Adjustable, broadband, selective excitation with uniform phase

Implementation and applications of shaped pulses in EPR

In this review, we describe the application of shaped pulses for EPR spectroscopy. Pulses generated by fast arbitrary waveform generators are mostly used in the field of EPR spectroscopy for broadband (200 MHz-1 GHz) excitation of paramagnetic species. The implementation and optimization of such broadband pulses in existing EPR spectrometers, often designed and optimized for short rectangular microwave pulses, is demanding. Therefore, a major part of this review will describe in detail the implementation, testing and optimization of shaped pulses in existing EPR spectrometers. Additionally, we review applications using such pulses for broadband inversion of longitudinal magnetization as well as for the creation and manipulation of transverse magnetization in the field of dipolar and hyperfine EPR spectroscopy. They demonstrate the great potential of shaped pulses to improve the performance of pulsed EPR experiments. We give a brief theoretical description of shaped pulses and their limitations, especially for adiabatic pulses, most often used in EPR. We believe that this review can on the one hand be of practical use to EPR groups starting to work with such pulses, and on the other hand give readers an overview of the state of the art of shaped pulse applications in EPR spectroscopy.

Composite pulse combinations for chirp excitation

Composite pulses are the efficient method for broadband excitation to get control of the limitations of high field NMR, such as resonance offset effects with constraints on rf power that leads to signal intensity distortion. Phase-modulated chirp pulses are used as ordered composite pulse sequences in this paper as CHORUS sequence in a high-field NMR spectrometer (BRUKER 750 MHz) for broadband excitation. The composite pulse sequence applies chirp pulses with the forward and the reverse sweep mechanisms. A single excitation pulse combines adiabatic and non-adiabatic rotation, explained as a three-phase rotation, which leaves the magnetizing vectors to a non-uniform phase dispersion as a function of the offset frequency. One adiabatic refocusing pulse of the double sweep rate after the excitation pulse cannot satisfactorily compensate for the phase dispersion. Hence, composite self-refocussing CHORUS excitation pulse, with forward, reverse, and their combinations are used to remove the non-uniform phase dispersion generated due to offset resonance frequency. Four such combinations of composite pulses are produced with analytical explanation in this paper. MATLAB simulation results and experimental verification on the BRUKER 750 MHz NMR spectrometer of the composite pulses are also presented in this paper.

SORDOR pulses: expansion of the Böhlen-Bodenhausen scheme for low-power broadband magnetic resonance

A novel type of efficient broadband pulse, called second-order phase dispersion by optimised rotation (SORDOR), has recently been introduced. In contrast to adiabatic excitation, SORDOR-90 pulses provide effective transverse 90∘ rotations throughout their bandwidth, with a quadratic offset dependence of the phase in the x , y plane. Together with phase-matched SORDOR-180 pulses, this enables the Böhlen-Bodenhausen broadband refocusing approach for linearly frequency-swept pulses to be extended to any type of 90∘ /180∘ pulse-delay sequence. Example pulse shapes are characterised in theory and experiment, and an example application is given with a 19 F -PROJECT experiment for measuring relaxation times with reduced distortions due to J -coupling evolution.

Improved design of frequency-swept pulse sequences

Frequency-swept pulses are extensively used in magnetic resonance spectroscopic techniques for the robust manipulation of spins across wide ranges of offset frequencies in the presence of B₁ field variations. Nevertheless, designing pulse sequences consisting of multiple frequency-swept pulses can be challenging, as they often require specific timings and parameter tweaking. In the present work we discuss a simple and general approach for constructing such sequences. We present new and improved pulse sequences for applications including broadband B₁-tolerant CPMG (CHORUS-CPMG), broadband chirped excitation with suppression of homonuclear J-modulation (PROCHORUS), and the further compression of frequency-swept pulse sequences by superposition of pulses which reduces pulse sequence durations by 25-40%. All sequence design strategies are accompanied by mathematical presentations, experimental results, and supporting simulations.

Optimization of phase dispersion enables broadband excitation without homonuclear coupling artifacts

In NMR spectroscopy, many specialized shaped pulses are available for broadband excitation, beyond the bandwidth of conventional high-powered hard pulses. These shaped pulses typically have long duration. However, long-duration pulses are unsuitable for spectra containing significant homonuclear couplings, such as polyfluorinated compounds in 19F NMR. J-coupling evolution during the excitation pulse leads to spectral artifacts and incorrect peak integrals. Here, we report an approach to optimal control pulse design which significantly reduces the pulse length required to excite large bandwidths of chemical shift frequencies. The target state phase is not chosen beforehand but is instead only constrained to be linearly dependent on offset frequency. The first-order phase of the target state is then treated as a free-variable, to be optimized at the same time as the RF waveform itself. The resulting spectra are easily phased using standard NMR processing software. We observe that the required pulse length is significantly shorter than for currently available in-phase excitation schemes. Spectral artifacts from homonuclear couplings are avoided. We also demonstrate that pure in-phase excitation can be obtained over the same bandwidth by appending two inversion pulses, at the expense of increased overall duration.

Chirped ordered pulses for ultra-broadband ESR spectroscopy

Recently, applications of swept-frequency pulses proved to be a useful approach to circumvent the problem of limited excitation bandwidth in pulsed ESR posed by conventional pulses. Here, we present a chirped excitation sequence, CHirped ORdered pulses for Ultra-broadband Spectroscopy (CHORUS), for ultra-broadband ESR spectroscopy. It will be demonstrated that the application of this sequence can address the problems of excitation non-uniformity and sensitivity to instrumental instabilities to a greater extent compared to the current state of the art. This sequence is highly promising for finding applications beyond single excitation in many ESR experiments. Theoretical and experimental results for the proposed method are presented along with calibration strategies for experimental implementation.

Internal Structure of Thermoresponsive Physically Crosslinked Nanogel of Poly[N-(2-hydroxypropyl)methacrylamide]-Block-Poly[N-(2,2-difluoroethyl)acrylamide], Prominent 19F MRI Tracer

Fluorine-19 MRI is a promising noninvasive diagnostic method. However, the absence of a nontoxic fluorine-19 MRI tracer that does not suffer from poor biodistribution as a result of its strong fluorophilicity is a constant hurdle in the widespread applicability of this otherwise versatile diagnostic technique. The poly[N-(2-hydroxypropyl)methacrylamide]-block-poly[N-(2,2-difluoroethyl)acrylamide] thermoresponsive copolymer was proposed as an alternative fluorine-19 MRI tracer capable of overcoming such shortcomings. In this paper, the internal structure of self-assembled particles of this copolymer was investigated by various methods including 1D and 2D NMR, dynamic light scattering (DLS), small-angle X-ray scattering (SAXS) and small-angle neutron scattering (SANS). The elucidated structure appears to be that of a nanogel with greatly swollen hydrophilic chains and tightly packed thermoresponsive chains forming a network within the nanogel particles, which become more hydrophobic with increasing temperature. Its capacity to provide a measurable fluorine-19 NMR signal in its aggregated state at human body temperature was also investigated and confirmed. This capacity stems from the different fluorine-19 nuclei relaxation properties compared to those of hydrogen-1 nuclei.

Spin dynamics during chirped pulses: applications to homonuclear decoupling and broadband excitation

Swept-frequency pulses have found applications in a wide range of areas including spectroscopic techniques where efficient control of spins is required. For many of these applications, a good understanding of the evolution of spin systems during these pulses plays a vital role, not only in describing the mechanism of techniques, but also in enabling new methodologies. In magnetic resonance spectroscopy, broadband inversion, refocusing, and excitation using these pulses are among the most used applications in NMR, ESR, MRI, and in vivo MRS. In the present survey, a general expression for chirped pulses will be introduced, and some numerical approaches to calculate the spin dynamics during chirped pulses via solutions of the well-known Liouville-von Neumann equation and the lesser-explored Wei-Norman Lie algebra along with comprehensive examples are presented. In both cases, spin state trajectories are calculated using the solution of differential equations. Additionally, applications of the proposed methods to study the spin dynamics during the PSYCHE pulse element for broadband homonuclear decoupling and the CHORUS sequence for broadband excitation will be presented.

MRI exploiting frequency-modulated pulses and their nonlinear phase

Frequency-modulated (FM) pulses can provide several advantages over conventional amplitude-modulated pulses in the field of MRI; however, the manner in which spins are manipulated imprints a quadratic phase on the resulting magnetization. Historically this was considered a hindrance and slowed the widespread adoption of FM pulses. This article seeks to provide a historical perspective of the different techniques that researchers have used to exploit the benefits of FM pulses and to compensate for the nonlinear phase created by this class of pulses in MRI. Expanding on existing techniques, a new method of phase compensation is presented that utilizes nonlinear gradients to mitigate the undesirable phase imparted by this class of pulses.

Improved ultra-broadband chirp excitation

The design and application of ultra-broadband excitation pulses have been among the most interesting and timely areas in NMR and EPR methodology in recent years, due especially to advances in hardware design in EPR, the advent and popularity of high- and ultrahigh-field NMR, and the application of numerical methods like optimal control theory to the design and optimization of radiofrequency pulses and pulse sequences. In this communication, we present a short, robust, and flexible version of the CHORUS family of constant-phase, very broadband excitation sequences. We demonstrate that more than 0.5 MHz excitation with uniform amplitudes and phases can be achieved with this excitation sequence.

Double electron-electron resonance with multiple non-selective chirp refocusing

A new approach to double electron-electron resonance (DEER) for distance determination involving nitroxide spin labels at dilute concentrations is presented. In general, DEER pulse sequences rely on double resonance between pump and observer spins excited by selective pulses at two distinct microwave frequencies. In the new approach abbreviated as nDEER, non-selective chirp pulses that refocus all relevant spin pairs are combined with DEER. This non-selective refocusing results in suppression of unmodulated contributions, such as the constant contribution as well as the background curvature due to inter-molecular spin partners in ordinary DEER data. Due to this dipolar attenuation effect, primary nDEER data are closer to the dipolar modulation of primary interest than ordinary DEER data. Restrictions of nDEER are that secondary information related to these unmodulated contributions becomes difficult to retrieve. Accordingly, incomplete deconvolution of the inter-molecular background prevents the application of nDEER to rigid spin pairs at high concentrations. A key advantage of nDEER is the high fidelity of the chirp refocusing pulses, which is important for nDEER schemes that incorporate dynamical decoupling to access longer distances. In this context, nDEER with Carr-Purcell (CP) pulse trains having N = 2 and N = 4 refocusing pulses are demonstrated. These CP nDEER sequences require a total of N + 2 pulses, which is less than the 2N + 1 pulses required for CP DEER schemes. The pump pulse position is incremented throughout the refocusing pulses, which restricts the minimum time increment to 96 ns on our spectrometer and therefore complicates application to distances below 3 nm. At Q-band frequencies, unwanted modulations related to pulse imperfections contribute only 3.5% relative to the principal nDEER modulation. Accordingly, there is no need for dedicated data reconstruction methods as in CP DEER methods.

Cooperative broadband spin echoes through optimal control

The Hahn echo sequence is one of the most common building blocks in magnetic resonance, consisting of an excitation pulse and a refocusing pulse. Conventional approaches to improve the performance of echo experiments focused on the optimization of individual pulses, compensating their own imperfections. Here we present an approach to concurrently design both pulses such that they also compensate each others imperfections. The fact that for such cooperative pulses the individual pulses do not need to be perfect provides additional degrees of freedom, resulting in improved overall Hahn echo performance. Single-scan cooperative pulses are compared to conventional approaches by simulations as well as experiments.

Broadband RF-amplitude-dependent flip angle pulses with linear phase slope

Pulse sequences in NMR spectroscopy sometimes require the application of pulses with effective flip angles different from 90° and 180°. Previously (Magn. Reson. Chem. 2015, 53, 886-893), offset-compensated broadband excitation pulses with RF-amplitude-dependent effective flip angles (RADFA) were introduced that are applicable in such cases. However, especially RF-amplitude-restricted RADFA pulses turned out to perform not as good as desired in terms of achievable bandwidths. Here, a class of RF-amplitude-restricted RADFA pulses with linear phase slope is introduced that allows excitation over much larger bandwidths with better performance. In this theoretical work, the basic principle of the pulse class is explained, their physical limits explored, and their properties, also compared with other pulse classes, discussed in detail. Copyright © 2017 John Wiley & Sons, Ltd.

Chirp excitation

The paper describes the design of broadband chirp excitation pulses. We first develop a three stage model for understanding chirp excitation in NMR. We then show how a chirp π pulse can be used to refocus the phase of the chirp excitation pulse. The resulting magnetization still has some phase dispersion in it. We show how a combination of two chirp π pulses instead of one can be used to eliminate this dispersion, leaving behind a small residual phase dispersion. The excitation pulse sequence presented here allows exciting arbitrary large bandwidths without increasing the peak rf-amplitude. Experimental excitation profiles for the residual HDO signal in a sample of 99.5% D₂O are displayed as a function of resonance offset. Although methods presented in this paper have appeared elsewhere, we present complete analytical treatment that elucidates the working of these methods.

Wideband frequency-swept excitation in pulsed EPR spectroscopy

Excitation of electron spins with monochromatic rectangular pulses is limited to bandwidths that are smaller than the spectral widths of most organic radicals and much smaller than the spectral widths of transition and rare earth metal ions. With frequency-swept pulses, bandwidths of up to 800MHz have previously been attained for excitation and detection of spin packets at frequencies of about 9.6GHz and bandwidths of up to 2.5GHz in a polarization transfer experiment at frequencies of about 34GHz. The remaining limitations, mainly due to resonator bandwidth and due to pulse length restrictions are discussed. Flip angles for state-space rotations on passage of a transition can generally be computed from the critical adiabaticity by the Landau-Zener-Stückelberg-Majorana expression. For hyperbolic secant pulses, the Demkov-Kunike model describes excitation for spin packets within and outside the sweep range. Well within the sweep range, the Bloch-Siegert phase shift is proportional to critical adiabaticity to a very good approximation. Because of the dependence of both flip angle and coherence phase on critical adiabaticity, it is advantageous to use pairs of amplitude and frequency modulation functions that provide such offset-independent adiabaticity. Compensation for the resonator response function should restore offset-independent adiabaticity. Whereas resonance offsets and Bloch-Siegert phase can be refocused at certain pulse length ratios, phase dispersion in coupled spin systems cannot generally be refocused. Based on the bandwidth limitations that arise from spin dynamics, requirements are derived for a spectrometer that achieves precise spin control over wide bands. The design of such a spectrometer and hardware characterization by EPR experiments are discussed.

Perspectives of shaped pulses for EPR spectroscopy

This article describes current uses of shaped pulses, generated by an arbitrary waveform generator, in the field of EPR spectroscopy. We show applications of sech/tanh and WURST pulses to dipolar spectroscopy, including new pulse schemes and procedures, and discuss the more general concept of optimum-control-based pulses for applications in EPR spectroscopy. The article also describes a procedure to correct for experimental imperfections, mostly introduced by the microwave resonator, and discusses further potential applications and limitations of such pulses.

Arbitrary waveform modulated pulse EPR at 200GHz

We report here on the implementation of arbitrary waveform generation (AWG) capabilities at ∼200GHz into an Electron Paramagnetic Resonance (EPR) and Dynamic Nuclear Polarization (DNP) instrument platform operating at 7T. This is achieved with the integration of a 1GHz, 2 channel, digital to analog converter (DAC) board that enables the generation of coherent arbitrary waveforms at K_u-band frequencies with 1ns resolution into an existing architecture of a solid state amplifier multiplier chain (AMC). This allows for the generation of arbitrary phase- and amplitude-modulated waveforms at 200GHz with >150mW power. We find that the non-linearity of the AMC poses significant difficulties in generating amplitude-modulated pulses at 200GHz. We demonstrate that in the power-limited regime of ω₁<1MHz phase-modulated pulses were sufficient to achieve significant improvements in broadband (>10MHz) spin manipulation in incoherent (inversion), as well as coherent (echo formation) experiments. Highlights include the improvement by one order of magnitude in inversion bandwidth compared to that of conventional rectangular pulses, as well as a factor of two in improvement in the refocused echo intensity at 200GHz.

Very broadband diffusion-ordered NMR spectroscopy: (19)F DOSY

A new pulse sequence, CHORUS Oneshot, allows measurements of diffusion-ordered spectroscopy (DOSY) spectra over the full chemical shift range of (19)F for the first time. Swept-frequency pulses are used to give very broadband excitation; the sequence is a prototype for a large family of very broadband liquid state NMR methods.

Ultra broadband NMR spectroscopy using multiple rotating frame technique

The paper describes the design of broadband excitation and inversion pulses by method of multiple rotating frame technique. The ideal situation for perfect excitation and inversion is to have no chemical shift offset and thereby everything on resonance. However, when chemical shifts span a wide range, this condition is not realized. We achieve this condition using a multiply modulated rf-field, whose effect can be understood by progressing into multiple frames. As we progress through the frames, the ratio of chemical shift dispersion to strength of static rf-field decreases, resulting in a final frame, where there is negligible chemical shift as compared to the effective rf-field and we get good excitation and inversion. Increasing the number of frames, increases excitation bandwidth and the ratio of bandwidth to rms excitation amplitude. We show, in principle, it is possible to excite arbitrary large bandwidth for a given rms rf-amplitude by increasing the number of frames. The time of excitation increases linearly with the bandwidth when we keep the rms rf-amplitude constant. Experimental demonstration of proposed method is presented on (1)H excitation over a bandwidth of 52 kHz with a rms amplitude of 10 kHz. Increasing the frames increases excitation bandwidth for same rms amplitude of 10 kHz. Experimental spectra obtained from 100%(13)C labeled arginine shows uniform excitation over the entire carbon spectra, obtained with a 8-frame pulse sequence.

EPR-correlated dipolar spectroscopy by Q-band chirp SIFTER

Frequency-swept chirp pulses uniformly excite the nitroxide spectrum at Q-band frequencies, which allows for acquisition of two-dimensional spectra correlating the dipolar spectrum to the EPR spectrum.

Increasing the quantitative bandwidth of NMR measurements

The frequency range of quantitative NMR is increased to hundreds of kHz, yielding accurate integrals even for ¹⁹F.

Gd(III)-Gd(III) distance measurements with chirp pump pulses

The broad EPR spectrum of Gd(III) spin labels restricts the dipolar modulation depth in distance measurements between Gd(III) pairs to a few percent. To overcome this limitation, frequency-swept chirp pulses are utilized as pump pulses in the DEER experiment. Using a model system with 3.4 nm Gd-Gd distance, application of one single chirp pump pulse at Q-band frequencies leads to modulation depths beyond 10%. However, the larger modulation depth is counteracted by a reduction of the absolute echo intensity due to the pump pulse. As supported by spin dynamics simulations, this effect is primarily driven by signal loss to double-quantum coherence and specific to the Gd(III) high spin state of S=7/2. In order to balance modulation depth and echo intensity for optimum sensitivity, a simple experimental procedure is proposed. An additional improvement by 25% in DEER sensitivity is achieved with two consecutive chirp pump pulses. These pulses pump the Gd(III) spectrum symmetrically around the observation position, therefore mutually compensating for dynamical Bloch-Siegert phase shifts at the observer spins. The improved sensitivity of the DEER data with modulation depths on the order of 20% is due to mitigation of the echo reduction effects by the consecutive pump pulses. In particular, the second pump pulse does not lead to additional signal loss if perfect inversion is assumed. Moreover, the compensation of the dynamical Bloch-Siegert phase prevents signal loss due to spatial dependence of the dynamical phase, which is caused by inhomogeneities in the driving field. The new methodology is combined with pre-polarization techniques to measure long distances up to 8.6 nm, where signal intensity and modulation depth become attenuated by long dipolar evolution windows. In addition, the influence of the zero-field splitting parameters on the echo intensity is studied with simulations. Herein, larger sensitivity is anticipated for Gd(III) complexes with zero-field splitting that is smaller than for the employed Gd-PyMTA complex.

Selective excitation with asymmetric adiabatic pulses for NMR spectroscopy

Existing selective pulses are mainly constructed in the forms of classically shaped pulses, such as the Gaussian pulses, or generated by using numerical optimization methods. However, all of these pulses are highly sensitive to radiofrequency (RF) intensity variation, which means their performance is highly dependent on the accuracy and stability of the RF intensity. Even a slight RF intensity deviation can cause severe degradation in the excitation profile. To solve this problem, we propose a method for narrow selective excitation by sequential application of a pair of phase-opposite asymmetric adiabatic pulses, all within two scans. By retaining the adiabatic character, the new method is highly robust to RF intensity variation. Moreover, it has flexible excitation bandwidth, ranging from line-selective to narrow-band-selective pulses. The method is tested both in numerical simulations and solution-state NMR experiments.

Fourier-transform electron spin resonance with bandwidth-compensated chirp pulses

Electron spin echo experiments using chirp pulses at X-band around 9GHz have been performed with a home-built spectrometer based on an arbitrary waveform generator. Primary echoes without phase dispersion were obtained by employing the Böhlen-Bodenhausen scheme with the refocusing pulse being half as long as the coherence-generating pulse. To account for physical bandwidth limitation by the resonator, the instantaneous sweep rate of the chirps was adapted to the spectrometer's frequency response function, which can be recorded from the sample under study within a few minutes. Such bandwidth-compensated chirp pulses are experimentally shown to achieve an almost uniform excitation bandwidth that exceeds the resonator bandwidth. This uniform excitation allows for computing frequency-domain spectra by Fourier-transformation (FT) of the echo signal. For a nitroxide in dilute solid solution with a spectral width of 200MHz, the FT EPR spectrum agrees remarkably well with a field-swept echo-detected EPR spectrum. The overall spectral perturbation for operation far beyond the resonator bandwidth was characterized by acquiring a 700MHz wide spectral range of a copper (II) EPR spectrum with nearly uniform amplitude with excitation and refocusing pulses of 200 and 100ns, respectively. Furthermore, peculiarities were observed in solid-state FT EPR spectra of disordered systems. To understand these peculiarities two-dimensional data sets were acquired that correlate the FT EPR spectrum to inversion recovery or nuclear modulation. The echo envelope modulation experiments reveal echo decay rates increased by enhanced instantaneous diffusion and passage-specific effects in the nuclear modulations. The latter effect can be suppressed by nuclear modulation averaging. Apparent longitudinal relaxation times for a given subset of orientations are influenced by nuclear modulation effects. Proper extraction of orientation-dependent relaxation times thus requires an experimental setup that minimizes the modulations.

BEBE(tr) and BUBI: J-compensated concurrent shaped pulses for 1H-13C experiments

Shaped pulses designed for broadband excitation, inversion and refocusing are important tools in modern NMR spectroscopy to achieve robust pulse sequences especially in heteronuclear correlation experiments. A large variety of mostly computer-optimized pulse shapes exist for different desired bandwidths, available rf-field strengths, and tolerance to B1-inhomogeneity. They are usually derived for a single spin 1/2, neglecting evolution due to J-couplings. While pulses with constant resulting phase are selfcompensated for heteronuclear coupling evolution as long as they are applied exclusively on a single nucleus, the situation changes for concurrently applied pulse shapes. Using the example of a (1)H,(13)C two spin system, two J-compensated pulse pairs for the application in INEPT-type transfer elements were optimized: a point-to-point pulse sandwich called BEBE(tr), consisting of a broadband excitation and time-reversed excitation pulse, and a combined universal rotation and point-to-point pulse pair called BUBI, which acts as a refocusing pulse on (1)H and a corresponding inversion pulse on (13)C. After a derivation of quality factors and optimization protocols, a theoretical and experimental comparison with conventionally derived BEBOP, BIBOP, and BURBOP-180° pulses is given. While the overall transfer efficiency of a single pulse pair is only reduced by approximately 0.1%, resulting transfer to undesired coherences is reduced by several percent. In experiments this can lead to undesired phase distortions for pairs of uncompensated pulse shapes and even differences in signal intensities of 5-10% in HSQC and up to 68% in more complex COB-HSQC experiments.

The Fantastic Four: A plug 'n' play set of optimal control pulses for enhancing NMR spectroscopy

We present highly robust, optimal control-based shaped pulses designed to replace all 90° and 180° hard pulses in a given pulse sequence for improved performance. Special attention was devoted to ensuring that the pulses can be simply substituted in a one-to-one fashion for the original hard pulses without any additional modification of the existing sequence. The set of four pulses for each nucleus therefore consists of 90° and 180° point-to-point (PP) and universal rotation (UR) pulses of identical duration. These 1ms pulses provide uniform performance over resonance offsets of 20kHz ((1)H) and 35kHz ((13)C) and tolerate reasonably large radio frequency (RF) inhomogeneity/miscalibration of ±15% ((1)H) and ±10% ((13)C), making them especially suitable for NMR of small-to-medium-sized molecules (for which relaxation effects during the pulse are negligible) at an accessible and widely utilized spectrometer field strength of 600MHz. The experimental performance of conventional hard-pulse sequences is shown to be greatly improved by incorporating the new pulses, each set referred to as the Fantastic Four (Fanta4).

Optimal control design of band-selective excitation pulses that accommodate relaxation and RF inhomogeneity

Existing optimal control protocols for mitigating the effects of relaxation and/or RF inhomogeneity on broadband pulse performance are extended to the more difficult problem of designing robust, refocused, frequency selective excitation pulses. For the demanding case of T(1) and T(2) equal to the pulse length, anticipated signal losses can be significantly reduced while achieving nearly ideal frequency selectivity. Improvements in performance are the result of allowing residual unrefocused magnetization after applying relaxation-compensated selective excitation by optimized pulses (RC-SEBOPs). We demonstrate simple pulse sequence elements for eliminating this unwanted residual signal.

Broadband excitation pulses for high-field solid-state nuclear magnetic resonance spectroscopy

In nuclear magnetic resonance spectroscopy, experimental limits due to the radiofrequency transmitter and/or coil means that conventional radiofrequency pulses ("hard pulses") are sometimes not sufficiently powerful to excite magnetization uniformly over a desired range of frequencies. Effects due to nonuniform excitation are most frequently encountered at high magnetic fields for nuclei with a large range of chemical shifts. Using optimal control theory, we have designed broadband excitation pulses that are suitable for solid-state samples under magic-angle-spinning conditions. These pulses are easy to implement, robust to spinning frequency variations, and radiofrequency inhomogeneities, and only four times as long as a corresponding hard pulse. The utility of these pulses for uniformly exciting (13) C nuclei is demonstrated on a 900 MHz (21.1 T) spectrometer.

NMR quantification of trace components in complex matrices by band-selective excitation with adiabatic pulses

The use of band-selective excitation with adiabatic pulses to rapidly obtain NMR spectra of trace components in the presence of strong signals is described, along with qualitative and quantitative examples from food matrices like olive oil and honey.

Spin-echo MRI using pi/2 and pi hyperbolic secant pulses

Frequency-modulated (FM) pulses have practical advantages for spin-echo experiments, such as the ability to produce a broadband pi rotation, with an inhomogeneous radiofrequency (RF) field. However, such use leads to a nonlinear phase of the transverse magnetization, which is why FM pulses like the hyperbolic secant (HS) pulse are not commonly used for multislice spin-echo magnetic resonance imaging (MRI). Here, a general theory and methods are described for conventional spin-echo imaging using a pi HS pulse for refocusing. Phase profiles produced by the HS pulse are analytically described. The analysis is extended to yield the specific relationships between pulse parameters and gradients, which must be satisfied to compensate the nonlinear phase variation produced with a spin-echo sequence composed of pi/2 and pi HS pulses (the pi/2 HS - pi HS sequence). The latter offers advantages for multislice spin-echo MRI, including excellent slice-selection and partial compensation for RF inhomogeneity. Furthermore, it can be implemented with a shorter echo time and lower power deposition than a previously described method using a pair of pi HS pulses.

Exploring the limits of broadband excitation and inversion: II. Rf-power optimized pulses

In [K. Kobzar, T.E. Skinner, N. Khaneja, S.J. Glaser, B. Luy, Exploring the limits of broadband excitation and inversion, J. Magn. Reson. 170 (2004) 236-243], optimal control theory was employed in a systematic study to establish physical limits for the minimum rf-amplitudes required in broadband excitation and inversion pulses. In a number of cases, however, experimental schemes are not limited by rf-amplitudes, but by the overall rf-power applied to a sample. We therefore conducted a second systematic study of excitation and inversion pulses of varying pulse durations with respect to bandwidth and rf-tolerances, but this time using a modified algorithm involving restricted rf-power. The resulting pulses display a variety of pulse shapes with highly modulated rf-amplitudes and generally show better performance than corresponding pulses with identical pulse length and rf-power, but limited rf-amplitude. A detailed description of pulse shapes and their performance is given for the so-called power-BEBOP and power-BIBOP pulses.

Frequency-swept HSQC sequences for high-throughput NMR analysis

This article describes new versions of the DEPT phase-edited heteronuclear single quantum correlation (HSQC) pulse sequence with sensitivity enhancement. The sequences incorporate frequency-swept carbon and proton pulses. The new experiments are inherently robust, well-suited for a high-throughput setting in which sample-to-sample variations may be ignored. The observed signal has the obvious benefit of sensitivity enhancement resulting from the preservation of two magnetization transfer pathways. The two pathways are maintained even in the version of the sequence in which all pulses are frequency-swept. There is an additional signal gain of roughly 10% that derives from the use of both proton and carbon frequency-swept pulses. Furthermore, the sequences use J compensation to provide optimal signal over a range of heteronuclear coupling constants. We demonstrate that the new sequences offer good sensitivity and perform well even when the NMR probe is deliberately mistuned.

Frequency-swept HMQC sequences for high-throughput NMR analysis

We describe here new versions of the DEPT phase-encoded HMQC experiment that offer robust performance and improved sensitivity. The new sequences rely on frequency-swept proton and carbon pulses to minimize signal losses from miscalibrated pulses while providing 'J compensation' to optimize the signal strength over a range of heteronuclear coupling constants. By including both proton and carbon-swept pulses, the new sequences also offer an additional signal gain of roughly 10% over well-calibrated hard-pulse experiments. The new sequences also demonstrate that one can construct a sequence that incorporates both 90 degrees and 180 degrees frequency-swept pulses. Although individual pulses in the sequence cause severe phase roll, the phase roll can be eliminated by the proper choice of pulse lengths and sweep directions.

High-resolution four-dimensional carbon-correlated 1H-1H ROESY experiments employing isotags and the filter diagonalization method for effective assignment of glycosidic linkages in oligosaccharides

Four-dimensional nuclear magnetic resonance spectroscopy of oligosaccharides that correlates 1H-1H ROESY cross peaks to two additional 13C frequency dimensions is reported. The 13C frequencies were introduced by derivatization of all free hydroxyl groups with doubly 13C-labeled acetyl isotags. Pulse sequences were optimized for processing with the filter diagonalization method. The extensive overlap typically observed in 2D ROESY 1H-1H planes was alleviated by resolution of ROESY cross peaks in the two added dimensions associated with the carbon frequencies of the isotags. This enabled the interresidue 1H-1H ROESY cross peaks to be unambiguously assigned hence spatially proximate sugar spin systems across glycosidic bonds could be effectively ascertained. An experiment that selectively amplifies interresidue ROESY 1H-1H cross peaks is also reported. It moves the magnetization of an intraresidue proton normally correlated to a sugar H-1 signal orthogonally along the z axis prior to a Tr-ROESY mixing sequence. This virtually eliminates the incoherent intraresidue ROESY transfer, suppresses coherent TOCSY transfer, and markedly enhances the intensity of interresidue ROESY cross peaks.

Optimal control design of constant amplitude phase-modulated pulses: application to calibration-free broadband excitation

An optimal control algorithm for generating purely phase-modulated pulses is derived. The methodology is applied to obtain broadband excitation with unprecedented tolerance to RF inhomogeneity. Design criteria were transformation of Iz-->Ix over resonance offsets of +/-25 kHz for constant RF amplitude anywhere in the range 10-20 kHz, with a pulse length of 1 ms. Simulations transform Iz to greater than 0.99 Ix over the targetted ranges of resonance offset and RF variability. Phase deviations in the final magnetization are less than 2-3 degrees over almost the entire range, with sporadic deviations of 6-9 degrees at a few offsets for the lowest RF (10 kHz) in the optimized range. Experimental performance of the new pulse is in excellent agreement with the simulations, and the robustness of the excitation pulse and a derived refocusing pulse are demonstrated by insertion into conventional HSQC and HMBC-type experiments.

Adiabatic JHSQC for 13C isotopomer analysis

A previous implementation of JHSQC enhanced the detection limits for 13C isotopomer analysis, but owing to experimental instabilities required extensive calibration prior to data collection. The addition of adiabatic pulses as well as a double spin-echo during the heteronuclear transfer periods has dramatically increased the precision of the experiment and done away with the need for calibration prior to running each sample. This new experiment allows the sensitivity gains from inverse detection to be realized in a time-efficient manner for the experimentalist.

A simple approach for phase-modulated single-scan 2D NMR spectroscopy

Conventional NMR spectroscopy techniques require long acquisition times due to the recovery time between the repeated excitations necessary for each increment of the evolution times in the indirectly detected dimensions. Here we outline a pulse sequence element for gradient-assisted ultrafast multidimensional NMR spectroscopy using frequency-modulated 'chirp' pulses to generate phase-modulated magnetization in an indirectly detected spectral dimension. The potential of this sequence element is demonstrated by acquiring a correlation spectroscopy (COSY) spectrum in 96 ms. This new pulse sequence element is an extension of ultrafast spectroscopy techniques based on the generation of amplitude modulation of the NMR signal in the indirectly detected spectral dimensions. The use of phase modulation instead of amplitude modulation helps broaden the applicability and may provide an increase of sensitivity in some experiments due to the ability to distinguish between positive and negative frequency offsets relative to the carrier frequency of the sequence element.

Pattern pulses: design of arbitrary excitation profiles as a function of pulse amplitude and offset

A novel class of pulses is presented which can be regarded as a generalization of both frequency-selective pulses and B1-selective pulses. The excitation profile of these pulses forms a pre-defined pattern in two dimensions, which are spanned by pulse offset and radio-frequency (RF) amplitude. The presented pulses were designed numerically based on principles of optimal control theory. For simple test patterns, we demonstrate the flexibility of this approach by simulations and experiments. This previously unknown flexibility may trigger novel applications in NMR spectroscopy and imaging. As a first practical application, we demonstrate a direct approach for calibrating RF pulses.

Rapid high-resolution four-dimensional NMR spectroscopy using the filter diagonalization method and its advantages for detailed structural elucidation of oligosaccharides

Four-dimensional nuclear magnetic resonance spectroscopy with high resolution of signals in the indirect dimensions is reported as an implementation of the filter diagonalization method (FDM). Using an oligosaccharide derivatized with 13C-labeled acetyl isotags, a four-dimensional constant-time pulse sequence was tailored for conjoint use with the FDM. Results demonstrate that high resolution in all dimensions can be achieved using a relatively short experimental time period (19 h), even though the spectrum is highly congested in the direct and all three indirect dimensions. The combined use of isotags, constant-time pulse sequences, and FDM permits rapid isolation of sugar ring proton spin systems in multiple dimensions and enables all endocyclic J-couplings to be simply measured, the key goal to assigning sugar stereochemistry and anomeric configuration. A general method for rapid, unambiguous elucidation of spin systems in oligosaccharides has been a long-sought goal of carbohydrate NMR, and isotags combined with the FDM now enable this to be easily performed. Additional general advantages of the FDM program for generating high-resolution 2D slices in any dimension from a 4D spectrum are emphasized.

Tailoring the optimal control cost function to a desired output: application to minimizing phase errors in short broadband excitation pulses

The de facto standard cost function has been used heretofore to characterize the performance of pulses designed using optimal control theory. The freedom to choose new, creative quality factors designed for specific purposes is demonstrated. While the methodology has more general applicability, its utility is illustrated by comparison to a consistently chosen example--broadband excitation. The resulting pulses are limited to the same maximum RF amplitude used previously and tolerate the same variation in RF homogeneity deemed relevant for standard high-resolution NMR probes. Design criteria are unchanged: transformation of I(z)--> I(x) over resonance offsets of +/-20 kHz and RF variability of +/-5%, with a peak RF amplitude equal to 17.5 kHz. However, the new cost effectively trades a small increase in residual z magnetization for improved phase in the transverse plane. Compared to previous broadband excitation by optimized pulses (BEBOP), significantly shorter pulses are achievable, with only marginally reduced performance. Simulations transform I(z) to greater than 0.98 I(x), with phase deviations of the final magnetization less than 2 degrees, over the targeted ranges of resonance offset and RF variability. Experimental performance is in excellent agreement with the simulations.

Exploring the limits of broadband excitation and inversion pulses

The design of broadband excitation and inversion pulses with compensation of B(1)-field inhomogeneity is a long standing goal in high resolution NMR spectroscopy. Most optimization procedures used so far have been restricted to particular pulse families to keep the scale of the problem within manageable limits. This restriction is unnecessary using efficient numerical algorithms based on optimal control theory. A systematic study of rf-limited broadband excitation by optimized pulses and broadband inversion by optimized pulses with respect to bandwidth and B(1)-field is presented. Upper limits on minimum pulse lengths are set for different degrees of pulse performance.

Rapid 3D NMR using the filter diagonalization method: application to oligosaccharides derivatized with 13C-labeled acetyl groups

Rapid 3D NMR spectroscopy of oligosaccharides having isotopically labeled acetyl "isotags" was made possible with high resolution in the indirect dimensions using the filter diagonalization method (FDM). A pulse sequence was designed for the optimal correlation of acetyl methyl protons, methyl carbons, and carbonyl carbons. The multi-dimensional nature of the FDM, coupled with the advantages of constant-time evolution periods, resulted in marked improvements over Fourier transform (FT) and mirror-image linear prediction (MI-LP) processing methods. The three methods were directly compared using identical data sets. A highly resolved 3D spectrum was achieved with the FDM using a very short experimental time (28 min).

Reducing the duration of broadband excitation pulses using optimal control with limited RF amplitude

Combining optimal control theory with a new RF limiting step produces pulses with significantly reduced duration and improved performance for a given maximum RF amplitude compared to previous broadband excitation by optimized pulses (BEBOP). The resulting pulses tolerate variations in RF homogeneity relevant for standard high-resolution NMR probes. Design criteria were transformation of Iz-->Ix over resonance offsets of +/-20kHz and RF variability of +/-5%, with a pulse length of 500 micros and peak RF amplitude equal to 17.5 kHz. Simulations transform Iz to greater than 0.995 Ix, with phase deviations of the final magnetization less than 2 degrees, over ranges of resonance offset and RF variability that exceed the design targets. Experimental performance of the pulse is in excellent agreement with the simulations. Performance tradeoffs for yet shorter pulses or pulses with decreased digitization are also investigated.

Equi-ripple design of quadratic-phase RF pulses

An improved strategy for the design of quadratic-phase RF pulses with high selectivity and broad bandwidths using the Shinnar-Le Roux (SLR) transformation is proposed. Unlike previous implementations, the required quadratic-phase finite impulse response (FIR) filters are generated using the complex Remez exchange algorithm, which ensures an equi-ripple deviation from the ideal response function. It is argued analytically that quadratic-phase pulses are near-optimal in terms of minimising the B1-amplitude for a given bandwidth and flip angle. Furthermore, several parameter relations are derived, providing practical design guidelines. The effectiveness of the proposed design method is demonstrated by examples of excitation and saturation pulses applied in vitro and in vivo.

PFG-assisted selection and suppression of 1H NMR signals in the solid state under fast MAS

Under fast MAS conditions, techniques for 1H signal selection and suppression, which have originally been developed for solution-state NMR, become applicable to solids. In this work, we describe how WATERGATE and DANTE pulse sequences can be used under MAS to selectively excite or suppress peaks in 1H solid-state spectra. As known from the liquid-state analogues, signal selection and/or suppression is supported by pulsed-field gradients which selectively dephase and rephase transverse magnetisation. Under MAS, the required field gradients are provided by a simple pair of coils which have been built into a standard fast-MAS probe. PFG-assisted techniques enable efficient selection or suppression of 1H peaks in a single transient of the pulse sequence without the need for phase cycles. Therefore, these tools can readily be incorporated into solid-state MAS NMR experiments, which is demonstrated here for 1H-1H double-quantum NMR spectra of supramolecular systems. In the examples presented here, the 1H signals of interest are relatively weak and need to be observed despite the presence of the strong 1H signal of long alkyl sidechains. PFG-assisted suppression of this strong perturbing signal is shown to be particularly useful for obtaining unambiguous results.

Application of optimal control theory to the design of broadband excitation pulses for high-resolution NMR

Optimal control theory is considered as a methodology for pulse sequence design in NMR. It provides the flexibility for systematically imposing desirable constraints on spin system evolution and therefore has a wealth of applications. We have chosen an elementary example to illustrate the capabilities of the optimal control formalism: broadband, constant phase excitation which tolerates miscalibration of RF power and variations in RF homogeneity relevant for standard high-resolution probes. The chosen design criteria were transformation of I(z)-->I(x) over resonance offsets of +/- 20 kHz and RF variability of +/-5%, with a pulse length of 2 ms. Simulations of the resulting pulse transform I(z)-->0.995I(x) over the target ranges in resonance offset and RF variability. Acceptably uniform excitation is obtained over a much larger range of RF variability (approximately 45%) than the strict design limits. The pulse performs well in simulations that include homonuclear and heteronuclear J-couplings. Experimental spectra obtained from 100% 13C-labeled lysine show only minimal coupling effects, in excellent agreement with the simulations. By increasing pulse power and reducing pulse length, we demonstrate experimental excitation of 1H over +/-32 kHz, with phase variations in the spectra <8 degrees and peak amplitudes >93% of maximum. Further improvements in broadband excitation by optimized pulses (BEBOP) may be possible by applying more sophisticated implementations of the optimal control formalism.