Efficient Time Propagation Technique for MAS NMR Simulation: Application to Quadrupolar Nuclei

Theory of radio-frequency pulses on periodically driven three-level systems: challenges and perspectives

Nuances of multiple-quantum transitions in periodically driven systems is discussed through analytical methods based on time propagators derived from Floquet theory.

A Modular Implementation for the Simulation of 1D and 2D Solid-State NMR Spectra of Quadrupolar Nuclei in the Virtual Multifrequency Spectrometer-Draw Graphical Interface

We present the implementation of the solid state (SoS)NMR module for the simulation of several 1D and 2D NMR spectra of all the elements in the periodic table in the virtual multifrequency spectrometer (VMS). This module is fully integrated with the graphical user interface of VMS (VMS-Draw) [Licari et al., J. Comput. Chem. 36, 2015, 321-334], a freeware tool which allows a user-friendly handling of structures and analyses of advanced spectroscopical properties of chemical compounds-from model systems to real-world applications. Besides the numerous modules already available in VMS for the study of electronic, optical, vibrational, vibronic, and EPR properties, here the simulation of NMR spectra is presented with a particular emphasis on those techniques usually employed to investigate solid state systems. The SoSNMR module benefits from its ability to work under both periodic and nonperiodic conditions, such that small molecules/molecular clusters can be treated, as well as extended three-dimensional systems enforcing (or not) translational periodicity. These features allow VMS to simulate spectra resulting from NMR calculations by some popular quantum chemistry codes, namely Gaussian09/16, Castep, and Quantum Espresso. The effectiveness of the SoSNMR module of VMS is examined throughout the manuscript, and applied to simulate 1D static, MAS, and VAS NMR spectra as well as 2D correlation (90°, MAS) and MQMAS spectra of active NMR nuclei embedded in different amorphous and crystalline systems of actual interest in chemistry and material science. Finally, the program is able to simulate the spectra of both the total ensemble of spin-active nuclei present in the system and of subensembles differentiated depending on the chemical environment of the first and second coordination sphere in a very general way applicable to any kind of systems.

Computer-intensive simulation of solid-state NMR experiments using SIMPSON

Conducting large-scale solid-state NMR simulations requires fast computer software potentially in combination with efficient computational resources to complete within a reasonable time frame. Such simulations may involve large spin systems, multiple-parameter fitting of experimental spectra, or multiple-pulse experiment design using parameter scan, non-linear optimization, or optimal control procedures. To efficiently accommodate such simulations, we here present an improved version of the widely distributed open-source SIMPSON NMR simulation software package adapted to contemporary high performance hardware setups. The software is optimized for fast performance on standard stand-alone computers, multi-core processors, and large clusters of identical nodes. We describe the novel features for fast computation including internal matrix manipulations, propagator setups and acquisition strategies. For efficient calculation of powder averages, we implemented interpolation method of Alderman, Solum, and Grant, as well as recently introduced fast Wigner transform interpolation technique. The potential of the optimal control toolbox is greatly enhanced by higher precision gradients in combination with the efficient optimization algorithm known as limited memory Broyden-Fletcher-Goldfarb-Shanno. In addition, advanced parallelization can be used in all types of calculations, providing significant time reductions. SIMPSON is thus reflecting current knowledge in the field of numerical simulations of solid-state NMR experiments. The efficiency and novel features are demonstrated on the representative simulations.

Applications of Floquet-Magnus expansion, average Hamiltonian theory and Fer expansion to study interactions in solid state NMR when irradiated with the magic-echo sequence

This work presents the possibility of applying the Floquet-Magnus expansion and the Fer expansion approaches to the most useful interactions known in solid-state nuclear magnetic resonance using the magic-echo scheme. The results of the effective Hamiltonians of these theories and average Hamiltonian theory are presented.

Understanding multi-quantum NMR through secular approximation

With the development of technology and improved understanding of nuclear spin-spin interactions and their behavior in static/oscillating magnetic fields, NMR spectroscopy has emerged as a powerful tool for characterizing molecular structure in a wide range of systems of chemical, physical and biological relevance. Here in this article, we revisit the important connection between "Secular-Approximation" (a well-known fundamental concept) and NMR spectroscopy. Employing recent experimental results as the background, an alternate interpretation of the secular approximation is presented for describing and understanding the nuances of Multi-Quantum (MQ) NMR spectroscopy of quadrupolar nuclei. Since MQ NMR spectroscopy of quadrupolar nuclei forms the basis of the structural characterization of inorganic solids and clusters, we believe that the analytic theory presented herein would be beneficial both in the understanding and design of MQ NMR experiments. Additionally, the analytic results are corroborated with rigorous numerical simulations and could be employed in the quantitative interpretation of experimental results.

Contribution of first-principles calculations to multinuclear NMR analysis of borosilicate glasses

Boron-11 and silicon-29 NMR spectra of xSiO(2)-(1-x)B(2)O(3) glasses (x=0.40, 0.80 and 0.83) have been calculated using a combination of molecular dynamics (MD) simulations with density functional theory (DFT) calculations of NMR parameters. Structure models of 200 atoms have been generated using classical force fields and subsequently relaxed at the PBE-GGAlevel of DFT theory. The gauge including projector augmented wave (GIPAW) method is then employed for computing the shielding and electric field gradient tensors for each silicon and boron atom. Silicon-29 MAS and boron-11 MQMAS NMR spectra of two glasses (x=0.40 and 0.80) have been acquired and theoretical spectra are found to well agree with the experimental data. For boron-11, the NMR parameter distributions have been analysed using a Kernel density estimation (KDE) approach which is shown to highlight its main features. Accordingly, a new analytical model that incorporates the observed correlations between the NMR parameters is introduced. It significantly improves the fit of the (11)B MQMAS spectra and yields, therefore, more reliable NMR parameter distributions. A new analytical model for a quantitative description of the dependence of the silicon-29 and boron-11 isotropic chemical shift upon the bond angles is proposed, which incorporates possibly the effect of SiO(2)-B(2)O(3) intermixing. Combining all the above procedures, we show how distributions of Si-O-T and B-O-T (T=Si, B) bond angles can be estimated from the distribution of isotropic chemical shift of silicon-29 and boron-11, respectively.

High-resolution 2H MAS NMR applied to deuterium analogs of hydrido eta2-dihydrogen complexes

(2)H solid-state, variable temperature magic angle spinning (MAS) NMR spectra of precipitated samples of the deutero dideuterium complexes Ru(D)(2)(eta(2)-D(2))(2)(PCy(3))(2) and RuD(eta(2)-D(2))I(PCy(3))(2) [Cy=cyclohexyl] are presented. They show that even at moderate MAS speed, high resolution is achieved at 7 and 14T allowing (2)H chemical shifts and quadrupole couplings to be obtained and assigned to different solid and gaseous (2)H species. These two parameters allow identifying chemically different hydrogen species in the material. The analysis of these parameters in this study reveals the presence of three different species in the sample, namely the complexes RuD(eta(2)-D(2))I(PCy(3))(2) and RuD(eta(2)-D(2))(2)I(PCy(3))(2), and highly mobile HD/D(2). These assignments are supported by (2)H T(1) relaxation times and (31)P MAS NMR spectra. Moreover, variable temperature MAS NMR spectra reveal temperature-dependent line-shape changes, which are clear indications of intramolecular hydrogen exchange of the deutero and the dideuterium ligands and which give an estimate for the activation energy of this process.

Polynomially scaling spin dynamics simulation algorithm based on adaptive state-space restriction

We report progress with an old problem in magnetic resonance -- that of the exponential scaling of simulation complexity with the number of spins. It is demonstrated below that a polynomially scaling algorithm can be obtained (and accurate simulations performed for over 200 coupled spins) if the dimension of the Liouville state space is reduced by excluding unimportant and unpopulated spin states. We found the class of such states to be surprisingly wide. It actually appears that a majority of states in large spin systems are not essential in magnetic resonance simulations and can safely be dropped from the state space. In restricted state spaces the spin dynamics simulations scale polynomially. In cases of favourable interaction topologies (sparse graphs, e.g. in protein NMR) the asymptotic scaling is linear, opening the way to direct fitting of molecular structures to experimental spectra.

Polymorphism ofN,N′′-Diacetylbiuret Studied by Solid-State13C and15N NMR Spectroscopy, DFT Calculations, and X-ray Diffraction

The molecular configuration and crystal structure of solid polycrystalline N,N''-diacetylbiuret (DAB), a potential nitrogen-rich fertilizer, have been analyzed by a combination of solid- and liquid-state NMR spectroscopy, X-ray diffraction, and DFT calculations. Initially a pure NMR study ("NMR crystallography") was performed as available single crystals of DAB were not suitable for X-ray diffraction. Solid-state 13C NMR spectra revealed the unexpected existence of two polymorphic modifications (alpha- and beta-DAB) obtained from different chemical procedures. Several NMR techniques were applied for a thorough characterization of the molecular system, revealing chemical shift anisotropy (CSA) tensors of selected nuclei in the solid state, chemical shifts in the liquid state, and molecular dynamics in the solid state. Dynamic NMR spectroscopy of DAB in solution revealed exchange between two different configurations, which raised the question, is there a correlation between the two different configurations found in solution and the two polymorphic modifications found in the solid state? By using this knowledge, a new crystallization protocol was devised which led to the growth of single crystals suitable for X-ray diffraction. The X-ray data showed that the same symmetric configuration is present in both polymorphic modifications, but the packing patterns in the crystals are different. In both cases hydrogen bonds lead to the formation of planes of DAB molecules. Additional symmetry elements, a two-fold screw in the case of alpha-DAB and a c-glide plane in the case of beta-DAB, lead to a more symmetric (alpha-DAB) or asymmetric (beta-DAB) intermolecular hydrogen-bonding pattern for each molecule.

Low-field optically detected EPR spectroscopy of transient photoinduced radical pairs

The effects of simultaneously applied weak static and weak radio frequency magnetic fields on the recombination of transient (<100 ns) radical pairs have been investigated using a low-field optically detected electron paramagnetic resonance technique. Measurements on the photoinduced electron-transfer reaction of perdeuterated pyrene with 1,3-dicyanobenzene using a approximately 0.3 mT radio frequency field at three separate frequencies (5, 20, and 65 MHz) in the presence of 0-4 mT static fields yield spectra that are strikingly sensitive to the frequency of the time-dependent field, to the strength of the static field, and to the relative orientation of the two fields. The spectra are simulated using a modified form of the gamma-COMPUTE algorithm originally devised for calculating magic angle spinning NMR spectra of polycrystalline samples. The essential features of the spectra are consistent with the radical pair mechanism and were satisfactorily simulated using parameters whose values are either known independently or for which estimates are readily available. The calculations included hyperfine couplings to four deuterons in the pyrene cation radical and three protons in the 1,3-dicyanobenzene anion radical. Spin-selective recombination was modeled using an exponential distribution of radical encounter times. The results are discussed in the context of the proposal that radical pair chemistry forms the basis of the magnetoreceptor that allows birds to sense the Earth's magnetic field as a source of compass information during migration.

Efficient orientational averaging by the extension of Lebedev grids via regularized octahedral symmetry expansion

Gaussian spherical quadrature methods in the guise of the Lebedev sampling grids are highly efficient for some orientational ("powder") averaging problems in solid state NMR. However, their applicability is currently restricted, as the sets of orientations are derived analytically and because they are not well adapted to simulate the broad peakshapes encountered, for example, in the NMR on static powders or on half-integer quadrupolar spins subject to second order quadrupolar interactions under magic-angle spinning conditions. We remedy these problems by (i) introducing the recursive procedure regularized octahedral symmetry expansion (ROSE), to which any existing Lebedev set may be subjected. Each recursive step gives a 9-fold enlarged set of orientations. (ii) We demonstrate that ROSE-expanded grids, in conjunction with spectral interpolation, is well suited for calculating broad peakshapes. These advances combine into the apparently most efficient general-purpose two-angle orientational averaging technique proposed to date for solid state NMR applications.

Investigation of multiaxis molecular motion by off-magic angle spinning deuteron NMR

The relatively new deuteron NMR method of off-axis-magic angle spinning (OMAS) has been extended and used to investigate multiaxis rotational jump motion. Floquet theory is developed for simulating deuteron OMAS spectra with multisite jumps at different rates about noncoincident axes, and efficient procedures are presented for computing the sideband line shapes. It is demonstrated experimentally that reproducible adjustment of the angle between the rotor axis and the static magnetic field is feasible with precision approaching +/- 0.01 degrees. This leads to the reintroduction of a scaled, first-order quadrupole coupling that defines a new kinetic window and makes deuteron OMAS much more sensitive than ordinary magic angle spinning to motion on the kilohertz time scale. Temperature-dependent deuteron OMAS line shapes of octanoic acid/urea-d4 inclusion compound have been recorded and fitted, using least-squares procedures, to provide rates of rotation about both CN and CO bonds. The Arrhenius activation parameters for rotation about CN bonds, Ea = 60.4+/-2.4 kJ/mol and ln(A) = 24.9+/-0.3, agree well with previous values determined by selective inversion experiments. However, OMAS yields Ea = 26.3+/-0.4 kJ/mole and ln(A) = 24.9+/-0.3 for whole-body rotation about the CO bond axis in contrast to previous analysis of static quadrupole echo (QE) line shapes which gave Ea = 22.3+/-0.3 kJ/mole and ln(A) = 24.8+/-0.6 for the same sample. The underlying homogeneous linewidths of OMAS spectra are much smaller than those of QE spectra, and this provides higher precision and less systematic error in the determination of rates.

EasySpin, a comprehensive software package for spectral simulation and analysis in EPR

EasySpin, a computational package for spectral simulation and analysis in EPR, is described. It is based on Matlab, a commercial technical computation software. EasySpin provides extensive EPR-related functionality, ranging from elementary spin physics to data analysis. In addition, it provides routines for the simulation of liquid- and solid-state EPR and ENDOR spectra. These simulation functions are built on a series of novel algorithms that enhance scope, speed and accuracy of spectral simulations. Spin systems with an arbitrary number of electron and nuclear spins are supported. The structure of the toolbox as well as the theoretical background underlying its simulation functionality are presented, and some illustrative examples are given.

Double-quantum filtered 1H MAS NMR spectra

It is shown that straightforward double-quantum filtered (1)H MAS NMR experiments yield spectral lineshapes that permit to estimate the minimum number of (1)H spins in a cluster. The approach may offer an alternative to multiple-quantum experiments for the characterisation of (1)H spin clusters of moderate size. The duration of the double-quantum excitation period has to be chosen suitably, it is necessary to find a practical compromise between optimum double-quantum filtration efficiency and optimum information content of the spectral lineshapes. Some (1)H MAS NMR experiments on partially deuterated maleic acid are reported as well as numerical simulations.

MAS NMR with and without double-quantum filtration at and near the n=0 rotational resonance condition

Spectral lineshapes of MAS NMR spectra of dipolar (re)coupled spin pairs exhibiting considerable chemical shielding anisotropies at and near the so-called n=0 rotational resonance (R2) condition are considered. The n=0 R2 condition is found to be not extremely sharp. Anisotropic interaction parameters such as chemical shielding tensor orientations and the magnitude of the dipolar coupling constant remain sensitively encoded in such lineshapes even when differences in isotropic chemical shielding values of up to 400 Hz (corresponding to ca. half the size of the dipolar coupling constant) are present. Additional double-quantum filtration (DQF) may enhance the sensitivity of spectral lineshapes to anisotropic interaction parameters for even larger differences in isotropic chemical shielding values. The dependence of the DQF efficiency on spin-system parameters as well as on external parameters (Larmor and MAS frequencies) is investigated. Away from R2 conditions a trend to lower DQF efficiencies is found whereas some spin-system parameters are more sensitively encoded in the corresponding spectral lineshapes. Our study is based on numerical simulations, with the known parameters of the 31P spin pair in Na4P2O7.10H2O representing our model case.

Rational reduction of periodic propagators for off-period observations

Many common solid-state nuclear magnetic resonance problems take advantage of the periodicity of the underlying Hamiltonian to simplify the computation of an observation. Most of the time-domain methods used, however, require the time step between observations to be some integer or reciprocal-integer multiple of the period, thereby restricting the observation bandwidth. Calculations of off-period observations are usually reduced to brute force direct methods resulting in many demanding matrix multiplications. For large spin systems, the matrix multiplication becomes the limiting step. A simple method that can dramatically reduce the number of matrix multiplications required to calculate the time evolution when the observation time step is some rational fraction of the period of the Hamiltonian is presented. The algorithm implements two different optimization routines. One uses pattern matching and additional memory storage, while the other recursively generates the propagators via time shifting. The net result is a significant speed improvement for some types of time-domain calculations.

Effects of pulse strength, width, and sample spinning speed on the spectral spin diffusion of multiquantum coherences of spin-32 quadrupolar nuclei

The effects of radio-frequency pulse strength, width, and sample spinning speed on the spin-diffusion spectrum of half-integer quadrupolar spins in solids have been studied by theoretical, numerical, and experimental investigations. It is revealed that the line shape of the cross peaks changes nonmonotonically with respect to the change of pulse strength, pulse width, or sample spinning speed. It is also found that the sample spinning speed has much more pronounced influence on the spin diffusion spectral line shape. In many cases of practical importance, the effect of sample spinning must be included in spectral analysis, in contrast to the practice of previous studies. Moreover, this effect can be exploited to further improve the precision in the determination of relative orientation of the electric-field gradient tensors of the exchange partners.

Rapid construction of solid-state magnetic resonance powder spectra from frequencies and amplitudes as applied to ESEEM

In many Fourier-transform spectroscopies, such as pulse magnetic resonance (NMR, EPR), time-domain signals are acquired. Parameters are extracted from these signals by fitting numerical simulations to the experimental data. At present, simulations are often performed in frequency domain (FD). These computations generate a list of frequencies and amplitudes associated with the complex exponential components evolving during one or several variable time intervals. In order to compare simulations with experiments, this peak list is converted to a finite-length time-domain (TD) signal. This can be achieved either by directly evoluting the exponentials in time (direct method) or by rounding their frequencies and binning their amplitudes into a frequency-domain array (histogram method). The first approach is equivalent to a brute-force TD simulation and is slow for a large number of peaks. The second approach is a fast, but very crude approximation and is usually applied without considering in detail the errors involved. A third method introduced and illustrated here is based on the convolution and deconvolution of a short finite impulse response filter kernel. This convolution approach is much faster than the direct method and by orders of magnitude more accurate than the histogram method. For both TD and FD signals a detailed analysis of the errors and of the associated computational costs is presented. The convolution approach is applicable to any simulation problem where TD signals consist of a large number of complex exponentials. In particular, it is the method of choice for simulating 1D and 2D electron spin echo envelope modulation (ESEEM) spectra of disordered systems.

Procedures for labeling the high-resolution axis of two-dimensional MQ-MAS NMR spectra of half-integer quadrupole spins

The increasing development and application of the multiple-quantum MAS NMR for half-integer quadrupole spins has led to various RF pulse sequences for improving the excitation of multiple-quantum coherences and their conversion to single-quantum coherences. As a result, several conventions for labeling the Fl dimension of a 2D MQ-MAS spectrum appear in the literature. The corresponding relations for extracting the isotropic chemical shift, the quadrupole coupling constant, and the asymmetry parameter from experimental data are not always provided. We analyze these various conventions systematically and propose a new one, similar to that introduced by J.-P. Amoureux and C. Fernandez (2000, Solid State NMR 10, 339-343). These various conventions are illustrated with 27Al (I = 5/2) nuclei in aluminum acetylacetonate Al(CH3COCHCOCH3)3. Another experimental problem often met, the aliasing of peaks in the 2D spectrum, is analyzed and illustrated with 27Al (I = 5/2) in NH4Y zeolite and 23Na (I = 3/2) in sodium pyrophosphate Na4P2O7.

Double-quantum-filtered rotational-resonance MAS NMR in the presence of large chemical shielding anisotropies

Double-quantum filtration under rotational resonance MAS NMR conditions where the chemical shielding anisotropies involved exceed the differences in isotropic chemical shielding is considered by means of numerical simulations and (13)C MAS NMR experiments. The responses of two different pulse sequences, suitable for double-quantum filtration specifically under rotational resonance conditions, to large chemical shielding anisotropies are compared. In the presence of large chemical shielding anisotropies a very recently introduced pulse sequence (T. Karlsson, M. Edén, H. Luthman, and M. H. Levitt, J. Magn. Reson. 145, 95-107, 2000) suffers losses in double-quantum-filtration efficiencies. The double-quantum-filtration efficiency of another pulse sequence (N. C. Nielsen, F. Creuzet, R. G. Griffin, and M. H. Levitt, J. Chem. Phys. 96, 5668-5677, 1992) is less afflicted by the presence of large chemical shielding anisotropies. Both sequences deliver double-quantum-filtered lineshapes that sensitively reflect chemical shielding tensor orientations. It is further shown that double-quantum-filtered rotational-resonance lineshapes of spin systems composed of more than two spins offer a suitable experimental approach for determining chemical shielding tensor orientations for cases where conventional rotational-resonance experiments are not applicable due to the presence of additional background resonances.

SIMPSON: a general simulation program for solid-state NMR spectroscopy

A computer program for fast and accurate numerical simulation of solid-state NMR experiments is described. The program is designed to emulate a NMR spectrometer by letting the user specify high-level NMR concepts such as spin systems, nuclear spin interactions, RF irradiation, free precession, phase cycling, coherence-order filtering, and implicit/explicit acquisition. These elements are implemented using the Tcl scripting language to ensure a minimum of programming overhead and direct interpretation without the need for compilation, while maintaining the flexibility of a full-featured programming language. Basically, there are no intrinsic limitations to the number of spins, types of interactions, sample conditions (static or spinning, powders, uniaxially oriented molecules, single crystals, or solutions), and the complexity or number of spectral dimensions for the pulse sequence. The applicability ranges from simple 1D experiments to advanced multiple-pulse and multiple-dimensional experiments, series of simulations, parameter scans, complex data manipulation/visualization, and iterative fitting of simulated to experimental spectra. A major effort has been devoted to optimizing the computation speed using state-of-the-art algorithms for the time-consuming parts of the calculations implemented in the core of the program using the C programming language. Modification and maintenance of the program are facilitated by releasing the program as open source software (General Public License) currently at http://nmr.imsb.au.dk. The general features of the program are demonstrated by numerical simulations of various aspects for REDOR, rotational resonance, DRAMA, DRAWS, HORROR, C7, TEDOR, POST-C7, CW decoupling, TPPM, F-SLG, SLF, SEMA-CP, PISEMA, RFDR, QCPMG-MAS, and MQ-MAS experiments.

Simulations of chemical exchange lineshapes in CP/MAS spectra using floquet theory and sparse matrix methods

This paper presents a general method for simulating the effect of chemical exchange on MAS NMR spectra of solid samples. The complication in MAS spectra is that the Hamiltonian itself is time-dependent, due to the spinning of the sample. The approach taken in this work is to use Floquet theory to convert the problem into a time-independent form, and then use established methods (used in liquid NMR simulations) to calculate the lineshape. Floquet theory has been admired for its elegance, but criticized for its computational inefficiencies. This is because it removes the time dependence of the system by expanding the problem in a Fourier-like series. This makes a relatively small, time-dependent calculation into a much larger time-independent one. Typically, we use twice as many Floquet blocks as there are spinning sidebands, so the increase in size is substantial. The problem that this creates stems from the fact that the usual Householder methods for diagonalizing a matrix scale as the cube of the size of the matrix. This would make a Floquet calculation prohibitively long. However, the Floquet matrix is inherently sparse, so sparse matrix methods can produce substantial computational savings. Also, fully diagonalizing a matrix is expensive, but converting the matrix to a tridiagonal form (using iterative Lanczos methods) is much cheaper. The use of the Lanczos methods makes the Floquet calculations feasible as a general method for systems of more than one spin. We show how to set up the full matrix describing chemical exchange in a spinning sample, but the details of how the Lanczos methods work are not included-they are described elsewhere. We then validate the theory by simulating the MAS spectra of dimethyl sulfone both with natural abundance (13)C and with methyl groups labeled with (13)C. The latter system has both dipolar and chemical shielding anisotropy terms contributing to the spectrum. Copyright 2000 Academic Press.

Double-quantum filtration under rotational-resonance conditions: numerical simulations and experimental results

The dependence of the performance of a recently introduced pulse sequence to achieve double-quantum excitation under the n = 1 rotational-resonance condition (T. Karlsson, M. Eden, H. Luthman, and M. H. Levitt, 2000, J. Magn. Reson. 145, 95-107) on different spin-system properties is investigated by means of numerical simulations and (13)C MAS NMR experiments. For spin systems where chemical shielding anisotropies amount to only an insignificant fraction of the isotropic chemical shielding difference, high efficiencies are found for large and small dipolar coupling interactions. In the presence of significant chemical shielding anisotropies the overall efficiencies decrease and become strongly dependent on the duration of the excitation period. It is demonstrated that those spin-system parameters which are sensitively encoded in the lineshapes of a conventional n = 1 rotational-resonance spectrum are similarly sensitively encoded in the corresponding rotational-resonance double-quantum-filtered lineshapes and may be quantitatively recovered by iterative lineshape-fitting approaches. In certain favorable circumstances, the in-built selectivity of the rotational-resonance double-quantum-filtration approach permits successful application of the experiment on spin systems with more than two spins. Copyright 2000 Academic Press.

Spin-locking mechanism of spin I = 3/2 quadrupolar nuclei undergo magic angle spinning

The spin-locking mechanism of the spin I = 3/2 quadrupolar nuclei under magic angle spinning (MAS) has been theoretically and experimentally investigated, and the criterion of adiabatic passage around zero-crossings of the quadrupole splitting was inferred from the time-dependent Shrödinger equation in this article. The theory, numerical simulations, and experiments conducted in this work all indicated that second-order quadrupole interaction and off-resonance play important roles in the spin-locking of the quadrupolar nuclei, and they were responsible for the great loss of the spin-locking signals. The spin-locking for a spin I = 3/2 nucleus might be achieved by minimizing the effect of the second-order quadrupole interaction by using a radio frequency (RF) offset. This offset was realized by setting the RF to the opposite position of the isotropic second-order quadrupolar shift of single quantum coherences.

Pure absorption-mode spectra using a modulated RF mixing period in MQMAS experiments

Different approaches to obtain pure absorption-mode lineshapes in MQMAS experiments employing a train of 180 degrees phase-alternating pulses for the multiple-quantum to single-quantum mixing period are investigated. Four pulse sequences, which achieve this by using either the shifted-echo approach or the hypercomplex approach with symmetric coherence transfer pathways, are presented and their improved lineshape- and sensitivity-performance is experimentally demonstrated by (87)Rb MQMAS of RbNO(3). Compared to the original modulated-rf mixing sequence, sensitivity enhancements by factors up to 1.3 are obtained with the sequences described here.

Magnitudes and orientations of interaction tensors determined from rotational resonance MAS NMR lineshapes of a four-(13)C-spin system

Possibilities and limitations of iterative lineshape fitting approaches for the complete determination of magnitudes and orientations of NMR interaction tensors in a four-(13)C-spin system from MAS NMR experiments are investigated. The availability of fast and numerically accurate computational methods is an important prerequisite. The model compound chosen for this investigation is the monoammonium salt of maleic acid. Various selectively and fully (13)C-labeled versions of this compound permit a stepwise reduction of the number of unknown parameters, necessary to fully describe the four-(13)C-spin system in the uniformly (13)C-labeled maleate moiety. This stepwise procedure allows one to monitor reliability and accuracy of multiparameter fits of the four-(13)C-spin system itself, as well as to characterize limitations and requirements for such fitting procedures. Satisfactory (1)H-decoupling performance is an essential experimental requirement; TPPM decoupling yields n = 1, 2 rotational resonance (13)C MAS NMR lineshapes suitable for analysis by iterative lineshape fitting methods. It is demonstrated that assumptions about "typical" chemical shielding tensor orientations, even if not deviating much from the real orientations, lead to severe errors in internuclear distance determinations. Copyright 1999 Academic Press.

Anomalous rotational resonance spectra in magic-angle spinning NMR

Magic-angle spinning NMR spectra of samples containing dilute spin-1/2 pairs display broadenings or splittings when a rotational resonance condition is satisfied, meaning that a small integer multiple of the spinning frequency matches the difference in the two isotropic shift frequencies. We show experimental rotational resonance NMR spectra of a 13C2-labeled retinal which are in qualitative disagreement with existing theory. We propose an explanation of these anomalous rotational spectra involving residual heteronuclear couplings between the 13C nuclei and the neighboring 1H nuclei. These couplings strongly influence the rotational resonance 13C spectrum, despite the presence of a strong radiofrequency decoupling field at the 1H Larmor frequency. We model the residual heteronuclear couplings by differential transverse relaxation of the 13C single-quantum coherences. We present a superoperator theory of the phenomenon and describe a numerical algorithm for rapid Liouville space simulations in periodic systems. Good agreement with experimental results is obtained by using a biexponential transverse relaxation model for each spin site.

Calculation of MAS spectra influenced by slow molecular tumbling

A numeric algorithm is proposed that is suitable to calculate spectral lineshapes influenced by isotropic and anisotropic tumbling under sample spinning conditions. It is based on the stochastic Liouville equation and a rotational diffusion process described by a stationary Markov operator. A corresponding FORTRAN program can be implemented on a regular personal computer. The calculations result in spectral lineshapes including a complete set of spinning sidebands. The sensitive time scale of the resulting lineshapes depends on the deviation of the sample spinning axis from the magic angle. An example is presented demonstrating the potential of off-magic-angle spinning as a tool to analyze slow tumbling motions.

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.