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.     

Fast amplitude-modulated pulse trains with frequency sweep (SW-FAM) in static NMR of half-integer spin quadrupolar nuclei

In solid-state NMR of quadrupolar nuclei with half-integer spin I, fast amplitude-modulated (FAM) pulse trains have been utilised to enhance the intensity of the central-transition signal, by transferring spin population from the satellite transitions. In this paper, the signal-enhancement performance of the recently introduced SW-FAM pulse train with swept modulation frequency [T. Br?uniger, K. Ramaswamy, P.K. Madhu, Enhancement of the central-transition signal in static and magic-angle-spinning NMR of quadrupolar nuclei by frequency-swept fast amplitude-modulated pulses, Chem. Phys. Lett. 383 (2004) 403-410] is explored in more detail for static spectra. It is shown that by sweeping the modulation frequencies linearly over the pulse pairs (SW1/tau-FAM), the shape of the frequency distribution is improved in comparison to the original pulse scheme (SWtau-FAM). For static spectra of 27Al (I=5/2), better signal-enhancement performance is found for the SW1/tau-FAM sequence, as demonstrated both by experiments and numerical simulations.     

Enhancing MQMAS sensitivity using signals from multiple coherence transfer pathways

Multiple-quantum magic-angle spinning experiment removes second-order quadrupolar broadening from the central-transition of half-integer quadrupolar nuclei. This paper presents a novel scheme to enhance the sensitivity of MQMAS using signals from multiple coherence transfer pathways. The enhancement can be obtained in two ways. The first method uses the multiplex phase cycling to acquire MQMAS spectra from various coherence transfer pathways simultaneously. An addition of spectra collected with no extra time enhances the efficiency of the experiment. The second method, soft-pulse-added-mixing, is designed based on a complete alias of coherence transfer pathways. By properly fixing the soft-pulse phase, signals from various coherence transfer pathways can add constructively resulting higher signal intensities. The two methods are demonstrated for sensitivity enhancement with samples of spin-3/2 and 5/2.     

四极核旋转边带的抑制

本文从自旋-1体系自旋空间的旋转特性的讨论建议了抑制四极核旋转边带的4(π/2)脉冲系列,进而给出了一种4(π/2)-4π脉冲系列,该系列可用于获得该四极核体系的化学位移各向同性固体高分辨谱。文中给出了相应的实验结果。     

Application of amplitude-modulated radiofrequency fields to the magic-angle spinning NMR of spin-7/2 nuclei

We report pulse sequences for the sensitivity enhancement of magic-angle spinning and multiple-quantum magic-angle spinning spectra of spin-72 systems. Sensitivity enhancement is obtained with the use of fast amplitude-modulated (FAM) radiofrequency pulses. In one-dimensional magic-angle spinning experiments, signal enhancement of 3 is obtained by a FAM pulse followed by a soft 90 degrees pulse. In two-dimensional multiple-quantum magic-angle spinning experiments, FAM pulses are used for both the excitation of multiple-quantum coherences and for their conversion into observable single-quantum coherences. The observed signal enhancements are 2.2 in 3Q experiments, 3.1 in 5Q experiments, and 4.1 in 7Q experiments, compared to the conventional two-pulse scheme. The pulse schemes are demonstrated on the 45Sc NMR of Sc2(SO4)3 x 5H2O and the 139La NMR of LaAlO3. We also demonstrate the generation of FAM pulses by double-frequency irradiation.     

Efficient 5QMAS NMR of spin-5/2 nuclei: use of fast amplitude-modulated radio-frequency pulses and cogwheel phase cycling

We report here an efficient multiple-quantum magic-angle spinning (MQMAS) pulse sequence involving fast amplitude-modulated (FAM) radio-frequency pulses for excitation and conversion of five-quantum (5Q) coherences of spin-5/2 nuclei. The use of a FAM-I type pulse train for the conversion of 5Q into 1Q coherences proves to be easier to implement experimentally than the earlier suggested use of a FAM-II type sequence [J. Magn. Reson. 154 (2002) 280], while delivering at least equal signal enhancement. Results of numerical simulations and experimental 27Al 5QMAS spectra of aluminium acetylacetonate for different excitation and conversion schemes are compared to substantiate these claims. We also demonstrate the feasibility of acquiring 5QMAS spectra of spin-5/2 systems using cogwheel phase cycling [J. Magn. Reson. 155 (2002) 300] to select the desired coherence pathways. A cogwheel phase cycle of only 57 steps is shown to be as effective as the minimum conventional nested 77-step phase cycle.     

Spin-locking and recoupling of homonuclear dipolar interaction between spin-3/2 nuclei under magic-angle sample spinning

Numerical simulations and experiments were used to examine the possibility of employing strong spin-lock fields for recoupling of homonuclear dipolar interactions between spin-3/2 quadrupolar nuclei and to compare it to the rotary-resonance recoupling at weak spin-lock fields. It was shown that strong spin-lock pulses under MAS conditions can lead to recoupling, provided that the electric-field gradient principal axes systems of the coupled nuclei are aligned and that their quadrupolar coupling constants are approximately the same. The phenomenon is based on the fact that strong spin-lock pulses induce adiabatic transfer of magnetization between the central-transition coherence and the triple-quantum coherence with equal periodicity as is the periodicity of the time-dependent dipolar coupling. Because of the synchronous variation of the state of the spin system and of the dipolar interaction, the effect of the latter on the central-transition coherence and on the triple-quantum coherence is not averaged out by sample rotation. The approach is, however, very sensitive to the relative orientation of the electric-field gradient principal axes systems and therefore less robust than the approach based on weak spin-lock pulses that satisfy rotary-resonance condition.     

粉末样品中自旋3/2核体系中心跃迁的布居数反转

在有限脉冲宽度条件下,本文利用矢量模型与计算机模拟设计了一个组合180°脉冲:45°_x112.5°_y45°_x,可以均匀地将自旋I=3/2核体系中心跃迁的布居数反转。并且用数值计算方法对该组合180°脉冲的布居数反转效果进行了分析。实验上用Na₂SO₄粉末样品进行了验证。     

New methods for the acquisition of ultra-wideline solid-state NMR spectra of spin-1/2 nuclides

The Wideband Uniform Rate Smooth Truncation - Carr-Purcell Meiboom-Gill (WURST-CPMG) pulse sequence was recently introduced as a new method of acquiring ultra-wideline solid-state NMR (SSNMR) patterns of quadrupolar nuclei (Chem. Phys. Lett. 464 (2008) 97). Herein, we describe the application of the WURST-CPMG pulse sequence to stationary samples (i.e., non-spinning or "static" samples) of various spin-1/2 nuclides ((119)Sn, (207)Pb, (199)Hg and (195)Pt) in order to examine its effectiveness for acquiring ultra-wideline SSNMR patterns. WURST-CPMG is compared to the CPMG and Cross Polarization (CP)-CPMG pulse sequences in select cases ((119)Sn and (207)Pb, respectively), and its usefulness in obtaining ultra-wideline SSNMR spectra in a piecewise fashion is explored. In addition, a preliminary investigation of pulses generated using optimal control theory (OCT) for the purpose of wideline excitation is presented; spectra acquired using these pulses are compared with standard, rectangular pulses of similar pulse powers. Both methods show much promise for acquiring high quality wideline patterns dominated by chemical shift anisotropy, with minimal distortions and significantly reduced experimental times.     

Double-quantum filtered STMAS

Double-quantum and double-quantum-filtered satellite-transition magic-angle spinning (STMAS) experiments are proposed. The experiments efficiently convert satellite-transition coherence from single- to double-quantum with a central-transition selective pi-pulse. The conversion allows the selection of double-quantum coherence transfer pathways with phase cycling that completely filters out unwanted diagonal and outer satellite-transition peaks. Both experiments are demonstrated with RbNO3 and AlPO4-berlinite as model compounds for obtaining clean STMAS spectra of spins 3/2 and 5/2, respectively.     

Using quaternions to design composite pulses for spin-1 NQR

The fictitious spin-1/2 operators are well known to describe the evolution of a pure nuclear quadrupole resonance (NQR) system; particularly, the application of a radio-frequency pulse at one of the NQR transition frequencies is equivalent to a three-dimensional rotation in a space defined by the corresponding fictitious spin-1/2 operators. We demonstrate, theoretically and experimentally, that consecutive noncommuting rotations applied at the same transition frequency are well described by a single rotation given by quaternion parameterization of the rotations in ficitious spin-1/2 operator space. This new route could greatly save computing time and efforts. We extend this approach to design composite pulses that compensate for the effects of the radio-frequency field inhomogeneity for a powder sample of spin-1 nuclei.     

粉末样品自旋3/2四极核中心跃迁的高分辨核磁共振谱

本文利用脉冲对自旋3/2四极核中心跃迁激发的选择性,在粉末样品中用一个90°脉冲将电场梯度张量在空间某一取向的核自旋磁化矢量转到旋转坐标系中XY平面进行检测,从而得到与单晶样品类似的高分辨谱线,在理论上用密度算符公式作了分析,实验上用NaNO₂和Na₂SO₄粉末样品进行了验证。 关键词：     

Generation of time-dependent ultra-short optical pulse trains in the presence of self-steepening effect

Starting from the extended nonlinear Schr?dinger equation in which the self-steepening effect is included, the evolution and the splitting processes of continuous optical wave whose amplitude is perturbed into time related ultra-short optical pulse trains in an optical fibre are numerically simulated by adopting the split-step Fourier algorithm. The results show that the self-steepening effect can cause the characteristic of the pulse trains to vary with time, which is different from the self-steepening-free case where the generated pulse trains consist of single pulses which are identical in width, intensity, and interval, namely when pulses move a certain distance, they turn into the pulse trains within a certain time range. Moreover, each single pulse may split into several sub-pulses. And as time goes on, the number of the sub-pulses will decrease gradually and the pulse width and the pulse intensity will change too. With the increase of the self-steepening parameter, the distance needed to generate time-dependent pulse trains will shorten. In addition, for a large self-steepening parameter and at the distance where more sub-pulses appear, the corresponding frequency spectra of pulse trains are also wider.     

A new sequence for the MQMAS/HETCOR experiment

Two-dimensional (2D) multiple quantum MAS (magic angle spinning) spectroscopy has been combined with cross-polarisation to obtain a heteronuclear correlation spectrum between a quadrupolar spin-3/2 and a spin-1/2 nucleus. The advantage over the conventional correlation experiment is the increased resolution obtained in the multiple quantum dimension. Pure absorption 2D spectra can be obtained by implementing a zero quantum filter between the evolution of multiple quanta and the subsequent cross-polarisation step. The current experiment shows a considerable improvement in sensitivity compared to a previously introduced sequence.     

PRAWN: mixing sequences for selective heteronuclear J cross polarization

In this work, we present a family of pulse sequences for selective heteronuclear J cross-polarization (JCP), which we have developed especially for indirect 13C imaging using JCP, for example in the CYCLCROP environment. The sequences are straightforward to implement and operate reliably. Results of an average Hamiltonian analysis are given for the basic sequence, which we term PRAWN (pulsed rotating frame transfer sequence with windows). It is shown experimentally that the pulse sequence, which operates efficiently with low RF duty cycles down to a few percent, has a useful tolerance range to absolute Hartmann-Hahn mismatch and generates coherence transfer spectra in close correspondence with the JCP average Hamiltonian. Computer simulation of the performance of the basic sequence on a heteronuclear spin-(1/2) AX system is also presented. The mismatch compensation of PRAWN may be markedly enhanced further by issuing a pi pulse to each spin halfway through the basic PRAWN train and in phase quadrature to it. A simple analysis of this modified sequence, PRAWN-pi, is given under conditions of mismatch and off-resonance irradiation.     

Selection rules for multiple quantum NMR excitation in solids: derivation from time-reversal symmetry and comparison with simulations and (13)C NMR experiments.

New derivations of selection rules for excitation and detection of multiple quantum coherences in coupled spin-1/2 systems are presented. The selection rules apply to experiments in which the effective coupling Hamiltonian used for multiple quantum excitation is both time-reversal invariant and time-reversible by a phase shift of the radiofrequency pulse sequence that generates the effective couplings. The selection rules are shown to be consequences of time-reversal invariance and time-reversibility and otherwise independent of the specific form of the effective coupling Hamiltonian. Numerical simulations of multiple quantum NMR signal amplitudes and experimental multiple quantum excitation spectra are presented for the case of a multiply (13)C-labeled helical polypeptide. The simulations and experiments confirm the selection rules and demonstrate their impact on multiple quantum (13)C NMR spectra in this biochemically relevant case.     

Supercycled symmetry-based double-quantum dipolar recoupling of quadrupolar spins in MAS NMR: I. Theory

Using average Hamiltonian (AH) theory, we analyze recently introduced homonuclear dipolar recoupling pulse sequences for exciting central-transition double-quantum coherences (2QC) between half-integer spin quadrupolar nuclei undergoing magic-angle-spinning. Several previously observed differences among the recoupling schemes concerning their compensation to resonance offsets and radio-frequency (rf) inhomogeneity may qualitatively be rationalized by an AH analysis up to third perturbation order, despite its omission of first-order quadrupolar interactions. General aspects of the engineering of 2Q-recoupling pulse sequences applicable to half-integer spins are discussed, emphasizing the improvements offered from a diversity of supercycles providing enhanced suppression of undesirable AH cross-terms between resonance offsets and rf amplitude errors.     

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.     

Sensitivity enhancement of NMR spectra of half-integer spin quadrupolar nuclei in solids using hyperbolic secant pulses

The experimental factors influencing the enhancements achievable for the central NMR transition, m(I)=1/2-->m(I)=-1/2, of spin-3/2 and spin-5/2 nuclei in the solid state using hyperbolic secant, HS, pulses for population transfer are investigated. In the case of powder samples spinning at the magic angle, it is found that the spinning frequency, the bandwidth and the frequency offset of the HS pulse play a crucial role in determining the maximum enhancements. Specifically, the bandwidth must be set to the spinning frequency for maximum signal enhancements. The (87)Rb NMR enhancement obtained for RbClO(4) using HS pulses was relatively insensitive to the magic angle spinning frequency; however, in the case of Al(acac)(3), the (27)Al enhancement increased with MAS frequency. In order to obtain an adiabatic HS sweep, one should optimize the rf field for a given pulse duration or optimize the pulse duration for a given rf field.