Pulse-transient adapted C-symmetry pulse sequences

Frame change technique for phase transient cancellation

The precise control of complex quantum mechanical systems can unlock applications ranging from quantum simulation to quantum computation. Controlling strongly interacting many-body systems often relies on Floquet Hamiltonian engineering that is achieved by fast switching between Hamiltonian primitives via external control. For example, in our solid-state NMR system, we perform quantum simulation by modulating the natural Hamiltonian with control pulses. As the Floquet heating errors scale with the interpulse delay, δt, it is favorable to keep δt as short as possible, forcing our control pulses to be short duration and high power. Additionally, high-power pulses help to minimize undesirable evolution from occurring during the duration of the pulse. However, such pulses introduce an appreciable phase-transient control error, a form of unitary error. In this work, we detail our ability to diagnose the error, calibrate its magnitude, and correct it for π/2-pulses of arbitrary phase. We demonstrate the improvements gained by correcting for the phase transient error, using a method which we call the "frame-change technique", in a variety of experimental settings of interest. Given that the correction mechanism adds no real control overhead, we recommend that any resonance probe be checked for these phase transient control errors, and correct them using the frame-change technique.

A modification of γ-encoded RN symmetry pulses for increasing the scaling factor and more accurate measurements of the strong heteronuclear dipolar couplings

Symmetry based γ-encoded RN_n^ν elements are broadly used in magic-angle spinning solid-state NMR experiments to achieve selective recoupling of the heteronuclear dipolar interactions. The recoupled dipolar couplings in such experiments are scaled by a factor, K_sc, which theoretically depends on the chosen symmetry numbers N, n, and ν. However, the maximum theoretical value of K_sc for γ-encoded RN_n^ν pulses is limited to ~0.25, resulting in long RN_n^ν experiment times. Also, the dependence of K_sc on the experimental parameters can result in systematic errors in the experimental determination of the dipolar couplings, especially at low and moderate MAS rates. In this manuscript, we investigate the use of MODifiEd RN_n^ν symmetry (MODERN_n^ν(ϕ_M)) pulses that increase the dipolar scaling factor by at least 1.45 fold compared to γ-encoded RN_n^ν. The second advantage of MODERN_n^ν(ϕ_M) pulses with respect to traditional RN_n^ν pulses is the reduced influence of experimental parameters on K_sc, which allows for more accurate measurement of short-range distances. The robustness of MODERN_n^ν(ϕ_M) is compared with γ-encoded R14₂³ symmetry pulses. The enhanced performance is demonstrated on two uniformly-¹³C-enriched samples, N-acetyl valine and the microcrystalline protein GB1, at a 31.111 kHz MAS rate.

Time and Frequency Domain Response of HTS Resonators for Use as NMR Transmit Coils

Replacing normal metal NMR coils with thin-film high-temperature superconductor (HTS) resonators can significantly improve the sensitivity of analytical NMR. To study the use of these resonators for excitation as well as detection, we investigated the radio frequency properties of the HTS NMR coils in both frequency and time domain at a variety of transmit power levels. Experiments were conducted on a double-sided, counter wound spiral resonator designed to detect NMR signals from ¹³C nuclei at 14.1 T. Power-dependent nonlinearity was observed in the transmission coefficient and quality factor. The ability of the HTS resonators to accurately generate short pulses was studied in the time domain over the range power levels. The results of this study show that some form of Q switching is needed to get good transmit performance from HTS coils for ¹³C. For that purpose, the effect of adding a shorted transmission line stub to improve the pulse shapes and reduce phase transients was studied.

Synthesis and characterization of methylammonium phosphates as crystalline approximants for anhydrous, low melting phosphate glasses

Low-melting methylammonium phosphate glasses are synthesized from crystalline starting agents. To this end crystalline tris(methylammonium) cyclotriphosphate [CH₃NH₃]₃P₃O₉, was synthesized by a novel and simple synthesis route from P₄O₁₀ and N-methylformamide. It, undergoes an irreversible phase transition to methylammonium catena-polyphosphate [CH₃NH₃]PO₃. The crystal structure of the catena-polyphosphate was solved and refined from X-ray powder diffraction data by the Rietveld method using constraints obtained by solid-state ³¹P and ¹H NMR spectroscopy. This compound crystallizes in a triclinic space group with a = 13.2236(9), b = 7.8924(6), c = 4.6553(2) Å, α = 91.068(4), β = 87.840(5) and γ = 106.550(3)°. Quantum chemical calculations confirm that the obtained structure lies at an energetic minimum. Finally the reaction of tris(methylammonium) cyclotriphosphate and P₄O₁₀ into methylammonium phosphate glass is presented. The synthesized, water-free phosphate glass shows a very low glass transition temperature T_g of 33 °C, which was verified by dynamic scanning calorimetry and NMR. The chain-like crystal structure of the high-temperature methylammoniumphosphate [CH₃NH₃]PO₃ serves as an approximation for the short-range order of the glass.

The novel glass shows the lowest glass transition temperature known for binary phosphate glass systems without acidic protons.

Transient effects in π-pulse sequences in MAS solid-state NMR

Dipolar recoupling techniques that use isolated rotor-synchronized π pulses are commonly used in solid-state NMR spectroscopy to gain insight into the structure of biological molecules. These sequences excel through their simplicity, stability towards radio-frequency (rf) inhomogeneity, and low rf requirements. For a theoretical understanding of such sequences, we present a Floquet treatment based on an interaction-frame transformation including the chemical-shift offset dependence. This approach is applied to the homonuclear dipolar-recoupling sequence Radio-Frequency Driven Recoupling (RFDR) and the heteronuclear recoupling sequence Rotational Echo Double Resonance (REDOR). Based on the Floquet approach, we show the influence of effective fields caused by pulse transients and discuss the advantages of pulse-transient compensation. We demonstrate experimentally that the transfer efficiency for homonuclear recoupling can be doubled in some cases in model compounds as well as in simple peptides if pulse-transient compensation is applied to the π pulses. Additionally, we discuss the influence of various phase cycles on the recoupling efficiency in order to reduce the magnitude of effective fields. Based on the findings from RFDR, we are able to explain why the REDOR sequence does not suffer in the recoupling efficiency despite the presence of effective fields.

Refinement of the crystal structure of Li4P2S6 using NMR crystallography

We report a new structural model for Li₄P₂S₆ derived from ³¹P MAS NMR and XRD data, symmetry relations and quantum-chemical calculations.

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.

Optimizing symmetry-based recoupling sequences in solid-state NMR by pulse-transient compensation and asynchronous implementation

Pulse imperfections like pulse transients and radio-frequency field maladjustment or inhomogeneity are the main sources of performance degradation and limited reproducibility in solid-state nuclear magnetic resonance experiments. We quantitatively analyze the influence of such imperfections on the performance of symmetry-based pulse sequences and describe how they can be compensated. Based on a triple-mode Floquet analysis, we develop a theoretical description of symmetry-based dipolar recoupling sequences, in particular, R26₄¹¹, calculating first- and second-order effective Hamiltonians using real pulse shapes. We discuss the various origins of effective fields, namely, pulse transients, deviation from the ideal flip angle, and fictitious fields, and develop strategies to counteract them for the restoration of full transfer efficiency. We compare experimental applications of transient-compensated pulses and an asynchronous implementation of the sequence to a supercycle, SR26, which is known to be efficient in compensating higher-order error terms. We are able to show the superiority of R26 compared to the supercycle, SR26, given the ability to reduce experimental error on the pulse sequence by pulse-transient compensation and a complete theoretical understanding of the sequence.

High radio-frequency field strength nutation NMR of quadrupolar nuclei

Owing to the introduction of microcoils, high RF field strength nutation NMR is a viable candidate for the study of quadrupolar nuclei with strong quadrupolar couplings, not accessible using contemporary NMR techniques. We show powder ²³Na nutation spectra on sodium nitrite for RF field strengths of up to 1170kHz, that conform to theoretical predictions. For lanthanum fluoride powder, ¹³⁹La nutation spectra taken at elevated RF field amplitudes show clear discrepancies when compared to the theory. These errors are shown to be mainly caused by pulse transients at the end of the pulse, which proved to be detrimental to the shape of the nutation spectra. Using a nutation pulse which ends in a sudden frequency jump, we show that these errors can be reduced, and nutation spectra that conform to theory can be readily acquired. This enables nutation NMR for the study of quadrupolar nuclei with a strong quadrupolar coupling, bridging the gap between NMR, which can only analyse nuclei with a weak to medium quadrupolar coupling, and NQR, were extensive searching for the right quadrupolar frequency is the limiting factor.

Quantification and compensation of the influence of pulse transients on symmetry-based recoupling sequences

Deviations of amplitude and phase of radio-frequency pulses from the desired values, can have a severe impact on the performance of multiple-pulse sequences in NMR spectroscopy. A particular problem are pulse transients that appear every time there is a discontinuity in amplitude or phase. Based on a Floquet description using pulses with arbitrarily shaped amplitudes and phases we present a systematic study of the influence of pulse transients on symmetry-based pulse sequences in solid-state NMR under magic-angle spinning. This treatment explains the dependence of the experimentally observed transfer efficiency on the details of experimental setups. In addition, three approaches are compared which have the aim to re-establish highly efficient recoupling. We demonstrate that the application of transient-compensated pulses as basic elements of symmetry-based sequences leads to a significantly improved robustness of the experiments with respect to variations in the experimental setup.

Low temperature synthesis of ionic phosphates in dimethyl sulfoxide

A new synthesis route for phosphates in an organic solvent at low temperatures is presented.

C-REDOR curves of extended spin systems

The convergence of simulated C-REDOR curves of (infinitely) large spin systems is investigated with respect to the number of spins considered in the calculations. Taking a sufficiently large number of spins (>20,000 spins) into account enables the simulation of converged C-REDOR curves over the entire time period and not only the initial regime. The calculations are based on an existing approximation within first order average Hamiltonian theory (AHT), which assumes the absence of homonuclear dipole-dipole interactions. The C-REDOR experiment generates an average Hamiltonian close to the idealized AHT behavior even for multiple spin systems including multiple homonuclear dipole-dipole interactions which is shown from numerically exact calculations of the spin dynamics. Experimentally it is shown that calculations accurately predict the full, experimental C-REDOR curves of the multi-spin systems (31)P-(19)F in apatite, (31)P-(1)H in potassium trimetaphosphimate and (1)H-(31)P in potassium dihydrogen phosphate. We also present (13)C-(1)H and (15)N-(1)H data for the organic compounds glycine, l-alanine and l-histidine hydrochloride monohydrate which require consideration of molecular motion. Furthermore, we investigated the current limits of the method from systematic errors and we suggest a simple way to calculate errors for homogeneous and heterogeneous samples from experimental data.

Microcoils and microsamples in solid-state NMR

Recent reports on microcoils are reviewed. The first part of the review includes a discussion of how the geometries of the sample and coil affect the NMR signal intensity. In addition to derivation of the well-known result that the signal intensity increases as the coil size decreases, the prediction that dilution of a small sample with magnetically inert matter leads to better sensitivity if a tiny coil is not available is given. The second part of the review focuses on the issues specific to solid-state NMR. They include realization of magic-angle spinning (MAS) using a microcoil and harnessing of such strong pulses that are feasible only with a microcoil. Two strategies for microcoil MAS, the piggyback method and magic-angle coil spinning (MACS), are reviewed. In addition, MAS of flat, disk-shaped samples is discussed in the context of solid-state NMR of small-volume samples. Strong RF irradiation, which has been exploited in wide-line spectral excitation, multiple-quantum MAS (MQMAS), and dipolar decoupling experiments, has been accompanied by new challenges regarding the Bloch-Siegert effect, the minimum time resolution of the spectrometer, and the time scale of pulse transient effects. For a possible solution to the latter problem, recent reports on active compensation of pulse transients are described.