2CALIS doubling the sensitivity of CALIS for calibration of the rf field strength for indirectly observed nuclei

A new set of pulse sequences, 2CALIS, that exhibit double sensitivity of the recent CALIS pulse sequences for accurate calibration of the rf field strength for an indirectly observed spin is introduced. The sensitivity gain is a result of not forming heteronuclear coherence transfer gradient echoes although they are excellent for artifact suppression. It is, however, demonstrated that the scheme in 2CALIS for suppression of non (13)C-attached proton magnetization is adequate for calibration of the (13)C rf field strength even on natural abundance samples. A 2CALIS version with Watergate applicable to biomolecules in aqueous solution is also presented and demonstrated both in (13)C natural abundance and on a (13)C, (15)N enriched protein sample.     

Investigations of low-amplitude radio frequency pulses at and away from rotary resonance conditions for I = 5/2 nuclei

Additional experimental evidence of rotary resonance effects for multiple-quantum coherence conversion in a spin-5/2 system is presented. Two-dimensional plots of the relative efficiency of MQ excitation and conversion are given as a function of radio frequency (rf) amplitude and pulse width. Data are presented for the excitation of five-quantum coherence (5QC), as well as for 5QC to three-quantum coherence (3QC) conversion, 5QC to IQC (the central transition coherence) conversion, and 3QC to IQC conversion. A two-fold increase in the signal-to-noise ratio is achieved by substituting low amplitude rf pulses in place of hard rf pulses for 5QC excitation and 5QC to 3QC conversion in a mixed multiple-quantum magic angle spinning (MAS) (MMQMAS) experiment. The anisotropic line shape for the low-amplitude rf pulse version of the MMQMAS experiment was observed to be distorted from the MAS line shape. The cause and implications of the distortion are discussed.     

Optimal control in NMR spectroscopy: Numerical implementation in SIMPSON

We present the implementation of optimal control into the open source simulation package SIMPSON for development and optimization of nuclear magnetic resonance experiments for a wide range of applications, including liquid- and solid-state NMR, magnetic resonance imaging, quantum computation, and combinations between NMR and other spectroscopies. Optimal control enables efficient optimization of NMR experiments in terms of amplitudes, phases, offsets etc. for hundreds-to-thousands of pulses to fully exploit the experimentally available high degree of freedom in pulse sequences to combat variations/limitations in experimental or spin system parameters or design experiments with specific properties typically not covered as easily by standard design procedures. This facilitates straightforward optimization of experiments under consideration of rf and static field inhomogeneities, limitations in available or desired rf field strengths (e.g., for reduction of sample heating), spread in resonance offsets or coupling parameters, variations in spin systems etc. to meet the actual experimental conditions as close as possible. The paper provides a brief account on the relevant theory and in particular the computational interface relevant for optimization of state-to-state transfer (on the density operator level) and the effective Hamiltonian on the level of propagators along with several representative examples within liquid- and solid-state NMR spectroscopy.     

Optimum excitation of “enhanced” central transition populations

Central transition (CT) sensitivity enhancement schemes that transfer polarization from satellites to the CT through selective saturation or inversion of neighboring satellite transitions have provided a welcome improvement for magic-angle spinning spectra of half-integer quadrupole nuclei. While many researchers have investigated and developed different methods of creating enhanced CT populations, here we investigate the conversion of these enhanced CT populations into observable CT coherence. We show a somewhat unexpected result that a conversion pulse length optimized for maximum sensitivity on equilibrium populations may not be optimum for an enhanced (non-equilibrium) polarization. Furthermore, CT enhancements can be lost if excessive rf field strength is used to convert this enhanced polarization into CT coherence. While a maximally enhanced CT signal is expected when using a perfectly selective CT conversion pulse, we have found that significant sensitivity loss can occur when using surprisingly low rf field strengths, even for sites with relatively large quadrupole coupling constants. We have systematically investigated these issues, and present some general guidelines and expectations when optimizing the conversion of enhanced (non-equilibrium) CT populations into observable CT coherence.     

Coherence selection in double CP MAS NMR spectroscopy

Applications of double cross-polarization (CP) magic-angle spinning (MAS) NMR spectroscopy, via (1)H/(15)N and then (15)N/(13)C coherence transfers, for (13)C coherence selection are demonstrated on a (15)N/(13)C-labeled N-acetyl-glucosamine (GlcNAc) compound. The (15)N/(13)C coherence transfer is very sensitive to the settings of the experimental parameters. To resolve explicitly these parameter dependences, we have systematically monitored the (13)C{(15)N/(1)H} signal as a function of the rf field strength and the MAS frequency. The data reveal that the zero-quantum coherence transfer, with which the (13)C effective rf field is larger than that of the (15)N by the spinning frequency, would give better signal sensitivity. We demonstrate in one- and two-dimensional double CP experiments that spectral editing can be achieved by tailoring the experimental parameters, such as the rf field strengths and/or the MAS frequency.     

Optimal control of spin dynamics in the presence of relaxation

Experiments in coherent spectroscopy correspond to control of quantum mechanical ensembles guiding them from initial to final target states. The control inputs (pulse sequences) that accomplish these transformations should be designed to minimize the effects of relaxation and to optimize the sensitivity of the experiments. For example in nuclear magnetic resonance (NMR) spectroscopy, a question of fundamental importance is what is the maximum efficiency of coherence or polarization transfer between two spins in the presence of relaxation. Furthermore, what is the optimal pulse sequence which achieves this efficiency? In this paper, we give analytical answers to the above questions. Unexpected gains in sensitivity are reported for one of the most commonly used experimental building blocks in NMR spectroscopy. Surprisingly, in the case when longitudinal relaxation is small, the relaxation optimized pulse elements (ROPE) that transfer maximum polarization between coupled spins are longer than conventional sequences.     

Selective averaging for high-resolution solid-state NMR spectroscopy of aligned samples

Solid-state NMR experiments benefit from being performed at high fields, and this is essential in order to obtain spectra with the resolution and sensitivity required for applications to protein structure determination in aligned samples. Since the amount of rf power that can be applied is limited, especially for aqueous protein samples, the most important pulse sequences suffer from bandwidth limitations resulting from the same spread in chemical shift frequencies that aids resolution. SAMPI4 is a pulse sequence that addresses these limitations. It yields separated local field spectra with narrower and more uniform linewidths over the entire spectrum than the currently used PISEMA and SAMMY experiments. In addition, it is much easier to set up on commercial spectrometers and can be incorporated as a building block into other multidimensional pulse sequences. This is illustrated with a two-dimensional HETCOR experiment, where it is crucial to transfer polarization from the amide protons to their directly bonded nitrogens over a wide range of chemical shift frequencies. A quantum-mechanical treatment of the spin Hamiltonians under high-power rf pulses is presented which gives the scaling factor for SAMPI4 as well as the durations of the rf pulses to achieve optimal decoupling.     

Time-optimal coherence-order-selective transfer of in-phase coherence in heteronuclear IS spin systems

Based on principles of geometric optimal control theory, coherence transfer building blocks can be derived which achieve optimal sensitivity. Here, experimental pulse sequences are presented that achieve the best possible coherence-order-selective in-phase transfer (S(-)-->I(-)) for a heteronuclear 2-spin system for any given mixing time in the absence of relaxation. For short mixing times, the optimal experiment improves the sensitivity of isotropic mixing by up to 12.5%.     

Chemical shift anisotropy and offset effects in cross polarization solid-state NMR spectroscopy

The effect of an offset term in the cross-polarization (CP) Hamiltonian of a heteronuclear spin-12 pair due to off-resonant radio frequency (rf) irradiation and/or chemical shift anisotropy on one of the rf channels is investigated. Analytical solutions, simulations, and experimental results are presented. Formulating the CP spin dynamics in terms of an explicit unitary evolution operator enables the CP period to be inserted as a module in a given pulse scheme regardless of the initial density matrix present. The outcome of post-CP manipulation via pulses can be calculated on the resulting density matrix as the phases and amplitudes of all coherence modes are available. Using these tools it is shown that the offset can be used to reduce the rf power on that channel and the performance is further improved by a post-CP pulse whose flip angle matches and compensates the tilt of the effective field on the offset channel. Experimental investigations on single crystalline and polycrystalline samples of peptides confirm the oscillatory nature of CP dynamics and prove the slowing down of the dynamics under offset and/or mismatch conditions.     

Optical pump-probe measurements of local nuclear spin coherence in semiconductor quantum wells

We demonstrate local manipulation and detection of nuclear spin coherence in semiconductor quantum wells by an optical pump-probe technique combined with pulse rf NMR. The Larmor precession of photoexcited electron spins is monitored by time-resolved Kerr rotation (TRKR) as a measure of nuclear magnetic field. Under the irradiation of resonant pulsed rf magnetic fields, Rabi oscillations of nuclear spins are traced by TRKR signals. The intrinsic coherence time evaluated by a spin-echo technique reveals the dependence on the orientation of the magnetic field with respect to the crystalline axis as expected by the nearest neighbor dipole-dipole interaction.     

J-ONLY-TOCSY: efficient suppression of RDC-induced transfer in homonuclear TOCSY experiments using JESTER-1-derived multiple pulse sequences

The main purpose of homonuclear Hartmann-Hahn or TOCSY experiments is the assignment of spin systems based on efficient coherence transfer via scalar couplings. In partially aligned samples, however, magnetization is also transferred via residual dipolar couplings (RDCs) and therefore through space correlations can be observed in COSY and TOCSY experiments that make the unambiguous assignment of covalently bound spins impossible. In this article, we show that the JESTER-1 multiple pulse sequence, originally designed for broadband heteronuclear isotropic Hartmann-Hahn transfer, efficiently suppresses the homonuclear dipolar coupling Hamiltonian. This suppression can be enhanced even further by variation of the supercycling scheme. The application of the resulting element in homonuclear TOCSY periods results in coherence transfer via J-couplings only. As a consequence, the assignment of scalar coupled spin systems is also possible in partially aligned samples. The bandwidth of coherence transfer for the JESTER-1-derived sequences is comparable to existing TOCSY multiple pulse sequences. Results are demonstrated in theory and experiment.     

Velocity sensitivity of slice-selective excitation

The purpose of this study was to investigate how flow affects slice-selective excitation, particularly for radiofrequency (rf) pulses optimized for slice-selective excitation of stationary material. Simulation methods were used to calculate the slice profiles for material flowing at different velocities, using optimal flow compensation when appropriate. Four rf pulses of very different shapes were used in the simulation study: a 90° linear-phase Shinnar-LeRoux pulse; a 90° self-refocusing pulse; a minimum-phase Shinnar-LeRoux inversion pulse; and a SPINCALC inversion pulse. Slice profiles from simulations with a laminar flow model were compared with experimental studies for two different rf pulses using a clinical magnetic resonance imaging (MRI) system. We found that, for a given rf pulse, the effect of flow on slice-selective excitation depends on the product of the selection gradient amplitude, the component of velocity in the slice selection direction, and the square of the rf pulse duration. The shapes of the slice profiles from the Shinnar-LeRoux pulses were relatively insensitive to velocity. However, the slice profiles from the self-refocusing pulse and the SPINCALC pulse were significantly degraded by velocity. Experimental slice profiles showed excellent agreement with simulation. In conclusion, our study demonstrates that slice-selective excitation can be significantly degraded by flow depending on the velocity, the gradient amplitude, and characteristics of the rf excitation pulse used. The results can aid in the design of rf pulses for slice-selective excitation of flowing material.     

Investigation of the effect of a variety of pulse errors on spin I=1 quadrupolar alignment echo spectroscopy

We report on an analysis of a well known three-pulse sequence for generating and detecting spin I=1 quadrupolar order when various pulse errors are taken into account. In the situation of a single quadrupolar frequency, such as the case found in a single crystal, we studied the potential leakage of single and/or double quantum coherence when a pulse flip error, finite pulse width effect, RF transient or a resonance offset is present. Our analysis demonstrates that the four-step phase cycling scheme studied is robust in suppressing unwanted double and single quantum coherence as well as Zeeman order that arise from the experimental artifacts, allowing for an unbiased measurement of the quadrupolar alignment relaxation time, T(1Q). This work also reports on distortions in quadrupolar alignment echo spectra in the presence of experimental artifacts in the situation of a powdered sample, by simulation. Using our simulation tool, it is demonstrated that the spectral distortions associated with the pulse artifacts may be minimized, to some extent, by optimally choosing the time between the first two pulses. We highlight experimental results acquired on perdeuterated hexamethylbenzene and polyethylene that demonstrate the efficacy of the phase cycling scheme for suppressing unwanted quantum coherence when measuring T(1Q). It is suggested that one employ two separate pulse sequences when measuring T(1Q) to properly analyze the short time behavior of quadrupolar alignment relaxation data.     

A theoretical study of coherence transfer by isotropic mixing

Computer simulations of coherence transfer functions under the isotropic mixing hamiltonian are presented for amino acids and the deoxyribose moiety in DNA. They allow the determination of the optimum mixing time in a two-dimensional TOCSY experiment. The effects of experimental parameters and pulse imperfections are discussed for practical pulse sequences.     

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.     

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.     

Slice profile improvement for a clinical MRI system

Optimal control methods have been recently introduced to improve the design of selective radio frequency pulses and several optimized selective pulses that can produce excellent slice profiles have been reported. These pulses usually require high peak rf amplitudes to implement and thus can not be widely utilized because of the limitations of the specific absorption rate and the rf power amplifier of a clinical system. We have a Siemens 1.5 T MRI clinical system. Several pulse files which consist of the bandwith matched 90° and 180° selective pulses are provided. Some of these can produce excellent slice profiles. However, they can only be used in the pulse sequences with the pulse length of 5.12 msec. The purpose of this paper is to improve the slice profiles produced by the pulse file in the pulse sequences with the shorter 2.56 msec pulse length. A pulse file optimized by the conjugate gradient method is proposed to substitute the 2.56 msec Siemens pulse file. Our experimental results confirm that the slice profiles and images are improved by the optimized pulse file with a lower peak voltage. The proposed pulse file can also be applied in other clinical MRI systems.     

Construction of Phase Cycles of Minimum Cycle Length: MakeCycle

An algorithm for the generation of a phase cycle of minimum length for a pulse sequence is developed from the basic requirement that only specified coherence transfer pathways will be accumulated. The efficacy of the algorithm is shown by determining the phase cycles of minimum length for DQFCOSY, GHMBC, and INEPT pulse sequences.     

The virtual NMR spectrometer: a computer program for efficient simulation of NMR experiments involving pulsed field gradients

This paper presents a software program, the Virtual NMR Spectrometer, for computer simulation of multichannel, multidimensional NMR experiments on user-defined spin systems. The program is capable of reproducing most features of the modern NMR experiment, including homo- and heteronuclear pulse sequences, phase cycling, pulsed field gradients, and shaped pulses. Two different approaches are implemented to simulate the effect of pulsed field gradients on coherence selection, an explicit calculation of all coherence transfer pathways, and an effective approximate method using integration over multiple positions in the sample. The applications of the Virtual NMR Spectrometer are illustrated using homonuclear COSY and DQF COSY experiments with gradient selection, heteronuclear HSQC, and TROSY. The program uses an intuitive graphical user interface, which resembles the appearance and operation of a real spectrometer. A translator is used to allow the user to design pulse sequences with the same programming language used in the actual experiment on a real spectrometer. The Virtual NMR Spectrometer is designed as a useful tool for developing new NMR experiments and for tuning and adjusting the experimental setup for existing ones prior to running costly NMR experiments, in order to reduce the setup time on a real spectrometer. It will also be a useful aid for learning the general principles of magnetic resonance and contemporary innovations in NMR pulse sequence design.     

PFT—NMR相位循环的计算机辅助设计

本文介绍了通过选择相干传递路径来计算相位循环的理论依据。在此基础上提出了一个计算机程序PHASE.BAS用于计算相位循环。使用此程序设计了一个128步的相循环用于一维和二维INADEQUATE实验。实验结果表明此相循环能很好地消除单量子信号、压制t_1噪声,其效果明显优于Bruker MSL脉冲序列库中的32次循环的结果。