Theoretical and experimental assessment of single- and multiple-quantum cross-polarization in solid state NMR

Continuous wave cross-polarization (CP) NMR experiments with magic angle spinning (MAS) are reviewed for the case of isolated spin pairs I-S, with spin quantum numbers I = ½ and S ½ (1/2, 3/2, …). For two spin-1/2 nuclei, the Hartmann-Hahn matching conditions are examined at various sample rotation rates ν_R, especially with regard to off-resonance behaviour. In addition to signal enhancement, the CPMAS experiment can be used for the selective determination of inter-nuclear distances between spin-1/2 nuclei. Theoretical examination of the CP transfers to single-quantum (1Q-CPMAS) and multiple-quantum (MQ-CPMAS) levels of quadrupolar nuclei is presented. Simple analytical formulae describing the Hartmann-Hahn matching under various experimental conditions are verified using computer simulations of the spin density matrix under MAS, and the experimental data. The strategies for the most efficient acquisition of 1Q-CPMAS and MQ-CPMAS spectra are extensively 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.     

Field-dependent nuclear relaxation of spins 1/2 induced by dipole-dipole couplings to quadrupole spins: LaF3 crystals as an example

A general theory of spin-lattice nuclear relaxation of spins I=1/2 caused by dipole-dipole couplings to quadrupole spins S1, characterized by a non-zero averaged (static) quadrupole coupling, is presented. In multispin systems containing quadrupolar and dipolar nuclei, transitions of spins 1/2 leading to their relaxation are associated through dipole-dipole couplings with certain transitions of quadrupole spins. The averaged quadrupole coupling attributes to the energy level structure of the quadrupole spin and influences in this manner relaxation processes of the spin 1/2. Typically, quadrupole spins exhibit also a complex multiexponential relaxation sensed by the dipolar spin as an additional modulation of the mutual dipole-dipole coupling. The proposed model includes both effects and is valid for an arbitrary magnetic field and an arbitrary quadrupole spin quantum number. The theory is applied to interpret fluorine relaxation profiles in LaF3 ionic crystals. The obtained results are compared with predictions of the 'classical' Solomon relaxation theory.     

固体中半整数四极核的自旋扩散

首先介绍固态中自旋扩散的一般理论，包括半经典描述和建立在投影算子理论上的密度矩阵描述. 接着以丰核环境中相互偶合的自旋-1/2系统以及自旋-3/2系统为典型列举了自旋扩散速率的计算. 最近藉助多量子魔角旋转(MQMAS)方法实现半整数四极核的多量子谱自旋扩散实验，可以测量固体粉末中半整数四极核体系四极张量相对方向. 结合作者最近的计算机模拟和实验测量结果对这一新兴方向作了重点介绍，尤其指出了射频
脉冲强度、宽度及样品旋转速度对交叉峰线型的影响.     

Coherence transfer between spy nuclei and nitrogen-14 in solids

Coherence transfer from 'spy nuclei' such as (1)H or (13)C (S=1/2) was used to excite single- or double-quantum coherences of (14)N nuclei (I=1) while the S spins were aligned along the static field, in the manner of heteronuclear single-quantum correlation (HSQC) spectroscopy. For samples spinning at the magic angle, coherence transfer can be achieved through a combination of scalar couplings J(I,S) and second-order quadrupole-dipole cross-terms, also known as residual dipolar splittings (RDS). The second-order quadrupolar powder patterns in the two-dimensional spectra allow one to determine the quadrupolar parameters of (14)N in amino acids.     

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.     

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.     

Kinetics of 1H→13C NMR cross-polarization in polymorphs and solvates of the antipsychotic drug olanzapine

The (1)H→(13)C NMR cross-polarization (CP) was studied under magic-angle spinning at 7.5 kHz in various crystal forms of the antipsychotic drug olanzapine: two polymorphs (metastable I and stable II) and eight solvates containing organic solvent and water molecules. The CP kinetics followed the non-classical I-I(*)-S model, in which CP begins in a spin cluster of proximate abundant spins I(*) and rare spins S, then is controlled by spin diffusion of the abundant spins I from bulk to the I(*) spins of the spin cluster and finally is governed by spin-lattice relaxation of the abundant spins in the rotating frame. The corresponding CP kinetics parameters were determined and analyzed. It was demonstrated that the, λ and T(df) values (the CP time constant, the cluster composition parameter and the (1)H spin-diffusion constant, respectively) were very useful to discriminate the functional groups, especially in the 3D parameter space. In order to conveniently analyze the large amount (175) of the collected CP parameters, the number of the observed variables was reduced using the principal component (PC) analysis. The 2D plot of PC2 vs. PC1 showed adequate separation of the CH(3), CH(2), CH and C cases (C stands for carbons without adjacent hydrogens). It was demonstrated that those cases were located along the PC1 axis in the order of increasing (1)H-(13)C dipolar couplings: C相似文献   

Relaxation-induced dipolar exchange with recoupling-An MAS NMR method for determining heteronuclear distances without irradiating the second spin

A new magic-angle spinning NMR method for distance determination between unlike spins, where one of the two spins in question is not irradiated at all, is introduced. Relaxation-induced dipolar exchange with recoupling (RIDER) experiments can be performed with conventional double-resonance equipment and utilize the familiar π-pulse trains to recouple the heteronuclear dipolar interaction under magic-angle spinning conditions. Longitudinal relaxation of the passive spin during a delay between two recoupling periods results in a dephasing of the heteronuclear coherence and consequently a dephasing of the magnetization detected after the second recoupling period. The information about the dipolar coupling is obtained by recording normalized dephasing curves in a fashion similar to the REDOR experiment. At intermediate mixing times, the dephasing curves also depend on the relaxation properties of the passive spin, i.e., on single- and double-quantum longitudinal relaxation times for the case of I = 1 nuclei, and these relaxation times can be estimated with this new method. To a good approximation, the experiment does not depend on possible quadrupolar interactions of the passive spin, which makes RIDER an attractive method when distances to quadrupolar nuclei are to be determined. The new method is demonstrated experimentally with ¹⁴N and ²H as heteronuclei and observation of ¹³C in natural abundance.     

19F/29Si rotational-echo double-resonance and heteronuclear spin counting under fast magic-angle spinning in fluoride-containing octadecasil

19F/29Si rotational-echo double-resonance (REDOR) and theta-REDOR NMR techniques have been applied under fast magic-angle spinning to a powder sample of fluoride-containing octadecasil. Efficient dipolar recoupling was observed and the effect of finite pulse lengths was found to be negligible using standard radiofrequency field strengths. Moreover, the determined internuclear distance of the 19F-29Si spin pairs formed by the silicons in the D4R units (T-1 site) and the fluoride anions is in very good agreement with previous REDOR and Hartmann-Hahn cross-polarization measurements. Numerical simulation of the REDOR dephasing curves at both the T-1 and T-2 sites considering all fluoride anions in the infinite solid lattice clearly confirm the X-ray crystal structure of octadecasil. Heteronuclear spin-counting theta-REDOR experiments are found to be very useful to obtain direct insight into the local network of dipolar interactions. Indeed, while 19F-29Si pair-like behavior is confirmed at the T-1 site, multiple dipolar interactions are clearly evidenced at the T-2 site.     

Q-shear transformation for MQMAS and STMAS NMR spectra

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

Repetitive cross-polarization contacts via equilibration-re-equilibration of the proton bath: Sensitivity enhancement for NMR of membrane proteins reconstituted in magnetically aligned bicelles

Thermodynamic limit of magnetization corresponding to the intact proton bath usually cannot be transferred in a single cross-polarization contact. This is mainly due to the finite ratio between the number densities of the high- and low-gamma nuclei, quantum-mechanical bounds on spin dynamics, and Hartmann-Hahn mismatches due to rf field inhomogeneity. Moreover, for fully hydrated membrane proteins refolded in magnetically oriented bicelles, short spin-lock relaxation times (T1ρ) and rf heating can further decrease cross polarization efficiency. Here we show that multiple equilibrations-re-equilibrations of the high- and low-spin reservoirs during the preparation period yield an over twofold gain in the magnetization transfer as compared to a single-contact cross polarization (CP), and up to 45% enhancement as compared to the mismatch-optimized CP-MOIST scheme for bicelle-reconstituted membrane proteins. This enhancement is achieved by employing the differences between the spin-lattice relaxation times for the high- and low-gamma spins. The new technique is applicable to systems with short T1ρ's, and speeds up acquisition of the multidimensional solid-state NMR spectra of oriented membrane proteins for their subsequent structural and dynamic studies.     

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.     

Dynamics of spin I=3/2 under spin-locking conditions in an ordered environment

We have derived approximate analytic solutions to the master equation describing the evolution of the spin I=3/2 density operator in the presence of a radio-frequency (RF) field and both static and fluctuating quadrupolar interactions. Spectra resulting from Fourier transformation of the evolutions of the on-resonance spin-locked magnetization into the various coherences display two satellite pairs and, in some cases, a central line. The central line is generally trimodal, consisting of a narrow component related to a slowly relaxing mode and two broad components pertaining to two faster relaxing modes. The rates of the fast modes are sensitive to slow molecular motion. Neither the amplitude nor the width of the narrow component is affected by the magnitude of the static coupling, whereas the corresponding features of the broad components depend in a rather complicated manner on the spin-lock field strength and static quadrupolar interaction. Under certain experimental conditions, the dependencies of the amplitudes on the dynamics are seen to vanish and the relaxation rates reduce to relatively simple expressions. One of the promising emerging features is the fact that the evolutions into the selectively detected quadrupolar spin polarization order and the rank-two double-quantum coherence do not exhibit a slowly relaxing mode and are particularly sensitive to slow molecular motion. Furthermore, these coherences can only be excited in the presence of a static coupling and this makes it possible to discern nuclei in anisotropic from those in isotropic environment. The feasibility of the spin-lock pulse sequences with limited RF power and a nonvanishing average electric field gradient has been demonstrated through experiments on sodium in a dense lyotropic DNA liquid crystal.     

Through-space R3-HETCOR experiments between spin-1/2 and half-integer quadrupolar nuclei in solid-state NMR

We present several new methods that allow to obtain through-space 2D HETCOR spectra between spin-1/2 and half-integer quadrupolar nuclei in the solid state. These methods use the rotary-resonance concept to create hetero-nuclear coherences through the dipolar interaction instead of scalar coupling into the HMQC and refocused INEPT experiments for spin n/2 (n>1). In opposite to those based on the cross-polarization transfer to quadrupolar nuclei, the methods are very robust and easy to set-up.     

~(13)C CP/MAS OF MOTIONS IN SOLID POLYMERS

High-resolution 13C spectra of solid polymers are often acquired with cross polarization with magic angle spinning (CP/MAS) to take advantage of the abunda ntly available protons in the polymer chains. The sequence for transferring mag netization from 1H to13C using Hartmann-Hahn spin locking in the rotating frame is now a standard in commercial solidstate NMR spectrometers.     

Sensitivity enhancement of the central-transition signal of half-integer spin quadrupolar nuclei in solid-state NMR: features of multiple fast amplitude-modulated pulse transfer

Sensitivity enhancement of solid-state NMR spectrum of half-integer spin quadrupolar nuclei under both magic-angle spinning (MAS) and static cases has been demonstrated by transferring polarisation associated with satellite transitions to the central m=-1/2-->1/2 transition with suitably modulated radio-frequency pulse schemes. It has been shown that after the application of such enhancement schemes, there still remains polarisation in the satellite transitions that can be transferred to the central transition. This polarisation is available without having to wait for the spin system to return to thermal equilibrium. We demonstrate here the additional sensitivity enhancement obtained by making use of this remaining polarisation with fast amplitude-modulated (FAM) pulse schemes under both MAS and static conditions on a spin-3/2 and a spin-5/2 system. Considerable signal enhancement is obtained with the application of the multiple FAM sequence, denoted as m-FAM. We also report here some of the salient features of these multiple FAM sequences with respect to the nutation frequency of the pulses and the spinning frequency.     

Magnetization-recovery experiments for static and MAS-NMR of I=3/2 nuclei

Multifrequency pulsed NMR experiments on quadrupole-perturbed I=3/2 spins in single crystals are shown to be useful for measuring spin-lattice relaxation parameters even for a mixture of quadrupolar plus magnetic relaxation mechanisms. Such measurements can then be related to other MAS-NMR experiments on powders. This strategy is demonstrated by studies of (71)Ga and (69)Ga (both I=3/2) spin-lattice relaxation behavior in a single-crystal (film) sample of gallium nitride, GaN, at various orientations of the axially symmetric nuclear quadrupole coupling tensor. Observation of apparent single-exponential relaxation behavior in I=3/2 saturation-recovery experiments can be misleading when individual contributing rate processes are neglected in the interpretation. The quadrupolar mechanism (dominant in this study) has both a single-quantum process (T(1Q1)) and a double-quantum process (T(1Q2)), whose time constants are not necessarily equal. Magnetic relaxation (in this study most likely arising from hyperfine couplings to unpaired delocalized electron spins in the conduction band) also contributes to a single-quantum process (T(1M)). A strategy of multifrequency irradiation with observation of satellite and/or central transitions, incorporating different initial conditions for the level populations, provides a means of obtaining these three relaxation time constants from single-crystal (71)Ga data alone. The (69)Ga results provide a further check of internal consistency, since magnetic and quadrupolar contributions to its relaxation scale in opposite directions compared to (71)Ga. For both perpendicular and parallel quadrupole coupling tensor symmetry axis orientations small but significant differences between T(1Q1) and T(1Q2) were measured, whereas for a tensor symmetry axis oriented at the magic-angle (54.74 degrees ) the values were essentially equal. Magic-angle spinning introduces a number of complications into the measurement and interpretation of the spin-lattice relaxation. Comparison of (71)Ga and (69)Ga MAS-NMR saturation-recovery curves with both central and satellite transitions completely saturated by a train of 90 degrees pulses incommensurate with the rotor period provides the simplest means of assessing the contribution from magnetic relaxation, and yields results for the quadrupolar mechanism contribution that are consistent with those obtained from the film sample.     

A practical guide for the setup of a 1H-31P-13C double cross-polarization (DCP) experiment

O-phospho-L-threonine is a convenient sample to setup a (1)H-(31)P-(13)C double cross-polarization (DCP) Hartmann-Hahn match. The (1)H-(31)P-(13)C technique is extremely sensitive to the rate of the sample spinning. Both zero-quantum (ZQ) and double-quantum (DQ) cross-polarization operate at an average spinning rate (6-7 kHz). At higher spinning rates (10 kHz), the DQCP mechanism dominates and leads to a reduction of signal intensity, in particular for lower (31)P RF field strength. The application of two shape pulses during the second cross-polarization greatly improves the signal to noise ratio allowing the recording of better quality spectra. (31)P-(13)C spectrally induced filtering in combination with cross-polarization (SPECIFIC-CP) experiments can be carried out under ZQCP and DQCP conditions if careful attention is paid to the choice of RF field amplitudes and carriers Ω. Application of 1D and 2D (1)H-(31)P-(13)C experiments is demonstrated on model samples; disodium ATP hydrate and O-phospho-L-tyrosine.