Design and application of robust rf pulses for toroid cavity NMR spectroscopy

Efficient sampling of molecular orientations for Cu(II)-based DEER on protein labels

Combining rigid Cu(II) labels and pulsed-EPR techniques enables distance constraint measurements that are incisive probes of protein structure and dynamics. However, the labels can lead to a dipolar signal that is biased by the relative orientation of the two spins, which is typically unknown a priori in a bilabeled protein. This effect, dubbed orientational selectivity, becomes a bottleneck in measuring distances. This phenomenon also applies to other pulsed-EPR techniques that probe electron-nucleus interactions. In this work, we dissect orientational selectivity by generating an in silico sample of Cu(II)-labeled proteins to evaluate pulse excitation in the context of double electron-electron resonance (DEER) at Q-band frequencies. This approach enables the observation of the contribution of each protein orientation to the dipolar signal, which provides direct insights into optimizing acquisition schemes to mitigate orientational effects. Furthermore, we incorporate the excitation profile of realistic pulses to identify the excited spins. With this method, we show that rectangular pulses, despite their imperfect inversion capability, can sample similar spin orientations as other sophisticated pulses with the same bandwidth. Additionally, we reveal that the efficiency of exciting spin-pairs in DEER depends on the frequency offset of two pulses used in the experiment and the relative orientation of the two spins. Therefore, we systematically examine the frequency offset of the two pulses used in this double resonance experiment to determine the optimal frequency offset for optimal distance measurements. This procedure leads to a protocol where two measurements are sufficient to acquire orientational-independent DEER at Q-band. Notably, this procedure is feasible with any commercial pulsed-EPR spectrometer. Furthermore, we experimentally validate the computational results using DEER experiments on two different proteins. Finally, we show that increasing the amplitude of the rectangular pulse can increase the efficiency of DEER experiments by almost threefold. Overall, this work provides an attractive new approach for analyzing pulsed-EPR spectroscopy to obtain microscopic nuances that cannot be easily discerned from analytical or numerical calculations.

Dynamical Uncertainty Propagation with Noisy Quantum Parameters

Many quantum technologies rely on high-precision dynamics, which raises the question of how these are influenced by the experimental uncertainties that are always present in real-life settings. A standard approach in the literature to assess this is Monte Carlo sampling, which suffers from two major drawbacks. First, it is computationally expensive. Second, it does not reveal the effect that each individual uncertainty parameter has on the state of the system. In this Letter, we evade both these drawbacks by incorporating propagation of uncertainty directly into simulations of quantum dynamics, thereby obtaining a method that is orders of magnitude faster than Monte Carlo simulations and directly provides information on how each uncertainty parameter influences the system dynamics. Additionally, we compare our method to experimental results obtained using the IBM quantum computers.

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.

Rf-inhomogeneity compensation using method of Fourier synthesis

In this paper, we propose a new method for design of composite pulses that are robust to rf-amplitude (rf-inhomogeneity). We call this, the method of Fourier synthesis. The method is general enough to design excitation, inversion, refocusing or arbitary flip angle pulses that are robust to rf-amplitude. The method can be tailored to have amplitude selective excitation. We experimentally show rf-compensation over a order of magnitude (20db) variation in rf-amplitude. The method is expected to find use in invivo NMR studies using surface coils, where there is large dispersion in rf-amplitude over the sample.

Towards single egg toxicity screening using microcoil NMR

Planar NMR microcoils are evaluated, their application to single eggs is demonstrated, and their potential for studying smaller single cells is discussed.

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).

Exploring the limits of broadband 90° and 180° universal rotation pulses

90° and 180° universal rotation (UR) pulses are two of the most important classes of pulses in modern NMR spectroscopy. This article presents a systematic study characterizing the achievable performance of these pulses as functions of bandwidth, pulse length, and tolerance to B(1)-field inhomogeneity/miscalibration. After an evaluation of different quality factors employed in pulse design algorithms based on optimal control theory, resulting pulses are discussed in detail with a special focus on pulse symmetry. The vast majority of resulting BURBOP (broadband universal rotations by optimal control) pulses are either fully symmetric or have one symmetric and one antisymmetric Cartesian rf component, where the importance of the first symmetry has not been demonstrated yet and the latter one matches the symmetry that results from a previously derived construction principle of universal rotation pulses out of point-to-point pulses [3]. Optimized BURBOP pulses are shown to perform better than previously reported UR pulses, resulting in shorter pulse durations for the same quality of broadband rotations. From a comparison of qualities of effective universal rotations, we find that the application of a single optimal refocusing pulse matches or improves the performance of two consecutive inversion pulses in INEPT-like pulse sequence elements of the same total duration.

Shaped optimal control pulses for increased excitation bandwidth in EPR

A 1 ns resolution pulse shaping unit has been developed for pulsed EPR spectroscopy to enable 14-bit amplitude and phase modulation. Shaped broadband excitation pulses designed using optimal control theory (OCT) have been tested with this device at X-band frequency (9 GHz). FT-EPR experiments on organic radicals in solution have been performed with the new pulses, designed for uniform excitation over a significantly increased bandwidth compared to a classical rectangular π/2 pulse of the same B(1) amplitude. The concept of a dead-time compensated prefocused pulse has been introduced to EPR with a self-refocusing of 200 ns after the end of the pulse. Echo-like refocused signals have been recorded and compared to the performance of a classical Hahn-echo sequence. The impulse response function of the microwave setup has been measured and incorporated into the algorithm for designing OCT pulses, resulting in further significant improvements in performance. Experimental limitations and potential new applications of OCT pulses in EPR spectroscopy will be discussed.

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.

New strategies for designing robust universal rotation pulses: application to broadband refocusing at low power

Optimizing pulse performance often requires a compromise between maximizing signal amplitude and minimizing spectral phase errors. We consider methods for the de novo design of universal rotation pulses, applied specifically but not limited to refocusing pulses. Broadband inversion pulses that rotate all magnetization components 180° about a given fixed axis are necessary for refocusing and mixing in high-resolution NMR spectroscopy. The relative merits of various methodologies for generating pulses suitable for broadband refocusing are considered. The de novo design of 180° universal rotation pulses (180(UR)(°)) using optimal control can provide improved performance compared to schemes which construct refocusing pulses as composites of existing pulses. The advantages of broadband universal rotation by optimized pulses (BURBOP) are most evident for pulse design that includes tolerance to RF inhomogeneity or miscalibration. Nearly ideal refocusing is possible over a resonance offset range of ± 170% relative to the nominal pulse B(1) field, concurrent with tolerance to B(1) inhomogeneity/miscalibration of ± 33%. We present new modifications of the optimal control algorithm that incorporate symmetry principles (S-BURBOP) and relax conservative limits on peak RF pulse amplitude for short time periods that pose no threat to the probe. We apply them to generate a set of low-power 180(BURBOP)(°) pulses suitable for widespread use in (13)C spectroscopy on the majority of available probes. A quantitative measure for the reduced spectral phase error provided by these symmetry principles is also derived. For pulses designed according to this symmetry, refocusing phase errors are virtually eliminated upon application of EXORCYCLE or an equivalent G-180(S-BURBOP)(°)-G gradient sandwich, independent of resonance offset and RF inhomogeneity. The magnitude of the refocused component is not significantly compromised in achieving such ideal phase performance.