Asynchronous symmetry-based sequences for homonuclear dipolar recoupling in solid-state nuclear magnetic resonance

Asynchronising five-fold symmetry sequence for better homonuclear polarisation transfer in magic-angle-spinning solid-state NMR

Recoupling, decoupling, and multidimensional correlation experiments in magic-angle-spinning (MAS) solid-state NMR can be designed by exploiting the symmetry of internal spin interactions. One such scheme, namely, C5₂¹, and its supercycled version SPC5₂¹, notated as a five-fold symmetry sequence, is widely used for double-quantum dipole-dipole recoupling. Such schemes are generally rotor synchronised by design. We demonstrate an asynchronous implementation of the SPC5₂¹ sequence leading to higher double-quantum homonuclear polarisation transfer efficiency compared to the normal synchronous implementation. Rotor-synchronisation is broken in two different ways: lengthening the duration of one of the pulses, denoted as pulse-width variation (PWV), and mismatching the MAS frequency denoted as MAS variation (MASV). The application of this asynchronous sequence is shown on three different samples, namely, U-¹³C-alanine and 1,4-¹³C-labelled ammonium phthalate which include ¹³C_α-¹³C_β, ¹³C_α-¹³C_o, and ¹³C_o-¹³C_o spin systems, and adenosine 5'- triphosphate disodium salt trihydrate (ATP⋅3H₂O). We show that the asynchronous version performs better for spin pairs with small dipole-dipole couplings and large chemical-shift anisotropies, for example, ¹³C_o-¹³C_o. Simulations and experiments are shown to corroborate the results.

Designing broadband pulsed dynamic nuclear polarization sequences in static solids

Dynamic nuclear polarization (DNP) is a nuclear magnetic resonance (NMR) hyperpolarization technique that mediates polarization transfer from unpaired electrons with large thermal polarization to NMR-active nuclei via microwave (mw) irradiation. The ability to generate arbitrarily shaped mw pulses using arbitrary waveform generators allows for remarkable improvement of the robustness and versatility of DNP. We present here novel design principles based on single-spin vector effective Hamiltonian theory to develop new broadband DNP pulse sequences, namely, an adiabatic version of XiX (X-inverse X)-DNP and a broadband excitation by amplitude modulation (BEAM)-DNP experiment. We demonstrate that the adiabatic BEAM-DNP pulse sequence may achieve a ¹H enhancement factor of ∼360, which is better than ramped-amplitude NOVEL (nuclear spin orientation via electron spin locking) at ∼0.35 T and 80 K in static solids doped with trityl radicals. In addition, the bandwidth of the BEAM-DNP experiments (~50 MHz) is about three times the ¹H Larmor frequency. The generality of our theoretical approach will be helpful in the development of new pulsed DNP sequences.

Effects of radial radio-frequency field inhomogeneity on MAS solid-state NMR experiments

Radio-frequency field inhomogeneity is one of the most common imperfections in NMR experiments. They can lead to imperfect flip angles of applied radio-frequency (rf) pulses or to a mismatch of resonance conditions, resulting in artefacts or degraded performance of experiments. In solid-state NMR under magic angle spinning (MAS), the radial component becomes time-dependent because the rf irradiation amplitude and phase is modulated with integer multiples of the spinning frequency. We analyse the influence of such time-dependent MAS-modulated rf fields on the performance of some commonly used building blocks of solid-state NMR experiments. This analysis is based on analytical Floquet calculations and numerical simulations, taking into account the time dependence of the rf field. We find that, compared to the static part of the rf field inhomogeneity, such time-dependent modulations play a very minor role in the performance degradation of the investigated typical solid-state NMR experiments.

Adiabatic Solid Effect

The solid effect (SE) is a two spin dynamic nuclear polarization (DNP) mechanism that enhances the sensitivity in NMR experiments by irradiation of the electron-nuclear spin transitions with continuous wave (CW) microwaves at ω_0S ± ω_0I, where ω_0S and ω_0I are electron and nuclear Larmor frequencies, respectively. Using trityl (OX063), dispersed in a 60/40 glycerol/water mixture at 80 K, as a polarizing agent, we show here that application of a chirped microwave pulse, with a bandwidth comparable to the EPR line width applied at the SE matching condition, improves the enhancement by a factor of 2.4 over the CW method. Furthermore, the chirped pulse yields an enhancement that is ∼20% larger than obtained with the ramped-amplitude NOVEL (RA-NOVEL), which to date has achieved the largest enhancements in time domain DNP experiments. Numerical simulations suggest that the spins follow an adiabatic trajectory during the polarization transfer; hence, we denote this sequence as an adiabatic solid effect (ASE). We foresee that ASE will be a practical pulsed DNP experiment to be implemented at higher static magnetic fields due to the moderate power requirement. In particular, the ASE uses only 13% of the maximum microwave power required for RA-NOVEL.

A unified heteronuclear decoupling picture in solid-state NMR under low radio-frequency amplitude and fast magic-angle-spinning frequency regime

Heteronuclear spin decoupling is a highly important component of solid-state NMR experiments to remove undesired coupling interactions between unlike spins for spectral resolution. Recently, experiments using a unification strategy of standard decoupling schemes were presented for high radio-frequency (RF) amplitudes and slow-intermediate magic-angle-spinning (MAS) frequencies, in the pursuit of deeper understanding of spin decoupling under phase-modulated RF irradiation [A. Equbal et al., J. Chem. Phys. 142, 184201 (2015)]. The approach, unified two-pulse heteronuclear decoupling (UTPD), incorporates the simultaneous time- and phase-modulation strategies, commonly used in solid-state NMR. Here, the UTPD based decoupling scheme is extended to the experimentally increasingly important regime of low RF amplitudes and fast MAS frequencies. The unified decoupling approach becomes increasingly effective in identifying the deleterious dipole-dipole and, in particular, J recoupling conditions which become critical for the low-amplitude RF regime. This is because J coupling is isotropic and therefore not averaged out by sample spinning unlike the anisotropic dipole-dipole coupling. Numerical simulations and analytic theory are used to understand the effects of various nuclear spin interactions on the decoupling performance of UTPD, in particular, the crucial difference between the low-phase and high-phase UTPD conditions with respect to J coupling. In the UTPD scheme, when the cycle-frequency of the pulse-sequence is comparable to the RF nutation frequency, the existence of a non-zero effective rotation in the basic two-pulse scheme becomes an essential feature for the efficient and robust averaging out of the scalar J coupling. This broad viewpoint is expected to bring different optimum low-power decoupling pulse schemes under a common footing.

Time-optimized pulsed dynamic nuclear polarization

Pulsed dynamic nuclear polarization (DNP) techniques can accomplish electron-nuclear polarization transfer efficiently with an enhancement factor that is independent of the Zeeman field. However, they often require large Rabi frequencies and, therefore, high-power microwave irradiation. Here, we propose a new low-power DNP sequence for static samples that is composed of a train of microwave pulses of length τ_p spaced with delays d. A particularly robust DNP condition using a period τ_m = τ_p + d set to ~1.25 times the Larmor period τ_Larmor is investigated which is a time-optimized pulsed DNP sequence (TOP-DNP). At 0.35 T, we obtained an enhancement of ~200 using TOP-DNP compared to ~172 with nuclear spin orientation via electron spin locking (NOVEL), a commonly used pulsed DNP sequence, while using only ~7% microwave power required for NOVEL. Experimental data and simulations at higher fields suggest a field-independent enhancement factor, as predicted by the effective Hamiltonian.

Efficient low-power TOBSY sequences for fast MAS

Through-bond J-coupling based experiments in solid-state NMR spectroscopy are challenging because the J couplings are typically much smaller than the dipolar couplings. This often leads to a lower transfer efficiency compared to dipolar-coupling based sequences. One of the reasons for the low transfer efficiency are the second-order cross terms involving the strong heteronuclear dipolar couplings leading to fast magnetization decay. Here, we show that by employing a symmetry-based C9 sequence, which was carefully selected to suppress second-order terms, efficient polarization transfers of up to 80% can be achieved without decoupling on fully protonated two-spin model systems at a MAS frequency of 55.5 kHz with rf-field amplitudes of about 25 kHz. In addition, we analyse the effects of rf inhomogeneity and crystallites selection due to the polarization preparation method on the TOBSY transfer efficiency. We demonstrate on small model substances as well as on deuterated and 100% back-exchanged ubiquitin that C9₃₉¹ and C9₄₈¹ are efficient and practical TOBSY sequences at experimental conditions ranging from proton Larmor frequencies of 400-850 MHz, and MAS frequencies ranging from 55.5 to 111.1 kHz.

γ-Independent through-space hetero-nuclear correlation between spin-1/2 and quadrupolar nuclei in solids

We introduce novel sequences using indirect detection to correlate quadrupolar nuclei and spin-1/2 isotopes, other than ¹H and ¹⁹F. These sequences use γ-encoded symmetry-based RN_n^ν schemes that reintroduce the space component |m| = 1 of the heteronuclear dipolar coupling. These schemes can be applied to the indirectly detected spin in Dipolar-mediated Heteronuclear Multiple-Quantum Correlation (D-HMQC) sequence or to the detected isotope in a novel sequence, named Dipolar-mediated Heteronuclear Universal-Quantum Correlation (D-HUQC). We show that the signal of these sequences using γ-encoded recoupling does not depend on the γ Euler angle relating the inter-nuclear vector between the coupled spins to the MAS rotor-fixed frame. Therefore, the transfer efficiency of these sequences is in principle higher than that of D-HMQC methods using non-γ-encoded recoupling. Furthermore, numerical simulations show that the heteronuclear correlation experiments employing γ-encoded recoupling are more robust to Chemical Shift Anisotropy (CSA) of the irradiated spin and MAS frequency fluctuations. These results are confirmed by ¹³C-{¹⁵N} heteronuclear correlation on glycine and ³¹P-²⁷Al ones on VPI-5 and Na₇(AlP₂O₇)₄PO₄. These experiments indicate that R16₃⁵ recoupling produces the highest signal-to-noise ratio in heteronuclear correlation 2D experiments when the detected spin-1/2 nuclei are subject to large CSA.

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.

A generalized theoretical framework for the description of spin decoupling in solid-state MAS NMR: Offset effect on decoupling performance

We present a generalized theoretical framework that allows the approximate but rapid analysis of residual couplings of arbitrary decoupling sequences in solid-state NMR under magic-angle spinning conditions. It is a generalization of the tri-modal Floquet analysis of TPPM decoupling [Scholz et al., J. Chem. Phys. 130, 114510 (2009)] where three characteristic frequencies are used to describe the pulse sequence. Such an approach can be used to describe arbitrary periodic decoupling sequences that differ only in the magnitude of the Fourier coefficients of the interaction-frame transformation. It allows a ∼100 times faster calculation of second-order residual couplings as a function of pulse sequence parameters than full spin-dynamics simulations. By comparing the theoretical calculations with full numerical simulations, we show the potential of the new approach to examine the performance of decoupling sequences. We exemplify the usefulness of this framework by analyzing the performance of commonly used high-power decoupling sequences and low-power decoupling sequences such as amplitude-modulated XiX (AM-XiX) and its super-cycled variant SC-AM-XiX. In addition, the effect of chemical-shift offset is examined for both high- and low-power decoupling sequences. The results show that the cross-terms between the dipolar couplings are the main contributions to the line broadening when offset is present. We also show that the SC-AM-XIX shows a better offset compensation.

Handling the influence of chemical shift in amplitude-modulated heteronuclear dipolar recoupling solid-state NMR

We present a theoretical analysis of the influence of chemical shifts on amplitude-modulated heteronuclear dipolar recoupling experiments in solid-state NMR spectroscopy. The method is demonstrated using the Rotor Echo Short Pulse IRrAdiaTION mediated Cross-Polarization ((RESPIRATION)CP) experiment as an example. By going into the pulse sequence rf interaction frame and employing a quintuple-mode operator-based Floquet approach, we describe how chemical shift offset and anisotropic chemical shift affect the efficiency of heteronuclear polarization transfer. In this description, it becomes transparent that the main attribute leading to non-ideal performance is a fictitious field along the rf field axis, which is generated from second-order cross terms arising mainly between chemical shift tensors and themselves. This insight is useful for the development of improved recoupling experiments. We discuss the validity of this approach and present quaternion calculations to determine the effective resonance conditions in a combined rf field and chemical shift offset interaction frame transformation. Based on this, we derive a broad-banded version of the (RESPIRATION)CP experiment. The new sequence is experimentally verified using SNNFGAILSS amyloid fibrils where simultaneous (15)N → (13)CO and (15)N → (13)Cα coherence transfer is demonstrated on high-field NMR instrumentation, requiring great offset stability.

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.