivable jump mechanisms are proposed for a tetrahedral two-site jump between occupied and unoccupied tetrahedral sites.

The influence of the radiofrequency excitation and conversion pulses on the lineshapes and intensities of the triple-quantum MAS NMR spectra of I = 3/2 nuclei

A rigorous examination of the various multiple-quantum magic angle spinning sequences is carried out with reference to sensitivity enhancement in the isotropic dimension and the lineshapes of the corresponding MAS peaks in the anisotropic dimension. An echo efficiency parameter is defined here, which is shown to be an indicator of the performance aspects of the various sequences. This can be used in the design of further new experiments in this field. A consequence of such a systematic analysis has been the combination of a spin-lock pulse for excitation of multiple-quantum coherences and an amplitude-modulated pulse for their conversion to observable single-quantum coherences. This approach has resulted in an improved performance over other sequences with respect to both the anisotropic lineshapes and the isotropic intensities.

Strategies for extracting NMR parameters from 23Na MAS, DOR and MQMAS spectra. A case study for Na4P2O7

The 23Na magic-angle spinning (MAS), double rotation (DOR) and multiple-quantum magic-angle spinning (MQMAS) NMR spectra of anhydrous sodium pyrophosphate, Na4P2O7, measured at five different Larmor frequencies (nuL) ranging from 105.8 MHz (corresponding to 400 MHz 1H frequency) to 211.6 MHz (800 MHz) are analysed and the complete set of NMR parameters (C(qcc), etaQ and delta(iso)) of the four crystallographically inequivalent sodium sites were determined with high accuracy. Different approaches of spectra evaluation are discussed and their results are compared. The most reliable results are obtained from a combined evaluation of five DOR and three MQMAS spectra but also from two DOR and one MAS spectra or even from a single MQMAS spectrum all data can be derived. It is shown that Na4P2O7 may serve as a useful reference material for experimental set-up and reliability tests of the various NMR experiments.

Quadrupolar and chemical shift tensors characterized by 2D multiple-quantum NMR spectroscopy

The present work discusses a new 2D NMR method for characterizing the principal values and relative orientations of the electric field gradient and the chemical shift tensors of half-integer quadrupolar sites. The technique exploits the different contributions that quadrupolar and shielding interactions impart on the evolution of multiple-quantum and of single-quantum coherences, in order to obtain 2D powder lineshapes that are highly sensitive to these nuclear spin coupling parameters. Different spinning variants of this experiment were assayed, but it was concluded that a static version can yield the highest sensitivity to the values of the principal components and to the relative geometries of the local coupling tensors. It was found that correlating the central transition evolution with the highest available order of the spin coherence was also helpful for maximizing this spectral information. Good agreement between data obtained on 87Rb (S = 32) and 59Co (S = 72) samples and ideal theoretical lineshape predictions of this experiment was obtained, provided that heterogeneities in the multiple-quantum excitation and conversion processes were suitably accounted by procedures similar to those described in the spin-(1/2) multiple-quantum NMR literature. Copyright 1999 Academic Press.

Triple quantum MQMAS spectroscopy of 59Co(I = 7/2) in Na3Co(NO2)6 and trans-Co[(en2)(NO2)2]NO3 interplay between the quadrupole coupling and anisotropic shielding tensors

The purpose of this paper is to investigate the interplay between the chemical shielding anisotropy and quadrupole interaction in MQMAS spectra. 59Co in the compounds Na3Co(NO2)6 and trans-Co[(en2)(NO2)2]NO3 provides model systems for such an investigation. Furthermore, only few results have been reported on the application of the MQMAS method to a spin I = 7/2. The possibilities of the MQMAS spectroscopy for determining the relative orientation of the two tensors and its advantage over previous techniques are discussed. Reported experimental spectra at different spinning speeds of Na3Co(NO2)6 are accurately reproduced by our theoretical simulations. The calculations are based on a recent approach, summarized in the present paper, which allows one to perform efficient simulations of MQMAS spectra including all interactions and their time-dependence throughout the experiment. This is necessary for calculating accurate MQMAS spectra including the spinning sideband pattern. In the case of trans-Co[(en2)(NO2)2]NO3 where the quadrupolar interaction and chemical shielding are stronger and their axes are non-coincident, the MQMAS spectrum is strongly distorted due to the unsufficient spinning speed and RF power. In this case, MAS at different spinning speeds is shown to provide valuable information.