Simulations of molecular dynamics in solid-state NMR spectra of spin-1 nuclei including effects of CSA- and EFG-terms up to second order

By numerical simulations MAS and QCPMG methods for acquiring spectra of spin-1 nuclei were compared in order to determine the most sensitive experiment for analysis of molecular dynamics. To comply with the large quadrupolar constants for 14N and the CSA reported for 6Li both of these interactions are included up to second order. For 2H and 6Li both QCPMG and single-pulse MAS experiments were suitable for dynamics studies whereas the single-pulse MAS experiment were the method of choice for investigation of 14N dynamics for C(Q)'s larger than 750kHz at 14.1T. This property prohibits excitation of the 14N lineshape using either single hard or softer composite rf-pulses. Focusing on 14N it was demonstrated that the centerband lineshape is sensitive toward both off-MAS and CSA effects. In addition, excitation by real-time pulses showed that proper lineshapes corresponding to a site with a C(Q) of 3MHz may be excited by a very short pulse.     

Single- and multiple-quantum cross-polarization in NMR of quadrupolar nuclei in static samples

Cross-polarization from a spin I=1/2 nucleus (e.g., ¹H) to a spin S = 3/2 nucleus (e.g., ²³Na) or a spin S = 5/2 nucleus (e.g., ²⁷A1 or ⁿO) in static powder samples is investigated. The results of conventional (single-quantum), three-quantum, and five-quantum cross-polarization experiments are presented and discussed. Based on a generalization of an existing theory of cross-polarization to quadrupolar nuclei, computer simulations are used to model the intensity and lineshape variations observed in cross-polarized NMR spectra as a function of the radio-frequency field strengths of the two simultaneous spin-locking pulses. These intensity and lineshape variations can also be understood in terms of the spin S = 3/2 or 5/2 nutation rates determined from experimental quadrupolar nutation spectra. The results of this study are intended as a preliminary step towards understanding single- and multiple-quantum cross-polarization to quadrupolar nuclei under MAS conditions and the application of these techniques to the MQMAS NMR experiment.     

A general strategy for the NMR observation of half-integer quadrupolar nuclei in dilute environments.

A general strategy for the observation of low gamma half-integer quadrupolar nuclides in biological systems is presented. The methodology combines low-temperature (4-100 K) techniques with cross-polarization (CP) experiments while employing a so-called Carr-Purcell-Meiboom-Gill spin-echo sequence (CPMG). This combined approach is termed CP/QCPMG. Also discussed are data processing issues that are unique to the induced signals that result from the QCPMG pulse sequence. Central to this strategy is the development of a stable low-temperature (4 to 250 K) NMR double-resonance probe. The probe is robust enough to handle multiple contact experiments and long acquisition periods with 1H decoupling. This approach is illustrated with low-temperature solid-state 67Zn and 25Mg NMR CP/QCPMG experiments on model compounds. The conclusion reached is that the strategy affords sufficient sensitivity to examine Zn2+ and/or Mg2+ binding sites in metalloproteins.     

To what extent does the centerband and each spinning sideband contain contributions from different crystallites of the powder sample?

It is shown that due to the destructive interference of the magnetization paths of crystallites taking place during the rotor period at slow spinning regime, the contribution of different crystallites to the centerband and to each spinning sideband is strongly weighted. For this, a separated-local-field experiment is used to tag the crystallites contributing to a given spinning sideband at different spinning speeds. The orientation dependence of spinning sidebands is also responsible for different lineshapes of the centerband and of each spinning sidebands observed under conditions of off-magic angle spinning.     

The influence of carrier level and frequency on modulation and beat-detection thresholds for sinusoidal carriers

This paper is concerned with modulation and beat detection for sinusoidal carriers. In the first experiment, temporal modulation transfer functions (TMTFs) were measured for carrier frequencies between 1 and 10 kHz. Modulation rates covered the range from 10 Hz to about the rate equaling the critical bandwidth at the carrier frequency. In experiment 2, TMTFs for three carrier frequencies were obtained as a function of the carrier level. In the final experiment, thresholds for the detection of either the lower or the upper modulation sideband (beat detection) were measured for "carrier" frequencies of 5 and 10 kHz, using the same range of modulation rates as in experiment 1. The TMTFs for carrier frequencies of 2 kHz and higher remained flat up to a modulation rate of about 100-130 Hz and had similar values across carrier frequencies. For higher rates, modulation thresholds initially increased and then decreased rapidly, reflecting the subjects' ability to resolve the sidebands spectrally. Detection thresholds generally improved with increasing carrier level, but large variations in the exact level dependence were observed, across subjects as well as across carrier frequencies. For beat rates up to about 70 Hz (at 5 kHz) and 100 Hz (at 10 kHz), beat detection thresholds were the same for the upper and the lower sidebands and were about 6 dB higher than the level per sideband at the modulation-detection threshold. At higher rates the threshold for both sidebands increased, but the increase was larger for the lower sideband. This reflects an asymmetry in masking with more masking towards lower frequencies. Only at rates well beyond the maximum of the TMTF did detection for the lower sideband start to be better than that for the upper sideband. The asymmetry at intermediate frequency separations can be explained by assuming that detection always takes place in filters centered above the stimulus spectrum. The shape of the TMTF and the beat-detection data reflects a limitation in resolving fast amplitude variations, which must occur central to the inner-ear filtering. Its characteristic resembles that of a first-order low-pass filter with a cutoff frequency of about 150 Hz.     

Solid-state 25Mg QCPMG NMR of bis(cyclopentadienyl)magnesium

Application of the "quadrupolar Carr-Purcell Meiboom-Gill" (QCPMG) sequence permits the first natural abundance solid-state 25Mg NMR study of an organometallic magnesium compound, bis(cyclopentadienyl)magnesium. Analytical and numerical simulations of both static and magic-angle spinning QCPMG NMR spectra beget an axially symmetric 25Mg electric field gradient (EFG) tensor (quadrupolar asymmetry parameter, eta(Q)=0.01(1)) with a nuclear quadrupole coupling constant of C(Q)=5.80(5)MHz. Restricted Hartree-Fock and hybrid density functional theory (B3LYP) calculations are in good agreement with experimental EFG values and predict a chemical shielding anisotropy of about 40-50 ppm, which we attempt to elucidate by numerical simulations. The parameters and orientation of the 25Mg EFG tensor are rationalized from examination of the crystal structure and molecular symmetry. The NMR properties of the cyclopentadienyl rings are examined by 13C[1H] CPMAS NMR, RHF and hybrid-DFT (B3LYP) calculations, and simulations of the effects of chemical exchange on the 13C powder pattern.     

Calculation of solid-state NMR lineshapes using contour analysis

Two new methods for calculating lineshapes in solid-state NMR spectra are described. The first method, which we refer to as semi-analytical, allows the rapid calculation of quadrupolar central-transition lineshapes in both static and magic-angle spinning cases. The second method, which is fully numerical, allows the calculation of lineshapes resulting from any combination of interactions, including quadrupolar, dipolar and chemical shift anisotropy, and is not restricted to cases in which the principal axis systems for the different interactions are aligned. Both methods are derived from consideration of the contour lines on a plot of the resonance frequency against the Euler angles, allowing the intensity of the lineshape to be calculated at each frequency. Consequently, highly accurate lineshapes can be calculated more rapidly than previously possible, since only orientations contributing to each specific frequency are considered. For our semi-analytical method, the intensity of each point in the lineshape can be directly calculated in tens of milliseconds on a standard PC. In contrast, established methods can take several hours to calculate the same lineshape.     

Satellite transitions in natural abundance solid-state (33)S MAS NMR of alums--sign change with zero-crossing of C(Q) in a variable temperature study

Experiences obtained from recent improvements in the performance of solid-state (14)N MAS NMR spectroscopy have been used in a natural abundance (33)S MAS NMR investigation of the satellite transitions for this interesting spin I=3/2 isotope. This study reports the first observation of manifolds of spinning sidebands for these transitions in (33)S MAS NMR as observed for the two alums XAl(SO(4))(2) x 12H(2)O with X=NH(4) and K. For the NH(4)-alum a variable temperature (33)S MAS NMR study, employing the satellite transitions, shows that the (33)S quadrupole coupling constant (C(Q)) exhibits a linear temperature dependence (in the range -35 degrees C to 70 degrees C) with a temperature gradient of 3.1 kHz/ degrees C and undergoes a sign change with zero-crossing for C(Q) at 4 degrees C (277 K). For the isostructural K-alum a quite similar increase in the magnitude of C(Q) with increasing temperature is observed, and with a temperature gradient of 2.3 kHz/ degrees C. Finally, for optimization purposes, a study on the effect of the applied pulse widths at constant rf field strength on the intensity and variation in second-order quadrupolar lineshape for the central (1/2<-->-1/2) transition of the K-alum has been performed.     

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.     

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 = ) and ⁵⁹Co (S = ) 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- multiple-quantum NMR literature.     

Refocussing of chemical and paramagnetic shift anisotropies in 2H NMR using the quadrupolar-echo experiment

A simple two-pulse spin-echo experiment is shown to refocus inhomogeneous broadening arising from both chemical and/or paramagnetic shift anisotropy and a first-order I=1 quadrupolar interaction. The method is shown to yield ²H NMR spectra of a paramagnetic solid (CuCl₂ · 2D₂O) and of a non-paramagnetic solid (D₂C₂O₄ · 2D₂O) that are significantly less distorted than those provided by the conventional quadrupolar-echo method. The technique will thus prove useful in studies of motion and dynamics where detailed analysis of the ²H lineshape is performed.     

High-field QCPMG NMR of strontium nuclei in natural minerals

The only stable NMR-active isotope of strontium, (87)Sr, is a spin-9/2 quadrupolar nucleus that has a low gyromagnetic ratio, a low natural abundance, and a large nuclear electric quadrupole moment. In this work, we utilize the quadrupolar Carr-Purcell-Meiboom-Gill (QCPMG) pulse sequence and a 21.14 T NMR spectrometer at the Pacific Northwest National Laboratory to characterize the strontium sites in the natural minerals strontianite (SrCO(3)) and celestine (SrSO(4)). QCPMG at 21.14 T was found to provide sensitivity enhancements of roughly two orders of magnitude over Hahn-echo experiments at an 11.74 T magnetic field. We extracted the quadrupolar parameters for the strontium nuclei through iterative simulations of the experimental spectra with the SIMPSON program by Bak, Rasmussen, and Nielsen. The data show that the quadrupolar parameters of (87)Sr appear to be highly sensitive to the symmetry of the strontium coordination environment and can thus provide information about the strontium binding environment in complex systems.     

Multiple-Rotor-Cycle QPASS Pulse Sequences: Separation of Quadrupolar Spinning Sidebands with an Application to La NMR

The quadrupolar phase-adjusted spinning sidebands (QPASS) pulse sequence has been recently demonstrated as a useful method for obtaining quadrupolar parameters with magic-angle spinning NMR. The sequence separates spinning sidebands by order in a two-dimensional experiment. A sheared projection of the 2D spectrum effectively yields the infinite spinning rate second-order quadrupolar powder pattern, which can be analyzed to determine quadrupolar coupling constants and asymmetry parameters. The RF power and spinning speed requirements of the original QPASS sequence make it an experimentally demanding technique. A new version of the sequence is demonstrated here and is shown to alleviate many problems associated with the original sequence. New solutions to the determining equations, based on the use of multiple rotor cycles in the QPASS sequence, lead to longer delays between the nine π pulses, provide less chance of pulse overlap, and allow for use of weaker RF field strengths that excite only the central quadrupolar transition. A three-rotor-cycle version of the new experiment is demonstrated on the ¹³⁹La nucleus.     

Magnetic resonance lineshape in the presence of slow motion

The effect on the magnetic resonance lineshape of slow molecular motion is considered. The molecules are assumed to undergo diffusive jumps of angle ε described by the distribution function W(ε)=(N/τ) exp (λ cos ε), where τ is the mean lifetime between jumps and λ a parameter describing the width of the distribution. As λ is varied from zero to infinity this distribution describes diffusion models that change continuously from the strong collision limit to Brownian rotational diffusion. Magnetic resonance lineshapes are calculated by Freed's method using the asymptotic expansion technique, and results are presented for an axially symmetric (secular) Zeeman hamiltonian.

An exact expression for the magnetic resonance lineshape is derived in the strong collision limit for any secular hamiltonian and a few examples are presented. It is also shown how this technique can be used as a basis for lineshape calculations in the presence of moderately large jumps.     

Manifestations of Slow Site Exchange Processes in Solution NMR: A Continuous Gaussian Exchange Model

The effects of site exchange due to slow conformational changes in rapidly rotating molecules in solution are examined in detail. Significant gaps in the currently available theory are filled. The effects of site exchange on the lineshape, decay of a simple spin-echo, decay of the even echoes in a Carr-Purcell-Meiboom-Gill (CPMG) pulse-sequence, and decay of the transverse magnetization in a resonant spin-locking field are investigated. Both trajectory and stochastic operator approaches are formulated and shown to be completely equivalent whenever the dynamics of population transfers among the inequivalent sites is governed by either a stationary or a nonstationary Markov process. A nonstationary Markov process may result from Brownian dynamics (a stationary Markov process) in a larger conformational space that contains the subspace of inequivalent sites. A continuous Gaussian exchange model is formulated in which a nucleus undergoes continuous one-dimensional motion in a harmonic potential well that is located in a linear chemical shift gradient. The effects of this Gaussian exchange model on the lineshape, simple spin-echo decay, and decay of the even echoes of a CPMG pulse train are treated rigorously via the trajectory approach. Compact analytical expressions are obtained for the relevant correlation functions in each case. The relevant decays are found to be exponential in the very short time and long time limits, which are not necessarily experimentally significant in any given case. In the fast exchange limit the relevant decays are exponential at all times, and explicit formulas are given for their decay rates. In the long time limit, all discrete multisite models with the same intrinsic Ro2 at every site are shown to be completely equivalent to a continuous Gaussian model with appropriate relaxation time and variance of the Larmor frequency. The effects of this Gaussian exchange model on the decay of the transverse magnetization in a resonant spin-locking field are treated heuristically by a trajectory approach. The intrinsic contribution (Ro1rho) of rapid rotations and dipole-dipole interactions to relax the transverse magnetizations of two nuclei of the same kind in the presence of a (nearly) resonant spin-locking field is also derived and found to be practically the same as the intrinsic contribution, Ro2, of those same rotations to the simple and CPMG spin-echo decay rates and linewidth. Literature data for the linewidth, decay rate of the CPMG even spin-echoes, and R(1rho) decay rate for the A9-H2 protons of adenines at the central TpA step in the sequence, 5'-GCAGGTTTAAACCTCG-3', are analyzed using the Gaussian exchange model to assess the time-scale and variance of the site exchange process as well as the intrinsic Ro2 rate. Although a single Gaussian exchange process with appropriate parameters can fit these three A9-H2 data rather well, this particular "solution" cannot be reconciled with NMR relaxation data on other protons in the same DNA molecule. Rather good agreement with all of the observations is obtained by using a model of two concurrent Gaussian exchange processes, whose relaxation times, tau = 7 and 460 micros, differ in time-scale by a factor of 65. The insensitivity of R1rho in the presence of a fast site exchange process to much slower concurrent site exchange processes is explicitly demonstrated. Protocols for detecting and characterizing a second slow site exchange process are suggested.     

Separation of quadrupolar and magnetic contributions to spin-lattice relaxation in the case of a single isotope

We present a NMR pulse double-irradiation method which allows one to separate magnetic from quadrupolar contributions in the spin–lattice relaxation. The pulse sequence fully saturates one transition while another is observed. In the presence of a Δm = 2 quadrupolar contribution, the intensity of the observed line is altered compared to a standard spin-echo experiment. We calculated analytically this intensity change for spins I = 1, , , thus providing a quantitative analysis of the experimental results. Since the pulse sequence we used takes care of the absorbed radiofrequency power, no problems due to heating arise. The method is especially suited when only one NMR sensitive isotope is available. Different cross-checks were performed to prove the reliability of the results obtained. The applicability of this method is demonstrated by a study of the plane oxygen ¹⁷O (I = ) in the high-temperature superconductor YBa₂Cu₄O₈: the ¹⁷O spin–lattice relaxation rate consists of magnetic as well as quadrupolar contributions.     

Application of fast amplitude-modulated pulse trains for signal enhancement in static and magic-angle-spinning 47,49Ti-NMR spectra

It is demonstrated that the use of fast amplitude-modulated RF pulse trains with constant (FAM-I) and incremented pulse durations (SW-FAM) leads to considerable sensitivity enhancement for the central-transition signal (via spin population transfer from the satellite transitions) for solid-state NMR spectra of titanium, 47Ti (I = [Formula: see text] and 49Ti (I = [Formula: see text]. For the magic-angle spinning spectra of TiO2 and BaTiO3, the intensity of the 49Ti central-transition line was more than doubled compared to simple Hahn-echo acquisition, while for the static case, enhancement factors of 1.6 (TiO2) and 1.8 (BaTiO3) were obtained. No lineshape distortions are observed in either MAS or static spectra of both compounds. Employment of the FAM and SW-FAM sequences should be useful in the routine acquisition of 47,49Ti spectra, as the NMR signal can be detected much faster.     

Signal enhancement in solid-state NMR of quadrupolar nuclei

Recent progress in the development and application of signal enhancement methods for NMR of quadrupolar nuclei in solids is presented. First, various pulse schemes for manipulating the populations of the satellite transitions in order to increase the signal of the central transition (CT) in stationary and rotating solids are evaluated (e.g., double-frequency sweeps, hyperbolic secant pulses). Second, the utility of the quadrupolar Carr–Purcell–Meiboom–Gill (QCPMG) and WURST-QCPMG pulse sequences for the rapid and efficient acquisition of particularly broad CT powder patterns is discussed. Third, less frequently used experiments involving polarization transfer from abundant nuclear spins (cross-polarization) or from unpaired electrons (dynamic nuclear polarization) are assessed in the context of recent examples. Advantages and disadvantages of particular enhancement schemes are highlighted and an outlook on possible future directions for the signal enhancement of quadrupolar nuclei in solids is offered.     

Observation of spinning sidebands in the Al magic-angle spinning nuclear magnetic resonance spectra of FAU and EMT structure-type zeolites

Wide-band (1 MHz) ²⁷Al magic-angle spinning nuclear magnetic resonance (MAS NMR) spectra were recorded for zeolite Y (Si/Al 2.7) and high-silica (Si/Al 3.8) FAU, EMT and mixed FAU-EMT structure-type zeolites synthesized using 15-crown-5 and/or 18-crown-6 ethers as templating agents. Spinning sidebands (related to first-order quadrupolar effects affecting satellite transitions) are observed in the spectra of the four calcined and fully rehydrated samples, reflecting a high symmetry of the framework aluminium atom surrounded by four oxygens. It is shown that the intensity of the spinning sidebands progressively increases after calcination and rehydration of the samples, indicating that the restoration of the high local order around the ²⁷Al nuclei is rather slow. On the other hand, second-order quadrupolar interactions rapidly decrease upon rehydration of the calcined samples which is achieved within one day, as indicated by thermogravimetry. Some hypotheses are proposed to explain such a difference, and the role of water is also discussed.     

Quadrupolar transitions evidenced by resonant auger spectroscopy

From absorption spectra, the only way to bring to the fore the occurrence of quadrupolar transitions is to study their angular dependence. Resonant spectroscopies offer a new opportunity to obtain more insight into excited electronic states by studying lineshape and intensity of decay processes. We show here that resonantly excited Ti KL(2,3)L(2,3) Auger spectra of TiO2(110) carry a clear signature of quadrupolar transitions to localized e(g) and t(2g) d-like states, giving access to a direct measurement of crystal field splitting.